Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers Science and Technology, 8 (2003) 55-60 © 2003 Sultan Qaboos University Steady State Analysis of a UPFC as Voltage Regulator for Optimal Position in the Transmission Line S. Ali Al-Mawsawi and Mohammed R. Qader Department of Electrical Engineering, University of Bahrain, P.O.Box 32038, Email: salmosawi@eng.uob.bh (UPFC) حيد سريان الطاقة الكهربائية في تو تحليل مرحلة االستقرار للمتحكم كمنظم للجهد من أجل موقع مثالي على خط نقل القوى محمد رضا قادرولي الموسوي عالسيد ب دوراً يلع) UPFC(في خالل السنة الحالية من الواضح أن تنصيب المتحكم في توحيد سريان الطاقة الكهربائية : خالصة معتمداً على )PWM(ولهذا السبب فإن عرض معدل النبض . استقرار النظام ةمهماً في قاعدة التأثير غير الخطي لسلوكي ) UPFC ( الكهربائية من ىكمنظم للجهد الكهربائي يمكن نمذجته وتحليله من أجل استنتاج الموقع المثالي على خط نقل القو . الذي يلعب دوراً ذا مغزى في التأثير غير الخطي ) UPFC ( لورقة، فقد تم توضيح موقع خالل الدراسة التي تمت في هذه ا و الطاقة الكهربائية ) Active Power(المستقاة من الحاسوب بأن توزيع الطاقة الكهربائية المؤثرة كما أنه تم استعراض النتائج .معامل التعديل للجهازالساريتان يمكن التحكم بهما بتغير ) Reactive Power(الحيثية ABSTRACT: it has recently been illustrated that the Unified Power Flow Controller (UPFC) installation location plays an important role in effecting nonlinearly in the UPFC steady state performance of the system. A Pulse Width Modulation (PWM) based on UPFC as a voltage regulator is modeled and analyzed to investigate the optimal position in the transmission line. From the study made in this paper, it is shown that the location of UPFC plays a significant part in effecting nonlinearly. It is also found from the simulation results that the distribution of the active and reactive power flows can be controlled by varying the modulation index of the device. KEYWORDS: FACTS, UPFC, Voltage Regulator , Active and Reactive Power. 1. Introduction The concept of a unified power flow controller (UPFC) has been proposed recently(Gyugyi, 1992; Gyugyi and Hingorani 1990; Gyugyi et al., 1995). The UPFC has the potential to become one of the most important Flexible AC Transmission Systems (FACTS) since it can provide various types of compensation, i.e., voltage regulator, phase shifting regulator, impedance compensation and reactive compensation. Practically, the UPFC is implemented by using two similar solid-state phase voltage source inverters (shunt compensation block and series compensation block) which are connected through a common DC link capacitor as shown in Figure 1 (Gyugyi et al., 1995) and each inverter is coupled with a transformer. In the last few years, a number of landmark publications have appeared in the literature, which described the basic operation of the UPFC (Gyugyi, 1992; Gyugyi and Hingorani, 1990; and Gyugyi et al., 1995). Gyugyi (1994) has proposed the concept of the UPFC to control independently both the real power and the reactive power flows at the sending and receiving ends of the transmission line. He also compared the performance and equipment of the UPFC to the more conventional, but related, 55 S. ALI AL-MAWSAWI and MOHAMMED R. QADER power flow controllers such as the Thyristor controller Series Capacitor and the Thyristor controller Phase Angle Regulator. He claimed that, due to the capability and performance of the UPFC in controlling the power flow in transmission lines, this device becomes the most important FACTS device. Furthermore, it has been presented in reference (Fuerte-Esquivel and Acha 1997) that the UPFC can control active and reactive power and voltage magnitude simultaneously. This showed that caution has to be exercised with the UPFC model since it has been assumed that the shunt converter is operating at unity power factor. This paper deals with the mathematical modeling and analysis of a Pulse-Width-Modulation (PWM) based UPFC operating as voltage regulator implemented on a single machine connected to infinite bus through parallel transmission lines. The steady-state performance simulation results of the system are presented for different value of the modulation index. In addition, the optimum position of the UPFC device is investigated. X2 Vr∠0 Inv2 Inv1 Vs∠δ α MpqMsh +Vpq − X4 X3 Pin ~ θ Figure 1. UPFC Controller. 