Multi-Area Load Frequency Control Using Ip Controller Tuned By Harmony Search

Transcription

1 Australian Journal of Basic and Applied Sciences, 5(9): -, ISSN ulti-area Load Frequency Control Using Ip Controller uned By Harmony Search Sayed ojtaba Shirvani Boroujeni, Babak Keyvani Boroujeni, ostafa Abdollahi, Hamideh Delafkar Islamic Azad University, Boroujen Branch, Department of Electrical Engineering, Boroujen, Iran. Abstract: In multi area electric power systems if a large load is suddenly connected (or disconnected) to the system, or if a generating unit is suddenly disconnected by the protection equipment, there will be a long-term distortion in the power balance between that delivered by the turbines and that consumed by the loads. his imbalance is initially covered from the kinetic energy of rotating rotors of turbines, generators and motors and, as a result, the frequency in the system will change. herefore he Load Frequency Control (LFC) problem is one of the most important subjects in the electric power system operation and control. In practical systems, the conventional PI type controllers are carried out for LFC. In order to overcome the drawbacks of the conventional PI controllers, numerous techniques have been proposed in literatures. In this paper an IP type controller is considered for LFC problem. he parameters of the proposed IP controller are tuned using Harmony Search (HS) method. A multi area electric power system with a wide range of parametric uncertainties is given to illustrate proposed method. o show effectiveness of the proposed method, a PI type controller optimized by HS is incorporated in order to comparison with the proposed IP controller. he simulation results on a multi area electric power system emphasis on the viability and feasibility of the proposed method in LFC problem. Key words: ulti Area Electric Power System, Load Frequency Control, Harmony Search, IP Controller. INRODUCION For large scale electric power systems with interconnected areas, Load Frequency Control (LFC) is important to keep the system frequency and the inter-area tie power as near to the scheduled values as possible. he input mechanical power to the generators is used to control the frequency of output electrical power and to maintain the power exchange between the areas as scheduled. A well designed and operated power system must cope with changes in the load and with system disturbances, and it should provide acceptable high level of power quality while maintaining both voltage and frequency within tolerable limits. any control strategies for Load Frequency Control in electric power systems have been proposed by researchers over the past decades. his extensive research is due to fact that LFC constitutes an important function of power system operation where the main objective is to regulate the output power of each generator at prescribed levels while keeping the frequency fluctuations within pre-specifies limits. A unified tuning of PID load frequency controller for power systems via internal mode control has been proposed by an (). In this paper the tuning method is based on the two-degree-of-freedom (DF) internal model control (IC) design method and a PID approximation procedure. A new discrete-time sliding mode controller for load-frequency control in areas control of a power system has been presented by (Vrdoljak et al., ). In this paper full-state feedback is applied for LFC not only in control areas with thermal power plants but also in control areas with hydro power plants, in spite of their non minimum phase behaviors. o enable full-state feedback, a state estimation method based on fast sampling of measured output variables has been applied. he applications of artificial neural network, genetic algorithms and optimal control to LFC have been reported by (Kocaarslan et al., 5; Rerkpreedapong et al., and Liu et al., ). An adaptive decentralized load frequency control of multi-area power systems has been presented by (Zribi et al., 5). Also the application of robust control methods for load frequency control problem has been presented by (Shayeghi et al., 7 and aher et al., 8). his paper deals with a design method for LFC in a multi area electric power system using a IP type controller whose parameters are tuned using HS. In order to show effectiveness of the proposed method, this IP controller is compared with a PI type controller whose parameters are tuned using HS too. Simulation results show that the IP controller guarantees robust performance under a wide range of operating conditions and system uncertainties. Apart from this introductory section, this paper is structured as follows. he system under study and system modeling are presented in section. IP type controller is presented in section. he design methodology is developed in section and the simulation results are presented in section 5. Corresponding Author: Syed ojtaba Shirvani Boroujeni, Islamic Azad University, Boroujen Branch, Department of Electrical Engineering, Boroujen, Iran. mo_shirvani@yahoo.com; el: +9888, Fax:

2 Aust. J. Basic & Appl. Sci., 5(9): -, Plant odel: A four-area electric power system is considered as a test system and shown in Figure. he block diagram for each area of interconnected areas is shown in Figure (Wood et al., ). Fig. : Four-area electric power system with interconnections. Fig. : Block diagram for one area of system (i th area). he parameters in Figure are defined as follow: : Deviation from nominal value i =H: Constant of inertia of i th area D i : Damping constant of i th area R i : Gain of speed droop feedback loop of i th area ti : urbine ime constant of i th area Gi : Governor ime constant of i th area G i : Controller of i th area P Di : Load change of i th area u i : Reference load of i th area B i =(/R i )+D i : Frequency bias factor of i th area P tie ij: Inter area tie power interchange from i th area to j th area. Where: i=,,, j=,,, and i j he inter-area tie power interchange is as () (Wood et al., ). Р tie ij=( ω i - ω j ) ( ij /S) Where: ij =77 (/X tie ij) (for a 6 Hz system) X tie ij: impedance of transmission line between i and j areas he P tie ij block diagram is shown as Figure. Figure shows the block diagram of i th area and Figure shows the method of interconnection between i th and j th areas. he state space model of four-area interconnected power system is as () (Wood et al., ). () 5

