Simplified Approach for Synthesizing Frequency Dependent Network Equivalents Including Dynamic Behaviors of Large Power Transmission Systems

Transcription

1 Simplified Approach for Sythesizig Frequecy Depedet Network Equivalets Icludig Dyamic Behaviors of Large Power Trasmissio Systems Q. Bui-Va (*) F. Beauchemi Études de réseau et Critères de performace, Plaificatio des actifs et Affaires réglemetaires Hydro-Québec TrasÉergie (*) Correspodig author s address: Bui_Va.Que@hydro.qc.ca Coceptio - Appareillage électrique et commade Igéierie de productio Hydro-Québec Équipemet Abstract The extet of Hydro-Québec power trasmissio system has substatially icreased the complexity of trasiet simulatio studies for the itegratio of ew power productio ad trasmissio facilities, eve if these studies were performed usig the powerful simulatio tool such as EMTP-RV owadays available. Furthermore, the specificatios of tur-key projects for static VAr compesators ad HVDC itercoectios ofte require precise trasmissio system data which have to be provided i a simplified maer. I order to reduce the size of power systems for trasiet simulatio studies ad to be able to provide trasmissio system data i a compact format, a simplified method for the sythesis of equivalets for large power trasmissio systems was developed. As a applicatio, the trasiet simulatio studies for the itegratio of Eastmai- Sarcelle (E-S) hydropower plats at the Némiscau kv substatio were performed usig this etwork sythesis approach. The steady states of the complex etwork are preserved by cotrollig the voltage ad the power ijectio at the equivalet bus bar (Némiscau 735 kv) i the reduced system. Furthermore, the frequecy depedet etwork impedaces of positive ad zero sequeces as well as the system dyamic behaviors durig a electromechaical trasiet disturbace are icluded i this etwork sythesis. Keywords Network Equivalet, Data Simplificatio, Power System Dyamic, Harmoic, Modelig Techique I. INTRODUCTION he Eastmai-Sarcelle (E-S) hydroelectric power T developmet, as illustrated i Fig., cosists of three geeratig statios: Eastmai- with 3 uits of 66 MVA, Eastmai-A with 3 uits of 65 MVA ad Sarcelle with 3 uits of 55 MVA. The total power geerated by these geeratig statios will be carried via a 59-km, 35-kV double-circuit lie ad ijected ito Hydro-Québec mai trasmissio grid from the Némiscau kV substatio. The Eastmai ad Sarcelle geeratig statios are itercoected by a 0-km, 35-kV sigle-circuit lie. System studies have to be coducted to assess the trasiet performaces of HV/EHV equipmet, protectio ad cotrol systems that will be implemeted for the itegratio of this project. However, the extet of Hydro-Québec power trasmissio system has substatially icreased the complexity of trasiet simulatio studies, eve if they were performed usig the powerful simulatio tool such as EMTP-RV owadays available. Therefore, a simplified method for the sythesis of equivalets for large power trasmissio systems was developed. This paper summarizes the methodology of this etwork sythesis approach as well as the results of its applicatio i trasiet simulatio studies for the itegratio of the E-S hydropower project. a) Hydro-Québec 735-kV mai trasmissio grid Preseted at the Iteratioal Coferece o Power Systems Trasiets (IPST 05) i Motreal, Caada o Jue 9-3, 005 Paper No. IPST05-00 b) Eastmai Sarcelle reduced equivalet system Fig.. Itegratio of Eastmai-Sarcelle hydropower plats i Hydro Québec 735-kV trasmissio system

