?_< lp,v!    C   ( :6666666666Ƿ wnݿvnݿ}~nݿ~nݿ~fݿvc}ǿ6666666666   ? ?                          ? ?        !6666666t\88;A ,  &       3]]` K   T W8 8 8DAEoBlTlTlQrH rQoQo? r9 x8r;;; ,  &       3]]` c   i>;6l9i <xKuNoTiZfHfHfKlDDDG>8 ,  &       3]]B B   BK:CCCCCC:@NlpX  .1  &! & MathType "-  ^  Arial-2 p32 pM132 pu22 p 122 p12 p 112 p1 Arial-2 i2 !dt2 TNd2 n 2 J L2  i2  dt2 T d2   2   L2 - 2 Pi2 dt2 Td2 " 2  L2 c 2 VSymbol-2 X+2 +2 = & "System-oS)uKc?lpX  .1  @&! & MathType "- [ '{  Arial-2 pn32 p232 p22 p 222 p12 pM122 p2 Arial-2 i2 dt2 Td2  2  L2 ei2  dt2 T d2 7  2   L2 v 2 i2 dt2 TKd2 k 2 J L2  2 VSymbol-2 +2  +2 E= & "System-oS)AxAKxAxA?lpX  .1  @&! & MathType "-^ -~  Arial-2 pq32 p332 p22 p 232 p12 pM132 p3 Arial-2  i2 dt2 Td2  2  L2 ki2  dt2 T d2 =  2   L2 y 2 i2 !dt2 TNd2 n 2 J L2  2 VSymbol-2 +2  +2 E= & "System-oS)AxAKxAxA? lp* )  {z  lzC ll(l ID>>Dw ,  &       3]]` c   i>;8 8 3 xE{Ex<u< x?x?xB{B{E{D ;>) )>;>} ,  &       3]]` c   iQ;8 5 5 5D?r?oQoQoNuE uNrNr< u6 {5o;;;> ,  &       3]]` c   i;8 5 3o 3oB~ExKrQoTlBlBoBrDDG>8 ,  &       3]]B B   BKY:CCCCCC:@W lpH  .1  `& ! & MathType "-  ^  Arial-2 p42 p142 p32 pM132 pu22 p 122 p12 p 112 p1 Arial-2 -i2 dt2 Td2  2  L2 i2 !dt2 TNd2 n 2 J L2  i2  dt2 T d2   2   L2 - 2 Pi2 dt2 Td2 " 2  L2 c 2 VSymbol-2 +2 X+2 +2 = & "System-;'lp  .1  &! & MathType "- [ '{k  Arial-2 p42 pZ242 pn32 p232 p22 p 222 p12 pM122 p2 Arial-2 i2 .dt2 T[d2 { 2 F L2 i2 dt2 Td2  2  L2 ei2  dt2 T d2 7  2   L2 v 2 i2 dt2 TKd2 k 2 J L2  2 VSymbol-2 T+2 +2  +2 E= & "System-AxAxAxA'lp  .1  &! & MathType "-^ -~k  Arial-2 p42 pZ342 pq32 p332 p22 p 232 p12 pM132 p3 Arial-2 i2 .dt2 T[d2 { 2 I L2  i2 dt2 Td2  2  L2 ki2  dt2 T d2 =  2   L2 y 2 i2 !dt2 TNd2 n 2 J L2  2 VSymbol-2 W+2 +2  +2 E= & "System-AxAxAxA'lp  .1  &! & MathType "-e 4+y  Arial-2 p%42 ph442 px32 p342 p22 p# 242 p12 pT142 p4 Arial-2 i2 <dt2 Tid2  2 P L2 i2 dt2 Td2  2  L2 ri2  dt2 T$ d2 D  2   L2  2 i2 (dt2 TUd2 u 2 Q L2  2 VSymbol-2 ^+2 +2  +2 L= & "System-AxAxAxAULlp""^  .1  &t & MathType "-'d  Arial-2 lb2 c Arial-2 3I2 A3ISymbol-2 "=Times New Roman-2 , & "System- L i dtlp  m .1   &  & MathTypeP Arial-2 @ 02 @ 2 @02 @   Arial-2  c2 b2 r2 beSymbol-2 @ =2 @=2 @`< Arial-2 @g I2 @vI2 @8V2 @VTimes New Roman-2 @;2 @, & "System-  i dtlp46  .1  @& & MathType`  Arial- 2 sat2  2 ~ce,2 ^ ce2  b2 c2 r2 be Arial-2 @  2 @  Arial-2 @ V2 @ V2 @I2 @vI2 @8V2 @VSymbol-2 @ >2 @=2 @`<Times New Roman-2 @ ;Times New Roman-2 @Times New Roman-2 @, & "System-  + =lp4B  .1  @& & MathType`  Arial- 2 sat2  2 ce,2 c ce2  b2 c2 r2 be Arial-2 @  2 @  Arial-2 @ V2 @ V2 @I2 @{I2 @=V2 @VSymbol-2 @ =2 @=2 @e=Times New Roman-2 @ ;Times New Roman-2 @Times New Roman-2 @, & "System-  +AxAxAxAZQlp""h  .1  &t & MathType "-'d  Arial-2 lb2 c Arial-2 3I2 A3ISymbol-2 "=Times New Roman-2 , & "System-Sybol-2 lp  m .1   &  & MathTypeP Arial-2 @ 02 @ 2 @02 @   Arial-2  c2 b2 r2 beSymbol-2 @ =2 @=2 @`< Arial-2 @g I2 @vI2 @8V2 @VTimes New Roman-2 @;2 @, & "System-ime Ne Roan-lp(4B  .1  `&  & MathType`  Arial- 2 sat2  2 ec,2 f ec2  b2 c2 r2 be Arial-2 @  2 @  Arial-2 @ V2 @ V2 @I2 @{I2 @=V2 @VSymbol-2 @ >2 @=2 @e=Times New Roman-2 @ ;Times New Roman-2 @Times New Roman-2 @, & "System-  +AxAxAxAlp(4B  .1  `&  & MathType`  Arial- 2 sat2  2 ec,2 a ec2  b2 c2 r2 be Arial-2 @  2 @  Arial-2 @ V2 @ V2 @I2 @{I2 @=V2 @VSymbol-2 @ =2 @<2 @e=Times New Roman-2 @ ;Times New Roman-2 @Times New Roman-2 @, & "System-  +AxAxAxA lp!1T h D   ID C II(I<))))))))))))8׿׿ Ç׿ z׿ z7 z׾ :׽ F;׽ ~8} ~o zoÇo"""""!}"""""""""""""w}{u;`}""""""""""""""!!!?!?!?!!!!"""))))))))))))lp^ y   nC nn(n? 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Hb `       Qb elNb _o Eb 3gb 'db db Bgb b b b b 0b 0@ Bg= ?d d( *gS !V $Y 'Y 'Y 'V $S  {J {A H     ' HJ N        ! ES f      0EV ]        -EY ]         ! HY `       QY eiQV _iES 3gH  d 'dK[ dK    $1 BgK     ! : 0K     $F 0K     $F K     'C H      '@   =  = 0J 0A 0J 0S 0V 0Y 0Y 0Y 0V 0S BgJ ?dA dJ *gS !V $Y 'Y 'Y 'V $1  {% { H     - E@ N        -Hb f      -Hb ]        EG ]         !HD `       HD elHG _oHb 3gb 'db db Bgb b b b b 0b 0b Bgb ?db db *gb !b $b 'b 'b 'b  {@ "{= N     ' K H        ! H( ]      -HS Z        *HV Z         $KY `       'HY ef HY bi KV $S 3gJ 'dD dJ BgV 0Y 0\ 0\ \ Y V 0J 0D 0J 0B  v 0Ey 0E    'F 0E     *L 0E     *L 0E     'I 0E     'F BgB      $: ?d 1 d{: *gS !V $Y 'Y 'Y " {V %{S W     $HJ N        ! HA W      $QJ Q        $NS W         'KV ]       'HY ef HY bi KY 'V $1 3g% 'd d@ Bgb b G D 0D 0G 0b Bgb ?db db *gb !b $b 'b 'b 'b  ~b ~b K     'Hb E        *Nb Z      *Nb W        'Nb W         'Nb ]       $Nb bi Nb _oNb $b 3gb 'db db Bg!!!!!!!!!!!!!!!!!!!!!!!!!!lp]h+ b  bC ( ' OR? M  0G  <@!-D6:G6{&u!!  G   <"u$'  J  jodldijcp`p]vW|T|QNH EB?| 963j  s0r 2  v*r/'I'K!-/$I$H/++)   $"((!!  5  '(%%*'  t[%%t^" a Y C+7. 71:y =%@i hILi  eK@OR<$D  <:UX6! J   9[ ^!) 6"[ ^ !!   G 9+ad*$  G XgjZt   vgjZt  vjmTt!jmO!jmL!jmsjmpjmmjmmjmmjmmjmpjmsjmsjmg jmjjmj gjW ,  agjW  /   *+ad'$/ '"[ ^!! / '[ ^!& :UX6!   /   *@OR<$  /  sILi?/?p=%@i?/?j 71: `n*+7. Cm % a%Z e( (T  bN((('!D   ?"++!! D   <..0 # 9LK!   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(N 0  rN 0s  oN   3 oN  6 y | x rN`y |rQNWK +%sv* 6   oK]H ".mp+! 3  o} +mp1 3] I gjK 3f  Ia"d K 3i`[(^%i]"O.R"H  -v"I:F"K   3s% =C@ %u ZK 0p"1L."r  ZK 0j"[%oZK 0^%y%i ZK   33 (%K(' 6QK  60 %Q( 3   ZK`0 (W( 3  ZKW0 C]B 3?ZH]N @cB 6?Z$i{i QolQulN{N   -|K   3l rK 0|f  oN 0K %"$ 3o] 0$ "" 3 rN   3H " " B QQ  6H =&< 3   o2K =,< 9  o)2/ 8>> Do ?J r?P r<" %i WT   -* %\ %$ 6  WQ   3' !e ( 3WQ 0' !t+ 6 WT 0' <h K E Nc 0! ? eZ 9   WT   3r e   WW  6r e PW8r h PW/o #5/#lp` W .1  @&! & MathType "- W  Arial-2 pp a2 p1 a2 pa2 pa2 pa2 pt Arial-2 x R2  I2 I2 dt2 TGd2 gL2 E2 VSymbol-2  2  +2 +2 = & "System- @ ;lp h ? .1   & ! & MathType "-k   Arial-2 pe f2 pf2 pMf2 p1f2 pf Arial-2  I2 |dt2 Td2 L2 NR2 I2 VSymbol-2  +2 2 = & "System- "ystmMDlp N  .1   &  & MathTypeP  Arial-2 m2 f2 af2 a Arial-2 @W2 @I2 @L2 @1ESymbol-2 @C2 @2 @+2 @= & "System- =PGlpV T  .1  ` &  & MathTypeP  Arial-2 a2 f2  af2 em Arial-2 @/I2 @I2 @RL2 @TSymbol-2 @2 @42 @+2 @= & "System- AxAxAxAcZlp z   .1   &@ ! & MathType "-0~  Arial- 2 p load2 pem2 pm Arial-2 T2 T2 W2 Adt2 Tnd2 6JSymbol-2 -2 = & "System-@@@@mlpV "4 G .1  ` & t & MathType "-?   Arial-2 l m2 lf2 Ja2  a2 t2 paf Arial-2 W2 OI2 ARR2 AI2 A2V2 1LSymbol-2 t2 A2 A-2 := & "System-"       lpRx&& b  bC ( dddddddddddddddddddddddddB }?  z?$0D? A?  - B  0:]`c~f{ixluomgr^[uR7RxIILxCUF{:a@~4m=+s7B  %4?   1?$j .? j+?  4 (B  =1 (xg.%i+$"o%LL"u@ @< =+=?   :1:? 0g7=7?  j7C7?  -44I4? 0=+1O1?$4O4<-1U1u.[.~.[.1[1 1[1 1[1Q; .a.N8 .18 .a.Q; .a. 1[11[1~1[1< y.[.?  s.[.c    B? F1U1c      ??  :(4O4r    K?  41O1u    K? m4I4i   K?6 7C7f B<? 7=7i  0K{:1:l 3 Wu=+=o"@ @B +LL"?  0C1$"? -:4%B 7 (?  0p (B $+  .1%4+s7~4m={:a@xCUFuLILrU7Roa[lpgixf{cz  \B d  _?  =  _? 7  _B   _?  F _B j _x.4  \'5*8dddddddddddddddddddddddddlp-   C (T XXXXXXXXXXXXXXXXXXXXXXXXq - 3   Mn  9  9  *  Vn  9  9*  Vq 9  9*  Vn  6  6  ' Sq  -  0    JFCXXXXXXTT6_}NN0\}NN0\TT6_XX:bXX:boXX:bl XX:boXX:b?  XX:bB  sXX:bB pXX:bB  :XX:bB ::UU:e? a7UU7hN7RR7kQ7OO7nT4OO4qW4LL4tZ4II4wZ4II1z]4FF1}`4CC1c1CC.f1@@.i1==. l.==+ o.::+r.77+B +77(?  j+%%(?$j(%? 7(  (?  :4(%%(B  d1(++%"Q1"++%T. (( (Z.((+]+ %% .c+""1f.""4i%%1o+ .r.+x1+{ 7(~:%@"%=((":4 +"7:14F44F4~4L4~1R1~1R1~.X.{1X1{1X1< 1X1?  m.^.QA? j.^.N>?  ..>?  m.^.QA? .^.?91X1<91X1{1X1f    B~.X.i      ?~1R1x    K~1R1x    K~4L4l   K4F4l B4F4l  0K7:7o 3 W:4:"=(="@@%~LL%{ !(x+r+o.i%1f. 4c47]:|:ZCv=TIj@B jUdF?  @[XI? 7dLB  eB p:N  h?  3"W  hB cc hQ hQ h: h1  eAXXXXXXXXXXXXXXXXXXXXXXXlp89(5 2     C ( C 0 _  <  E ~  <  B        9  ?f  0  6  _`  S *  c  -    c  -  f $  Z  -    f  -    -6TJE666f000c000f666j:::m:::^ :::[ :::^ :::m:::m:::m:::m:::p7:7v777y747|447444@ $111@  !411C$6g1..F g..1F  34.+.L  6:1.++p1+++v1+((|1(%+.+%(.(%% .%"%.%"."  %+"  "!+$.*.  0+6+p % j    g$$j d j a  !4  a  $=1  m. " +% (%( +. 1R . + 1U   417R 6g7=7R  j7C7O  344I4O 6=+1O1O*4O4I31U1 .[..[.1[11[11[1QC.a.N@.1@.a.QC.a.1[11[11[1F .[.L  y.[.L $F1U1Z      :(4O4Z      ~  !41O1l      $m4I4l     67C7`   E 7=7` D:1:`  0G=+=f 3 M"@ @X  +LLX  6C1$X 3:4^ 7 ^  6p a *3 33%3+s34m6:a6CU9LI<U7?aEpNq  Cz  C}   j   $=  !7      $=   ^Y\\8/lpk 8   C (P5 RRRRRRRRRRRRRRRRRRRRRRRRRRRRj  7j  4| 1m1j1j   4m   7 C C  lC 9 9 9 9 9 *  @  ! R 3 C$ @-!@   !   C  '  RRRR ?   (  9   %  9   %  9   % ?   (F""+F""+1""+. ""+1""+F""+F""+F""+F""+''jF"""'jF"""'jF"""'jF"""'jF"""'jF"""'jF"""'jC'j@   N! j=K j=H0 F:  H0 %C:  H3 %C=K F(@=N F+=@   '+=C'.:3'173'173'443'713'713':.3':.3'=+3'@(3'@"-'C'F.'F:'F@'CL '@R '=X':^':^'7d'4j|'4j|'1py'1py'1pyH L1pyK I1pyK .vv _K .vv \K : \K  .vv \K $ .vv _KX1pyKX1pyHX1py'1py'1py*    T'4j|*      Q'4j|*    `'7d9   `':^-  `':^*   `'=X*    T'@R *  <`'CL -  <`'F@E?l'F:'F.'C'@"-'@]'=`':c':c'7f'7f'4i'1l'1l'.o'+r'+r'(uK  %r  H  %u    H x  K   Z! K I  N L  '            ' ' ' 'RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR{rlp90 F"  "C ( RRRRRRRRRRRRRRRRRRRRRRRRRRRR  6 9 9 9 9 9 <RRRRRRRRRR 9  6  6  6 9<<<<<<<<<''j3'j3'j3'j3'j3'j3'j3'j3'j3N! j3K j3H0 F3H0 %C3H3 %C3K F(@3N F+=3'+=3'.:3'173'173'443'713'713':.3':.3'=+3'@(3'@"-'C'F.'F:'F@'CL '@R '=X':^':^'7d'4j|'4j|'1py'1py'1pyH L1pyK I1pyK .vv _K .vv \K : \K  .vv \K $ .vv _KX1pyKX1pyHX1py'1py'1py*    T'4j|*      Q'4j|*    `'7d9   `':^-  `':^*   `'=X*    T'@R *  <`'CL -  <`'F@E?l'F:'F.'C'@"-'@]'=`':c':c'7f'7f'4i'1l'1l'.o'+r'+r'(uK  %r  H  %u   H x   K   Z!   K I  N L    '           ' ' ' 'RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRlpx!   C ( ))))))))))))))))))))))))5O;xD;~M;uM;~,5~M;xD> M[ D)))))))))GDD AD AGDHGHGHGHGHGHGHGHGHGikikT  nQtTR)))))))))))?  BB  !B B  !^B !7^? a[K[NXNXQUQUTRTRTRWOWOZLZL]I]IB yF?  !OF?$LF? !C?  !:CB  a@N@Q=Q=T=W:Z:Z7]7`4`4cf f( i4c:`F}]Lz]LzZRwWXtWXtT^qT^qT^q< m^q?  !@dB&? =d?#?  !1#?  !@dB&? gdn?^q<^qT^qT^qWXB    BWXB      ?ZRT    K]LW    K]LK   K`FK Bc:N  0Ki4W 3 Wf( f c`F`F]IZLZLWc  DTf GQu GQuGB go G?  !:oG? 7oGB !u  D?  !B ?)) )))))))))))))))))))))))#))lpO%Q .   i C ii(i_ CCCCCCCCCCCCCCCCCCCCCCCCCCCC}  vz   w  w!* w$! z       C}     @6   ''* UW;'' U];''  U >     @M     @q`dhcd8  gfd5 *    _2''     u2'$- ' r2'!$- '*e    ~5  $*' b         8  *      b  \N  $     e   Sxc-   h   *Yf ZNt    L cQn   , t9/69/QkCz    ?    ?    ? w    9    9    9 w    9    9    9 w    9    9    9 z    ?    ?    ? ~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"~"""F"""F"""F"Z}Zf}Zf}Zf}Zf}Zf}Zf}Zf}Zf}Zpf}WE f}TW f}TW <}T' f}W E f}Z mf}Zf}Zf}Zf}Zf}W^E}T^E}Q$6 If}Q$3 F*? }Q* u   9 $  }T 3      ? ' }W 6   ? ' }x^  ?  }x^  ?    }Z#    9  }Z#   0! }Z# *! }Z ' }Zj }Z$?}Zf}Zf}Zf}Zf}Zf}Zf}Zf}Zf}Zf}K |f}N yf}NN f VNK f SN0 < SN N )          SN T ,               VN ,  $     *}N ,     }K ,   *   }Z,              }Z,        }Z  0Q $    QK d3Q $      NN < G t$    ]N9 E3   ]N9 <'  ]N0 E$   ]N < E$    QN dE$  <]N!dE'  <]N!df??iK f}Zf}Zf}Zf}Zf}Zf}Zf}Zf}ZG       6}ZG          9}ZG    9}ZV    9}K yJ       9}H |G         9}H|G        9}K|G H9H9}Z 6 J H9H9}K Q _NE9}N T  Y}/ f}2 f}Zf}Zf}Zf}Zf}N df}K dE}KdE}N< E}] 0 E}N 9 <}Q 9 E}r< E}rdE}ZE}Zf}Zf}Zf}Zf}Zf}Zf}Zf}Z}CCCCCCCCCCCCCCCCCCCCCCCClp*   .1   &@  & MathType "-^F  "-NqV-q^WWWm +   Arial-2 ` )2 \ 22 \22 `n(2 `( 2 \32 2  Arial-2  c2 8 b2 a2 d Arial-2 2 v2 tv2 `v2 `'vSymbol-2 `> -2 `-2 `2 `= & "System-2 ^W N lp$H>b n  cnC cc(c,,,/////  K   K   ?  ((((()?,,    ߟ     ߟ"?""" " " " " " " " " " " " " " "-s"w"ۻ"ۛ [  3                  ߿   ߿                                       ["m [l { { y"  .1  `& 5 & MathType Times New Roman- 2 @min Arial-2 @+L2 @1LSymbol-2 @5= & "System-O @lp< ( O .1  `& ! & MathType "-rTimes New Roman-2 C Arial-2 d2 TdL2 i 2 Tem  Arial-2 2 Arial-2  22 T1Symbol-2 = & "System- C;2lp*  .1  ` & & MathType "- Arial-2  k2 i 2 Tem  Arial-2 2 Arial-2  22 T1Symbol-2 = & "System-o1lp`  .1  &U & MathType0 Arial-2 @0Symbol-2 @= Arial- 2 @Tem & "System- jG>lpB   .1  `& & MathType "- Arial-2 k2 i 2 Tem  Arial-2 r2 Arial-2 22 T1Symbol-2 -2 = & "System-9lp`  .1  &U & MathType0 Arial-2 @0Symbol-2 @= Arial- 2 @Tem & "System-mOjRIlp}!XX  .1   `&  & MathTypeP Arial-2 )2 |2 |2 *|2 |2 u|2  |2 m c2 )(2 (2 [ 2 !sign  Arial-2 32 m2 032 22  m2 22 Tm2  12 mTimes New Roman-2 2 $2 o2  Arial-2 8K2 K2 2 K2  T2 T  Arial- 2 loadSymbol-2 +2 +2 P +2 &= & "System-lpX } .1  ` &  & MathTypePTimes New Roman- 2 @ maxTimes New Roman-2 @ Arial-2 @ T2 @T  Arial- 2 loadSymbol-2 @u 2 @&= Arial-2 @)2 @(2 @[ 2 @!sign  Arial-2 m & "System-e\lph ~  A .1  ``&  & MathType0 "-& Times New Roman-2 |Times New Roman-2 Times New Roman-2 m|2 / 2 /G maxTimes New Roman-2  2 Times New Roman-2 G |Times New Roman-2 GTimes New Roman-2 G|2 G /Times New Roman-2 G  Arial-2 ^m2 ^m2 m2 m Arial-2 /)2  2 602  22   2 k (2 w)2 ,(2  2 sign 2 @ 2 G)2 G(2 G[ 2 G!sign  Arial- 2 base 2 load Arial-2 /n2 / T 2 G Power2 GTSymbol-2 /m2  2  2 =2 Gu 2 G&= & "System-7  lpE &kk  PkC PP(P (r:r:r:rr r r r r r r # .  /7?       $   !               '       *   ' !      *   * '        *    F K  !   $   = ? 0z 'B B 0Q T W r r r r r rr:r:r:r* lp]` ~ .1  &! & MathType "- Z  Arial- 2 p load2 p}m2 p22 pM1 Arial-2 o)2 ,( Arial-2  T 2  Tem2 dt2 TJd2 J2 JSymbol-2 R -2 =2 +Times New Roman-2  & "System-lp 4@  .1  & & MathType`  Arial- 2 step 2 step2  in2 in2 o Arial-2 @t2 @ t2 @ t2 @ V2 @t2 @V2 @T2 @t2 @VTimes New Roman-2 @ /2 @)2 @( Arial-2 @))2 @ (2 @)2 @(2 @(Symbol-2 @ -2 @3 -2 @82 @A= & "System- lpU   nm  mC ( 6666666666666666666666666666G >G  ;Y  ;J ;G ;G   ;J   ;h ;h ;k >6666_ M\ J\ J\ J_ McPcPcPcPcPcPcP63a00d0d0d0d0d0d0d0dQ  .dN  dK  dK dK  dN  dQ 7d]7d] 7dZ7d0d0d0   0      $Q0     'W0   'W0   'W0    *W0    9T0      6 Q0d3N0d0 K0d0dQ  4dN    dK    dK   dK    dN    dQ   1d]  1d]  1dZ 4d0d0d0d0d06666666666666666666666666lpn D    C ( 6666666666666666666666666666) )'  ;9  ,* )'' ) '   , *   SH JH PK 666666D ?  A 9 A 9 A 9 D ?  HF#HF#HF#HF#HF#HF#HF#HF#HF#<99d9d9d9d9d9dQ  =dN  :dK! dK  dK! dN  !  dQ ! d]:d]  :dZ =d9d9dQ :dN  :dK 0 dK*  dK$ dN !  dQ ! d] :d] :dZ =d9d9d9d9   9      Q9     W9   W9   W9    !W9    0T9      - Q9d*N9d' K9dT  4dQ =dN$ dN!  dN! dQ !  dT $ d`=d` =d]=d9d9d9d9dQ  $ dN     dK   dK    dK  ! dN   :dQ   :d]  :d]  :dZ =d9d9d9d96666666666666666666666666!lp' $  C (Y 666666666666666666666666666M2M;_;P;M';M ;P ;w;n;t;666# _# $  5 3  &B  #$- # ' & $   A'   AE DH   66666A   #>    >    >    A   #E""&E""&E""&E""&E""&E""&E""&E""966d6d6d6d6d6dQ @dN @dK=dK$ dK!  dN  dQ   d] d] 7dZ 7d6d6d6d6d6d d  d d  d d6d6d6d6d6d6d6d d  d d  d d6d6d6d6d6d6d6          ~       Q    !W     !W     $W6    6W6      3T6d0 Q6d-N6d* K6d6d d  d d  d d6d6d6d6d6d6d6d d  d d  d d6d6d6d6d6d6d6d d  d d  d d6d6d6d6dN  =dK   :dH  :dH  ! dH    dK    dN     dZ  ! dZ  :dW =d6d6d6d6d6d6d6d6666666666666666666666666lpx0  .1    &  & MathType "-   Arial-2  22 22 2 Arial-2 2  Arial-2  c2 c2 c Arial-2 ] s2  s2 Lk2 `s2 `"GTimes New Roman-2 ' 2 O2 Times New Roman-2 `=)2 `%(Symbol-2 @ +2 +2 `= & "System-lpx`  .1  ` &  & MathType "-PP   Arial-2 7 22 722 2 Arial-2 2  Arial-2  c2 c Arial-2 ] s2  s2 ^ks2 s2 "GTimes New Roman-2 ' 2 OTimes New Roman-2 =)2 %(Symbol-2 @ +2 +2 = & "System- lpg F  .1  @ &  & MathType "-   Arial-2 ( 22 2  Arial-2 % c Arial-2 GBs2 G s 2 TbkBs2 s2 "GTimes New Roman-2 G< Times New Roman-2 =)2 %(Symbol-2 GU+2 G+2 = & "System-5lpg    .1   @ &  & MathType "-   Arial-2 + 22 22 < 22 2 Arial-2 1 )2   2 q 2  (  Arial-2 ( c2 9 c Arial-2 Bs2 s2 s2 Yk2 `s2 `"GTimes New Roman-2 ? 2 PTimes New Roman-2 `>)2 `&(Symbol-2 W+2 +2 h+2 `= & "System-X O lpe ` Fu"u  `"uC ``(` qqqqqqqqqqqqqqqqqqqqqqqqqqqqqccjcjch   jck   ! jck! jck ! jck$ jck   Ljch  LjcILjcI1jcC .* 4c}61c 1c  1 B 1 ? 1 ? 1 ? . BUcjc)Ojc8Rjc8 OQ cK       OWcT       LWcT    $ ? cT      WcT    TcT         jcN         jcjciTu!Tu!qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqlpFh ^ .1  & & MathType "-  Arial- 2 real 2 gimag Arial-2 <V2 7V2 @tg  Arial-2 1 Symbol-2 X-Symbol-2 @=Times New Roman-2 @1 & "System-lp4h E .1   & & MathType`  Arial-2 l22 1 Times New Roman-2 -,2 _,  Arial-2 sin2 in2 o Arial-2 @V2 @V2 @VSymbol-2 @E2 @= & "System-pglp4   .1  &@ & MathType`>Symbol-2 ?[>Symbol-2 ?]  Arial-2 2n2 in Arial-2 @s a2 @a2 @Za2 @a2 @VTimes New Roman- 2 @p . Times New Roman-2 ,  Arial-2  32 22 12 1Symbol-2 @= & "System-lp:4  r .1  &` & MathType`>Symbol-2 ?[>Symbol-2 ?$]  Arial-2 hn 2 in, Arial-2 @ b 2 @ .2 @ b2 @zb2 @b2 @V  Arial-2  32 322 12 2Symbol-2 @= & "System-lp{  .1  @&@ & MathType`  Arial-2 n2 `n2 T2 vin2 in2 o Arial-2 b2 a2 2b2  a2  b2 ` a2 V2 V2 VSymbol-2 +2 +2  +2 j=2 G2 =Times New Roman- 2 . Times New Roman-2 0,2 a,  Arial-2 22  22 2 12  12 o22 1 & "System-;2lpO*  .1  `& & MathTypep  Arial-2 T2 V` Arial-2 hin Arial-2 V  Arial-2 H2 Times New Roman-2  , & "System- n o f lpd^ a b>  n>C nn(n80 I                                                                   _c_` Fz = : : = DGG>A;>&{FxxFxFxFxFx"xx%      O"(           XF(      0  F       - F      -            ' F        !  F <F]" l QZ"ZF]FxFxF{Eullp! 0 .1  ``&   & MathType`` Arial-2 8in  Arial-2 V2 o Arial-2 K2 K2 V  Arial-2 22 1Symbol-2 2 = & "System- NRIlp XX  .1   `&  & MathTypeP Arial-2 252  02  52  02  52 02 S52 O02 1  Arial-2 !2Times New Roman-2 l.2 r .2 .2 .Symbol-2  =2  2 =2 {2 =  Arial-2 o Arial-2 V & "System-$MDlpXN   .1   @& & MathTypeP` Arial-2 $\in  Arial-2 V2 o Arial-2 e2 k2 V  Arial-2 1Symbol-2 = & "System-qhlp 0 .1  ` &  & MathType`` Arial-2 8v2  Arial-2 1  Arial-2 k2 in2 o Arial-2 V2 K2 VSymbol-2 2 = & "System-  rilp;  / .1   &  & MathTypePTimes New Roman-2 @P ) 2 @Jln(2 @) 2 @log(  Arial-2 f in2 in2 o Arial-2 @ V2 @v2 @VSymbol-2 @O=2 @= & "System-mdlp]  . .1  &@ & MathTypePTimes New Roman-2 @)2 @( 2 @log  Arial-2 in2 o Arial-2 @$v2 @V  Arial-2 10Symbol-2 @= & "System- $lp Xx   .1    & & MathTypeP  Arial-2 N2 3in 2 scale Arial-2 VV2 V Arial-2 10Symbol-2 B2 ~= & "System-jbYlpx  .1  &` & MathType0  Arial-2 N Arial-2 10 & "System--g^lp  .1  &` & MathType0  Arial-2 N Arial-2 10 & "System- lp  wbw  `bwC ``(`  njkjkj 0     2j *      /j *   Aj -   /j ?   /jQ      2jT    5j2Vj2Vj, Vj    c ` ` `   c       j j j j }jj fj '         ?j $           <j $     Nj *     <jZ     <<         ;<        A3H{3Hu ]kg^lp4  .1  &{ & MathType   Arial-2 N Arial-2 62 & "System-lpF @  a .1  & & MathType "-Times New Roman-2 <)2 <(2 <)2 <(2 7))2 7( 2 7))(2 7(2 7 )2 7 (2 7 (2 @\)2 @0( Arial-2 <=k2 <v2 <\k2 <' V2 7k2 7v2 7v2 7k2 7v2 7T k2 7e v2 @k2 @V2 @V  Arial-2 in2 in2 in 2 input2 o2 - o2 o 2 outputSymbol-2 <F-2 <N+2 7"-2 7>-2 7F +2 @+2 @= Arial-2 <12 7 1 & "System-+ lp'W   C (D+00000000''''''''''''''''''''''''''''''''''''''''''''':'f'i           ~? x `    ` x [~? [ [ Ç[ ޽{G { { { { { { ޽{ Ç        ?  ? "? ?? ??_ __ _ o o ?o o w w w w w w {  { { { } } } ~ ~  ?        ?                                    뚿 뺿  횿 '''''''''''''''''''''''''''''''''''''''''?'?'?''''++++++00000000  lpN%HS   iC ii(i)-----------------------%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% _                               ޽^ ޽^ ޽^ ޽N ѽ ޽_ ޽_w ޽^     "?           ?߁߁%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)-----------------  lp  F"  `"C ``(` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRgKdNd<        Qd?                Zd          Zd           Zd          *Zd              Zd          Zd?c?Zd?c?ZdBQA ZdNdNdNd-   4NE 0  1NB 0   .NB 0   .NB 0  .NE 0   .Nd'  1Nd'   4NdNdNdNdNdNd   Cd    @d   =d   =d ! =d<   =d-   =*    @*  C?RRRRRRRRRRRRRRRRRRRRRRRRRRRRRlp  r .1   &` * & MathType "-*R  "-RD-D^^^. N   Arial-2 ,612 Qn 22 1 12 Q2 Arial-2 jV2 PV2 V 2 THD  Arial- 2 1rmsSymbol-2 -2 = & "System-lp\"x  N .1  `& t & MathType "-  Arial-2 l[02 l12 l12 l 22 l 22 G02 12 12  22  2 Arial-2 A2 #s2  A2 W s2  A2 s2 A2 AhB2 As2 A B2 AW s2 A B2 As2 AB2 k2 s2 "G  Arial-2 l8n2 ln2 Bn2 nSymbol-2 +2  +2 %+2 A+2 A +2 A/+2 =Times New Roman- 2 . 2 A .2 >)2 &( & "System- #lpfh  .1  &A & MathType "- Arial- 2 GT 4002 G! 10 2 T 4002 52 1  Arial-2 o2Symbol-2 Gg +2 GR+2 2 = Arial-2 G s2 Gs2 s2 "GTimes New Roman-2 .2 >)2 &( & "System-lp\"  N .1  `& t & MathType "-  Arial-2 l[02 l12 l12 l 22 l 22 G02 12 12  22  2 Arial-2 A2 #s2  A2 W s2  A2 s2 A2 AhB2 As2 A B2 AW s2 A B2 As2 AB2 k2 s2 "G  Arial-2 l8n2 ln2 Bn2 nSymbol-2 +2  +2 %+2 A+2 A +2 A/+2 =Times New Roman- 2 . 2 A .2 >)2 &( & "System-$mdlp, P @ .1   (&@( & MathTypeP "-@ZTimes New Roman-2 @'Times New Roman-2  $/ 2 %.2 @"/2 ["/2 s"/ 2 (_.2  / 2  . 2 #p. 2 #. 2 # . 2 # . 2 #. 2 #".2 C0/ 2 C .2 c/ 2 c .2 0/ 2  . 2 (D.Symbol-2 &2 u&2 E&2 &2 &2 &2 i &2 &2 2 u2 E2 2 2 2 i 2 2  -2 @-2 [-2 s-2 @+2 2 x2 H2 2 2 2 f 2 2 2 x2 H2 2 2 2 f 2 2 @r2 2 2 T2 $2 2 2 Z 2 2 2 2 T2 $2 2 2 Z 2 2  -2 C~-2 c-2 ~-2 @=2 2 x2 H2 2 2 2 f 2 2 2 x2 H2 2 2 2 f 2  Symbol-2 U !-2 U z-2 S [-  Arial-2 U &n2 U #n2 U o"12 U w!n2 U 12 U n2 u$n2 "n2  22 22 $n2 !n2 k 12 12 u$n2 "n2  02 02 n2 632 922 (12 S n2 S 12 S n2 n2 H22 n2 M12 n2 E02 32 22  1 Arial-2  .12  / 02  602  =02 C!02 C/ 02 CC12 C=02 c!02 c/ 02 c602 cJ12 !02 / 02 602 =0 Arial-2  N%A2  "B2  A2  B2 @#A2 @:!B2 @A2 @B2 [J#A2 [ B2 [A2 [B2 s#A2 s:!B2 sA2 sB2 <A2 t#k2  }x2 @}x2 [}x2 v}x2  AA2  A2 CA2 CpA2 cA2 cA2 A2 pA2  bx2 @bx2 [bx2 vbx2 <Qdt2 t~d  Arial-2 X 9n2 X n & "System--wlp "@ < .1  &q & MathType "-Times New Roman -2   Arial-2 ln2 n2 pn Arial-2 A2 DB2 k2 Yx2 @ySymbol-2 +2 O= & "System-- lp! > T&WordMicrosoft Word  ,"System 0-@Times New RomanIwIw0-  2 , c&-TC aA,(Aa$>!!!!!!!wwww5//5//5//5//5//5//5//5//5//5//5//5//5//5//5//5//5//5//ww5//              5//5//wwww!!!!!!!!&-  lp!D @ P#,#  mE,#C mEmE(EmE##############wwww6//6//6//6//6//6//6//6//6//6//6//6//6//6//6//6//6//6//ww6//                   6//6//wwww#############lp* 8N ''  a'C aa(aNOOOOOOOOwHwwHw5/_5/_5/_  $#$#$#$#$#$#  $#  +#  +#  ;#5/_H5///5///5///5///   / / /5///H5///5///5///  5 5 5 5///H5/9$5/8$5/:$!!! !"! ! ! !!-1-1-15/_5/_wGw5///5///5///5///5///5///wGwwGwOOOOOOO lpD* D .& &  ] &C ]](]KMMMMwHwwHw5/_5/_5/_$#$#$#$#$#$#$#+#+#;#5/_H5///5///5///5//////5///H5///5///5///5555///H5/9$5/8$5/:$!!! !"! ! ! !!-1-1-15/_5/_wGw5///5///5///5///5///5///wGwwGwMMMMMMMlp4 R! //  _/C __(__wxwwxw5//_5//-,5//-,5///, ''''')'''''' '' ' * ' * 4*5//_x5////5////5////     5////x5////5////5////     5////x5//_5//9$5//8$5//:$ !!! !"! ! !  !! -1 -1 -15//_5//_www5////5////5////5////5////wwwwww/ z lp$H> n  enC ee(e,,,/////////////&&&&&?_ ?    ?cwz߼&&& ?    #|vg==կ =tw^n '#=ڽ~/O~&&&&&&&&&? ? [?  |     G&&&,,,,,,,,,,,,,,,,C3:3lp.Yn6f r  rC ( PPPPPPPPPPPPPPPPPPPy`Hv]HvR]RHvR]RHvR]RHvR]RHvR]RHvR]RHvR 8 RHv*   2  1Hv* 2  1Hv*  8  1Hv*] 1Hv* ]  1HvR]RHvR]RHvR]RHvR]RHc R 8 RH` 7 2 RHi  =; RHf# = ;# RHfR6 =MR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHf*  $R ( R# RHf*  !R " 4  RHf* !R"  4 RHf*  $R (  1# RHf* 6RM  16RHfR6RM  16RHfR6RMR6RHfR6RMR6RHfR6RMR6RHB   1R6RMR6RH?     $ R $R ( R# RH?  $ 7 !R " R  RH?   $ =!R"R RH?     $ = $R ( R# RHB    1 =6RMR6RH`?@R6RMR6RH]<@R6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR $R ( R# RHfR !R " R  RHfR!R"R RHfR $R ( R# RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR61HfR61MR6 HfR     ( R#   6fR     " R    3fR  "R  3fR     ( R#   6fR6  MR6  HfR9 [ MR6'(HfR9  X'(MR6RHfR6  XRMR6RH{  +R6  XRM16RH{ .16  XRM 6RHx     !  [R (    RHx     pR ;  '    Q RHx   mR; *   NRHu      $R ; -     Q RHu ^  6RM @  *  dRHr  L 6RM@'(*  dRHf'(6RJ  CR'  gRHfR6RJ pR' |RHfR6RG  ^R$  yRHfR6RMR6RHfR $R ( R# RHfR !R " R  RHfR!R"R RHfR $R ( R# RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR $R ( R# RHfR !R " R  RHfR!R"R RHfR $R ( R# RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR $R ( R# RHf-  !*   "  1   1Hf- !*" 1  1Hf- $* ( 1# 1Hf- 6*M 16 1Hf- 6* M  16  1HfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHfR6RMR6RHf9P9K%u%u%u%u%u%u%u ! r o o ! rPPPPPPPk  \  ^kegh b gh  b  gh   b   ge  V  ^e <_ <gb  < S  < ^PPPPPPPPPPPPPPPPPPPPPPPPlp " S .1   &@ ~ & MathType "-&  Arial-2 g$12 gy2  Arial- 2 yo_min 2 o_maxSymbol-2 gZ-2 7-2 @=  Arial-2 ?N Arial-2 7V2 7V2 @1dv & "System- lp90  x .1  @& & MathType "-nE$:$k Arial- 2 t 672 t02 P12 22 852 K52 S82 O12 2 02 102 : 52 : 52 :6 02 :u22 :q32 :85  Arial-2 4Times New Roman-2 tp .2 )2 (2 .2 :]))2 : (2 : )(2 :%.2 :(Symbol-2 t=2 -2 -2 3-2 t5=2 -2 =2 T -2 : -2 : -2 :X-2 : +2 :-2 i= Arial-2 t1dV2 V  Arial-2 \ox & "System-icrlpX%XX  r .1   !&! & MathTypeP Arial-2 1! 2  )2 Ea2  2  2  2  2 7z2  2 a2  2  2  2 /z2  2 (a 2  / 2 Z)2 b2 } 2 ~ 2 /  2 P  2  z2 e  2 $ b2  2  2 M 2 z2 (b2 ` 2 f 2 'H(z)  Arial-2 N2 (12 -2 FN2 ^12 >N2 702 N2 12 i -2 N2  12 N2 M 2 0Symbol-2 P+2 2 R+2 +2 f 2 +2 = & "System- 9ullpC38   .1  .&@. & MathTypeP Arial- 2 @,N)]2 @,- 2 @) y(n2 @Q(a2 @( 2 @' 2 @&.2 @% 2 @$ 2 @#2)2 @6#- 2 @  y(n2 @a2 @A 2 @B 2 @91)2 @- 2 @y y(n2 @8a2 @ 2 @[2 @W 2 @-2 @ 2 @N)]2 @- 2 @u(n2 @D 2 @b2 @{ 2 @| 2 @.2 @P 2 @Q 2 @H 1)2 @ - 2 @ u(n2 @  2 @B b2 @ 2 @ 2 @u(n)2 @ 2 @#b2 @ 2 @[2 @G 2 @M 2 @@y(n)  Arial-2 )N2 Z 22 12 N2  12 0Symbol-2 @\'+2 @1%+2 @+2 @+2 @+2 @R+2 @= & "System-)MDlpnXN  .1   &` & MathTypeP Arial-2  2  2 z2 * 2  b2 }  2 ~  2 /  2  2 Iz2  2 b2  2  2 b2 ` 2 f 2 'H(z)  Arial-2 -N2  n2 b -12 p12 q0Symbol-2  +2 f 2 i+2 = & "System-   @ b @ ~ulp[   .1  & & MathTypeP Arial-2 @}N)2 @- 2 @u(n2 @ 2 @+b2 @ 2 @ 2 @.2 @ 2 @  2 @ 1)2 @. - 2 @3 u(n2 @  2 @b2 @f 2 @g 2 @Au(n)2 @ 2 @b2 @G 2 @M 2 @@y(n)  Arial-2 N2 i 12 X0Symbol-2 @;+2 @+2 @+2 @= & "System- @u()2 2 -$lp4V   .1  ` & & MathType0  Arial-2  N2 S12 s0 Arial-2 CN Arial-2 6b2 Wb2 #@bTimes New Roman- 2 }. & "System-O olp%X  b .1   @"&" & MathTypeP Arial-2 ! 2 L!)2  2 0z2  2 Xa2   2  2  2 o 2 z2  2 Ca2  2  2 (a 2 t / 2 )2  2 z2  2 +b2   2   2   2   2 H  2 z2 ] 2 b2 | 2 } 2 (b2 ` 2 f 2 'H(z)  Arial-2 I -N2 N2 -12 12 02 -N2 N2 -12 12 0Symbol-2 c+2 2 +2 ; +2  2  +2 +2 = & "System-+ @lpC3   .1  .&@. & MathTypeP Arial-2 @-]2 @- 2 @h,N)2 @+- 2 @) y(n2 @(a2 @' 2 @& 2 @%.2 @% 2 @$ 2 @#2)2 @#- 2 @!y(n2 @qa2 @& 2 @' 2 @1)2 @- 2 @y(n2 @8a2 @ 2 @[2 @W 2 @-2 @ 2 @N)]2 @- 2 @u(n2 @D 2 @b2 @{ 2 @| 2 @.2 @P 2 @Q 2 @H 1)2 @ - 2 @ u(n2 @  2 @B b2 @ 2 @ 2 @u(n)2 @ 2 @#b2 @ 2 @[2 @G 2 @M 2 @@y(n)  Arial-2 (N2   2 ? 22 I 2 12 N2  12 0Symbol-2 @&'+2 @$+2 @|+2 @+2 @+2 @R+2 @= & "System-jInfo*qhlp4 / .1  & & MathType  Arial-2 N2 02 02  N2 S12 s0 Arial-2 C1a2 1a2 1a2 ,b 2 ".2 ,b2 #,b2 C'NTimes New Roman- 2 c'. & "System- ;2lp=V *  .1  ` & & MathType0  Arial-2  N2  N2 S12 S12 s02 s0 Arial-2 a2 ,b 2 . 2 ".2 a2 ,b2 #a2 #,b2 C'N & "System- joB9lp+X8  .1   '&' & MathTypeP Arial-2  ' 2 &)2 N% 2 $z2 c$ 2  0.64142 I  2 J 2  2 dz2  2 !1.5612  2 1-2  2 (1 2  / 2 W)2 z2 F 2 0.02012 Y 2 Z 2   2 t z2   2 U 0.04022  2  2 (0.02012 ` 2 f 2 'H(z)  Arial-2 %-22 }-12 Z-22 -1Symbol-2 +2 +2 +2 = & "System--t Entry.%lp+V   .1  ` & & MathType0  Arial-2  N2 P22 k1 Arial-2 1a2 5 2 1a2 1a2 ;'NSymbol-2 l2  & "System-201    QHlpV  .1   & & MathTypeP>Symbol-2 ?\[>Symbol-2 ?]  Arial-2 12 r 22 * m2 12 m2 m Arial- 2 @4 .2 @  Arial-2 @Ua2 @q a2 @a2 @a2 @EA Symbol-2  -2 I-Symbol-2 @h= & "System-MDlp N  .1  `&  & MathTypeP>Symbol-2 ?R[>Symbol-2 ?]  Arial-2 912  22  n2 212 :n2 n Arial- 2 @j .2 @  Arial-2 @b2 @b2 @b2 @b2 @1B Symbol-2 $ -2 -Symbol-2 @^= & "System- lpH&  .1   & & MathTypeP>Symbol-2 ?[>Symbol-2 ?] Arial-2 @& 2 @c 2 @.2 @   Arial-2 12 22  n2  m2 P 12 X n2 m Symbol-2 -2 } +2  -2 +Symbol-2 @=2 @x2 @h= Arial-2 @ c2 @_c2 @B2 @rA2 @"C & "System--$lp{)    .1  `%&`% & MathTypepSymbol-2 ~*[Symbol-2 ~Z ]Symbol-2 Symbol-2 $-2 U"+2 =2  -2 K+2 =2 -2 -+2 n =2 2 = Symbol-2 )-2 + Arial-2 $12 3#n2 !m 2 1,.,2 j2 1;2 )n2 m 2 0,.,2 j2 1;2  n2 m 2 d 0,.,2 s k2     Arial-2 k2 j2 *i2 $k2 iTimes New RomanS-2  ; Arial-2 &b2 ka2 1c & "System-n E&lp.X   .1   )&) & MathTypeP Arial-2 ))2 $32 !22 32 22  32 2  Arial-2 .(c2 b2  a2 d Arial- 2 %) * V2 # /2 s" 2 Q! 2 (X 2  2  2 z) * V2 / 2 V 2 1(X - 2  2 <  2  X * V 2  * (2 w/2 F 2  2 VTimes New Roman-2 #Times New Roman- 2 cosTimes New Roman-2 Times New Roman- 2 ccos 2 cosSymbol-2 _ +2 *+2  +2 A= & "System-icr Eq mpObj lp-4   .1  (&( & MathType` Arial-2 @3() 2 @ %) * V2 @#/2 @" 2 @  2 @(X 2 @ 2 @V 2 @C) * V2 @ /2 @ 2 @(X - 2 @ 2 @  2 @ X * V 2 @ * (2 @w/2 @F 2 @ 2 @V  Arial-2 'c2 b2 l a2 q Arial-2 @9$32 @V!22 @q32 @C22 @ 32 @2Times New Roman-2 @"Times New Roman- 2 @xsinTimes New Roman-2 @Times New Roman- 2 @1sin 2 @sinSymbol-2 @+2 @+2 @ +2 @A= & "System- Eq mpObjlpR b .1  &` & MathTypeP Arial-2 @~) 2 @  V2 @  2 @4  V2 @ 2 @ * (V2 @:/2 @J 2 @ 2 @V  Arial-2 c2 d b2 a2 o Arial-2 @32 @1Symbol-2 @ +2 @B +2 @E= & "System- 2 C2  lpV d &zz  dzC dd(d u $= $=vR   :v$   :v$ v*    v$      v$     v'    G   1 vB    0 =vE /vu   2v 2vsvsvsvsvsvsvsvsv $@v$J$@v$   = B      $        !       (!      ($     1   (B G @ (r 0@ %5vsvsvsvsvsvsvsvsvsvsv$G$@v$G$@vE       v'           v$           v$           v'          1 vE        =vu   G   @v 0 .v^ va  lpM H <  wC ww(w# wwwwwwwwwwwwwwwwwwwwwwwww@ .C1C1    b      e   e   e  e      e    h+3+3% 0forK  'K   ']  NN   ?  aK   <  ^K      '  ^N    '  ^h  al"dl"dldodrdu [l ^o^ua`1`^4`^4cX7cX7fR:i =i=l @l B    Qo  !        Nr    `r     Nu    Nx !       Qx.E     T{(2!u{(2!u~"2 uUUXX[ ^ ^aadddddd a  ^  ^  ^ awwwwwwwwwwwwwwwwwwwwww lpJ 2&   tC tt(t nnnnnnnnnnnnnnnnnnnnnnnnnnnnnRUUUUU#&fL)oR&rS   &K  u    #K   r $#]  9       N   6     $   K   6        K      !      N    $   !0bf""$0bf""!* bi"=i@l@c=f@W(Wd.Wd.Z^1Z^1]X4`  7`7c:c :f =i  7i   !    Ql          Nl     `o4     Nr.     Nr.?       Qu(W     Tu(/!ux"2!u{2 u{R~U~UX [ [^^ a a a a a a ^ [ [ [ ^nnnnnnnnnnnnnnnnnnnnnn(bblp,'U F"  "C ( ########################@W##7N###.EC]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]C]@W7 N1H.+ (+1++" +(       "(   %  %   %     %   "% " (   (?+ "B+1B.+E1H7N=TC]C]C]4 ]1 ]4 ]C]C]C]C]C]C]C]C]C]C]C?C?C?C9C?C?=?=W@W@Z=W4N1"K+(E+.E( B%+ ?%%?%" 3 "6yy"0 \| % 0_ %?cW (?< + *c# *cN&.*6&(!c,"*c/"*c E8+*-!]B!]B!]B!]B!]B!]B!]B!]B!]B!]B!];WB!]2 NB!],HB!])+EB!]&1BB!]&1BB!]#7?B!]#7?B!]  ?B!]    <B!] B!]" !]"   !]"  !]%7!]%7!]1W 1 N+}H.z  +E4}(  B:. 1BL.7?I4   7?      &=<   )< !  ,<$   )< "$    #<  %'   /?% %    /? 4!  / BL. BL. EO( HR NXT^!]d!]d!]d!]o   !]l    !^k '  !^k ' !^k ' !F k ' !^k ';}!^k ! ;w!^n *;q!XZ k![]e![`_ \]:yY S Q7S MK^7^+M J+H^7^1J G1E^7..4D GE^7 .:> D (B^7" .@8 D%B^7%.F2 A"B .(.L, 4%6!"1+.R& 4"9! "7..X ! " [ 4"3! "..(U!!4 "B! "+ .%O'!C%B 7. "I-!+ (B^7. C3!+E^7. .9!+1E^7.. (?!%+H^7^ "E!+K^7^K!+%Q= Q%+x W V]Sc %M i +Mo 1Rhu7Un{UlUlRlRlRl L l Rl  E7E7E 1H +K %KQ T[  ## #  k  %k_"nBnb  qyqyt|t|w w z7:[:[=[_=[=[=[V=[=[=[=[M>[b >[b >[b >[b >[b >[b >[b >[b >[a ] t^^ ZXa ] [b a^b a^b a^b a^b a^b a^b a^b a^F$ a[Fs$ aOFs$ aI)Fs$ aO#Fs$ aUFs$ a[Fs!adFs  jFs pFs+ gFs 1  ^Fs     XFs 7 "   O Fs 7 "  1LB ZFN :   1O6 WFQ=~ 1X<WF    ~LL6WF  ~K-WF  ~T ZF   TcFU  LR!cF U  a^*WFs aXFs aO Fs+  aL)Fs aO Fs aXFsaaFs$!agFsc !apFs`  !ajF$4o gadF$ :o Aa^F' :o A`^F':c  A`^F* 4c A`^F' 4c g`^Fsc p '`L Fs$p  '` IFs$p  'ZLFs$p  'W^Fs$p# P W F$p  MQa L:  C W L:& IL:& IL:&IL:"%7L:"7 L:( =L 8;L ~L  xL oL l"LH s( E^] s.  