Application of non-dominated sorting genetic algorithm-II technique for optimal FACTS-based controller design
Introduction
Real-world problems often have multiple conflicting objectives competing with each other. For example, while designing a control system, we would usually like to have a high-performance controller, but we also want to achieve desired performance with little control efforts (cost). In these types of multi-objective problems generally there is no single solution that is the best when measured on all objectives and so several trade-off solutions (called the Pareto optimal set) are usually preferred [1]. Control systems optimization problems involving the optimization of multiple objective functions require high computational time and effort [2], [3]. As conventional techniques are difficult to apply, modern heuristic methods are preferred to obtain Pareto optimal set [4].
The Non-dominated sorting genetic algorithm (NSGA) proposed by Srinivas and Deb [5] has been widely used successfully applied to solving many multi-objective problems. However, the main demerit of this approach has been its high computational complexity of non-dominated sorting, lack of elitism, and need for specifying a tunable parameter called sharing parameter. To address all the above issues Deb et al. [6] proposed an improved version of NSGA, called NSGA-II that has a better sorting algorithm, incorporates elitism and no sharing parameter needs to be chosen a priori.
Recent development of power electronics introduces the use of flexible ac transmission systems (FACTS) controllers in power systems. Subsequently, within the FACTS initiative, it has been demonstrated that variable series compensation is highly effective in both controlling power flow in the lines and in improving stability. Thyristor controlled series compensator (TCSC) is one of the important members of FACTS family that is increasingly applied with long transmission lines by the utilities in modern power systems. It can have various roles in the operation and control of power systems, such as scheduling power flow; decreasing unsymmetrical components; reducing net loss; providing voltage support; limiting short-circuit currents; mitigating subsynchronous resonance; damping the power oscillation and enhancing transient stability [7], [8], [9]. Most of the available technical literature in TCSC based controller design usually deals with either local signals [10] or remote signals [11]. In some papers, comparison has been made between two or more local signals [12] or remote signals [13] for FACTS based controller input signal.
In this paper, NSGA-II technique is applied to obtain Pareto optimal set pertaining to the design a TCSC-based controller. The design objective is to get maximum damping (performance) with minimum control effort (cost). Further a fuzzy based membership function value assignment method is employed to choose the best compromise solution from the obtained Pareto set. The detailed analysis on the selection of control signals; both local (active power) and remote (speed deviation) signals on the effectiveness of the proposed controller is carried. Simulation results are presented under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach.
Section snippets
Modeling the power system under study
The SMIB power system with TCSC shown in Fig. 1 is considered in this study. The synchronous generator is represented by model 1.1, i.e. with field circuit and one equivalent damper on q-axis. The generator has a local load of admittance Y=G+jB and a double circuit transmission line of total impedance Z=R+jX. In the figure VT and VB are the generator terminal and infinite bus voltage, respectively, and XT is the reactance of the transformer. The system data and the initial operating conditions
Problem formulation
In case of lead-lag structured controller, the washout time constants TWT and the sensor time constants are usually prespecified [14], [15]. In the present study, TWT=10 s and TSN=10 ms are used. The controller gain KT and the time constants T1T, T2T, T3T and T4T are to be determined. During steady state conditions Δσ and σ0 are constant. During dynamic conditions, conduction angle (σ) and hence XTCSC(α) is modulated to improve power system stability. The desired value of compensation is obtained
Non-dominated shorting genetic algorithm-II
A multi-objective optimization problem differs from a single-objective optimization problem because it contains several objectives that require optimization. In case of single objective optimization problems, the best single design solution is the goal. But for multi-objective problems, with several and possibly conflicting objectives, there is usually no single optimal solution. Therefore, the decision maker is required to select a solution from a finite set by making compromises. A suitable
Application of NSGA-II
In the present study, after initializing the population the individuals in the populations are sorted based on non-domination into each front. The first front being completely non-dominant set in the current population and the second front being dominated by the individuals in the first front only and the front goes so on. Each individual in the each front are assigned rank (fitness) values or based on front in which they belong to. Individuals in first front are given a fitness value of 1 and
Conclusion
An optimal TCSC-based controller design using the multi-objective optimization method is presented in this paper. The design objective is to get maximum performance of controller with minimum control effort. In this context, NSGA-II technique is applied to obtain Pareto optimal set for the given multi-objective optimization problem. Further a fuzzy based membership function value assignment method is employed to choose the best compromise solution from the obtained Pareto optimal set. A
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