SSR. A Novel Approach to Construct the State-space Model of Power System Grid and Its Application in SSR Study

Transcription

1 34 4 Vol.34 No.4 Feb.5, Proceedings of the SEE 2014 hin.soc.for Elec.Eng. 605 DOI /j pcsee (2014) TM 712TM734 SSR (() ) A Novel Approach to onstruct the State-space Model of Power System Grid and Its Application in SSR Study ZHU Xinyao, SUN Haishun, HEN Meng, WEN Jinyu, HENG Shijie (State Key Laboratory of Advanced Electromagnetic Engineering and Technology (Huazhong University of Science and Technology), Wuhan , Hubei Province, hina) ABSTRAT: The configuration feature of the transmission grid was summarized, then a method to choose state-variables of the grid was presented and the dynamic conductance matrix of capacitor branch was defined, and finally a novel method to construct the state-space model of the network was proposed. Without using the network normal tree to choose state-variables of the network, and without ranking the branches and nodes under strict rules, the method constructs the state-space model of the network conveniently, and the state-space model of the network modifies with the network change easily. That makes the method very effective to study subsynchronous resonance (SSR) of multi-machine power systems. SSR problem of a compensated multi-machine system and its damping by static var compensator (SV) were studied by the proposed method, and the results were verified by time domain simulations. The method is supposed to be helpful for the planning of power plant integrating and the design of the countermeasure of SSR. KEY WORDS: subsynchronous resonance (SSR); eigenvalue analysis; dynamic conductance matrix of capacitor branch; multi-machine power system; static var compensator (SV) 863 (2011AA05A119) (SG-MPLG ) The National High Technology Research and Development of hina 863 Program (2011AA05A119); State Grid orporation of hina, Major Projects on Planning and Operation ontrol of Large Scale Grid (SG-MPLG ). (subsynchronous resonancessr) SSR SSR SSR 0 [1-2] (subsynchronous resonancessr) SSR [3-6] SSR SSR SSR SSR [7] SSR

2 SSR / [8-10] SSR [11-12] [13] [14-15] [16-17] KL (Kirchhoff's current laws) KVL (Kirchhoff's voltage laws) KL/KVL [14-17] SSR SSR d q dq [18-19] px A X B U IGdq G dq XG dq G dq G XG dq Gdq G XG dq Gdq Gdq Gdq Gdq Gdq (1) X Gdq U Gdq I Gdq dq Gdq Gdq pd/dt 1.2 SSR / [8] xy [19] pxnet Anet Xnet Bnetunet Y X D u D pu net net net pnet net net net (2) X net u net Y net 1.3 dq xy [17,20] dq xy 1 G q x y q G 1 Fig. 1 Relation of dq and xy coordinates 1 Xx sing0 cosg0xd X y cosg0 sin X G0 q cosg0 sin X G0 d 0 G sing0 cos X G0 q0 TXTX (3) X u i G x d b G

3 4 SSR (3)(1)(2) [13] px A X (4) sys sys sys X sys [X net X Gdq ] T A sys A sys SSR 2 SSR Fig. 2 Diagram of the branches connected to a bus [13] 2 SSR / R-L [13] R-L xy 0 [13] ix ux p i y x 0 1 u y x 1 0 ux ux ( p p+ ) u y u y (5) u i (Y p py) 3.2 R-L xy R-L urlx xl 0 irlx r x i l RLx p u RLy 0 x i l RLy x i l r RLy u i R-L 4 (6) 4.1 / n k m(mn) 3 ( Y p + Y ) U = B I B I (7) p 1 line 2 inject AlineU Bline1 piline Bline2I line (8) U[u 1x u 1y u nx u ny ] T I line [i line1x i line1y i linekx i lineky ] T I inject [i lx i ly i nx i ny ] T /

4 Fig. 3 Flow diagram of the dynamic conductance matrix and state-space of line current construction (7) Y p Y B 1 B 2 (8) A line B line1 B line2 B line1 B line2 (7)(8) Y p Y B 1 B 2 / Unode A Al Unode B I inject Iline Al All Iline p 0 (9) Y Unode U node I inject / R-L / / I I D I (10) inject inject RL inject Gxy / pirl ARLIRL BRLUnode U RLp pirl RL IRL + DRLUnode (11) DRLp pig xy DRLIG xy 4 R-L Fig. 4 Flow diagram of the capacity node injecting current and state-space of the remaining R-L current construction (10)(11)I RL R-L I Gxy xy 4.3 (10)(9) /(11) xy pxnet Anet Xnet Bnet IG xy U X D I D pi net net net Gxy pnet Gxy (12) X net [U node I line I RL ] T I Gxy xy (7)(8)(10)(11) (12) (1)(3) SSR [19-20]

5 4 SSR % SSR 2 (static var compensatorsv) SSR [21] SV SSR 80 Mvar MW MW % 35% 35% 3 35% 35% 5 Fig. 5 Single-line diagram of typical power system with series compensation 1 1 st TR 1 k 1 stm 1 st 2 T s, k 200, T s, T s m SV Fig. 6 ontrol strategy and parameters of the SVs pu s SSR 1 SSR SV 3 35% 2 5%~95% (a) SV 2 35% 3 5%95% 2 1 7(b) % 2 30% 1 /s 1 /s 1 Fig (a) (b) Real-part of shaft modes of power plant 1 units 3 SSR 2 25% SSR 2 35% 3 20% SSR 2 SSR SV (fixed capacitorf) (thyristor controlled reactortr) 6 (5)(6) % SV SSR SV SV 2 SV SSR 2

6 Tab. 1 SV Torsional and electrical resonance modes of power plant 1 and 2 units /s /Hz /s 1 /Hz SV 2 SV SSR 1 SSR 4 SV s A 0.1 s SV 3 35% 2 20% 35% % 1 SSR 2 35% 1 SSR 2 35% Gen /(rad/s) LAP-LBP /pu 4 SV2 SV SSR (a) 2 20% Gen /(rad/s) LAP-LBP /pu /pu (b) 2 35% Fig Shaft speed deviation and torque of G2 of power plant f/hz % 1 Fig. 9 Time-frequency features of the shaft torque of power plant 1 unit when lines 2 are 35% compensated SV 1 SSR 4 SV 1 Gen /(rad/s) LAP-LBP /pu Gen /(rad/s) LAP-LBP /pu (a) 4 SV (b) 2 SV 10 SV 1 Fig. 10 Shaft speed deviation and torque of G2 of power plant 1 when SVs are in service 50

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