Voltage/Power Steady State Stability Enhancement of AC-DC for both SIF and MIF System Configurations by Shunt SVC

Transcription

1 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. Voltage/Power Steay State Stability Enhancement o AC-DC or both SIF an MIF System Conigurations by Shunt SVC Ibrahim B. M. Taha, an Mohame G. Ashmawy, Electrical Department, Faculty o Engineering, Tai University Electrical Power an Machines Department, Faculty o Engineering, Tanta University Electrical Power an Machines Department, El Shorouk Acaemy, Cairo, Egypt. Abstract The reactive power generations play an important role or electrical power system voltage stability margins. The static var compensators an other reactive power resources were use or voltage stability enhancements. In this work, moeling, control, analysis, an stability enhancement o interconnecte AC-DC power systems were presente. The propose stuy will cover moeling, control, AC-DC power low an steay state stability o ierent conigurations o AC-DC systems. The propose stuy was introuce the system moel o ierent HVDC system conigurations, HVDC system control characteristics, AC-DC power low o ierent AC-DC system conigurations, AC-DC system Stability enhancement. The propose object is to stuy an enhance AC-DC system operations an stability. The results obtaine illustrate the strength o the propose moel. Keywors: Voltage collapse, Voltage instability, SVC, Continuation power low. INTRODUCTION The phenomena o voltage/power instability have been observe on the AC systems when operating close to its steay state stability limit. Recently, it has also been etecte that AC systems may experience voltage stability problems at locations with special loa characteristics []. Converter terminals, use or HVDC transmission or back-to-back links, may be regare as one o such special loas. AC systems at the terminals o HVDC are becoming relatively weaker ue to the growth o the relative portion o DC to AC power. Many serious problems in the overall perormance o the combine AC-DC system can arise with consequences relecte on the total cost o HVDC station []. The more important problem is the voltage/power instability at HVDC terminals specially when connecte to weak AC systems [- 5]. To overcome this problem, aitional AC components must be ae to the AC terminals o HVDC system such as synchronous conensers or static var compensators. The overall cost o HVDC station is thus increase, which can reuce the major economic avantage o HVDC system. This chapter presents the ierent methos use in voltage stability analysis o HVDC systems. The problem o instability was ealt with rom a static view point beore ynamic an transient aspects were consiere. STATIC METHODS OF VOLTAGE/POWER INSTABILITY OF HVDC SYSTEMS The static methos use to analyze the voltage/power instability problem are maximum available power metho, voltage stability actor, an control sensitivity inex. Maximum Available Power Metho : The maximum available power concept (MAP) was irst introuce by Ainsworth et al or single-inee HVDC system coniguration [6]. It epens on calculating the rate o change o DC line active power transer ue to change o DC line P current. The positive sign o means stable operations when the HVDC system is operate in constant power control moe while a negative sign inicates that the operation in constant power control moe is unstable [7]. Fig. () shows the relation between P an short circuit ratio (SCR) o the AC system connecte to the converter bus. It shows that P is relatively constant with positive sign with large values o SCR while it ecreases with small SCR values. Further ecrease in SCR causes to be converte to negative sign, which inicates the system's loss o stability. Figure : versus Short Circuit Ratio The maximum power curve is shown in Fig. (). When DC current is increase starting rom a small value, the DC line power increases while the AC line voltage ecreases. This process is repeate until the DC line power reaches its 97

