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, time-varying 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.

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.

This paper presents two modified versions of the Tasmanian Devil Optimization (TDO) for dealing with the optimal power flow (OPF) problem in both conventional and advanced power systems. The original TDO is enhanced with two distinct constraint handling techniques: weighted factors (WF) in addition to the superiority of feasible solutions (SF).The two developed algorithms (TDO-WF and TDO-SF) are applied to tackle both single and multi-objective functions of the OPF problem. Two test systems are used for verifying the two developed algorithms in different case studies. The first test system is the IEEE-30 bus system in its conventional form, while the second system is an advanced version of the IEEE-30 bus system that contains three distinct sorts of renewable energy plants and a variable load. The MATLAB software is used for simulation purposes. The two developed algorithms overcame the problem of violating the system’s constraints in the original TDO and achieved better results than alternative approaches in the related research. A statistical analysis and a Wilcoxon signed rank test are carried out to define the best one of the two developed techniques. The results of the two suggested techniques are quite similar, and we verified the validity of both of them to tackle the OPF problem in both conventional and advanced power systems.