Optimal tuning of pid power system stabilizer in simulink environment


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Optimal tuning of pid power system stabilizer in simulink environment

  1. 1. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME & TECHNOLOGY (IJEET)ISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 4, Issue 1, January- February (2013), pp. 115-123 IJEET© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEMEwww.jifactor.com OPTIMAL-TUNING OF PID POWER SYSTEM STABILIZER IN SIMULINK ENVIRONMENT FOR A SYNCHRONOUS MACHINE Mr. Gowrishankar kasilingam1, Ms.Tan Qian Yi2 1&2 Faculty of Engineering & Computer Technology, AIMST University, Kedah, Malaysia Email:gowri200@yahoo.com ABSTRACT In this paper, an optimum algorithm approach is presented for determining the optimal Proportional-Integral-Derivative (PID) Controller parameters of a typical power system stabilizer (PSS) in a single machine infinite bus system. The paper is modeled in the MATLAB Simulink Environment to analyze the performance of a synchronous machine under normal load conditions. The functional blocks of PID controller with PSS are generated and the simulation studies are conducted to observe the dynamic performance of the power system. This paper suggests the use of Ziegler-Nichols method to form the intervals for the controller parameters in which the tuning to be done. In order to assist the estimation of the performance of the proposed PID-PSS controller, a time-domain performance criterion function has been used. The proposed approach yields better solution in term of rise time, settling time, and maximum overshoot of the system. Analysis in this paper reveals that the Ziegler-Nichols method of optimal tuning PID controller gives better dynamic performance as compared to that of conventional trial and error method. Simulation results indicate that the performance of the PID controlled system can be significantly improved by the Ziegler- Nichols-based method. Keywords: Power System Stabilizer, Z&N method, PID Controller 1. INTRODUCTION Tuning of supplementary excitation controls for stabilizing system modes of oscillations has been the focus of many researches during the past two decades. PID control is one of the earlier control strategies. Since many control systems using PID control has been proven satisfactory, it still has a wide range of applications in industrial control [1]. The 115
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEreason is that it has s simple structure which is easily understood and under practicalconditions, it performed with higher reliability compared to more advanced and complexcontrollers. The main purpose of designing a PID controller is to determine the three gainswhich are proportional gain (Kp), integral gain (Ki) and derivative gain (Kd) of the controller.However, the three adjustable PID controller parameters should be tuned appropriately. Apurely mathematical approach to the study of automatic control is certainly the mostdesirable course from a standpoint of accuracy and brevity [2]. Many approaches have been developed to determine the PID controller parameters forsingle input single output (SISO) systems. Among the well-known approaches are theZiegler-Nichols (Z-N) method, the Cohen-Coon method, integral of squared time weightederror rule (ISE), integral of absolute error rule (IAE), and the gain-phase margin method.Ziegler and Nichols proposed rules for tuning PID controllers are based on the transientresponse characteristics of a given plant [2]. The Ziegler-Nichols formulation is a classicaltuning method which is found in a wide range of applications in the controller design process.However, computing the gains does not always give best results because the tuning criteriapresume a one-fourth reduction in the first two peaks [3]. Hence the industrial controllersdesigned with this method should be tuned further before actual usage [4]. In a power system, the excitation system performs control and protective functionsessential to the satisfactory performance of the power system by controlling the field voltageand field current. Properly tuned, a PSS can considerably enhance the dynamic performanceof a power system stabilizer [5]. The power system, however, is a highly complex system.The system of study is the one machine connected to infinite bus system through atransmission line having resistance (re) and inductance (xe) shown in Figure 1. Figure 1: One machine to infinite bus system This paper presents the optimal tuning Proportional-Integral-Derivative (PID) Controllerwith power system stabilizer (PSS) for a synchronous machine in a MATLAB Simulinkmodel environment. The aim is to compare the optimal tuning of Ziegler-Nichols methodwith the conventional trial and error tuning method. Several simulations have been carriedout in order to generate the output using a single machine infinite bus power system. Themain features of the proposed PID PSS is that it is simpler for practical implementation andyields better dynamic performances than that obtained with conventional lead-lag stabilizer[6]. Results presented in this paper clearly show the effectiveness of tuning the PID controllerwith Ziegler-Nichols method in comparison to other methods. This paper is organized as the following. Section II defines and explains the powersystem stabilizer (PSS). Section III discusses the design of a PID controller. In Section IV,optimum tuning with performance estimation of PID controller is provided. The simulationresults and discussion is established in Section V and Section VI provides importantconclusions. 116