2 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. maximum value (MAP) relate to critical DC line current (I Crit). Ater I Crit, the DC power will ecrease ue to a urther increase o DC line current, which causes a large reuction in AC as well as DC line voltages [, 6]. short circuit ratio, the VSF becomes negative (unstable operation). The application o available power metho was extene to HVDC systems with parallel AC line incorporating AC loa moel [8]. The concept o maximum power was extene to stuy multi-inee HVDC systems [9, ]. There, ue to the multi-imensionality o the system moel, a moal or eigenvalue ecomposition technique was employe in orer to obtain the ecouple orm o the voltage sensitivity inex. Figure : VSF against Short circuit ratio Figure : DC Line Power against DC Line Current Voltage Stability Factor Metho : The concept o voltage stability actor (VSF) was irst introuce by Hamma et al or single-inee HVDC system coniguration [, an ]. The voltage stability actor is eine to be the per unit incremental change in AC line voltage ue to a per unit change in reactive power injecte at converter bus at constant DC power as given in Equation (): VSF V () Q s P The positive sign o VSF means stable operation when the HVDC system is operate on constant power or control moe, while a negative sign inicates that the operation in constant power or control moe is unstable [, ]. High values o VSF mean that the system is expecte to show high voltage luctuations when subjecte to transient changes []. The VSF thus acquires more importance or correlating static an transient analysis o voltage/power instability o HVDC system. Fig. () shows the VSF against the SCR ratio. With large values o SCR ratio, the VSF actor has a small positive value (stable operation). When the SCR at the converter's AC bus ecreases, the VSF will be increase. This process continues until a critical SCR ratio (CSCR) at which the VSF reaches very high values (theoretically ininity). Below the critical Figure : VSF an P against SCR Franken et al, compare between VSF an MAP an oun that they similarly escribe the system's voltage/power instability in single inee HVDC system as illustrate in Fig. (). Control Sensitivity Inex Metho : The control sensitivity inex (CSI) was presente by Nayak et al []. The authors ivie the system parameters to three categories; the controlle parameter, the controlling parameter, an other parameters o the system aecte inirectly by the controller. In the constant current control moe, or example, the controller attempts to maintain the DC line current, I, (controlle parameter) at a speciie value by irectly varying the converter iring angle (controlling parameter). AC-DC STEADY SATE STABILITY MODEL Due to the rapi increase o HVDC applications in the electric networks, the relative portion o the DC power to the total system power is growing. AC systems at the terminals o HVDC schemes are becoming relatively weaker ue to some 98

3 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. problems o reactive power require which aect on the perormance o the combine AC/DC system. The stability at the HVDC terminals inclues all perormance problems relate to AC voltage control uner the steay state an transient operating conitions. These problems can be solve by applying reactive power resources at HVDC terminals such as static capacitors an static VAR compensator. This section introuces a static moel suitable or application in stuies o the steay state stability stuies. This moel is base on sensitivity analysis o the AC/DC system. Also the system variables' limits are obtaine at the ierent control moes o HVDC system. STATIC AC-DC POWER EQUATIONS The AC-DC system equations o both SIF an MIF conigurations or both rectiier an inverter sies are introuce in the next section. In this section a etaile moel o single inee HVDC system. The moel is applicable to etermine the instability o HVDC system at ierent control moes an the associate stability margins o AC an DC system variables. The active an reactive powers are written as a unction o state an control variables x, u respectively, which is expresse as ollows: T x I,, V,, V ) () ( t t u ) () ( a,,, Ps, Qs, E, a,,, Ps, Qs, E Where x an u are vectors o state an control variables respectively. The system equations are: sp I I 5 s s s s ac ac ac ac c c c c L L L L svc T () The operating point x, u is a solution to: ( x, u ) (5) ( 5 Where x, u ) [ ] Expaning Equations (), Taylor's series yiels: Gx x Gu u (6) Where G an G can be obtaine as ollows: x u i Gxij i, j,,..., 5 (7) x ij i Guij i,,.., 5 & j,,..., (8) u ij The mismatch in the state variables can be obtaine as ollows: x G x G u G u xu u So that the voltage stability actor at the inverter sie can obtaine by: VSF Gxu (5,) () The strength o the AC systems connecte to converter terminals is measure by short-circuit ratio, SCR, which eine as the relation between the short-circuit capacity o the AC bus at the converter bus an the rate DC power transer [,], which can be expresse by: ti ci (9) V Yii SCRi () P Another actor known as the eective short-circuit ratio, ESCR [8, 6, 7], can be expresse as: ti V Yii ESCRi P ci INJi () where Q ai is the total injecte reactive power injecte at the i th converter bus. The stability problem can be improve by applying reactive power sources, such as static capacitor, an Static var compensators, SVC. The exact moel o SVC is presente in the next section. RESULTS AND DISCUSSIONS OF SIF CONFIGURATIONS The stability moel is applie to a suggeste simple -bus AC-DC system shown in Fig. (5). The per unit system ata o the -bus or both AC an DC is introuce in Table. Fig. (5) SIF AC-DC test system The MATLAB script ile is built or CC control an constant extinction angle at the inverter sies respectively. AC system ata DC system ata Table : Data o Simple -bus AC-DC system E =.5 P L =.5 P L =.5 E =.5 Q L =. Q L =. y = y = j. Z = Z = j. R L =.5 x c = x c =. a sp = a sp =.9 Fig. (6) illustrates the VSF at inverter bus in SIF conigurations against the ESCR at inverter bus. It shows that the VSF actor is positive with higher values o ESCR ratios, greater than, an its changes. When the ESCR is reuce less than the rate o change o VSF is increase compare to that with higher values o ESCR. This rate o changes is still 99

