Online Decentralized Tracking for Nonlinear Time-Varying Optimal Power Flow of Coupled Transmission–Distribution Grids

The coordinated transmission–distribution alternating current optimal power flow (TD-ACOPF) has become crucial to handle problems related to high penetration of renewable energy sources (RESs). However, obtaining all system details and solving TD-ACOPF centrally is sometimes less preferable in practice due to privacy concerns. Intermittent RESs and uncontrollable loads can swiftly change the operating condition of the power grid. Existing decentralized optimization methods can seldom track the optimal solutions of time-varying TD-ACOPFs. Here, we develop a continuous-time dynamic approach based on the primal-dual interior point method to online track the saddle points of the Lagrangian for time-varying ACOPFs from a control system perspective. To improve tracking accuracy, a prediction term denoted by the partial derivative with respect to time is added to the dynamic system. Next, a decentralized implementation for solving the dynamic system is designed based on only a few information exchanges with respect to boundary variables. Moreover, the proposed continuous-time dynamic approach is derived from the first-order optimality condition of the ACOPF model (without approximation) for coping with the nonlinear power flow equation model without the need for real-time measurements. Numerical test results reveal the effectiveness and fast-tracking performance of the proposed algorithm.