Self-adaptive Differential Evolution Based Optimal Power Flow for Units with Non-smooth Fuel Cost Functions

This paper presents a self-adaptive differential evolution with augmented Lagrange multiplier method (SADE_ALM) for solving optimal power flow (OPF) problems with non-smooth generator fuel cost curves. The SADE_ALM is a modified version of conventional differential evolution (DE) by integrating mutation factor (F) and crossover constant (CR) as additional control variables. An augmented Lagrange multiplier method (ALM) is applied to handle inequality constraints instead of traditional penalty function method, whereas the sum of the violated constraint (SVC) index is employed to ensure that the final result is the feasible global or quasi-global optimum. The proposed algorithm has been tested with the IEEE 30-bus system with different fuel cost characteristics, i.e. 1) quadratic cost curve model, and 2) quadratic cost curve with rectified sine component model (valve-point effects). Numerical results show that the SADE_ALM provides very impressive results compared with the previous reports.