B^ ] p4  B^ ] m:  B^] m  B^] p EY   ZS    WY uh uh uk  xk:xk:xn4{q.~q(~w"z#####################lp~   ^ .1   & & MathTypePTimes New Roman-2 @)Times New Roman-2 @Times New Roman- 2 @sin(2 @)Times New Roman-2 @ Times New Roman- 2 @ sin(2 @)Times New Roman-2 @Times New Roman- 2 @sin(2 @)2 @( Arial-2 @ t2 @V2 @t2 @ V2 @t2 @]V2 @St2 @'v  Arial-2 u32 32 22  22 12 )1Symbol-2 @,+2 @5 +2 @= & "System-%i`lp  .1   @& & MathType "-pe p   "-  - ^L ^L ^ Arial-2  22 2  2 8 2 Reading2 ` 2 'Meter  Arial-2 Q22 132 Q<22 1 22 Qv 22 1$ 1 Arial-2 V2  V2 X VSymbol-2 +2 Y +2 = & "System-lp?   ^ .1  & & MathTypePTimes New Roman-2 @F)Times New Roman-2 @QTimes New Roman- 2 @lsin(2 @)Times New Roman-2 @ Times New Roman- 2 @ sin(2 @)Times New Roman-2 @0Times New Roman- 2 @Ksin(2 @)2 @( Arial-2 @t2 @I2 @'t2 @x I2 @t2 @+I2 @t2 @6i  Arial-2 :32 32  22  22  12 1Symbol-2 @A+2 @+2 @:= & "System-%aXlpwv  .1   & & MathType "-pe pZ   "-  - ^L ^L ^z Arial-2  22 2  2 8 2 Reading2 ` 2 'Meter  Arial-2 Q22 1~32 QL 22 13 22 Q 22 1 1 Arial-2  I2  I2 q ISymbol-2 /+2  +2 = & "System-LClp~L $ .1   & & MathTypePTimes New Roman- 2 @.2 @x)Times New Roman-2 @2 @ Times New Roman- 2 @(sin(2 @ )Times New Roman-2 @ 2 @Times New Roman- 2 @sin(2 @)2 @(Symbol-2 @+2 @ +2 @ +2 @+2 @=  Arial-2 22 12 O 22 x 12 12 +1 Arial-2 @]t2 @r V2 @t2 @qv2 @St2 @'v & "System- PGlpT $ .1  & & MathTypePTimes New Roman- 2 @.2 @E)Times New Roman-2 @2 @Times New Roman- 2 @ sin(2 @K )Times New Roman-2 @ 2 @0Times New Roman- 2 @Ksin(2 @)2 @(Symbol-2 @+2 @+2 @ +2 @,+2 @:=  Arial-2 22 12 ? 22  12  12 1 Arial-2 @Mt2 @ i2 @t2 @5i2 @t2 @6i & "System- lpEz  .1  &@ & MathTypeP  Arial- 2 rms 2  rms Arial-2 @II2 @6V2 @,SSymbol-2 @2 @^= & "System-%d[lp |  .1    &  & MathType "-ppa  3  "-3k-saaa  Arial-2 22  2  2 @V  Arial-2 T22 4r22 T22 41 2 rmsTimes New Roman- 2 o .Symbol-2  +2 +2 = Arial-2 V2 V & "System- g^lpM   .1   @ &  & MathType "-pKp z  "--a2a2a  Arial-2 22  2  2 "I  Arial-2 T222 422 T22 41 2 rmsTimes New Roman- 2 .Symbol-2 +2 +2 s= Arial-2 I2 WI & "System-mdlp   .1  ` &@  & MathType "-rpSymbol-2 Symbol-2 2 m=  Arial-2 (<T Arial-2  dt2 ;t2 ii2 t2 v2 jT2 1P  Arial-2 0 Arial-2 T1Times New Roman-2 )2 (2 a)2 ( & "System- lpF  .1  &U & MathType0 Arial-2 @S2 @0P2 @1PFTimes New Roman-2 @Y/Symbol-2 @:= & "System-#lp  Q .1   &@  & MathTypePTimes New Roman-2 @ )Times New Roman-2 @2 @2Times New Roman- 2 @cos(  Arial-2 L 12 1Symbol-2 @+2 @ = Arial- 2 @1DPF & "System- lp 0 } .1   &  & MathTypeP Arial-2 @ 0Symbol-2 @ =2 @a+2 @+Times New Roman-2 @C )2 @b(2 @)2 @(2 @4)2 @S( Arial-2 @t2 @Ii2 @Gt2 @i2 @t2 @6i  Arial-2 c2 (b2 a & "System-xolp;  0 .1   &  & MathTypeP  Arial-2 0 c2 0 c2 b2 b2 a2 a Arial-2 @ I2 @V V2 @3I2 @V2 @I2 @6V2 @,SSymbol-2 @+2 @+2 @^= & "System- lp5p   .1  `&@ & MathType "-rpSymbol-2 Symbol-2 2 +2 2 2 +2 2 m=  Arial-2 (<T2 pc2 pc2 pb2 p b2 pa2 pa Arial-2  dt2 t2 Ti2 t2 v2 t2 ui2  t2  v2  t2 i2 t2 +v2 jT2 1P  Arial-2 0 Arial-2 T1Times New Roman-2 N))2 m(2 L)2 k(2 v)2 (2 m)2  (2  )2  (2 )2 (2 ( & "System-atilpF  .1  &U & MathType0 Arial-2 @S2 @0P2 @1PFTimes New Roman-2 @Y/Symbol-2 @:= & "System-#lpn  .1  &` & MathTypeP  Arial- 2 *offset2 m2 0 Arial- 2 @1802 @2 Arial-2 @ V2 @) 2 @B/ Arial-2 @ * Arial- 2 @ f t2 @ (2 @U*2 @V2 @VSymbol-2 @+2 @ +2 @=Times New Roman-2 @P 2 @Times New Roman- 2 @sin & "System- Ne Roan-g^lpv{  " .1  @`&  & MathTypeP "-W?  "-G-"crcrc Arial-2 ) 2 1802  22 32 2  Arial-2 II2 a Arial-2 / Arial-2 * Arial-2  ft2   (2 *2 I/2 *2 V2 VTimes New Roman-2 "2  Times New Roman- 2 KsinSymbol-2  +2 = & "System- ymbllp{ T  b .1  @& & MathTypeP "-W?  "-G9-Accc Arial-2 ) 2 /2  -2 3/ Arial-2 * Arial-2  ft2 )  (2 *2 h/2 '*2 V2 V  Arial-2 II Arial-2 32 2 2 1802  22 32 2  Arial-2 bTimes New Roman-2 2 A2  Times New Roman- 2 jsinSymbol-2  +2 = & "System-"ystmlp{8 d  j .1  @@& & MathTypeP "-W?  "-G:-Bccc Arial-2 )2 ;/2  2 4/ Arial-2 * Arial-2  ft2 *  (2 *2 i/2 (*2 V2 V  Arial-2 II Arial-2 32 a2 2 1802  22 32 2  Arial-2 cTimes New Roman-2 I2 B2  Times New Roman- 2 ksinSymbol-2 y+2  +2 = & "System-ystm!/&;)z48|CONTEXT{ |CTXOMAP* |FONTS |KWBTREEv3 |KWDATA+ |KWMAPM3 |SYSTEMn|TOPICr|TTLBTREEc |bm0|bm1N|bm10^N|bm100d|bm1011|bm102|bm103|bm104|bm105:|bm106|bm107|bm108|bm109X|bm11sR|bm110 |bm111#|bm112P|bm113@|bm114|bm115]|bm116|bm117#|bm118&|bm119Y)|bm12V|bm120,|bm121_0|bm1225|bm123:|bm124?|bm125B|bm126Q|bm127]|bm128gk|bm129|bm13Z|bm130A|bm131|bm132\|bm133|bm134 |bm135Y|bm136<|bm137|bm138|bm139t|bm14^bm17g|bm18k|bm19n|bm2 |bm20'q|bm21t|bm22x|bm23|bm24|bm25{|bm26|bm27|bm28.|bm29)|bm3"%|bm30?|bm31e|bm32|bm33u|bm34|bm35a|bm36|bm37|bm38Ԥ|bm39n|bm45(|bm40d|bm41X|bm42|bm43 |bm44/|bm45Y|bm46\|bm47h|bm48:j|bm49l|bm5H+|bm50)n|bm51o|bm52r3|bm53t|bm54v|bm55x|bm56z|bm57~|bm58|bm59I|bm65|bm60g|bm61s|bm62|bm63|bm64޳|bm65|bm66|bm67K|bm68`|bm69K|bm7u9|bm70|bm71}|bm72|bm73|bm74z|bm75o|bm76|bm77|bm78|bm79|bm8=|bm80-|bm81 |bm82 |bm83}|bm84|bm85|bm86j|bm87b|bm88 |bm89%|bm9@|bm9013|bm91@@|bm92KM|bm937P|bm94T|bm95X|bm96\|bm97k|bm98m|bm99T{|bm140|bm53PB|bm140=|bm141|bm142|bm143l|bm144|bm145P|bm146-|bm147 |bm148d|bm149ȵ|bm15=a|bm150k%|bm1512|bm152B8|bm153j>|bm154G|bm1553J|bm156UQ|bm157S|bm158V|bm159Y|bm16=d|bm160\|bm161`|bm162=h|bm163bl|bm17g|bm18k|bm19n|bm2 |bm20'q|bm21t|bm22x|bm23|bm24|bm25{|bm26|bm27|bm28.|bm29)|bm3"%|bm30?|bm31e|bm32|bm33u|bm34|bm35a|bm36|bm37|bm38Ԥ|bm39n|bm45(|bm40d|bm41X|bm42|bm43 |bm44/|bm45Y|bm46\|bm47h|bm48:j|bm49l|bm5H+|bm50)n|bm51o|bm52r9 0 lp'M& |X  XC (d&00000000000000000000 & & & & &        { y { a  w a  y w    ޷  / & & &           o     ???  ? $??      ?  ?      ?   _   _ ?  o ?  w   {   }   }   ~                              ymkav׶ۭ{a jyqK                                                          ?  ?         &&&&&?&?&?& & & &0000~1>?k_)B00000000000000000000000lp& 8-  N *   7* C 77(7&&&&''''''''''''''''''   dG ޭ m v #     ''''                zo~ѷڗ\'oow#   ''''''''''''''''''''''''(lpC#    C (@  DٿFj_0 o???  ? y?aKnaym[&  ? #mny'?  ?   ?     }˿     ?  G???T K lp`!@\ 0   C C CC(C()(((((((((7(B(((p$xm{mm~omy%{mK|s(((((((((((( Ǹǰǰ        ((((((((((   """"""""""""""""""" ?7? ?                ?o  ?        ??? ??""""""""""""""""""""""""""""""(((((((((((((((((ullpM   $ .1  @ &  & MathTypeP Times New Roman- 2 offset2 m2 0Times New Roman-2 @* Arial-2 @V2 @`n2 @V2 @VSymbol-2 @R+2 @= & "System- Ar w"lpE4  &MM  PMC PP(P _fcfjmmmjg-1 3m. 0jm+-"ROL".  C(Q   I(Q   F.K   (. 3   +4 9  +. 6   9 (. 3 6 ~  -% 6  ' #F L O !+ -m(*jm1 3z+ (+(+(1.=mlfcfElp* ` 4 .1   &  & MathTypeP Times New Roman- 2 in1 2 in22 oTimes New Roman-2 @^*2 @]2 @*2 @[ Arial-2 @V2 @V2 @8k2 @VSymbol-2 @= & "System- Aral-2 1,lpV  < .1  ` &  & MathTypeP Times New Roman- 2  in2 2 Bin1Times New Roman-2 @/2 @* Arial-2 @2V2 @hV2 @k2 @V  Arial-2 oSymbol-2 @= & "System-2 Ish_lpf  .1  `&` & MathType` "-Ali  "-ti-cccD  Arial-2 Iin Arial-2  V2 k*2 VoSymbol-2 = & "System-"Sytem-ylp1X8  .1   &@ & MathTypeP  Arial-2 22  1  Arial-2 7k2 o Arial-2  V2  k2 K2 V2 VTimes New Roman-2 )2 J *2 { (2  *2 *2 X)2 E(2  2 sign Times New Roman-2  in2 jinSymbol-2 = & "System-  cYcZlp z % .1  & & MathTypeP  Arial- 2 [offset2 m2 o Arial-2 @I2 @[ft2 @I2 @,ISymbol-2 @ +2 @a +2 @=Times New Roman-2 @j)2 @ /Times New Roman-2 @ Times New Roman-2 @" *Times New Roman-2 @Times New Roman-2 @(2 @N 2 @sin2 @* Arial- 2 @N 1802 @2Symbol-2 @+ q & "System- 2 y2  SJlpE4V &MM  PMC PP(P _fcfjmmmjg-1 3m. 0jm+ -" R O L.  CQ   IQ   FK   ( K   + 0  .3   9 +3 6 ~  -(   -  ' # 1 L O !+-m(*jm1 3z+ (+(+(1.=mlfcfE%lpX  .1    & & MathTypePTimes New Roman-2 g)2 *2 *2  *2  (2 `*2 )2 T 2 (2  2 sign  Arial-2 32 +32 m22 22 & 1  Arial-2 wi2 ,i2 Si2 dc2 Ti2 o Arial-2 V2 3K2 OV2 K2 v V2 < K2 I2 wV2 ,ISymbol-2 P+2 +2 Y +2 = & "System-  "ystrilp( & .1  `@& & MathType` "-l  "-tO-Wccc  Arial-2 in2 o Arial-2  V2 k*2 6lSymbol-2 = & "System-c2 T2 #l!8?PSIM  ̡̡̡̡̡\9S9 EQ1QSimcad Help Contents P- (PSIM Help ContentsThis Help file covers both PSIM and its add-on Modules: Motor Drive Module, Digital Control Module, and SimCoupler Module. Subjects are organized based on the function menu as follows.MQ;#F$A,㡪Element MenuJP;#FA,jFile MenuJ1;#FA,=\Edit MenuJ{;#FA,DmzView MenuL18#@(A&W4hˀSubcircuit MenuN{;#F&A,.dSimulate MenuH]8#@ A&HOption MenuH8#@ A&SWindow Menua<]% xIn addition, the following help information is available:IO8#@"A& ľHelpful Tips{@;#FA,BnPower/Control Circuit Representation and Interface in PSIMSO8#@6A&erError/Warning MessagesMj;#F$A, FFT Analysis52#4A5j2#4A,'  : :1_ :kAFile menul@, (File MenuThe File menu includes the following functions:n:P#p<>  NewCreate a new circuitj#~G#^F> OpenOpen an existing circuits,G#^X> CloseClose the current circuit windowp,~aD#XX> Close AllClose all the circuit windowsf"D#XD> SaveSave the current circuit~:aE D#Xt> Save AsSave the current circuit to a different file g# D#XF> Save AllSave all the circuitsE X#~> <*Save with PasswordSave the circuit with the password protection. Once the circuit is password protected, one must enter the correct password in order to view the circuit schematic. However, without entering the password, one can still simulate the circuit and view the simulation waveforms.The password protection can be disabled by selecting Disable Password in the Options menu.` D#X8> PrintPrint the circuitk' X D#XN>  Print PreviewPreview the printout< D#Xx> $Print Selected Print a portion of the circuit selectedMX i D#X> 2Print Selected PreviewPreview the circuit portion selected for printingv2 D#Xd> &Print Page SetupSet up the print page legendi%i HD#XJ>  Printer SetupSet up the printerz0 J#d`> " ExitExit PSIMs schematic program SIMCADwJHEA- (The password protection feature is useful if you let others to simulate the circuit you created, but do not wish to reveal the circuit schematic. For example, you create a model of a device and save it as a subcircuit. You can password protect this subcircuit file, and EAshare the model with others without releasing the details of the model.Warning: You must write down the password and keep it in a safe place. If you forget the password, you will no longer be able to view the schematic. It is strongly recommended that you make a backup copy of the file before protecting it.&kA# : EAA1 ALEdit menuh?kA B) "~Edit MenuThe Edit menu includes the following functions:t-ABG#^Z> Undo DeleteUndo the last delete actionE B CG#^> CutRemove the selected circuit block and save it to the buffero(B|CG#^P> CopyCopy a selected circuit blocks, CCG#^X> PastePaste the selected circuit blockl(|C[DD#XP> Select AllSelect the whole circuitkCEc#> *\^Copy to Clipboard - Color- Black & WhiteCopy the selected circuit schematic, in color, to the clipboardCopy the selected circuit schematic, in black and white, to the clipboard. The image in black and white is smaller than that in color in memory size.X[DFD#X(> TextPlace textYEwFD#X*> WireDraw a wireFlGE#Xa> LabelPlace a label. Labels provide another way of connecting two or more nodes together. If nodes are connected to labels having the same name, these nodes are connected.t0wFGD#X`> AttributesEdit the attribute of an elementx4lGXHD#Xh> DisableDisable an element or part of a circuitFGHD#X> EnableEnable the element or circuit that was disabled previouslyt0XHVID#X`> RotateRotate the selected element or blocky5HID#Xj> Flip L/RFlip left/right of the selected elementy5VIHJD#Xj> Flip T/BFlip top/bottom of the selected elementx4IJD#Xh> FindFind an element based on its type and namey5HJ9KD#Xj> Find NextFind the next element of the same typew*JKM#jT> (-W$Edit LibraryEdit the PSIM libraryz69K*LD#Xl> EscapeEscape from any of the above editing modesKL+ $OThe text of a label can be moved. To select the text, left click on the label, and press the Tab key. Then drag the mouse while keeping the left mouse pressed.B*L>M1 >M2Edit library menutL 1 0Edit LibraryThe PSIM library consists of two parts: the netlist library (psim.lib) and the image library (psimimage.lib). The netlist library defines the netlist format of each element, and the netlist is used by PSIM simulator for simulation. The netlist library can not be modified by users.On the other hand, the image library contains the image information of an element. Users can either modify the default PSIM image library, or create an image library from scratch. It is possible to have multiple image libraries. Any image libraries that are placed in the PSIM directory will be loaded into the Elements menu.>M L&>M2# : l1>lpView menuh?2Ԁ) "~View MenuThe View menu includes the following functions:|5lPG#^jY Status BarEnable or disable the status displayz3ԀʁG#^fY ToolbarEnable or disable the toolbar displaytPG#^Y &Element ToolbarEnable or disable the element toolbar. The element toolbar stores commonly used PSIM elements.^ʁ*G#^Y <Recently Used Element ListDrop-down list box that shows the most recently used elements\G#^*Y Zoom InZoom inZ*D#X,Y Zoom OutZoom outx4XD#XhY Fit to PageFit the whole circuit to the screenv2΄D#XdY &Zoom in SelectedZoom in to a selected regionv2XDD#XdY List ElementList the elements of the circuit,΄p'  @D1!Subcircuit menutKp$) "Subcircuit MenuThe Subcircuit menu includes the following functions:s,G#^X $New SubcircuitCreate a new subcircuit>$G#^| &Load SubcircuitLoad an existing circuit as a subcircuitHG#^ &Edit SubcircuitEdit the subcircuit file name and other attributesp,D#XX Set SizeSet the size of the subcircuitUG#^ Place PortPlace the interface port between the main circuit and the subcircuitFAD#X Display PortDisplay the connection ports of the subcircuit blockIF#Z :Edit Default Variable ListEdit the default list of the subcircuit variables. Note that the default variable list can be overwritten in the main circuit, and the default list of the subcircuit is not saved to the netlist and is not used for simulation. AYE#X Edit ImageEdit the subcircuit image. One can create and customize the image of the subcircuit. By default, the image is a rectangle.ED#X 4Display Subcircuit NameDisplay the name of the subcircuit block#YE#X .Show Subcircuit PortShow the names of the subcircuit ports in the main circuit. Once displayed, each port name can be moved to a different location. Click on the Delete key to disable the display of this port name.]D#X .Hide Subcircuit PortDisable the display of all the subcircuit ports in the main circuitz6 D#Xl $Subcircuit ListList the names of the subcircuits{7D#Xn One Page UpGo from a subcircuit to a higher levelt0 D#X` Top PageGo to the top level of the circuitTo: B5Note: The subcircuit menu is disabled in the PSIM demo version.Functions Set Size, Place Port, Display Port, Edit Variable List, and Edit Image are only enabled when tophe subcircuit schematic window is active (currently being edited).Creating a Subcircuit:The creation of a subcircuit includes two steps: creating the subcircuit block in the main circuit; and creating the actual subcircuit.In the main circuit: - In the main circuit, go to the Subcircuit menu. Choose New Subcircuit if the subcircuit does d6. *m not exist, or Load Subcircuit if the subcircuit already exists. - A subcircuit block (rectangle) will appear on the screen. Place the subcircuit block.In the subcircuit: - Double click on the subcircuit block to enter the subcircuit. Once inside the subcircuit window, create/edit the subcircuit in exactly the same way as in the main circuit. - Set the size of the subcircuit block. Choose Set Size in the Subcircuit menu to specify the subcircuit block size. Note that size of the subcircuit should be chosen such that it gives the U)o(, &S proper appearance and allows easy wire connection in the main circuit. - Once the subcircuit is complete, define ports to connect the subcircuit nodes with the corresponding nodes in the main circuit. Choose Place Port in the Subcircuit menu, and a port image will appear. After the port is placed in the circuit, a pop-up window will appear. The diamonds on the four sides represent the connection nodes and the positions of the subcircuit. They correspond to the connection nodes of the subcircuit block in the main<1 0 circuit. There are no diamonds at the four corners since connections to the corners are not permitted. When a diamond is selected, it is colored red. By default, the diamond at the top of the left side is selected and marked with red color. Click on the desired diamond to select and specify the port name. Repeat the same procedure to place all the ports. Note that the subcircuit size should be set before the ports are placed. If the subcircuit size?({) - is changed after ports are placed, port locations will be messed up and need to be restored. - Select Save As in the File menu to save the subcircuit to the desired name and location. Note that the subcircuit does not have to be in the same directory as the main circuit.Go back to the main circuit. Connection ports (hollow circles) will appear on the border of the subcircuit block. Connect the main circuit to the subcircuit ports. Note that these ports are the only connection points for the subcircuit block. <1 0Passing Values from the Main Circuit to the Subcircuit:Parameter values in the subcircuit do not have to be specified in the circuit. It can be specified in the main circuit instead. For example, the resistance of a resistor can be specified as R1, and R1 can be defined in the main circuit.- In the subcircuit, specify the parameter values as a variable. - In the main circuit, highlight the subcircuit block, and choose Edit Subcircuit in the SubcircuitD{2 2% menu. Click on the Subcircuit Variables, and click on Add to add the variable name and value. The variable name must be the same as the corresponding variable name in the subcircuit. Click on the check box next to the variable name to display the variable name and value.Changing the Location of an Existing Port:To change the location of an existing port, double click on the port. A pop-up window with diamonds will appear. Delete the port name, click on the desired location, and type the port name again.? 3 4Customizing the Subcircuit Image:The default image of the subcircuit block is a rectangle. To customize the image, follow these steps:- Inside the subcircuit, go to the Subcircuit menu and select Edit Image. A window will appear with diamonds on fopur sides. The ports are highlighted with red color. Click on the Zoom In or Zoom Out icons of the toolbar to enlarge or reduce the image if necessary.- Use to drawing toolbar to create the image. The toolbar includes: line, rectangle, oval, arc, text,&+ $ and Select function (with the arrow icon). To create square, press and hold the ctrl key, and click on the rectangle icon. To create circle, press and hold the ctrl key, and click on the circle icon. Select an image by click on the arrow icon, and then on the image. After the image is selected, it can be moved or deleted.- Go back to the subcircuit window, and save the subcircuit. Go back to the main circuit, and the subcircuit block image will be changed.65 8Adding Subcircuits to the Element List:To have a subcircuit appear in the PSIM Elements menu as an element item, create a directory called User Defined under the PSIM directory, and place the subcircuit file into this directory. The subcircuit will appear under Elements | User Defiled. You can also create subdirectories under User Defined and place subcircuits inside the subdirectories. For example, the Elements menu may look like this: - Power`&2 2 - Control - Other - Sources - Symbols - User Defined Subcircuit 1 Project A Subcircuit 2 Subcircuit 3 Project B Subcircuit 4With this feature, common-used subcircuits can be grouped together and easily managed and accessed.= 61~GElement menusHx+ &Element menuPSIM elements are stored in the following libraries: '$ @x2S#v8} (t "PowerPower library that stores power circuit elementsFS#v8} (㽃  "ControlControl library that stores control circuit elements2 T#vE8} (} "OtherOther library that stores switch controllers, voltage/current sensors, voltage/current probes, and other elements common to power/control circuitsDX S#v8} (Z "SourcesSource library that stores voltage/current sources`  J#d8}  SymbolsIt stores symbols for drawing purposes. These symbols are not for simulation use.X  Y#'8}  8 User DefinedAny schematic files in the PSIM\User Defined directory will appear as items in this menu. For example, if the directory contains a file called sub.sch, there will be an item called sub in the menu.One may, therefore, stores common-used subcircuits in the PSIM\User Defined directory and these subcircuits will appear as if they are one of the built-in elements in PSIM.)  & P &M hIB^8K{>HSClick on Motor Drive Module, Digital Control Module, and SimCoupler Module to see the list of elements in each module.The parameter value of an element can be specified directly in the parameter specification dialog window, or defined in the main circuit (if the element is in the subcircuit), or defined in a separate parameter file. For example, for the capacitance value of a capacitor, it can be defined as one of the following:& L# &M@/ ,@0.000151.5E-4 [or 1.5e-4]1.5D-4 [or 1.5d-4]150u150uF150uFarad30uF/2. [a mathematical LM@expression]C1C1+C2 [a mathematical expression]LB' IIn the case of C1 and C2, the capacitors are either in a subcircuit and the values of C1 and C2 are defined in the main circuit (and passed into the circuit), or C1 and C2 are defined in a user-defined external parameter file specified by the .FILE element (refer to .FILE for the use of the external parameter file). The power-of-ten suffix letters are allowed in PSIM. The following suffix letters are supported:<M@TB* $$@HG1.e+9M1.e+67BB( @Hk or K1.e+3Q#TBB. ,F@Hm1.e-3u1.e-6n1.e-9p1.e-12)BC& HBC& 'HA mathematical expression can contain brackets (such as SQRT(Vs)/(R1+R2)) and is not case sensitive. The following math functions are supported:(CC% H5 CD( @H+addition8CSD( PH-subtractionsGDD, (H*multiplication/division^to the power of [Example: 2^3 = 2*2*2]X.SDE* $\HSQRTsquare-root functionSINsine function>D\E( ,HCOScosine functionCEE' 8HTAN tangent functionJ#\EE' FHATAN inverse tangent function_8EHF' pHEXP exponential (base e) [Example: EXP(x) = e^x]E-G/ ,mHLOGlogarithmic function (base e) [Example: LOG(x) = ln(x)]LOG10logarithmic function (base 10)ABSabsolute functionSIGNsign function [Example: SIGN(1.2) = 1; SIGN(-1.2) = -1](HFUG% H)-G~G& HCUGG12GcMotor Drive ModuleX~GEH, (Motor Drive ModuleThe following is a list of elements in the Motor Drive Module.aGHJ#d.P   NameDescriptionfEH IJ#d8P (“ DC MachineDC machineWHIJ#dP (/ր@Squirrel-Cage Ind. Machine3-phase squirrel-cage induction machine (symmetrical)o IfJJ#dP (/րTSquirrel-Cage Ind. Machine (neutral)3-phase squirrel-cage induction machine (symmetrical, with neutral)bIKJ#dP (RSquirrel-Cage Ind. Machine (linear)3-phase squirrel-cage induction machine (general model)efJKJ#dP (XSquirrel-Cage Ind. Machine (nonlinear)3-phase squirrel-cage induction machine with saturationTK_LJ#dP (/ >Wound-Rotor Ind. Machine 3-phase wound-rotor induction machine (symmetrical)^KMJ#dP (pNWound-Rotor Ind. Machine (linear)3-phase wound-rotor induction machine (general model)a_LMJ#dP (pTWound-Rotor Ind. Machine (nonlinear)3-phase wound-rotor induction machine with saturationOMKNJ#dP ( 4Brushless DC Machine3-phase brushless dc machine (trapezoidal back emf)MOK#dP (tHPermanent Magnet Sync. Machine3-phase permanent-magnet synchronous machine (sinusoidal back emf, current-type interface)KN K#d P (tPPermanent Magnet Sync. Machine (V)3-phase permanent-magnet synchronous machine (sinusoidal back emf, voltage-type interface)O ~GuOˀJ#dP (NqT2Synchronous Machine3-phase conventional synchronous machine with external excitation (voltage-type interface)y J#dP (NqT:Synchronous Machine (I)3-phase conventional synchronous machine with external excitation (current-type interface)Rˀ*J#dP (p+SRM33-phase switched reluctance machine (6 stator teeth and 4 rotor teeth)8J#dpP ( >Mechanical Load (general)General mechanical loadI*?J#dP (R*qPMechanical Load (constant-torque) Constant-torque mechanical loadFσJ#dP (N*qLMechanical Load (constant-power)Constant-power mechanical loadF?_J#dP (dLMechanical Load (constant-speed)Constant-speed mechanical loadLσJ#dP (YJMechanical-Electrical InterfaceMechanical-electrical interface blockb_WJ#d0P (l$Gear BoxGear boxl"ÅJ#dDP (,&Torque SensorTorque sensorj W-J#d@P (P0$Speed Sensorspeed sensor'ÅT$ -c% Additional information, such as Voltage Rating, Current Rating, Power Rating, Speed Rating, Manufacturer, and Part No. can be stored for motors by clicking on the Other Info tab of the parameter specification window.GT1V Digital Control Module`c6, (Digital Control ModuleThe following is a list of elements in the Digital Control Module.aJ#d.J   NameDescriptionc6J#d2J ( ArrayVector array5yJ#djJ ( Array (1)Vector array (with data from a file)p&J#dLJ (Z6>*Circular BufferCircular buffern$yWJ#dHJ ("ConvolutionConvolution blockw-ΊJ#dZJ (㷒(DifferentiatorDiscrete differentiatorv,WDJ#dXJ (T20Quantization BlockQuantization blockn$ΊJ#dHJ ((Digital FilterDigital filterHDDJ#dJ (0Digital Filter (1)Digital filter (with coefficients from a file)n$J#dHJ (J7 FIR FilterFIR digital filterHDDJ#dJ (J7(FIR Filter (1)FIR digital filter (with coefficients from a file)o%J#dJJ (Զ IntegratorDiscrete integrator9D6J#drJ (㒟΀4Resetable IntegratorResetable discrete integratorn$J#dHJ (kJl"Memory ReadMemory read blockB60J#dJ (@z-domain Transfer Functionz-domain transfer function blockfJ#d8J (*bH Unit DelayUnit delayp&0J#dLJ (4*Zero-Order-HoldZero-order chold\nJ#d$J (NStackStack'$ nm% gNote: For a multi-rate system (where there are more than one sampling frequency), a zero-order-hold must be used between two blocks that have different sampling rates.-( &m# B1  SimCoupler Module}Q, (SimCoupler ModuleThe following are the elements in the SimCoupler Module.aJ#d.JR   NameDescriptionj JJ#d@JR (D$In Link NodeIn link nodel"J#dDJR (D&Out Link NodeOut link node'J$ '2 2  The SimCoupler Module, as an add-on option to the PSIM software, provides interface between PSIM and Matlab/Simulink for co-simulation. With the SimCoupler Module, part of a system can be implemented and simulated in PSIM, and the rest of the system in Simulink. One can therefore make full use of PSIMs capability in power simulation and Matlab/Simulinks capability in control simulation in a complementary way.The SimCoupler Module supports Matlab/Simulink Release 11, 12.0, 12.1, and 13.)-' Certain restriction is imposed on the selection of the solver type and the time step in Simulink when performing the PSIM-Matlab/Simulink co-simulation. Simulink must be set up to have the Solver Type as Fixed-step with the time step the same or close to the PSIM time step, or if the Solver Type is Variable-step, a zero-order-hold must be used with the sample time the same or close to PSIM time step.The SimCoupler consists of two parts: the link nodes in PSIM, and the SimCoupler model block in Simulink.)* "The use of the SimCoupler Module is easy and straightforward. An example of an one-quadrant chopper with current mode control is provided with the power circuit implemented in PSIM, and the control in Simulink. The file is chop1q_ifb_simulink_R11.mdl (the file was created in Matlab/Simulink Release 11) and chop1q_ifb_psim.sch.The following are the steps to set up SimCoupler for PSIM-Matlab/Simulink co-simulation for the one-quadrant example.In PSIM:y-9 @P:x-After the rest of the power circuit is created, connect one OUT SLINK node to the current sensor output and rename it as iL.-Connect one IN SLINK node to the positive input of the comparators, and rename it as Vm. -If there are more than one IN and OUT SLINK node, you need to arrange the order of the link nodes. Go to the Simulate menu, and select Arrange SLINK Nodes. A dialog window will appear. Arrange the order of the SLINK_IN nodes and SLINK_OUT nodes to be the same as how the input/output ports would appear in the SimCoupler model block in Simulink (the order of the ports is from the top to the bottom). V)f5 8P:x-Go to the Simulate menu, and select Generate Netlist File. A netlist file with the .cct extension will be generated and saved under the same directory as the schematic file. In this example, we assume that the netlist is located in the directory C:\PSIM6.0. The netlist file name and path will be C:\PSIM6.0\chop1q_ifb_psim.cct.(% x 7f& "H0In Simulink:*& H + $P:x-Start Matlab. Change the working directory to the PSIM directory. If PSIM is installed in the directory C:\PSIM6.0, change the directory to C:\PSIM6.0. Then launch Simulink and open the existing file or create a new file. -After the rest of the system is created, open the Simulink file SimCoupler_Block_R11.mdl (created in Matlab/Simulink Release 11) that stores the SimCoupler model block. Copy and paste the SimCoupler model block into the chopper example file. h-m; D[P:x-In the chopper example file, double click on the SimCoupler block, and enter the name and the location of the PSIM netlist name, and click on Apply. In this example, it will be C:\PSIM6.0\chop1q_ifb_psim.cct. The number of input and output ports for the SimCoupler model block will automatically match those defined in the PSIM netlist. In this case, there will be 1 input port and 1 output port. If the number of link nodes in the netlist is changed later, go to the Edit menu and choose Update Diagram. This will update the model block ports.p?1 0P:x -Go to the Simulation menu and select Simulation Parameters. Under Solver Options, set the Type to Fixed-step. Set the step size to be the same as or close to PSIMs time step. In this case, the time step is set to 2us. -The setup of the co-simulation is now complete. Go to Simulink and start the simulation.)m& x f@l& xPlease note that the SimCoupler file SimCoupler.dll is created in Matlab/Simulink Release 11. It is found that this file also works with higher releases of Matlab/Simulink. However, the speed is slightly slower. For this reason, we also compiled and provided this file for different Matlab/Simulink releases. They are stored in SimCoupler_Rxx.dll where xx is the release version number. For example, to use SimCoupler.dll compiled for Release 13, first delete SimCoupler.dll, then copy SimCoupler_R13.dll to another file, and rename that file to SimCoupler.dll.