Multi-period voltage stability-constrained optimal power flow with uncertainties

Most multi-period optimal power flow (MP-OPF) focuses on economic goals. However, with the increasing penetration of renewables, power systems face specific challenges to ensure secure and stable operation due to the fluctuation of renewables and the heavy loading demand. Hence, this paper proposes a multi-period voltage stability-constrained optimal power flow (MP-VCOPF) considering the uncertainty of the renewables and loads problem with both the economic and stable goals, i.e., minimizing the generation cost and ensuring a desirable static voltage stability margin. Unlike most models in the literature, the proposed problem formulation uses the nonlinear parameterized AC continuation power flow equations to model the voltage stability and exact AC power flow constraints. Furthermore, the thermal limits, voltage limits, ramping constraints, and security operation requirements are all considered in the proposed formulation. As another main novelty, the joint scenarios of renewables and loads are established, and a tailored scenario reduction technique is employed in this paper. To solve it reliably, the MP-VCOPF problem is decomposed into two subproblems, and a three-stage method is proposed to solve the large-scale stochastic nonlinear constrained programming problem. Computational and comparison results on IEEE 30-bus system, 118-bus system and 300-bus system verify the proposed method's effectiveness and accuracy under the short and long scheduling horizon and the robustness on different loading conditions.