Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers Science and Technology, 7 (2002) 81-90 © 2002 Sultan Qaboos University Comparative Study of Load Frequency Controller Designs for Interconnected Power Systems M. Albadi*, A. Awladthani**, B. Alomeiri*** and K. Ellithy* *Department of Electrical Engineering, College of Engineering, Sultan Qaboos University, P.O. Box 33, Al Khod 123, Muscat, Sultanate of Oman. Email: mbadi@squ.edu.om** Oman Liquefied Natural Gas, Sur, Sultanate of Oman, Email: ahmedawladthani@omanlng.co.om, ***Ministry of Electricity and Water, Muscat, Sultanate of Oman, Email: so10456@hotmail.com. دراسة مقارنة لطرق تصميم نظم التحكم في تردد التيار الكهربائي نتيجة تغير األحمال في نظم القوى الكهربائية المرتبطة لليثي محمد البادي ، أحمد أوالد ثاني ، بدر العميري ، و خالد ا تـناقش هذه الورقة ثالث طرق لتصميم نظم التحكم في تردد التيار الكهربائي والطاقة المنقولة بين الشبكات في نظم :خالصـة أما التصميم الثاني فهو يعتمد على طريقة تحديد . يسمى التصميم األول بالتحكم التفاضلي الكالسيكي . القـوى الكهربائية المرتبطة تهدف جميع هذه .)Optimal Control( أما التصميم الثالث فيدعى نظام التحكم الكهربائي األفضل . مأقطـاب مصـفوفة الـنظ تحت تأثير تغير مفاجىء في الحمل الكهربائي أو ) التردد والطاقة المنقولة ( التصـميمات الى تحسين استجابة الشبكات المرتبطة فعالية التصميمات ) MATLAB( نتائج المستخرجة من برنامج المحاكاة وقد أظهرت ال . انفصال احدى وحدات التوليد عن الشبكة و نظام ) Optimal Control( التحكم الكهربائي األفضل كما أظهرت النتائج أيضا ان استخدام تصميم يجمع بين نظام . الـثالثة .التحكم التفاضلي الكالسيكي يعطي أفضل النتائج ABSTRACT: This paper presents a comparative study of three different load frequency (LF) controller designs for interconnected power systems. They are the conventional integral controller, a controller based on the pole-placement technique, and a controller based on optimal control law. Each controller has been designed to improve the dynamic response of system frequency and tie line power flow under a sudden load change. The results obtained using a MATALB computer program show the effectiveness of the LF controller designs. The results also show that the combined optimal controller with conventional integral controller can provide good damping to the system and reduce the overshoot. KEYWORDS: Load Frequency Control, Integral Control, Pole Placement, Optimal Control, Decentralized Control. 1. Introduction L arge-scale power systems are normally composed of control areas or regions representing coherent groups of generators. The various areas are interconnected through tie lines. The tie lines are utilized for energy exchange between areas and provide inter-area support in case of abnormal condition (Fosha and Elgerd, 1999; Wood, 1996). Area load-changes and abnormal conditions, such as outages of generation, leads to mismatch in scheduled power interchanges between areas. These mismatches have to be corrected via supplementary control. In recent years, usually large tie-line power fluctuations have been observed as a result of increased system capacity and very close interconnection among power systems. This observation suggests a strong need for establishing a more advanced Load Frequency Control (LFC) scheme. 81 mailto:mbadi@squ.edu.om mailto:ahmedawladthani@omanlng.co.om ALBADI, AWLADTHAN, ALOMEIRI and ELLITHY LFC of interconnected systems is defined as the regulation of power output of generators within a prescribed area, in response to change in system frequency, tie-line loading so as to maintain scheduled system frequency and/or established interchange with other areas within predetermined limits (Fosha and Elgerd, 1999; Wood, 1996). In general, LFC is a very important item in power system operation and control for supplying sufficient and reliable electric power with good quality. The basic load frequency control (LFC) loop is shown in Figure 1. It is known that changes in real power affect mainly the system frequency and thus the rotor angle. The input mechanical power to generators is used to control the frequency of the output electrical power. The change in tie line real power (∆Ptie) and the change in frequency (∆f) are sensed and transformed into a real power command signal ∆Pv which is sent to the prime mover to call for the increment in the input torque or input mechanical power to the generator. Therefore, the prime mover makes change in the generator output by an amount of ∆Pg, which will changes the values of ∆f and ∆Ptie within a specified tolerance. A