Analytical reliability evaluation and weak-link identification of complex distribution systems integrated with distributed generation and soft open points

• The FEIM -based model improves the efficiency of reliability evaluation. • The impact of DG and SOPs on distribution system reliability is considered. • An explicit analytical expression for the reliability indexes is achieved. • Quantified the impact of reliability parameters on the reliability indexes. • The proposed method efficiently supports weak-link identification for operators. Power supply reliability evaluation is an essential foundational task in the planning and operation of distribution system, which lies in the measurement and analysis of the system unreliability. Existing reliability evaluation methods mainly rely on multi-layered iterative searches based on fault scenarios, which result in time-consuming and low efficiency for the large scale distribution system. Meanwhile, current studies fail to achieve explicit analytical calculation of reliability indexes in complex distribution system integrated with distributed generation (DG) and soft open points (SOPs), posing significant challenges for identifying the weak links. To address this issue, this paper proposes an analytical calculation method for reliability indexes in distribution system, based on fault effect incidence matrix ( FEIM ). First, for traditional passive distribution system, a group of incidence matrices, named FEIM s, are constructed to describe the spatial relationships between the fault events and the affected loads and the impact levels. Based on FEIM s, the analytical calculation method of reliability indexes for complex distribution system is presented. Next, for complex distribution system integrated with DG and SOPs, the island recovery matrix of DGs( IRM DG ) and the power transfer matrix of SOPs ( PTM SOPs ) are constructed, considering the dynamic and time-series characteristics. Incorporating FEIM s, IRM DG , PTM SOPs and fault event parameter vectors, the power supply reliability can be evaluated explicitly considering the impacts of DG and SOPs. Then, for reliability parameters, the partial derivative transformation method is employed to calculate the sensitivity on reliability indexes and to identify the weak links of the distribution system. Finally, the effectiveness of the proposed model and method is validated using the IEEE RBTS bus-6 and 137-node system. The results demonstrate that the FEIM -based method can significantly improve the computation efficiency, as well as provide sufficient support of weak links identifying for distribution network operators.