2 II. OBJECTIVES OF NETWORK SYNTHESIS The mai objectives for sythesizig a large power trasmissio system are to reduce its size i order to facilitate trasiet simulatio studies as well as to be able to provide trasmissio system data i a simplified maer for tur-key power projects such as static VAr compesators, HVDC itercoectios, etc. Furthermore, i order to maitai sufficiet degree of accuracy for trasiet simulatio studies usig the reduced sythesized system, the followig performace criteria should be fulfilled: The steady-state coditios as well as the short circuit levels i the itegrated etwork should be preserved i the reduced equivalet system. The frequecy resposes of the itegrated etwork should be sythesized for a wide bad of frequecies coverig all the electromagetic trasiet pheomea uder study. Fially, the dyamic behaviors of the itegrated etwork could be reproduced by usig the reduced sythesized system. III. STEADY-STATE CONDITIONS AND SHORT-CIRCUIT LEVELS IN THE INTEGRATED NETWORK The simplest equivalet of a large power system is the steady state Thévei equivalet at the power frequecy of 60 Hz (or 50 Hz). For a balaced three-phase power system, i which positive ad egative sequece impedaces are supposed equal, the Thévei impedaces ca be represeted by the positive ad zero sequece short-circuit impedaces see at the equivalet bus bar, as illustrated i Fig. a. Furthermore, to preserve the steady-state coditios accordig to the load-flow i the itegrated etwork, the iteral equivalet voltage, V i δ i, is calculated from the steady state termial voltage, V T δ T, ad the power ijectio, P+jQ, at the equivalet bus bar usig the followig equatios (Fig. b): a) Represetatio of short-circuit levels of a isolated complex etwork V P + T cos( φ) Z δ = φ arcta V Q + T si( φ) Z V Z = + si( φ ) Q T i Z si( φ V T V () δ ) δ = δ i T + δ (3) Where: Z φ Positive-sequece impedace at the system frequecy of 60 Hz (or 50 Hz), as see at the equivalet bus bar, of the isolated etwork to be sythesized V T δ T Steady-state voltage at the equivalet bus bar accordig to the load-flow i the itegrated system P + j Q Power ijectio ito the equivalet bus bar accordig to the load-flow i the itegrated system V i δ i Calculated iteral equivalet voltage Table I shows the steady state termial voltage, V T δ T, the power ijectio, P+jQ, as well as the short circuit levels at Némiscau 735 kv obtaied by EMTP simulatios usig the itegrated etwork ad the E-S reduced system with the calculated iteral equivalet voltage, V i δ i. TABLE I VALIDATION OF STEADY-STATE THÉVENIN EQUIVALENT Results Calculated iteral equivalet voltage (phase-to-grd. peak), V i δ i, usig (), () ad (3) Steady-state termial voltage at Némiscau 735 kv (phaseto-grd. peak): V T δ T Power ijectio (P + j Q) to Némiscau 735 kv With the itegrated etwork () With the E-S reduced system Not applicable 67.0 kv kv kv 67.5 ( j 50.4) MVA ( j 56.7) MVA Three-phase short-circuit curret at Némiscau 735 kv 0.0 ka 0. ka Phase-to-groud short-circuit curret at Némiscau 735 kv 7. ka 7.5 ka It ca be oticed that there is a good agreemet betwee the results obtaied with the E-S reduced system ad those with the itegrated etwork. b) Represetatio of steady state coditios i the itegrated etwork Fig.. Steady state equivalet at power frequecy of a large power system IV. SIMPLIFIED APPROACH FOR THE SYNTHESIS OF NETWORK FREQUENCY RESPONSES The previous steady state equivalet is ot adequate for aalyzig electromagetic trasiet pheomea which iclude high frequecy spectrum such as temporary/switchig overvoltages, irush trasiets, harmoic pheomea, etc. Therefore, the frequecy resposes of the itegrated etwork should be represeted i the reduced equivalet system.

