VSC STEADY2STATE MOD EL AND ITS NONL INEAR CONTROL OF VSC2HVDC SYSTEM VSC (1. , ; 2. , )

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ἐλπίς Κεδίκογλου
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1 Vol. 22 No. 1 Jan Proceedings of the CSEE ν 2002 Chin. Soc. for Elec. Eng. : (2002) VSC 1, 1 2, (1., ; 2., ) STEADY2STATE MOD EL AND ITS NONL INEAR CONTROL OF VSC2HVDC SYSTEM ZHAN G Gui2bin 1, XU Zheng 1, WAN G Guang2zhu 2 (1. Zhejiang University, Hangzhou ,China ; 2. Shandong U niversity, Jinan ,China) ABSTRACT: In this paper,the mathematical model and its con2 trol strategy of the VSC2HVDC system are studied. Because the voltage source converter has two degrees of freedom for control, four controlled variables in the two volage source converters of the HVDC system are determined. The steady state mathemati2 cal model for the VSC2HVDC system is developed in the paper, and the approximately decoupled relationship between the two controlling variables and the two controlled variables in the volt2 age source converter is proposed. An inverse steady state model controller for the VSC2HVDC system is proposed. The control strategy for the VSC2HVDC systemis using the inverse steady state model controller to trace the operating point and using the two decoupled controlling loops to eliminate the steady state de2 viations. Simulation results show the validity of the established steady state model and the effectiveness of the proposed control strategy. KEY WORDS:voltage source converter ; HVDC ; inverse mod2 VSC el ; nonlinear control VSC 2 2 : 2 PI, 4,, 2 2, : ( ) ; ( G ) Project Supported by National Natural Science Foundation of China ( ) ; Project Supported by Special Funds for major State Basic Research Projects of P. R. China ( G ) : (VSC) ; ( HVDC) ; ; : TM721 :A 1, VSC [13 ],,VSC 2 ( PWM ) 2 (VSC ), VSC 2 VSC ( VSC) U s

2 18 22 U c U c U s,, L X 3 VSC VSC P = U su c sin (1) X Q = U s ( U s - U c cos ) X 1 Fig. 1 Voltage source converter (2) (1) (2), U c Q s2, X 1 = L 1 X 2 = L 2 Z 1 = VSC PWM, PWM, U c PWM M, 1 = arctan R 1 / X 1 2 = arctan R 2 / X 2 PWM M 2 P Q, 2, R 1 R 2 R lim1 R lim2, 2, P s1 Q s1, P c1 Q c1, P c1 Q s1 ; P s2 Q s2, P c2 Q c2,, P c2 R X 2 1 Z 2 = R X 2 2 Y 1 = 1/ Z 1 Y 2 = 1/ Z 2 P c1 = U s1 U c1 Y 1 sin ( ) - U 2 c1 Y 1 sin 1 (3) VSC, Q s1 = U s1 U c1 Y 1 cos( 1-1 ) - U 2 s1 Y 1 cos 1 (4) 3 : ( 3) ( 4), U s1 U c1, P c1 Q s1, U s1 U c1, ; ( ), P ( ) ; c1 Q s1 VSC,,, VSC PWM 1 ( PWM) M 1,0 M 1 1, U c1 = M 1 U d1 / 2 (5), VSCVSC R 1, 2 VSC Fig. 2 Steady2state physical model for VSC2HVDC

3 1 : VSC 19 P c1 = U d1 I d1 (6) I d2 = M 2 2 U d1 Y 2 sin M 2 U s2 Y 2 sin ( 2-2 ) (3) (6) VSC 2 + M 2 2 R d Y 2 sin 2 (17) (16) (17) (15), P c2 = U s2 U c2 Y 2 sin ( 2-2 ) + U 2 c2 Y 2 sin 2 (7) 2 U c2 U s2 Q s2 = U s2 U c2 Y 2 cos( ) - U 2 s2 Y 2 cos 2 (8) U c2 = M 2 U d2 / 2, 0 < M 2 < 1 (9) 2 M 2 U s2 Y 2 sin ( 2-2 ) ) cos( ) ]/ P c2 = U d2 I d2 (10) ( M 2 2 R d Y 2 sin 2 ) (18),, (17) (18) 2 2 I d = I d1 = I d2 = ( U d1 - U d2 ) / R d (11) 4 VSC 2 2 R d PI VSC VSC 2 2, 2 2,, 2 :, I d1, ; 2 U d2, - 90 (3) (6), U d1 Q s1, M ; , 1 1 VSC, ; 2 VSC : (5) (6) (3) U d1 = U s1sin ( ) 2 I d1 - M 1 sin 1 M 2 (12) 1 Y 1 sin 1 (12) ( 13), U (5) (12) (4) d1 Q s1 1 M 1 Q s1 = U 2 s1sin2 1 2 U s1 I d1 cos( 1-1 ) I d1, 5 U d1 > 0, - (13) R 1 M 1 sin 1 5 U d1 (12) (13) 2 5 Q s1 5 Q s1, 5 M M 1 2 : (7) (10) U d1 > 2 U s1 VSC, I d2 Q s2, M 2 2, U d1 µ I d1 R d, : (9) (10) (7) I d2 = M 2 2 U d2 Y 2 sin 2 / 2 + M 2 U s2 Y 2 sin ( 2-2 ) / 2 (14) (9) (8) Q s2 = M 2 U s2 U d2 Y 2 cos( ) / 2 - U 2 s2 Y 2 cos 2 (15) (11) U d2 = U d1 - I d2 R d (16) (16) (14), Q s2 = M 2 2 U s2 U d1 Y 2 cos( ) - U 2 s2 Y 2 cos 2 - [ M 2 U s2 Y 2 R d ( M 2 2 U d1 Y 2 sin VSC 5 % R 1 1 < 45,,,, :5 U d1 / 5 M 1 < 0 5 U d1 /

