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This paper presents artificial bee colony optimization for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.

Economic dispatch (ED) [1] is one of the important optimization problems in power system operation. ED allocates the load demand among the committed generators most economically while satisfying the physical and operational constraints in a single area. Generally, the generators are divided into several generation areas interconnected by tie-lines. Multi-area economic dispatch (MAED) is an extension of economic dispatch. MAED determines the generation level and interchange power between areas such that total fuel cost in all areas is minimized while satisfying power balance constraints, generating limits constraints and tie-line capacity constraints. The economic dispatch problem is frequently solved without considering transmission constraints. However, some researchers have taken transmission capacity constraints into account. Shoults et al. [2] solved economic dispatch problem considering import and export constraints between areas. This study provides a complete formulation of multi-area generation scheduling, and a framework for multi-area studies. Romano et al. [3] presented the Dantzig–Wolfe decomposition principle to the constrained economic dispatch of multi-area systems. Doty and McEntire [4] solved a multi-area economic dispatch problem by using spatial dynamic programming and the result obtained was a global optimum. An application of linear programming to transmission constrained production cost analysis was proposed in Ref. [5]. Helmick and Shoults [6] solved multi-area economic dispatch with area control error. Ouyang and Shahidehpour [7] proposed heuristic multi-area unit commitment with economic dispatch. Wang and Shahidehpour [8] proposed a decomposition approach for solving multi-area generation scheduling with tie-line constraints using expert systems. Network flow models for solving the multi-area economic dispatch problem with transmission constraints have been proposed by Streiffert [9]. An algorithm for multi-area economic dispatch and calculation of short range margin cost based prices has been presented by Wernerus and Soder [10], where the multi-area economic dispatch problem was solved via Newton–Raphson’s method. Yalcinoz and Short [11] solved multi-area economic dispatch problems by using Hopfield neural network approach. Jayabarathi et al. [12] solved multi-area economic dispatch problems with tie line constraints using evolutionary programming. The direct search method for solving economic dispatch problem considering transmission capacity constraints was presented in Ref. [13]. Manoharan et al. [14] explored the performance of the various evolutionary algorithms on multi-area economic dispatch (MAED) problems.Here, evolutionary algorithms such as the Real-coded Genetic Algorithm (RCGA), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adapted Evolution Strategy (CMAES) are considered. Multi-area economic environmental dispatch (MAEED) problem is proposed in [15]. Here, MAEED problem is handled by an improved multi-objective particle swarm optimization (MOPSO) algorithm for searching out the Pareto-optimal solutions. Sharma et al. [16] have presented a close comparison of classic PSO and DE strategies and their variants for solving the reserve constrained multi-area economic dispatch problem with power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In [17] a discussion of ‘‘Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation” has been presented. Swarm intelligence [18], [19] and [20], a branch of natural inspired algorithms, focuses on the behavior of insect in order to develop some meta-heuristics algorithms. Artificial bee colony optimization (ABCO) algorithm [21] is a new member of swarm intelligence and it mimics the food foraging behavior of honey bees. This algorithm is simple, robust and capable to solve difficult combinatorial optimization problems. In this paper, ABCO has been applied to solve MAED problem. Here, three types of MAED problems have been considered. These are (A) multi area economic dispatch with quadratic cost function, prohibited operating zones and transmission losses (MAEDQCPOZTL), (B) multi area economic dispatch with valve point loading (MAEDVPL), (C) multi area economic dispatch with valve point loading multiple fuel sources and transmission losses (MAEDVPLMFTL). The proposed ABCO approach has been validated by applying it to three different test systems. The performance of the proposed ABCO in terms of solution quality has been compared with differential evolution (DE), evolutionary programming (EP) and real coded genetic algorithm (RCGA).

In this paper, ABCO has been successfully implemented to solve MAED problems. The effectiveness of the proposed method is illustrated by using three different test systems and the test results are compared with the results obtained from DE, EP and RCGA. It is seen from the comparison that the proposed ABCO has the ability to converge to a better quality solution than DE, EP and RCGA.