EVALUATION OF A NEW MODEL FOR UPFC OPERATING AS IMPEDANCE COMPENSATION APPLIED TO MULTI- MACHINE SYSTEMS WITH NONLINEAR LOAD

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1 Journal of Engineering Science and Technology ol. 9, No. 6 (04) School of Engineering, Taylor s University EALUATION OF A NEW MODEL FOR UPFC OPERATING AS IMPEDANCE COMPENSATION APPLIED TO MULTI- MACHINE SYSTEMS WITH NONLINEAR LOAD S. ALI Al-MAWSAWI University of Bahrain, College of Engineering, Department of Electrical & Electronics Engineering, Isa Town, P.O. Box 3038, Kingdom of Bahrain aalmossawi@uob.edu.bh Abstract In this paper, a new developed steady-state model of the UPFC is proposed. The proposed model consists of one unt compensation block and two series compensation blocks. In this case, the UPFC with the new model will be investigated when it is installed in multi-machine systems with non-linear load model. In addition, the steady state performance of the new model operating as impedance compensation will be presented and compared with that obtained from the original Gyugyi model. Keywords: UPFC, FACTS, PWM, Multi-machine systems, Nonlinear load.. Introduction The rapid development of power electronics technology provides exciting opportunities to design new power system equipment for better utilization of existing systems. During the last decade, a number of control devices under the term "Flexible AC Transmission Systems (FACTS) technology have been proposed and implemented [-6]. FACTS devices can be effectively used for power flow control, loop-flow control, load aring among parallel corridors, voltage regulation, enhancement of transient stability, and mitigation of system oscillations. In 99, a unified power flow controller (UPFC) concept was proposed by Gyugyi []. It is a multi-functional FACTS controller with the primary function of power flow control plus possible secondary duties of voltage support, transient stability improvement and oscillation damping, etc. [, ]. The installation of the UPFC in power systems has recently come under intensive investigation into its modeling and various control functions, including damping control for single-machine infinite-bus power systems. Many papers have been publied related to modeling the UPFC into 678

2 Evaluation of a New Model for UPFC Operating as Impedance Nomenclatures I n M M P nm nm n Current in n transmission line, Amp Modulation index of the series compensation block of UPFC. Modulation index of the unt compensation block of UPFC Active power flow in the line from point n to m, watt Reactive power flow in the line from point n to m, ar. oltage at n point of the transmission line, olt Injection voltage from the UPFC, olt Greek Symbols α Angle of the unt compensation block of UPFC, deg., Angles of 3 and with respect to the slack bus voltage, deg. θ Angle of the transmission line current I, deg. ρ Angle of the series compensation block of UPFC, deg. multi-machine power systems in steady-state mode of operation for studying power flow control [7-]. However, most of the work done used the original Gyugyi model of the UPFC (series compensation block (Converter ) and unt compensation block (Converter ) as illustrated in Fig. [7-]. In this paper, a new steady-state model of a UPFC is proposed. The model consists of one unt compensation block and two series compensation blocks. A UPFC with the new construction model installed in multi-machine systems with non-linear load model will be investigated. In addition, the steady state performance of the new model operating as an impedance compensation will be presented and compared with that obtained from the Gyugyi model. Fig.. A Block Diagram of UPFC.. Multi-machine Systems with UPFC as Impedance Compensation (Model ) The block diagram and the steady-state model of a Pulse-Width Modulation (PWM) based UPFC operating as impedance compensation installed in the multimachine systems are own in Figs. and 3, respectively. Journal of Engineering Science and Technology December 04, ol. 9(6)

3 680 S. A. Al-Mawsawi Fig.. Multi-machine Systems with UPFC (Model ). Fig. 3. The Steady State Model of the Multi Machine Systems with UPFC (Model ). If the system has a nonlinear load that depends on the terminal voltage 3, then the active and reactive power could be characterized as follows [3]: a 3 P = P () b 3 = () where, a and b are constant values and P 0, 0 and 30 are equal to the initial values of P 3, 3 and 3, respictively. In order to operate the UPFC as an impedance compensator, the voltage ould be injected into the transmission line in quadrature with the transmission line current I, and thus the angle of must be: Journal of Engineering Science and Technology December 04, ol. 9(6)

4 Evaluation of a New Model for UPFC Operating as Impedance = 90 ρ θ (3) where θ is the angle of the current I with respect to the reference voltage. From the complex powers of the system, all active and reactive powers can be calculated for the system as follows: = (4) 3 ( θ ) + Sin( ) Cos δ P P Sin 3 ( δ ) ( θ ) 3 3 = Cos δ 3 = Sin( θ ) Cos( δ) + (6) 3 3 = δ 3 3 Cos( δ ) Sin( θ ) (7) 3 P ( θ ) Cos( δ θ ) (8) = Cos P = Sin( α ) (9) 3 = Sin( θ ) + Sin( δ θ ) (0) P + = Cos( α ) () = Sin( α ) () = Cos( α ) (3) All the other active and reactive powers in the other lines can be found in a similar manner. Since the operation of the converters of the UPFC is based on PWM method, the magnitude of the output voltage () from the series compensation block can be calculated as [4]: K = M (4) dc where, K is equal to 0.6 [4] and M is the modulation index of the converter () that can be varied from (0% to 00%). On the other hand, the magnitude of the voltage in the unt compensation block is: K = M (5) dc where, K is equal to 0.6 [4] and M is the modulation index of converter () which will be set to 00%. (5) Journal of Engineering Science and Technology December 04, ol. 9(6)

