Efficient power dispatch optimization via the active set approach for nonconvex third-degree polynomial cost models

Economic power dispatch problems (EPDPs) with quadratic cost functions have usually been solved using deterministic and metaheuristic optimization techniques by researchers. To ensure more accuracy in solutions for more realistic EPDPs, fuel cost functions of third-degree polynomials (cubic) are considered in this study. Cubic cost function-based EPDPs with equality and inequality constraints are highly nonlinear, nonsmooth optimization problems. To handle these constrained nonlinear EPDPs, one of the constrained nonlinear optimization algorithms, the active set algorithm (ASA), is employed. The purpose is to investigate the performance of ASA when applied to EPDPs with cubic cost functions, which otherwise performs well for quadratic cost functions. For this purpose, the power systems having different generating units (3-unit, 5-unit, 6-unit, 13-unit, and 26-unit) readily available in the literature with cubic cost functions (only) are considered. The proposed method is very efficient in calculating the total fuel cost of considered power systems having generating units with cubic fuel cost function, and it remarkably reduces the computation time as it performs fewer iterations to reach the optimal point. The MATLAB-based results confirm the efficacy of employing the constrained ASA method for addressing economic power dispatch problems involving cost functions characterized by higher-order polynomials.