* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Power factor wikipedia, lookup

Power inverter wikipedia, lookup

Immunity-aware programming wikipedia, lookup

Control theory wikipedia, lookup

Ground (electricity) wikipedia, lookup

Pulse-width modulation wikipedia, lookup

Power over Ethernet wikipedia, lookup

Opto-isolator wikipedia, lookup

Electronic engineering wikipedia, lookup

Buck converter wikipedia, lookup

Stray voltage wikipedia, lookup

Three-phase electric power wikipedia, lookup

Variable-frequency drive wikipedia, lookup

Electric power transmission wikipedia, lookup

Wireless power transfer wikipedia, lookup

Electrical substation wikipedia, lookup

Life-cycle greenhouse-gas emissions of energy sources wikipedia, lookup

Electrification wikipedia, lookup

Electric power system wikipedia, lookup

Voltage optimisation wikipedia, lookup

Distributed generation wikipedia, lookup

Control system wikipedia, lookup

Power electronics wikipedia, lookup

Switched-mode power supply wikipedia, lookup

Mains electricity wikipedia, lookup

Alternating current wikipedia, lookup

Transcript

©International society of academic and industrial research www.isair.org International Journal of Academic Research in Applied Science IJARAS 1(4): 16-23, 2012 ijaras.isair.org Robust Stabilizer Design by Using QFT Ahmad Memaripour Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen, Iran Email: [email protected] Abstract Static Synchronous Series Compensator (SSSC) is a voltage-sourced converter-based series compensator and was proposed within the concept of using converter-based technology uniformly for shunt and series compensation, as well as for transmission angle control. It has been successfully applied in power systems. This paper presents the application of supplementary stabilizer based on SSSC in order to stability enhancement. The ability of the proposed method is evaluated in an electric power system. Quantitative feedback theory (QFT) is used to design the proposed stabilizer. Keywords Quantitative Feedback Theory, Static Synchronous Series Compensator, Low Frequency Oscillations, Stabilizer Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 1. Introduction With the practical applications of converter-based flexible AC transmission system (FACTS) controllers [1] such as the static synchronous compensator (STATCOM) [2], static synchronous series compensator (SSSC) [3] and unified power- flow controller (UPFC) [4], modeling and analysis of these FACTS controllers in power-system operation and control is of great interest. Power-flow calculations are fundamental to the operation, planning and control of power systems. In recent years, significant work has been done in the modeling of the FACTS controllers in and optimal-power-flow studies [3, 5-16]. SSSC is a voltage-sourced converter-based series compensator and was proposed within the concept of using converter-based technology uniformly for shunt and series compensation, as well as for transmission angle control. It has been successfully applied in power systems. In this paper, SSSC is used to increase power system stability. A supplementary stabilizer is equipped based on SSSC. The proposed stabilizer is designed by using QFT. 2. 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 τR = {TR} of acceptable command or tracking input-output relations and sets τD = {TD} 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) TR =Y/R is a member of τR and TD=Y/D is a member of τD 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 [17]. 3. Static Synchronous Series Compensator (SSSC) SSSC is one of the most important FACTS devices. It is installed in series with transmission line. This device has a voltage source converter serially connected to a transmission line through a transformer. It is necessary an energy source to provide a continuous voltage through a condenser and to compensate the losses of the VSC. A SSSC is able to exchange active and reactive power with the transmission system. But if our only aim is to balance the reactive power, the energy source could be quite small. The injected voltage can be controlled in phase and magnitude if we have an energy source that is big enough for the purpose. With reactive power compensation only the voltage is controllable, because the voltage vector forms 90º degrees with the line intensity. In this case the serial injected voltage can delay or advanced the line current. This means that the SSSC can be uniformly controlled in any value, in the VSC working slot. 17 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 The Static Synchronous Series Compensator (SSSC) uses a VSC interfaced in series to a transmission line, as shown in the Figure 1. Again, the active power exchanged with the line has to be maintained at zero hence, in steady state operation, SSSC is a functional equivalent of an infinitely variable series connected capacitor. The SSSC offers fast control and it is inherently neutral to sub-synchronous resonance. Figure 1: SSSC - A VSC interfaced in series to a transmission line As mentioned, Static Synchronous Series Compensator (SSSC) is placed in the group of series connected FACTS devices. As shown in Figure 2, SSSC consists of a voltage source inverter connected in series through a coupling transformer to the transmission line. A source of energy is required for providing and maintaining the DC voltage across the DC capacitor and compensation of SSSC losses. Figure 3 shows the model of SSSC which consists of a series connected voltage source in series with impedance. This impedance represents the impedance of coupling transformer. Figure 2: basic configuration of SSSC Figure 3: equivalent circuit of SSSC The SSSC when operated with an appropriate DC supply (an energy source and/or sink, or suitable energy storage) can inject a component of voltage in anti-phase with the voltage 18 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 developed across the line resistance, to counteract the effect of the resistive voltage drop on the power transmission. 