2. Mathematical model The study system on which the UPFC device is implemented is shown as a single line diagram in Figure 2. A synchronous machine feeds an active power P1 and reactive power Q1 to an infinite bus-bar via a parallel transmission lines. Vs is the sending end voltage with δ load angle, Vr is the receiving end voltage, and X2, X3, X4 are the transmission lines impedance. Vpq is the series injected voltage of inverter (2). Ipq is the transmission line current passing through the series compensation block of the UPFC. Vsh is the shunt input voltage of inverter (1) and Xsh is the leakage reactance of the shunt transformer, which is assumed to be purely inductive for simplicity. P3, Q3 ~ Psh + Ppq = 0 Vsh Ish Ipq Is Vp • V q • Xsh +Vpq -- ~ X4X3 X2 Vr∠0 Vs∠δ P2, Q2 Pin ~ Figure 2. Single Line Diagram of the Study System. In order to operate the UPFC systems as a voltage regulator, the voltage Vpq should be injected to the transmission line in phase with the transmission line voltage Vp. This can be seen in the vector diagram shown in Figure 3. 56 STEADY STATE ANALYSIS OF A UPFC AS VOLTAGE REGULATOR β∠= pqp VV (1) Ish Vp jIshXsh Vr δ β jIs X1 Is Vpq Vq jIpq X2 Vsh Vs Ipq Figure 3. Vector Diagram of Figure 2. If the UPFC is an operating base on the PWM method, the magnitude of Vpq can be calculated as (Mohan, et al. 1998), 0.35pq pqV M= V dc (2) where Mpq is the modulation index of the inverter (2) and it is varying from 10% to 100%. On the other hand, the voltage magnitude of the input voltage Vsh of the inverter (1) is: 0.35sh shV M V= dc (3) where Msh is the modulation index of the inverter (2) and its value is assumed to be constant (Msh = 100%). Therefore, from equation (2) and (3), we can confirm that; pq pq shV M V= (4) In general, sh shV V α= ∠− (5) where α is the angle with respect to the transmission line voltage Vp as shown in Figure 3. This angle will determine the amount of the power demand to the inverter (2) from inverter (1). From the vector diagram of Figure 3 it can be seen that; ( ) (p sh sh s pqV V jX I Iβ α= ∠ − + − ) (6) Equating the real and imaginary parts of equation (6) leads to; 3 4 3 4 4 cos( )[1 ] cos( ) cos( ) cos( ) sh ssh sh p sh sh pq sh r X VX X V V X X X X V X V X X β β α δ β + + = − + + + (7) 3 4 3 4 sin( )[1 ] sin( ) sin( ) sin( )sh pqsh ssh shp sh X VX VX X V V X X X X β β α δ β+ + = − + − (8) Hence, the active and reactive power at the shunt compensation block is calculated as 57 S. ALI AL-MAWSAWI and MOHAMMED R. QADER sin( )sh psh sh V V P X α= , 2 cos( )sh p shsh sh s V V V X X α= h −Q (9),(10) The active and reactive power of the series compensation block is determined as 4 cos( 90)pq rpq V V P X β= − + (11) 2 4 4 4 sin( 90)pq p pq pq rpq V V V V V Q X X X β= − − + (12) For the sake of simplicity, it is assumed that the active power consumed by this FACTS device is zero. Therefore, from (9) and (11) 0pq shP P+ = (13) Hence, the input power (P1) can be determined as 1 2 3 sin( ) sin( - )s ps r V VV V P X X δ δ β= + (14) Therefore; if shrs VVVP and ,,,1 are given (known), then equations (4), (7), (8), (13) and (14) can be solved. Accordingly, the UPFC can be operated as a voltage regulator with different operation points by varying the modulation index Mpq from 10% to 100%. In addition, if X3 is varied with respect to X4, then an investigation for locating the optimum position of the FACTS device along the transmission line is also possible. 3. Simulation results The system in Figure 1 has been modeled and simulated by using the Matlab package program. An active power (P1) supplied to the grid by the synchronous machine selected to be 40 MW, the terminal sending end voltage Vs = 66.9 kV and the receiving end voltage Vr = 65.4 kV. The two parallel transmission lines are assumed to be identical and each having a series reactance of (X=20 Ω). Hence the power injected by the generator will be equally divided on the two transmission lines before installing the FACTS device (i.e. P2 = P3 = 20 MW). On the other hand, Vsh is selected to be 20% of the terminal line voltage Vp before the installation of the FACTS device. The steady-state performance results have been tested by varying the series modulation index Mpq from 10% to 100%. In addition, the effect of the installation location of the FACTS device has been investigated. Figure 4 shows that at each position the terminal line voltage (Vp) can be controlled by varying the modulation index Mpq. However it can be seen that, the Vp is more sensitive to the variation of the modulation index Mpq as the installation of the FACTS