5 68 S. A. Al-Mawsawi Therefore, from Eqs. (4) and (5), the magnitude of the injection voltage can be written as: = M (6) The voltage has an angle α with respect to the transmission line voltage. This angle will determine the amount of power transfer needed from converter () to converter (). For the sake of simplicity, it is assumed that the active power consumed by this FACTS device is zero. Therefore, P P = 0 (7) + 3. Multi-machine Systems with the New UPFC as Impedance Compensation and oltage Regulator (Model ) The new proposed UPFC steady-state model with three converters that are all connected to the DC link is own in Fig. 4. Operation of the three converters is based on PWM method. The first converter is the unt converter and its modulation index is selected to be 00%. The second converter (series injection) is installed between the Bus and Bus 3. This converter is operated as an impedance compensator with an amplitude and a phase angle of (ρ = -θ-90) degrees so that its output voltage is in quadrature with the line current I. The magnitude of the output voltage of this converter can be controlled by varying its modulation index M from 0% to 00%. The third converter is installed at the line between Bus and Bus. This converter is operated as a voltage regulator of amplitude of and at an angle in phase with the terminal voltage at Bus (angle of 0 degrees). The magnitude of the output voltage of this converter can be controlled by varying its modulation index M from 0% to 00%. Therefore, the advantage of this model is that only one FACTS device is required to control two lines in the transmission system rather than installing two different FACTS devices. The steady-state model of the multi machine systems with the new developed UPFC is own in Fig. 5. Fig. 4. Multi-machine Systems with the New Developed UPFC (Model ). Journal of Engineering Science and Technology December 04, ol. 9(6)

6 Evaluation of a New Model for UPFC Operating as Impedance Fig. 5. The Steady State Model of the Multi Machine Systems with New Developed UPFC (Model ). In this case, the same nonlinear load is considered as was presented in Eqs. () and (). From the complex powers of the system, all active and reactive powers can be calculated for the system as follows: = (8) 3 ( θ ) + Sin( ) Cos δ P 3 = Sin( θ ) Cos( δ ) + (9) P = Sin Cos 3 ( δ ) ( θ ) 3 3 δ (0) 3 δ () 3 ( ) Sin( θ ) 3 3 = Cos δ 3 P ( θ ) Cos( δ θ ) () = Cos 3 = Sin( θ ) + Sin( δ θ ) (3) ( ) Sin δ P = (4) Journal of Engineering Science and Technology December 04, ol. 9(6)

7 684 S. A. Al-Mawsawi P = (5) Cos δ ( ) = Sin (6) ( δ ) Sin( ) δ δ (7) ( ) Cos( ) = Cos δ Sin δ P = ( ) (8) = (9) Cos δ ( ) All the other active and reactive powers in other lines can be found in a similar way. As explained earlier, the relation between the magnitude of the voltages of and with the magnitude of voltage of as a function of the modulation index can be written as: = K M (30) = K M (3) For simplicity, it is again assumed that the active power consumed by the converters is zero (No losses). Therefore, P P + P 0 (3) + = 4. Simulation Results The two systems own in Figs. 3 and 5 have been modelled and simulated using Matlab. In both systems, an active power (P ) supplied to the grid by the synchronous machine () is selected to be.479 p.u. and the active power (P ) is considered as variable power demanded by the load. The impedance of the reactance of the transmission lines are selected to be: =0.04 p.u., = 3 =0. p.u. and 4 = p.u. [5]. The constants a and b of the non-linear load given in Eqs. () and () are considered to be.38 and 3., respectively [4]. These values represent the residential load model. The other parameters are 30 = p.u., P 0 =6.38 p.u., 0 =0.458 p.u., =.08 p.u., and =.0 p.u. For the system own in Fig. 3, the steady state performance of the UPFC is investegated for different values of the modulation index. The flow of active and reactive powers in all the lines is recorded. It is found that, by varying the modulation index (M ) of converter, both the active and reactive powers in all transmission lines can be varied. The most important result found is that the active power (P 3 ) can be controlled by the modulation index and this power can be raised from p.u. (without compensated system) to approximately 4.9 Journal of Engineering Science and Technology December 04, ol. 9(6)