4 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. increase until ESCR reaches to critical value,.65. AT the critical value o the ESCR, the VSF increases to very high value beore changing its sign to negative an then increasing as shown. The system is stable when the ESCR is greater than critical value,.65, while it is consiere unstable when its ESCR is smaller than critical value. Thereore, the SVC eective reactance at the i th converter can be calculate as ollows: X SVCi = X CX TCR πx L X C = X TCR X C X C [(α svc π) si n α svc ] + πx L (5) 5 Stable The SVC equivalent susceptance as a unction o SVC iring angle can be calculate as ollows: B SVCi = = X C [(α svc π) si n α svc ] + πx L X SVCi πx L X C (6) VSF -5 - Unstable.5.5 ESCR Figure 6: VSF at inverter bus in SIF conigurations versus ESCR at inverter Bus SVC Compensator Moel an Stability Enhancement : The are two system moels o SVCS. These moels are calle: SVC iring angle moel an SVC total susceptance moel [5, 6]. The secon type is presente an analyze in this research work. The SVC system moel consists o a parallel combination o a thyristor controlle reactor, TCR, an a ixe capacitor as shown in Fig. 7. The inuctive susceptance o the thyirstor controlle reactor, TCR, connecte to the i th converter bus can be calculate as a unction o SVC iring angle, 9 < α svc < 8, as ollows [5-9]: B TCRi = X L (π α svc sin α svc ) π () where XL is reactor inuctive reactance which equal to ωl. The reactive power injecte by the SVC connecte to the i th converter can be calculate as a unction o iring angle as ollows: Q svc = B SVCi V ti = X C [(α svc π) si n α svc ] + πx L πx L X C V ti (7) Figs. 8 an 9 illustrate the variations o the equivalent reactance an susceptance o SVC, respectively, against the SVC iring angle with SVC reactive power varies rom -. p. u. to. p. u. These results correspon to capacitance reactance o.5 p. u. an variable inuctive reactance o.5 p. u. Results in Figs. 8 an 9 illustrate that the equivalent reactance is inuctive or the iring angle range o 9 α <.8 while it is capacitive or the iring angle range o.8 < α 8. Xeq, p.u. 5 C L svc, Degrees Figure 8: SVC equivalent reactance versus iring angle.. T T. Capacitive Qsvc, p.u. Inuctive Figure 7: SVC iring angle moel The equivalent reactance o TCR at the i th converter bus as a unction o SVC iring angle, can be expresse as ollows: X TCRi = π = X B L TCR [(α π) si n α] () svc, Degrees Figure 9: SVC reactive power per unit versus iring angle. 9

5 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. Fig. () illustrates the eect o ecreasing system ESCR at inverter bus rom operating value when the inverter is operate with SVC(otte line), with aing ixe capacitor o. susceptance (ashe line) an without inserting reactive power sources (soli line). The critical ESCR ratios are.,.8 an.9 or SVC, ixe capacitor an without any inserting any reactive sources. It is note that the inserting o at the inverter bus enhance system stability range compare to inserting ixe capacitor an without aing any reactive power resources. VSF Figure : VSF versus ESCR with SVC, FC an without Loa Change Eect : In this section, a etaile moel o SIF system incorporating the eect o static loa moels at the inverter terminals on the stability is introuce. The maximum AC loa power at ierent loa power actors has been also assesse. The inserte active an reactive power at the inverter bus is expresse as ollows: P La = P L V t Q La = P L V t tan Vt, p. u ESCR.8.9 (8) (9) SVC Without FC.98 Lea PL, p. u. Figure : Rectiier line voltage at ierent impeance loa power actors versus active loa change at inverter bus Vt, p. u PL, p. u. Figure : Inverter line voltage at ierent impeance loa power actors versus active loa change at inverter bus Figs. an illustrate the change o AC line voltage at both the rectiier an inverter AC buses against the ae active loa power at the inverter bus at.98 leaing, unity,.9 lagging an,8 lagging power actor respectively. The soli line represent the AC line voltage with SVC inserte at the inverter bus, the ashe line represent the case o inserting ixe capacitor at the inverter bus while the otte line represent the case without inserting any reactive power sources at the inverter bus. The stability margins are increase or case o SVC compare to ixe capacitor an without any reactive power sources cases. Fig. illustrates the reactive power inserte by the SVC with loa changes at the inverter bus at.98 leaing, unity,.9 lagging an.8 lagging power actors respectively., Degrees Lea.98 Lea PL, p. u. Figure : SVC iring angle at ierent impeance loa power actors versus active loa change at inverter bus RESULTS AND DISCUSSION FOR MIF CONFIGURATIONS The system moel is applicable to etermine the instability o MIF coniguration o AC-DC system at constant current at rectiier o the two lines an constant extinction angle o each inverter o the two DC lines an the associate stability margins o AC an DC system variables. The system ata are introuce in Table. 9

