Enhancing stochastic optimal power flow with modified cheetah optimizer for integrating renewable energy sources

In this paper, a modified cheetah optimizer (MCO) algorithm is presented, which has been designed to address the optimal power flow (OPF) problem in power grids that utilize renewable energy sources (RES). The issue of uncertainty in cost models for wind turbines (WTs) and photovoltaics (PVs), which can result in overestimation or underestimation of RES, is addressed by including the uncertain cost value in the direct cost of these renewable units to calculate their cost value accurately. The MCO methodology was applied to various objective functions such as overall operating cost, voltage deviation, pollutant emissions, and power loss, which were evaluated under different cases. Regarding the valve point effect observed in case 1, the optimal response provided by MCO amounts to $781.9862. Upon assessing the emission costs in case 2, a resultant value of $810.6655 is determined. Considering the POZs in case 3, the aggregate cost is $781.7165. The minimum network loss is recorded in case 4, which is 2.0738 MW. By mitigating the voltage deviations in case 5 to 2.0738 p.u., the loss incurred exceeds twice that of the preceding case. Furthermore, due to its applicability to large-scale problems, the reserve constraint dynamic economic dispatch problem was chosen as an additional test case for the MCO. A backward-forward correction method was used to correct errors in three types of reserves, improving the solution quality. The effectiveness of the MCO in solving practical large-scale optimization problems was demonstrated by the results of the 10-unit and 30-unit dynamic economic dispatch, achieving lower cost values than previously published papers. In the 10-unit economic dispatch, the response surpasses the 15 top publications at $1,016,361. In the 30-unit dispatch, the MCO algorithm produced a unique solution of $3,048,405.