Assessment of Continuous-Time Transmission-Distribution-Interface Active and Reactive Flexibility for Flexible Distribution Networks

With the widespread use of power electronic devices, modern distribution networks are turning into flexible distribution networks (FDNs), which have enhanced active and reactive power flexibility at the transmission-distribution-interface (TDI). However, owing to the stochastics and volatility of distributed generation, the flexibility can change in real time and can hardly be accurately captured using conventional discrete-time (DT) assessment methods. This paper first proposes the notion of continuous-time (CT) TDI active and reactive flexibility and establishes its mathematical model. This model comprehensively considers the flexible devices in the FDN and the impact of uncertainty of photovoltaic power generation and load. In particular, a novel direction-factor-based metric is proposed to model CT-TDI PQ flexibility. Moreover, an efficient solution method is designed to address the difficulties in handling the infinite dimension of CT model and the complexity of bi-objectivity from assessing both active and reactive flexibility to be assessed. The solution successfully transforms the infinite dimensional optimization into a finite dimensional problem and effectively explores the PQ plane in a parallel pattern. Case studies show that the method can more effectively assess the real-time TDI flexibility of an FDN relative to conventional DT counterparts, and also reveals the impact of the relevant factors, such as penetrations of flexible devices and levels of uncertainty.