General description of the translation of the static generator model with easy application of any type of generator without rotation Mustafa Eydyany, Amir Yaali Abstract: The static generator is an easy-to-use model of any type of stationary generator (without rotation). They have applications such as: photovoltaic generators, fuel cells, storage devices, HVDC terminals, reactive power compensators, wind generators. Wind generators, which are connected to the grid through a full-size converter, can also be modeled as static generators, since the behavior of the power plant (from the grid-side view) is determined by the converter. ١ 1 - 4 1 - 1 ............................................................................................................................. 4 1 - 1 - 1 .................................................................................................. / 5 1 - 2 ............................................................................................................ !"# ................... 6 1 - 2 - 1 %& '() *+ (+ ,- . / ................................................................ ............... 6 1 - 2 - 2 . 0!( "' Slack ....................................................................................... 8 1 - 2 - 3 3 *4(5 *+ (+ ........................................................................................... 8 1 - 2 - 4 ......................................................................................................... .!) 6"+7 8 9 1 - 2 - 5 !(+# ,- : ;)& ............................................................................................ 9 1 - 2 - 6 ............................................................................................ !(+ ,- : ;)& 10 1 - 3 =& *+ > .......... ........................................................................................................ 10 1 - 3 - 1 ? @ *+ > VDEC/IEC ............. ....................... ..... ................ .. ... ... .. ....... 10 1 - 3 - 2 A+ *+ > ........................................................................................................... 13 1 - 3 - 3 *+ > ANSI .............................................. ... ...................................... .. ... ... ....... 15 1 - 3 - 4 IEC 61361 ............................................................................................................... 16 1 - 4 0!"- - ....................................................................................................................... ......... 16 1 - 5 B .!=C , RMS ...................................................................................................................... 