3 A. Frequecy resposes of the isolated Hydro-Québec 735-kV mai grid I order to represet the frequecy behaviors of the itegrated etwork, the frequecy scas were first performed for the frequecy depedet impedaces i zero ad positive sequeces, Z 0 (f) ad Z (f), see at Némiscau 735 kv i the isolated Hydro-Québec mai trasmissio grid. Fig. 3 shows the magitudes ad the imagiary parts of Z 0 (f) ad Z (f). B. Properties of parallel R-L-C circuits Parallel R-L circuit: Z ( f ) = Impedace of the parallel R-L circuit R jπ f jπ f + ( R / L) As a example, the magitudes of Z (f), for R=0 Ω ad L varyig betwee mh ad 0 mh, are illustrated i Fig. 5. (4) Fig. 5. Magitudes of Z (f) for R=0Ω ad L varyig betwee mh ad 0 mh Sythesizig properties []. R = lim Z ( f ) f (5) Z L = (liear slope of Z(f) f 0 ) (6) π f Parallel R-C circuit: Impedace of the parallel R-C circuit Fig.3. Magitudes (top) ad imagiary parts (bottom) of Z 0 (f) ad Z (f) see at Némiscau 735-kV i the isolated Hydro-Québec 735-kV mai grid O these frequecy resposes, the followig parameters ca be idetified for the th pole of Z 0 (f) or Z (f): R is the magitude of the th pole of Z 0 (f) or Z (f). f X max is the frequecy at which the imagiary part, X 0 (or X ), of Z 0 (or Z ) is maximum. f X mi is the frequecy at which the imagiary part, X 0 (or X ), of Z 0 (or Z ) is miimum. These parameters together with the properties of parallel R-L-C circuits allow sythesizig the frequecy depedet impedaces, Z 0 (f) ad Z (f), which have idetifiable poles, usig the Foster equivalet circuit as illustrated i Fig. 4 []. Z ( f ) = jπ f / C + (/ RC) Fig. 6 shows a example of the magitudes ad imagiary parts of Z (f) for R=0 Ω ad C varyig betwee µf ad 00 µf. (7) Fig. 6. Magitudes (top) ad imagiary parts (bottom) of Z (f) for R=0 Ω ad C varyig betwee µf ad 00 µf Sythesizig properties []. Fig. 4. Foster equivalet circuit sythesizig Z 0 (f) or Z (f) havig idetifiable poles R = Z ( f ) f = 0 (8) C = π R f X mi. (9) 3

4 Where f X-mi is the frequecy at which the imagiary part of Z is miimum. Parallel R-L-C circuit: Impedace of the parallel R-L-C circuit ( / C )( jπ f ) Z ( f ) = ( jπ f ) + ( / R C )( jπ f ) + ( / L C ) (0) Fig. 7 depicts a example of the magitudes ad imagiary parts of Z (f) for L = 33. mh, C = 54.3 µf ad R varyig betwee 50 Ω ad 50 Ω. Fig. 7. Magitudes (top) ad imagiary parts (bottom) of Z (f) for L=33. mh, C=54.3 µf ad R varyig betwee 50 Ω ad 50 Ω Sythesizig properties [], [3]. C. Sythesized circuits for Z 0 (f) ad Z (f) see at Némiscau 735 kv Table II summarizes the parameters of sythesized parallel R-L-C circuits, which were calculated for Z 0 (f) ad Z (f), usig (), (), (3) ad (4) as well as the data for R, f -X max, f -X mi, of idetifiable poles o Fig. 3. POLE NO. TABLE II PARAMETERS OF SYNTHESIZED CIRCUITS FOR Z 0 (f) AND Z (f) Parameters of the sythesized parallel R-L-C circuits for Z 0 (f) see at Némiscau 735 kv R L C (Ω) (m H) (µf) Parameters of the sythesized parallel R-L-C circuits for Z (f) see at Némiscau 735kV R L C (Ω) (m H) (µf) Although the sythesis results were ot preseted i Table II, few other poles of Z 0 (f) ad Z (f) at sub-sychroous frequecies were also icluded i the fial sythesized circuits i order to represet the effects of series compesatio at Némiscau 735 kv. Moreover, ideal trasformers were used i the three-phase coectios of the sythesized circuits to decouple the zero-sequece impedace, Z 0 (f), from the positive sequece impedace, Z (f), as illustrated i Fig. 8 [4]. Furthermore, to represet the steady state coditios i the itegrated etwork, the magitude ad the phase agle of the three-phase iteral voltages were set at the value of iteral equivalet voltage, V i δ i, previously calculated i Table I. R = Z ( f ) () o R ( f f ) X mi X max L = () π ( f f ) X mi X max k C = 4π ( f f ) (3) X mi X max = k L (4) Where: f o = /( π ) = resoace frequecy R L C Magitude of Z at resoace frequecy f o f -X max Frequecy at which the imagiary part of Z is maximum f -X mi Frequecy at which the imagiary part of Z is miimum Fig. 8. Three-phase coectios of sythesized circuits for Z 0 (f) ad Z (f) see at Némiscau 735 kv V. VALIDATION OF FREQUENCY DEPENDENT NETWORK EQUIVALENT (FDNE) AT NÉMISCAU 735 kv A. Validatio i frequecy domai The frequecy depedet impedaces i zero ad positive 4

