An AC optimal power flow framework for active–reactive power scheduling considering generator capability curve

This paper presents a simplified optimal power flow (OPF) framework to facilitate co-optimised active and reactive power scheduling for synchronous generators and price-sensitive demands. The proposed framework creates an opportunity for generators and loads to simultaneously participate in a combined market for active and reactive power. The co-optimisation of active and reactive power generation is constrained by the interdependence of the active and reactive power capacities, which is represented by the generator capability curve. Thus, a detailed mathematical derivation of the opportunity costs across various regions of the generator capability curve is presented. This study considers a detailed generator capability curve that considers the armature, field, under-excitation, and prime mover limits. The interdependence of active and reactive power consumption for demand is modelled using the concept of power-factor. The OPF problem for generator and load scheduling is formulated as a non-linear optimisation task, leveraging the inherent properties of the generator capability curve, that is, piecewise smoothness, continuity, and the monotonically increasing slope magnitudes. Furthermore, to simplify the OPF formulation, the non-linear capability curve is represented as a combination of the linear curves. To demonstrate the effectiveness of the proposed OPF methodologies, suitable case studies are conducted using different test systems.