This study proposes a novel hybrid multi-objective evolutionary algorithm (MOEA) based on decomposition and invasive weed optimization (IWO) algorithm for the optimal power flow (OPF) problem in transmission networks. The conventional OPF is modified as a stochastic OPF with the integration of WE, PV, and PEV systems uncertainty. This paper proposes a new constraint-handling method (CHM) that adds the penalty adaptively and avoids parameter reliance on penalty computation. The selection features in the IWO method are deployed to improve the diversity of the proposed method. The OPF problem is represented as a multi-objective optimization (MOO) problem using four objectives: generation cost, emission, power loss, and voltage variation. The generation costs of WE, PV, and PEV sources are evaluated using Monte Carlo simulations to mitigate the whole cost and the influence of intermittency of these systems is investigated in terms of affordability and feasibility. Weibull, lognormal, and normal probability distribution functions (PDFs) are employed to define the uncertainty of WE, PV, and PEV sources respectively. The suggested method's viability is evaluated on IEEE 57 and IEEE 118- bus systems under all conceivable scenarios. In addition, one-way ANOVA test, a statistical approach, is used to evaluate the superiority of the suggested algorithm.

In this paper, a novel hybrid decomposition and local dominance-based multi-objective evolutionary algorithm (MOEA) is proposed for the multi-objective optimal power flow (MOOPF) problem with conflicting objectives. The suggested method has been tested for several multi-objective cases. The testing cases are divided into multi-objective problem containing two objectives and three objectives. The cases are formulated using combination of four objective functions including the total cost of the fuel (FC), total emission, active power loss, and voltage magnitude deviation. A penalty function strategy is deployed to tackle various constraints of the MOOPF problem. Further, a fuzzy method is employed to get the best trade-off solution from Pareto-optimal solutions. The proposed method hybridizes the decomposition and the local dominance techniques to improvise the performance, i.e., exploration and exploitation of MOEA. To test the proposed method, standard IEEE 57-bus power system and IEEE 118-bus power systems are considered with distinct cases and the obtained outcomes are reviewed with the multi-objective particle swarm optimization and non-dominated sorting genetic algorithm-II methods.

A new hybrid decomposition-based multiobjective evolutionary algorithm is proposed for optimal power flow (OPF) including wind and solar generation uncertainty. This study recommends a novel constraint-handling method, which adaptively adds the penalty function and eliminates the parameter dependency on penalty function evaluation. The summation-based sorting and improved diversified selection methods are utilized to enhance the diversity of multiobjective optimization algorithms. The OPF problem is modeled as a multiobjective optimization problem with four objectives such as minimizing (i) total fuel cost (TC) including the cost of renewable energy source (RES), (ii) total emission (TE), (iii) active power loss (APL), and (iv) voltage magnitude deviation (VMD). The impact of RESs such as wind and solar energy sources on integration is considered in optimal power flow cost analysis. The costs of RESs are considered in the OPF problem to minimize the overall cost so that the impact of intermittence and uncertainty of renewable sources is studied in terms of cost and operation wise. The uncertainty of wind and solar energy sources is described using probability distribution functions (PDFs) such as Weibull and lognormal distributions. The efficiency of the algorithm is tested on IEEE 30-, IEEE 57-, and IEEE 118-bus systems for all possible conditions of renewable sources using Monte Carlo simulations.