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.

This study introduces an Enhanced Local Search (ELS) technique integrated into the Bee Colony Optimization (BCO) algorithm to address the Economic Dispatch (ED) problem characterized by a continuous cost function. This paper combines Lambda Iteration and Golden Section Search with Bee Colony Optimization (BCO) into a more efficient method called Enhanced Local Search for Bee Colony Optimization (ELS-BCO). The proposed methodology seeks to enhance search efficiency and solution quality. One of the main challenges with standard BCO is random initialization, which can lead to slow convergence. The ELS-BCO algorithm overcomes this issue by using Lambda Iteration for better initial estimation and Golden Section Search to refine the movement direction of the bees. These enhancements significantly improve the algorithm’s capacity to identify optimal solutions. The performance of ELS-BCO was evaluated on two benchmark systems with three and six power generators, and the results were compared with those of the original BCO, LI-BCO, GS-BCO, and traditional optimization methods such as Particle Swarm Optimization (PSO), Hybrid PSO, Lambda Iteration with Simulated Annealing, the Sine Cosine Algorithm, Mountaineering Team-Based Optimization, and Teaching–Learning-Based Optimization. The results demonstrate that ELS-BCO achieves faster convergence and higher-quality solutions than these existing methods.

Motor control circuits need cut-off current from supply to load, when an abnormal situation occurs. The motor current cut-off control is realized by relay contacts in series and they are inserted into motor drive systems. This article presents relay drive circuit for safe operation order. The relay drivers system based on safe design. A circuit without CPUs with on-delay and off-delay, using IC LM 317 is a delay circuit and forward boost converter circuit step up voltage to the relay. The failure analysis used Failure Modes and Effects Analysis (FMEA). The performances test and analyze with simulation program.