In this paper, a novel improved Stochastic Fractal Search optimization algorithm (ISFSOA) is proposed for finding effective solutions of a complex optimal reactive power dispatch (ORPD) problem with consideration of all constraints in transmission power network. Three different objectives consisting of total power loss (TPL), total voltage deviation (TVD) and voltage stabilization enhancement index are independently optimized by running the proposed ISFSOA and standard Stochastic Fractal Search optimization algorithm (SFSOA). The potential search of the proposed ISFSOA can be highly improved since diffusion process of SFSOA is modified. Compared to SFSOA, the proposed method can explore large search zones and exploit local search zones effectively based on the comparison of solution quality. One standard IEEE 30-bus system with three study cases is employed for testing the proposed method and compared to other so far applied methods. For each study case, the proposed method together with SFSOA are run fifty run and three main results consisting of the best, mean and standard deviation fitness function are compared. The indication is that the proposed method can find more promising solutions for the three cases and its search ability is always more stable than those of SFSOA. The comparison with other methods also give the same evaluation that the proposed method can be superior to almost all compared methods. As a result, it can conclude that the proposed modification is really appropriate for SFSOA in dealing with ORPD problem and the method can be used for other engineering optimization problems.

This paper proposes applications of a modified stochastic fractal search algorithm (MSFS) to solve the economic load dispatch problem (ELD) in which valve-point effects, prohibited operating zones, power losses in all conductors, multi-fuel sources and other constraints of power system are taken into consideration. The proposed method is first developed in the study by performing two modifications on two procedures of new solution generation from conventional stochastic fractal search (SFS). The first modification is used to change the strategy of producing new solutions of the first and the second update procedures while the second one is to newly update the worst solutions in the first update process and the best solutions in the second update process. These modifications have major influence on the solution search performance of the proposed method. All improvements of the proposed method can be illustrated by solving and analyzing results from various test systems with different system scales including 3-unit, 6-unit, 10-unit, and 20-unit systems. Comparison of results obtained by MSFS, SFS, and other existing methods indicates that the proposed MSFS method is more effective and robust than compared methods in terms of solution quality, high-quality solution search stability and convergence process. Consequently, the proposed method should be used as a very favorable optimization method for the ELD problem and it should be tried for other optimization problems in electrical engineering.

In this paper, a Modified Adaptive Selection Cuckoo Search Algorithm (MASCSA) is proposed for solving the Optimal Scheduling of Wind-Hydro-Thermal (OSWHT) systems problem. The main objective of the problem is to minimize the total fuel cost for generating the electricity of thermal power plants, where energy from hydropower plants and wind turbines is exploited absolutely. The fixed-head short-term model is taken into account, by supposing that the water head is constant during the operation time, while reservoir volume and water balance are constrained over the scheduled time period. The proposed MASCSA is compared to other implemented cuckoo search algorithms, such as the conventional Cuckoo Search Algorithm (CSA) and Snap-Drift Cuckoo Search Algorithm (SDCSA). Two large systems are used as study cases to test the real improvement of the proposed MASCSA over CSA and SDCSA. Among the two test systems, the wind-hydro-thermal system is a more complicated one, with two wind farms and four thermal power plants considering valve effects, and four hydropower plants scheduled in twenty-four one-hour intervals. The proposed MASCSA is more effective than CSA and SDCSA, since it can reach a higher success rate, better optimal solutions, and a faster convergence. The obtained results show that the proposed MASCSA is a very effective method for the hydrothermal system and wind-hydro-thermal systems.

This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are introduced in the paper by employing two different random walk generators for diffusion process in which SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from three test system. These systems with 6, 10, and 20 units with different objective function forms and different constraints are inspected. Numerical result comparison can confirm that the applied approach has better solution quality and fast convergence time when compared with some recently published standard, modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving the ELD problem.

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In this paper, optimal load dispatch problem under competitive electric market (OLDCEM) is solved by the combination of cuckoo search algorithm (CSA) and a new constraint handling approach, called modified cuckoo search algorithm (MCSA). In addition, we also employ the constraint handling method for salp swarm algorithm (SSA) and particle swarm optimization algorithm (PSO) to form modified SSA (MSSA) and modified PSO (MPSO). The three methods have been tested on 3-unit system and 10-unit system under the consideration of payment model for power reserve allocated, and constraints of system and generators. Result comparisons among MCSA and CSA indicate that the proposed constraint handling method is very useful for metaheuristic algorithms when solving OLDCEM problem. As compared to MSSA, MPSO as well as other previous methods, MCSA is more effective by finding higher total benefit for the two systems with faster manner and lower oscillations. Consequently, MCSA method is a very effective technique for OLDCEM problem in power systems.

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