Effects of STATCOM_ SSSC and UPFC on Voltage Stability

Effects of STATCOM, SSSC and UPFC on Voltage Stability R. Natesan Department of Electrical and Computer Engineering Tennessee Technological University Cookeville, Tennessee, USA email: rnatesan2 1@,tntech.edu G. Radman, Member, IEEE Department of Electrical and Computer Engineering Tennessee Technological University Cookeville, Tennessee, USA email: gradman@tntech.edu Keywords: STATCOM, SSSC, UPFC, Maximum Loadability, Bifurcations, Voltage Collapse. Abstract-The purpose of this paper is to study the effects of three FACTS controllers: STATCOM, SSSC and UPFC on voltage stability in power systems. Continuation power flow, with accurate model of these controllers, is used for this study. Applying saddle node bifurcation theory with the use of Power System Analysis Toolbox (PSAT), the optimal location of these controllers are determined. Using a 6-bus test system the effects of these controllers on voltage stability are examined. It is found that these controllers significantly increase the loadability margin of power systems. I. INTRODUCTION Voltage collapse phenomena in power systems have become one of the important concerns in the power industry over the last two decades, as this has been the major reason for several major blackouts that have occurred throughout the world including the recent Northeast Power outage in North America in August 2003. Point of collapse method and continuation method are used for voltage collapse studies [l]. Of these two techniques continuation power flow method is used for voltage analysis. These techniques involve the identification of the system equilibrium points or voltage collapse points where the related power flow Jacobian becomes singular [2, 31. The voltage collapse occurs when a system is loaded beyond its maximum loadability point. Voltage collapse studies are carried out with the aim to maximize the loading capability of a particular transmission line. Traditionally shunt and series compensation is used to maximize the transfer capability of a transmission line [4]. Recently the new concept of Flexible AC Transmission System (FACTS) was developed by Electric Power Research Institute (EPRI), which involves a family of fast acting, high power electronic devices, with advanced and reliable controls. By using FACTS controllers one can control the variables such as voltage magnitude and phase angle at chosen bus and line impedance. Canizares and Faur studied the effects of SVC and TCSC on voltage collapse [6]. So far no work has been reported in open literature for the effects of STATCOM, SSSC and UPFC on voltage stability. This paper considers three FACTS controllers namely STATic COMpensator (STATCOM), Static Synchronous Series Compensator (SSSC) and Unified Power Flow Controller (UPFC) and their optimal location in order to increase the loadability margin of a power system. The mathematical tools needed for voltage collapse studies are discussed in section I1 and the models of the three FACTS controllers are discussed in section 111. Section IV examines the effects of these controllers on voltage stability using a 6-bus test system. Section V reviews the main points discussed in this paper. 11. MATHEMATICAL REPRESENTATION OF POWER SYSTEMS A power system can be mathematically represented by a set of ordinary differential and algebraic equations of the type [6]: M z = f(Z,U, A) 0 =g(z,u,4 where ZE (1) S n represents the system state variables such as the dynamic states of generators, loads, etc., U E S n represents the algebraic variables corresponding to the steady state element models, A E %' represents a set of uncontrolled variable that drive the system to voltage collapse, f ( z , u , A ) represents a vector function of the differential equations, g(z,u, A) groups all terms representing algebraic equations and is a constant positive definite matrix. The system model can be reduced by the term A z = f ( z , h(2, A), A) = s(2, A) 4 (2) A saddle node bifurcation of the system (2) occurs when the Jacobian D,s(z, A) is singular at equilibrium 0-7803-8281-1/04/$20.00 02004 IEEE 546 point (zo,/20) where two solutions of the system, stable and unstable, merge and then disappear as the parameter R , i.e. system load changes. At the bifurcation point ( Z O , ~ ) ,the Jacobian DZs(zo,/2o) has a simple and unique zero eigenvalue with normalized right eigenvector v and left eigenvector w [ 11. D,s(zo, &)v = 0 wT Dzs(z0,/2o)v=OT (3) The power injection at the AC bus to which the STATCOM is connected has the following form: P = V2G - KVdVGcos(0 -a)- kV&9sh(@ -a) Q = -V2B + kVd,VB cos(@ -a)- kV&VGsh(@ - a) (6) where k = J3 Ism . wT [D,2s(zo, Ro)vJv 0 # The above equations guarantee quadratic behavior near bifurcation point and are used to determine the voltage collapse point [l]. The eigenvectors at the bifurcation point provide information on the areas prone to voltage collapse and the control strategies to most effectively prevent this problem. Two known basic tools based on bifurcation theory are direct and continuation methods and are used to compute the voltage collapse point. One is more interested in voltage collapse point and its corresponding zero eigenvectors and eigenvalues. It is shown in [SI that not all dynamical equations are needed and accurate results can be obtained if the set of equations used to determine the voltage collapse point sufficiently represent the equilibrium equations of the full dynamical system. Accurate model of the FACTS controllers is required for reproducing their steady state and dynamic behavior. 111. MODEL OF FACTS CONTROLLERS Fig. 1 STATCOM circuit The following general model is proposed for correct representation of STATCOM, SSSC and UPFC in voltage collapse studies [9]. The model includes a set of differential and algebraic equations of the form: xc = B. SSSC The SSSC circuit is shown is Fig. 2. The AC circuit is considered in steady state and assuming the tap ratio mof the transformer is nominal(m=l), the following equations can be obtained: f , (xc v,0, U) 2 (4) p = g p ( x c ,v , 8) V , 6) ' Where xc represents the control system variables, and the algebraic variables V and 0 denote the voltage magnitudes and phases at the buses to which the FACTS devices are connected. 