simple control strategy for any LF controller design is to keep the frequency approximately at the nominal value i.e. 50 Hz, to maintain the tie-line flow at about the schedule and each area should absorb its own load changes to minimize the cost. C∆Ρ G V∆Ρ GG Q∆∆Ρ , Frequency sensor Load frequency control (LFC) ∆PtieValve control mechanism Turbine Steam Many inves reported and a n order to achieve comparative of effectiveness of MATALB comp 2. System Mo The single l block diagram r assumed to have system as shown The state v will be used to d invariant is given Figure 1. Schematic diagram of LFC and AVR of a generator. tigations in the area of LFC problem of interconnected power systems have been umber of control strategies have been employed in the design of LF controller in better performance (Talaq and Albassi, 1999; Yang et al., 1998; Hiyana, 1982). A three different controller designs for LFC is presented in this paper. The each controller on the system dynamic performance is investigated using uter software. delling ine diagram the two interconnected systems (two-area) is shown in Figure 2. The epresenting the interconnection of two areas is shown in Figure 3. Each area is only one equivalent generator. The generator is equipped with governor- turbine in Figure 3. ariable (state-space) (Fosha and Elgerd, 1999; Yang et al., 1998; Fellach, 1987) esign the LF controller. The standard form of state-space equations of a linear time by the equations 82 COMPARATIVE STUDY OF LOAD FREQUENCY CONTROLLER DESIGNS Area 1 Area 2 Tie-line Figure 2. Single-line diagram of two-area. LPuBxAx Γ∆+∆+∆=∆ • (1) uDxCy ∆+∆=∆ (2) Where:                                           − −− − − − −− −− − −− = 0000000 11 0 1 00000 0 11 000000 00 2 1 22 1 0000 0000000 0000000 00000 11 0 1 000000 11 0 0000 2 1 00 2 1 2 222 2222 22 22 2 2 1212 111 1111 11 111 1 BKK R HH D H TT KBK R HHH D A ggg TT ggg TT τττ ττ τττ ττ [ ]Tvmcvmc PPPfPPPPfx 2222121111 ∆∆∆∆∆∆∆∆∆=∆ T G GB             = 0 1 0000000 000000 1 00 2 1 τ τ u =[u1 u2]T is the input vector The disturbance matrix Γ equals to 83 ALBADI, AWLADTHAN, ALOMEIRI and ELLITHY T H H             − − =Γ 000 2 1 00000 00000000 2 1 2 1 The disturbance to the system is [ ]21 LLL PPP ∆∆=∆ 11 1 gsτ+ 11 1 Tsτ+ 112 1 DsH +Σ ∆_ PL1 ∆Pm1∆PV1 ∆f1 Σ 1 1 R Generator & loadTurbineGovernor ∆ u1 + + _ _ Σ 21 1 gsτ+ 21 1 Tsτ+ 222 1 DsH +Σ ∆PL2 ∆Pm2∆PV2 ∆f2 2 1 R ∆ u2 + + -Σ _ + ∆P12 + _ B1 Σ + + s K1− B2 Σ _ s K1− + _ ACE1 ACE2 s T12 Figure 3. Block diagram of load frequency control (LFC) of two-area. 3. Design of LF Controller 3.1 Conventional Integral Controller Design Conventional LF controller is based upon tie-line bias control, where each area tends to reduce the Area Control Error (ACE) to zero. The block diagram of two-area power system including area control error is shown in Figure 3. The control error for each area consists of a linear combination of frequency and tie-line power deviation (Saadat, 1999). (∑ = ∆+∆= n j iiji PACE 1 ωγ ) (3) 84 COMPARATIVE STUDY OF LOAD FREQUENCY CONTROLLER DESIGNS An overall satisfactory performance is achieved when γi is selected to be equal to the frequency bias factor of that area. So i i ii DR B +== 1 γ . Thus, the ACEs for a two-area are 22212 11121 ω ω ∆+∆= ∆+∆= BPACE BPACE (4) To get the simulation results, use the prameters given in Table 1. Table 1: The prameters of two area systems. Area 1 2 Speed regulation –R R1=0.05 R2=0.0625 Frequency sensitive load coefficient –D D1=0.6 D2=0.9 Inertia constant –H H1=5 H2=4 Governor time constant - Gτ 1Gτ =0.2 s 2Gτ =0.3 s Turbine time constant - Tτ 1Tτ =0.5 s 2Tτ =0.6 s Synchronizing coefficient –T12 T12=2 pu Load disturbance - LP∆ 1LP∆ =0.1875 pu 2LP∆ =0 The system response having the integral controller is shown in Figures 5-7. The integral controller satisfies the desired objectives of the LFC. The only problem of this type of controller is that the system response is less damped and the overshot is large. To solve this problem, another control signals (∆u1,∆u2) are added to the system in presence of integral controller. These signals are derived from the controller designed based on pole-placement technique or based on the optimal control theory. Both controllers uses the same control law XKu ∆−= (5) where K =[k1 k2 …….. kn] is the controller gain vector. 