Incorporating renewable reactive-power capability curves into multi-objective AC optimal power flow: a comparative assessment of cost, voltage performance, and reactive flexibility

In current power systems, the rising use of inverter-based renewable energy sources (RESs) is altering voltage control and reactive-power management. Although photovoltaic (PV) and wind generation units can provide substantial reactive-power support through their power-electronic interfaces, their actual reactive-power capabilities depend on operating conditions and are frequently overlooked or oversimplified in traditional optimal power flow (OPF) formulations. This paper presents a multi-objective AC OPF framework that explicitly integrates renewable reactive-power capability curves into power-system operation studies. Seven representative capability-curve models are systematically compared within a common optimization framework. The proposed framework simultaneously minimizes generation operating cost, active-power losses, and voltage deviation while maximizing renewable reactive-power flexibility through a Reactive Flexibility Index (RFI). The approach is validated using a modified IEEE 30-bus system with three RESs. The results reveal that renewable reactive-power capability curves greatly influence operational cost, transmission losses, voltage performance, upward and downward renewable reactive-power reserves, and renewable reactive-power flexibility. The Constant Reactive-Power model attains the lowest operating cost and active-power losses, the Triangular model provides the lowest voltage deviation, and the Oversized-Inverter model offers the highest upward and downward renewable reactive-power reserves, the highest RFI, and the highest TOPSIS score. Parameter-sensitivity analysis further confirms the robustness of the principal capability-curve conclusions and demonstrates increasing reactive flexibility with inverter oversizing. These results highlight the importance of accurately representing renewable reactive-power capability when assessing the operational flexibility and voltage performance of renewable-integrated power systems.