Multi-scenario robust stochastic programming based distributed energy resources allocation in distribution networks: Balancing economic efficiency and resilience

With the intensification of global climate change, the configuration of distributed energy resources (DERs) faces growing challenges from extreme weather events. To enhance system resilience while maintaining economic efficiency in normal operations, a multi-scenario robust stochastic programming (MS-RSP) method is proposed for optimal DERs configuration, strategically combining high-cost fixed and low-cost emergency power supplies (EPS). The proposed approach integrates the advantages of stochastic programming (SP) and robust optimization (RO), addressing uncertainties in both normal and extreme disaster scenarios through innovative model decomposition. To overcome potential computational complexity in DERs configuration optimization, an improved alternating direction method of multipliers (ADMM) is developed to decompose the hybrid model into SP and MS-RO subproblems for parallel solving, significantly reducing computational burden while improving solution efficiency. For the MS-RO component of the DERs configuration problem, a nested column-and-constraint generation (NC&CG) and progressive hedging (PH) algorithm is implemented, enabling efficient large-scale scenario processing and enhanced computational performance. Simulation results on IEEE 33 and 123 bus distribution networks demonstrate that the proposed model successfully achieves the optimal balance between resilience and economic efficiency, showing remarkable adaptability across various operating conditions. The methodology proves particularly effective in addressing the dual challenges of normal operational economics and extreme event resilience through differentiated resource allocation strategies.