5 sequeces that are see at the equivalet bus bar of the threephase sythesized circuit i Fig. 8, were compared to the frequecy resposes, Z 0 (f) ad Z (f), previously obtaied with the isolated Hydro-Québec 735-kV mai grid. Simulatio results, as illustrated i Fig. 9, idicated that there is a good agreemet betwee the sythesized ad the complex etworks. geeratig statios Eastmai-, Eastmai-A ad Sarcelle as well as the FDNE at Némiscau 735 kv, were simulated with iteral dyamic voltage models, as illustrated i Fig. [5], [6]. a) Three-phase-to-groud fault at Némiscau 735 kv Fig. 9. Validatio i frequecy domai of the sythesized circuits for Z 0 (f) (top) ad Z (f) (bottom) see at Némiscau 735 kv b) Lie-to-groud fault at Némiscau 735 kv Fig. 0. Voltages at Némiscau 735 kv durig three-phase-to-groud (a) ad lie-to-groud (b) faults at Némiscau 735 kv I this figure, oe ca also observe a perfect matchig betwee the positive ad zero sequece impedaces at 60 Hz see at Némiscau 735 kv i the isolated Hydro-Québec mai grid ad those obtaied with the sythesized parallel R-L-C circuits. Therefore, for this case, it is ot ecessary to make additioal adjustmets to the sythesized circuit to preserve short-circuit levels i the itegrated system. For geeral applicatio, i case of mismatch betwee impedaces at 60 Hz (or 50 Hz), additioal parallel R-L or R-C circuits ca be used to adjust short-circuit levels i the reduced sythesized system. B. Validatio i time domai The simulatios i time domai of three-phase-to-groud ad lie-to-groud faults at Némiscau 735 kv were performed with the E-S reduced sythesized etwork as well as with the itegrated complex etwork. Agai, it ca be observed i Fig. 0a ad 0b that there is a good agreemet betwee the results obtaied with the reduced sythesized etwork ad those with the itegrated complex etwork. VI. MODELING COMPLEX SYSTEM DYNAMIC BEHAVIORS The previous FDNE at Némiscau 735 kv with costat three-phase iteral voltages does ot allow studyig the dyamic behaviors of Hydro-Québec itegrated complex etwork. Therefore, i order to reproduce these dyamic behaviors usig EMTP ad the E-S reduced system, all the Fig.. Iteral dyamic voltage model For each geeratig statio (or FDNE), the iteral dyamic voltage, V a (t), was applied to the phase A behid the geeratig statio equivalet (or the FDNE). The iput sigals, V i (t) ad δ i (t), were calculated from the positive sequece equivalet impedace, Z φ, at power frequecy ad from the results of system stability simulatio, P (t)+jq (t) ad V T (t) δ T (t), usig (), () ad (3). For the phases B ad C, the iteral dyamic voltages, V b (t) ad V c (t), have the same magitude as V a (t), but their phase agles were respectively displaced -0 ad +0 with respect to the phase A. This modelig techique was used to simulate the dyamic behavior of Eastmai Sarcelle geeratig statios durig a three-phase fault at Eastmai- 35 kv implyig the loss of oe 35-kV circuit betwee Eastmai- ad Némiscau. EMTP results were 5

6 the compared to those obtaied by system stability simulatio usig PSS/E ad Hydro-Québec itegrated complex etwork. Although there are some discrepacies iheret to the two simulatio techiques (PSS/E vs. EMTP), it ca be observed i Fig. a ad b that the overall dyamic behavior of Hydro-Québec itegrated complex etwork was accurately reproduced usig the E-S reduced sythesized system. The dyamic behaviors of a complex itegrated trasmissio grid could be well reproduced usig iteral dyamic voltage models i the reduced sythesized system. Fially, this simplified sythesis approach allows providig large trasmissio system data i a simplified maer for tur-key power projects such as: static VAr compesators, HVDC itercoectios, etc. VIII. ACKNOWLEDGMENT The authors gratefully ackowledge the cotributio of Mr. Bruo Picard for the PSS/E simulatio results used to validate the sythesized model. a) Variatio