3 Aust. J. Basic & Appl. Sci., 5(9): -, Fig. : Block diagram of inter area tie power ( P tie ij). X AX BU () Y CX Where: U= [ P D P D P D P D u u u u ] Y= [ ω ω ω ω Р tie, Р tie, Р tie, Р tie, Р tie, Р tie,] X= [ P G P ω P G P ω P G P ω P G P ω Р tie, Р tie, Р tie, Р tie, Р tie, Р tie,] he matrixes A and B in () and the typical values of system parameters for the nominal operating condition are given in appendix. As refereed before, the IP type controller is incorporated to LFC problem. IP type controller is introduced in the next section. IP Controller: As referred before, in this paper IP type controllers are considered for LFC problem. Figure shows the structure of IP controller. It has some clear differences with PI controller. In the case of IP regulator, at the step input, the output of the regulator varies slowly and its magnitude is smaller than the magnitude of PI regulator at the same step input (Seung, ). Also as shown in Figure 5, If the outputs of the both regulators are limited as the same value by physical constraints, then compared to the bandwidth of PI regulator the bandwidth of IP regulator can be extended without the saturation of the regulator output (Seung, ). U i K P U i,ref Fig. : Structure of the IP controller K I s U o Fig. 5: Output of IP and PI regulators with the same damping coefficient ( ) and the same band width at the Same step input signal command. Design ethodology: he proposed IP controller performance is evaluated on the proposed test system given in section. he parameters of the IP controllers are obtained using HS. In the next subsection a brief introduction about HS is presented. Harmony Search Algorithm: Harmony search (HS) algorithm is based on natural musical performance processes that occur when a 6

4 Aust. J. Basic & Appl. Sci., 5(9): -, musician searches for a better state of harmony, such as during jazz improvisation. he engineers seek for a global solution as determined by an objective function, just like the musicians seek to find musically pleasing harmony as determined by an aesthetic (Hong-qi et al., 8). In music improvisation, each player sounds any pitch within the possible range, together making one harmony vector. If all the pitches make a good solution, that experience is stored in each variable s memory, and the possibility to make a good solution is also increased next time. HS algorithm includes a number of optimization operators, such as the harmony memory (H), the harmony memory size (HS, number of solution vectors in harmony memory), the harmony memory considering rate (HCR), and the pitch adjusting rate (PAR). In the HS algorithm, the harmony memory (H) stores the feasible vectors, which are all in the feasible space. he harmony memory size determines how many vectors it stores. A new vector is generated by selecting the components of different vectors randomly in the harmony memory. For example, Consider a jazz trio composed of saxophone, double bass and guitar. here exist certain amount of preferable pitches in each musician s memory: saxophonist, {Do, i, Sol}; double bassist, {Si, Sol, Re}; and guitarist, {La, Fa, Do}. If saxophonist randomly plays {Sol} out of {Do, i, Sol}, double bassist {Si} out of {Si, Sol, Re}, and guitarist {Do} out of {La, Fa, Do}, that harmony (Sol, Si, Do) makes another harmony (musically C-7 chord). And if the new harmony is better than existing worst harmony in the H, the new harmony is included in the H and the worst harmony is excluded from the H. his procedure is repeated until fantastic harmony is found. When a musician improvises one pitch, usually he (or she) follows any one of three rules: () playing any one pitch from his (or her) memory, () playing an adjacent pitch of one pitch from his (or her) memory, and () playing totally random pitch from the possible sound range (Hong-qi et al., 8). Similarly, when each decision variable chooses one value in the HS algorithm, it follows any one of three rules: () choosing any one value from HS memory (defined as memory considerations), () choosing an adjacent value of one value from the HS memory (defined as pitch adjustments), and () choosing totally random value from the possible value range (defined as randomization). he three rules in HS algorithm are effectively directed using two parameters, i.e., harmony memory considering rate (HCR) and pitch adjusting rate (PAR). he steps in the procedure of harmony search are as follows (Verma et al., ): Step. Initialize the problem and algorithm parameters. Step. Initialize the harmony memory (H). Step. Improvise a new harmony from the H. Step. Update the H. Step5. Repeat Steps and until the termination criterion is satisfied. IP Controller uning Using HS: In this section the parameters of the proposed IP controllers are tuned using HS. he IP controller has two parameters denoted by K P and K I and for each area there is one IP controller. herefore in four-area electric power system with four IP controllers, there are 8 parameters for tuning. hese K parameters are obtained based on the HS. In section, the system controllers showed in Figure as G i. Here these controllers are substituted by IP controllers and the optimum values of K P and K I are accurately computed using HS. In optimization methods, the first step is to define a performance index for optimal search. In this study the performance index is considered as (). In fact, the performance index is the Integral of the ime multiplied Absolute value of the Error (IAE). IAE t t t Δω dt t Δω dt t Δω dt t t t Δω dt () he parameter "t" in IAE is the simulation time. It is clear to understand that the controller with lower IAE is better than the other controllers. o compute the optimum parameter values, a % step change in P D is assumed and the performance index is minimized using HS. It should be noted that HS algorithm is run several times and then optimal set of parameters is selected. he optimum values of the parameters K P and K I are obtained using HS and summarized in the able. able : Optimum values of K P and K I for IP controllers First area IP parameters Second area IP parameters hird area IP parameters Fourth area IP parameters.885. K P K I 7

