6545(Print), ISSN (Online) Volume 4, Issue 1, January- February (2013), IAEME & TECHNOLOGY (IJEET)

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1 INTERNATIONAL International Journal of JOURNAL Electrical Engineering OF ELECTRICAL and Technology (IJEET), ENGINEERING ISSN 0976 & TECHNOLOGY (IJEET) ISSN (Print) ISSN (Online) Volume 4, Issue 1, January- February (2013), pp IAEME: Journal Impact Factor (2012): (Calculated by GISI) IJEET I A E M E OPTIMAL-TUNING OF PID POWER SYSTEM STABILIZER IN SIMULINK ENVIRONMENT FOR A SYNCHRONOUS MACHINE Ms.Tan Qian Yi 1, Mr. Gowrishankar kasilingam 2, Mr.Raman Raghuraman 3 1, 2 & 3 Faculty of Engineering & Computer Technology, AIMST University, Kedah, Malaysia 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 reason is that it has s simple structure which is easily understood and under practical conditions, it performed with higher reliability compared to more advanced and complex controllers. The main purpose of designing a PID controller is to determine the three gains which are proportional gain (K p ), integral gain (K i ) and derivative gain (K d ) of the controller. However, the three adjustable PID controller parameters should be tuned appropriately. A purely mathematical approach to the study of automatic control is certainly the most desirable course from a standpoint of accuracy and brevity [2]. Many approaches have been developed to determine the PID controller parameters for single input single output (SISO) systems. Among the well-known approaches are the Ziegler-Nichols (Z-N) method, the Cohen-Coon method, integral of squared time weighted error 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 transient response characteristics of a given plant [2]. The Ziegler-Nichols formulation is a classical tuning 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 criteria presume a one-fourth reduction in the first two peaks [3]. Hence the industrial controllers designed with this method should be tuned further before actual usage [4]. In a power system, the excitation system performs control and protective functions essential to the satisfactory performance of the power system by controlling the field voltage and field current. Properly tuned, a PSS can considerably enhance the dynamic performance of 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 a transmission line having resistance (r e ) and inductance (x e ) shown in Figure 1. Figure 1: One machine to infinite bus system This paper presents the optimal tuning Proportional-Integral-Derivative (PID) Controller with power system stabilizer (PSS) for a synchronous machine in a MATLAB Simulink model environment. The aim is to compare the optimal tuning of Ziegler-Nichols method with the conventional trial and error tuning method. Several simulations have been carried out in order to generate the output using a single machine infinite bus power system. The main features of the proposed PID PSS is that it is simpler for practical implementation and yields 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 controller with Ziegler-Nichols method in comparison to other methods. This paper is organized as the following. Section II defines and explains the power system 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 simulation results and discussion is established in Section V and Section VI provides important conclusions. 116

3 2. POWER SYSTEM STABILIZER Damping of low frequency oscillations in interconnected power system is essential for secure and stable operation of the system. The basic function of power system stabilizer is to add damping to the generator rotor oscillations by controlling its excitation using auxiliary stabilizing signal(s). In this paper, an optimal method based on the PID controller is considered to the tuning parameters of the PID-PSS. Power system stability is similar to the stability of any dynamic system, and has fundamental mathematical underpinnings. In order to provide damping, the stabilizer will produce electrical torque in phase with rotor speed deviations. The excitation system is controlled by an automatic voltage regulator (AVR) and a 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 not shown 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 gain block and a signal washout block. The phase compensation block provides the appropriate phase-lead characteristic to compensate for the phase lag between the exciter input and the electrical torque of generator. The stabilizer gain K STAB determines the amount of damping introduced 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 feedback mechanism widely used to enhance the dynamic response as well as to eliminate the steady state error. A PID controller will correct the error between a measured process variable and the desired input or set point by calculating and giving an output of correction that will adjust the process accordingly. The PID Controller transfer function relating the error e(s) and controller output u(s) is given as, Where, T i and T d are the reset and the derivative times, respectively. The first term in the equation represents proportionality effect on the error signal, whereas the second and third term represents the integral effect and the derivative effects. 117

