A non-simulation-based linear model for analytical reliability evaluation of radial distribution systems considering renewable DGs

One of the most critical goals in the operation and planning of distribution networks is the creation of networks with sufficient reliability. Existing models are often simulation-based or try to introduce topology-independent algebraic reliability measures with simplifications or extensive computations. This paper presents new and efficient topology-variable-based linear expressions that can evaluate the reliability indices of practical radial distribution networks. Furthermore, the model is extended to consider the inclusion of renewable distributed generation (DG) units to restore part of restorable loads in the islanded mode of operation. Also, the stochastic nature of renewable generation, as well as load demand, is considered. Therefore, the proposed model can be readily used in various optimization models to operate and plan distribution networks with reliability concerns. The application of the proposed method to several small- to large-scale test cases ranging from standard 37-node up to practical 1080-node benchmarks shows the proposed model's accuracy and computational effectiveness compared to the state-of-the-art conventional simulation-based topology-variable-based approaches. The impact of the system's islanded operation on the reliability indices is also evaluated on the modified DG-enhanced 37-node test system.