8 Evaluation of a New Model for UPFC Operating as Impedance p.u. as can be seen in Fig. 6. In addition, it was found that the direction of the flow of power in the parallel lines can be reversed at approximately 0.8 modulation index as own in Fig P M Fig. 6. The Flow of Active Power (P 3 ) as Modulation Index is arying. Fig. 7. The Flow of Active Powers in Parallel Lines as Modulation Index is arying. On the other hand, for the system own in Fig. 5, the steady state performance of UPFC was investegated for two different values of the modulation index. The flow of active and reactive powers in all the lines is also recorded. In this case, the modulation index of converter 3 (M ) has very little affect on the power flow in all lines as own in Fig. 8. However, the most changes in active power flow come from changing the modulation index of converter (M ). Therefore, converter 3 has much less sensitivity than converter on controlling the active power flow between Bus and Bus 3. But, it can be seen that converter 3 has much higher sensitivity effect on the reactive power flow on some transmission lines as own in Fig. 9. Journal of Engineering Science and Technology December 04, ol. 9(6)

9 686 S. A. Al-Mawsawi P M M Fig. 8. The Flow of Active Power (P 3 ) as Modulation Index of Converters and 3 are arying. Fig. 9. The Flow of Reactive Power ( 3 and ) as Modulation Index of Converters and 3 are arying. In addition, Figs. 0 and compare the active and reactive power flows in the lines before compensation and after the compensation with Model () and Model () at 00% modulation index. These two figures ow that both Models can be used when controlling the flow of the active and reactive power in the transmission lines. However, both figures also ow that the amount of compensation of active and reactive powers in the transmission lines in case of Model () is slightly better than that of Model (). Moreover, Model () can be used to control two transmission lines at the same time and therefore the range of controlling the power flow in this case will be larger and more flexible. Journal of Engineering Science and Technology December 04, ol. 9(6)

10 Evaluation of a New Model for UPFC Operating as Impedance In addition, Fig. ows that, there is improvement in reactive power control as a result of modelling the series controller ( ) as a voltage regulator. Furthermore, an investigation ould be done in order to see the effect of such controller ( ) if it is modelled as impedance compensator P P P3 P P3 P4 P3 P34 P P P3 Before compensation mode mode Fig. 0. The Flow of Active Power in the Transmission Line without the Compensation and with the Compensation Using Model () and () Fig.. The Flow of Reactive Power in the Transmission Line without the Compensation and with the Compensation Using Model () and () Before compensation mode mode Conclusions A new steady-state model of UPFC was proposed. This model consists of one unt compensation block and two series compensation blocks. The UPFC with the new proposed model is investigated when installed in multi-machine systems with non-linear load model. The steady state performance of the new model Journal of Engineering Science and Technology December 04, ol. 9(6)

11 688 S. A. Al-Mawsawi operating as impedance compensation and voltage regulator is presented and compared with that obtained from the original Gyugyi model. The results found in this paper would be very useful in selecting the highest possible amount of compensation of active or reactive power flow in transmission lines. References. Gyugyi, L. (99). A unified power flow control concept for flexible ac transmission systems. IEE Proceedings C Generation Transmission Distribution, 4(39), Hingorani, N.G. (993). Flexible AC transmission. IEEE spectrum, Fuerte-Esquivel, C.R.; and Acha, E. (997). Unified power flow controller: a critical comparison of Newton-Raphson UPFC algorithms in power studies. IEE Proceeding-C Generation Transmission Distribution, 44(5) Gyugyi, L. (989). Solid-state control of electrical power in an AC transmission system. International Symposium on Electric Energy Converters in Power Systems. Invited paper T- IP (4), Italy. 5. Gyugyi, L.; Schauder, C.D; Williams, S.L. ; Rietman, T.R. ; Torgerson, D.R.; and Edris, A. (995). The unified power flow controller: a new approach to power transmission control. IEEE Transactions on Power Delivery, 0() Wang, H.F. (999). Damping function of unified power flow controller. IEE Proceedings of Generation, Transmission and Distribution, 46(), Wang, H.F.; Swift, F.J; and Li, M. (998). A unified model for the analysis of FACTS devices in damping power system oscillations Part II: multimachine infinite-bus power systems. IEEE Transactions on Power Delivery, 3(4), Larsen, E..; Sanchesz-Gasca, J.J.; and Chow, J.H. (995). Concept for design of FACTS controlling to damp power swings. IEEE Transactions on Power Systems, 0(), Wang, H.F. (999). Selection of robust installing locations and feedback signals of FACTS based stabilizers in multi-machine power systems. IEEE Transactions on Power Systems, 4(), Wang, H.F. (999). Applications of modelling UPFC into multi-machine power systems. IEE Proceeding Transmission Distribution, 46(3), Zhengyu, H.; and Yinxin, N. (000). Application of unified power flow controller in interconnected power systems-modelling, interface, control strategy and case study. IEEE Transactions on Power Systems, 5(), Wang, H.F. (003). Modelling multiple FACTS devices into multi-machine power systems and applications. International Journal of Electrical Power Systems, 5(3), Al-Mawsawi, S.A.; and ader, M.R. (004). Optimal location of a UPFC applied to non-linear load model. EPC&S: The International Journal for Electric Power Components and Systems, 3(), -. Journal of Engineering Science and Technology December 04, ol. 9(6)

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