Interval Optimization-Based Probabilistic Evaluation of PV Hosting Capacity in Flexible Distribution Networks

Distribution networks (DNs) with high penetration of photovoltaic (PV) systems are evolving towards a novel structural architecture, namely soft open point (SOP)-based flexible distribution networks (FDNs). However, traditional photovoltaic hosting capacity (PVHC) evaluation methods designed for conventional distribution networks cannot be directly applied to FDNs due to inherent structural differences. To address this challenge, this paper proposes a probabilistic PVHC evaluation method oriented towards flexibly interconnected and extensible FDNs. An interval optimization model is established to accurately calculate the elementary intervals of PVHC, wherein the outer layer captures short-term uncertainties and their correlations in PV generation and load demand, while the inner layer evaluates the PVHC considering precise loss characteristics of FDNs. To efficiently handle the model's inherent nonconvexity and bi-layer structure, second-order cone constraints (SOCC), difference-of-convex constraints (DCC), and successive linear constraints (SLC) are employed. An iterative algorithm incorporating the convex-concave procedure and duality theory is developed for solving the proposed model efficiently. Additionally, a novel evaluation framework is presented to obtain probabilistic global intervals of PVHC considering long-term uncertainties. Case studies on three FDN test systems illustrate the effectiveness and superiority of the proposed method.