of geerator frequecy at Eastmai- b) Three-phase voltages at Eastmai- 3.8 kv Fig.. Variatio of geerator frequecy at Eastmai- (a) ad three-phase voltages at Eastmai- 3.8 kv (b) durig a three-phase fault at Eastmai- 35 kv implyig the loss of oe 35-kV circuit Eastmai- Némiscau. VII. CONCLUSIONS A simplified approach usig the properties of parallel R-L-C circuits for sythesizig Hydro-Québec 735-kV mai trasmissio grid has bee developed ad described i this paper. The results of its applicatio for the trasiet simulatio studies usig the E-S reduced sythesized system lead to the followig coclusios: The short-circuit levels i a complex itegrated trasmissio grid could be maitaied i the reduced equivalet system by usig the zero ad positive sequece short-circuit impedaces at power frequecy as see at the equivalet bus bar. The steady state coditios i the complex itegrated trasmissio grid could be preserved by cotrollig the termial voltage ad the power ijectio at the equivalet bus bar. The frequecy resposes i zero ad positive sequeces, Z 0 (f) ad Z (f), of a complex trasmissio grid with idetifiable poles could be accurately sythesized by a combiatio of parallel R-L-C circuits. IX. REFERENCES [] Erst A. Guillemi, Sythesis of passive etworks, New York: Joh Wiley & Sos, Ic. 957, pp [] E. Portales ad Q. Bui-Va, "New Cotrol Strategy of Irush Trasiet Durig Trasformer Eergizatio at Toulustouc Hydropower Plat Usig a Double-break 330-kV Circuit Breaker," Paper No. 9b-3 preseted at IPST 003 i New Orleas, USA, o September 8 th to October d. [3] E. Breer ad M. Javid, Aalysis of electric circuits - d editio, McGraw-Hill Book Compay, 967, chapter 0, pp [4] A. Clerici ad L. Marzio, "Coordiated Use of TNA ad Digital Computer for Switchig-Surge Studies: Trasiet Equivalet of a Complex Network," IEEE Trasactio o Power Apparatus ad Systems, Vol. PAS-89, No. 8, November/December 970. [5] Q. Bui-Va ad M. Rousseau, "Cotrol of Overvoltages o Hydro- Québec 735-kV Series-Compesated System Durig a Major Electromechaical Trasiet Disturbace," Paper No. 04 preseted at IPST 00 i Rio de Jaeiro, Brazil, o Jue 4-8 th. [6] IEC , TR, Ed. (004): "Isulatio co-ordiatio Part 4: Computatioal guide to isulatio co-ordiatio ad modelig of electrical etworks" X. BIOGRAPHIES Que Bui-Va has received B. A. Sc. i Electrical Egieerig from École Polytechique de Motréal i 975. He has bee with the System Studies ad Equipmet Performace Criteria group of Hydro-Québec TrasÉergie sice his graduatio. Mr. Bui-Va has bee workig o HV/EHV equipmet specificatios, lightig performace of trasmissio lies, isulatio coordiatio of HV/EHV AC/DC power cables ad GIS. He was resposible of electrical performace specificatios for power cables from 5 kv to 345 kv used i Hydro-Québec power system. Mr. Bui-Va has bee ivolved i several system studies for the implemetatio of special surge protective devices, static VAr compesators, series compesatio ad HVDC itercoectios i Hydro-Québec 735-kV trasmissio system. Durig the 990s, he has also bee ivolved i several system studies for iteratioal power system projects especially: the Vietamese (EVN), the Libya (GECOL), the Saudi Arabia (SCECO Cetral), the Iraia (Water & Power Resource Developmet Co.), the Peruvia (Cosorcio TrasMataro S. A.) ad the Chilea (Traselec) power systems. Mr. Bui-Va is the Chairma of the Caadia Subcommittee o IEC s TC8: Isulatio Coordiatio, a active member of the CIGRÉ WG A3-3: Chagig Network Coditios ad System Requiremets as well as a Registered Professioal Egieer i the Provice of Québec. Fracis Beauchemi has graduated from Istitut e Géie de l Éergie Électrique École Polytechique de Motréal i 003. Durig this year, he has joied the System Studies ad Equipmet Performace Criteria group of Hydro-Québec TrasÉergie for a short traiig period. Sice 004, Mr. Beauchemi has bee with Coceptio - Appareillage électrique et commade, Igéierie de productio, Hydro-Québec Équipemet where he has bee ivolvig i the Périboka 385-MW hydroelectric power developmet as well as i several refurbishmet projects of existig hydroelectric geeratig statios. 6