5 Aust. J. Basic & Appl. Sci., 5(9): -, RESULS AND DISCUSSIONS In this section the proposed IP controller is applied to the system for LFC. In order to comparison and show effectiveness of the proposed method, another PI type controller optimized by HS is designed for LFC. he optimum value of the IP controllers Parameters are obtained using genetic algorithms and summarized in the able. able : Optimum values of K P and K I for PI controllers K P K I First area PI parameters Second area PI parameters hird area PI parameters Fourth area PI parameters.6. In order to study and analysis system performance under system uncertainties (controller robustness), three operating conditions are considered as follow: i. Nominal operating condition ii. Heavy operating condition (% changing parameters from their typical values) iii. Very heavy operating condition (% changing parameters from their typical values) In order to demonstrate the robustness performance of the proposed method, he IAE is calculated following step change in the different demands (P D ) at all operating conditions (Nominal, Heavy and Very heavy) and results are shown at ables -. Following step change, the IP controller has better performance than the PI controller at all operating conditions. able : 5% Step increase in demand of st area ( Р D) Nominal operating condition Heavy operating condition Very heavy operating condition IP..8.5 he calculated IAE PI.59.. able : 5% Step increase in demand of st area ( Р D) and % step increase in demand of rd area ( Р D) he calculated IAE IP PI Nominal operating condition.78. Heavy operating condition Very heavy operating condition Figure 6 shows ω at nominal, heavy and very heavy operating conditions following % step change in the demand of first area (P D ). It is seen that the IP controller has better performance than the other method at all operating conditions Speed Deviations (p.u.) ime (sec) (a) 8

6 Aust. J. Basic & Appl. Sci., 5(9): -, Speed Deviations (p.u.) ime (sec).8 (b).6. Speed Deviations (p.u.) ime (sec) (c) Fig. 6: Dynamic response ω following step change in demand of first area ( Р D ) a: Nominal b: Heavy c: Very heavy, Solid (IP controller), Dashed (PI controller). Appendix: he typical values of system parameters for the nominal operating condition: st area parameters =.5 G=.8 =.667 R =. D =.8 B =. =.5 =.5 =. =.55 =.5 =.6 nd area parameters =.5 G=.9 =.55 R =. D =.9 B =. =.5 =.5 =. =.55 =.5 =.6 rd area parameters =. G=.7 =.78 R =.9 D =.7 B =.8 =.5 =.5 =. =.55 =.5 =.6 th area parameters =. G=.85 =.5 R =.995 D =.9 B =.98 =.5 =.5 =. =.55 =.5 =.6 Conclusions: In this paper a new HS based IP controller has been successfully carried out for Load Frequency Control problem. he proposed method was applied to a typical four-area electric power system containing system 9

7 Aust. J. Basic & Appl. Sci., 5(9): -, parametric uncertainties and various loads conditions. Simulation results demonstrated that the IP controllers capable to guarantee the robust stability and robust performance under a wide range of uncertainties and load conditions. Also, the simulation results showed that the IP controller is robust to change in the system parameters and it has better performance than the PI type controller at all operating conditions. Also the matrixes A and B in () are as follow: B G G G G D R D R D R D R A G G G G G G G G REFERENCES Kocaarslan, I., E. Cam, 5. Fuzzy logic controller in interconnected electrical power Systems for loadfrequency control. Electrical Power and Energy Systems, 7: Liu, F., Y.H. Song, J. a, S. ai, Q. Lu,. Optimal load frequency control in restructured power systems. IEE Proceedings Generation, ransmissions and Distribution, 5(): Randy, L.H., E.H. Sue. Practical Genetic Algorithms, Second Edition, John Wiley & Sons, pp: Rerkpreedapong, D., A. Hasanovic, A. Feliachi,. Robust load frequency control using genetic algorithms and linear mmatrix inequalities. IEEE ransactions Power Systems, 8():

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