3.2 Design Based on Pole-Placement technique Pole placement technique (Phillips and Harbor, 1998) depends on shifting the poles of the open-loop system (system without controller) to desired locations on the left-half of the complex plane.The characteristic equation of the closed-loop system (system with controller) is given by SI-A+BK=0 (6) Suppose that the design specifications require that the poles of the equation (6) at -λ1, -λ2, ….., -λn. The desired characteristic equation for the system is Sn + αn-1Sn-1 +……..+ α1S + α0 = (S+λ1)(S+λ2)……(S+λn)=0 (7) The pole-placement design procedure results in a gain vector K such that equation (6) is equal to equation (7), that is SI-A+BK= Sn+αn-1Sn-1+…...+α1S+α0 (8) 85 ALBADI, AWLADTHAN, ALOMEIRI and ELLITHY In equation (8) there are n unknowns (k1 k2 …….. kn). Equating coefficients in equation (8) yields n equations in the n unknowns. A program using MATLAB is developed to design the LF controller based on pole-placement technique. Ackerman formula (Phillips and Harbor et al., 1998) is used in the program to calculate the gain vector K to satisfy equation (8). Table 2 shows the poles of the system having integral controller and the desired ones, which will be achieved by the pole-placement technique. Table 3 shows the damping ratio of the complex poles. From Table 3, it can be observed that the damping ratio of the closed-loop system (with the pole-placement controller) is increased. The effect of the damping ratio improvement can be seen from the system dynamic response shown in Figures 5-7. It can also be seen from Figures 5-7 that the overshoot of the frequency deviations and tie-line power flow deviation is decreased. 3.3 Optimal Controller Design Many approaches have been proposed for LF controller design. The most promising approach is the application of linear optimal control (Fosha and Elgerd, 1999; Yang et al., 1998; Fellach, 1987). The linear optimal control has excellent characteristics in that it is able to control a system with small transients and relatively short settling time. The optimal controller is design to minimize the quadratic performance index of the following form ∫ ∞ += 0 )( dtuRuxQxJ TT ∆∆∆∆ (9) Subject to the dynamic system equation in (9), Q is a positive semi-definite matrix and R is a positive definite matrix. The optimal gain vector is given by PBRK T1−= (10) Where P is determined by solving the following Riccati equation (Nobele and Daniel et al., 1988). 01 =+−+ − QPBPBRPAPA TT (11) Table 2: Poles of the system having integral controller and the desired ones. The poles The system with integral controller only The system with integral controller and Pole-Placement Controller λ1 -5.8468 -5.8178 λ2 -4.2717 -4.1669 λ3,4 -0.3768 ± j1.7234 -1.2480 ± j2.8824 λ5,6 -0.2231 ± j1.5992 -0.8596 ± j2.1385 λ7,8 -0.2537 ± j0.0484 -2.9886 , -0.2155 λ9 -0.3468 -1.7282 Table 3: Damping ratio of the complex poles. The system Poles Damping ratio (ζ) -0.3768 ± j1.7234 0.2136 -0.2231 ± j1.5992 0.1382 With integral controller only -0.2537 ± j0.0484 0.9823 -1.2480 ± j2.8824 0.3937 With integral controller and the pole-placement -0.8596 ± j2.1385 0.3730 86 COMPARATIVE STUDY OF LOAD FREQUENCY CONTROLLER DESIGNS In an interconnected power system, each area takes charge of the LFC functions that is, it is operating its own LFC without any commitment from other systems except the case of determining the amount of power exchange. Table 4 listed the gains of the centralized optimal LF controller. It is impractical to adopt a centralized LFC for interconnected systems. Therefore, it is useful to apply the decentralized LFC (Fosha and Elgerd, 1999; Yang et al., 1998) in which each system in the interconnected system makes use of locally available information to compute the control signal ∆u. Table 4: Gains of centralized optimal LF controller. State variable X Gain vector K of Area 1 (∆u1= Kx) Gain vector K of Area 2 (∆u2= Kx) ∆f1 86.8 -32.16 ∆Pm1 2.53 -0.79 ∆Pv1 0.72 -0.196 ∆Pc1 -20 7.73 ∆P12 1.68 -0.69 ∆f2 -41.35 71.1 ∆Pm2 -1.27 3.06 ∆Pv2 -0.29 0.99 ∆Pc2 12.12 -17.8 Figure 4. System dynamic response with centralized / decentralized optimal controller. 