An improved flower pollination solution for economic dispatch with valve point effect

<span>The economic dispatch is used to find the best optimal output of power generation at the lowest operating cost of each generator, to fulfill the requirements of the consumer. To get a practical solution, several constraints have to be considered, like transmission losses, the valve point effect, prohibited operating region, and emissions. In this research, the valve point effect is to be considered which increases the complexity of the problem due to its ripple effect on the fuel cost curve. Economic load dispatch problems are well-known optimization problems. Many classical and meta-heuristic techniques have been used to get better solutions. However, there is still room for improvement to get an optimal solution for the economic dispatch problem. In this paper, an Improved Flower Pollination Algorithm with dynamic switch probability and crossover operator is proposed to solve these complex optimization problems. The performance of our proposed technique is analyzed against fast evolutionary programming (FEP), modified fast evolutionary programming (MFEP), improved fast evolutionary programming (IFEP), artificial bee colony algorithm (ABC), modified particle swarm optimization (MPSO) and standard flower pollination algorithm (SFPA) using three generator units and thirteen thermal power generation units, by including the effects of valve point loading unit and without adding it. The proposed technique has outperformed other methods in terms of the lowest operating fuel cost.</span>

Quantum-Behaved Bat Algorithm for Solving the Economic Load Dispatch Problem Considering a Valve-Point Effect

Quantum computing-inspired metaheuristic algorithms have emerged as a powerful computational tool to solve nonlinear optimization problems. In this paper, a quantum-behaved bat algorithm (QBA) is implemented to solve a nonlinear economic load dispatch (ELD) problem. The objective of ELD is to find an optimal combination of power generating units in order to minimize total fuel cost of the system, while satisfying all other constraints. To make the system more applicable to the real-world problem, a valve-point effect is considered here with the ELD problem. QBA is applied in 3-unit, 10-unit, and 40-unit power generation systems for different load demands. The obtained result is then presented and compared with some well-known methods from the literature such as different versions of evolutionary programming (EP) and particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), simulated annealing (SA) and hybrid ABC_PSO. The comparison of results shows that QBA performs better than the above-mentioned methods in terms of solution quality, convergence characteristics and computational efficiency. Thus, QBA proves to be an effective and a robust technique to solve such nonlinear optimization problem.

A Probabilistic Multi-Objective Approach for Power Flow Optimization in Hybrid Wind-Based Power Systems Using Grasshopper Optimization Algorithm

This article introduces a grasshopper optimization algorithm (GOA) to efficiently prove its superiority for solving different objectives of optimal power flow (OPF) based on a mixture thermal power plant that incorporates uncertain wind energy (WE) sources. Many practical constraints of generators, valve point effect, multiple fuels, and the various scenarios incorporating several configurations of WEs are considered for both singles along with multi-objectives for the OPF issue. Within the article, the considered method is verified on two common bus experiment systems, i.e. IEEE 30-bus as well as the IEEE 57-bus. Here, the fuel amount minimization and emission minimization are studied as the primary purposes of a GOA-based OPF problem. However, the proposed algorithm yields a reasonable conclusion about the better performance of the wind turbine. Computational results express the effectiveness of the proposed GOA approach for the secure and financially viable of the power system under various uncertainties. The comparison is tabulated with the existing algorithms to provide superior results.

Distributed Prescribed Finite Time Consensus Scheme for Economic Dispatch of Smart Grids with the Valve Point Effect

The distributed prescribed finite time consensus schemes for economic dispatch (ED) of smart grids with and without the valve point effect are researched in this paper. First, the optimization problem is transformed into a consensus of multiagent system problem, where both with and without the valve point effect are considered. Second, for the directed balance network, a prescribed finite time method has been arranged to solve the ED problem with and without the valve point effect. Third, with considering the constraints of generation units, the prescribed finite time result is also achieved. Finally, from the simulations, the efficiency of the proposed algorithms is validated.

Economic Load Dispatch With Multiple Fuel Options and Valve Point Effect Using Cuckoo Search Algorithm With Different Distributions

The cuckoo search algorithm (CSA), a new meta-heuristic algorithm based on natural phenomenon of the cuckoo species and Lévy flights random walk has been widely and successfully applied to several optimization problems so far. In the article, two modified versions of CSA, where new solutions are generated using two distributions including Gaussian and Cauchy distributions in addition to imposing bound by best solutions mechanisms are proposed for solving economic load dispatch (ELD) problems with multiple fuel options. The advantages of CSA with Gaussian distribution (CSA-Gauss) and CSA with Cauchy distribution (CSA-Cauchy) over CSA with Lévy distribution and other meta-heuristic are fewer parameters. The proposed CSA methods are tested on two systems with several load cases and obtained results are compared to other methods. The result comparisons have shown that the proposed methods are highly effective for solving ELD problem with multiple fuel options and/nor valve point effect.

Quantum-Behaved Bat Algorithm for Solving the Economic Load Dispatch Problem Considering a Valve-Point Effect

Quantum computing-inspired metaheuristic algorithms have emerged as a powerful computational tool to solve nonlinear optimization problems. In this paper, a quantum-behaved bat algorithm (QBA) is implemented to solve a nonlinear economic load dispatch (ELD) problem. The objective of ELD is to find an optimal combination of power generating units in order to minimize total fuel cost of the system, while satisfying all other constraints. To make the system more applicable to the real-world problem, a valve-point effect is considered here with the ELD problem. QBA is applied in 3-unit, 10-unit, and 40-unit power generation systems for different load demands. The obtained result is then presented and compared with some well-known methods from the literature such as different versions of evolutionary programming (EP) and particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), simulated annealing (SA) and hybrid ABC_PSO. The comparison of results shows that QBA performs better than the above-mentioned methods in terms of solution quality, convergence characteristics and computational efficiency. Thus, QBA proves to be an effective and a robust technique to solve such nonlinear optimization problem.