17 1 - 5 - 1 E= .................................. .................. ........................................................ 17 1 - 5 - 2 .............................................................................................................. '() E= 18 1 - 5 - 3 ................................. / ................................................................ 19 1 - 6 B .!=C , EMT ...................................................................................................................... 19 1 - 6 - 1 E= ...................... ...................................................................................... 19 1 - 6 - 2 .............................................................................................................. '() E= 20 ٢ 1 - 6 - 3 ........... ..................................................................................................... 20 2 - / !" # $! 22 2 - 1 , F (RMS) .................................................................................................................. 22 2 - 1 - 1 E= ............................................................................................................ 22 2 - 1 - 2 .............................................................................................................. '() E= 23 2 - 2 EMT ................................................................................................................. ................. 24 2 - 2 - 1 E= ............................................................................................................ 24 2 - 2 - 2 ............................................................................ '() E= ................................... 24 3 - &' ( ! " 25 3 - 1 > G!( "' ................................................................................................................ 25 27 29 ٣ 1 - H+ "' I" - B # ; + 0 0!( "' ; +.: (K3L ) ) - : " "; • 0!O()(7 ,-"' • (3 ,- % • ,B *!3P ,- *4(; • ,- ." F HVDC • !(+ ,- *+ = • "' ; , ,-"' . " Q"C A>( .G=C . A+ *B" = ? B .+ Q,; ,-"' 0!( !" (7 B Q"C */)!" ;C H!!R = S (.G=C :T ,T" B) 1 - * ' ' U3 ; + "' ;+ VW(" , .(; ;+ ; 0!( AGC 1 - 1 , ,- *;; "' 0!( ۴ B!( H!XT- ) ,B ,- H!C ;R MVA ) )4 A+ Q%+ . .;+ ;) "' 0 )3 Mvar "' B 0!( ; "' 0 B!( Q ; .; -3 *C YWZ ,B ,- H!C ;R ; ; "' .(; U3 :[ , \ , .]@ ; ; ! 8!] ! A !^_ :& H *) )3 Q ;; ?%R # . .+ ;!/ 1 - 1 - 1 +$ / +, -' T!` . .;C a!` ,) .Z!T- B ;; 4(5 : ,;)) (F : • Iearthed : H!B r0 Q :)] r0 ) : R7!b ;C R7!b / ( x0 6"(+# Q x0 ) : R7!b ;C R7!b / ( AGC 2 - 1 , .(; AGC 3 - 1 .]@ AGC 4 - 1 ۵ : QC R7!b . / / 1 - 2 . / ! 0- 12 1 - 2 - 1 3 &- *$$ &$ 4$!05 c%(W :[ . . %& '() *+ (+ cos ) Q V 7 Q ('() : .