Capability-Curve-Constrained Optimal Reactive Power Flow for Renewable-Integrated Transmission Systems

Optimal reactive power flow (ORPF) is a steady-state optimization problem used to determine reactive-power-related control settings in AC power systems while satisfying network operating constraints. In renewable-integrated transmission systems, explicitly representing the feasible reactive-power contribution of inverter-interfaced resources is essential, because wind, photovoltaic (PV), and battery energy storage system (BESS) units cannot operate as unlimited or overly flexible reactive-power sources. Their reactive capability depends on active-power output, apparent-power rating, voltage conditions, and equipment-level capability curves. This paper evaluates the impact of including these capability curves in the solution of the ORPF problem. A MATLAB-DIgSILENT PowerFactory co-simulation framework is implemented, in which MATLAB applies a hybrid particle swarm optimization-pattern search procedure and DIgSILENT PowerFactory performs repeated AC power-flow evaluations using detailed network models and predefined capability limits. The framework is tested on modified IEEE 39-bus and IEEE 118-bus systems with wind, PV, and BESS resources. The results show that neglecting capability curves can produce unrealistic reactive-power allocations for inverter-based units, whereas enforcing these limits shifts the ORPF solution toward operating points consistent with the modeled equipment capability. The study demonstrates the importance of capability-curve representation for obtaining physically meaningful steady-state ORPF results and supports clearer comparison of constrained and unconstrained dispatch cases.