International society of academic and industrial research www.isair.org IJARAS International Journal of Academic Research in Applied Science 1(4): 1-8, 2012 ijaras.isair.org Robust controller design for LFO damping Hasan Fayazi Boroujeni Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen, Iran Email: Hasanfayaziboroujeni@gmail.com Abstract Static synchronous compensator (STATCOM) is one of the most important FACTS devices and it is based on the principle that a voltage-source inverter generates a controllable AC voltage source behind a transformer-leakage reactance so that the voltage difference across the reactance produces active and reactive power exchange between the STATCOM and the transmission network. This paper presents the application of static synchronous compensator (STATCOM) to improvement dynamic stability of a multi-machine electric power system installed with STATCOM. Quantitative Feedback Theory (QFT) is used to design the STATCOM supplementary stabilizer. In order to show the ability of STATCOM in damping of low frequency oscillations (LFO), the results are compared with the system without STATCOM. Several nonlinear time-domain simulation tests visibly show the ability of STATCOM in damping of power system oscillations and consequently stability enhancement. Keywords Quantitative Feedback Theory, Flexible AC Transmission Systems; Static Synchronous Compensator; Damping of Power System Oscillations
1. Introduction The rapid development of the high-power electronics industry has made Flexible AC Transmission System (FACTS) devices viable and attractive for utility applications. FACTS devices have been shown to be effective in controlling parameters of power system and also in damping power system oscillations. In recent years, new types of FACTS devices have been investigated that may be used to increase power system operation flexibility and controllability, to enhance system stability and to achieve better utilization of existing power systems [1]. The static synchronous compensator (STATCOM) is one of the most important FACTS devices and it is based on the principle that a voltage-source inverter generates a controllable AC voltage source behind a transformer-leakage reactance so that the voltage difference across the reactance produces active and reactive power exchange between the STATCOM and the transmission network. The can be used for dynamic compensation of power systems to provide voltage support [2, 3]. Also STATCOM can be used for transient stability improvement by damping of low frequency power system oscillations [4-12]. The objective of this paper is to investigate the ability of STATCOM for dynamic stability improvement via damping of low frequency oscillations. An auxiliary stabilizer based on STATCOM is used to increase power system damping torque. QFT technique is used to design the STATCOM supplementary stabilizer. A multi machine power system installed with a STATCOM is chosen as case study. Different load conditions are incorporated to show effectiveness of STATCOM. Simulation results show the validity of STATCOM in LFO damping and stability enhancement at large electric power systems. 2. System under study In this paper IEEE 14 bus test system is considered to evaluate the proposed method. The system data are completely given in IEEE standards. Figure 1 shows the system with a STATCOM installed in bus 14. Detail of the system data are given in [13]. To evaluate the effectiveness and robustness of the proposed method over a wide range of loading conditions, two different cases as nominal and heavy loading are considered. Where, in the heavy condition, the active and reactive powers of loads are considered by 20% increasing from the nominal vales. Also, in this paper, turbine-governor system is also modeled to eliminate steady state error of responses. Figure 1: Multi-machine electric power system installed with STATCOM 2
2.1. Dynamic model of the system with STATCOM The nonlinear dynamic model of the system installed with STATCOM is given as (1). The dynamic model of the system installed with STATCOM is completely presented in [1]. = ( ) = ( 1) = + = + = (K (V V) b ) T (1) Where, δ: Rotor angle; ω: Rotor speed (pu); P m : Mechanical input power; P e : Electrical output power (pu); M: System inertia (Mj/MVA); E q: Internal voltage behind x d (pu); E fd : Equivalent excitation voltage (pu); T do: Time constant of excitation circuit (s); K a : Regulator gain; T a : Regulator time constant (s); V ref : Reference voltage (pu); V t : Terminal voltage (pu). By controlling m E, the output voltage of the shunt converter is controlled. By controlling E, exchanging active power between the STATCOM and the power system is controlled. 