Abstract
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.
Highlights
Optimal power flow (OPF) has been a crucial tool for power systems’ operation in an efficient and secured way since its inception in 1962 by Carpentier [1]
A modified IEEE 30–bus system incorporating one solar photovoltaic generators (SPGs) and two wind power generators (WPGs) was used for testing the validity of the proposed algorithm in reaching the optimal solution for OPF problem with uncertain renewable energy sources (RESs), variable load demand and ramp rate effect of thermal power generators (TPGs), in addition to some theoretical cases
TPGs have constant power outputs, while WPGs and SPG have variable power outputs that must be balanced with the aid of the energy mix of all involved generators and the reserve power, the total power cost consists of the operation costs for all the involved power generators, penalty cost, and reserve cost
Summary
Optimal power flow (OPF) has been a crucial tool for power systems’ operation in an efficient and secured way since its inception in 1962 by Carpentier [1]. In [9], a genetic algorithm, the two-point estimation method, and Monte Carlo simulation were applied to solve the OPF problem including RESs and an energy storage system, and the uncertain nature of wind, solar, and load demand was handled by a new strategy. The uncertain output power of RESs and load demand are handled in [13] by providing uncertainty probability distribution to optimize the conventional generation. A modified IEEE 30–bus system incorporating one SPG and two WPGs was used for testing the validity of the proposed algorithm in reaching the optimal solution for OPF problem with uncertain renewable energy sources (RESs), variable load demand and ramp rate effect of TPGs, in addition to some theoretical cases.
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