+ ;+ a!` B ,- A>7 B ; : *C *;; dC : 6 7! &$ I" 0 . e . / H 8 PQ AGC ; # f% ;T" ) : 1,7 .: *C *;; Z" ,- )3 " + \ h i (+ !(+ YWZ + + 0!( "' # ; .+ !(+ ) + ) 8 . (PQ :C; -3 4(5 *C VW(" ,;)) :[ . ;] H H!!R j) :7 ) '() ] .=R '() : R7!b (+7 (+ . / , sum P ) sum Q (+ ;R(" ; C -3 AGC 5 - 1 . / / “Earthed” C R7 AGC 6 - 1 ,;)) :[ ۶ 3 &- &$ I" 0 . e . / H 8 PV AGC ; # f% ;T" ) : 7 - 1 '() (+ .: *C *;; Z" ! ; *C YWZ %& '() ;C (+ "' !(+ )3 R Q;; kl" %& . )3 .;C A[ # !(+ , E B ] ) *C R7 '() a!` .=R Q. / H VW(" .: : ^ ;C ;) # 3 &- ' &$ I" 0 . / H 8 DV AGC ; # ;T" f% ) ;; :] @ 7 - 1 "' .: *C *;; Z" 3 ! ; %& '() ;+ a!` (+ .+ (+ YWZ a!` .@]" 0 . ; () :7 ' . :[ - ; *C a!` .@]" B a! T" T!` .@]" S ) droop du ( a!` .@]" . ! , B ;C l :7 (+ : .: B!" ,(Z! !(+ \ . Q0!( "' % '() '() H ; + : 0 B K! . + (+ '() " .!C 0 ; H!C :7 ] Q;C a!` '() (+ ,) .+ 4- '() ;+ ;) . . %& .!C ; '() AGC ; G!7/ . m;R H .+ ;C (+ B m;R 8 - 1 : *C *;; Z" AGC 7 - 1 '() (+ . / ٧ : a ; l ; u : ! .!C ; R\) '() ] setpoint u : 0!( "' '() *C a!` .@]" Q : 0!( R\) !(+ )3 setpoint Q : *-; K+) E B 0!( "' B *C YWZ nom S : ,-n \ " : droop *C YWZ ; ; .+ : (7 ] 1 - 2 - 2 /'$8 4. # &' '13 Slack B !" , S]7 "' . 0!( 0% ;+ *;( .G , "Active Power Control" . 7 ; Dispatched Q;C a!` 6"m S Static Generator ; Reference Bus . 0!( "' 0 Q;C a!` 8 .;C A>( *C VW(" 0!( "' %& '() *+ (+ 0% ,) Voltage Droop ;C a!` 1 - 2 - 3 * 9&:!' *$$ &$ *+ (+ 0 B ZW " H!XT- 0!( "' o :5F + (+ Q([ H!L ; .C * o :5F *+ (+ *&" .;; : ) 0!( "' %& '() *+ (+ . :=5" 3 :5F o ,-"' . 0!( .& T!` . Load Flow + , *+ ( o :5F *+ (+ 7 E . .;; 4(5 F :5 o !+ .R AGC 8 - 1 '() :7 (+ ٨ 1 - 2 - 4 4-' ;1 < ! . ;l B 6F +" (3 Q -")/ ,-[) S= ) *;; K-+ K 7 ;3 H! .!) (+ ; . . ) : 6"+7 p&" h( "' \ ; !!q .+ 0 ; " # T ] . 6"+7 K 7 (Kpf) ,-[) ! ; r"# % ,- *+ (+ S= H Q;C a!5] Ii AGC ; 9 - 1 Z" : *C *;; . / / Active Power Control according to Primary Control 7 ; 7 k" ; Power Factory QC *C VW(" 6"m (5- % *+ (+ 0 ,; .+ -"' .T- S . 6"+7 :7 . . (F) Prim 6"+7 8 h B Load Flow Q;C ;l (: ^ "' R\) E B . "' *C B ;C .=& : : a ; l ; dP : !!q )3 "' dF : !!q 6"+7 Kpf : *+ (+ % (F "' AGC 9 - 1 .!) 6"+7 8 ٩ 1 - 2 - 5 & 2 /' ! ;+ H!!R j) ); . !(+ ,- : ;)& : . = > ? '> / @6'> : !(+ ] s+[ ) A\[ A ; ] H Q[ s+[ / A\[ ; ; " .;C a!` *!3P ,; *r , ; ; R7 ; ) (5- !%T *;; !(+ ,- : ;)& .+ !C .(C; . / *T- " .+ Q: H!!R A \ *;)& - , ,t/ 8!] (+7 0 Q ;] H + ; ."C "Consider Reactive Power Limits Scaling Factor" *;( .=& ,- . / ; ;C ,- Ii :!% \ & (IntQlim) c%(W d@ ; !(+ s+[ / YWZ ;] H(7/ `" ; G .CF A3; ; :!% \ ,- & .+ a-7 R7 ? 'Mvar Limits Curves' !%T ."W (+ ; ,-"' ."C *!3P )G (ElmSym) ,-"' ) 0!( (ElmGenstat) c R .G=C ; .+ T- B " " *C object .: *C *!3P !