(% xlz & xAlso, when the SimCoupler model block is used in a feedback system in Simulink, the SimCoupler model block may be part of an algebraic loop. Some versions of Matlab/Simulink can not solve a system containing algebraic loops, while other can solve the system but with degraded performance. To break an algebraic loop, place a memory block at each output of the SimCoupler model block. The memory block introduces one integration time step delay. ) & x > z  1 }Simulate menutH U , (Simulate menuThe Simulate menu includes the following functions:9  P#pr8 (jHtd 0Simulation controlSpecify simulation parameters:U b J#dt8  Run PSIMRun PSIM simulator to simulate the circuit;  J#dv8  Run SIMVIEWRun the waveform display program SIMVIEW6b g J#dl8  2Generate Netlist FileGenerate the netlist filex.  J#d\8  *View Netlist FileView the netlist filefg  J#d8  .Arrange SLINK NodesArrange the order of the SLINK_IN and SLINK_OUT nodes for SimCoupler ModuleU .J#d8  4Define Runtime DisplayDefine the waveforms to be viewed while simulation runs) W% &.}# CW1 }-/ .|Simulation ControlSimulation control parameters are: x.J#d\8}  Time StepSimulation time step, in sec.z0-+@J#d`8}  Total TimeTo+@}tal simulation time, in sec.@K#d 8}  Print TimeTime from which simulation results are saved to the output file (default = 0). No output is saved before this time.5+@0BK#d8}  Print StepPrint step (default = 1). If the print step is set to 1, every data point will be saved to the output file. If it is 10, only one out of 10 data points will be saved. This helps to reduce the size of the output file.@6CK#dw8}  Load FlagFlag for the LOAD function (default = 0). If the flag is 1, the previous simulation values will be loaded from a file (with the .ssf extension) as the initial conditions.0B*DK#dS8}  Save FlagFlag for the SAVE function (default = 0). If the flag is 1, values at the end of the current simulation will be saved to a file with the .ssf extension.'6CQD$ *DMF$ With the SAVE and LOAD functions, the circuit voltages/currents and other quantities can be saved at the end of a simulation session, and loaded back as the initial conditions for the next simulation session. This provides the flexibility of running a long simulation in several shorter stages. Component values and simulation parameters, such as time step, can be changed from one simulation session to the other. The circuit topology, however, should remain the same.'QDtF$ MFH$ In PSIM, the simulation time step is fixed throughout the simulation. In order to ensure accurate simulation results, the time step must be chosen properly. Factors that limit the time step include the switching period, widths of the pulses/waveforms, and intervals of transients. It is recommended that the time step be at least one magnitude smaller than the smallest of the above.'tFAH$ ^HI$ In Version 6.0, an interpolation technique is implemented which will calculate the exact switching instants. With this technique, the error due to the misalignment of the switching instants and the discrete simulation points is significantly reduced. It is possible to simulate with a large time step which still maintaining very accurate results.'AHI$ R'I \16P_C_INTERFACEwn* $Power/Control Circuint Representation and Interface in PSIMA system is represented in PSIM in the following way:0, ( " n3 4Based on this representation, a sensor must be used to bring a power circuit quantity (it could be voltage, current, torque, or speed) into the control circuit. Similarly, a switch controller or an interface block must be used to bring a control circuit quantity into the power circuit. Circuits should be built based on this convention.The power circuit and the control circuit are solved separately, and there is one time step delay between these two solutions.]3* $fThe following are the power circuit elements:( ]@- All the elements under the Elements/Power menu;- All the elements under the Elements/Other/Probes menu;- All the elements under the Elements/Sources menu_5<* $jThe following are the control circuit elements:9) @- All the elements under the Elements/Control menu;- Independent voltage sources under the Elements/Sources/Voltage menu, including VDC, VDC_GND, VSIN, VSIN3, VTRI, VSQU, VSTEP, VGNL, and VRAND.uK<* $The following elements are common to both power and control circuits:9) U@- ABC-DQ0 transformation blocks;- External DLL blocks;- Voltage probe VP in Elements/Other/Probes;- Time element Time under the Elements/Sources menu;T+) "VThe following are the sensor elements:gB<% @- All the elements under the Elements/Other/Sensors menu.mC* $The following are the switch controllers and interface block:<g' /@- All the elements under the Elements/Other/Switch Controllers menu.- Control-power interface block CTOP under the Elements/Other menu.S6 :;Based on this definition:- All the RLC branches, switches, transformers, electric machines, and mechanical loads are power elements.- All the current sources, controlled voltage/current sources, and nonlinear sources (such as VNONM) are power elements.- Switch gating blocks (GATING) is a power element. Note that the gating block can be connected to the gate node of a switch ONLY. It can not be connected to any other elements.- All the function blocks (such as MULT, SIN, etc.), s-domain and z-domain transfer functionOg 5 85 blocks and elements, and logic elements are control elements.- Op. amp. is an exception. Op. amp. is a subcircuit which is modeled using voltage- controlled voltage source, resistor, diodes, and dc voltage sources. Based on above definition, it is a power element. However, op. amp. is a control element in the conventional sense. That is why op. amp. is placed under the Elements/Control menu rather than under Elements/Power.- The gate node of a controlled switch (such as MOSFET, IGBT) can be connected to a#8, & switch gating block GATING or the output of a switch controller ONLY. It can not be connected to any other elements.In order to make the power-control interface easier and more transparent to users, PSIM does allow a power circuit node to be connected DIRECTLY to the input node of a control element. In this case, a voltage sensor is inserted automatically by the program.However, PSIM does NOT allow the output node of a control element to be connected directly to a power element. The user would have to connect a CTOP (control-power interface block) from the control node to the power node. (Exception: DIRECT connection of the control element output to a RLC branch is allowed. In this case, a CTOP 8is inserted automatically by the program.) ' aWe do not automatically insert CTOP for all other elements because doing so might result in indiscriminate use of the power and control elements in mixture (such as the case where an op. amp. is followed by a comparator or a control element, which is followed by another op. amp., and another comparator). In this case, the delay in the solution is more than one time step, and this could cause problems in certain situations.'86$ > t1P t ERROR_WARNINGJ67 <'Error/Warning MessagesError/warning messages are listed as below:* Error Message: The node of an element is floating-------------------------------------------------------------------- Reason: This can be caused by a poor connection or a floating input node of an element in PSIM. When drawing a wire between two nodes, make sure that the wire is connected to the terminal of the element. Solution: Search for the element, and re-do the connection. For example, if the error messageJt3 4/ is: Error: The RLC branch R1 is floating! Go to Edit menu in PSIM and select Find. Specify Type of Element as R, and Name including wide card as R1, then click on the Find button to find the element.* Error Message: No. of an element exceeds the limit.---------------------------------------------------------------------- Reason: The total no. of elements exceeds the limit specified by the program. NV 2 29 Solution: This problem can only be solved by upgrading to an more advanced version or by re-compiling the PSIM simulator (by Powersim). Please contact Powersim for assistance. * Warning!!! The program failed to converge after 10 iterations when determining switch positions.------------------------------------------------------------------------------------------------------------------- Reason: This warning occurs when, in rare occasions, the program failed to converge. ) _ when determining switch positions. Since the computation continues based on the switch positions at the end of the 10th iterations, results could be inaccurate. One should be cautious when analyzing the results. Solution: The following measures can be taken to isolate and solve the problem: - Check the circuit and make sure the circuit is correct. V  ) - Check the switch gating signals.- Connect R-C snubber branches across active switches and diodes.- Connect small resistors/inductors in series with switches.- Vary simulation time step.?. W ( . /  ) " = W  1 BFFT_ANALYSISt e. *FFT AnalysisWhen using FFT for the harmonic analysis, one should make sure that the following requirements are satisfied: - The waveforms have reached the steady state. - The length of the data selected for FFT should be the multiple integer of the fundamental period.For a 60-Hz waveform, for example, the data length should be restricted to 16.67 ms (or multiples of 16.67 ms). This can be done by clicking on X Axis in SIMVIEW, de-selecting Auto-scale in Range, and specifying the starting time and the final time. The FFT analysis is only performed on the data that are displayed on the screen., B{ Āc Note that the FFT results are eB discrete. The FFT results are determined by the time interval between two consecutive data points, t, and the data length Tlength. The data point interval t is equal to the simulation time step multiplied by the print step. In the FFT results, the frequency incremental step will be 1/ Tlength, and the maximum frequency will be 1/(2*t).For example, if you take the FFT of a 1-kHz square waveform with a data length of 1ms and a data point interval of 10s, that is, Tlength = 1 ms, and t = 10 s, the frequency incremental step will be: f = 1 / Tlength = 1 kHz. The maximum frequency will be: fmax = 1/(2*t) = 50 kHz. 0eB) "> B C1  CFPower Library5B@C$ "Power LibraryG CC' @The power library contains: &@CC# NCIDN#l8# (|$RLC BranchesResistors, inductors, capacitors, and coupled inductors.ECDN#l8# (Z=ZSwitchesDiode, thyristors, transistors, and switch modules.;IDeEN#lv8# (z9$TransformersSingle-phase and 3-phase transformersq#DEN#lF8# ( OtherOther power elementsfeEFM#j8# (IB^0Motor Drive ModuleMotor Drive Module. It includes various machine and mechanical load models.&EF# )FF% = FG1E G!RLC Branches4FIG$  RLC BrancheskGGP#p68, (" ResistorResistor kIGHP#p68, ( InductorInductor mGHP#p:8, ( CapacitorCapacitor p#HHM#jF8, (RLResistor-inductor branchq$HmIM#jH8, (RCResistor-capacitor branchq$HIM#jH8, (LCInductor-capacitor branch{.mIYJM#j\8, (YRLCResistor-inductor-capacitor brancho"IJM#jD8, (R33-phase resistor branchy,YJAKM#jX8, (IRL33-phase resistor-inductor branchz-JKM#jZ8, (RC33-phase resistor-capacitor branch7AK?LM#jn8, ( *RLC33-phase resistor-inductor-capacitor branchfKLM#j28, (`ppـRheostatRheostatz-?LMM#jZ8, (p0Saturable InductorSaturable inductorBLMM#j8, (?$4Coupled Inductor (2)Coupled inductor branch (2 inductors)BM=NM#j8, (?$4Coupled Inductor (3)Coupled inductor branch (3 inductors)BMNM#j8, (?$4Coupled Inductor (4)Coupled inductor branch (4 inductors)K=NdOM#j8, (QJ%<Nonlinear Element v=f(i)Resistance-type nonlinear element [v=f(i)]eN"M#j8, (QJ%@Nonlinear Element v=f(i,x)Resistance-type nonlinear element with additiodO"Fnal input [v=f(i,x)]LdOM#j8, (DJ%<Nonlinear Element i=f(v)Conductance-type nonlinear element [i=f(v)]f"nM#j8, (DJ%@Nonlinear Element i=f(v,x)Conductance-type nonlinear element with additional input [i=f(v,x)](% @en!& Additional information can be stored for the RLC elements by clicking on the Other Info tab of the parameter specification window. For example, Power Rating can be specified for resistors, Voltage Rating for capacitors, Core Type and Wire Type for inductors. For all these elements, Manufacturer and Part No. information can be specified.Ef1SftOther Power Elements<!$ 0Other Power Elementsd=f' zThe other elements that belong to the power library are: &,# u%P#pJ8# (7 OP_AMPOperational amplifier?,0P#p~8# (7 OP_AMP_1Operational amplifier with floating reference?P#p~8# (7 OP_AMP_2Operational amplifier with floating referencef0%M#j28# ( Adv/dtdv/dt block&K# )%t% 9K1'Resistor4t$  Description:bCJ#d0J=  ResistorResistor(k% @1C# Parameters:n$k J#dHJ=  ResistanceResistance, in OhmAKE#XJ= Current FlagFlag for branch current output. If the flag is zero, there is no current output. If the flag is 1, the current will be saved to the output file for display. The current is positive when it flows into the dotted terminal of the branch.( s% @(K$ 9sԉ1ԉmInductor4$  Description:bԉjJ#d0J=  InductorInductor(% @1jÊ# Parameters:l"/J#dDJ=  InductanceInductance, in Hw3ÊD#XfJ= $Initial CurrentInitial inductor current, in A[/ED#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)(m$ CE1Saturable Inductor4m$  Description:v,ZJ#dXJ=  ,Saturable InductorSaturable Inductor(% @1Z# Parameters:liJ#dJ=  6Current v.s. InductanceCharacteristics of the current versus the inductance (i1, L1), (i2, L2), etc.[D#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)ri) A saturable inductor takes into account the saturation effect of the inductor magnetic core.A nonlinear B-H curve is represented by piecewise linear approximation. Since the flux density B is proportionaml to the flux linkage and the magnetizing force H is proportional to the current i, the B-H curve can be represented by curve of flux linkage v.s. current instead.The inductance is defined as: L = flux_linkage / current, which is the slope of the flux linkage v.s. current curve at different points. The saturation characteristics can then be expressed by pairs of data points as: (i1, L1), (i2, L2), (i3, L3), etc.: 1 Capacitor4$  Description:dJ#d4J=  CapacitorCapacitor(% @1# Parameters:n$HJ#dHJ=  CapacitanceCapacitance, in F}9D#XrJ= .Initial Cap. VoltageInitial capacitor voltage, in V[HdD#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output),'  @(d$ B1KResistor-Inductor4.$  Description:l"J#dDJ=   RLResistor-inductor branch(.% @1# Parameters:f"YD#XDJ= ResistanceResistance, in Ohml"J#dDJ=  InductanceInductance, in Hw3Y<D#XfJ= $Initial CurrentInitial inductor current, in A[D#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)(<$ CF1MFPResistor-Capacitor4z$  Description:m#FJ#dFJ=   RCResistor-capacitor branch(z% @1@# Parameters:f"D#XDJ= ResistanceResistance, in Ohmf"@ D#XDJ= CapacitanceCapacitance, in F}9D#XrJ= .Initial Cap. VoltageInitial capacitor voltage, in V[ (D#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)(P$ C(1Inductor-Capacitor4P$  Description:m#4J#dFJ=   LCInductor-capacitor branch(\% @14# Parameters:l"\J#dDJ=  InductanceInductance, in Hf"_D#XDJ= CapacitanceCapacitance, in Fw3D#XfJ= $Initial CurrentInitial inductor current, in A}9_SD#XrJ= .Initial Cap. VoltageInitial capacitor voltage, in V[D#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)&S# Ld1EdeResistor-Inductor-Capacitor4$  Description:w-dJ#dZJ=  RLCResistor-inductor-capacitor branch(C% @1t# Parameters:f"CD#XDJ= ResistanceResistance, in Ohml"tFJ#dDJ=  InductanceInductance, in Hf"D#XDJ= CapacitanceCapacitance, in Fw3F#D#XfJ= $Initial CurrentInitial inductor current, in A}9D#XrJ= .Initial Cap. VoltageInitial capacitor voltage, in V[#?D#XJ= Current FlagFlag for branch current output (1: current output; 0: no current output)&e# 9?1'Resistor4e$  Description:k!=J#dBJ=   R33-phase resistor branch(e% @1=# Parameters:x.eJ#d\J=  ResistanceResistance per phase, in Ohm]D#XJ= "Current Flag_ACurrent flag for Phase A branch (1: current output; 0: no current output)w3&D#XfJ= "Current Flag_BCurrent flag for Phase B branch5J#djJ=  $Current Flag_CCurrent flag for Phase C branch\&'& The phase with a dot is Phase A.The resistances of the three-phase branches are equal.Bi1}i Resistor-Inductor4'$  Description:u+iJ#dVJ=  RL33-phase resistor-inductor branch(:% @1k# Parameters:x.:J#d\J=  ResistanceResistance per phase, in Ohmv,kY J#dXJ=  InductanceInductance per phase, in H] D#XJ= "Current Flag_ACurrent flag for Phase A branch (1: current output; 0: no current output)w3Y q D#XfJ= "Current Flag_BCurrent flag for Phase B branch5  J#djJ=  $Current Flag_CCurrent flag for Phase C branchq  ( The phase with a dot is Phase A.The resistances and inductances of the three-phase branches are equal. The initial currents are zero.C  1 4@Resistor-Capacitor4  $  Description:v,  J#dXJ=  RC33-phase resistor-capacitor branch(  % @1  # Parameters:x. b J#d\J=  ResistanceResistance per phase, in Ohmp,  D#XXJ= CapacitanceCapacitance per phase, in F]b sD#XJ= "Current Flag_ACurrent flag for Phase A branch (1: current output; 0: no current output)w3 D#XfJ= "Current Flag_BCurrent flag for Phase B branch5siJ#djJ=  $Current Flag_CCurrent flag for Phase C branch4@( /The phase with a dot is Phase A.The resistances and Capacitances of the three-phase branches are equal. Thi4@ e initial capacitor voltages are zero.Li@1I!@}EResistor-Inductor-Capacitor44@@$  Description:6@4AJ#dlJ=  RLC33-phase resistor-inductor-capacitor branch(@\A% @14AA# Parameters:x.\ABJ#d\J=  ResistanceResistance per phase, in Ohmv,A{BJ#dXJ=  InductanceInductance per phase, in Hp,BBD#XXJ= CapacitanceCapacitance per phase, in F]{BCD#XJ= "Current Flag_ACurrent flag for Phase A branch (1: current output; 0: no current output)w3BDD#XfJ= "Current Flag_BCurrent flag for Phase B branch5CDJ#djJ=  $Current Flag_CCurrent flag for Phase C branch*DD' PD}E& WThe phase with a dot is Phase A.The resistances and capacitances of the three-phase branches are equal. The initial inductor currents and capacitor voltages are zero.9DE1"E-IRHEOSTAT4}EE$  Description:bELFJ#d0J=  RheostatRheostat(EtF% @, LFF# Image:2tFF. , @"1FG# Parameters:IFG\#J=  @(   Total ResistanceTotal resistance R from Node k to m, in OhmfGvHh#J=  X2     Tap Position (0 to 1)The tap position Tap. The resistance from Node k to t is R*Tap.@GIM#jJ=  "  Current FlagFlag for the current that flows into Node k*vH-I' PBIoI1!#oItCoupled Inductors4-II$  Description:=oI*JJ#dzJ=  0Coupled Inductor (2)Coupled inductors with 2 branches(IRJ% @, *J~J# Image:2RJJ. , @"1~JJ# Parameters:5JfKP#pjJ= (  L11 (self)Self inductance of Branch 1, in HDJKP#pJ= ( $L12 (mutual)Mutual inductance between Branch 1 and 2, in H5fKLP#pjJ= (  L22 (self)Self inductance of Branch 2, in H3KLM#jfJ= " i1initialInitial current of Branch 1, in A3LMM#jfJ= " i2initialInitial current of Branch 2, in At'LMM#jNJ= " Iflag1Current flag of Branch 1t'MgNM#jNJ= " Iflag2Current flag of Branch 23M L fg    The branch labeled with circle is Branch 1, and the other branch labeled with square is Branch 2. Let V1 and V2 be the voltages across Branch 1 and 2, and i1 and i2 are the currents flowing into Branch 1 and 2, respectively, the voltage and current equations of the coupled inductors are:gN -I>gNJ8 @@""* t%  BJ10 $Coupled Inductors4t$  Description:=qJ#dzJ=  0Coupled Inductor (3)Coupled inductors with 3 branches(% @, qŁ# Image:2. , @"1Ł(# Parameters:5P#pjJ= (  L11 (self)Self inductance of Branch 1, in HD(AP#pJ= ( $L12 (mutual)Mutual inductance between Branch 1 and 2, in H5ƃP#pjJ= (  L22 (self)Self inductance of Branch 2, in HDAZP#pJ= ( $L13 (mutual)Mutual inductance between Branch 1 and 3, in HDƃP#pJ= ( $L23 (mutual)Mutual inductance between Branch 2 and 3, in H5ZsP#pjJ= (  L33 (self)Self inductance of Branch 3, in H3M#jfJ= " i1initialInitial current of Branch 1, in A3ssM#jfJ= " I2initialInitial current of Branch 2, in A3M#jfJ= " I3initialInitial current of Branch 3, in At'sgM#jNJ= " Iflag1Current flag of Branch 1t'ۇM#jNJ= " Iflag2Current flag of Branch 2t'gOM#jNJ= " Iflag3Current flag of Branch 3(ۇw% @\O0]       The branch labeled with circle is Branch 1, the one with square is Branch 2, and the one with triangle is Branch 3. Let V1, V2, and V3 be the voltages across Branch 1, 2, and 3, and i1, i2, and i3 are the currents flowing into Branch 1, 2, and 3, respectively, the voltage and current equations of the coupled inductors are:JwzB T@"""*0& Bz1 %Coupled Inductors4$  Description:=J#dzJ=  0Coupled Inductor (4)Coupled inductors with 4 branches(ɋ% @, # Image:2ɋ'. , @" 1X# Parameters:5'݌P#pjJ= (  L11 (self)Self inductance of Branch 1, in HDXqP#pJ= ( $L12 (mutual)Mutual inductance between Branch 1 and 2, in H5݌P#pjJ= (  L22 (self)Self inductance of Branch 2, in HDqP#pJ= ( $L13 (mutual)Mutual inductance between Branch 1 and 3, in HDP#pJ= ( $L23 (mutual)Mutual inductance between Branch 2 and 3, in H5P#pjJ= (  L33 (self)Self inductance of Branch 3, in HDCP#pJ= ( $L14 (mutuaCl)Mutual inductance between Branch 1 and 4, in HDP#pJ= ( $L24 (mutual)Mutual inductance between Branch 2 and 4, in HDCkP#pJ= ( $L34 (mutual)Mutual inductance between Branch 3 and 4, in H5P#pjJ= (  L44 (self)Self inductance of Branch 4, in H(k% @o         The branch labeled with circle is Branch 1, the one with square is Branch 2, the one with triangle is Branch 3, and the one with plus is Branch 4. Let V1, V2, V3, and V4 be the voltages across Branch 1, 2, 3, and 4, and i1, i2, i3, and i4 are the currents flowing into Branch 1, 2, 3, and 4, respectively, the voltage and current equations of the coupled inductors are:V lL h@" " " " ,&  5l1W&NONV4$  Description:JJ#dJ  8Nonlinear Element v=f(i)Resistance-type nonlinear element [v=f(i)]b;D#XJ :Nonlinear Element v=f(i,x)Resistance-type nonlinear element with additional input [v=f(i,x)](c% @1;# Parameters:crZ# J= ( .>Expression f(i) or f(i,x)Expression v = f(i) for Nonlinear Element v=f(i) and v = f(i,x) for Nonlinear Element v=f(i,x)]J#dJ=  (Expression df/diThe derivative of the voltage v versus the current i, i.e. df(i)/di|8rD#XpJ= &Initial Value ioThe initial value of the current iz6D#XlJ= &Lower Limit of iThe lower limit of the current i8J#dpJ=  (Upper Limit of iThe upper limit of the current i*' P4 * "Unlike linear resistors, inductors, or capacitors, the voltage-current relationship of these elements are nonlinear.The additional input x must be a voltage signal. The correct initial value and lower/upper limits will help the convergence of the solution. 5$15 '$NONI4X$  Description:J$J#dJ  8Nonlinear Element i=f(v)Resistance-type nonlinear element [i=f(v)]bXD#XJ :Nonlinear Element i=f(v,x)Resistance-type nonlinear element with additional input [i=f(v,x)](% @1# Parameters:Z# J= ( .>Expression f(v) or f(v,x)Expression i = f(v) for Nonlinear Element i=f(v) and i = f(v,x) for Nonlinear Element i=f(v,x)YlJ#dJ=  (Expression df/dvThe derivative of the current versus the voltage, i.e. df(v)/dv|8D#XpJ= &Initial Value voThe initial value of the current vz6lbD#XlJ= &Lower Limit of vThe lower limit of the current v8 J#dpJ=  (Upper Limit of vThe upper limit of the current vb *b6' P 85 8 Unlike linear resistors, inductors, or capacitors, the voltage-current relationship of these elements are nonlinear.The additional input x must be a voltage signal. The correct initial value and lower/upper limits will help the convergence of the solution. Examples: Nonlinear DiodeThe nonlinear element above can be used to model a nonlinear diode. The diode current can be expressed as a function of the voltage as: i = 10^-14 * (e ^ 40*v - 1). gB6% In PSIM, the specifications of the nonlinear element will be:8^6 :@HExpression f(v)1e-14*(EXP(40*v)-1)Expression df/dv40e-14*EXP(40*v)Initial Value vo0Lower Limit of v-1e3Upper Limit of v1(% H9^1(GSwitches4 ( SwitchesQs/ .The following switches and switch modules are provided in PSIM. SwitcheseP#p*8> (㇍2 DiodeDiode cs;P#p&8> ( DIACDIAC jP#p48> (pW ZenerZener diodel;P#p88> (5 ThyristorThyristorduP#p(8> ( TRIACTRIACLM#j8> (H8MOSFETMetal-Oxide-Semiconductor Field Effect Transistor (n channel)x+uM#jV8> (Wn/0MOSFET (p channel)p-channel MOSFET{.M#j\8> (IGBTInsulated Gate Bipolar Transistor6M#jl8> (,(npn Transistornpn bipolar junction transistor6 M#jl8> (J(pnp Transistorpnp bipolar junction transistorI M#j8> (D0npn Transistor (1)npn bipolar junction transistor (linear model)I 3 M#j8> (㪤0pnp Transistor (1)pnp bipolar junction transistor (linear model)p#  M#jF8> (JGTOGate-Turn-Off thyristorx+3  M#jV8> (y+6Bi-directional SwitchSimple switch( C % @8 { & $Switch Modules4C  P#ph8> (2 .1-ph Diode BridgeSingle-phase diode bridge<{  P#px8> (Za 61-ph Thyristor BridgeSingle-phase thyristor bridge/  P#p^8> (2 .3-ph Diode Bridge3-phase diode bridge6  M#jl8> (\a63-ph Thyristor Bridge3-phase thyristor bridgeG !M#j8> (/&VSI3 (MOSFET)3-phase PWM voltage source inverter (with MOSFET)C M#j8> (/"VSI3 (IGBT)3-phase PWM voltage source inverter (with IGBT)}0!.M#j`8> ( CSI33-phase PWM current source inverterFM#j8> (Z-@3-ph Thyristor Half-bridge3-pulse thyristor half-wave bridgeF.`@M#j8> ( [-`@@6-ph Thyristor Half-bridge6-phase thyristor half-wave bridgeH@- *6Switch Gating Block U`@MAP#p8> (),̀ $Gating BlockSwitch gating block. It is used for switch gating specificationP@AP#p8> (),̀ ,Gating Block (1)Switch gating block. Gating data are read from a file. MAC: BAdditional information, such as Voltage Rating, Current Rating, Manufacturer, and Part No. can be stored for switches by clicking on the Other Info tab of the parameter specification window.Modeling of a SwitchSwitch models are ideal, that is, both turn-on and turn-off transients are neglected. A switch has an on-resistance of 10 uOhm and an off-resistance of 10 MOhm. Switch snubber circuits are optional.Control of a Switch/Switch ModuleA F\ q),̀"cHQ } There are two ways to specify the gating of a switch/switch module. One is to use a switch gating block (GATING). Another is to use a switch controller (ONCTRL or ACTRL or PATTCTRL). Both the switch gating block and the controller should be connected to the gate (base) node of the switch, or the control node of a switch module.Note: The gate node of a controlled switch (such as MOSFET, IGBT) must be connected to aqCG- (  switch gating block GATING or the output of a switch controller ONLY. It can not be connected to any other elements.For switch modules, only the gatings of the first switch in the module need to be specified. The gatings of all other switches will be automatically derived. The upper left switch of the module is defined as the first switch.6 FG1)G.KDiode4GH$  Description:\GqHJ#d$J=  DiodeDiode(HH% @1qHH# Parameters:;HIID#XvJ= *Diode Voltage DropDiode conduction voltage drop, in VLHIJ#dJ=  (Initial PositionFlag for initial diode position (0: open; 1: closed)JIIsJJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(IJ% @nsJ.K% The diode conduction voltage drop is usually around 0.6 to 0.7 V. It may be higher for high power diodes.5JcK1*cKNDIAC4.KK$  Description:ZcKKJ#d J=  DIACDIAC(KL% @1KJL# Parameters:WLLD#XJ= (Breakover VoltageBlocking voltage beyond which the device starts to conduct, in V6JLeMJ#dlJ=  *Breakback VoltageConduction voltage drop, in VJLMJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(eM!N% @MN& 9A DIAC is a bi-directional diode. It does not conduct until the breakover voltage is reached. At that point, the device goes into avalanche conduction.< !NO1+OZener Diode4NSO$  Description:cOOJ#d2J=  ZenerZener diode (SOO% @1O# ONParameters:COJ#dJ=  *Breakdown VoltageBreakdown voltage of the zener diode, in V(Ѐ% @i!9H ^C    The zener model is ideal. When the zener is positively biased, it behaviors as a regular diode. When it is reverse biased, if the cathode-anode voltage VKA is less than the breakdown voltage VB, it will block the conduction. Otherwise, the voltage VKA will be clamped to VB.(Ѐa% @&9# : a1,]Thyristor4$  Description:dYJ#d4J=  ThyristorThyristor(% @1Y# Parameters:}9/D#XrJ= Voltage DropThyristor conduction voltage drop, in V{D#XJ= $Holding CurrentMinimum conduction current, in A, below which the device stops conducting and return to the OFF state./E#XJ= &Latching CurrentMinimum ON state current, in A, required to keep the device in the ON state after the triggering pulse is removed.LQJ#dJ=  (Initial PositionFlag for initial diode position (0: open; 1: closed)JJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(Q % @P]6 :5 A thyristor is controlled at turn-on. The turn-off is determined by the circuit conditions.Note: The gate node of the thyristor can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.6 1-/TRIAC4]Lj$  Description:\#J#d$J=  TRIACTRIAC(LjK% @1#|# Parameters:s/KD#X^J= Voltage DropConduction voltage drop, in VJ|J#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(% @N/6 : A TRIAC is a device that conducts current in both directions. It behaviors in the same way as two thyristors in parallel in the opposite direction.Note: The gate node of the TRIAC can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.5d1.dIGBT4/$  Description:adJ#d.J=  IGBTIGBT switch(!% @1R# Parameters:K!D#XJ= *Saturation VoltageConduction voltage drop when the switch is on, in VPRuD#XJ= *Diode Voltage DropConduction voltage drop of the anti-parallel diode, in VQJ#dJ=  (Initial PositionFlag for initial transistor position (0: open; 1: closed)euJ#dJ=   Current FlagFlag for current output of the whole switch module (0: no output; 1: with output)( % @ /$ An IGBT consists of a transistor in anti-parallel with a diode. It is turned on when the gating is high and the switch is positively biased. It is turned off when the gating is low or the current drops to zero.( -%  iq# The current that is displayed is the current through the whole switch module (the transistor plus the diode). (-%  i1 0o Note: The gate node of the IGBT can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.71e/6MOSFET4<$  Description:o%J#dJJ=  MOSFETn-channel MOSFET switch(<% @1# Parameters:RD#XJO  On ResistanceResistance of the MOSFET transistor during the on state, in OhmP.D#XJO *Diode Voltage DropConduction voltage drop of the anti-parallel diode, in VQJ#dJO  (Initial PositionFlag for initial transistor position (0: open; 1: closed)e.xJ#dJO   Current FlagFlag for current output of the whole switch module (0: no output; 1: with output)(% @x$ An n-channel MOSFET consists of a transistor in anti-parallel with a diode. It is turned on when the gating is high and the drain-to-source is positively biased. It is turned off when the gating is low or the current drops to zero.