6 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. Table : The per unit ata o DC line in MIF coniguration. Rect. x c =.7 Inv. x c =. Rect. x c =.7 Inv. x c =. α min = 5 γ min = 8 α min = 5 γ min = 8 B c =. B c =.7 B c =.5 B c =.5 R L =.5 R L =.5 The active an reactive powers are written as a unction o state an control variables x, u respectively, which is expresse as ollows: T x I,, V,, V, I,, V,, V ) () ( t t t t u ( a,,, P, Q, E, a,,, P, Q, E, s s s a,,, P, Q s s s s, E, a,,, P, Q, E ) s T () Where x an u are vectors o state an control variables respectively. The system equations are: I I s s s s s s s I s sp I ac ac ac ac sp ac ac ac ac c c c c c c c c L L L L L L L L svc () VSF ESCR Figure : VSF against ECR at the inverter o irst DC line with an without SVC Fig. illustrates the VSF at the inverter o irst DC line against ESCR. It illustrates that the stability margins increases with SVC (at the inverter o irst DC line) case, ashe line (ESCR=.), compare to that without inserting any reactive power sources, soli line (ESCR=.5). It also illustrate that the stability margins increase compare to SIF conigurations ue to power transer rom the AC bus connecte at the inverter o the secon DC line to the AC bus connecte to the inverter o irst DC line..9 Vt Vt The operating point x, u is a solution to: ( x, u ) () Where ( x, u ) [ ] Vt, Vt, p. u Vt.9 Vt Expaning Equations (), Taylor's series yiels: Gx x Gu u () Where G x an Gu can be obtaine as ollows: i Gxij i, j,,..., () x ij i Guij i,,.., & j,,..., (5) u ij The mismatch in the state variables can be obtaine as ollows: x G G u G u (6) x u xu So that the voltage stability actor at the inverter sie o irst DC line can obtaine by: VSF Gxu (5,) (7).5. Vt PL, p. u. Figure 5: AC line voltage at rectiier an inverter o irst DC line against ESCR Fig. 5 shows the AC line voltage at rectiier an inverter o irst DC line against ESCR with an without SVC at unity,.9 lagging an.8 lagging power actors. It illustrates that the stability margins are enhance with SVC compare to without SVC at ierent power actors. Fig. 6 shows the SVC reactive power injecte at unity,.9 lagging an.6 lagging power actors at the inverter o irst DC line. Vt 9

