Today's electrical power system became more complex interconnected network that is expanding every day. The transmission lines of the power system are more severely loaded than ever before. Hence, the power system is facing many problems such as power losses increasing, voltage instability, line overloads, etc. The optimization of real and reactive powers due to the installation of energy resources at appropriate buses can minimize the losses and improve the voltage profile especially, for congested networks. As a result, the optimal power flow problem (OPF) is considered more important tool for the processes of planning and operation of power systems. OPF is a very significant tool for power system operators to meet the electricity demand of the consumers efficiently, and for the reliable operation of the power system. However, the incorporation of renewable energy sources (RESs) into the electrical grid is a very challenging problem due to their intermittent nature. In this paper, the proposed power flow model contains three different types of energy sources: thermal power generators representing the conventional energy sources, wind power generators (WPGs), and solar photovoltaic generators (SPGs) representing RESs. Uncertain output powers from WPGs and SPGs are forecasted with the aid of Weibull and lognormal probability distribution functions (PDF), respectively. The under and overestimation output powers of RESs are taken into consideration while formulating the objective function through adding a penalty and reserve cost, respectively. Moreover, carbon tax is imposed to the main objective function to help in reducing carbon emissions. A jellyfish search optimizer (JS) is employed to reach optimization in the modified IEEE 30-bus test system to validate its feasibility. To examine the effectiveness of the proposed JS algorithm, its simulation results are compared with the results of four other nature-inspired global optimization algorithms. The developed OPF algorithm considers several practical cases such as generation uncertainty of renewable energy sources, timevarying load and the ramp rate limits of thermal generators. The simulation results show the effectiveness of the JS algorithm in solving the OPF problem in terms of minimization of total generation cost and solution convergence.

In this work, an enhanced slime mould algorithm (ESMA) based on neighborhood dimension learning (NDL) search strategy is proposed for solving the optimal power flow (OPF) problem. Before using the proposed ESMA for solving the OPF problem, its validity is verified by an experiment using 23 benchmark functions and compared with the original SMA, and three other recent optimization algorithms. Consequently, the ESMA is used to solve a modified power flow model including both conventional energy, represented by thermal power generators (TPGs), and renewable energy represented by wind power generators (WPGs) and solar photovoltaic generators (SPGs). Despite the important role of WPGs and SPGs in reducing CO2 emissions, they represent a big challenge for the OPF problem due to their intermittent output powers. To forecast the intermittent output powers from SPGs and WPGs, Lognormal and Weibull probability density functions (PDFs) are used, respectively. The objective function of the OPF has two extra costs, penalty cost and reserve cost. The penalty cost is added to formulate the underestimation of the produced power from the WPGs and SPGs, while the reserve cost is added to formulate the case of overestimation. Moreover, to decrease CO2 emissions from TPGs, a direct carbon tax is added to the objective function in some cases. The uncertainty of load demand represents also another challenge for the OPF that must be taken into consideration while solving it. In this study, the uncertainty of load demand is represented by the normal PDF. Simulation results of ESMA for solving the OPF are compared with the results of the conventional SMA and two further optimization methods. The simulation results obtained in this research show that ESMA is more effective in finding the optimal solution of the OPF problem with regard to minimizing the total power cost and the convergence of solution.

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In recent years, more efforts have been exerted to increase the level of renewable energy sources (RESs) in the energy mix in many countries to mitigate the dangerous effects of greenhouse gases emissions. However, because of their stochastic nature, most RESs pose some operational and planning challenges to power systems. One of these challenges is the complexity of solving the optimal power flow (OPF) problem in existing RESs. This study proposes an OPF model that has three different sources of renewable energy: wind, solar, and combined solar and small-hydro sources in addition to the conventional thermal power. Three probability density functions (PDF), namely lognormal, Weibull, and Gumbel, are employed to determine available solar, wind, and small-hydro output powers, respectively. Many meta-heuristic optimization algorithms have been applied for solving OPF problem in the presence of RESs. In this work, a new meta-heuristic algorithm, weighted mean of vectors (INFO), is employed for solving the OPF problem in two adjusted standard IEEE power systems (30 and 57 buses). It is simulated by MATLAB software in different theoretical and practical cases to test its validity in solving the OPF problem of the adjusted power systems. The results of the applied simulation cases in this work show that INFO has better performance results in minimizing total generation cost and reducing convergence time among other algorithms.

Optimal power flow (OPF) is a crucial issue to maintain the reliable operation of power systems. However, achieving this objective is not easy, especially when renewable energy sources (RESs) are penetrated into the power system due to their uncertainty nature. This paper provides an optimal solution for the power flow problem including two different types of RESs based on a marine predator algorithm (MPA). The OPF model used in this paper has three different types of energy resources (thermal, wind, and solar). The output power from wind or solar generator has two probabilities either underestimation or overestimation consequently. These two probabilities have been translated into the objective function by two extra costs, penalty cost, and reserve cost, respectively. To check the validity of the proposed algorithm, it is applied to a modified IEEE-30 and IEEE-57 bus systems. The obtained results are compared with some recent optimization methods. The results show the effectiveness of marine predator algorithm in providing the optimal solution for the power flow problem with maintaining the power system constraints inviolate.

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