Distributionally robust hierarchical multi-objective voltage risk management for unbalanced distribution systems

•A novel Wasserstein-based distributionally robust method for voltage risk assessment is proposed.•A new risk management model is proposed for unbalanced DSs, which is formulated as a hierarchical multi-objective structure.•Multiple uncertainties in different levels and objectives are formulated by the corresponding Wasserstein ambiguity sets.•Hierarchical multi-objective DRO model is reformulated into tractable bilevel mixed-integer convex programs. The large-scale integration of renewable energy generators (REGs) is key to reducing carbon emissions. However, the intermittency of REG outputs poses operational risk challenges on distribution systems (DSs). This paper proposes a novel Wasserstein-based distributionally robust assessment for the voltage risk index that represents both likelihood and non-linearly increasing severity of voltage violations. We propose a hierarchical DRO model for risk management that integrates a multi-objective distributionally robust optimization (DRO) at the distribution system operator (DSO) level and a basic DRO at the user level. Then, a systematic solution method is developed, where the proposed model is equivalently reformulated into tractable bilevel mixed-integer convex programs. The effectiveness, advantages, and scalability of the proposed method are validated on the IEEE 33-bus system and unbalanced IEEE-123-bus system.