(%  i`*66 :U The current that is displayed is the current through the whole switch module (the transistor plus the diode). Note: The gate node of the MOSFET can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.9o1r0oMOSFET_P46$  Description:{1oJ#dbJ5  ,MOSFET (p channel)p-channel MOSFET switch(F% @1w# Parameters:RF D#XJO  On ResistanceResistance of the MOSFET transistor during the on state, in OhmPwD#XJO *Diode Voltage DropConduction voltage drop of the anti-parallel diode, in VQ <J#dJO  (Initial PositionFlag for initial transistor position (0: open; 1: closed)eJ#dJO   Current FlagFlag for current output of the whole switch module (0: no output; 1: with output)(<% @  $ A p-channel MOSFET consists of a transistor in anti-parallel with a diode. It is turned on when the gating is low and the drain-to-source is negatively biased. It is turned off when the gating is high or the current drops to zero.(H%  i`* 6 :U The current that is displayed is the current through the whole switch module (the transistor plus the diode). Note: The gate node of the MOSFET can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.4H11GTO4$  Description:o%J#dJJ=  GTOGate-Turn-Off (GTO) switch(% @1# Parameters:s/WD#X^J= Voltage DropConduction voltage drop, in VMJ#dJ=  (Initial PositionFlag for initial switch position (0: open; 1: closed)JWJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(% @6 :] GTO switches are symmetrical devices with both forward-blocking and reverse-blocking capabilities. It is turned on when the gating is high and the switch is positively biased. It is turned off when the gating is low or the current drops to zero.Note: The gate node of the GTO can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.412k NPN4$  Description:5uJ#djJ=  $npn Transistornpn bipolar junction transistor(% @1u# Parameters:RdD#XJ= *Saturation VoltageSaturation voltage between the collector and emitter, in VMJ#dJ=  (Initial PositionFlag for initial switch position (0: open; 1: closed)JdJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(% @- , & An npn transistor is turned on when the gating is high (voltage at the base node is logic 1) and the switch is positively biased (collector-emitter voltage is positive). It is turned off when the gating is low (logic 0) or the current drops to zero. This is different from the real npn device which is controlled by the base current. Also, contrary to the real device behavior, the npn model in PSIM can block reverse voltage.Note: The gate node of the npn switch can be connected to a switch gating block \k + &  or a switch controller ONLY. It can not be connected to any other elements.4  13 N@PNP4k  $  Description:5 R J#djJ=  $pnp Transistorpnp bipolar junction transistor( z % @1R  # Parameters:Nz = D#XJ= *Saturation VoltageSaturation voltage between emitter and collector, in VM  J#dJ=  (Initial PositionFlag for initial switch position (0: open; 1: closed)J= h J#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(  % @+h , & A pnp transistor is turned on when the gating is low (voltage at the base node is logic 0) and the switch is negatively biased (collector-emitter voltage is negative). It is turned on when the gating is high (logic 1) or the current drops to zero. This is different from the real pnp device which is controlled by the base current. Also, contrary to the real device behavior, the pnp model in PSIM can block reverse voltage.Note: The gate node of the pnp switch can be connected to a switch gating block \ N@+ &  or a switch conN@k troller ONLY. It can not be connected to any other elements.> @14@DSimple Switch4N@@$  Description:9@CAJ#drJ=  2Bi-directional SwitchSimple bi-directional switch(@kA% @1CAA# Parameters:MkA3BJ#dJ=  (Initial PositionFlag for initial switch position (0: open; 1: closed)JABJ#dJ=   Current FlagFlag for current output (0: no output; 1: with output)(3BB% @lBD4 6 A simple switch conducts current in both directions. It is on when the gating is high, and is off when the gating is low, regardless of the voltage bias conditions of the switch.Note: The gate node of the switch can be connected to a switch gating block or the output of a switch controller ONLY. It can not be connected to any other elements.*BD& @(DD$ 6DE1 5ENPN_14DKE$  Description:HEEJ#dJ=  ,npn Transistor (1)npn bipolar junction transistor (linear model)(KEF% @1E6F# Parameters:7FFJ#dnJ=  *Current Gain betaCurrent gain of the transistorL6FSGP#pJ= ( *Bias Voltage VrBase-emitter forward bias voltage (default = 0.7 V)HFGU#zJ= .H  HVce,satCollector-emitter saturation voltage (default = 0.2 V)*SGH' @HwGH7 >H  The current gain beta is defined as the ratio of the collector current Ic versus the base current Ib, that is:@HI. ,&H" (H0I% HI0J& HUnlike the ideal switch model which will operate in either the off state (cut-off state) or the on state (saturation state), the npn BJT linear model can operate in all three states: cut-off, linear, and saturation.(0IXJ% HQ,0JJ% XHThe properties of these three states are:(XJJ% H9J K& &H- Cut-off state:)J3K& H5 KhK1 2 P H")3KK& H8hKK& $H- Linear state:(KK% H5K&L1 2 P H"(KNL% H)&LwL& H<NLL& ,H- Saturation state:(wLL% H5LM1 2 PH"*L:M' H*MdM' HxS:MM% Hwhere Vbe is the base-emitter voltage, and Vce is the collector-emitter voltage.(dMN% H{SMN( H Note: For other switches (such as thyristor, IGBT, MOSFET, etc.), the gate nodeaNO% H must be connected to either a gating block or a switch controller. But for npn or pnpwRN|O% H transistors, the base node is a power node and it must be connected togO% H a power element (such as a resistor or a source). It can not be connected to a gating|OD blockI$|O]% HH or a switch controller .(% H]m& HWARNING: It has been found that the linear models of the npn and pnp transistors works well in simple circuits, but may not work when circuits are complex. Please use this model with caution.(% H(m% H617 6PNP_14'$  Description:HJ#dJ=  ,pnp Transistor (1)pnp bipolar junction transistor (linear model)('% @1# Parameters:7J#dnJ=  *Current Gain betaCurrent gain of the transistorL/P#pJ= ( *Bias Voltage VrEmitter-base forward bias voltage (default = 0.7 V)GȄR#tJ= (H  HVec,satEmitter-collector saturation voltage (default = 0.2 V)*/' @HqȄ% HThe current gain beta is defined as the ratio of the collector current Ic versus the base current Ib, that is:=Ņ. , H" (% HŅ& HUnlike the ideal switch model which will operate in either the off state (cut-off state) or the on state (saturation state), the npn BJT linear model can operate in all three states: cut-off, linear, and saturation.(% HQ,f% XHThe properties of these three states are:(% H9fLJ& &H- Cut-off state:(% H5LJ$1 2 P H")M& H8$& $H- Linear state:(M% H51 2 P H") & H<G& ,H- Saturation state:( o% H5G1 2 P H"(ỏ% HxSD% Hwhere Veb is the emitter-base voltage, and Vec is the emitter-collector voltage.(̉l% H{SD( H Note: For other switches (such as thyristor, IGBT, MOSFET, etc.), the gate nodealm% H must be connected to either a gating block or a switch controller. But for npn or pnpwR% H transistors, the base node is a power node and it must be connected togmp% H a power element (such as a resistor or a source). It can not be connected to a gating blockI$% HH or a switch controller .(p% H̍& HWARNING: It has been found that the linear switch model for npn and pnp transistors works well in simple circuits, but may not work when circuits are complex. Please use this model with caution.(% H= ̍1171Diode Bridge4e$  Description:t01َD#X`JF (1-ph Diode BridgeSingle-phase diode bridge(e% @1َ2# Parameters:;D#XvJF *Diode Voltage DropDiode conduction voltage drop, in VQ2XJ#dJF  ,InitXial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<J#dxJF  ,Initial Position_2Initial position flag for Switch 2<XdJ#dxJF  ,Initial Position_3Initial position flag for Switch 3<J#dxJF  ,Initial Position_4Initial position flag for Switch 4YdJ#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/J#d^JF  $Current Flag_2Current flag for Switch 2y/J#d^JF  $Current Flag_3Current flag for Switch 3y/J#d^JF  $Current Flag_4Current flag for Switch 4[w$ The sequence of the switches is: clockwise from the upper left, Switch 1, 3, 2, and 4. (% @(w$ A18OThyristor Bridge4<$  Description:~:D#XtJ> 21-ph Thyristor Bridge Single-phase thyristor bridge (<% @1# Parameters:}9D#XrJF Voltage DropThyristor conduction voltage drop, in VQ+J#dJF  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<J#dxJF  ,Initial Position_2Initial position flag for Switch 2<+7J#dxJF  ,Initial Position_3Initial position flag for Switch 3<J#dxJF  ,Initial Position_4Initial position flag for Switch 4Y7`J#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/J#d^JF  $Current Flag_2Current flag for Switch 2y/`RJ#d^JF  $Current Flag_3Current flag for Switch 3y/J#d^JF  $Current Flag_4Current flag for Switch 4(R% @\3O) gThe sequence of the switches is: clockwise from the upper left, Switch 1, 3, 2, and 4. The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.= 1c 9Diode Bridge4O$  Description:q-1D#XZJF *3-ph Diode Bridge 3-phase diode bridge (Y% @11# Parameters:;Y D#XvJF *Diode Voltage DropDiode conduction voltage drop, in VQJ#dJF  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)< *J#dxJF  ,Initial Position_2Initial position flag for Switch 2<J#dxJF  ,Initial Position_3Initial position flag for Switch 3<*BJ#dxJF  ,InitiBOal Position_4Initial position flag for Switch 4<J#dxJF  ,Initial Position_5Initial position flag for Switch 5<BNJ#dxJF  ,Initial Position_6Initial position flag for Switch 6YJ#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/NjJ#d^JF  $Current Flag_2Current flag for Switch 2y/J#d^JF  $Current Flag_3Current flag for Switch 3y/j\J#d^JF  $Current Flag_4Current flag for Switch 4y/J#d^JF  $Current Flag_5Current flag for Switch 5y/\NJ#d^JF  $Current Flag_6Current flag for Switch 6(v% @`N# The sequence of the switches is: clockwise from the upper left, Switch 1, 3, 5, 2, 6, and 4. (v!% @E"f# DThe node with a dot is Phase A.*!& @(f$ A1 :Thyristor Bridge4-$  Description:x4D#XhJ> 23-ph Thyristor Bridge 3-phase thyristor bridge(-% @1# Parameters:}9{D#XrJF Voltage DropThyristor conduction voltage drop, in VQJ#dJF  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<{J#dxJF  ,Initial Position_2Initial position flag for Switch 2<" J#dxJF  ,Initial Position_3Initial position flag for Switch 3< J#dxJF  ,Initial Position_4Initial position flag for Switch 4<" . J#dxJF  ,Initial Position_5Initial position flag for Switch 5<  J#dxJF  ,Initial Position_6Initial position flag for Switch 6Y. W J#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/  J#d^JF  $Current Flag_2Current flag for Switch 2y/W I J#d^JF  $Current Flag_3Current flag for Switch 3y/  J#d^JF  $Current Flag_4Current flag for Switch 4y/I ; J#d^JF  $Current Flag_5Current flag for Switch 5y/  J#d^JF  $Current Flag_6Current flag for Switch 6(;  % @Y _* "The sequence of the switches is: clockwise from the upper left, Switch 1, 3, 5, 2, 6, and 4. The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. The node with a dot is Phase A.Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.( % @&_# H @1 ; @aLVoltage Source Inverter @4@@$  Description:T @@J#dJj  "VSI3 (MOSFET)3-phase PWM voltage source inverter (with MOSFET-type switches)P@@xAJ#dJj  VSI3 (IGBT)3-phase PWM voltage source inverter (with IGBT-type switches)(@A% @1xAA# Parameters:mABJ#dJj " On ResistanceResistance of the MOSFET transistor during the on state, in Ohm (for VSI3 (MOSFET) only)aA3CJ#dJj "*Saturation VoltageConduction voltage drop of the IGBT switch, in V (for VSI3 (IGBT) only)PBCD#XJj *Diode Voltage DropConduction voltage drop of the anti-parallel diode, in VQ3CbDJ#dJj  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<CDJ#dxJj  ,Initial Position_2Initial position flag for Switch 2<bDnEJ#dxJj  ,Initial Position_3Initial position flag for Switch 3<DEJ#dxJj  ,Initial Position_4Initial position flag for Switch 4<nEzFJ#dxJj  ,Initial Position_5Initial position flag for Switch 5<EGJ#dxJj  ,Initial Position_6Initial position flag for Switch 6YzFGJ#dJj  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/GHJ#d^Jj  $Current Flag_2Current flag for Switch 2y/GHJ#d^Jj  $Current Flag_3Current flag for Switch 3y/HIJ#d^Jj  $Current Flag_4Current flag for Switch 4y/HIJ#d^Jj  $Current Flag_5Current flag for Switch 5y/IJJ#d^Jj  $Current Flag_6Current flag for Switch 6(I(J% @J L* "wThe sequence of the switches is: clockwise from the upper left, Switch 1, 3, 5, 2, 6, and 4. Each switch consists of a MOSFET (or IGBT) switch with one transistor and one anti-parallel diode.The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. The node with a dot is Phase A.Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.,(J9L'  @( LaL$ H9LL1L <LCurrent Source Inverter4aLL$  Description:q-LNMD#XZJF CSI33-phase PWM current source inverter(LvM% @1NMM# Parameters:=vM(ND#XzJF Voltage DropConduction voltage drop of the switch, in VQMNJ#dJF  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<(NIOJ#dxJF  ,Initial Position_2Initial position flag for Switch 2<NOJ#dxJF  ,Initial Position_3Initial position flag for Switch 3<IOaJ#dxJF OaaL ,Initial Position_4Initial position flag for Switch 4<OJ#dxJF  ,Initial Position_5Initial position flag for Switch 5<amJ#dxJF  ,Initial Position_6Initial position flag for Switch 6YJ#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/mJ#d^JF  $Current Flag_2Current flag for Switch 2y/J#d^JF  $Current Flag_3Current flag for Switch 3y/{J#d^JF  $Current Flag_4Current flag for Switch 4y/J#d^JF  $Current Flag_5Current flag for Switch 5y/{mJ#d^JF  $Current Flag_6Current flag for Switch 6Q. *mThe sequence of the switches is: clockwise from the upper left, Switch 1, 3, 5, 2, 6, and 4. Each switch consists of a MOSFET (or IGBT) switch in series with a reverse-blocking diode. The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. The node with a dot is Phase A.Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.(my% @&Q# Ky1=Half-Wave Thyristor Bridge4$  Description:BD#XJG :3-ph Thyristor Half-Bridge3-pulse half-wave thyristor bridge(̇% @1# Parameters:}9̇zD#XrJF Voltage DropThyristor conduction voltage drop, in VQJ#dJF  ,Initial Position_1Initial position flag for Switch 1 (0: open; 1: closed)<zJ#dxJF  ,Initial Position_2Initial position flag for Switch 2<!J#dxJF  ,Initial Position_3Initial position flag for Switch 3YĊJ#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/!=J#d^JF  $Current Flag_2Current flag for Switch 2y/ĊJ#d^JF  $Current Flag_3Current flag for Switch 3(=ދ% @xNV* "The sequence of the switches is: from the top to the bottom, Switch 1, 2, and 3. The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. The node with a dot is Phase A.Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.(ދ~% @(V$ K~1 >Half-Wave Thyristor Bridge4%$  Description:BD#XJF :6-ph Thyristor Half-Bridge6-pulse half-wave thyristor bridge(%ӎ% @1# Parameters:}9ӎD#XrJF Voltage DropThyristor conduction voltage drop, in VQ(J#dJF  ,Initial Position_1Initial position flag for Swit(ch 1 (0: open; 1: closed)<J#dxJF  ,Initial Position_2Initial position flag for Switch 2<(4J#dxJF  ,Initial Position_3Initial position flag for Switch 3<J#dxJF  ,Initial Position_4Initial position flag for Switch 4<4@J#dxJF  ,Initial Position_5Initial position flag for Switch 5<J#dxJF  ,Initial Position_6Initial position flag for Switch 6Y@iJ#dJF  $Current Flag_1Current flag for Switch 1 (0: no current output; 1: current output)y/J#d^JF  $Current Flag_2Current flag for Switch 2y/i[J#d^JF  $Current Flag_3Current flag for Switch 3y/J#d^JF  $Current Flag_4Current flag for Switch 4y/[MJ#d^JF  $Current Flag_5Current flag for Switch 5y/J#d^JF  $Current Flag_6Current flag for Switch 6(M% @P(>( QThe sequence of the switches is: from the top to the bottom, Switch 1 to 6. The node at the bottom of the module is the control node. It is the gate (base) node of Switch 1. Only the gating of Switch 1 needs to be specified. The gating of all other switches will be automatically derived.(f% @(>$ = f1 ?Gating Block4$  Description:q'pJ#dNJb   Gating BlockSwitch gating block?J#d~Jb  (Gating Block (1)Switch gating block with the file input(p!% @1R# Parameters:i!J#dJb  FrequencyOperating frequency, in Hz, of the switch or switch module connected to the gating blockURP#pJb  ("No. of PointsNo. of switching points in one period (for Gating Block only)Q#pJb  ((Switching PointsSwitching points, in degree (for Gating Block only). If the frequency is zero, the switching points are in second.rIP#pJb  (2File for Gating TableThe name of the file where the gating table is stored (for Gating Block (1) only). (q% @J$I& IThe switch gating block defines the gating pattern of a switch or a switch module. Each turn-on or turn-off action is counted as one switching point.For example, for the following gating pattern, there are 6 switching points, and the switching points are: 35, 92, 175, 187, 345, and 357.2q. , @", &?For Gating Block (1), the file for the gating table must be in the same directory as the schematic file. The gating table file has the following format:}] HnG1G2... ... ...Gnwhere G1, ..., Gn are the switching points.NOTE: The gating block can be connected to the gate node of a switch only. It can not be connected to any other elements.Example:A switch operates at 2000 Hz, and has on-time pulses from 0 to 90. deg., and from 180. to 240. deg. Using the gating block GATING, the specification will be:O+> L@HFrequency2000.No. of Points4Switching Points0. 90. 180. 240.z% HUsing the gating block GATING_1, assuming the gating table is stored in the file test.tbl, the specification will be:(+% Hi5[4 8j@HFrequency2000.File for gating tabletest.tbl(% HW2[% dHThe file test.tbl will contain the following:(% H+-' @H4,Y'  @H0.--'  @H90..Y' @H180..' @H240.* ' @H*6' @H* `' @H*6' @H(`% H(% H= 1 @ATransformersg0 0TransformersThe following transformer modules are provided in PSIM. Single-Phase Transformers:8P#ptJ (u3 .Ideal TransformerSingle-phase ideal transformer.fP#pJ (u3 6Ideal Transformer (1)Single-phase ideal transformer with reversed polarity on the secondary.38qP#pfJ (q ,1-ph TransformerSingle-phase transformer._ P#pJ (q 41-ph Transformer (1)Single-phase transformer with reversed polarity on the secondary.AqP#pJ (Q. 41-ph 3-w TransformerSingle-phase 3-winding transformer.A B P#pJ (|. 41-ph 4-w TransformerSingle-phase 4-winding transformer.A P#pJ (㧦. 41-ph 5-w TransformerSingle-phase 5-winding transformer.ZB } P#pJ (_鿀 <1-ph 5-w Transformer (1)Single-phase 5-winding transformer with different image.@  P#pJ (. 41-ph 7-w TransformerSingle-phase 7-winding transformer?}  P#p~J ((. 21-ph 8-w TransformeSingle-phase 8-winding transformer*  & @>  & 03-Phase Transformers5  P#pjJ (㰳? 43-ph Y/Y Transformer3-phase Y/Y transformer5  P#pjJ (㛳? 43-ph Y/D Transformer3-phase Y/D transformer5  P#pjJ (? 43-ph D/D Transformer3-phase D/D transformer; P#pvJ (q ,3-ph Transformer3-phase transformer (unconnected)I P#pJ (N/ 43-ph 3-w Transformer3-phase 3-winding transformer (unconnected)IPP#pJ (N/ 43-ph 4-w Transformer3-phase 4-winding transformer (unconnected)9P#prJ (. 83-ph Y/Y/D Transformer3-phase Y/Y/D transformer9Pn@P#prJ (n@+ 83-ph Y/D/D Transformer3-phase Y/D/D transformer(@% @n@A& Additional information, such as Core Type, Wire Type, Manufacturer, and Part No. can be stored for transformers by clicking on the Other Info tab of the parameter specification window.B@A1AA*EIdeal Transformer4AA$  Description:y5ArBD#XjJ5 (Ideal TransformerSingle-phase ideal transformerUACJ#dJ5  4Ideal Transformer (1)Single-phase ideal transformer (with reversed polarity)(rB9C% @1CjC# Parameters:y59CCD#XjJ5 Np (primary)No. of turns of the primary winding;jChDJ#dvJ5  $Ns (secondary)No. of turns of the secondary winding(CD% @thD*E& The winding with the larger dot is the primary winding. Ideal transformers have no losses and no leakage flux.IDsE1BsELSingle-Phase Transformer4*EE$  Description:r.sEFD#X\J5 &1-ph TransformerSingle-phase transformerMEFJ#dJ5  01-ph Transformer (1)Single-phase transformer (with reversed polarity)(FF% @1F G# Parameters:5FGJ#djJ,   Rp (primary)Resistance of the primary winding9 G HJ#drJ,  $Rs (secondary)Resistance of the secondary windingBGHJ#dJ,  *Lp (pri. leakage)Leakage inductance of the primary windingD H%IJ#dJ,  *Ls (sec. leakage)Leakage inductance of the secondary windingLHIJ#dJ,  (Lm (magnetizing)Magnetizing inductance seen from the primary winding7%I  (Rp_1 (primary 1)Resistance of the 1st primary winding=|E F J#dzJ>  (Rp_2 (primary 2)Resistance of the 2nd primary windingAF G J#dJ>  ,Rs_1 (secondary 1)Resistance of the 1st secondary windingAF G J#dJ>  ,Rs_2 (secondary 2)Resistance of the 2nd secondary windingAG +H J#dJ>  ,Rs_3 (secondary 3)Resistance of the 3rd secondary windingAG H J#dJ>  ,Rs_4 (secondary 4)Resistance of the 4th secondary windingA+H AI J#dJ>  ,Rs_5 (secondary 5)Resistance of the 5th secondary windingAH I J#dJ>  ,Rs_6 (secondary 6)Resistance of the 6th secondary windingJAI `J J#dJ>  2Lp_1 (pri. 1 leakage)Leakage inductance of the 1st primary windingJI J J#dJ>  2Lp_2 (pri. 2 leakage)Leakage inductance of the 2nd primary windingL`J K J#dJ>  2Ls_1 (sec. 1 leakage)Leakage inductance of the 1st secondary windingLJ L J#dJ>  2Ls_2 (sec. 2 leakage)Leakage inductance of the 2nd secondary windingLK L J#dJ>  2Ls_3 (sec. 3 leakage)Leakage inductance of the 3rd secondary windingL L LM J#dJ>  2Ls_4 (sec. 4 leakage)Leakage inductance of the 4th secondary windingLL M J#dJ>  2Ls_5 (sec. 5 leakage)Leakage inductance of the 5th secondary windingLLM xN J#dJ>  2Ls_6 (sec. 6 leakage)Leakage inductance of the 6th secondary windingLM O J#dJ>  (Lm (magnetizing)Magnetizing inductance seen from the primary winding?xN O J#d~J>  (Np_1 (primary 1)No. of turns of the 1st primary winding?O , J#d~J>  (Np_2 (primary 2)No. of turO , C ns of the 2nd primary windingCO J#dJ>  ,Ns_1 (secondary 1)No. of turns of the 1st secondary windingC, F J#dJ>  ,Ns_2 (secondary 2)No. of turns of the 2nd secondary windingA ˁ D#XJ> *Ns_3 (secondary 3)No. of turns of the 3rd secondary windingAF P D#XJ> *Ns_4 (secondary 4)No. of turns of the 4th secondary windingCˁ ݂ J#dJ>  ,Ns_5 (secondary 5)No. of turns of the 5th secondary windingCP j J#dJ>  ,Ns_6 (secondary 6)No. of turns of the 6th secondary winding(݂ % @wj 0 ' The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the first primary winding.With the transformer image in its upright position, the winding on the upper left (with the largest dot) is the first primary winding. The 1st to the 6th secondary windings are on the right, from the top to the bottom, respectively. * Z & @(0 $ DZ ƅ 1Iƅ G 3-Phase Transformer4 $  Description:^2ƅ X , (d@H3-ph Y/Y Transformer3-phase Y/Y transformer 3 % HParameters:7X  P#pnJ, ( $Rp (primary)Resistance of the primary winding; P#pvJ, ( (Rs (secondary)Resistance of the secondary windingD 1 P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingF Lj P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingN1 e P#pJ, ( ,Lm (magnetizing)Magnetizing inductance seen from the primary winding9Lj P#prJ, ( $Np (primary)No. of turns of the primary winding=e { P#pzJ, ( (Ns (secondary)No. of turns of the secondary windingzO + $The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side and s refers to the secondary side. Phase A, B, and C are from the top to the bottom. The nodes at the bottom are the neutral points of the Y connections. *{  & @( G $ D 1J 6 3-Phase Transformer4G $  Description:^2  , (d@H3-ph Y/D Transformer3-phase Y/D transformer 3 P % HParameters:7 ׍ P#pnJ, ( $Rp (primary)Resistance of the primary winding;P b P#pvJ, ( (Rs (secondary)Resistance of the secondary windingD׍ P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingFb P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingN 6 P#pJ, ( ,Lm (magnetizing)Magnetizing i 6 G nductance seen from the primary winding9 P#prJ, ( $Np (primary)No. of turns of the primary winding=6 L P#pzJ, ( (Ns (secondary)No. of turns of the secondary winding( t % @pIL ' The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side and s refers to the secondary side. Phase A, B, and C are from the top to the bottom. The node at the bottom is the neutral point of the Y connection. *t  & @( 6 $ D z 1{Kz 3-Phase Transformer46 $  Description:^2z , (d@H3-ph D/D Transformer3-phase D/D transformer 3 ? % HParameters:7 P#pnJ, ( $Rp (primary)Resistance of the primary winding;? Q P#pvJ, ( (Rs (secondary)Resistance of the secondary windingD P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingFQ { P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingN  P#pJ, ( ,Lm (magnetizing)Magnetizing inductance seen from the primary winding9{ P#prJ, ( $Np (primary)No. of turns of the primary winding= / P#pzJ, ( (Ns (secondary)No. of turns of the secondary winding0 _ * " The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side and s refers to the secondary side. Phase A, B, and C are from the top to the bottom.*/ & @(_ $ N 1 L  3-Phase 3-Winding Transformer4 3 $  Description:nA - *@H3-ph Y/Y/D Transformer3-phase 3-winding Y/Y/D transformer 33 % HParameters:7 [ P#pnJ, ( $Rp (primary)Resistance of the primary winding; P#pvJ, ( (Rs (secondary)Resistance of the secondary winding9[ o P#prJ, ( &Rt (tertiary)Resistance of the tertiary windingD  P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingFo P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingI 2 P#pJ, ( 6Lt (tertiary leakage)Leakage inductance of the tertiary windingN P#pJ, ( ,Lm (magnetizing)Magnetizing inductance seen from the primary winding92 Y P#prJ, ( $Np (primary)No. of turns of the primary winding= P#pzJ, ( (Ns (secondary)No. of turns of the secondary windingY ;Y P#pvJ, ( &Nt (tertiary)No. of turns of the tertiary winding  ) The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side, s to the secondary, and t to the tertiary side. For the primary and secondary windings, Phase A, B, and C are from the top to the bottom. For the tertiary winding, Phase A, B, and C are from the left to the right. The neutral points of the primary/secondary windings are at the top.*  & @(  $ N / 1M/ 3-Phase 3-Winding Transformer4 c $  Description:nA/  - *@H3-ph Y/D/D Transformer3-phase 3-winding Y/D/D transformer 3c  % HParameters:7  P#pnJ, ( $Rp (primary)Resistance of the primary winding;  P#pvJ, ( (Rs (secondary)Resistance of the secondary winding9  P#prJ, ( &Rt (tertiary)Resistance of the tertiary windingD 3 P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingF  P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingI3 b P#pJ, ( 6Lt (tertiary leakage)Leakage inductance of the tertiary windingN  P#pJ, ( ,Lm (magnetizing)Magnetizing inductance seen from the primary winding9b  P#prJ, ( $Np (primary)No. of turns of the primary winding=  P#pzJ, ( (Ns (secondary)No. of turns of the secondary winding; P#pvJ, ( &Nt (tertiary)No. of turns of the tertiary winding * "The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side, s to the secondary, and t to the tertiary side. For the primary and secondary windings, Phase A, B, and C are from the top to the bottom. For the tertiary winding, Phase A, B, and C are from the left to the right. The neutral point of the primary winding is at the top.* & @( $ D $ 1)N$ B 3-Phase Transformer4 X $  Description:B$ J#dJ5  (3-ph Transformer3-phase transformer (windings unconnected)(X % @, 8 # Image:3 k . , @" 18 # Parameters:7k # P#pnJ, ( $Rp (primary)Resistance of the primary winding;  P#pvJ, ( (Rs (secondary)Resistance of the secondary windingD# B P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingF  P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingNB @ P#pJ, ( @  ,Lm (magnetizing)Magnetizing inductance seen from the primary winding9 A P#prJ, ( $Np (primary)No. of turns of the primary winding=@ A P#pzJ, ( (Ns (secondary)No. of turns of the secondary windingQ& A B + $MThe resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side and s refers to the secondary side. The windings of the transformer are not connected. The node assignments are: DA -C 1 O-C L 3-Phase Transformer4B aC $  Description:P-C C J#dJ=  03-ph 3-w Transformer3-phase 3-winding transformer (windings unconnected)(aC #D % @, C OD # Image:2#D D . , @"1OD D # Parameters:7D 9E P#pnJ, ( $Rp (primary)Resistance of the primary winding;D E P#pvJ, ( (Rs (secondary)Resistance of the secondary winding99E MF P#prJ, ( &Rt (tertiary)Resistance of the tertiary windingDE F P#pJ, ( .Lp (pri. leakage)Leakage inductance of the primary windingFMF wG P#pJ, ( .Ls (sec. leakage)Leakage inductance of the secondary windingIF H P#pJ, ( 6Lt (tertiary leakage)Leakage inductance of the tertiary windingNwG H P#pJ, ( ,Lm (magnetizing)Magnetizing inductance seen from the primary winding9H 7I P#prJ, ( $Np (primary)No. of turns of the primary winding=H I P#pzJ, ( (Ns (secondary)No. of turns of the secondary winding;7I OJ P#pvJ, ( &Nt (tertiary)No. of turns of the tertiary windingbI K * "The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the primary side.The label p refers to the primary side, s refers to the secondary side, and t refers to the tertiary side. The windings of the transformer are not connected.The node assignments of the transformer are as follows:(OJ L % @DK GL 1 PGL 3-Phase Transformer4L {L $  Description:PGL M J#dJ5  03-ph 4-w Transformer3-phase 4-winding transformer (windings unconnected)({L =M % @0 M mM & Image:2=M M . , @"1mM M # Parameters:=M WN J#dzJ=  (Rp_1 (primary 1)Resistance of the 1st primary winding;M N D#XvJ= &Rp_2 (primary 2)Resistance of the 2nd primary winding9WN YO J#drJ=  $Rs (secondary)Resistance of the secondary winding7N O J#dnJ=  "Rt (tertiary)Resistance of the tertiary windingJYO z J#dJ= O z L  2Lp_1 (pri. 1 leakage)Leakage inductance of the 1st primary windingJO  J#dJ=  2Lp_2 (pri. 2 leakage)Leakage inductance of the 2nd primary windingDz J#dJ=  *Ls (sec. leakage)Leakage inductance of the secondary windingG - J#dJ=  2Lt (tertiary leakage)Leakage inductance of the tertiary windingP ǂ J#dJ=  (Lm (magnetizing)Magnetizing inductance seen from the 1st primary winding?- P J#d~J=  (Np_1 (primary 1)No. of turns of the 1st primary winding?