Multi-objective GA with fuzzy decision making for security enhancement in power system
Graphical abstract
Highlights
► Power system security enhancement is a major concern in the operation of power system. ► In this paper, the task of security enhancement is formulated as a multi-objective optimization problem. ► Multi-objective genetic algorithm is applied to solve this security optimization problem. ► A fuzzy set theory-based approach is employed to obtain the best compromise solution over the trade-off curve. ► The excellent robustness and efficiency of the proposed method suggests to apply it in real life conditions on very large scale problems.
Introduction
In any power system, unexpected outage of transmission lines occurs due to faults or other disturbances. These events referred to as contingencies, may cause significant overloading of transmission lines, which in turn may lead to total or partial system blackout. Security constrained optimal power flow (SCOPF) is the main tool used in the energy control centers to avoid limit violation in the contingency state. SCOPF [1] adjusts base case decision variables to minimize the defined objective function subject to base case and contingency state operating constraints. The solution of an SCOPF is useful for both system operation and planning.
The SCOPF does not take advantage of the post-contingency corrective rescheduling that is possible in static security enhancement. In [2], a mathematical framework was proposed for the solution of the SCOPF problem taking into account the system corrective capabilities such as generation rescheduling after the outage has occurred. The resulting dispatch has the same security level as the SCOPF, but with lower operating costs. An iterative approach is proposed in [6] to solve the SCOPF with corrective action.
Apart from generation re-scheduling, FACTS devices [3], [4] based on power electronics technology can also be used for power flow control through transmission lines. Thyristor Controlled Series Capacitors (TCSC), one of the FACTS devices can be used effectively in alleviating the line overload in case of a contingency. In this work, the base case generator active power, generator bus voltages and contingency state TCSC reactance values are used as the decision variables for security enhancement. For a large-scale power system, more than one FACTS device may have to be installed to achieve the desired performance. Studies have been conducted to identify the suitable location for FACTS devices to improve power system security. In this work, the location of TCSC is identified based on line overload severity index computed for every line in the system. While using FACTS devices for the performance improvement of power system, the installation cost need to be taken into account which is not done in the above papers. In this work, the installation cost of TCSC is taken as the additional objective of the OPF problem.
In the literature, the SCOPF with corrective action is treated as a single-objective optimization problem [5], [6]. In this paper, the SCOPF with corrective action is treated as a true multi-objective optimization problem with minimization of fuel cost and the installation cost of TCSC as the objectives. Because of the presence of conflicting multiple objectives, a multi-objective optimization problem results in a number of optimal solutions, known as pareto optimal solutions [7], [8]. In a multi-objective optimization, effort must be made in finding the set of trade-off optimal solutions by considering all objectives to be important.
One, straightforward approach to solve the multi-objective optimization problem is to convert them into a single objective problem by linear combination of different objectives as a weighted sum and then solve it similar to single objective optimization problems [9]. The important aspect of this weighted sum method is that a set of non-inferior (or pareto optimal) solutions can be obtained by varying the weights. Unfortunately, this requires multiple run as many times as the number of desired pareto optimal solutions. Furthermore, this method cannot be used to find pareto optimal solutions in problems having a non-convex pareto optimal front. To avoid this difficulty, the -constraint method [10] is used for multi-objective optimization problem. This method is based on optimizing the most preferred objective and considering the other objectives as constraints bounded by some allowable levels. These levels are then altered to generate the entire pareto optimal set. This approach is time-consuming and tends to find weak pareto optimal solutions. The ability of Evolutionary Computation techniques like Genetic Algorithm to find multiple optimal solutions in one single simulation run makes them unique in solving multi-objective optimization problems [7]. In this work, the multi-objective security optimization problem is solved using multi-objective genetic algorithm (MOGA) [11].
Like the other approaches such as NSGA II, SPEA2, IBEA and DEMO, MOGA is also a population-based search algorithm. Each algorithm differs in the way fitness value is assigned to the individuals while solving the multi-objective optimization problem. The environmental selection in NSGA-II [12] first ranks the individuals using non-dominated sorting. To distinguish between individuals with the same rank, the crowding distance metric is used, which prefers individuals from less crowded regions of the objective space. SPEA2 [13] works similarly, calculating the raw fitness of the individuals according to Pareto dominance relations between them and using a density measure to break the ties. The individuals that reside close together in the objective space are discouraged from entering the archive of best solutions. IBEA [14], on the other hand, uses a different approach. The fitness of individuals is determined only according to the value of a predefined indicator. This indicator has to be dominance preserving and no other explicit diversity preserving mechanism (such as crowding in NSGA-II or density in SPEA2) is applied. In DEMO (Differential Evolution for Multi-objective Optimization) [15], the fitness of an individual is first calculated using Pareto-based ranking and then reduced with respect to the individual's crowding distance value. This single fitness value is then used to select the best individuals for the new population.