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME2. POWER SYSTEM STABILIZER Damping of low frequency oscillations in interconnected power system is essential forsecure and stable operation of the system. The basic function of power system stabilizer is toadd damping to the generator rotor oscillations by controlling its excitation using auxiliarystabilizing signal(s). In this paper, an optimal method based on the PID controller isconsidered to the tuning parameters of the PID-PSS. Power system stability is similar to thestability of any dynamic system, and has fundamental mathematical underpinnings. In orderto provide damping, the stabilizer will produce electrical torque in phase with rotor speeddeviations. The excitation system is controlled by an automatic voltage regulator (AVR) anda power system stabilizer (PSS). Figure 2 shows the block diagram of the excitation system,including the AVR and PSS. The stabilizer output limits and exciter output limits are notshown as we are only concerned with small-signal performance. Figure 2. Power System Stabilizer The PSS representation in Figure 2 is made up of: a phase compensation block, a gainblock and a signal washout block. The phase compensation block provides the appropriatephase-lead characteristic to compensate for the phase lag between the exciter input and theelectrical torque of generator. The stabilizer gain KSTAB determines the amount of dampingintroduced by PSS whereas the signal washout block serves as a high-pass filter.3. DESIGN OF PID CONTROLLER Proportional–integral–derivative (PID) controller is a generic control loop feedbackmechanism widely used to enhance the dynamic response as well as to eliminate the steadystate error. A PID controller will correct the error between a measured process variable andthe desired input or set point by calculating and giving an output of correction that will adjustthe process accordingly. The PID Controller transfer function relating the error e(s) andcontroller output u(s) is given as, Where, Ti and Td are the reset and the derivative times, respectively. The first term in theequation represents proportionality effect on the error signal, whereas the second and thirdterm represents the integral effect and the derivative effects. 117
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME The control signal u(t) from the controller to the plant is equal to the proportional gain(Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the errorplus the derivative gain (Kd) times the derivative of the error. It is given as: u(t) = Kp e(t) + Ki + Kd Figure 3. Block Diagram of a PID controller.The process of determining the PID controller parameters Kp, Ti, and Td to achieve high andconsistent performance specifications is known as controller tuning. In the design of a PIDcontroller, these controller parameters must be optimally selected in such a way that theclosed loop system will give desired response.Typical steps for designing a PID controller are:• Determine what characteristics of the system need to be improved.• Use KP to decrease the rise time.• Use KD to reduce the overshoot and settling time.• Use KI to eliminate the steady-state error. PID Controllers are widely used in industry due to its simplicity and excellent if notoptimal performance in many applications. PID controllers are used in more than 95% ofclosed-loop industrial processes [7]. It can be tuned by operators without extensivebackground in Controls, unlike many other modern controllers that are much more complexbut often provide only marginal improvement. In fact, most PID controllers are tuned on-site.In addition to design the controller, the lengthy calculations for an initial guess of PIDparameters can often be circumvented if we know a few useful tuning rules. In the past fourdecades, there are numerous papers dealing with the tuning of PID controllers.4. OPTIMUM TUNING WITH PERFORMANCE ESTIMATION OF PID CONTROLLER There are several rules of thumb for determining how the quality of the tuning of acontrol loop. Traditionally, quarter wave decay has been considered to be the optimum decayratio. This criterion is used by the Ziegler Nichols tuning method, among others. There is nosingle combination of tuning parameters that will provide quarter wave decay. If the gain isincreased and the reset rate decreased by the correct amount the decay ratio will remain thesame. Quarter wave decay is not necessarily the best tuning for either disturbance rejection orset point response. However, it is a good compromise between instability and lack ofresponse [8]. 118