ǂ ك J#d~J=  (Np_2 (primary 2)No. of turns of the 2nd primary winding;P ^ J#dvJ=  $Ns (secondary)No. of turns of the secondary winding9ك J#drJ=  "Nt (tertiary)No. of turns of the tertiary winding(^ % @\ ( The resistance is in Ohm and the inductance is in H. All the resistance and inductance values are referred to the 1st primary winding.The label p_1 refers to the 1st primary side, p_2 refers to the 2nd primary side, s refers to the secondary side, and t refers to the tertiary side. The windings of the transformer are not connected.6 Æ 1VQÆ DV_DT4 $  Description:fÆ ] J#d8J5  dv/dtThe dv/dt block( % @^6] ( mThe dv/dt block has the same function as the differentiator in the control circuit, except that it is used in the power circuit. The output of the dv/dt block is equal to the derivative of the input voltage versus time. It is calculated as: Vo = (Vin(t) - Vin (t-delt))/delt where delt is the time step.4  1 R m DCM4 K $  Description:f J#d8JF  DC MachineDC machine(K ى % @1 # Parameters::ى P#ptJF ( &Ra (armature)Armature winding resistance, in Ohm8  P#ppJF ( &La (armature)Armature winding inductance, in H4 P#phJF (  Rf (field)Field winding resistance, in Ohm2 " P#pdJF (  Lf (field)Field winding inductance, in H7 J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m0" # P#p`JF (  Vt (rated)Rated terminal voltage, in V0 P#p`JF (  Ia (rated)Rated armature current, in Ay/#  J#d^JF  N (rated)Rated mechanical speed, in rpm}- P#pZJF (  If (rated)Rated field current, in A? " J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)I J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave)!" * "The master/slave flag defines the mode of operation of the machine. In a mechanical system, only one machine or mechanical-electrical interface block and at least one machine/mechanical-electrical interface block should be set to the master mode (referred to as the master unit), and the rest to the slave mode. We use the concept *reference direction* to define the positive notation of speed sensors, torque sensors, and loads in a mechanical system. The reference direction of the mechanical system is defined as the direction from the shaft node of the master unit to the rest of the mechanical system along the shaft. Furthermore, we define the mechanical speed to be positive if the armature and field currents of the master machine are positive. * "MBased on this notation, if the reference direction enters an element from the dotted side, it is said that this element is along the reference direction. Otherwise, it is opposite to the reference direction.Therefore, if a speed sensor is along the reference direction, a positive speed produced by the master machine will give a positive speed sensor output. A dc machine is described by the following equations:4 / . H" 4  0 0 @H"!4 N 0 0 @H""4 0 0 @H"#4N 0 0 @H"$( % H. % Hwhere:( 4 % H* ^ g @H      Vt:terminal voltageEa:back emfIa:armature currentIf:field currentWm:mechanical speed, in rad./sec.Laf:mutual inductance between the field and the armature windings4 S & HThe term Laf * If is often defined as k phi in many text books. Note that the relationship between the flux phi and the field current If is assumed to be linear. Magnetic saturation is not considered.(^ { % HgS  % HThe mutual inductance Laf is calculated as follows based on the specified rated operating condition:< { C 3 6H"%* m ' @H8C 1c S  INDM_3S4m $  Description: M#hwJ  Squirrel-cage Ind. MachineSquirrel-cage Ind. Machine (neutral)3-phase symmetrical squirrel-cage induction machine3-phase symmetrical squirrel-cage induction machine with neutral( % @1 : # Parameters:6 P#plJF ( "Rs (stator)Stator winding resistance, in Ohm<: L P#pxJF ( "Ls (stator)Stator winding leakage inductance, in H4 P#phJF (  Rr (rotor)Rotor winding resistance, in Ohm:L Z P#ptJF (  Lr (rotor)Rotor winding leakage inductance, in H6 P#plJF ( ,Lm (magnetizing)Magnetizing inductance, in Hl"Z L J#dDJF  $No. of Poles PNo. of poles7 J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m?L V J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)I J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave)V m IV  : BAll the parameters are referred to the stator side.Both machine models are symmetrical and are connected in Y on the stator.For more explanation on how to set up the Master/Slave Flag, refer to the relevant section under the DC Machine. Equations that describe the machine operations are given in the User Manual. (  % @<   1 T INDM3_S_LIN4 ' $  Description: D M#hJ  Squirrel-cage Ind. Machine (linear)Squirrel-cage Ind. Machine (nonlinear)3-phase squirrel-cage induction machine (general model, unconnected).3-phase squirrel-cage induction machine with saturation.(' l % @0 D  & Image:2l  . , @"&1  # Parameters:6  P#plJF ( "Rs (stator)Stator winding resistance, in Ohm<  P#pxJF ( "Ls (stator)Stator winding leakage inductance, in H4  P#phJF (  Rr (rotor)Rotor winding resistance, in Ohm:  P#ptJF (  Lr (rotor)Rotor winding leakage inductance, in HV  P#pJF ( ,Lm (magnetizing)Magnetizing inductance, in H (for general linear model only)l" 1 J#dDJF  $No. of Poles PNo. of poles7  J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m?1 ; J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)I  J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave); K#dJF  4Im v.s. Lm (Im1,Lm1) Nonlinear characteristics of the magnetizing current versus the magnetizing inductance (for nonlinear model only) W , &All the parameters are referred to the stator side.For both models, the stator windings are unconnected and can be connected in any way by the user.For the model with saturation, the curve of the magnetizing current versus the inductance is entered. Note only the first quadrant curve needs to be specified. The program will automatically derive the data for the third quadrant.* & @9W 1BU C INDM3_WR4 $  Description:Q J#dJ  8Wound-rotor Ind. Machine3-phase symmetrical wound-rotor induction machine( % @, # Image:2  . , @"'1 @ # Parameters:6 P#plJF ( "Rs (stator)Stator winding resistance, in Ohm<@ R P#pxJF ( "Ls (stator)Stator winding leakage inductance, in H4  P#phJF (  Rr (rotor)Rotor winding resistance, in Ohm:R ` P#ptJF (  Lr (rotor)Rotor winding leakage inductance, in H6 @ P#plJF ( ,Lm (magnetizing)Magnetizing inductance, in H` @ =` @ D#XzJF (Ns/Nr Turns RatioRatio of the stator and rotor windingsl" @ @ J#dDJF  $No. of Poles PNo. of poles7@ zA J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m?@ B J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)IzA B J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave) B C , &All the parameters are referred to the stator side.The machine is symmetrical, and both the stator and rotor windings are connected in Y.Equations that describe the machine operations are given in the User Manual. (B C % @= C D 1D VD N INDM3_WR_LIN4C :D $  Description:D OE M#hJ  Wound-rotor Ind. Machine (linear)Wound-rotor Ind. Machine (nonlinear)3-phase wound-rotor induction machine (general model, unconnected).3-phase wound-rotor induction machine with saturation.(:D wE % @0 OE E & Image:2wE E . , @"(1E F # Parameters:6E F P#plJF ( "Rs (stator)Stator winding resistance, in Ohm< F G P#pxJF ( "Ls (stator)Stator winding leakage inductance, in H4F G P#phJF (  Rr (rotor)Rotor winding resistance, in Ohm:G *H P#ptJF (  Lr (rotor)Rotor winding leakage inductance, in HVG H P#pJF ( ,Lm (magnetizing)Magnetizing inductance, in H (for general linear model only)=*H QI D#XzJF (Ns/Nr Turns RatioRatio of the stator and rotor windingsl"H I J#dDJF  $No. of Poles PNo. of poles7QI >J J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m?I J J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)I>J ZK J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave)J 4L K#dJF  4Im v.s. Lm (Im1,Lm1) Nonlinear characteristics of the magnetizing current versus the magnetizing inductance (for nonlinear model only)ZK M , &All the parameters are referred to the stator side.For both models, the stator windings are unconnected and can be connected in any way by the user.For the model with saturation, the curve of the magnetizing current versus the inductance is entered. Note only the first quadrant curve needs to be specified. The program will automatically derive the data for the third quadrant.*4L N & @6M CN 1`WCN BDCM34 N wN $  Description:cCN $O J#dJ,  0Brushless DC Machine3-phase permanent magnet brushless dc machine with trapezoidal back emf(wN LO % @0 $O |O & Image:2LO O . , @")1|O O # Parameters:AO v J#dJ# O v N  2R (stator resistance)Stator winding resistance R, in Ohm.9O J#drJ#  0L (stator self ind.)Stator self inductance, in H=v L#f{J#  4M (stator mutual ind.)Stator mutual inductance, in H.The stator mutual inductance M is a negative value. Depending on the winding structure, the ratio between M and the stator self inductance L is normally between -1/3 and -1/2. If M is unknown, a reasonable value of -0.4*L can be used as the default value.V ( P#pJ# (  Vpk / krpmPeak line-to-line back emf constant, in V/krpm (mechanical speed).` ڄ R#rJ# ( "Vrms / krpmRms line-to-line back emf constant, in V/krpm (mechanical speed).The values of Vpk/krpm and Vrms/krpm should be available from the machine data sheet. If these data are not available, they can be obtained through experiments by operating the machine as a generator at 1000 rpm and measuring the peak and rms line-to-line voltages.s/( M D#X^J# "No. of Poles PNo. of poles of the machiney5ڄ ƅ D#XjJ# (Moment of InertiaMoment of inertia J, in kg*m*m~:M D D#XtJ# ,Mech. Time ConstantMechanical time constant tau_mechKƅ L#fJ# "0Initial rotor angle, in electrical deg.The initial rotor angle is the rotor angle at t=0. The zero rotor angle position is defined as the position where Phase A back emf crosses zero (from negative to positive) under a positive rotation speed. >D  L#f}J# "advancePosition sensor advance angle, in electrical deg.The advance angle is defined as the angle difference between the turn-on angle of Phase A upper switch and 30 deg. in an 120-deg. conduction mode. For example, if Phase A is turned on at 25 deg., the advance angle will be 5 deg. (i.e. 30 - 25 = 5 deg.)o) F#ZSJ# 2Conduction Pulse widthPosition sensor conduction pulse width, in electrical deg.Positive conduction pulse can turn on the upper switch and negative pulse can turn on the lower switch in a full bridge inverter. The conduction pulse width is 120 electrical deg. for 120 deg. conduction mode.Z , J#dJ#  Torque FlagOutput flag for internal developed torque Tem (1: output; 0: no output)& R L#fJ#  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave).The flag defines the mode of operation of the machine. A detailed explanation of the definition and usage is given in the Help for DC machines.@, * "-In the image, Node a, b, c are the stator winding terminals for Phase A, B, and C, respectively, and Node n Is the neutral point. The stator windings are Y-connected. Node sa, sb, and sc are the Phase A, B, and C outputs of the built-in six-pulse hall effect position sensors. The output signal of the position sensor is a bipolar commutation pulse (1, 0, and -1) which can be used to operate the three-phase voltage source inverter in a six-step mode. They are all control nodes and should be connected to the control circuit.fR 4 0 .More Explanation on the Hall Effect Position Sensor:A hall effect position sensor consists of a set of hall switches and a set of trigger magnets.The hall switch is a semiconductor switch (e.g. MOSFET or BJT) that opens or closes when the magnetic field is higher or lower than a certain threshold value. It i 4 N s based on the hall effect, which generates an emf proportional to the flux-density when the switch is conducting a current supplied by an external source. It is common to detect the emf using a signal conditioning circuit integrated with the hall switch or mounted very closely to it. This provides a TTL-compatible pulse with sharp edges and high noise immunity for connection to the controller via a screened cable. For a three-phase brushless dc motor, three hall switches are spaced 120 electrical deg. apart and are mounted on the stator frame.1  e %  The set of trigger magnets can be a separate set of magnets, or it can use the rotor magnets of the brushless motor. If the trigger magnets are separate, they should have the matched pole spacing (with respect to the rotor magnets), should be mounted on the shaft in close proximity to the hall switches. If the trigger magnets use the rotor magnets of the machine, the hall switches must be mounted close enough to the rotor magnets, where they can be energized by the leakage flux at the appropriate rotor positions.(4 $ (e % H6 1X  PMSM36 ! &  HDescription:U v M#hJ  Permanent Magnet Sync. MachinePermanent Magnet Sync. Machine (V)3-phase permanent magnet synchronous machine with sinusoidal back emf (current-type interface).3-phase permanent magnet synchronous machine with sinusoidal back emf (voltage-type interface).(! % @, v # Image:2 . , @"*1 - # Parameters:D P#pJ# ( 8Rs (stator resistance)Stator winding resistance R, in Ohm.8- I P#ppJ# ( ,Ld (d-axis ind.)Stator d-axis inductance, in H8 Q#pJ# ( ,Lq (q-axis ind.)Stator q-axis inductance, in H. The d-q coordinate is defined that the d-axis passes through the center of the magnet, and the q-axis is in the middle between two magnets. The q-axis is leading the d-axis.DI  L#fJ#  Vpk / krpmPeak line-to-line back emf constant, in V/krpm (mechanical speed).The value of Vpk/krpm should be available from the machine data sheet. If this data is not available, it can be obtained through an experiment by operating the machine as a generator at 1000 rpm and measuring the peak line-to-line voltage.s/ D#X^J# "No. of Poles PNo. of poles of the machiney5 D#XjJ# (Moment of InertiaMoment of inertia J, in kg*m*m~: { D#XtJ# ,Mech. Time ConstantMechanical time constant tau_mechZ  J#dJ#  Torque FlagOutput flag for internal developed torque Tem (1: output; 0: no output)&{ E L#fJ#  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave).The flag defines the mode of operation of the machine. A detailed explanation of the definition and usage is given in the Help for DC machines.P  6 :The stator windings are Y-connected. Depending on the way the internal model interfaces with the external stator circuitry, there are two types of interface: one is the voltage-type interface (Permanent Magnet Sync. Machine (V)), and the other is the current-type interface (Permanent Magnet Sync. Machine). The model for the voltage-type interface consists of controlled voltage E  sources on the stator side, and this model is suitable in situations where the machine operates as a generator and/or the stator external circuit is in series with inductive branches. On the other hand, The model for the current-type interface consists of controlled current sources on the stator side, and this model is suitable in situations where the machine operates as a motor and/or the stator external circuit is in parallel with capacitive branches.&E  # 6 3 1Y3 @ SYNM34 g $  Description:3  N#jJ   `Synchronous MachineSynchronous Machine (I)3-phase synchronous machine with external excitation (voltage-type interface).3-phase synchronous machine with external excitation (current-type interface).(g  % @0   & Image:2  . , @"+1 A # Parameters:9  P#prJ# ( "Rs (stator)Stator winding resistance R, in Ohm.|2A F J#ddJ#  Ls (stator)Stator leakage inductance, in HA  J#dJ#  4Ldm (d-axis mag. Ind.)d-axis magnetizing inductance, in HAF \ J#dJ#  4Lqm (q-axis mag. Ind.)q-axis magnetizing inductance, in Ht0  D#X`J# Rf (field)Field winding resistance, in OhmD\ X D#XJ# 6Lfl (field leakage ind.)Field winding leakage inductance, in HD  D#XJ# *Rdr (damping cage)Rotor damping cage d-axis resistance, in OhmKX o D#XJ# ,Ldrl (damping cage)Rotor damping cage d-axis leakage inductance, in HD  D#XJ# *Rqr (damping cage)Rotor damping cage q-axis resistance, in OhmKo D#XJ# ,Lqrl (damping cage)Rotor damping cage q-axis leakage inductance, in HB  I#bJ# H*HNs/Nf (effective)Stator-field winding effective turns ratio{) R#tRJ# H*Number of Poles PNumber of Poles PC  D#XJ# (Moment of InertiaMoment of inertia J of the machine, in kg*m2Z J#dJ#  Torque FlagOutput flag for internal developed torque Tem (1: output; 0: no output)& L#fJ#  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave).The flag defines the mode of operation of the machine. A detailed explanation of the definition and usage is given in the Help for DC machines.J o@ < FAll the parameters are referred to the stator side.Depending on the way the internal model interfaces with the external stator circuitry, there are two types of interface: one is the voltage-type interface (Synchronous Machine), and the other is the current-type interface (Synchronous Machine (I)). The model for the voltage-type interface consists of controlled voltage sources on the stator side, and this model is suitable in situations where the machine operates as a generator and/or the stator external circuit is in series with inductive branches. On the other hand, The model for the current-type interface consists of controlled current sources on the stator side, and this model is suitable in situations where the machin o@  e operates as a motor and/or the stator external circuit is in parallel with capacitive branches.. @ ( 5o@ @ 1dZ@ SRM34@ A $  Description:c@ A J#dJ5  >Switched Reluctance Machine3-phase switched reluctance machine (6 stator and 4 rotor teeth)(A A % @, A B # Image:2A 9B . , @",1B jB # Parameters:}39B B J#dfJF  ResistanceStator phase resistance R, in Ohm5jB fC J#djJF  &Inductance LminMinimum phase inductance, in H5B C J#djJF  &Inductance LmaxMaximum phase inductance, in HQfC D J#dJF  r (deg.)Duration of the interval where the inductance increases, in deg.7C E J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m?D E J#d~JF  Torque FlagOutput flag for internal torque Tem (0 or 1)IE F J#dJF  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave)^2E {H , &eThe master/slave flag defines the mode of operation of the machine. A detailed explanation of the definition and usage is given in the Help for DC machines. In the image, Node a+, a-, b+, b-, c+, c- are the winding terminals of Phase A, B, and C, respectively. They are all power nodes and should be connected to the power circuit.Node c1ac4a, c1bc4b, and c1cc4c are the control signals for Phase A, B, and C, respectively. Node theta is the mechanical rotor angle (in rad.). They are all control nodes and should be connected to the control circuit._F J ( The control signal defines the inductance of the winding. For example, when c1a is high (1), the winding inductance in Phase A is in the rising stage (see below). The rotor angle is defined such that when the stator and the rotor teeth are completely out of alignment, theta = 0.The equation of the switched reluctance machine for one phase is:< {H >J 0 0H"-where:TJ J D X@H    v:phase voltagei:phase currentL:phase inductanceR:phase resistance[6>J 1K % lHThe inductance L is a function of the rotor angle .(J YK % H(1K K % H6YK K 1 2 H".(K K % H(K L % H(K /L % HL L ; DHr is the duration where the inductance rises (or falls). Let k = (Lmax-Lmin) / r, we can express the inductance as a function of :_,/L WM 3 6ZH"/[rising stage; control signal c1=1]_,L M 3 6Z@H"0[flat-top stage; control signal c2=1]WM O l AH"1"2"3"4[falling stage; control signal c3=1][flat-bottom stage; control signal c4=1] The selection of the operating state is done through the control signals c1, c2, c3, and c4 which are applied externally. For example, when c1a is high (1), the rising stage is selected and L = Lmin + k * . The developed torque per phase is:Based on the inductance expression, we have:[rising stage]LM  4 82@H"5[flat-toO  @ p stage]kO ŀ D XH"6"7[falling stage][flat-bottom stage]Note that, in this model, saturation is not considered.* ' @H6ŀ % 1 [%  MLOAD4 Y $  Description:B% J#dJG  :Mechanical Load (general)General resistive mechanical load(Y % @1 > # Parameters:l" J#dDJ=  Tc Torque constant, in N*m9> 0 M#jrJ= " , K1 (coefficient)Coefficient for the linear term7 J#dnJ=  (K2 (coefficient)Coefficient for the square term60 1 J#dlJ=  (K3 (coefficient)Coefficient for the cubic term7 J#dnJ=  *Moment of InertiaMoment of inertia J, in kg*m*mb:1  ( tA general resistive mechanical load is expressed as:4 H / . H"8* r ' @H. H % Hwhere:(r ȅ % HS U : D@Hm:mechanical speed, in rad./sec.sign(m):sign of the mechanical speed l7ȅ 5 :nP!H(1 if m is positive; and -1 if m is negative)(U % Hl z % HThis load is of resistive type. That is, the load torque is always against the direction of the rotation.( % Hbz ) % HBy choosing the coefficients properly, one can model various types of mechanical load, such as:( Q % Hb&) < HLH - Conveyor (Tload = K1 * m)OQ J H `@H - Fans, centrifugal pumps, and compressors (Tload = K2 * m * m)( r % H4 J ( HExample:(r Ή % HsN A % HTo define a resistive constant-torque load with a value of 10 N*m, we have:L#Ή ) "FPHTc = 10; K1 = 0; K2 = 0; K3 = 0.,A ) "PH, '  H*  ' @H* 9 ' @H( a % H*9 ' @H*a ' @H( ݋ % H(  % H8݋ = 1\= MLOAD_T4 q $  Description:H=  J#dJF  JMechanical Load (constant-torque)Constant-torque mechanical load(q + % @1 \ # Parameters:k!+ Ǎ J#dBJF   TcTorque constant, in N*m7\ H J#dnJF  *Moment of InertiaMoment of inertia J, in kg*m*m`8Ǎ ( pA constant-torque mechanical load is expressed as:MH 8 @*@  Tload = Tc 2 3 C T   where Tc is a constant. Typical loads include belt conveyors with a fixed loading, extruders, hoists, and mine lifts.Note that this type of constant-torque load is different from the resistive c 3  onstant-torque load defined by MLOAD. With MLOAD_T, the load torque is always in one direction, independent of the speed; whereas with MLOAD, the load torque direction changes with the rotation direction.The loading torque of the constant-load MLOAD_T depends on its position relative to the machine. If the load is along the reference direction of the mechanical system (the reference direction enters the dotted side of the load), the loading torque to the master machine is Tc. Otherwise, the loading torque to the master machine is - Tc.* ] & @&3 # *] & @( $ 8 1] MLOAD_P4 A $  Description:F J#dJ>  HMechanical Load (constant-power)Constant-power mechanical load(A % @1 * # Parameters:s/ D#X^J "Maximum TorqueMaximum torque Tmax, in N*mv2*  D#XdJ ,Base Speed (in rpm)Base speed n_base, in rpm7 J#dnJ  *Moment of InertiaMoment of inertia J, in kg*m*m R + $'A constant-power mechanical load is expressed as: When the absolute value of the mechanical speed n is less than the base speed limit:4 / . H"9*R ' @H|W , % H When the absolute value of the mechanical speed is above the base speed limit:> j 1 2H":where:S, : D@Hm:mechanical speed, in rad./sec.sign(m):sign of the mechanical speed [2j R ) "dP!H(1 if Wm is positive; and -1 if Wm is negative)( z % H^R % HThis load is of resistive type. That is, the load torque is always against the direction of5z 2 %  Hthe rotation.( Z % H(2 % H(Z % H9 1^ MLOAD_WM4  $  Description:F J#dJ5  HMechanical Load (constant-speed)Constant-speed mechanical load( % @1 # Parameters:|2 | J#ddJ5  0Constant Speed (rpm)Speed constant, in rpm7 J#dnJ5  *Moment of InertiaMoment of inertia J, in kg*m*m| , &5A constant-speed mechanical load defines the speed of a mechanical system, and the speed will remain constant, as defined by the speed constant. 8 1B_  GEARBOX4 / $  Description:b J#d0J5  Gear BoxGear Box(/ % @, # Image:2  . , @";1 H # Parameters:l M#j>J5  " Gear RatioGear Ratio aQH  = H)   If the numbers of teeth of the first gear and the second gear are n1 and n2, respectively, the gear ratio a is defined as: a = n1 / n2. Let the radius, torque, and speed of these two gears be: r1, r2, T1, T2, w1, and w2, we have: T1 / T2 = r1 / r2 = w2 / w1= a.  : K 1 `K MECH_ELEC4  $  Description:LK  J#dJ5  FMechanical-Electrical InterfaceMechanical-electrical interface block( = % @1 n # Parameters:I=  J#dJ5  *Master/Slave FlagFlag for master/slave mode (1: master; 0: slave)0n 1 - ( The master/slave flag defines the mode of operation of the machine. In a mechanical system, only one machine or mechanical-electrical interface block and at least one machine/mechanical-electrical interface block should be set to the master mode (referred to as the master unit), and the rest to the slave mode. For further explanation on the master/slave flag, refer to the Help for the dc machine (DCM).This block allows users to access the internal equivalent circuit of the mechanical system for a machine. Lets assume that a drive system consists of a motor (with a developed torque of Tem and a moment of inertia of J1) and a mechanical load (with a load torque of Tload and a moment of inertia of J2). The equation that describes the mechanical system is:& W # S1  ΀H"<        where Wm is the shaft mechanical speed. In PSIM, this equation is represented by an equivalent circuit consisting of two current sources in parallel with two capacitors. The two current sources have the values of Tem and Tload, and the capacitors have the values of J1 and J2 (in F). The node-to-ground voltage represents the mechanical speed Wm. This is analogous to C dV/dt = i for a capacitor where C=J1+J2, V= m, and i=Tem-Tload. W ' HIn PSIM, the mechanical equivalent circuit for motors and mechanical loads all uses the capacitor-based circuit model. The mechanical-electrical interface block provides the access to the internal mechanical equivalent circuit. If the mechanical side of the interface block (with the letters MECH) is connected to a mechanical shaft, the electrical side (with the letters ELEC) will be the speed node of the mechanical equivalent circuit. One can thus connect any electrical circuits to this node.z k ' HWith this element, users can connect the built-in motors or mechanical loads with custom-built load or motor models. * ' @H(k % H( % H8  1 a F ControlsD / .Control LibraryThe control library contains the following: o P#p>J ('B FiltersFilter blocks.; P#pvJ (o 4Computational BlocksVarious computational blocks.7  P#pnJ (o 6Other Function BlocksVarious function blocks.w' P#pNJ (ô (Logic ElementsLogic elements.^ 6 P#pJ (8K 8Digital Control ModuleDigital Control Module. It contains various discrete elements.u  P#pJ ({>HS .SimCoupler ModuleSimCoupler Module. It contains the link nodes to be used for interface to Matlab/Simulink.}-6 x P#pZJ (  $ProportionalProportional (P) block.o @ P#p>J (  IntegratorIntegrator.x @ 2x @ P#pdJ (Fc^. 4Resetable IntegratorResetable integratorw' @ A P#pNJ ( (DifferentiatorDifferentiator.1@ A P#pbJ (y PIProportional-Integral (PI) controllernA A P#p<J (  ComparatorComparatorhA \B P#p0J ( LimiterLimiter}-A B P#pZJ (6+ ,Summer (1-input)Summer with 1 inputO\B xC P#pJ (7+ $Summer (+/-)Summer with 2 input (one positive and the other negative)2B C P#pdJ (]O $Summer (+/+)Summer with 2 positive input}-xC wD P#pZJ (8+ ,Summer (3-input)Summer with 3 input-C D ( @H wD E & }HAdditional information, such as Manufacturer and Part No., can be specified for some of the control elements by clicking on the Other Info tab of the parameter specification window.@D E 2 4@H)E E & H(E F % H2E KF 1bKF !I P4F F $  Description:P$KF F , (H@HProportionalProportional block3F G % HParameters:LF NG - *>@HGainGain k of the block a<G G % xHThe output and the input have the following relationship:(NG G % HTG +H < H0@H   Vout = k * Vin*G UH ' @H(+H }H % H*UH H ' @H*}H H ' @H(H H % H(H !I % H3H TI 1cTI L PI4!I I $  Description:[.TI I - *\@HPIProportional-integral (PI) controller3I J % HParameters:kI J A R@H  GainGain k of the PI controllerTime ConstantTime constant T of the PI controller, in second a<J #K % xHThe transfer function of the PI controller is defined as:(J KK % Hh&#K K B TL@H     G(s) = k * (1 + sT) / (sT)*KK K ' @H(K L % H*K /L ' @H*L YL ' @H(/L L % H(YL L % H2L L 12dL  I4L M $  Description:fL uM J#d8JF  IntegratorIntegrator(M M % @1uM M # Parameters:?M WN J#d~JF "  Time ConstantTime constant T of the integrator, in sec.BM N J#dJF  0Initial Output ValueInitial output value of the integrator/WN O ) " @H ^9N pO % rHThe transfer function of the integrator is defined as:(O O % HMpO 6 <.@H   G(s) = 1 / (sT)O L *O 6 ' @H( ^ % H*6 ' @H*^ ' @H( ڀ % H(  % H7ڀ 9 1e9 RESETI5 n $ "Description: z09 J#d`JF  0Resetable IntegratorResetable integrator(n  % @1 A # Parameters:C Ԃ P#pJF  (" Time ConstantTime constant T of the integrator, in secondAA Y D#XJF .Initial Output ValueInitial output value of the integrator <Ԃ ߃ J#dxJF  Reset FlagReset flag (0: edge reset; 1: level reset)&Y  # (߃ - % @^: $ tThe transfer function of the integrator is defined as:M- ؄ 5 :0@   G(s) = 1 / (sT)e a $ The output of the resetable integrator can be reset through an external control signal (at the bottom of the block). For the edge reset (reset flag = 0), the integrator output is reset to zero at the rising edge of the control signal. For the level reset (reset flag = 1), the integrator output is reset to zero as long as the control signal is high (1).*؄ & @(a $ 2 1f 5 D4  $  Description:N" g , (D@HDifferentiatorDifferentiator3 % HParameters:m;g  2 4v@H Time ConstantTime constant T of the differentiator b= i % zHThe transfer function of the differentiator is defined as:( % HGi ؈ 6 <"@H   G(s) = sT*  ' @HJ%؈ L % JHA differentiator is calculated as: ? Y 7H"=      where tstep is the simulation time step, Vin (t) and Vin (t - tstep) are the input values at the present and the previous time step.