87 ALBADI, AWLADTHAN, ALOMEIRI and ELLITHY Table 5: Gains of decentralized optimal LF controller. State variable X Gain vector K of Area 1 (∆u1= Kx) Gain vector K of Area 2 (∆u2= Kx) ∆f1 86.8 0 ∆Pm1 2.53 0 ∆Pv1 0.72 0 ∆Pc1 -20 0 ∆P12 1.68 -0.69 ∆f2 0 71.1 ∆Pm2 0 3.06 ∆Pv2 0 0.99 ∆Pc2 0 -17.8 It has been found that the decentralized optimal controller gives very close results to the Centralized optimal controller. This can be shown in Figure 4. The effect of the optimal LF controller on the system performance can be seen from Figures 5-7. The overshoot of the frequency and tie line power flow deviations is decreased and the system response is well damped. Computer simulations for different sudden load change in area 1 and area 2 are reported in (Al-Badi et al., 2000). Figure 5. Area 1 dynamic response under a sudden load change in area 1. 88 COMPARATIVE STUDY OF LOAD FREQUENCY CONTROLLER DESIGNS Figure 6. Area 2 dynamic response under a sudden load change in area 1. Figure 7. Tie-line dynamic response after a sudden load change in area 1. 89 ALBADI, AWLADTHAN, ALOMEIRI and ELLITHY 4. Conclusions A load frequency controller has been designed to improve the dynamic performance of interconnected power systems. The conventional integral controller, the controller based-pole placement technique and the controller based-optimal control law were considered and a comparative study between these controllers has been investigated. The results of computer simulation show that the integral controller restores the original value of the frequency and the tie-line power deviations. Adding a signal derived from the optimal controller or derived from the pole-placement controller enhance the system damping and reduce the overshoot. The simulation results also show that the combined integral controller with optimal controller is more effective means for improving the dynamic performance of the system than the other controllers. The of optimal LF controller type is relatively simple and suitable for practical implementation for on-line implementation. 5. Acknowledgments The authors would like to thank Electrical Engineering Department at Sultan Qaboos University for their support. References AL-BADI, M., AWLADTHANI, A., ALOMEIRI, B. 2000. Load Frequency Control of Interconnected Power Systems. undergraduate final year project, SQU, Muscat. FELIACH, A. 1987. Optimal Decentralized Load Frequency Control. IEEE Trans. on Power Systems, 2: 379-386 FOSHA, C.E. and ELGERD, O.I. 1999. The megawatt-frequency control problem: a new approach via optimal control theory. IEEE Trans. on Power Systems, 4: 563-577. HIYANA, T. 1982. Design of Decentralized Load Frequency Regulators for Interconnected Power Systems. IEE Proceeding, PAS.129: 17-23 NOBELE, B. and DANIEL, J. 1988. Applied Linear Algebra. Third Edition. Printice Hall. OHNO, H., 1996. Basic study to improve performance of automatic generation control. Proceeding of 12th Power Systems Computation Conference: 1157-1162 PHILLIPS and HARBOR , 1996. Feedback Control Systems, Third Edition, Prentice Hall. SAADAT, H., 1999. Power System Analysis, McGraw-Hill. TALAQ, J. and F. ALBASRI. 1999. Adaptive Fuzzy Gain Scheduling for Load Frequency Control. IEEE Trans. on Power Systems,14: 145-151 WOOD, A. 1996. Power Generation, Operation and Control. Prentice-Hall. New York. YANG, T., CIMEN, H. AND O. ZHU. 1998. Decentralized Load-Frequency Controller Design Based On Structured Singular Values. IEE Proceeding on Gener. Transm. Distrib, 145: 7-13 Received 21 June 2001 Accepted 11 November 2001 90 M. Albadi*, A. Awladthani**, B. Alomeiri*** and K. Ellithy* In recent years, usually large tie-line power fluctuations have been observed as a result of increased system capacity and very close interconnection among power systems. This observation suggests a strong need for establishing a more advanced Load Frequ The basic load frequency control (LFC) loop is shown in Figure 1. It is known that changes in real power affect mainly the system frequency and thus the rotor angle. The input mechanical power to generators is used to control the frequency of the outpu Table 1: The prameters of two area systems. Area 1 2 Speed regulation –R R˜1=0.05 R˜2=0.0625 Frequency sensitive load coefficient –D D˜1=0.6 D˜2=0.9 Inertia constant –H H˜1=5 H˜2=4 Governor time constant - =0.2 s =0.3 s Turbine time constant - =0.5 s =0.6 s Synchronizing coefficient –T12 T12=2 pu Load disturbance - =0.1875 pu =0 Table 2: Poles of the system having integral controller and the desired ones. Figure 4. System dynamic response with centralized / decentralized optimal controller. Figure 5. Area 1 dynamic response under a sudden load change in area 1. Figure 6. Area 2 dynamic response under a sudden load change in area 1. Figure 7. Tie-line dynamic response after a sudden load change in area 1. Acknowledgments References