4. Power system stabilizer An AVR (without supplementary control loops) can weaken the damping provided by the damper and field windings. This reduction in the damping torque is primarily due to the voltage regulation effects inducing additional currents in the rotor circuits that oppose the currents induced by the rotor speed deviation Δω. Adding supplementary control loops to the generator AVR or FACTS devices is one of the most common ways of enhancing both smallsignal (steady-state) stability and large-signal (transient) stability. The Stabilizer can be used to add damping signal to the SSSC, where the output signal of the stabilizer is used as an additional input (vstab) to the SSSC. The stabilizer input signal can be either the machine speed deviation, Δω, or its acceleration power. The stabilizer is modeled by the nonlinear system depicted in Figure 4. Figure 4: Conventional stabilizer The model consists of a low-pass filter, a general gain, a washout high-pass filter, a phasecompensation system, and an output limiter. The general gain K determines the amount of damping produced by the stabilizer. The washout high-pass filter eliminates low frequencies that are present in the Δω signal and allows the stabilizer to respond only to speed changes. The phase-compensation system is represented by a cascade of two first-order lead-lag transfer functions used to compensate the phase lag between the excitation voltage and the electrical torque of the synchronous machine. 5. Test system Figure 5 shows a two area system installed with SSSC. Bus 4 is aggregation of a large number of generators and it can be modeled as an infinite bus. The SSSC is installed in one of two parallel lines. The system data are given in [18]. 19 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 Figure 5: power system installed with SSSC 6. 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 6. 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. disturbance Input + Controller + + Uncertain Plant output - Figure 6: 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: Controller=192.5 × . . × . . 7. Simulation result The proposed stabilizer is evaluated based on the test system given in section 4.1. Large disturbance is considered to show ability of the proposed stabilizer. The simulation results are depicted in figures 7-8. It is seen that the system without stabilizer contains insufficient 20 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 damping and the responses are pendulous. But the stabilizer can greatly enhance power system stability and damp out the oscillations and the advantages of the proposed stabilizer are visibly seen. 1.015 1.01 Speed(pu) 1.005 1 0.995 0.99 0.985 0 5 10 15 Time(s) Figure 7: speed following 6 cycle three phase short circuit in bus 2 Solid: with stabilizer dashed: without stabilizer 1.015 1.01 Speed(pu) 1.005 1 0.995 0.99 0.985 0 5 10 15 Time(s) Figure 8: speed following 10 cycle three phase short circuit in bus 3 Solid: with stabilizer dashed: without stabilizer 21 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 8. Conclusion In this paper a supplementary stabilizer has been successfully applied based SSSC. A power system installed with a SSSC has been assumed to demonstrate the ability of the proposed stabilizer. Nonlinear simulation results demonstrated that the designed stabilizer capable to guarantee the robust stability and robust performance under disturbances. Also, simulation results show that the QFT is a suitable tool to design stabilizer parameters. 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] Bhowmick S, Das B, Kumar N. An indirect model of SSSC for reducing complexity of coding in Newton power flow algorithm. Electric Power Systems Research. 2007;77:143241. [4] Ajami A, Hosseini SH, Khanmohammadi S, Gharehpetian GB. Modeling and control of C-UPFC for power system transient studies. Simulation Modelling Practice and Theory. 2006;14:564-76. [5] Ambriz-Pérez H, Acha E, Fuerte-Esquivel CR. TCSC-firing angle model for optimal power flow solutions using Newton's method. International Journal of Electrical Power & Energy Systems. 2006;28:77-85. [6] Angeles-Camacho C, Fuerte-Esquivel CR. A three-phase SSVS model for power flow studies in unbalanced transmission networks. International Journal of Electrical Power & Energy Systems. 2006;28:696-706. [7] Basu M. Optimal power flow with FACTS devices using differential evolution. International Journal of Electrical Power & Energy Systems. 2008;30:150-6. [8] Fang W, Ngan HW. A robust load flow technique for use in power systems with unified power flow controllers. Electric Power Systems Research. 2000;53:181-6. [9] Jain T, Singh SN, Srivastava SC. Dynamic ATC enhancement through optimal placement of FACTS controllers. Electric Power Systems Research. 2009;79:1473-82. [10] Mahdad B, Srairi K, Bouktir T. Optimal power flow for large-scale power system with shunt FACTS using efficient parallel GA. International Journal of Electrical Power & Energy Systems. 2010;32:507-17. [11] Menniti D, Pinnarelli A, Scordino N, Sorrentino N. Using a FACTS device controlled by a decentralised control law to damp the transient frequency deviation in a deregulated electric power system. Electric Power Systems Research. 2004;72:289-98. [12] Mihalič R, Papič I. Static synchronous series compensator—a mean for dynamic power flow control in electric power systems. Electric Power Systems Research. 1998;45:65-72. [13] Nayeripour M, Narimani MR, Niknam T, Jam S. Design of sliding mode controller for UPFC to improve power oscillation damping. Applied Soft Computing. 2011;11:4766-72. 22 Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012 [14] Ongsakul W, Bhasaputra P. Optimal power flow with FACTS devices by hybrid TS/SA approach. International Journal of Electrical Power & Energy Systems. 2002;24:851-7. [15] Padiyar KR, Prabhu N. Investigation of SSR characteristics of unified power flow controller. Electric Power Systems Research. 2005;74:211-21. [16] Padiyar KR, Uma Rao K. Modeling and control of unified power flow controller for transient stability. International Journal of Electrical Power & Energy Systems. 1999;21:1-11. [17] Horowitz I. Quantitative feedback theory. Proceedings D: IET; 1982. p. 215-26. Control Theory and Applications, IEE [18] Kundur P, Balu NJ, Lauby MG. Power system stability and control: McGraw-hill New York; 1994. 23