*L i ' @H(? % H*i ' @H* ' @H( % H( 5 % H5 j 1gj L COMP45 $  Description:Fj , (4@HComparatorComparatoruP Y % HThe output of a comparator is high (value=1) when the non-inverting input is vQ ό % Hhigher than the inverting input. When the positive input is lower, the output yTY H % His zero. If the two input are equal, the output is undefined and it will keep the8ό % &Hprevious value. (H % H* ҍ ' @H* ' @H(ҍ $ % H( L % H7$ 1h Q OP_AMP4L $  Description:h$  D#XHJF Op. Amp. Operational amplifierN D#XJF Op. Amp. (1)Operational amplifier (with the reference ground accessible)N O D#XJF  Op. Amp. ( O L 2)Operational amplifier (with the reference ground accessible)( w % @1O # Parameters:Hw 4 D#XJF Voltage Vs+Upper voltage source level of the operational amplifierJ J#dJF  Voltage Vs-Lower voltage source level of the operational amplifierH4  6 :%For Op. Amp (1) and Op. Amp. (2), the node at the bottom is the reference ground node.The model of the operational amplifier is ideal. It consists of a controlled voltage source in series with an output resistor. The amplitude of the controlled voltage source is equal to the op. amp. gain multiplied by the input voltage difference. The output of the op. amp. is limited by the upperand the lower source voltages Vs+ and Vs-. In PSIM, the op. amp. gain is set at 100,000. and the output resistance is set at 80 Ohms.C ] The difference between Op. Amp. and Op. Amp. (1)/ Op. Amp. (2) is that, for Op. Amp., the op. amp. reference node is connected to the power ground; whereas for Op. Amp (1)/ Op. Amp. (2), the op. amp. reference node is accessible and can be floating. Op. Amp. (1) and Op. Amp. (2) are identical except that the plus sign and minus sign are reversed.Therefore, if the op. amp. reference ground is the same as the power circuit ground, Op. Amp. can be used. But if the op. amp. reference ground is floating, either Op. Amp. (1) or Op. Amp. (2) must be used.t Q - *Note: One limitation of the op. amp. model in PSIM is that it does not work in the positive feedback mode. 8 1i / Limiter4Q $  Description:B - **@HLimiterLimiter3 2 % HParameters:V 4 8@HLower LimitLower limit of the limiter Upper LimitUpper limit of the limiter vQ2 2 % HThe output of a limiter is clamped to the upper/lower limit whenever the input{V % Hexceeds the limiter range. If the input is within the limit, the output is equal to2 2 % Hthe input.(  % H( / % H;  j 1Yjj LIMIT_DVDT4/ $  Description:W+j , (V@Hdv/dt LimiterGradient (dv/dt) limiter3 ( % HParameters:X, , (X@Hdv/dt LimitLower limit of the limiter ( 8 & %HA gradient (dv/dt) limiter limits the rate of change of the input. If the rate of change is within the limit, the output is equal to the input.( ` % H(8 % H7` 1k 2Summer4 $  Description:U) H , (R@HSummer (1-input)Summer with 1 input3 { % HParameters:P$H , (H@HGain_1 (+)Gain k of the input xS{ C % HThe 1-input summer is primarily designed for the summation of a vector elements,P+ % VHalthough the input can also be a scalar.(C % H^9  % rHIf the input is a scalar, the output of the summer is:{  H       Vo = k * Vinwhere Vin is the input value.If the input i  s a vector, let Vin = [a1 a2 a3 ... an], the output of the summer is:Vo = k * (a1 + a2 + a3 + ... + an)Example:( % HpE8+ &H If the input is a vector defined as Vin = [1 2 3 4], and k=1,V#3 6FH Vo = 1 + 2 + 3 + 4 = 10.*8' @H*' @H( % H(2% H7 i1liSummer42$  Description:Q%i, (J@HSummer (+/-)Summer with 2 input3!% HParameters:Z4 8@HGain_1 (+)Gain k1 of the positive input Gain_2 (-)Gain k2 of the negative input (!% HjEA% HThe input of a 2-input summer can be either a scalar or a vector. (i% HiDA% HIf the inputs are scalar, the output of the summer is defined as:b'i4; DOHVo = k1 * Vin,1 + k2 * Vin,2where Vin,1 and Vin,2 are the positive and negative input, respectively.If the inputs are vector, letVin,1 = [a1 a2 a3 ... an]Vin,2 = [b1 b2 b3 ... bn]thenVo = k1 * Vin,1 + k2 * Vin,2 = [k1*a1+k2*b1 k1*a2+k2*b2 ... k1*an+k2*bn]*^' @H*4' @H(^% H(% H71nmF Summer4C$  Description:Q%, (J@HSummer (+/+)Summer with 2 input3C% HParameters:OL6 <@HGain_1Gain k1 of the first input Gain_2Gain k2 of the second input yT% HIn the default upright position, the input on the middle left is the first input.(L% HjEW % HThe input of a 2-input summer can be either a scalar or a vector. ( % HiDW  % HIf the inputs are scalar, the output of the summer is defined as:^% F 9 @KHVo = k1 * Vin,1 + k2 * Vin,2where Vin,1 and Vin,2 are the positive and negative input, respectively.If the inputs are vector, letVin,1 = [a1 a2 a3 ... an]Vin,2 = [b1 b2 b3 ... bn]thenVo = k1 * Vin,1 + k2 * Vin,2 = [k1*a1+k2*b1 k1*a2+k2*b2 ... k1*an+k2*bn]7 } 1n} [Summer6F  &  HDescription:U)}  , (R@HSummer (3-input)Summer with 3 input3 ; % HParameters:u  ? N@HGain_1Gain k1 of the first input Gain_2Gain k2 of the second input Gain_3Gain k3 of the third input O*; > % THThe output of the summer is defined as: [, &HVo = k1 * Vin,1 + k2 * Vin,2 + k3 * Vin,3where Vin,1, Vin,2, and Vin,3 are the first, second, and the third input, respectively. The input with a dot is the first input.Note that the input of the 3-input summer can only be a scalar.5> 1o@MUX26[&  HDescription:X-+ &Z@HMultiplexer (2-input)2-input multiplexer(F% H2 x( HImage:2F. , H">;x @% ,HThe truth table is: @[(4@% Hq @@2 4H s0Y-------------0d01d1Note that the input d0 and d1 can be either an analog or a digital signal.54@ A1up ALCMUX46@BA&  HDescription:X- AA+ &Z@HMultiplexer (4-input)4-input multiplexer(BAA% H2 AA( HImage:2A&B. , H"?;AaB% ,HThe truth table is:(&BB% HaBLC> J H s1s0Y------------------------00d001d110d211d3Note that the input can be either analog or digital signals.5BC1qCdFMUX86LCC&  HDescription:X-CD+ &Z@HMultiplexer (8-input)8-input multiplexer(C7D% H2 DiD( HImage:27DD. , H"@;iDD% ,HThe truth table is:(DD% H_4D]E+ &hH s2s1s0Y-----------------------------------5 DE* $@H000d0]EdFK dH001d1010d2011d3100d4101d5110d6111d7Note that the input can be either analog or digital signals.8EF1,rFHFilters1 dFF& HFiltersKFH` @HqK7K77J7J72nd-order Low-pass Filter2nd-order low-pass filter2nd-order High-pass Filter2nd-order high-pass filter2nd-order Band-pass Filter2nd-order band-pass filter2nd-order Band-stop Filter2nd-order band-stop filter(F@H% H(HhH% H(@HH% H@hHH19sHKLow-Pass Filter4HI$  Description:d8HhI, (p@H2nd-order Low-pass Filter2nd-order low-pass filter3II% HParameters:hIJi @H   GainGain k Damping RatioDamping ratio Cut-off FrequencyCut-off frequency fc, in Hz (fc=c/2)b=IJ% zHThe transfer function of the 2nd-order low-pass filter is:@ J%K5 :H"A*JOK' @H*%KyK' @H(OKK% H(yKK% HAK L18t LOHigh-Pass Filter4K>L$  Description:f: LL, (t@H2nd-order High-pass Filter2nd-order high-pass filter3>LL% HParameters:LMc @H   GainGain k Damping RatioDamping ratio Cut-off FrequencyCut-off frequency fc, in Hz (fc=c/(2 ))c>LN% |HThe transfer function of the 2nd-order high-pass filter is:A M]N5 :H"B *NN' @H*]NN' @H(NN% H(NO% HANBO1uBOBand-Pass Filter4OvO$  Description:f:BOO, (t@H2nd-order Band-pass Filter2nd-order band-pass filter3vO% HOOParameters:Oc 1@H    GainGain k Center FrequencyCenter frequency fo, in Hz (fo = o / (2 ))Passing BandFrequency width fb of the passing band, [ q; F@PH  in Hz (fb = B / (2 )) *' @Hc>q% |HThe transfer function of the 2nd-order band-pass filter is:@ >5 :H"C*h' @H*>' @H(h% H(% HA#1v#Band-Stop Filter4W$  Description:g;#, (v@H2nd-order Band-stop Filter 2nd-order band-stop filter3W% HParameters:c 5@H    GainGain k Center FrequencyCenter frequency fo, in Hz (fo = o / (2 ))Stopping BandFrequency width fb of the stopping band, [ I; F@PH  in Hz (fb = B / (2 )) *s' @Hc>Iօ% |HThe transfer function of the 2nd-order band-stop filter is:C s6 <H"D *օC' @H*m' @H(C% H(m% H@1.wFunction Blocks74$ &Function Blocks/P#p^J (} (Absolute ValueAbsolute function blocku%4(P#pJJ (㓎 CosineCosine function block5P#pjJ ( (Cosine InverseCosine inverse function blockh(P#p0J ( DividerDivider5P#pjJ (ㅞ .Exponential (a^x)Exponential function block~.P#p\J (㼢 FFTFast Fourier Transformation block/P#p^J ( |" &dv/dt LimiterGradient (dv/dt) limiter>%P#p|J ( @2-dimensional Lookup Table2-dimensional lookup tableBM#jJ (E0*<Lookup Table (Trapezoid)Trapezoidal waveform lookup table:%;M#jtJ (0*6Lookup Table (square)Square waveform lookup table~1M#jbJ (@$ 6Multiplexer (2-input)2-input multiplexer~1;7M#jbJ (@$ 6Multiplexer (4-input)4-input multiplexer~1M#jbJ (@$ 6Multiplexer (8-input)8-input multiplexern7#P#p<J (>$  MultiplierMultipliery)P#pRJ (E "Power (x^a)Power function block2#P#pdJ ( RMSRoot-mean-square (RMS) function blockz*P#pTJ (Mײ RoundoffRound-off function block}-!P#pZJ (* ,Sampler-and-holdS!ampling/hold blockm M#j@J (.+SignSign function blockw'!P#pNJ ( SineSinusoidal function block/P#p^J (J "Square RootSquare-root function block}-P#pZJ (oß?  Time DelayTime delay function blockDP#pJ (@q @s-domain Transfer Functions-domain transfer function block`EP#pJ (z@ Hs-domain Transfer Function (1)s-domain transfer function block with initial conditions7P#pnJ (T, *Tangent InverseTangent inverse function block2ENP#pdJ (  THDTotal-Harmonic-Distortion (THD) blockB3 6@H(N% H(% H41xzABS4H$  Description:Y,- *X@HAbsolute ValueAbsolute function blocklGH % HThe output of the block is equal to the absolute value of the input.)6% H ( ^% H(6% H(^% H(% H*' @H**' @H(R% H(*z% H5R1+ySIGN4z$  Description:aDD#X:J SignSign function block*n& @DSV z     The output of the sign function block Vo is the sign of the input Vin. For example, if Vin=5,Vo=1; and if Vin=-5, Vo=-1.*n}& @(S$ 7}1zWCosine4$  Description:O"_- *D@HCosineCosine function blocksN% HThe input of the cosine function block is in degree. The output is equal toA_% 8Hthe cosine of the input. (;% H(c% H(;% H(c% H*' @H*' @H(/% H(W% H?/1{Cosine inverse4W$  Description:_2)- *d@HCosine InverseCosine inverse function blockuP% HThe output is equal to the cosine inverse of the input, and it is in degree. ()% H(% H(% H(>% H*h' @H*>' @H(h% H(% H51|Sine4K$  Description:K- *<@HSineSine function blockqLK% HThe input of the sine function block is in degree. The output is equal to?R% 4Hthe sine of the input. (z% H(R% H(z% H(% H*' @H*F' @H(n% H(F% H= n1}@Sine inverse4$  Description:Y-`, (Z@HSine InverseSine inverse function blocksN% HThe output is equal to the sine inverse of the input, and it is in degree. )`% H ($% H(L% H($t% H(L% H*t' @H*' @H(% H(@% H4t1~tTan4@$  Description:O#t, (F@HTangentTangent function blocktOk% HThe input of the tangent function block is in degree. The output is equal toB% :Hthe tangent of the input. (k% H(% H(%% H(M% H*%w' @H*M' @H(w% H(% H@11w1h Tangent inverse4e$  Description:_31, (f@HTangent InverseTangent inverse function block2 e( HImage:4*0 0 @H"E*T' @HuP*% HThe output is equal to the tangent inverse of the input, and it is in degree.(T% HhCY % HThe output is the arc tangent of the ratio between the imaginaryk4 7 >hH  input Vimag and the real input Vreal, i.e. (Y  % H8 $ 0 0H"F. ( L % H($ t % H(L  % H(t  % H*  ' @H*  ' @H( @ % H( h % H; @  1F Multiplier4h  $  Description:F  , (4@HMultiplierMultipliere@  % HThe input of a multiplier can be either a scalar or a vector.(  % HP+  % VHIf the inputs are scalar, the output is:g  c H"G"H"I"J"KIf the inputs are vectors, let:thenwhere means that the vector is transposed.(  % H0 % HExample:( D% Hm67 >lH  If Vin,1 = [1 2 3], Vin,2 = [2 3 4], thenY%D 4 8JH Vo = 1x2 + 2x3 + 3x4 = 20*4' @H* ^' @H(4% H(^% H8 @1( @ADivider @4@@$  Description:B @@- **@HDividerDivider2 @@@( HImage:4@@0 0 @H"LrM@ZA% HThe output of a divider is equal to the division of the two input signals.(@A% H(ZAA% H(AA% H(AA% HBAH "Tflag is 1, the output is equal to the integer part of Vscale divided by . If the truncationaf7 >H "Uflag is 0, the output is equal to Vscale rounded off to nearest integer, then divided by .(% H6( HExample: (% H_#|< HF@H   Vin=34.5678, N=0, Tflag=08 - *@H Vo=35.*|ފ' @H_#=< HF@H   Vin=34.5678, N=0, Tflag=18 ފu- *@H Vo=34.*=' @H_#u< HF@H   Vin=34.5678, N=1, Tflag=19 7- *@H Vo=34.5*a' @H`$7< HH@H   Vin=34.5678, N=-1, Tflag=18 a- *@H Vo=30.*#' @H*M' @H(#u% H(M% H4uэ1э[FFT4$  Description:o+эtD#XVJ  FFTFast Fourier Transform (FFT) block(% @0 t̎& Image:2. , @"V1̎/# Parameters:=D#XzJ "No. of SamplesNo. of samples N in one fundamental cycleu1/1D#XbJ *Sampling Fr1equencySampling frequency, in Hz0a* $ @HpK1% HThe FFT block calculates the fundamental component of the input. The FFTjEa;% Halgorithm is based on the radix-2/decimation-in-frequency method. (c% HpB;. ,H"WThe number of the samples in one fundamental period should be xMcK+ &H where N is an integer. The maximum number of sampling points allowed is -x% H1024.(K% HyTx% HThe output gives the amplitude (peak) and the phase angle (in deg.) of the input >W% 2Hfundamental component.(% H4 W( HExample:(% H{PV+ &H If the input is 100sin(t), the output will be: Amplitude = 100; Angle = 0.\1 2H If the input is 100sin(t+/6), the output will be: Amplitude = 100; Angle = 30. deg.(V % H(3% H( [% H531HLKUP4[$  Description:J, (<@HLookup TableLookup table3A% HParameters:b7+ &n@HFile NameName of the file storing the lookup table(A% HuP@% HThe lookup table stores two data arrays in a file, one for the input and the d?% ~Hother for the output. The format of the table is as follows:(@% HL6 <,@H  Vin(1), Vo(1)Ld6 <,@H  Vin(2), Vo(2)L6 <,@H  Vin(3), Vo(3)3 d' @H L/6 <,@H  Vin(n), Vo(n)*Y' @H}O/. ,H The input array Vin must be monotonically increasing. Between two points,uPYK% Hlinear interpolation is used to obtain the output. For example, if the input aI bH     Vinput is greater than Vin(k) but less than Vin(k+1), the output will be equal to:#Kr eH"X    If the input is less than Vin(1) or greater than Vin(n), the output will be clampedto Vo(1) or Vo(n).Note that the lookup table can be used in both the power circuit and control circuit.Example:The following shows a lookup table:1., 10.2., 30.3., 20.4., 60.5., 50.If the input is 0.99, the output will be 10. If the input is 1.5, the output will be10 + (30 - 10) x (1.5 - 1) / (2 - 1) = 20.0H) "H81LKUP_TZ6H&  HDescription:?9D#X~J 6Lookup Table (trapezoid)Trapezoidal waveform lookup table(a% @19# Parameters:Ja D#XJ *Rising Angle thetaThe rising angle from 0 to the peak value, in deg.r.D#X\J Peak ValueThe peak value of the waveform  h K  "YThe Hrelationship between the input Vin and the output Vo of the trapezoidal waveform lookuptable is shown as follows:The input Vin of the lookup table block is in degree. The range of the input value can be from-360 deg. to 360 deg. The waveform is half-wave and quarter-wave symmetrical.Example:Let =30 and the peak value of the waveform be 10, if Vin=15, Vo will be 5. If Vin=90, Vo=10..' 81LKUP_SQ4D$  Description:{7D#XnJ 0Lookup Table (square)Square waveform lookup table(D% @1# Parameters:ND#XJ *Pulse Width (deg.)The one-time width of the pulse in half cycle, in deg.] u"Z  The relationship between the input Vin and the output Vo of the square waveform lookuptable is shown as follows:where theta is the pulse width. The input Vin of the lookup table block is in degree. The range of the input value can be from -360 deg. to 360 deg. The waveform is half-wave and quarter-wave symmetrical.Example:Let =120, Vo=0 when Vin is from 0 to 30 deg., and Vo=1 when Vin is from 30 to 150. deg. .' 7%1 % @LKUP2D4Y$  Description:f:%, (t@H2-dimensional Lookup Table2-dimensional lookup table3Y% HParameters:b7T+ &n@HFile NameName of the file storing the lookup table(|% HoJT% HThe 2-dimensional lookup table has two input and one output. The outputrM|]% Hdata is stored in a 2-dimensional matrix. The two input correspond to the pK% Hrow and column indices of the matrix. For example, if the row index is 3P]N 1 2H  and the column index is 4, the output will be A(3,4) where A is the data 0 ~ % Hmatrix. (N  % HqL~  % HThe data for the lookup table are stored in a file and have the following/ F % Hformat:* p ' @H2F  * $@H m, nX"p  6 Hrest of the sampling period.(|BB% H{VBcC% HNote: This block is treated as a continuous-domain element, not a discrete element.`BC1 2HOne other difference between Sample-and-Hold and the discrete element Zero-Order Hold is_cC~D+ &Hthat the sampling moment can be controlled in Sample-and-Hold, whereas the sampling momentL!CD+ &BHin Zero-Order Hold is fixed.(~DD% HyNDkE+ &HFor digital control or discrete circuits, Zero-Order Hold should be used.(DE% H(kEE% H(EE% H(E F% H(E3F% H* F]F' @H*3FF' @H(]FF% H(FF% HAFG1GITime delay block4FLG$  Description:JGG+ &>@HTime DelayTime delay block(LGG% H3GG% HParameters:O$G@H+ &H@HTime DelayTime delay, in second(GhH% HsN@HH% HA time delay block delays the input waveform by a specified amount of time sNhHNI% Hinterval. It can be used to model the propagation delay of a logic element.(HvI% H(NII% H4vII1oI4THD4IJ$  Description:\/IbJ- *^@HTHDTotal Harmonic Distortion (THD) block(JJ% H2 bJJ( HImage:4JJ0 0 @H"[3J#K% HParameters:DJKD#XJ 0Fundamental FrequencyFundamental frequency of the input, in Hz=#K,LD#XzJ Passing BandPassing band of the band-pass filter, in Hz,KXL( @HkF,LL% HFor an ac waveform that contains both the fundamental and harmonic pKXL3M% Hcomponents, the total harmonic distortion of the waveform is defined as:L9OM huH"\  where V1 is the fundamental component and Vrms is the overall rms value of the waveform. A 2nd-order band-pass filter is used to extract the fundamental component. The center frequency (fundamental frequency) and the passing band of the filter are the parameters that need to be specified.For the THD block, the output terminal with a dot is for the THD valueand the other is for the fundamental component of the input.03MiO) "H*9OO' @H*iOO' @H(O % HO I(O4% H6 j1bjTFCTN44$  Description:@j"D#XJ :s-domain Transfer Functions-domain transfer function block(J% @1"{# Parameters:q-JD#XZJ Order nOrder n of the transfer functionu+{aJ#dVJ " GainGain k of the transfer functionKh#J ::*  Coeff. B0BnCoefficients of the nominator (from Bn to B0)MaɃh#J ::*  Coeff. AnA0Coefficients of the denominator (from An to A0)(% @oKɃ`$ A s-domain transfer function block is expressed in polynomial form as: ;K dH"]"^ The initial values of the function block are zero. Use the block TFCTN1 if you need to specify the initial conditions of the function block.Example:The following is a 2nd-order transfer function: The specifications are:^`RY @H    Order n2 Gain1.5 Coeff. BnB00. 0. 400.Coeff. AnA01. 10. 400.(z% H(R% H(zʆ% H(% H*ʆ' @H*F' @H(n% H(F% H7n͇1p ͇TFCTN14$  Description:\͇D#XJ Bs-domain Transfer Function (1)s-domain transfer function block with initial conditions(Ɉ% @1# Parameters:q-ɈkD#XZJ Order nOrder n of the transfer functionu+J#dVJ " GainGain k of the transfer functionKkh#J ::*  Coeff. BnB0Coefficients of the nominator (from Bn to B0)MHh#J ::*  Coeff. AnA0Coefficients of the denominator (from An to A0)W\#J ..6Initial Values xnx1Initial values of the state variables (from xn to x1)(H#% @oK$ A s-domain transfer function block is expressed in polynomial form as: #j3 4MH"_Let Y(s) = G(s) * U(s) where Y(s) is the output and U(s) is the input, we can convert the s-domain expression into the differential equation form as follows:40 0 @H"`(jƍ% HqL7% HThe corresponding output equation in the time domain can be expressed as:]ƍ_ H"a     The initial values of the state variables xn to x1 are specified at the input.Example:The 1st-order transfer function G(s) = 1.5 * (0.01 s + 1) / (0.1 s + 1) has an initial state variable value of 25. The specifications will be:(7% Hvl @H      Order n1 Gain1.5 Coeff. BnB00.01 1Coeff. AnA00.1 1Initial Values xn..x125(% HC% <HMore on Initial Conditions:(=% Hp P nAH      The initial output of a block is determined by the initial value of the state variable xn and the initial input u. For the first-order transfer function G(s) = Bo / (s + A0), for example, if the initial value of the state variable x1 is x1(0), the initial output will be:(=% HB0 0$@H y(0) = x1(0)*A' @H:Y AH      If the transfer function is G(s) = (B1 s + B0) / (s + A0), and the initial value of the state variable is x1(0), the initial output will be:MA? NH y(0) = x1(0) + B1 * u(0)where (0) is the input initial value.?:1 Logic Elements8=& $HLogic ElementsfM#j2J (ּ\AND GateAND gate~1=!M#jbJ (ּ\0AND Gate (3-input)AND gate with 3 inputsdM#j.J (F_OR GateOR gate|/!M#j^J (F_.OR Gate (3-input)OR gate with 3 inputsfgM#j2J (/XOR GateXOR gatefM#j2J (>NOT GateNOT gatehg5M#j6J (=걀NAND GateNAND gatefM#j2J (㔻&>NOR GateNOR gate|/5M#j^J (so+2Set-Reset Flip-FlopSet-Reset flip-flopo"M#jDJ (Q $JK Flip-FlopJ-K flip-floplM#j>J ()"D Flip-FlopD flip-flopx+jM#jVJ ($ MonostableMonostable multivibratorAM#jJ (O6Controlled MonostableControlled monostable multivibrator|/jtM#j^J (d'2Pulse Width CounterPulse width counter~1M#jbJ (8~6A/D Converter (8-bit)8-bit A/D converter3trM#jfJ (8~8A/D Converter (10-bit)10-bit A/D converter~1M#jbJ (8~6D/A Converter (8-bit)8-bit D/A converter3rpM#jfJ (8~8D/A Converter (10-bit)10-bit D/A converter,( @H,p'  H91  AND gate67&  HDescription:vB4 8@HAND GateAND gateAND Gate (3-input)AND gate with 3 inputs(7% H[60% lHThe output is the AND of the input logic signals. *Z' @H*0' @H(Z% H( % H 8D1zDOR gate4 x$  Description:g4D3 6h@HOR GateOR gateOR Gate3OR gate with 3 inputs(x% HY4`% hHThe output is the OR of the input logic signals. (% HP+`% VHThe truth table of a 2-input OR gate is:(% H440 0 @H"b*^' @H(4% H9^1cXOR gate4$  Description:I<+ &<@HXOR Gateexclusive-OR gate(d% HS.<% \HThe truth table of an exclusive-OR gate is:(d% H* ' @H(1% H2 c. , H"c911>NOT gate4c$  Description:B, (,@HNOT GateNOT gate(:% H`;% vHThe output is the inversion of the input logic signal. *:' @H*' @H(% H(>% H: x1`xNAND gate4>$  Description:Bx+ &.@HNAND GateNAND gate(% H`;v% vHThe output is the NAND of the two input logic signals. (% H9v1\NOR gate4 $  Description:@K+ &*@HNOR GateNOR gate( s% H_:K% tHThe output is the NOR of the two input logic signals. (s% H5/ 1/  SRFF4c $  Description:p,/  D#XXJ ,Set-Reset Flip-FlopSet-Reset Flip-Flop3c  $ Parameters:F  D#XJ Trigger FlagTrigger flag (0: edge-triggered; 1: level-triggered) A ( A set-reset flip-flop can be either edge-triggered or level-triggered.The truth table of an edge-triggered set-reset flip-flop is:0 q , ( "d8A  ' "Px: do not care&q  # pF ? * $H The truth table of a level-triggered set-reset flip-flop is:2 q . , H"e(?  % H5q  1P JKFF4  $  Description:I K + &<@HJK Flip-FlopJ-K flip-flop( s % HT/K  % ^HThe truth table of a J-K flip-flop table is:(s  % H( % H2 I. , H"f(q% H(I% H(q% H(% H51@D_FF4R$  Description:F+ &6@HD Flip-FlopD flip-flop(R% HR-@% ZHThe truth table of a D fli@p-flop table is:g0@7 >`HDClockQQn00 -> 10110 -> 110(@@%  H(@@% H5@ A1 ACMONO4@>A$  Description:R' AA+ &N@HMonostableMonostable multivibrator(>AA% H3AA% HParameters:W,ABB+ &X@HPulse WidthOn-time pulse width, in sec.(AjB% HtOBBB% HThe positive (or negative) edge of the input signal triggers the monostable.qLjBOC% HA pulse, with the specified pulse width, will be generated at the output.0BC( H 6OCC1sCEMONOC6CC&  HDescription:h=CSD+ &z@HControlled MonostableControlled monostable multivibrator(C{D% HvQSDD% HThe controlled monostable multivibrator allows the pulse width to be specifieduP{DfE% Hexternally. The node at the bottom of block is for the input that defines the4DE% Hpulse width.(fEE% H0EE( H 5E'F1P'FBIPWCT6E]F&  HDescription:V+'FF+ &V@HPulse Width CounterPulse width counter(]FF% HnIFIG% HThe pulse width counter measures the width of a pulse. The rising edgexSFG% Hof the input activates the counter. At the falling edge of the input, the outputP+IGH% VHgives the width of the pulse, in second.(G9H% HvQHH% HDuring the interval of two falling pulse edges, the pulse width counter output;9HH% ,Hremains unchanged. (HI% H0HBI( H 4IvI1vIMADC6BII&  HDescription:vIJE Xm@HA/D Converter (8-bit)8-bit A/D converterA/D Converter (10-bit)10-bit A/D converterD/A Converter (8-bit)8-bit D/A converterD/A Converter (10-bit)10-bit D/A converter2 IJ( HImage:4J K0 0 @H"gUJK+ &H Let N be the number of bits, for the A/D converter, the output is calculated as:( KK% HgKGL+ &H For example, if Vref = 5 V, Vin = 3.2 V, N = 8 bits, Vo = 256/5*3.2 = 163.84 = 10100011 (binary). (KoL% H[6GLL% lHFor the D/A converter, the output is calculated as:(oLL% HdLM+ &H For example, if Vref = 5 V, Vin = 10100011 (binary) = 163, N = 8 bits, Vo = 163/256*5 = 3.1836.(LM% H(MM% HLMN1NÅQuantization function block4MQN$  Description:5NNJ#djJ5  ,Quantization BlockQuantization function block7QNO'  Parameters:j NqOJ#d@J5  No. of BitsNo. of bits N{1O J#dbJ5  Vin (min)Lower limit of the input Vin_minqO Ms/qOD#X^J5 Vin (max)Upper limit of the input Vin_maxr. D#X\J5 Vo (min)Lower limit of the output Vo_minr.cD#X\J5 Vo (min)Upper limit of the output Vo_max9J#drJ5  ,Sampling FrequencySampling frequency of the block,c( @HpK% HThe quantization block performs two functions: scaling and quantization.(% H|W&% HThe input value Vin, sampled at the given sampling frequency, is first scaled based 9_% (Hon the following:P&2 4H"hThe no. of bits determines the output resolution dV which is defined as:I_Å H"i        "j The output Vo will be equal to the truncated value of Vox based on the resolution dV.Example:if N=4, Vin_min=0; Vin_max=10; Vo_min=-5, Vo_max=5; and Vin=3.2: The value -1.8 is between -2.33332 and -1.66665. The lower value is selected, that is,Vo = -1.66665. : 1PZOH block6Å3&  HDescription:N#+ &F@HZero-Order-HoldZero-order hold(3% H7( HParameters:a6A+ &l@HSampling FrequencySampling frequency of the block(i% HrMAۇ% HThis is a zero-order sampling/hold block (ZOH). The ZOH samples the input uPiP% Hat the beginning of a clock cycle, and holds the sampled value until the next4ۇ% Hclock cycle.(P% HqL% HThe difference between the element ZOH and the sampling/hold element SAMP~Y% His that, while the clock is provided externally in SAMP, the clock is free-running for,lj% HZOH.(% HyTljh% HFor example, if the sampling frequency of ZOH is 1000, the sampling will occur atH#% FH0., 0.001 sec., 0.002 sec., etc.(h؊% H(% H(؊(% H(P% HA(1Unit delay block4Pŋ$  Description:L , (@@HUnit DelayUnit delay block(ŋ9% H3l% HParameters:j99֌1 2r@HSampling FrequencySampling frequency of the block (l% Hd?֌b% ~HA unit delay block delays the input by one sampling period. (% H(b% H(ڍ% H(% H4ڍ61~6I_D4j$  Description:x.6J#d\J5  .Discrete IntegratorDiscrete integrator(j % @1;# Parameters:z M#jJ5  "$Algorithm FlagFlag for integration algorithm 0: trapezoidal rule 1: backward Euler 2: forward Euler;z0;J#d`J5  0Initial Output ValueInitial output value>J#d|J5  ,Sampling FrequencySampling frequency of the integrator(8% @( If we define u(t) as the input, y(t) as the output, T as the sampling period,and H(z) as the transfer function, in discrete domain, an integrator is expressed as:With Trapezoidal Rule:N)8m% R@y(n) = y(n-1) + T/2 * (u(n) + u(n-1)) (#  orH"m& DHH(z) = T/2 * (z + 1) / (z - 1)*' @H<C% .HWith Backward Euler:(k% HCC' 8@Hy(n) = y(n-1) + T * u(n) Dk' :HorH(z) = T * z / (z - 1)*' @H;W% ,HWith Forward Euler:(% HEW' <@Hy(n) = y(n-1) + T * u(n-1) @' 2HorH(z) = T / (z - 1)*.' @H*X' @H(.% H: X1 #I_RESET_D4$  Description:BzJ#dJ5  BResetable Discrete IntegratorDiscrete resetable integrator(% @1z# Parameters:zM#jJ5  "$Algorithm FlagFlag for integration algorithm 0: trapezoidal rule 1: backward Euler 2: forward Eulerz0J#d`J5  0Initial Output ValueInitial output value<J#dxJ5  Reset Flagreset flag (0: edge reset; 1: level reset)>"J#d|J5  ,Sampling FrequencySampling frequency of the integrator9 [, &The output of the resetable integrator can be reset through an external control signal (at the bottom of the block). For the edge reset (reset flag = 0),the integrator output is reset to zero at the rising edge of the control signal.For the level reset (reset flag = 1), the integrator output is reset to zero as longas the control signal is high (1).If we define u(t) as the input, y(t) as the output, T as the sampling period,and H(z) as the transfer function, in discrete domain, the integrator is expressed as:@"% 6With Trapezoidal Rule:M([% P@y(n) = y(n-1) + T/2 * (u(n) + u(n-1))(#  orH"X& DHH(z) = T/2 * (z + 1) / (z - 1)*' @H<X% .HWith Backward Euler:(% HC)' 8@Hy(n) = y(n-1) + T * u(n) Dm' :HorH(z) = T * z / (z - 1)*)' @H;m% ,HWith Forward Euler:(% HE?' <@Hy(n) = y(n-1) + T * u(n-1) @' 2HorH(z) = T / (z - 1)*?' @H*' @H(% H(#% H4W1W.D_D4#$  Description:6WJ#dlJ5  6Discrete DifferentiatorDiscrete differ#entiator(?% @1p# Parameters:v,?J#dXJ5  ,Sampling FrequencySampling frequency(p% @& UIf we define u(t) as the input, y(t) as the output, T as the sampling period,and H(z) as the transfer function, in discrete domain, a differentiator is expressed as:B % :@y(n) = (u(n) - u(n-1)) / T(H#  orB ' 6HH(z) = 1/T * (z-1) / z*H' @H*' @H(% H(.% H8f1fFTFCTN_D4.$  Description:Bf&J#dJ5  <z-domain Transfer Functionz-domain transfer function block(N% @1&# Parameters:y/NJ#d^J5  Order NOrder N of the transfer functionAJ#dJ5   Coeff. b0bNCoefficients of the nominator (from b0 to bN)AD#XJ5 Coeff. a0aNCoefficients of the denominator (from a0 to aN)v,~J#dXJ5  ,Sampling FrequencySampling frequency(% @S/~$ ^A transfer function block is expressed as: j> LH"k"lIf a0 = 1, the output y and the input u can be expressed by the following difference equation:+' @H.*' @H(% H(F% H; 1 PFILTER_FIR4F$  Description:65 J#dlJ5  FIR FilterFIR (finite impulse response) filterz0 J#d`J5  $FIR Filter (1)FIR filter with file input(5  % @L! # + &BParameters:For FILTER_FIR:z0  J#d`JG  Order NOrder N of the transfer function B# ) J#dJG   Coeff. b0bNCoefficients of the nominator (from b0 to bN) :  J#dtJG  ,Sampling FrequencySampling frequency of the filter<)  ' *For FILTER_FIR1:@ m D#XJG .File Name for Coeff.Name of the file storing coefficients :  J#dtJG  ,Sampling FrequencySampling frequency of the filtera<m R % xThe transfer function of a FIR filter is expressed as: 4 S tH"m"n"oThe output y and the input u can be expressed by the following difference equation:For the FILTER_FIR1 block, the order N and the coefficients are stored in a file.The format of the file is as follows:*R ' @H(% H(% H((% H(P% H9(1 LFILTER_D4P$  Description:n$7@J#dHJ5  $7@PDigital FilterDigital filter8@J#dpJ5  ,Digital Filter (1)Digital filter with file input(7@@% @J@+A+ &>Parameters:For FILTER_D:z0@AJ#d`JG  Order NOrder N of the transfer function B+A1BJ#dJG   Coeff. b0bNCoefficients of the nominator (from b0 to bN) BABD#XJG Coeff. a0aNCoefficients of the denominator (from a0 to aN) :1B;CJ#dtJG  ,Sampling FrequencySampling frequency of the filter:BuC' &For FILTER_D1:@;CCD#XJG .File Name for Coeff.Name of the file storing coefficients :uC}DJ#dtJG  ,Sampling FrequencySampling frequency of the filtermHCD% The transfer function of a general digital filter is expressed as: H}D2FP nH"p"q"rIf a0 = 1, the output y and the input u can be expressed by the following difference equation:For the FILTER_FIR1 block, the order N and the coefficients are stored in a file. The format of the file can be one of the following:*D\F%  Horj*2FG@ NWH"sWhen denominator coefficients are non zero, this type of filter is also called IIR (infinite impulse response) filter.Example:To design a 2nd-oder low-pass Butterworth filter with the cut-off frequency fc = 1 kHz, assuming the sampling frequency fs = 10 kHz, using MATLAB, we have:E\F H' <@HNyquist fn = fs / 2 = 5 kHzb;GmH' v@HNormalized cut-off frequency fc* = fc / fn = 1 / 5 = 0.2A HH' 4@H[B, A] = butter(2, fc*)(mHH% H;HI% ,Hwhich will give us:dHI) "HB = [ 0.0201 0.0402 0.0201] = [b0 b1 b2]A = [ 1 -1.561 0.6414] = [a0 a1 a2](II% HM(IJ% PHThe transfer function in z domain is:IK: BH"tThe input-output difference equation is:y(n) = 0.0201 u(n) + 0.0402 u(n-1) + 0.0201 u(n-1) + 1.561 y(n-1) - 0.6414 y(n-2)The parameter specification of the filter in PSIM will be:yJK2 4@HOrder N2 Coeff. b0bN0.0201 0.0402 0.0201Coeff. a0aN1. -1.561 0.6414Sampling frequency10000.