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure 4. Quarter Wave Decay There are several criteria for evaluating tuning that are based on integrating the errorfollowing a disturbance or set point change. These methods are not used to test control loopsin actual plant operation because the usual process noise and random disturbances will affectthe outcome. They are used in control theory education and research using simulatedprocesses. The indices provide a good method of comparing different methods of controllertuning and different control algorithm. The followings are some commonly used criteriabased on the integral error for a step set point or disturbance response:IAE - Integral of absolute value of errorISE - Integral of error squaredITAE - Integral of time times absolute value of errorITSE - Integral of time times error squared Ziegler-Nichols method is also known as Ultimate Gain method (or Closed-Loop method).In 1942, J. G. Ziegler and N. B. Nichols, both of the Taylor Instrument Companies(Rochester, NY) published a paper [2] that described two methods of controller tuning thatallowed the user to test the process to determine the dynamics of the process. Both methodsassume that the process can be represented by the model (described above) comprising theprocess gain, a “pseudo dead time”, and a lag. The methods provide a test to determineprocess gain and dynamics and equations to calculate the correct tuning. The Ziegler Nichols methods provide quarter wave decay tuning for most types ofprocess loops. This tuning does not necessarily provide the best ISE or IAE tuning but doesprovide stable tuning that is a reasonable compromise among the various objectives. If theprocess consists of a true dead time plus a single first order lag, the Z-N methods will providequarter wave decay. If the process has no true dead time but has more than two lags (resultingin a “pseudo dead time”) the Z-N methods will usually provide stable tuning but the tuningwill require on-line modification to achieve quarter wave decay.Because of their simplicity and because they provides adequate tuning for most loops, theZiegler Nichols methods are still widely used. Ziegler Nichols closed loop method is straightforward. At first, the controller is set to PIDmode by using trial and error value. Next, adjust Kp until a response is obtained that produces 119
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEcontinuous amplitude oscillation. This is known as the ultimate gain (Gu). Note the period ofthe oscillations (Pu) from the continuous oscillation as shown in Figure 5. Figure 5. Constant Amplitude OscillationThe final PID gain settings are then obtained using equation below: Kp: 0.6 GU Nm/rad; Nm/(rad·sec); Nm/(rad·sec)Based on previous trial and error results, the optimum PID gains according to Zigler-Nicholsmethod are then: Kp = 30 Nm/rad Ki = 3.226 Nm/(rad·sec) Kd = 2.8 Nm/(rad·sec)It is unwise to force the system into a situation where there are continuous oscillations as thisrepresents the limit at which the feedback system is stable. Generally, it is a good idea to stopat the point where some oscillation has been obtained. It is then possible to approximate theperiod (PU) and if the gain at this point is taken as the ultimate gain (GU), then this willprovide a more conservative tuning regime. Changes in system’s closed loop responsebecause of the changes in PID parameters with respect to a step input can be best describedusing the chart shown in Table 1 below. Table 1: Changes in PID parameters with respect to a step input Response Rise Time Overshoot Settling Time Steady State Error Kp Decrease Increase Small change Decrease Ki Decrease Increase Increase Eliminate Small Kd Decrease Decrease Small change changeAlgorithm for tuning PID ControllerThe closed loop (or ultimate gain method) determines the gain that will cause the loop tooscillate at a constant amplitude. Most loops will oscillate if the gain is increased sufficiently.The following steps are used:• Place controller into automatic with low gain, no reset or derivative.• Gradually increase gain, making small changes in the set point, until oscillations start.• Adjust gain to make the oscillations continue with a constant amplitude.• Note the gain (Ultimate Gain, Gu) and Period (Ultimate Period, Pu). 120