%T ."W (+ ; .+ + *;( :!% \ & B .G!" B \ & . / / Q;C *;( :!% Consider Reactive Power Limits 7 ; Load Q;C R7 E B " \ ;3 s+[ ) A\[ *;)& ; .Z!T- "' C ;l *&" object 0T+ :!% \ & 7 k" PowerFactory : *C *;; u!i $$ B' * +&' ! Mvar C8 41 D. & B' : "' 0 ,) ; "' :!% \ & T , : • KW "Reactive Power Limit" "' .& ; 0!( !+ !F • :T5\ + ; " Capability Curve " !-; Z7 • KW “Select. . . ” ,l(5 .CF ; h & 0 “ Mvar Limit Curves ” .CF ; Operational Library ” ” .!+ VW(" 1 - 2 - 6 & ' /' ! , [ H!!R , !(+ Q!C *;+ = [ ); B G B .=& k4- ; / .;; ; ) j) ); 0 k!F ;C *;; K T" )3 *lF ; *-; Z- Active Power: Operational Limits " " ` B *+ ! )4 )3 s+[ s+[ ) A\[ : ;)& . :=5" ,m : ) B r"# .: !%T "Active Power Rating" (5- ;3 ١٠ "Active Power Ratings" s+[ . ; Vi ) : "' R7 )3 MVA ; "' k" f F ;C ;l , . ; h i ) h i 1 - 3 * F' G 1 - 3 - 1 . H. I * F' VDEC/IEC *+ > .=& ; VDE / IEC 0!( "' 0 H(7/ `" ; , c%(W G . ;; ; ) : • (;"( ?= ) *+ > 0T+ ) • = !7 0!( - ; • s+[ [) @3 ; :+Z . J8 * F' K *+ > =& ; VDEC / IEC ;"( ? @ v mTR 0!( ,-"' Q (Option No Circuit Contribution) . "C T" .(7/ `" ; # &' G - !' ;+ R7 . / Static Converter Fed Drive *+ > .=& k4- 0!( "' Q VDE / IEC ? @ 0!( = *+ . tq ; 0 " IEC 60909 (VDE 0102) 7 ,- ; .+ ( *+ > . S]7 r"# .: *C .(7/ `" ; B7 . *+ > , S]7 0!( = *+ . tq .!) ]( ik 0!F *+ > s+[ . ) ip + 0T+ ]( *+ > E@\ . r"# ib :[ ) F *+ > ik + T" 0T+ .=& , 0!( = *C . tq ,- ; Q.l!(" ; ,- . Z C) . *+ > )G# ."C (7 AGC ; # ;R 11 - 1 " *C *;; Z : AGC 10 - 1 *+ > .& VDEC/IEC ١١ ;C .=& B dC . 6"w : H!XT- : : a ; l ; rM U : " '() rm I : " rM S : " ,-n Y3C rM k ; 0!( = , . ; .G=C :T ; 0!( = 5" , . ; + YWZ 6" ; ) ? '> >' I K . .X"L *+ > 0T+ s+[ " + QC=" R7 0!( = ; !7 ." ) *+ > :+Z ." + ;) .+ ;C .=& ;R "' 0 . . Static Converter Fed Drive AGC 11 - 1 . / , Q;R "' ١٢ ;C .=& B dC . 6"w : max c '() h i c : .+ !C .(C; . max c .=& ; x1 B : B!" ; x1 ) .u max c ;C .=& .X"L h i max c ;;/ pt[ *+ > ,-n kl" .+ , . t/ B : *C ;) ] ]( *+ *+ > , H Ib : *C .(7/ `" ; 3 .G=C 0 " : : ^ :[ *+ > , Ik , .+ : ,] T- Ik H!C . Z ;G ) H .;C *;( )G# : ,;)) ,-(F B \ . (5- : ;" *+ > ar x!- ) *C .(7/ * ;" v + *+ > A\[ , "& M I '. - ) 0!( "' B ;R(" ,-@3 , KW ; v =\ .+ ;C *;( 1 - 1 - 1 : *C *;; dC / ;" *+ > ar x!- ) *C .(7/ * ;" v + *+ > A\[ , AGC 12 - 1 ;R "' :=s ;T" Q ١٣ 1 - 3 - 2 @ * F' A+ j) B *;( *+ > , + *y ) u@ B t/ . t/ ) *+ > *+ > . :=5" ) R / X'' ;+ c R :=5" H!XT-) X''/ R ( : *C a!` B dC . A+ j) B *;( *+ > .=& , 0!( "' : ) t/ , B . *+ > 6"w B ;C .=& t/ : h i c j tF ) ldf Y (+7 H .;C *;( .!) -;] A+ j) , S]7 c '() ; R\) "' + 6GR [) ; B 0!( *C ;) ] *+ > "' ! ; *+ > , '' k I ) ' k I ); *+ > , .: : v = ] *+ > "& M I '. - KW ; v =\ .+ ;C *;( ) 0!( "' B ;R(" ,-@3 , 1 - 1 - 1 / : *C *;; dC ;" *+ > ar x!