(KK% HKLB RHIf the coefficients are read from a file, the content of the file is as follows:20.02010.04020.02011.-1.5610.6414or the content can be:20.020110.0402-1.5610.02010.64149K%M1%MC_BUFFER6L[M&  HDescription:p&%MMJ#dLJ5  &Circular BufferCircular buffer([MM% @1M$N# Parameters:6MNJ#dlJ5  "Buffer LengthThe length of the circular bufferv,$NOJ#dXJ5  ,Sampling FrequencySampling frequency(NBO% @9O6 :A circular buffer stores data in a buffer. When it reaches the end of the buffer, it willstart again from the beginning.The value ofBOL the memory location can be accessed using the memory read block (MEMREAD).Example:Assume a circular buffer has a buffer length of 4 and sampling frequency of 10 Hz, wehave:Time Input Value at Memory Location 1 2 3 4---------------------------------------------------------------------------wMBO* "0. 0.11 0.11 0. 0. 0.0.1 0.22 0.11 0.22 0. 0.0.2 0.33 0.11 0.22 0.33 0.0.3 0.44 0.11 0.22 0.33 0.44 0.4 0.55 0.55 0.22 0.33 0.44 ... ... ... (&% @,R&  *&|& @(R$ 6|ڃ1ڃARRAY4$  Description:o%ڃ}J#dJJ>  Array1-dimensional data arrayE J#dJ>  Array (1)1-dimensional data array (with the data from a file)(}4% @G {+ &8Parameters:For ARRAY:z04J#d`J>   Array LengthThe length of the data arrayk!{`J#dBJ>  ValuesValues of the array(% @5`& For ARRAY1:LSJ#dJ>  2File for CoefficientsThe name of the file that stores the data array ) IThis is a 1-dimensional array. The output is a vector, not a scalar. For ARRAY1, the data array is stored in a text file. The file has the following format:oS[ +H"uwhere N is the number of points. Example:To define the array c = [2 4 6 8], we will have:For ARRAY:Array length:4Values:2 4 6 8For ARRAY1:File for Coefficients:test.tblThe file test.tbl will have the following content:42.4.6.8.* ' @H51mCONV4"$  Description:n$J#dHJ>  ConvolutionConvolution block("% @jG% The output of the block is the convolution of the two input vectors. If Input A and B are defined as:J > LH"v"wm$GI bLH"x"ythenwhereExample:(&% HO= JH    If A = [1 2 3] and B = [4 5], we have the convolution of A and B as:A&( 2H C = [ 4 13 22 15 ].*' @H(E% H(m% H8E1s;MEMREAD4mٍ$  Description:n$GJ#dHJ  Memory ReadMemory read block(ٍo% @1G# Parameters:Co-J#dJ,  .Memory Index OffsetOffset from the starting memory location(U% @P-< F This block allows users to access the memory location of a vector output (such asconvolution block, vector Umarray, circular buffer). The index offset defines the offsetfrom the starting memory location.Example:If A = [2 4 6 8], when offset = 0, the memory read block output is 2. When theoffset is 2, the output is 6.(U% @&;# 6q1qUSTACK4;$  Description:bqJ#d0J  StackStack block(/% @1`# Parameters:h/J#d<J5  Stack DepthStack Depth(`% @e=U( {A stack is a first-in-last-out register. The rising edge triggers the push or pop action. When a pop action is performed and the stack is empty, the output remains unchanged. When a push action is performed and the stack is already full, the data at the bottom of the stack will be pushed out and will be lost.61Other- U$ OtherD( 8POther elements include: &"# ~.P#p\JF (@ 0Switch ControllersSwitch controllers|,"P#pXJF (I A SensorsVoltage and current sensorsz*P#pTJF ([Dy ProbesVoltage and current probes~.P#p\JF (rR *Function BlocksOther function blocksDP#pJF (B @Control-to-power InterfaceControl-to-power interface blockJD#X JF  fXP#p,JF (wEЀ GroundGround1P#pbJF (㯺꿀  Ground (1)Ground with a different image1XZP#pbJF (㯺꿀  Ground (2)Ground with a different image8P#ppJF (Hj .FILEFile that stores element parameter valuesBZtP#pJF (j& .ACSWEEPSetup for ac sweep (frequency response analysis)~.P#p\JF (y ".PARAMSWEEPSetup for parameter sweep*t& HFb1qbOther Function Blocks?& 2HOther Function BlocksM#b* $FPHOther function blocks include: (% H0P#p`JF ( 馀 ABC2DQOabc-to-dqo transformation block0P#p`JF (ơ# DQO2ABCdqo-to-abc transformation blockr"P#pDJF (n" $Lookup TableLookup tablez*P#pTJF (H>T &Math FunctionMath function block6P#plJF (H>T .Math Function (2)2-input math function block6P#plJF (H>T .Math Function (3)3-input math function block6P#plJF (H>T .Math Function (5)5-input math function block8(P#ppJF (H>T 0Math Function (10)10-(input math function block8P#ppJF (j DLL_EXT1External DLL block (1 input, 1 output):(:P#ptJF (j DLL_EXT3External DLL block (3 inputs, 3 outputs):P#ptJF (j DLL_EXT6External DLL block (6 inputs, 6 outputs)=:QP#pzJF (j DLL_EXT12External DLL block (12 inputs, 12 outputs)=P#pzJF (j DLL_EXT20External DLL block (20 inputs, 20 outputs)=QkP#pzJF (j DLL_EXT25External DLL block (25 inputs, 25 outputs)*& H8k11 ABC2DQO6&  HDescription:=J#dzJ  4ABC-DQO Transformationabc to dqo transformation block(% @e) This block transforms 3-phase abc quantities to dqo quantities. This block can be used in both the power circuit and the control circuit. Note that only the voltage quantities can be transformed used this block. To transform current quantities, they must first be converted to voltage quantities using current-controlled voltage sources.The transformation equations from abc to dqo are:F = JH"z"{ 9e3 6@H "| ( % Hf+ &H The angle X, in rad., is specified externally through the input node at the bottom of the block. ( % H(% H1 % HExamples:(F% He:+ &tH Let phases a, b, and c to be symmetrical, and X = wt.(F% Hr5E = JjH    If Va = 10*sin (wt), then Vd = 0, Vq = 10.(m % HAE  C VH    If Va = 10*sin (wt + / 6), then Vd = 5, Vq = 8.66.(m  % HB  C VH    If Va = 10*sin (wt - / 6), then Vd = -5, Vq = 8.66.(  % H8  12  @DQO2ABC4 2 $  Description:=  J#dzJ  4DQO-ABC Transformationdqo to abc transformation block(2  % @  ) This block transforms dqo quantities to abc quantities. This block can be used in both the power circuit and the control circuit. Note that only the voltage quantities can be transformed used this block. To transform current quantities, they must first be converted to voltage quantities using current-controlled voltage sources.The transformation equations from dqo to abc are:y/ J d^H      Va = cosX * Vd + sinX * Vq + VoI T x@H      Vb = cos(X - 2 / 3) * Vd + sin(X - 2 / 3) * Vq + VoI?T x@H      Vc = cos(X + 2 / 3) * Vd + sin(X + 2 / 3) * Vq + Vo(g% Hf? @+ &H The angle X, in rad., is specified externally through the input node at the bottom of the block..g @ 9gE@1YE@dGFCN_MATH4 @y@$  Description:r(E@@J#dPJ  "Math FunctionMath function block~4y@iAJ#dhJ  *Math Function (2)2-input math function block~4@AJ#dhJ  *Math Function (3)3-input math function block~4iAeBJ#dhJ  *Math Function (5)5-input math function block6ABJ#dlJ  ,Math Function (10)10-input math function block(eB C% @1B>C# Parameters:j CCJ#dJ  8Expression f(x1,x2,,xn)Expression of the output versus the input where n is the number of inputs L>CDJ#dJ  *Expression df/dxiThe derivative of the function versus the ith input(CD% @fD>G( The output of a math function block is expressed as the mathematical function of the inputs. With this block, one can implement complex and nonlinear relationship easily and conveniently. Blocks with 1, 2, 3, 5, and 10 inputs are provided.The derivative df/dxi can be set to zero. The variables that are allowed in the expression are: T or t for time, and xi (i from 1 to n) which represents the ith input. For example, for the 3-input math function block, the allowed variables are: T, t, x1, x2, and x3. For the 1-input math function block, the variable x, which refers to the only input, is also allowed.&DdG# 5>GG1G>KCTOP4dGG$  Description:g<G4H+ &x@HControl-to-Power InterfaceControl-power interface block(G\H% HoJ4HH% HIn PSIM, power circuit and control circuit are separated and are solvedpK\H;I% Hsequentially. The control-power interface block allows a control circuitoJHI% Hquantity to be passed unchanged to the power circuit. The output of theuP;IJ% Hinterface block is treated as a constant voltage source in the power circuit.(IGJ% HpKJJ% HBy using this block, some of the functions that can only be generated in_:GJK% tHthe control circuit can be passed to the power circuit.(J>K% H8KvK1vKDLL_EXT4>KK$  Description:EvK3LD#XJ5 ,DLL Block (1-input)External DLL block with 1 input and 1 outputGKLD#XJ5 ,DLL Block (3-input)External DLL block with 3 inputs and 3 outputsG3LIMD#XJ5 ,DLL Block (6-input)External DLL block with 6 inputs and 6 outputsLLMJ#dJ5  0DLL Block (12-input)External DLL block with 12 inputs and 12 outputsLIMuNJ#dJ5  0DLL Block (20-input)External DLL block with 20 inputs and 20 outputs(MN% @1uNN# Parameters:o%N=OJ#dJJ5  File NameName of the DLL file(NeO% @wT=OO# The node assignments for the 3-input-3-output block (DLL_EXT3), for example, are:0eO, ( "O>K}sO# The input pin with a dot is for the first input in[0]. Note that unused input nodes must be connected to ground.(ր% @$$ This block allows the user to write code in C, compile it into DLL, and link it with PSIM. PSIM calls the DLL routine at each simulation time step. However, when the inputs of the DLL block are connected to the output of one of these discrete elements (zero-order hold ZOH, unit delay UDELAY, integrator I_D, differentiator D_D, z-domain transfer function block TFCTN_D, and digital filters), the DLL block is considered as a discrete element. In this case, the DLL block is called only at the discrete times. ր) The DLL block receives the values from PSIM as the input, performs the calculation, and sends the output back to PSIM. The node assignments are: the input nodes are on the left, and the output nodes are on the right. The sequence is from the top to the bottom.The name of the DLL file can be arbitrary. The DLL file, however, must be in the same directory as the schematic file that uses the DLL file.The following shows two sample programs, one for Microsoft C/C++ compiler. &6 :H--------------------------------- DLL Routine for Microsoft C/C++ -----------------------------------begin// This sample program implement the control of the circuit "pfc-vi-dll.sch" in a C routine. //Input: in[0]=Vin; in[1]=iL; in[2]=Vo//Output: Vm=out[0]; iref=out[1]// You may change the variable names (say from "t" to "Time").// But DO NOT change the function name, number of variables, variable type, and sequence.// Variables:// t: Time, passed from PSIM by value#I0 .H// delt: Time step, passed from PSIM by value// in: input array, passed from PSIM by reference// out: output array, sent back to PSIM (Note: the values of out[*] can be modified in PSIM)// The maximum length of the input and output array "in" and "out" is 20.// Warning: Global variables above the function simuser (t,delt,in,out) are not allowed!!!#include __declspec(dllexport) void simuser (t, delt, in, out)// Note that all the variables must be defined as "double"M&&' LHdouble t, delt;double *in, *out;{R+I' V@H// Place your code here............beginkDS' @Hdouble Voref=10.5, Va, iref, iL, Vo, Vm, errv, erri, Ts=33.33e-6;S,' X@Hstatic double yv=0., yi=0., uv=0., ui=0.;*SЊ' @H2 ' @H// Input9Њ;' $@HVa=fabs(in[0]);3 n' @HiL=in[1];3 ;' @HVo=in[2];*nˋ' @H7'  @H// Outer Loop8ˋ:' "@Herrv=Voref-Vo;=w' ,@H// Trapezoidal RuleF:' >@Hyv=yv+(33.33*errv+uv)*Ts/2.;<w' *@Hiref=(errv+yv)*Va;*#' @H7Z'  @H// Inner Loop7#'  @Herri=iref-iL;=Z΍' ,@H// Trapezoidal RuleG ' @@Hyi=yi+(4761.9*erri+ui)*Ts/2.;9΍N' $@HVm=yi+0.4*erri;*x' @H=N' ,@H// Store old values8x' "@Huv=33.33*errv;9&' $@Hui=4761.9*erri;*P' @H3 &' @H// Output4 P' @Hout[0]=Vm;6 ' @Hout[1]=iref; >K*6' @HP) ' R@H// Place your code here............end)6% H}lF+ &H--------------------------------- DLL Routine for Microsoft C/C++ ----------------------------------end(n% H(F% H6n1i.FILE4$  Description:6J#dlJ  .FILEFile for storing element parameter values(% @1# Parameters:u+NJ#dVJ5  File NameName of the parameter file(v% @c<N' yThis element defines the name of the file that stores the component parameters and limit settings. For example, the resistance of a resistor can be specified as R1, and in the parameter file, the value of R1 is defined.The parameter file is a text file created by the user. The format of the parameter file is:@vk H           = LIMIT % A comment lineThe field can be either a numerical number (e.g. R1 = 12.3) or a mathematical expression (e.g. R3 = R1 + R2/2.). The name and the value can be separated by either an equation sign (e.g. R1=12.3) or a space (e.g. R1 12.3). Text from the character % to the end of the line is treated as comments (e.g. % R3 is the load resistance).: BYHFor example, a parameter file may look like the following:R1=12.3R2 23.4Ohm% R3 is the load resistanceR3=R1+R2/2.L1=3mC1=20uFN=234LIMIT R3 5. 25.981 8 .ACSWEEP6n&  HDescription:s)8J#dRJ  .ACSWEEPSetup for the ac analysis(n % @1:# Parameters:= J#dzJ5  &Start FrequencyStart frequency of the ac sweep, in Hz{7:<D#XnJ5  End FrequencyEnd frequency of the ac sweep, in Hzl(D#XPJ5  No. of PointsNumber of data points<J#bsJ5  $ Flag for PointsFlag to define how the data points is generated.Flag = 0: Points are distributed linearly in LOG10 scaleFlag = 1: Points are distributed linearly in linear scaler.D#X\J5 Source NameName of the excitation sourceGD#XJ5 $Start AmplitudeExcitation source amplitude at the start frequencyC/D#XJ5  End AmplitudeExcitation source amplitude at the end frequency&UE#XJ5 2Freq. for extra PointsFrequencies of additional data points. If the frequency-domain characteristics change rapidly at a certain frequency range, one can add extra points in this region to obtain better data resolution.(/}% @^:U$ tThe following are the steps to set up the ac analysis:h}~/ ,P:x-Identify a sinusoidal source (VSIN) as the excitation source for the ac sweep. -Place the ac sweep probes (ACSWEEP_OUT) at the desired output location. To measure the loop response of a closed control loop, use the node-to-node probe (ACSWEE~P_OUT2). -Place the .ACSWEEP element on the schematic, and define the parameters of the ac sweep. -Run PSIM.(% x _~+& xWith the ac analysis, the frequency response of a circuit or a control loop can be obtained. A key feature of the ac analysis in PSIM is that, if a circuit is switchmode, it can be in its original switchmode form, and no average model is required. Nevertheless, with the average model, the time it takes to perform the ac analysis will be shorter. (S% x+q& xThe principle of the ac analysis is that a small ac excitation signal is injected into the system as the perturbation, and the signal at the same frequency is extracted at the output. To obtain accurate ac analysis results, the excitation source amplitude must be set properly. The amplitude must be small enough so that the perturbation stays in the linear region. On the other hand, the excitation source amplitude must be large enough so that the output signal is not affected by numerical errors. (S% xX2q& exIn general, a physical system has low attenuation in the low frequency range and high attenuation in the high frequency range. A good selection of the excitation source amplitude would be to have a relatively small amplitude at the start frequency, and a relatively large amplitude at the end frequency.(% x|W% xSometimes, after ac analysis is complete, a warning message is displayed as follows:(% xpV) "0x Warning: The program did not reach the steady state after 60 cycles. See File message.doc for more details.(~% x V & xThis message occurs when the software fails to detect the steady state at the ac sweep output after 60 cycles. To address this problem, one may increase damping in the circuit (by including parasitic resistances, for example), or adjust the excitation source amplitude, or reduce the simulation time step. The file message.doc gives the information on the frequency at which this occurs and the relative error. The relative error will indicate how far the data point is from reaching the steady state.(~ % x(  % x< * 1 * C.PARAMSWEEP4 ^ $  Description:v,*  J#dXJ  .PARAMSWEEPSetup for parameter sweep(^  % @1 - # Parameters:|2  J#ddJ  Start ValueStarting value of the parameterm)-  D#XRJ End ValueEnd value of the parameterf" | D#XDJ "Increment StepIncrement stept0  D#X`J 0Parameter to be SweptParameter to be swept(|  % @fB ~ $ Parameter sweep can be performed for the following parameters: 5 8@- Resistance, inductance, and capacitance of RLC branches- Gain of proportional blocks (Proportional)- Time constant of integrators (Integrator)- Gain and time constant of PI (proportional-integral) controllersZ~ % - Gain, cut-off frequency, and damping ratio of 2nd-order low-pass/high-pass filters 3@@ N@ (2nd-order Low-pass Filter/2nd-order High-pass Filter)- Gain, center frequency, and passing/stopping band of 2nd-order bandpass/bandstop filters (2nd-order Band-pass 3@ Filter/2nd-order Band-stop Filter)@& EFor example, if a resistor R1 has a resistance of Ro. To sweep the resistance Ro from 2 Ohm to 10 Ohm, with a step of 2 Ohm, the specification will be:^3@YAJ#d(J  Start Value2U@AD#X"J End Value10YYABD#X*J "Increment Step2aAhBD#X:J 0Parameter to be SweptRo8BC1 0Please note that the value for Parameter to be Swept should be the parameter value, not the name of the branch. For example, in this case, you should define Parameter to be Swept as Ro, not as R1 since R1 is the branch name, not the parameter value.7hBC1CeEGround4C D$  Description:^CiDJ#d(J5  GroundGround( DD% @iDeE) WThe ground provides a common point or a reference for power/controlcircuits. Since the power circuit and control circuit are separate, the twogrounds are isolated.7DE1sEFGround4eEE$  Description::EUFK#ftJ5  2Ground (1)Ground (2)Grounds with different images^EF% These ground elements are the same as the standard ground, except the image is different.CUFG10GISwitch Controllers:FUG$ ,Switch Controllers2GGM#jdJ5 ("c.On-off ControllerOn-off switch controller5UGVHM#jjJ5 (,Alpha ControllerDelay angle alpha controller6GHP#plJ5 (HQ } 8PWM Pattern ControllerPWM pattern controller,VHI&  7H?I1?ILONCTRL4IsI$  Description:Y.?II+ &\@HOn-Off ControllerOn-off switch controller(sII% H?I3K& 3HThe on-off switch controller interfaces between the control circuit and the power circuit. The input is a logic signal (0 or 1) from the control circuit. The output is connected to the gate (base) node of a switch (or multiple switches) to control the conduction of the switch. (I[K% Hd?3KK% ~HThe signal level of 1 is for switch on and 0 for switch off.([KK% H(KL% H6KEL1\EL\ACTRL4LyL$  Description:T'ELL- *N@HAlpha Controlleralpha controller2 yLL( HImage:4L3M0 0 @H"~3LfM% HParameters:h=3MM+ &z@HFrequencyOperating frequency of the controlled switch or@fMN) ".P!Hswitch module, in HzmBM{N+ &@HPulse WidthOn-time pulse width of the gating signal, in deg. (NN% H{NQO& HThe alpha controller is used for the delay angle control of thyristor switches or bridges. There are three input for the controller: (NyO% HY2QOO' d@H- alpha value, in degree (at the center bottom)W0yO5' `@H- syncO5Lhronization signal (at the left bottom)W0O' `@H- enable/disable signal (at the middle right)*5' @H_:% HThe alpha controller is enabled (or disabled) if the enable/disable signal is high (or low).(b% HZ4:& iHThe transition of the synchronization signal from low to high (from 0 to 1) provides the synchronization and this moment corresponds to when the delay angle alpha equals zero. A gating pulse with a delay of alpha degrees is generated and sent to the thyristors. The alpha value is updated instantaneously.(b% H( % H(4% H( \% H941 ZPATTCTRL4\Ƀ$  Description:`3)- *f@HPWM Pattern ControllerPWM pattern controller2 Ƀ[( HImage:4)0 0 @H"3[„% HParameters:h=*+ &z@HFrequencyOperating frequency of the controlled switch or@„j) ".P!Hswitch module, in HzP*= H'@HUpdate AngleUpdate angle, in deg., based on which the switchgatings are internally updated. If the angle is 360o, the gatings are updated at every cycle. If it is 60o,the gatings are updated at every 60o. File NameName of the file storing the PWM patterns (j% H,&  HThe PWM pattern controller is used to control a switch or switch module with pre-calculated PWM patterns. A series of PWM patterns is stored in a lookup table in a file. Based on the input, a particular PWM pattern will be selected and switch gatings updated.(6% HQ,% XHThere are four input for the controller: (6% HS,' X@H- modulation index (at the center bottom)U.W' \@H- delay angle, in deg. (at the left bottom)X1' b@H- synchronization signal (at the right bottom)W0W' `@H- enable/disable signal (at the middle right)*0' @H & oHThe PWM pattern is selected based on the modulation index. The synchronization signal provides the synchronization to the PWM pattern. The switch gatings are updated when the synchronization signal changes from low to high. The delay angle defines the relative angle between the gating pattern and the synchronization signal. For example, if the delay angle is 10o, the gating pattern will be leading the synchronization signal by 10o.(05% He % HThe PWM pattern controller is enabled (or disabled) if the enable/disable signal is high (or low).(5% Heq% HA lookup table, which is stored in a file, contains the PWM patterns. It has the following format:0 4H                     n, m1, m2, , mnk1G(1,1), G(1,2), , G(1,k1) knG(n,1), G(n,2), , G(n,kn)where n is the number of PWM patterns, mi is the modulation indexcorresponding to Pattern i, and ki is the number of points in Pattern i. The modulation index array m1 to mn should be monotonically increasing. The output will select the ith pattern if the input modulation index is smaller than or equal to mi. If the input exceeds mn, tq0\he last pattern will be selected. *qZ& H801Sensors1 Z& HSensorsv&9P#pLJ (B/ (Voltage SensorVoltage sensorv&P#pLJ (T (Current SensorCurrent sensor*9%  51VSEN4B$  Description:N", (D@HVoltage SensorVoltage sensor(B% H3% HParameters:P$;, (H@HGainGain of the voltage sensor(c% Hl;% HThe voltage sensor measures the voltage of the power circuit and passes the value to the control circuit.(c% H(D% H(l% H(D% H5l1ISEN4$  Description:N"K, (D@HCurrent SensorCurrent sensor(s% H3K% HParameters:P$s, (H@HGainGain of the current sensor(% Hl% HThe current sensor measures the current of the power circuit and passes the value to the control circuit.(% H`;7% vHThe current sensor has an internal resistance of 1 uOhm.(_% H(7% H5_1/WSEN4$  Description:H8+ &:@HSpeed SensorSpeed sensor(`% H38% HParameters:N"`, (D@HGainGain of the speed sensor( % H`% HThe current sensor measures the speed of a mechanical system. The speed is by default in rpm.( % H51=TSEN4$  Description:Ji+ &>@HTorque SensorTorque sensor(% H3i% HParameters:O#, (F@HGainGain of the torque sensor(;% He% HThe torque sensor measures the torque transferred from one side of the torque sensor to the other.(;% H(% H(=% H7t1 t>Probes\=( ProbesThe following probes and meters are used to measure voltage, current, and power.*t"& H5P#pj"J ( &Voltage ProbeVoltage probe (node to ground)G">P#p"J ( DVoltage Probe (node-to-node)Voltage probe (between two nodes)t$P#pH"J (S &Current ProbeCurrent prober">$P#pD"J (z. $AC VoltmeterAC voltmeterr"P#pD"J (&{. $DC VoltmeterDC voltmetern$P#p<"J (  AC AmmeterAC ammete=rn~P#p<"J (  DC AmmeterDC ammetermP#p:"J ('  Watt MeterWattmeterz*~eP#pT"J ( *3-ph Watt Meter3-phase wattmeter4P#ph"J (dY 6VA/Power Factor MeterVA-power factor meterAezP#p"J (P @3-ph VA/Power Factor Meter3-phase VA-power factor meterlP#p8"J (s VAR MeterVAR metery)z_P#pR"J (T. (3-ph VAR Meter3-phase VAR meterv&P#pL"J (D݀ (AC Sweep ProbeAC sweep probeP_uP#p"J (㷏* 6AC Sweep Probe (loop)AC sweep probe (measuring loop transfer function)>* "?Note that in the control circuit, only node-to-ground voltage probe VP is allowed. All other probes and meters should be used in the power circuit only.3uq1cqVP4>$  Description:c8q+ &p@HVoltage ProbeVoltage probe (between node to ground)(0% H& HThe voltage probe measures the voltage between a node and the ground. The voltage value is saved to the output file for display.(0% H()% H(Q% H()y% H(Q% H4y1_ VP24 $  Description:mBv+ &@HVoltage Probe (node-to-node)Voltage probe (between two nodes)( % HvH &  HThe node-to-node voltage probe measures the voltage between two nodes. The voltage value is saved to the output file for display.(p % HwRH  % HNote that the node-to-node voltage probe can only be used in the power circuit.(p  % H( 7 % H( _ % H< 7  15 ACSWEEP_OUT4_  $  Description:L!  + &B@HAC Sweep ProbeAC sweep probe( C % H , & HThe ac sweep probe gives the ac sweep output at the output node. The ac sweep output consists of two parts: the amplitude in dB and the phase angle in degree. The amplitude output is defined as the amplitude ratio between the output voltage (the voltage at the node which the ac sweep probe is connected to) and the excitation voltage. The phase angle output is defined as the phase difference between the output voltage and the excitation voltage.(C T % H{,  % HNote that the amplitude output is in dB. Assuming that the amplitude ratio is kv, the output in dB will be 20*LOG10(kv).(T % H( D% H(l% H(D% H= l1`?CACSWEEP_OUT24$  Description:qEv, (@HAC Sweep Probe (loop)AC sweep probe for measuring loop response(% HS-v@& [HThe ac sweep probe (loop) measures the loop transfer functi@on of a closed-loop control system. With the loop transfer function, one can determine the bandwidth and phase margin of the control system. Again, the probe output consists of two parts: the amplitude in dB and the phase angle in degree. (%A% H@B& 5HThe example below illustrates how an ac sweep probe (loop) is used to determine the loop transfer function of a closed-loop circuit. This circuit has a current feedback loop, and the excitation source Vsweep is added to the current in the feedback path. Please note that the ac sweep probe should be connected in such a way that the dotted side is connected to the node after the excitation source is added.2%AC. , H"(B?C% H3CrC1rC)FIP4?CC$  Description:^3rCD+ &f@HCurrent ProbeCurrent probe (between two nodes)(C,D% HzDD% HThe current probe measures the current of the power circuit. The current value is saved to the output file for display.(,DD% HDE& 1HNote that IP can only be used in the power circuit. Also, in the current probe, a small resistor of 1 uOhm is used internally to measure the current.(DE% H(EF% H(E)F% H5F^F1i^FJV_AC4)FF$  Description:j ^FFJ#d@JY   AC VoltmeterAC voltmeter;F7G* $"Parameters:5FGJ#djJY  "Op. FrequencyOperating frequency of the meter97G9HJ#drJY  *Cut-off FrequencyCut-off frequency of the filter yQGI( The ac voltmeter measures the rms value of the ac voltage at the operating frequency. The cut-off frequency is for the high-pass filter in the meter model for dc component filtering.If the ac voltage contains the fundamental as well as harmonic components, the meter will give the rms value of the total waveform. For example, if 9HJV zH""where 1 is the fundamental (operating) frequency, and 2 and 3 are harmonic frequencies, the meter reading will be:5IJ1\JLV_DC6JJ&  HDescription:j JgKJ#d@JY   DC VoltmeterDC voltmeter;JK* $"Parameters:9gK%LJ#drJY  *Cut-off FrequencyCut-off frequency of the filter KL* "?The dc voltmeter measures the dc value of the voltage. The cut-off frequency is for the low-pass filter in the meter model for ac component filtering.5%L#M1#M΁A_AC4LWM$  Description:f#MMJ#d8JY  AC AmmeterAC ammeter;WMM* $"Parameters:5MwNJ#djJY  "Op. FrequencyOperating frequency of the meter9MNJ#drJY  *Cut-off FrequencyCut-off frequency of the filter wOwN}( The ac ammeter measures the rms value of the ac current at the operating frequency. The cut-off frequency is for the high-pass filter in the meter model for dc component filtering.If the ac voltage contains the fundameN}Lntal as well as harmonic components, the meter will give the rms value of the total waveform. For example, if 4N/ . H"(}ـ% H~7 >Hwhere 1 is the fundamental (operating) frequency, and 2 and 3 are harmonic frequencies, the meter reading will be:@ ـ΁5 :H"51V$A_DC6΁9&  HDescription:fJ#d8JY  DC AmmeterDC ammeter;9ڂ* $"Parameters:9]J#drJY  *Cut-off FrequencyCut-off frequency of the filter ڂ$* ";The dc ammeter measures the dc value of the current. The cut-off frequency is for the low-pass filter in the meter model for ac component filtering.2]V1kVW4$$  Description:eVJ#d6JY  Watt MeterWattmeter;** $"Parameters:9J#drJY  *Cut-off FrequencyCut-off frequency of the filter ** "qThe wattmeter measures the real power (also called average power) of a circuit. The cut-off frequency is for the low-pass filter in the meter model for ac component filtering.3†1†W34$  Description:r(†hJ#dPJY  &3-ph Watt Meter3-phase Wattmeter;* $"Parameters:9h&J#drJY  *Cut-off FrequencyCut-off frequency of the filter \, &The 3-phase wattmeter measures the real power (or average power) of a 3-phase 3-wire circuit. The cut-off frequency is for the low-pass filter in the meter model for ac component filtering.Note that this meter can not be used to measure the power of a 3-phase 4-wire circuit. In such a case, 3 single-phase meters should be used instead.6&1+ VA_PF4$  Description:|2J#ddJ#  2VA/Power Factor MeterVA-power factor meter;ϊ* $"Parameters:ZsJ#dJ5  .Operating FrequencyOperating frequency (fundamental frequency) of the meter, in HzQϊJ#dJ5  *Cut-off FrequencyCut-off frequency of the internal low-pass filter, in HzDsD#XJ5 $VA Display FlagFlag for VA display (0: no display; 1: display)N(D#XJ5 $PF Display FlagFlag for power factor display (0: no display; 1: display)\ȍD#XJ5 &DPF Display FlagFlag for displacement power factor display (0: no display; 1: display)(( kThe VA-power factor meter measures the apparent power (VA), the power factor, and the displacement power factor of a circuit. Given the voltage and current of the circuit as:^ȍ[X H"" "where 1 is the fundamental frequency. The apparent power S is defined as:(% H`[&7 >H  where Vrms and Irms are the rms values of the voltage and curre&nt which are defined as:F l< HH""*&' @HT/l% ^HThe real (average) power of the circuit is: 6 :H"A low-pass filter is used to obtain the real power. There is a compromise in selecting the low-pass filter cut-off frequency fc. If fc is too low, it will give a good attenuation to the ac components but it takes a long time to reach the steady state. On the other hand, if fc is too high, the transient is shorter, but the filtering to the ac components is not good. A good selection is around 20 Hz for a 60-Hz system.The power factor is defined as:C TiH""The displacement power factor is defined as:One needs to find out whether the power factor is leading or lagging by inspecting the voltage and current waveforms. 