3. QFT method Quantitative Feedback Theory (QFT) is a unified theory that emphasizes to use of feedback for achieving the desired system performance tolerances despite plant uncertainty and plant disturbances. QFT quantitatively formulates these two factors as following form: (i)- Sets τ R = {T R } of acceptable command or tracking input-output relations and sets τ D = {T D } of acceptable disturbance input-output relations. (ii)- Sets ρ = {P} of possible plants. The object is to guarantee that the control ratio (system transfer function) T R =Y/R is a member of τ R and T D =Y/D is a member of τ D for all P(S) in ρ. QFT is essentially a frequency-domain technique and in this paper is used for multiple input single output (MISO) systems. It is possible to convert the MIMO system into its equivalent sets of MISO systems to which the QFT design technique is applied. The objective is to solve the MISO problems, i.e., to find compensation functions which guarantee that the performance tolerance of each MISO problem is satisfied for all P in ρ. The detailed step-by-step procedure to design controllers using QFT technique is given in [14]. 4. Stabilizer design In this section the SSSC supplementary stabilizer is designed by using QFT method. QFT method leads to a controller which satisfies system performance over all operating conditions and plants. The topology of control loop in the QFT method is depicted in figure 2. The uncertain plant is obtained by using system model presented and then the controller is designed to satisfy the output under all uncertainties in the plant. 3
Figure 2: control loop in the QFT method The controller is design by using QFT toolbox of MATLB software. In order to obtain a good response, minimum damping ratios ζ for the dominant roots of the closed-loop system is considered as ζ=1.2, this amount, on the Nichols chart establishes a region which must not be penetrated by the template of loop shaping for all frequencies. The boundary of this region is referred to as U-contour. The resulted controller is as follows: Stabilizer=0.92 (1+s0.8/1+s0.01) (1+s0.05/1+s0.033) 5. Results and discursions The designed stabilizer is tested based on the STATCOM. Following fault is considered: Fault Scenario: disconnection of the line between bus 2 and bus 4 by breaker It is worth to mention that in fault scenario, the line is disconnected by breaker and after one second the line is connected again. Also the simulation results are presented in Figures 3-6. Each figure contains two plots; solid line which indicates the system installed with STATCOM and dashed line for system without STATCOM. The simulation results show that applying the supplementary stabilizer signal greatly enhances the damping of the generator angle oscillations and therefore the system becomes more stable. With changing operating condition from the nominal to heavy, while the performance of system without STATCOM becomes poor, the system with STATCOM has a stable and robust performance. The results clearly show that in large electric power systems, STATCOM can successfully increase damping of power system oscillations and the system with STATCOM based stabilizer is more robust and stable after disturbances. 4
1.001 1.0008 1.0006 Speed G1(pu) 1.0004 1.0002 1 0.9998 0.9996 0 2 4 6 8 10 12 Time(s) Figure 3: Speed G 1 following fault (Solid (With STATCOM), Dashed (Without STATCOM)) 1.0014 1.0012 1.001 1.0008 Speed G2(pu) 1.0006 1.0004 1.0002 1 0.9998 0.9996 0.9994 0 2 4 6 8 10 12 Time(s) Figure 4: Speed G 2 following fault (Solid (With STATCOM), Dashed (Without STATCOM)) 5
1.001 1.0008 1.0006 Speed G3(pu) 1.0004 1.0002 1 0.9998 0.9996 0.9994 0 2 4 6 8 10 12 Time(s) Figure 5: Speed G 3 following fault (Solid (With STATCOM), Dashed (Without STATCOM)) 6
1.0025 1.002 1.0015 Speed G4(pu) 1.001 1.0005 1 0.9995 0.999 0.9985 0 2 4 6 8 10 12 Time(s) Figure 6: Speed G 4 following fault (Solid (With STATCOM), Dashed (Without STATCOM)) 6. Conclusions In this paper QFT method was used to design STATCOM stabilizer. A multi-machine electric power system installed with a STATCOM was assumed to demonstrate the ability of STATCOM in damping of power system oscillations. Simulation results demonstrated that the designed STATCOM capable to guarantee the robust stability and robust performance under disturbances. References [1] Hingorani NG, Gyugyi L, El-Hawary M. Understanding FACTS: concepts and technology of flexible AC transmission systems: IEEE press New York; 2000. [2] Cañizares CA, Pozzi M, Corsi S, Uzunovic E. STATCOM modeling for voltage and angle stability studies. International Journal of Electrical Power & Energy Systems. 2003;25:431-41. [3] HOOSHMAND RA, BANEJAD M, AZIMI M. Voltage Sag Mitigation Using A New Direct Control In D-Statcom For Distribution Systems. UPB Sci Bull, Series C. 2009;71:1454-234. [4] Abido MA. Analysis and assessment of STATCOM-based damping stabilizers for power system stability enhancement. Electric Power Systems Research. 2005;73:177-85. 7
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