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME5. SIMULATION RESULTS AND DISCUSSION In this study, an optimal tuning method for determining the PID Controller parameterswas carried out. A Simulink model of PID Power System Stabilizer was developed and simulatedto tune the controller. The Ziegler-Nichols rules were used to form the intervals for the designparameters in tuning the controller by minimizing an objective function. Through the simulationof PID-PSS, the results show that the proposed controller can perform an efficient search toobtain optimal PID controller parameter that can achieve better performance criterion. Thecontroller gains were computed by using both trial and error method and Ziegler-Nichols rules.The gains found from both methods were listed in Table 2. Table 2: Controller parameters defined from the two methods Method Kp Ki Kd Trial & Error 50 5 2 Ziegler-Nichols 30 3.226 2.8Figure 6 showed the response of speed deviation with continuous oscillations. The result isobtained by adjusting the Kp value of the PID Controller to maximum. This is known as theultimate gain (Gu). From the output, we can note the period of the oscillations (Pu). Figure 6. Calculation of Gu & Pu Figure 7. Response of Speed DeviationFigure 7 shows both the results of the PID power system stabilizer with tuning done using Trialand Error method and Ziegler-Nichols method. It is clearly shown in figures that the optimaltuning of Ziegler-Nichols method is less oscillatory than the trial and error method. Theovershoot is slightly higher for Ziegler-Nichols method. Although a comparatively smaller risetime (Tr) were obtained from trial and error method, Ziegler-Nichols give shorter settling time(Ts). It takes about 2.5 sec to settle down while the system using trial and error method needs 3 121
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEsec to finally settle. These results were presented in Table 3. In conclusion, superior results wereobtained in terms of system performance and controller output by using Ziegler-Nichols methodfor tuning PID controllers when these values compared on tables and figures. Table 3: Response characteristics of the System Settling Rise time, Oversho Method time, Tr (sec) ot (p.u.) Ts (sec) Trial & Error 3 0.055 0.0082 Ziegler-Nichols 2.5 0.065 0.01267Figure 8-10 shown below are the response for rotor angle deviation, load angle and field voltage ofthe PID PSS. It is clear that PID controller with Ziegler-Nichols tuning method provides acomparatively better damping characteristic to low frequency oscillations by stabilizing the systemmuch faster. Figure 8. Response of Rotor Angle Deviation Figure 9. Response of Load Angle Figure 10. Response of Field Voltage 122
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME6. CONCLUSION In this study, the proportional-integral-derivative power system stabilizer (PID-PSS)has been proposed for the enhancement of the dynamic stability of single machine infinitebus. Gain settings of PID-PSS have been optimized using the proposed methods. The Ziegler-Nichols method was used to form the intervals for the PID tuning. Analysis reveals that thismethod gives much better dynamic performances as compared to that of trial and errormethod. It has more robust stability and efficiency. Hence, it can help to solve the searchingand tuning problems of PID controller parameters more easily and quickly than the trial anderror method. Analysis also shows that the PID gain settings obtained for nominal loadingcondition gives satisfactory dynamic performances. Modeling of proposed controller inSimulink environment provides an accurate result when compared to mathematical designapproach.REFERENCE1. N.M. Tabatabaei, M. Shokouhian Rad (2010), “Designing Power System Stabilizer with PID Controller”, International Journal on “Technical and Physical Problems of Engineering” (IJTPE), Iss. 3, Vol. 2, No. 22. J. G. Ziegler and N. B. Nichols(1942), “Optimum settings for automatic controllers,” Transactions of American Society of Mechanical Engineers, Vol. 64, pp.759-768.3. Goodwin, G.C., Graebe, S.F. and Salgado, M.E. (2001), “Control System Design”, Prentice Hall Inc, New Jersey4. Wu, C.J. and Huang, C.H., “A Hybrid Method for Parameter Tuning of PID Contollers”, J.Franklin Inst., 224B(4), 547-5625. T KSunil Kumar and Jayanta Pal2, “Robust Tuning of Power System Stabilizers Using Optimization Techniques”, IEEE 2006, pp 1143-11486. P.Bera, D.Das and T.K. Basu (2004), “Design of P-I-D Power System Stabilizer for Multimachine System”, IEEE India Annual Conference 2004, pp 446-4507. Astrom K. J. and Hagglund T. H. (1995), “New tuning methods for PID controllers”, Proceedings of the 3rd European Control Conference8. John A. Shaw(2003), “The PID Control Algorithm: How it works, how to tune it, and how to use it, 2nd Edition”, Process Control Solutions9. VenkataRamesh.Edara, B.Amarendra Reddy, Srikanth Monangi and M.Vimala, “Analytical Structures For Fuzzy PID Controllers And Applications” International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 1 - 17, Published by IAEME10. Preethi Thekkath and Dr. G. Gurusamy, “Effect Of Power Quality On Stand By Power Systems” International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 118 - 126, Published by IAEME11. A.Padmaja, V.s.Vakula, T.Padmavathi and S.v.Padmavathi, “Small Signal Stability Analysis Using Fuzzy Controller And Artificial Neural Network Stabilizer” International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 47 - 70, Published by IAEME12. M. A. Majed and Prof. C.S. Khandelwal, “Efficient Dynamic System Implementation Of FPGA Based PID Control Algorithm for Temperature Control System” International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 2, 2012, pp. 306 - 312, Published by IAEME 123