International Journal of Electrical Power & Energy Systems
Application of evolutionary programming to security constrained economic dispatch
Introduction
Evolutionary programming is a stochastic optimisation strategy, which places emphasis on the behavioural linkage between parents and their offsprings. It is a powerful optimization method, which does not depend on the first- and second-derivatives of the objective function and the constraints of the problem. The most important advantage of EP is that, it uses only the objective function information; independent of the nature of the search space such as smoothness, convexity, etc. the optimisation algorithm based on EP revolves around three steps: natural selection, mutation and competition. Depending on the characteristics of the optimisation problem to be solved, each step could be modified and configured to achieve the optimum result.
Several optimisation techniques such as linear programming (LP) non-linear programming (NLP), quadratic programming (QP) and interior point method (IPM) are employed for solving the security constrained economic dispatch problem [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. Dommel and Tinney [2] presented a penalty function based NLP technique to solve optimal power flow problem. Alsac and Stott [3] extended the penalty function method to preventive control problem, by augmenting all the contingency case constraints to the optimal power flow problem. In this method, the functional inequality constraints are handled as soft constraints using penalty function technique. The drawback of this approach is the difficulty involved in choosing proper penalty weights for different systems and different operating conditions, which if not properly selected, may lead to excessive oscillatory convergence. This combined with prohibitively large computing time, makes this method not suitable for on-line implementation.
EP based algorithms are increasingly applied for solving power system optimisation problems in recent years. In Ref. [13], Lai and Ma have developed an EP based algorithm for reactive power planning. Yang et al. [14] have used the EP based algorithm for solving economic dispatch (ED) problem with non-smooth fuel cost functions. Wong and Yuryevich [15] presented a method to solve the environmentally constrained ED problem by using EP. Jayabarathi et al. [16] have solved the ED problem with units having prohibited operating zones, and multiple fuel options [17] through the application of EP. Attaviriyanupap et al. [18] have developed a hybrid EP and sequential quadratic programming, to solve the ED problem with non-smooth fuel cost function. However, none of these works considered the operating and security constraints, which are important for practical implementation.
This paper presents an efficient and reliable EP based algorithm [19] for solving the SCED problem. The proposed method solves the SCED problem, subject to power balance equality constraints, limits on the active power generations and limits on MW line flow or line phase angle as the inequality constraints pertaining to base case state as well as contingency case states. Two representative systems: 10-bus [10] and adapted IEEE 30-bus [20] systems are taken for investigations. The SCED results obtained using EP are compared, with those obtained using quadratic programming [10] and successive linear programming [20].
Section snippets
SCED problem formulation
The adjustable system quantities such as controllable real and reactive power generations, the switchable shunt capacitors, transformer tap ratios, the phase-shifter ratios, etc. in the base case state may be taken as control variables. The equality constraint set comprises of power flow equations, corresponding to the base case and the postulated contingency cases. The inequality constraints include control constraints, voltage magnitude constraints, and line flow constraints pertaining to the
Proposed approach for solution of SCED through EP
EP starts with an initial population of randomly generated solutions, and evolves toward better solutions over a number of generations or iterations [19]. Being population based model, this method is able to produce a family of good solutions with respect to the objective or fitness function. A new population called offspring population is formed from an existing parent population through a mutation operator. This operator perturbs each individual in the parent population by a random amount to
Sample system studies and results
The algorithm discussed earlier has been tested on 10-bus [10] and adapted IEEE 30-bus [20] systems to assess the performance of the proposed algorithm.
Conclusions
This paper presents an efficient and simple approach for solving the SCED problem. To the best of the author's knowledge, SCED problem has not been solved through EP although ED problem is solved. This paper demonstrates with clarity, chronological development and successful application of EP to the solution of SCED. Two test systems (10-bus [10] and adapted IEEE 30-bus [20]) have been tested and the results are compared with those of quadratic programming technique and successive linear
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