OPTIMIZATION OF POWER SYSTEMS USING REAL CODED GENETIC ALGORITHMS
Kusum Deep, Nader Nassif Barsoum, Sermsak Uatrongjit, Pandian Vasant · AIP conference proceedings · 2008
This talk highlights the recently proposed Real Coded Crossover Operator, called the Laplace Crossover (LX) of [1] and Real Coded Mutation Operator called Power Mutation (PM) of [2], wherein The performance of LX and PM is compared with Heuristic Crossover (HX) and Non‐Uniform Mutation (NUM) and Makinen, Periaux and Toivanen Mutation (MPTM). The test bed is a set of 20 test problems available in global optimization literature. Various performance criterion like computational cost, success rate, solution quality, efficiency and reliability are reported using two kinds of analysis. The results show that LX‐PM outperforms all other GAs considered. In this paper, the above algorithms are extended for obtaining global optimal solution of constrained optimization problems. Constraints are handled using the parameter less approach proposed by Deb and the six RCGAs described above are modified accordingly. Comparison is shown with other existing RCGAs using Simulated Binary Crossover (SBX) and Polynomial Mutation (POL) of [3], [4]. Inclusion of two operators, SBX and POL, gives rise to two more combinations namely, LX with POL and SBX with PM. Two new RCGAs namely, LX‐POL and SBX‐PM are proposed by taking these two operators into account. Thus, in all, nine RCGAs are used for comparative study, namely: LX‐POL, LX‐PM, LX‐MPTM, LX‐NUM, HX‐PM, HX‐MPTM, HX‐NUM, SBX‐POL and SBX‐PM. A set of 25 benchmark test problems are chosen, consisting of linear/nonlinear objective function and equality/inequality constraint. Comparison is made with respect to percentage of success, the average number of function evaluations and execution of successful runs. It is observed that the overall success rate of LX‐POL is better than all other RCGAs. Based on extensive analysis, it is concluded that LX‐POL clearly outperform other RCGAs considered in this study. The problem of optimization of Directional Over current Relay is modeled as a nonlinear constrained optimization problem. It is required to compute the values of the decision variables called “Relays,” which control the act of isolation of faulty lines from the system without disturbing the healthy lines. The objective function to be minimized is the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones. The constraints are bounds on all decision variables, complexly interrelated times of the various relays (called selectivity constraints) and restrictions on each term of the objective function to be between certain specified limits. The IEEE 3‐bus, 4‐bus, 6‐bus, 14‐bus and 30‐bus systems are considered. The complexity of the problem increases as the number of line increases. Larger systems have more decision variables and constraints. All the cases of this constrained optimization problem are solved by all the RCGAs mentioned above, namely LX‐PM, LXMPTM, LX‐NUM, LX‐POL, HX‐MPTM, HX‐NUM, HX‐MPTM, SBX‐POL, SBX‐NUM. The results are compared amongst themselves as well as with the previously quoted results using Random Search Technique of [5] as described in [6]. It is concluded that all the methods of LX family are able to give satisfactory results for each of the cases. However, LX‐POL outperforms all other methods for each of the cases.