- ) *C .(7/ * ;" v + *+ > A\[ , AGC 13 - 1 A+ *+ > .=& ١۴ @ . / ! NO /. > j) B / . / B *;( ) A+ *+ Load Flow Initialisation .& ; Advanced Options ;C *;( B B Q;C *;( *+ > .=& (; B 6"w t/ ;C .=& B dC . :=s : C'' (+7 c : ('() (+7) t/ *+ > u@ / ' ) k I Q '' k S ( 6"w ? B S]7 QC t/ B 6"w .;C *;; Z" %3; '() E= ) t/ ' o u "C .(7/ * ;" 6"w t/ ;C .=& B dC . :=s : C' (+7 c : ('() (+7) AGC 14 - 1 , :=s ;T" @3 ,- t/ B AGC 15 - 1 , :=s ;T" @3 ,- t/ ١۵ "& M I '. - KW ; v =\ .+ ;C *;( ) 0!( "' B ;R(" ,-@3 , 1 - 1 - 1 : *C *;; dC / ;" *+ > ar x!- ) *C .(7/ * ;" v + *+ > A\[ , 1 - 3 - 3 ' * F ANSI .=& , *+ > ANSI ;; ; ) 0!( "' B *;( G ); • (;"( ?= ) *+ > 0T+ ) • @3 ; :+Z [) / ] Q;Z" R7 *+ > 0!( "' =& .;C T" .(7/ `" ; . / / No Short-Circuit Contribution s+[ QC=" R7 ] ;C ;) " *+ > ;C .=& B dC . 6"w : prefault U '() h5[ @3 B) B A=\ P.U ;C .(7/ `" ; B dC . . *+ > ,- , 0!( "' : • ) , .`& AG! () : .+ r1 ) x1 ;C *;( (: *C c R m m;R ; .+ @"T-) • E@\ : " AG! . .Z!T- ) ) " ); * B ar " ;C .(7/ `" ; • *+ > 30 AG! : ;C .(7/ * ;" Q*+ > 0T+ ) (;C E@\) AGC 16 - 1 :=s ;T" ١۶ 1 - 3 - 4 IEC 61361 *+ > IEC 61361 >WZ . . 0!( "' , ; >WZ .;C .=& A>7 IEC 61361 :7 T- V(+ ; 1 - 4 #1 E= " 0!"- A!%& k4- 0!( "' H .+ (7 *C *;( ;R E= : h H!!R G 0!"- Q C VW(" c! .+ a-7 0!"- E . tq 0!"- - : HGT ;C ;) ;R(" ;R( . / ); B G ? @ C .(C; *C " ,;! . " 0!"- QH!XT- ;C VW(" " / AGC) 18 - 1 B # : B .+ .!) t/ '() . )B B H ; ( ;C *;( B7 . )B E c R ; ; (Z! :7 T- V(+ . e A>7 ; 0!"- AGC 17 - 1 ;R( ,- 0!"- – ;R( " :=s AGC 18 - 1 *C *C 0!"- ١٧ 1 - 5 B 4GO RMS + "=!(ZF c%(W ); B 0!( "' : • E= • '() E= ; .;C *;( '() E= B + A>( (5- ,;)) ,- 4! k+ .G . .(5 "' QC=" A>( ,;)) 4! / .;C *;( '() E= B Q4! h!+ ); - > (7 : ^ E= 0 " 0!( ;C *;( B A[ ;] .+ / ;R(" ,B .!=C , .+ H!!R '() ;G%T A\[ ."(# ); - ; " + KW ; .+ @"T- 1 - 1 - 1 ;C .=& *C *;; dC 1 - 5 - 1 / ! PG$ : ,;)) 4! Id-ref E : & d h5[ P.U Iq-ref E : & q h5[ P.U cosref : Cos E . )B dq sinref : Sin E . )B dq AGC 19 - 1 ) ,;)) RMS ( *C *C 0!"- ١٨ 4! cosref Q sinref 0 B PLL ;+ A>( :[ H ; ;C *;( B m;R B : ,;)) ,- 4! / "cosref" ) "sinref" C A>( : ! :=s '() B *;( QC=" A>( ,;)) ,- 4! / u1 ;] Q sinu ) cosu . "C .=& %3; : '() / C a+ " A\ [ ,; *r '() " : '() / 5 ٪ (Z! B " A\[ ,; *r '() " .;C HC) * ); *4(; QC AGC 20 - 1 E= ١٩ 1 - 5 - 2 3 &- PG$ ,;)) ,- 4! : • : u1r-in ]!][ :T5\ ,;)) '() :=s ; h5[ P.U • : u1i-in - :T5\ ,;)) '() h5[ :=s ; P.U ,;)) (F : • Uk : , (+ *+ > 6"w % h5[ • Pcu : 5 % , (+ h5[ KW ,;)) 4! ); > ; "u1r in" ) "u1i in" B H !b ; ;C *;( '() E= B E= ;C *;( :[ H ; ;C *;( B m;R B : ;] R ) X ,;)) (F B "uk" ) "Pcu" "C .=& '() / C a+ " A\ [ '() ,; *r " : '() / 5 ٪ (Z! B " A\[ ,; *r '() " .;C HC) * ); *4(; QC AGC 21 - 1 '() E=