Aims This paper presents a multiple hybrid methods combining the lambda iteration and simulated annealing methods (MHLSA) to solve an economic dispatch (ED) problem with smooth cost function characteristics. The constraints of the economic dispatch were load demand and transmission loss. Methods The proposed MHLSA algorithm is a hybrid of the lambda iteration and simulated annealing methods and increases efficiency by adding multiple search mechanisms. It is a sequential execution of an individual hybrid algorithm of the lambda iteration and simulated annealing algorithm (HLSA) using only one personal microcomputer. The MHLSA algorithm introduces additional techniques for improvement of the search processes, such as the hybrid method, scope for multiple adaptive searches, and multiple searches. Results To show its effectiveness, the MHLSA is applied to two systems consisting of three and six power generating units. The optimized results from MHLSA are compared with those from HLSA and from conventional approaches, such as bee colony optimization (BCO), hybrid particle swarm optimization (HPSO) and simulated annealing (SA). Results confirm that the proposed MHLSA approach is capable of obtaining the greater speed of convergence and a higher quality solution efficiently. Conclusions Thus, it has great potential to be implemented in different types of power system optimization problem.

This article is focused on hybrid method for solving the non-smooth cost function economic dispatch problem. The techniques were divided into two parts according to: the incremental cost rates are used to find the initial solution and bee colony optimization is used to find the optimal solution. The constraints of economic dispatch are power losses, load demand and practical operation constraints of generators. To verify the performance of the proposed algorithm, it is operated by the simulation on the MATLAB program and tests three case studies; three, six and thirteen generator units which compared to particle swarm optimization, cuckoo search algorithm, bat algorithm, firefly algorithm and bee colony optimization. The results show that the proposed algorithm is able to obtain higher quality solution efficiently than the others methods.

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