device is more close to the receiving terminal bus. In addition, minimum value of Vp can be obtained when the device is installed at position around mid point of the transmission line. Figures 5 and 6 show that, at each position, the distribution of the active power flow in both lines can be controlled by varying the modulation index Mpq. However, it can be seen that, in some positions the power flows in both lines are more sensitive to the variation of the modulation index Mpq. Figure 7 shows that the reactive power flow (Q3) through the transmission line on which the FACTS device is installed, is highly sensitive to the change of the modulation index Mpq , whereas 58 STEADY STATE ANALYSIS OF A UPFC AS VOLTAGE REGULATOR the reactive power flow of the other line (Q2) is slightly sensitive to the change of the modulation index Mpq as shown in Figure 8. Furthermore, Figure 7 shows that the reactive power (Q3) is decreasing as the position is increasing and this is because both angles β and δ are also decreasing as the percentage position is increasing as shown in Figures 9 and 10. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0.5 1 1.5 2 x 10 7 PositionM index P3 0 0.2 0.4 0.6 0.8 1 0 0.5 1 2 3 4 5 6 x 10 4 Position M index Vp Figure 4. Terminal voltage Vp for various Figure 5. Active power Flow P2 for various Modulations index. Modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 2 4 6 8 10 x 10 8 PositionM index Q3 Figure 6. Active Power Flow P2 for various. Figure 7. Reactive power Flow Q3 for various Modulations index. Modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 2 2.5 3 3.5 x 10 7 PositionM index P2 Figure 8. Reactive power flow Q2 for various Figure 9. Variation of angle (β) for 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.05 0.1 0.15 0.2 PositionM index Beta 0 0.2 0.4 0.6 0.8 1 0 0.5 1 6 6.5 7 7.5 x 10 6 PositionM ind e x Q 2 various Modulation index. Modulation index. 59 S. ALI AL-MAWSAWI and MOHAMMED R. QADER Figure 10. Load angle (δ) for various Modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0.1 0.12 0.14 PositionM index Delat 6. Conclusions s been modeled as a voltage regulator. The system with parallel transmission lines has been simulated using a Matlab program package. In this case a PWM scheme has been used GYUGYI, L. 1992. Unified power flow co pt for flexible e AC transmission systems, IEE Proceeding-C, 139(4): 323-331. r Systems 9(2): 904-911. R ns, CIGRE .23-203. smission FUE wer studies, IEE Proceeding-C MOH eceived 4 August 2001 ccepted 25 April 2003 The UPFC ha to control the operation of the series compensation block of the UPFC. It has been shown that by varying the modulation index (Mpq), the active power flow distribution in the parallel transmission lines can be controlled. In addition, the effect of the installation location of such FACTS device has been discussed. Furthermore, the simulation results have shown that the reactive power flow is highly sensitive to the variation of the modulation index (Mpq) on the line connected to the device, while it is much less sensitive to the variation of Mpq on the other line. References ntroller conce GYUGYI, L. 1994. Dynamic compensators of AC transmission lines by solid state synchronous voltage source. IEEE Trans. On Powe GYUGYI, L. and HINGORANI, N.G., Nannery, P.R. and Tai, N. 1990. Advanced static VA compensators using Gate-turn-off thyristors for utility applicatio GYUGYI, L., SCHAUDER, C.D., WILLIAMS, S.L., RIETMAN, T.R., TORGERSON, D.R. and EDRIS, A. 1995. The unified power flow controller: a new approach to power tran control, IEEE Transactions on Power Delivery, April 1995. RTE-ESQUIVEL, C.R. and ACHA, E. 1997. Unified power flow controller: a critical comparison of Newton-Raphson UPFC algorithms in po Generation Transmission Distribution, 144(5):457-464. AN, N. UNDELARD, T.M. and ROBBINS, W.P. 1998. Power electronics converters applications and design, John Wiley and Sons. R A 60 Steady State Analysis of a UPFC as Voltage Regulator for Optimal Position in the Transmission Line S. Ali Al-Mawsawi and Mohammed R. Qader Department of Electrical Engineering, University of Bahrain, P.O.Box 32038, Email: salmosawi@eng.uob.bh Figure 1. UPFC Controller. 2. Mathematical model 3. Simulation results Figure 6. Active Power Flow P2 for various. Figure 7. Reactive power Flow Q3 for various Modulations index. Modulation index. 6. Conclusions References