• An OPC model for SVS of ITDNs under multiple N -1 contingencies considering uncertain renewables is proposed. • Fault parameters are introduced to simplify the SVSM interval constraints. • A simplification method based on Galerkin approximation is proposed to simplify the DN constraints. • Results on different ITDNs demonstrate the correctness and effectiveness of the proposed method. To maintain the secure operation of integrated transmission and distribution networks (ITDNs) with renewables, an optimal preventive control (OPC) method for static voltage stability of ITDNs under multiple N -1 contingencies considering uncertain renewables is proposed in this paper. In the OPC model, the uncertain power outputs of renewable energy stations are described as intervals, and the lower bounds of the static voltage stability margin (SVSM) intervals of ITDNs under both normal operation state and multiple N -1 contingencies are required to meet the allowable security thresholds. The original OPC model is a three-level optimization model including multiple bi-level optimization problems for computing the lower bounds of SVSM intervals, which is difficult to solve directly. To address this, the constraints of multiple SVSM intervals are simplified to the active constraints of the SVSM interval of the most severe state by introducing the fault parameters. Next, a simplification method based on Galerkin approximation is proposed to obtain the relationship between the injected power at the boundary connection bus and key variables of a distribution network (DN), and the operational constraints of each DN are simplified to several second-order cone inequality constraints. Then, the three-level optimization model is converted into a single-level optimization model through convex relaxation, dual convex programming, and Karush-Kuhn-Tucker condition construction. Thus, the preventive control scheme of ITDNs is obtained by solving the single-level optimization model. Case studies on a modified IEEE 39-33&69 bus ITDNs and an actual 2285-bus ITDNs demonstrate the correctness and effectiveness of the proposed method.
Jiang et al. (Fri,) studied this question.