Discrete optimal power flow with prohibited zones, multiple-fuel options, and practical operational rules for control devices

Although the optimal power flow (OPF) problem has been extensively studied, solving realistic OPF models that accurately represent the operating behavior of power system components remains challenging. This paper proposes a novel model for the AC OPF problem, aiming to minimize the fuel costs of thermal units while taking into account valve-point loading effects (VPLE), prohibited operation zones (POZ), multiple fuel options (MFO), and operational rules associated with the discrete tap ratios of on-load tap changer (OLTC) transformers and with the discrete shunt susceptances of capacitor/reactor banks. These rules are represented using complementarity constraints. We propose a solution approach that integrates several strategies to address the non-smooth features of the objective function related to VPLE, the disjoint constraints and functions tied to POZ and MFO, the discrete characteristics of the reactive control variables, and the complementarity constraints governing operational rules linked to voltage control devices such as OLTC transformers and capacitor/reactor banks. The resulting optimization problem is designed to be compatible with commercial solver packages. Numerical tests on the IEEE 30, 118, and 300-bus systems aim to examine the cumulative impact of these operational factors on the optimal solution. The solution strategy proposed has demonstrated its effectiveness in solving the proposed OPF problem within reasonable computation times.