多区域互联电力系统的PI 滑模负荷频率控制 - 东北大学电气自动化 ...

21 3 2001 3 Vol. 21 No. 3 Mar. 2001Proceedings of the CSEEν 2001 Chin. Soc. for Elec. Eng. :025828013 (2001) 0320006206PI 1 , 2 2, (1. , 130012 ; 2. , 110006)PI SL IDING MODE LOAD FREQUENCY CONTROLOF MULTI2AREA POWER SYSTEMSMEN G Xiang2ping 1 , XU E Chang2fei 2 , ZHAN G Hua2guang 2(1. Changchun Institute of Technology , Changchun , 130012 , China ;ABSTRACT:A synthetic PI sliding mode control method usedfor load frequency control of multiarea power systems has beenproposed , the method has the advantages of PI and sliding modecontrol , sliding mode superface with integral item make the sys2tem can reach on sliding mode from initial time. After reachingon sliding mode , system is controlled by PI control based on A2CEN. When considering generation rate constraint ( GRC) anddeadband , the proposed synthetic control method can make sys2tem to have good performance , and can overcome the disadvan2tages of each control method. Results of simulation show thatthe proposed method is simple , effective , and to ensure that thewhole systems are asymptotic stable.KEY WORDS:load frequency control ; PI control ; sliding modecontrol ; robustness ; decentralised control ; power system.2. Northeastern University , Shenyang , 110006 , China) :GRC(generation rate constraint) PI , ,, ,, , [3 ], T p 20 %,,,GRC , , , A CEN PI :; PI ; ; ; ; : TP 273 ; TM732 :A , ,1 ,,, :(69404003) ;(96014518) [1] , PI P tie f A CE , I Kothari [2 ]A CEN L FC (load fre2quency control) , A CEN PI PI ,I ,,PI,, , GRC,

3 : PI 7 ; R i ; i 2 ;P ci ; u i , ;P di ; f i ;P tiei ; P ri n ; T ij i j 1 , T gi ; T ti ; T pi ; T ri 2. 1 ; K ri ; K pi ;P gi ;X ei 1 Fig. 1 Dynamic model diagram of electric power system2. 2 gX = AX + Bu + FP d X (0) = 0 (1)X = [ X 1 , X 2 , , X n ] T , u = [ u 1 , u 2 , , L FC ; u n ] T ,P d = [P d1 ,P d2 , ,P dn ] T ; X i , u i ,P di L FC i , , , X i= [f i ,P gi ,P ri ,X ei ,P tiei , A CE id t ,A CEN id t , A CEN i ] TA 11 A 12 A 1 n,A 21 A 22 A 2 nA = A ii A ij ,A n1 A n2 A nn [4] ,B = [ B 1 , B 2 , B n ] T B i = [0 0 K ri 10 0 0 0 ] T 2 s ,T gi T giF = [ F 1 , F 2 , F n ] T F i = [ -K pi i ] T , i = 1 ,2 , nT piK piT pi0 0 0 0 0 0 -L FC ,2 : 0. 1/ min0. 2F( x , gx ) = 0. 8 x - gx1x = u - f ,0. 05 %R

8 21 3 PI , A C E N P I, ,1 ,id t , PI , PI , ,P tie f , n A CE I [5 2 : K , K 3. 1 , i ,: , L FC , GRC , gX i = A ii X i + B i u i + F i P di + 6 nA ij X j (2) ,j = 1j iPI X j j (2) ,, gX i = ( A ii +A ii ) X i + ( B i +B i ) u i +(5) ,( F i +F i )P di + 6 nj = 1j iA ij X j (3) A ii ,B i ,F i K pi K ri T pi T ri T ti T gi P di (2) gX i = A ii X i + B i ( u i + f i ( X , t) ) (4) f i ( X , t) = B + iA ii X i + B + iB i u i + B + i ( F i + , CF i )P di + B + i 6 ni = B T i , (5) A ij X j ,B + i = ( B T i B i ) - 1 B T i S i = B T i ( X i - W i ) (7)j = 1j i,S i (0) = 0 , , (4) ,3. 2 A B (7) ,i , [7] :[6] :uS i = C i [ X i - i = u eqi + u si (8)t( A ii - B i K i ) X i ( ) d] = 0 (5) u eqi , 0C i ; K i ; u si , (5) ,(4) ,S i = 0 ,(5) ,C i K i 1 := [0 0 0 0 0 0 k iI k i P ] ,S i = gS i ( t) = 0,u eqi ,(4) (6) : ,gX i = ( A ii - B i K i ) X i (6) (5) S = 0 PI u si S = 0 , ,S i = 0 , K iu i = - k i P A CEN i - k iI,: S i 0 ,t 0 , X i (0)W i= t ( A ii - B i K i ) X i ( ) d0gW i = ( A ii - B i K i ) X i= 0 , W i (0) = X i (0) = 0 ,u eqi = - K i X i = - k ip A CEN i - k iIA CEN id t