7 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. svc, p. u PL, p. u. Figure 6: SVC reactive power injecte at unity,.9 lagging an.6 lagging power actors in MIF conigurations. CONCLUSIONS The steay state voltage/power stability o AC-DC system is stuie an analyze using voltage stability actor metho, VSF. The AC-DC system voltage/power stability moels or SIF an MIF conigurations o AC-DC systems were propose. The loa eect was or voltage stability o AC-DC system were iscusse an analyze at loa power actor or both SIF an MIF conigurations. Furthermore, the SVC moel was presente to AC-DC moel to enhance stability margins o SIF an MIF conigurations. Finally, the AC-DC steay state voltage/power stability o ierent AC-DC system conigurations was enhance using static capacitor an static var compensator. ACKNOWLEDGMENT This research was supporte by the Vice-Presiency or Grauate Stuies an Acaemic Research in Tai University. The research has been carrie out uner the project No REFERENCES.9 [] Franken B. an Anersson G. "Analysis o HVDC Converters Connecte to weak AC Systems", IEEE Transmission on Power Systems. Vol. 5, No., pp. 5-, February 99. [] Fan Y. K., Niebur D., Nwankpa C. O., an Kwanty H., "Multiple Power Flow Solutions o Small Integrate AC/DC Power System'', IEEE Int. Symposium on Circuits an Systems, Vol., Switzerlan, pp. -7, May (). [] Franken B. an Anersson G. "Analysis o HVDC Converters Connecte to weak AC Systems", IEEE Transmission on Power Systems. Vol. 5, No., pp. 5-, February 99. [] L. A. S. Pilotto, M. Szechtman, A. E. Hamma "Transient AC Voltage Relate Phenomena or HVDC Schemes Connecte to weak ac Systems", IEEE Transactions on Power Delivery. Vol. 7, No., pp. 96-, July 99 [5] Hamma A. E. an Kuhn W. "A Computation Algorithm or Assessing Voltage Stability at AC/DC Interconnections", IEEE Transactions on Power Systems. Vol. PWRS-, No., pp. 9-9, February 98. [6] Huang G. M., an Krishnaswamy V., "HVDC Controls or Power System Stability", Power Engineering Society Summer Meeting, Vol., pp , 5 July, (). [7] Grun C. et. al. "Functional Moel o Two Terminal HVDC Systems or Transient an Steay State Stability-IEEE Committee Report", IEEE Trans. Apparatus & systems, Vol., No. 6, pp. 9-55, July (98). [8] Aik D. L. H., Anerson G., "Qausi-Static Stability o HVDC Systems Consiering Dynamic o Synchronous Machines an Excitations Voltage Control", IEEE Transactions on Power Delivery, Vol., No., pp. 5-5, January (6). [9] Szechtman M., et al. "First Benchmark Moel or HVDC Control Stuies", Elecrtra, Vol. 5, pp 55-7, April (99). [] Mithulananthan C. N., Ganizares A., an Reeve J., "Inices to Detect Hop Biurcations in Power Systems", NAPS-, pp. -7, (). [] Huang G. M., Zhao L. an Song X., "A New Biurcation Analysis or Power System Dynamic Voltage Stability Stuies", Power Engineering Society Winter Meeting, Vol., pp , 7- January, (). [] Arrillaga J., ''High Voltage Direct Current Transmission'', n Eition, The Institution o Electrical Engineers, ISBN , 998. [] Paiyar K. R., ''HVDC Power Transmission Systems - Technology an System Interactions'', John Wiley & Sons, ISBN , 99 [] Rosehart W. D., an Canizares C. A., "Biurcation Analysis o Various Power System Moels", Elsevier Science Lt. Electrical Power & Energy Systems, vol., pp. 7-8, (999) [5] H. A. PBrez, E. Acha, an C. R. F. Esquivel, "Avance SVC Moels or Newton-Raphson Loa Flow an Newton Optimal Power Flow Stuies", IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 5, NO., February. [6] Ibrahim B. M. Taha, Best Locations o Shunt SVCs or Steay State Voltage Stability Enhancement, 5 IEEE International conerence on Energy Conversion (CENCON), Johor Bohru, Malaysia, PP. -5, 9- Oct., 5. [7] A. Kazemi, B. Barzaeh, "Moeling an simulation o SVC an TCSC to stuy their limits on maximum loaability point ", Elsevier Lt., Electrical Power an Energy Systems,. 9

8 International Journal o Applie Engineering Research ISSN Volume, Number 8 (6) pp 97-9 Research Inia Publications. [8] M. O. Hassan, S. J. Cheng, Z. A. Zakaria, "Steay- State Moeling o SVC an TCSC or Power Flow Analysis", Proceeings o the International Multi Conerence o Engineers an Computer Scientists 9 Vol. II, IMECS 9, March 8 -, 9, Hong Kong. [9] Y. Chang, R. Chang, "Utilization Perormance base FACTS Devices Installation Strategy or Transmission Loaability Enhancement", th IEEE conerence on Inustrial Electronics an Applications, ICIEA 5-7 May 9. 9