4 > 0,U d1 1/ M 1 ;5 Q s1 / 5 1 > 0 5 Q s1 / 5 M 1 PI I d1 = 0, Q s1 M 1,, 1 Q s1 M 1 U d (17) 5 I d2 / 5 2 > 0,5 I d2 / 5 M 2 2 I d2 U d1, I d2 R d 2 VSC U d2 = U d1 - I d2 R d U d1, (15) :5 Q s2 / ( M 2 / 2) U s2 U d1 Y 2 sin ( ), 2,5 Q s2 / 5 M 2 U s2 U d1 Y 2 cos( ) / 2 > 0 U d1 = U dref Q s1 = Q ref 1 I d1 ( ),,, Q s2 M 2 (12) (13) 01 M 01,, M 2 Q s2 01 = f01 ( U dref, Q ref 1, I d1 ) (19), 2 M 01 = f M01 ( U dref, Q ref 1, I d1 ) (20) I d2 M 2 Q s PI, U dref, 2, 01 = f01 ( Q ref 1, I d1 ) (21) 3 4 ( ) PI M 01 = f M 01 ( Q ref 1, I d1 ) (22) (12) (13),(21) (22),,, U d1 = U dref VSC, (12) (13) I d1 = M 1 U s1 Y 1 sin ( ) / 2 - M 2 1 U dref Y 1 sin 1 / 2 (23) Q s1 = M 1 U s1 U dref Y 1 cos( 1-1 ) / 2 - U 2 s1 Y 1 cos 1 (24) (23) (24) M 1 Q s1, M 1 I d1, 3 Fig. 3 Control diagram for dc voltage controlling station 2 ;, ( ), 1 I d1, 1 Q s1 2, (21) (22), 5. 2 I d2 = I dref Q s2 = Q ref 2, (17) (18) 02 M 02, 02 = f02 ( Q ref 2, I dref ) (25) 4 Fig. 4 Control diagram for dc current controlling station M 02 = f M 02 ( Q ref 2, I dref ) (26) VSC 2, (17)

5 1 : VSC 21 (18) (25) (26), : (17) ( 18) 4. 2, M 2 R 1 = R 2 = 0. 8 L 1 = L 2 = Q s2, M 2 I d2 10 mh C 1 = C 2 = 100F 2 ;, 10 kv R 0 = ( ), 2 I d2 / km L 0 = mh/, 2 Q s2 2 km 10 km VSC 3 MVA,,(25) (26) R d = 5. 4, U dref = 20 kv ( IG2, B T GTO) VSC, ( 2 [3, ) ], 900 Hz 5 6, N ETOMAC 7 5 Fig. 5 Numerical solution of the dc voltage controlling station s steady2state inverse model U d1 I d2 P d1 7 (a), PI 2 M 2 ( Fig. 6 Numerical solution of the dc current controlling station s steady2state inverse model ), 3 4 PI 02 M 02 ;7 (b) (c),, PI 7 8 PI, VSC, 1 M 1 ( ), 01,, M : 6 U s1 = U s2 = 10 kv [5 ], VSC 1 2 6,, ( w 1 Q 2 s1 + w 2, 0 U 2 d1 + w 3 Q 2 s2 + w 4 I 2 d2) td t, w 1 w 2 w 3 w 4 ; : Obj = t, 3 4 PI, Q s1 Q s2, ; 5 6 a i a1 i a2 ; 9, ;,,N ETOMAC [4 ] 2

6 Fig. 7 Simulation results ;, 1 M 1 2 M 2 0, : ;,, PI,, PI, 3 4 PI N ETOMAC, 7 (a), ; 7 ( b) (c),, 7 VSC, 2 VSC 2 2, PI :, 2 2 ; [1 ] Asplund G, Eriksson K, et al. DC transmission based on voltage source converters[ C]. CIGRE, [ 2 ] Stendius L, Eriksson K. HVDC Light An excellent tool for city center infeed[ C]. Power Gen Conference, Singapore, [3 ] Gr nbaum R, Halvarsson B, Wilk2Wilczynski A. FACTS and HVDC Light for power system interconnections[ C]. PowerDeliv2 ery Conference, Madrid, Spain, [ 4 ] Lei X, Lerch E, Povh D, Ruhle O. A large integrated power sys2 tem software package2netomac[ C]. Proceedings of POWER2 CON 98, Beijing, China : [5 ] A. B. ( Posh A B). ( HVDC sys2 tem structure and operating modes) [ M ]. : (Beijing : Water Resources and Electric Power Press),1979. [6 ] Suzuki Hirokazu, Nakajima Tatsuhito, et al. Development and ; testing of prototype models for a high2performance 300 MW self2 commutated AC/ DC converter[j ]. IEEE Trans. on Power Deliv2 ery, 1997 ;12 (4) : : ; : (19712),,, (19622),,,, (19642),, ( )

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