3 Q = g p (xc i; = V I - (R+ j X ) l Vk= v+ vm+ (RT + j X T ) l . (7) where V I = k V d c d P = &%Vdc,jP From equations (7) we can obtain the expressions for current A. STATCOM STATCOM circuit is shown in Fig. 1. The DC circuit is described by the following differential equations, in terms of the voltage vdc of the capacitor. r and voltage v : - I= (1+il)(Vk-Vrn)-i2 V I RT +jxT (8) 547 where voltage v d c is common for the two inverters, as shown in Fig. 3. From Fig. 3 the power flow equations are: Now, the algebraic equations of the power injections at the buses k and m are: * . S m =-Fm .I Qshabsorbed by the shunt component are The DC circuit is considered as dynamic and the following deferential equation applies: The DC circuit has the following differential equations: R 6.j x *_*_ ?- _r -& A" " - Fig. 2. SSSC circuit C. UPFC Fig. 3. UPFC circuit UPFC circuit model is obtained from the models of the associated STATCOM and SSSC, where the DC 548 LIla ? .................................................................................................................................................. .................................................................... IV.TEST SYSTEM A 6-bus test system as shown in Fig. 4 is used for voltage stability studies. PSAT is a power system analysis software, zhich has many features including power flow and continuation power flow. Using continuation power flow feature of PSAT, voltage stability of the test system is investigated. The behavior of the test system with and without FACTS devices undei- different !oading conditions is studied. The- location of the FACTS controllers are determined through bifbrcation analysis. A typical PQ model is used for the loads and the generator !irnits are ignored. Voltage stability analysis is performed by starting fiom an initial stable operating point and then increasing the loads by a factor h until singdar point of power flow linearization is reached. The loads are defined as ............................................................................................ ..................................................................................................... . " ........ .I h ( ' U :I I I<,,* 1 I iIii I$*, 6 .................... --- F i g . 4 . 6 - b ~ system test P/=;U>, Qi =@o where Poand Q are the active and reactive base loads, whereas Pland Qlare the active and reactive loads at bus I for the current operating point as defined by A. The critical buses are identified as buses 4, 5 and 6 and their voltage profiles obtained through continuation method are shown in Fig. 5. Bus 4 has the weakest voltage profile and hence its profile is needed to be improved using FACTS controllers. Maximum loading point or bifurcation point where the Jacobian matrix becomes singular occurs at A =I 1.1614. With SSSC connected between buses 2 and 4, bifimation for the system occurs at a higher load value than for the system without the SSSC as shown in Fig. 6. When STATCOM is connected at bus 4 we can observe from Fig. 7 that bus-4 has a flatter voltage profile. Also a UPFC connected to line 4-5 near bus 4 helps bus 4 to maintain a flat voltage profile, which is illustrated in Fig. 8. ol............I.............. 0 1 i.. 2 ..........1.............i.. i.............i............. .............t ............l.. ........1............ ........ I ... 3 4 5 6 7 6 9 1 0 1 1 Loading Parameter h (P.u.) Fig. 5. PV curve for 6-bus system wthout FACTS 3 ?I 7 I x ~ " F "I "~ -- - " ~ - - - ~ ~ lr^' -"-------- 0.g Fig. 6. PV curve with SSSC between bus 2 and 4 549 [2] Dobson and H. D. Chiang, "Towards a theory of voltage collapse in electric power systems," Systems & Control Letters, vol. 13, 1989, pp. 253-262. C. A. Canizares, F. L. Alvarado, C. L. DeMarco, I. Dobson, and W. F. Long, "Point of collapse methods applied to acldc power systems," IEEE Trans. Power Systems, vol. 7, no. 2, May 1992, pp. 673-683. [3] 0.4i : : . . . . . 11 i [4] R. Bergen, Power Systems Analysis. Prentice-Hall, New Jersey. 1986. -of FATES devices m xooltage collaqse: phenomena," Mi-i&m'$ t&asis, p,JJ 2.T Ebm,,-I' . U Univexsi$yofWa+edb 1996. [6] C. A. Canlzares, Z. T. Faur, "AnaTpsisof S V C d TCSC Controllers in Voltage Collapse," IEEE Trans. Power Systems, Vol. 14, No. 1, February 1999, pp. 158-165. [7] H. Fink, editor, Proc. Bulk Power System Voltage Phenomena 111-Voltage Stability and Security, ECC Inc., Fairfax, VA, August 1994. Dobson, "The irrelevance of load dynamics for the loading margin to voltage collapse and its sensitivities," pp. 509-518 in [7]. C. A. Canizares,. "Power Row and Transient f8] " ' 0 1 2 3 4 5 [9] Loading Parameter7. (P.u.) Fig. 8. PV curve with UPFC at bus 4-5 V. CONCLUSIONS The effects of three FACTS controllers: STATCOM, SSSC and UPFC on voltage stability in power systems were studied. Using the continuation power flow with accurate model of the FACTS controllers the study was performed for a 6-bus test system. It was found that these controllers significantly enhance the voltage profile and thus the loadability margin of power systems. VI. REFERENCES [l] C. A. Canizares, F. Alvarado, "Point of Collapse and Continuation Methods for Large ACDC Systems," lEEE Transaction on Power Systems, Vol 8, No 1. February 1993, pp 1-8 Stability Models of FACTS controllers. for Voltage and Angle Stability Studies," IEEE/PES WM Panel on Modeling, Simulation and Applicatfons of FACTS Controllers in Angle and Valtage Stability Studies, Singapore, Jan. 2000 [lo] PSAT Version 1.2.2, Software and Documentation, copyright 0 2003 Federico Milano. [l 13 G. B. Sheble, Computational Auction Mechanism for Restructured Power Industry Operation, Kluwer Academic Publishers, Boston, 1998. 550