Generally, binary strings are used to represent the decision variables of the optimization problem in the genetic population irrespective of the nature of the decision variables. This binary-coded GA has Hamming cliff problems [17] which sometimes may cause difficulties in the case of coding continuous variables. Also, for discrete variables with total number of permissible choices not equal to 2k (where k is an integer) it becomes difficult to use a fixed length binary coding to represent all permissible values. To overcome these difficulties, in this paper, the optimization variables namely, generator active power generation Pgi, generator bus voltages Vgi and TCSC settings are represented as floating point numbers in the genetic population. For effective genetic operation, crossover and mutation operators which can directly operate on floating point numbers [24] are used. The effectiveness and potential of the proposed approach to solve the multi-objective optimal power flow (OPF) problem has been demonstrated using IEEE 30-bus and IEEE 118-bus systems. Lesser computational time taken by the MOGA to reach the optimal solutions makes it suitable for solving the large scale optimization problem like SCOPF.
Section snippets
Modelling and placement of Thyristor Controlled Series Capacitors (TCSC)
Thyristor Controlled Series Capacitors (TCSC) consist of a fixed capacitor in parallel with a thyristor controlled reactor. The primary function of the TCSC is to provide variable series compensation to a transmission line. This changes the line flow due to change in series reactance. Fig. 1 shows a model of transmission line with TCSC connected between buses ‘i’ and ‘j’.
For steady state analysis, the TCSC can be considered as a static reactance −jxc. The controllable reactance xc is directly
Problem formulation
In general, the optimal power flow (OPF) problem is formulated as an optimization problem in which one or more objective functions are minimized while satisfying a number of equality and inequality constraints. In the security enhancement problem considered here the goal is to determine the optimal values of generator active power, generator bus voltage magnitudes and TCSC that enhance the systems security level while minimizing the generator fuel cost and investment cost of TCSC. Minimization
Multi-objective genetic algorithm
Genetic algorithms (GA) [22] are generalized search algorithms based on the mechanics of natural genetics. GA maintains a population of individuals that represent the candidate solutions to the given problem. Each individual in the population is evaluated to give some measure of its fitness to the problem from the objective function. GAs combine solution evaluation with stochastic genetic operators namely, selection, crossover and mutation to obtain near optimality. Being a population-based
Best compromise solution
Upon having the pareto optimal set of non-dominated solution, it is preferred to get the best compromise solution for implementation. The Many-objective Distinct Candidates Optimization using Differential Evolution (MODCODE) algorithm [16] discovered a low number of solutions within a region of interest on the true pareto front. It aims at returning a few optimal distinct solutions within a region of interest, with both result set cardinality and distinctiveness being user defined in compliance
Genetic algorithm implementation
While applying GA for solving the SCOPF problem, the following issues need to be addressed:
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solution representation and
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fitness evaluation.
Simulation results
The proposed multi-objective genetic algorithm approach has been applied to solve the security enhancement problem in IEEE-30 bus and IEEE 118-bus test systems. The IEEE 30-bus system has 6 generator buses, 24 load buses and 41 transmission lines, of which 4 branches (6–9), (6–10), (4–12) and (28–27) are with tap setting transformers. The generator and transmission-line data relevant to the system are taken from [1]. The upper and lower voltage limits at all the bus bars except slack bus are
Conclusion
In this paper, the security enhancement task has been formulated as a multi-objective optimization problem and multi-objective genetic algorithm was applied to solve the same. The location of TCSC was identified based on Line Overload Sensitivity Index. It has considered as optimization criteria, the minimization of fuel cost and installation cost of TCSC. The algorithm has been tested on the standard IEEE 30-bus and IEEE 118-bus test systems. The proposed multi-objective GA has performed well
Dr. R. Narmatha Banu is an associate professor in Department of Electrical and Electronics Engineering, Kalasalingam University, Tamil Nadu, South India. She completed her B.E. (EEE) degree in Mohammed Sathak Engineering College, Kilakarai, Tamil Nadu, India in the year 1999 and M.E. (Power System Engg) degree in Annamalai University, Chidambaram, Tamil Nadu in the year 2002. She pursued Ph.D. in the Department of Electrical Engineering, Anna University, Chennai in the year 2010. Her area of
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Dr. R. Narmatha Banu is an associate professor in Department of Electrical and Electronics Engineering, Kalasalingam University, Tamil Nadu, South India. She completed her B.E. (EEE) degree in Mohammed Sathak Engineering College, Kilakarai, Tamil Nadu, India in the year 1999 and M.E. (Power System Engg) degree in Annamalai University, Chidambaram, Tamil Nadu in the year 2002. She pursued Ph.D. in the Department of Electrical Engineering, Anna University, Chennai in the year 2010. Her area of interest is Power system Security, Genetic Algorithm and FACTS devices. She has got the Young Scientist Award for the year 2009 from Tamil Nadu State Council for Science and Technology (established by Government of Tamil Nadu).
Dr. D. Devaraj is a graduate from Thiagarajar College of Engineering in Electrical and Electronics Engineering (1992). He did his Masters in Power System Engineering from Madurai Kamaraj University, Madurai (1994). He obtained his Ph.D. from the Indian Institute of Technology, Chennai (2000) with specialization in power systems engineering. His research interests include power system engineering, power system automation, power system simulation, computational intelligent techniques, intelligent control techniques. He is currently working as a senior professor and Dean (research and development) in the Kalasalingam University, Krishnankoil, Tamil Nadu.