3 : PI 9 u si = - h i sng ( S i ) sng ( S i ) ; h i ,1 (4) , (9) ,| f i ( X , t) | < h i (9)S i gS i = S i B T i ( gX i - gW i ) = S i { B T i A ii X i + B i ( u i +f i ( X , t) ) - B T i ( A ii - B i K i ) X i } = S i { B T i ( A ii X i +B i ( - K i X i - h i sgn ( S i ) + f i ( X , t) ) ) - B T i ( A ii -B i K i ) X i } = S i { -f i ( X , t) } -B T i B i h i sgn ( S i ) + B T i B i B T i B i h i | S i | + B T i B i 3. 3 (8) , u eqi = - K i X i , u si = - h i sgn ( S i ) , ( i = 1 , 2 , , n) ,C i = B T i ,S = [ S 1 S 2 S N ] T ,X ( t) | S i | f i ( X , t) | < 0, , (8) | f i ( X , t) | < h i , S i gS i < 0 (8) 4 , u eqi , A CEN i PI ; 25 , u si V ( X , t) =12 S T S ,gV = 1 2 gS T S + 1 2 S T gS = S T gS =6 nS i gS i < 0i = 1 S = 0 , 2 3 : ,: f = 60 Hz; T pi = 20 s; T gi = 0. 08 s;, T ri = 10s ; i = 0 . 035 ; T ti = 0 . 3s ; K ri = 0 . 5 ; R i =, 2. 4 ; K pi = 120 Hz/ pu ;2T ij = 0 . 545 ; i = 0 . 425 2 1 Fig. 2 Dynamic responses of system in area 1

10 21 3 2 Fig. 3 Dynamic response of system in area 24 u s Fig. 4 Response of control u and sliding mode s vs time t5 I Fig. 5 Curves of time error and inadvertent intercharge I : k ip = 0. 15 , k iI = 0. 02 ,,3 ; 4 s GRC , GRC 0. 1 min ,:gP gi = 0. 0017 ,MW/ s ,; 5 PI ,A CEN PI : GRC I, 2 ; , ,A CE PI T p + 20 % GRC

3 : PI 11 I , k iI k i P .5 PI ,GRC ,C i = B T i , PI ,,;,,, :[1 ] . [ M ] . : , 1996.[2 ] Kothari M L ,Nanda J , Koathari D P , et al . Discrete2mode auto2matic generation control of a two2area reheat thermal system withnew area control error[J ] . IEEE Trans on Power Systems ,1989 ,A ii =(i i ----26 N1T pi0 -K riR i T gi0 -10 (5) :7302738.[3 ] Al2hamouz A Z ,Abdel Magid Y L . Variable structure load fre2quency controllers for multiarea interconnected power systems[J ] .Int . J . Electric Power Energy System ,1993 ,15 (4) :2932300.[4 ] Chang C S , Fu W H ,Wen F S. Load frequency control using ge2netic algorithm based fuzzy gain scheduling of PI controllers[J ] .Electric Machines and Power Systems ,1998 ,26 (2) :39252.[5 ] Lim K Y , Wang K , Zhou R. Robust decentralised load2frequencycontrol of multi2area power systems [ J ] . IEE Proc. GenerTransm. Distrib. ,1996 ,143 (5) :3772386.[ 6 ] Shyu K K ,Shieh H J . A new switching surface sliding2mode speedcontroller for induction motor drive systems[J ] . IEEE Trans on ,PE ,1996 ,11 (1) :6602667.[ 7 ] Drakunov S V ,Utkin V I. Sliding mode control in dynamic sys2tems[J ] . Int . J . Control ,1992 ,55 (4) :102921037.A ij =K piT pi0 0 -0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0- 2T ij 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0- 2T ij 0 0 0 0 0 0 0K piT pi0 0 01 10 0 0 0 0T ti T ti1T ri( 1 T ri-1R i T gi0 0 -j =1j iK ri)T gi0 0 0 01T gi0 0 0 0T ij 0 0 0 0 0 0 0 i 0 0 0 1 0 0 0 i 0 0 0 1 i 0 0 i+ 26 N i K piT ij )0 0 T i - i K pi0 0 0pi T piT pij = 1j i :2000209229 ; :2001201221 : (19612) ,, , ,; (19742) ,, ,; (19592) ,,, ,()2000 11 ,36 1999 ,, 1372 , 280 217 ; 0. 432 , 148 ( )