71 lVA_PF36P&  HDescription:?J#d~J  <3-ph VA/Power Factor Meter3-phase VA-power factor meter;P* $"Parameters:ZJ#dJ5  .Operating FrequencyOperating frequency (fundamental frequency) of the meter, in HzQSJ#dJ5  *Cut-off FrequencyCut-off frequency of the internal low-pass filter, in HzDD#XJ5 $VA Display FlagFlag for VA display (0: no display; 1: display)NSmD#XJ5 $PF Display FlagFlag for power factor display (0: no display; 1: display)\ D#XJ5 &DPF Display FlagFlag for displacement power factor display (0: no display; 1: display)m'& The VA-power factor meter measures the apparent power (VA), the power factor, and the displacement power factor of a 3-phase 3-wire circuit. For the 3-phase 3-wire circuit, the summation of the phase voltages or currents is zero, that is: 2 Y. , @"wB'5 :H"The apparent power S of a 3-phase system is defined as:Y\ H      where Va, Vb, Vc, and Ia, Ib, Ic are the total rms values of the phase voltages and currents, respectively. *' @HT/+% ^HThe real (average) power of the circuit is: 17 <H"A low-pass filter is used to obtain the real power. There is a compromise in selecting the low-pass filter cut-off frequency fc. If fc is too low, it will give a good attenuation to the ac components but it takes a long time to reach the steady state. On the other hand, if fc is too high, the transient is shorter, but the filtering to the ac components is not good. A good selection is around 40 Hz for a 60-Hz system.The power factor is defined as:P+G ^H" The displacement power factor is defined as:DPF = cos (1 - 1)(1% H2 2 HWhere 1 is the phase angle of the phase A fundamental voltage, and 1 is the phase angle of the phase A fundamental current. (% Hxl% HOne needs to find out whether the power factor is leading or lagging by inspecting the voltage and current waveforms.41#VAR4l$  Description:dDJ#d4J> Dl VAR MeterVAR meter;* $"Parameters:VDJ#dJ>  .Operating FrequencyOperating frequency, or fundamental frequency, of the metertH, &The VAR meter measures the reactive power of a circuit. If the voltages or currents contain harmonics, the meter will give the reactive power at the fundamental frequency. The sign of the VAR meter is defined such that the reactive power by an inductive circuit (for example, a resistor-inductor circuit) is positive.51VAR34$  Description:q'mJ#dNJ>  $3-ph VAR Meter3-phase VAR meter;* $"Parameters:VmHJ#dJ>  .Operating FrequencyOperating frequency, or fundamental frequency, of the meterZ) The 3-phase VAR meter measures the reactive power of a 3-phase circuit. If the voltages or currents contain harmonics, the meter will give the reactive power at the fundamental frequency. The sign of the VAR meter is defined such that the reactive power by an inductive circuit (for example, a resistor-inductor circuit) is positive.Note that this meter can not be used to measure the power of a 3-phase 4-wire circuit. In such a case, 3 single-phase meters should be used instead.*H%  8Z1xSources6$ $Source Libraryp bP#p@J (A@ VoltageVoltage sources&# p bP#p@J (i+B CurrentCurrent sources&# kP#p6J (1f, TimeTime, in sec.&# '$ &# 84 1n 4 nEVoltage/ c $ Voltagem4  P#p:J ( DCDC voltage sourceAc a P#pJ ( $DC (battery)DC voltage source (with battery cell image)w'  P#pNJ (/ SineSinusoidal voltage source4a \ P#phJ ( 3-ph Sine3-phase sinusoidal voltage source}-  P#pZJ (#/  TriangularTriangular voltage source/\ X P#p^J (  StepStep voltage source (from 0 to 1)=  P#pzJ (j~' Step (1)Step voltage source (from Vstep1 to Vstep2)z*X _ P#pTJ (M/ SquareSquare-wave voltage source:  P#ptJ (. ,Piecewise LinearPiece-wise linear voltage sourceT_ P#pJ (OQ 4Piecewise Linear (1)Piece-wise linear voltage source (time and value pair)u% P#pJJ ( RandomRandom voltage source=P#pzJ ( 0Voltage-controlledVoltage-controlled voltage sourceYD@P#pJ (nT LVariable-gain Voltage-controlleD@dVariable-gain voltage-controlled voltage source=@P#pzJ ( 0Current-controlledCurrent-controlled voltage sourceAD@bAP#pJ (gG 8Current-controlled (1)Current-controlled voltage sourceR@BM#jJ (㎠@Nonlinear (multiplication)Nonlinear voltage source (input multiplication)FbABM#jJ (ㅠ4Nonlinear (division)Nonlinear voltage source (input division)LB-CM#jJ (;S:Nonlinear (square-root)Nonlinear voltage source (input square root){.BCM#j\J ( &저"Grounded DCGrounded dc voltage source7-C,DM#jnJ (P PowerNonlinear voltage source (power function)?CDM#j~J (&Math FunctionVoltage source expressed in math function',DD$ lDnE# Note that controlled voltage sources and nonlinear voltage sources are allowed in the power circuit only.5DE1EGTime4nEE$  Description:CEF, (.@HTimeTime, in sec.(EBF% HaFF% HThe Time element gives the time of the simulation, in sec. It behaviors like a voltage source.(BFF% HFG& cHThe time can also be implemented using the piecewise linear voltage source VGNL with zero frequency, and two points: one at t=0 with V=0, and the other at t=100. with V=100. (FG% H4G#H1#HJVDC4GWH$  Description:.#HH) " @HeWHHJ#d6J4   DCDC voltage source?HsIJ#d~J4   DC (battery)DC voltage source (with battery cell image)3HI$ Parameters:S(sII+ &P@HAmplitudeAmplitude of the dc source(I!J% HkFIJ% HThese two dc sources are the same, except the images are different.(!JJ% H8JJ1JLVDC_GND4J K$  Description:W+JwK, (V@HGrounded DCGrounded dc voltage source( KK% H3wKK% HParameters:X,K*L, (X@HAmplitudeAmplitude of the source, in V(KRL% HU0*LL% `HThe source is grounded at the reference node.(RLL% H5LM1MVSIN4L8M$  Description:Q$MM- *H@HSineSinusoidal voltage source(8MM% H3MM% HParameters:]MAOg @H   Peak AmplitudeAmplitude Vm of the source, in VFrequencyFrequency f, in HzPhase AngleInitial phase angle , in deg.DC OffsetDC offset Voffset, in VTstartStarting time, in sec. Before this time, the source is zero.(MiO% HJ%AOO% JHA sinusoidal source is defined as:(iOO% H4O0 0 @HOL"*OE' @H(m% H(E% H6mˀ1ˀAVSIN34$  Description:h<ˀg, (x@H3-ph Sine3-phase Y-connected sinusoidal voltage source(% H3g% HParameters:yG;2 4@H V (line-line-rms)Line-to-line rms voltage amplitude Vll of the @{) ".PH3-phase source, in V-;W |@H  FrequencyFrequency f, in HzInit. Angle (phase A)Initial phase angle for Phase A, in deg.DC OffsetDC offset Voffset, in VTstartStarting time, in sec. Before this time, the source is zero.({Ѓ% Hj_% HThe three phases are symmetrical and are Y-connected. The dotted phase of the module refers to Phase A.(Ѓ% HT/_ۄ% ^HThe 3-phase voltage sources are defined as: (% H4ۄ70 0 @H"4k0 0 @H"470 0 @H"*kɅ' @H(% H(Ʌ% H(A% H5v1vӌVSQU4A$  Description:T'v- *N@HSquareSquare-wave voltage source(&% H3Y% HParameters:0&r a@H    Vpeak-peakPeak-to-peak voltage amplitude Vpp, in VFrequencyFrequency f, in HzDuty CycleDuty cycle D of the high-potential intervalDC OffsetDC offset Voffset, in VTstart Starting time, in sec. Before this time, the source is zero.Phase DelayPhase delay, in deg.(Y#% H, &mH The duty cycle D is defined as the ratio between the high-potential interval and the period. The Phase Delay defines the phase shift of the waveform from the original position. (#-% H4 6=HFor example, ifVpeak-peak = 1Frequency = 1kHzDuty Cycle = 0.5DC Offset = 0Tstart = 0and if Phase Shift = 0, the waveform will be 1 from 0 to 0.5 msec., and 0 from 0.5 msec. to 1 msec.But if Phase Shift = 90., the waveform will be shifted to the right by 90 deg. (0.25 msec. in this case). That is, the waveform will be 0 from 0 to 0.25 msec., 1 from 0.25 to 0.75 msec., and 0 from 0.75 to 1 msec.*-)' @H(Q% H2). , H"(Q% H(ӌ% H51YVTRI4ӌ<$  Description:U), (R@HTriangularTriangular voltage source(<% H3% HParameters:.r ]@H    Vpeak-peakPeak-to-peak voltage amplitude Vpp, in VFrequencyFrequency f, in HzDuty CycleDuty cycle D of the rising slope intervalDC OffsetDC offset Voffset, in VTstart Starting time, in sec. Before this time, the source is zero.Phase DelayPhase delay, in deg.(% H, &mH The duty cycle D is defined aӌs the ratio between the high-potential interval and the period. The Phase Delay defines the phase shift of the waveform from the original position. (% H 4 6HFor example, ifVpeak-peak = 1Frequency = 1kHzDuty Cycle = 0.5DC Offset = 0Tstart = 0and if Phase Shift = 0, the waveform will be triangular, starting from 0 at 0 sec., linearly increasing to 1 at 0.5 msec., and decreasing back to 0 at 1 msec.But if Phase Shift = 90., the waveform will be shifted to the right by 90 deg. (0.25 msec. in this case). That is, the waveform will be 0.5 at 0 sec., 0 at 0.25 msec., 1 at 0.75 msec., and back to 0.5 at 1 msec.*& H21. , H"(Y% H611 VSTEP4Y$  Description:I , (:@HStepStep voltage source(4% H3 g% HParameters:u4A R@H  VstepValue Vstep, in V, after the step changeTstepTime Tstep, in sec., at which the step change occurs(gE% H{J1 2H  The step voltage source changes from 0 to Vstep at the time Tstep. (E% H(% H2B. , H"(j%  H(B%  H(j%  H(%  H( %  H8B1BVSTEP_14 v$  Description:M!B, (B@HStep (1)Step voltage source(v% H3% HParameters::XP n@HVstep1Value Vstep1, in V, before the step changeVstep2Value Vstep2, in V, after the step changeTstepTime Tstep, in sec., at which the step change occursT_transitionTransition time, in sec., from Vstep1 to Vstep2(% HXE8 >H   The step voltage source changes from Vstep1 to Vstep2 at the time Tstep. The transition time from Vstep1 to Vstep2 is T_transition. (m% H(E% H.m+ &"51% VGNL4,$  Description:_4+ &h@HPiecewise LinearPiecewise linear voltage source(,% H3% HParameters:H ^K@HFrequencyFrequency of the waveform, in HzNo. of Points nNo. of pointsValues V1VnValues at each point, in VTime T1TnTime at each point, in sec.(% Hq% HThis source has a waveform consisting of many linear segments. The value and time at each point are specified.(% H0 % HExample:nIW% HThe following waveform has 4 points, and it can be defined as follows:(% HeW2 4@HFrequency0.No. of Points n4Values V1Vn1 1 3 3 Time T1Tn0. 0.1 0.2 0.3(>% H2p. , H"(>%  H(p%  H( %  H 7C1ECQVGNL_14 w$  Description:d9C+ &r@HPiecewise Linear (1) Piecewise linear voltage source(w% H36% HParameters:w4 8@HFrequency Frequency of the waveform, in HzTimes, Values (t1,v1) Time and value at each point, in sec. and V(6 % H& HThe waveform of the source consists of many linear segments. The time and value pair at each point is specified and they must be enclosed in brackets. A space or comma separates the time and the value.( #% H0 S% HExample:d?#% ~HA straight line with a slope of 1 can be defined as follows:(S% HrFQ, (@HFrequency 0.Times, Values (t1, v1) (0, 0) (1., 1.).61#tVRAND4Q$  Description:M!, (B@HRandomRandom voltage source(0% H3c% HParameters:a0@ P@H  Peak-peak AmplitudeAmplitude Vm of the source, in VDC OffsetDC offset Voffset, in V(c,% HN)z% RHA random voltage source is defined as:,tK daH"  where n is a random number in the range of 0 to 1. Example:To create a random voltage source that varies from -10V to 10 V, choose Vm=20V and Voffset=-10V.6z1 VVCVS6t&  HDescription:d9D+ &r@HVoltage-controlledVoltage-controlled voltage source (l% H3D% HParameters:Hl, (8@HGainGain of the source( % H & IHThe voltage source value is equal to the gain multiplied by the controlling voltage. The positive and negative nodes of the controlling voltage are on the left. (  % H7 8 1B8 O@VVCVSV4 l $  Description:W8  J#dJ4  HVariable-gain Voltage-controlledVariable-gain voltage-controlled voltage source. l ; $ Image:2 m . , @"1;  # Parameters:hm  J#d<J4  GainGain of the source. 4 ) " @Hf  % HThe voltage source value is equal to the gain multiplied by two controlling voltages Vin1 and Vin2:\4 '@M h!H"The 1st input Vin is on the side with the multiplication sign, and the 2nd input is on the side with the letter k. The difference between this source and the nonlinear voltage source Nonlinear (multiplication) (where Vo = k * Vin1 * Vin2) is that, with Nonlinear (multiplication), both Vin1 and Vin2 are updated at each iteration. But with Variable-gain Voltage-controlled voltage source, it is assumed that the change of Vin2 is small, and the value of Vin2 at the previous time step is used at the current time step. This assumption is valid as long as Vin2 changes at a much slower rate as compared to Vin1. This source can be used in circuits which may have the problem of math floating point overflow if the voltage source Nonlinear ( '@ multiplication) is used.( O@% H6'@@1 @ZCVCCVS6O@@&  HDescription:d9@A+ &r@HCurrent-controlledCurrent-controlled voltage source (@GA% H3AzA% HParameters:HGAA, (8@HGainGain of the source(zAA% H A C& HThe voltage source value is equal to the gain multiplied by the controlling current. The control nodes, on the left, should be connected across a resistor/inductor/capacitor branch, and the arrow indicates the direction of the controlling current.(A2C% H( CZC% H82CC1*CFVCCVS_14ZCC$  Description:h=C.D+ &z@HCurrent-controlled (1)Current-controlled voltage source (CVD% H3.DD% HParameters:HVDD, (8@HGainGain of the source(DD% H;D4F& +HThe voltage source value is equal to the gain multiplied by the controlling current. The controlling current flows into one control node, and out of the other. The current flow direction is indicated by the arrow. A 10-uOhm resistor is used to sense the controlling current.(D\F% H(4FF% H6\FF1F*IVNONM4FF$  Description:}RFkG+ &@HNonlinear (multiplication)Nonlinear voltage source with input multiplication (FG% H3kGG% HParameters:R GH2 4@@H GainGain k of the source(G@H% H~YHH% HThe voltage source value is equal to the multiplication of the two input voltages, or:l%@H*IG ^JH     Vo = k * Vin1 * Vin26H`I1`IKVNOND6*II&  HDescription:b7`II+ &n@HVNONDNonlinear voltage source with input division (I J% H3ISJ% HParameters:R JJ2 4@@H GainGain k of the source(SJJ% HxSJEK% HThe voltage source value is equal to the division of the two input voltages, or:h5JK3 6lH"Input 1 is on the side of the division sign.7EKK1KVNVNONSQ6KL&  HDescription:yMKL, (@HNonlinear (square-root)Nonlinear voltage source with input square-root 8LL) "PAHcalculation (LL% H3L&M% HParameters:R LxM2 4@@H GainGain k of the source(&MM% HvQxMN% HThe voltage source value is equal to the square-root of the input voltage, or:@ MVN5 :H"8NN1NrVPOWERS6VNN&  HDescription:6NDOJ#dlJ4  PowerNonlinear voltage source (power function)7N{O'  Parameters:TDOOD#X J4 GainGain Kf"{OAD#XDJ4 OAVN"Coefficient k1Coefficient k1n$OJ#dHJ4  $Coefficient k2Coefficient k2.A݀) " @H|~% HFor the VPOWERS voltage source, the relationship between the output voltage Vo and the input voltage Vin is expressed as:݀r7 <}H"where the term sign(Vin) is 1 if Vin is positive, and -1 if Vin is negative. The symbol ^ means to the power of. Note that this source can be used in the power circuit only.6~1(VMATH6rނ&  HDescription:DfD#XJ4  Math FunctionVoltage source expressed in mathematical function7ނ'  Parameters:}9fD#XrJ4 ExpressionThe mathematical expression of the sourceh$D#XHJ4 TstartStart time of the source) The math function source allows one to define the source in any mathematical expression. In the expression, T or t represents time. For example, to implement a sinusoidal source, the expression can be: sin(2*3.14159*60*t+2.09).8҅1 ҅uCurrent/ $ Currentm҅nP#p:J ( DCDC current sourcew'P#pNJ (wU SineSinusoidal current source}-nbP#pZJ (.^  TriangularTriangular current source/P#p^J ( C StepStep current source (from 0 to 1)5bfP#pjJ ( Step (1)Step current source (from I1 to I2)z*P#pTJ (V SquareSquare-wave current source:fjP#ptJ ( .Piecewise Linear Piecewise linear current sourceTP#pJ (L߀ 4Piecewise Linear (1)Piece-wise linear current source (time and value pair)u%jP#pJJ (A RandomRandom current source=P#pzJ (F 0Voltage-controlledVoltage-controlled current source=P#pzJ (/ 0Current-controlledCurrent-controlled current sourceA.P#pJ ()v 8Current-controlled (1)Current-controlled current sourceSьP#pJ (u= @Nonlinear (multiplication)Nonlinear current source (input multiplication)G.hP#pJ (u= 4Nonlinear (division)Nonlinear current source (input division)MьP#pJ (~R :Nonlinear (square-root)Nonlinear current source (input square root)=hP#pzJ (In  PolynomialNonlinear current source (special type 1)A#P#pJ (In (Polynomial (1)Nonlinear current source (special type 2)Y̏P#pJ (7 LVariable-gain Voltage-controlledVariable-gain voltage-controlled current sourcevO#N' Note that ȁNll the current sources are allowed in the power circuit only.'̏u$ 4N1KIDC4u$  Description:E", (2@HDCDC current source(J% H3"}% HParameters:V+J+ &V@HAmplitudeAmplitude of the source, in A(}% H(#% H(K% H5#1KISIN4K$  Description:Q$- *H@HSineSinusoidal current source(-% H3`% HParameters:M-d @H   Peak AmplitudeAmplitude Im of the source, in AFrequencyFrequency f, in HzPhase AngleInitial phase angle theta, in deg.DC OffsetDC offset Ioffset, in ATstartStarting time, in sec. Before this time, the;`) "$PHsource is zero.(% HJ%Z% JHA sinusoidal source is defined as:< 3 6H"5Z1ISQU6&  HDescription:T'U- *N@HSquareSquare-wave current source(}% H3U% HParameters:0}Rr a@H    Ipeak-peakPeak-to-peak current amplitude Ipp, in AFrequencyFrequency f, in HzDuty CycleDuty cycle D of the high-potential intervalDC OffsetDC offset Ioffset, in ATstart Starting time, in sec. Before this time, the source is zero.Phase DelayPhase delay, in deg.(z% HR\, &mH The duty cycle D is defined as the ratio between the high-potential interval and the period. The Phase Delay defines the phase shift of the waveform from the original position. (z% H7\% $HFor example, if6 :#HIpeak-peak = 1Frequency = 1kHzDuty Cycle = 0.5DC Offset = 0Tstart = 0and if Phase Shift = 0, the waveform will be 1 from 0 to 0.5 msec., and 0 from 0.5 msec. to 1 msec.But if Phase Shift = 90., the waveform will be shifted to the right by 90 deg. (0.25 msec. in this case). That is, the waveform will be 0 from 0 to 0.25 msec., 1 from 0.25 to 0.75 msec., and 0 from 0.75 to 1 msec.51ITRI6&  HDescription:U)B, (R@HTriangularTriangular current source(j% H3B% HParameters:.j=r ]@H    Ipeak-peakPeak-to-peak current amplitude Ipp, in AFrequencyFrequency f, in HzDuty CycleDuty cycle D of the rising slope intervalDC OffsetDC offset Ioffset, in ATstart Starting time, in sec. Before this time, the source is zero.Phase DelayPhase delay, in deg.(e% H=G, &mH The duty cycle D is defined as the ratio between the high-potential interval and the period. The Phase Delay defines the phase shift of the waveform from the original position. (eo% H7G% $HFor example, ifo6 :HIpeak-peak = 1Frequency = 1kHzDuty Cycle = 0.5DC Offset = 0Tstart = 0and if Phase Shift = 0, the waveform will be triangular, starting from 0 at 0 sec., linearly increasing to 1 at 0.5 msec., and decreasing back to 0 at 1 msec.But if Phase Shift = 90., the waveform will be shifted to the right by 90 deg. (0.25 msec. in this case). That is, the waveform will be 0.5 at 0 sec., 0 at 0.25 msec., 1 at 0.75 msec., and back to 0.5 at 1 msec.61CISTEP6&  HDescription:Ig, (:@HStepStep current source(% H3g% HParameters:uxA R@H  IstepValue Istep, in A, after the step changeTstepTime Tstep, in sec., at which the step change occurs(% H{Jx1 2H  The step current source changes from 0 to Istep at the time Tstep. (C% H8{1${gISTEP_14C$  Description:M!{, (B@HStep (1)Step current source($% H3W% HParameters:$${E X@HAmplitude 1Value I1, in A, before the step changeAmplitude 2Value I2, in A, after the step changeTstepTime Tstep, in sec., at which the step change occursT_transitionTransition time, in sec., from I1 to I2(W% Hw{?% HThe step current source changes from I1 to I2 at the time Tstep. The transition time from I1 to I2 is T_transition. (g% H5?12 IGNL4g$  Description:`50+ &j@HPiecewise LinearPiece-wise linear current source(X% H30% HParameters:Xx H ^K@HFrequencyFrequency of the waveform, in HzNo. of Points nNo. of pointsValues I1InValues at each point, in ATime T1TnTime at each point, in sec.( % Hqx 6 % HThis source has a waveform consisting of many linear segments. The value and time at each point are specified.( ^ % H0 6  % HExample:d?^  % ~HA straight line with a slope of 1 can be defined as follows:(  % HM  2 4@HFrequency0.No. of Points n2Values I1In0. 1.Time T1Tn0. 1.7  1F  @IGNL_14  $  Description:e: i + &t@HPiecewise Linear (1) Piece-wise linear current source(  % H3i  % HParameters:w o 4 8@HFrequency Frequency of the waveform, in HzTimes, Values (t1,i1) Time and value at each point, in sec. and A(  % Ho & HThe waveform of the source consists of many linear segments. The time and value pair at each point is specified and they must be enclosed in brackets. A space or comma separates the time and the value.( % H0 % HExample:d?E% ~HA straight line with a slope of 1 can be defined as follows:(m% HrFE @, (@HFrequency 0.Times, Values (t1, i1) (0, 0) (1., 1.).m @ 6mB@1B@CIRAND4 @v@$  Description:M!B@@, (B@HRandomRandom current source(v@@% H3@A% HParameters:]@A4 8@HPeak-peak AmplitudeAmplitude Im of the source, in ADC OffsetDC offset Ioffset, in A(AA% HN)A%B% RHA random voltage source is defined as:AC6 :}HIo = Im * n + Ioffsetwhere n is a random number in the range of 0 to 1. Example:To create a random current source that varies from -10A to 10A, choose Im=20A and Ioffset=-10A.6%BOC1HOCaFIVCCS6CC&  HDescription:d9OCC+ &r@HVoltage-controlledVoltage-controlled current source (CD% H3CDD% HParameters:HDD, (8@HGainGain of the source(DDD% H`D9E% HThe current source value is equal to the gain multiplied by the controlling voltage. That is:PDE9 B.H   Io = k * Vin(9EE% HcE9F% HThe positive and negative nodes of the controlling voltage are on the left of the source image. (EaF% H79FF1FMIVCCSV4aFF$  Description:WFmGJ#dJ4  HVariable-gain Voltage-controlledVariable-gain voltage-controlled current source(FG% @0 mGG& Image:2GG. , @"1G(H# Parameters:hGHJ#d<J4  GainGain of the source.(HH) " @HfHII% HThe current source value is equal to the gain multiplied by two controlling voltages Vin1 and Vin2:.HLb ]H     Io = [k * Vin2] * Vin1The 1st input Vin is on the side with the multiplication sign, and the 2nd input is on the side with the letter k. The difference between this source and the nonlinear current source Nonlinear (multiplication) (where Io = k * Vin1 * Vin2) is that, with Nonlinear (multiplication), both Vin1 and Vin2 are updated at each iteration. But with Variable-gain Voltage-controlled current source, it is assumed that the change of Vin2 is small, and the value of Vin2 at the previous time step is used at the current time step. This assumption is valid as long as Vin2 changes at a much slower rate as compared to Vin1. This source can be used in circuits which may have the problem of math floating point overflow if the current source Nonlinear (multiplication) is used.(IIM% H6L7M1 7M4ICCCS6MmM&  HDescription:d97MM+ &r@HCurrent-controlledCurrent-controlled current source (mMM% H3M,N% HParameters:HMtN, (8@HGainGain of the source(,NN% H tNO& HThe current source value is equal to the gain multiplied by the controlling current. The control nodes, on the left, should be connected across a resistor/inductor/capacitor branch, and the arrow indicates the direction of the controlling current.(N % HO M(O4% H8 l1*l^ICCCS_144$  Description:h=l+ &z@HCurrent-controlled (1)Current-controlled current source (0% H3c% HParameters:H0, (8@HGainGain of the source(cӁ% H;& +HThe current source value is equal to the gain multiplied by the controlling current. The controlling current flows into one control node, and out of the other. The current flow direction is indicated by the arrow. A 10-uOhm resistor is used to sense the controlling current.(Ӂ6% H(^% H661INONM4^ȃ$  Description:}RE+ &@HNonlinear (multiplication)Nonlinear current source with input multiplication (ȃm% H3E% HParameters:R m2 4@@H GainGain k of the source(% H~Y% HThe current source value is equal to the multiplication of the two input voltages, or:d#A RFH    Io = k * Vin1 * Vin26212INOND6h&  HDescription:qF2ن+ &@HNonlinear (division)Nonlinear current source with input division (h% H3ن4% HParameters:R 2 4@@H GainGain k of the source(4% HxS&% HThe current source value is equal to the division of the two input voltages, or:PB TH    Io = k * Vin1 / Vin2Input 1 is on the side of the division sign.9&1INONSP_16'&  HDescription:h;- *v@HPolynomial Current source with polynomial expression3'‰% HParameters:m#/J#dFJF  Constant Constant Idc, in A7‰J#dnJF  (K1 (coefficient)Coefficient for the linear term7/1J#dnJF  (K2 (coefficient)Coefficient for the square term6J#dlJF  (K3 (coefficient)Coefficient for the cubic termh1A( This current source is designed primarily for the modeling of mechanical load. It is expressed as:@2 4H"where:k@A+ &@HVi:controlling voltagesign(Vi):sign of the input voltage [2G) "dP!H(1 if Vi is positive; and -1 if Vi is negative),s'  H*G' @H*sǍ' @H(% H*Ǎ' @H*C' @H(k% H(C% H9k̎1 ̎INONSP_24$  Description:l?̎l- *~@HPolynomial (1)Current source with polynomial expression 3% HParameters:k!lJ#dBJ>  ImaxMaximum current, in AbxD#X<J> Vi,low Lower input limitcD#X>J> Vi,high Upper input limitx+ $This current source is designed primarily for the modeling of mechanical load. It is expressed as:When the absolute value of the controlling voltage Vi is less than the lower limit Vi,min:3 & @Io = Imaxd$ When the absolute value of the controlling voltage Vi is between the lower and the upper limits:U/& ^@Io = P / | Vi | = (I_max * Vi_low) / | Vi |~ZX$ When the absolute value of the controlling voltage Vi is greater than the upper limit:. % @Io = 0&X# 71aINONSQ4$  Description:wL+ &@HSquare-rootNonlinear current source with input square-root calculation (% H3% HParameters:R ;2 4@@H GainGain k of the source(c% HvQ;% HThe current source value is equal to the square-root of the input voltage, or:(c% H450 0 H",a'  H651"SLINK6a&  HDescription:v@C6 <@HIn Link NodeIn link node Out Link NodeOut link node F2 2HThe link nodes are used in PSIM to provide interface to Simulink. An In Link Node receives a value from Simulink, and the node behaviors as a voltage source. An Out Link Node passes a value to Simulink.(Cn% HZF1 2H{>HSRefer to the SimCoupler Module section regarding the setup of the SimCouple Module.)n"& H11~~H}Times New RomanArialCourier NewSymbolTimesHelveticaCourierGenevaTms RmnHelvMS SerifMS Sans SerifNew YorkSystemWingdingsMinchoBatangSimSunPMingLiUGothicDotumSimHeiMingLiUMS MinchoGulimMS GothicCenturyTahomaArial BlackAngsana New?? ??MS SongAlleycat ICGBoca Raton ICGBoca Raton ICG SolidChilada ICG CuatroChilada ICG DosChilada ICG TresChilada ICG UnoCopperplate31abCopperplate33bcDecotura ICGDecotura ICG InlineFajita ICG MildFajita ICG PicanteFranklin Gothic CondensedFranklin Gothic No.2AGaramond BoldAGaramondGoudyLitterbox ICGNuptialScriptOCRAPark AvenuePaisley ICG 01Paisley ICG 01 AltPaisley ICG 02Paisley ICG 02 AltPrestige EliteBernhard Modern RomanSaturday Sans ICGStencilTrajanTektonUltra Condensed Sans OneUltra Condensed Sans TwoVAG Rounded ThinVAG Rounded LightWhimsy ICGWhimsy ICG HeavyMyriad RomanWonton ICGMarlettComic Sans MSBook 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B MTQuickTypeQuickType CondensedQuickType MonoQuickType PiZTR81C4.TMPZTR81D1.TMPZTR81D4.TMPZTR81E0.TMPZTR81E2.TMPZTR81E4.TMPZTR8324.TMPZTR93A2.TMPZTR93A5.TMPZTR93B0.TMPZTR93B3.TMPZTRA000.TMPZTRA004.TMPZTRA010.TMPTerminalSmall FontsLucida BlackletterBankGothic Md BT TurCommercialScript BT TurSwis721 BT TurSwis721 LtCn BT TurGeorgia Ref CEGeorgia Ref CyrGeorgia Ref GreekGeorgia Ref TurGeorgia Ref BalticGoudy Old Style CEGoudy Old Style TurGoudy Old Style BalticAlbertus CEAlbertus TurAlbertus BalticAntique Olive Compact CEAntique Olive Compact TurAntique Olive Compact BalticBodoni CEBodoni TurBodoni BalticBodoni Black CEBodoni Black TurBodoni Black BalticClarendon CEClarendon TurClarendon BalticClarendon Extended CEClarendon Extended TurClarendon Extended BalticGoudy Old Style Extrabold CEGoudy Old Style Extrabold TurUnivers Light Condensed CEUnivers Light Condensed TurUnivers Light Condensed BalticUnivers Extended CEUnivers Extended TurUnivers Extended BalticGraphos CEGraphos TurGraphos 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block|RotateROUNDOFFround-off blockRun PSIMRun SIMVIEWSAMPsampling/hold blocksaturable inductorSaveSave assensorsset-reset flip-flopSettingSIGNSign functionSimCoupler Modulesimple switchSimulate menusimulation controlSINSIN_1Sine inversesingle-phase 3-winding transformersingle-phase 4-winding transformersingle-phase 5-winding transformersingle-phase 7-winding transformersingle-phase 8-winding transformersingle-phase transformersinusoidal current sourceSinusoidal functionsinusoidal voltage sourceSLINK_INSLINK_OUTsources speed sensorSQROTsquare-root blocksquare-wave current sourcesquare-wave voltage source SRFF$SRM3(SSWI,STACK0Status Bar4step current source8step voltage source@SubcircuitHSUM1LSUM2PSUM2PTSUM3Xsummer with 1 input\summer with 2 input`switch controllersdswitched reluctance motorlswitchespSYNM3xSYNM3_I|TANTangent functiontangent 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motorwound-rotor induction motor (linear and with saturation)WSENXORGATE z-domain transfer function block$ZENER(zener diode,zero-order hold0ZOH4Zoom in8Zoom out<switch controllersdswitched reluctance motorlswitchespSYNM3xSYNM3_I|TANTangent functiontangent inverseTDELAYTextTF_1FTF_1F_1TF_1F_3WTF_1F_4WTF_1F_5WTF_1F_5W_1TF_1F_7WTF_1F_8WTF_3DDTF_3FTF_3F_3WTF_3F_4WTF_3YDTF_3YDDTF_3YYTF_3YYDTF_IDEALTF_IDEAL_1TFCTNTFCTN_DTFCTN1TG_1THDTHYthyristorTileTimetime delay blocktime stepTipsToolbar torque sensortotal harmonic distortiontotal timeTprintatorDIGITlogarithmic (base 10) function blockRC3, 3-phase resistor-capacitortransfer function block/&;)LzvSimcad Help ContentsFile menuEdit menuŅEdit library menuView menuDSubcircuit menu$Element menu\Motor Drive ModuleDigital Control ModuleЀSimCoupler ModuleuSimulate menu Simulation ControlOption menuWindow Menu Web Simulation MenuHELPFUL_TIPSZ P_C_INTERFACEERROR_WARNING FFT_ANALYSISPower LibraryRLC BranchesOther Power Elements5ResistorInductorSaturable 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