Transmission–Distribution Coordinated Multi-Time-Scale Rolling Optimal Control Considering Static Voltage Stability

The increasing penetration of distributed energy resources has strengthened the operational coupling between transmission and distribution grids, intensified voltage fluctuations, and reduced static voltage stability margins under bidirectional power-flow conditions. In transmission–distribution coordinated operation, conventional scheduling methods have difficulty simultaneously addressing boundary power interaction, renewable generation forecasting errors, real-time corrective control, and static voltage stability constraints. To address these issues, this paper proposes a transmission–distribution coordinated multi-time-scale rolling optimal control method considering static voltage stability. First, based on local network equivalencing, a static voltage stability index (SVSI) calculation method is developed for scenarios with bidirectional power-flow variations, enabling fast online assessment of static voltage stability boundaries. Second, the transmission–distribution boundary exchange power is selected as the key coordination variable, and a multi-time-scale rolling optimization framework is established to coordinate main-grid operational requirements with distribution-side flexible resources. At the long time scale, a baseline scheduling plan is generated by considering economic operation, renewable energy accommodation, and transmission–distribution boundary power exchange. At the short time scale, model predictive control (MPC) is adopted to perform closed-loop correction of control variables using rolling forecast information and real-time measurements, thereby achieving rolling coordinated control of distributed generation, energy storage systems, flexible regulation resources, and boundary exchange power. Furthermore, the SVSI is embedded into the rolling optimization model as a security constraint, forming a multi-objective coordinated control method that jointly considers economic performance, renewable energy accommodation capability, transmission–distribution interaction, and static voltage security margin. Case study results show that the proposed method can effectively improve renewable energy accommodation and reduce network losses while enhancing the static voltage stability margin. In addition, it improves the adaptability of the coordinated transmission–distribution system to operating-condition variations, forecasting deviations, and boundary power fluctuations.