4 The control signal u(t) from the controller to the plant is equal to the proportional gain (K p ) times the magnitude of the error plus the integral gain (K i ) times the integral of the error plus the derivative gain (K d ) times the derivative of the error. It is given as: u(t) = K p e(t) + K i + K d Figure 3. Block Diagram of a PID controller. The process of determining the PID controller parameters Kp, Ti, and Td to achieve high and consistent performance specifications is known as controller tuning. In the design of a PID controller, these controller parameters must be optimally selected in such a way that the closed 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 K P to decrease the rise time. Use K D to reduce the overshoot and settling time. Use K I to eliminate the steady-state error. PID Controllers are widely used in industry due to its simplicity and excellent if not optimal performance in many applications. PID controllers are used in more than 95% of closed-loop industrial processes [7]. It can be tuned by operators without extensive background in Controls, unlike many other modern controllers that are much more complex but 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 PID parameters can often be circumvented if we know a few useful tuning rules. In the past four decades, 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 a control loop. Traditionally, quarter wave decay has been considered to be the optimum decay ratio. This criterion is used by the Ziegler Nichols tuning method, among others. There is no single combination of tuning parameters that will provide quarter wave decay. If the gain is increased and the reset rate decreased by the correct amount the decay ratio will remain the same. Quarter wave decay is not necessarily the best tuning for either disturbance rejection or set point response. However, it is a good compromise between instability and lack of response [8]. 118

5 Figure 4. Quarter Wave Decay There are several criteria for evaluating tuning that are based on integrating the error following a disturbance or set point change. These methods are not used to test control loops in actual plant operation because the usual process noise and random disturbances will affect the outcome. They are used in control theory education and research using simulated processes. The indices provide a good method of comparing different methods of controller tuning and different control algorithm. The followings are some commonly used criteria based on the integral error for a step set point or disturbance response: IAE - Integral of absolute value of error ISE - Integral of error squared ITAE - Integral of time times absolute value of error ITSE - 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 that allowed the user to test the process to determine the dynamics of the process. Both methods assume that the process can be represented by the model (described above) comprising the process gain, a pseudo dead time, and a lag. The methods provide a test to determine process gain and dynamics and equations to calculate the correct tuning. The Ziegler Nichols methods provide quarter wave decay tuning for most types of process loops. This tuning does not necessarily provide the best ISE or IAE tuning but does provide stable tuning that is a reasonable compromise among the various objectives. If the process consists of a true dead time plus a single first order lag, the Z-N methods will provide quarter wave decay. If the process has no true dead time but has more than two lags (resulting in a pseudo dead time ) the Z-N methods will usually provide stable tuning but the tuning will require on-line modification to achieve quarter wave decay. Because of their simplicity and because they provides adequate tuning for most loops, the Ziegler Nichols methods are still widely used. Ziegler Nichols closed loop method is straightforward. At first, the controller is set to PID mode by using trial and error value. Next, adjust K p until a response is obtained that produces 119

6 continuous amplitude oscillation. This is known as the ultimate gain (G u ). Note the period of the oscillations (P u ) from the continuous oscillation as shown in Figure 5. Figure 5. Constant Amplitude Oscillation The final PID gain settings are then obtained using equation below: K p : 0.6 G U Nm/rad; Nm/(rad sec); Nm/(rad sec) Based on previous trial and error results, the optimum PID gains according to Zigler-Nichols method are then: K p = 30 Nm/rad K i = Nm/(rad sec) K d = 2.8 Nm/(rad sec) It is unwise to force the system into a situation where there are continuous oscillations as this represents the limit at which the feedback system is stable. Generally, it is a good idea to stop at the point where some oscillation has been obtained. It is then possible to approximate the period (P U ) and if the gain at this point is taken as the ultimate gain (G U ), then this will provide a more conservative tuning regime. Changes in system s closed loop response because of the changes in PID parameters with respect to a step input can be best described using 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 K p Decrease Increase Small change Decrease K i Decrease Increase Increase Eliminate K d Small change Decrease Decrease Small change Algorithm for tuning PID Controller The closed loop (or ultimate gain method) determines the gain that will cause the loop to oscillate 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, G u ) and Period (Ultimate Period, P u ). 120

7 5. SIMULATION RESULTS AND DISCUSSION In this study, an optimal tuning method for determining the PID Controller parameters was carried out. A Simulink model of PID Power System Stabilizer was developed and simulated to tune the controller. The Ziegler-Nichols rules were used to form the intervals for the design parameters in tuning the controller by minimizing an objective function. Through the simulation of PID-PSS, the results show that the proposed controller can perform an efficient search to obtain optimal PID controller parameter that can achieve better performance criterion. The controller 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 K p K i K d Trial & Error Ziegler-Nichols Figure 6 showed the response of speed deviation with continuous oscillations. The result is obtained by adjusting the K p value of the PID Controller to maximum. This is known as the ultimate gain (G u ). From the output, we can note the period of the oscillations (P u ). Figure 6. Calculation of Gu & Pu Figure 7. Response of Speed Deviation Figure 7 shows both the results of the PID power system stabilizer with tuning done using Trial and Error method and Ziegler-Nichols method. It is clearly shown in figures that the optimal tuning of Ziegler-Nichols method is less oscillatory than the trial and error method. The overshoot is slightly higher for Ziegler-Nichols method. Although a comparatively smaller rise time (T r ) were obtained from trial and error method, Ziegler-Nichols give shorter settling time (T s ). It takes about 2.5 sec to settle down while the system using trial and error method needs 3 121

8 sec to finally settle. These results were presented in Table 3. In conclusion, superior results were obtained in terms of system performance and controller output by using Ziegler-Nichols method for tuning PID controllers when these values compared on tables and figures. Table 3: Response characteristics of the System Method Settling time, T s (sec) Rise time, T r (sec) Oversho ot (p.u.) Trial & Error Ziegler-Nichols Figure 8-10 shown below are the response for rotor angle deviation, load angle and field voltage of the PID PSS. It is clear that PID controller with Ziegler-Nichols tuning method provides a comparatively better damping characteristic to low frequency oscillations by stabilizing the system much faster. Figure 8. Response of Rotor Angle Deviation Figure 9. Response of Load Angle Figure 10. Response of Field Voltage 122

9 6. 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 infinite bus. 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 this method gives much better dynamic performances as compared to that of trial and error method. It has more robust stability and efficiency. Hence, it can help to solve the searching and tuning problems of PID controller parameters more easily and quickly than the trial and error method. Analysis also shows that the PID gain settings obtained for nominal loading condition gives satisfactory dynamic performances. Modeling of proposed controller in Simulink environment provides an accurate result when compared to mathematical design approach. REFERENCE 1. 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 J. G. Ziegler and N. B. Nichols(1942), Optimum settings for automatic controllers, Transactions of American Society of Mechanical Engineers, Vol. 64, pp Goodwin, G.C., Graebe, S.F. and Salgado, M.E. (2001), Control System Design, Prentice Hall Inc, New Jersey 4. Wu, C.J. and Huang, C.H., A Hybrid Method for Parameter Tuning of PID Contollers, J.Franklin Inst., 224B(4), T KSunil Kumar' and Jayanta Pal2, Robust Tuning of Power System Stabilizers Using Optimization Techniques, IEEE 2006, pp 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 Astrom K. J. and Hagglund T. H. (1995), New tuning methods for PID controllers, Proceedings of the 3rd European Control Conference 8. John A. Shaw(2003), The PID Control Algorithm: How it works, how to tune it, and how to use it, 2nd Edition, Process Control Solutions 9. 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 IAEME 10. 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 , Published by IAEME 11. 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 , Published by IAEME 12. 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 , Published by IAEME 123