Decentralized Distributionally Robust Coordination Between Distribution System and Charging Station Operators in Unbalanced Distribution Systems

Coordination between the distribution system operator (DSO) and charging station operators (CSOs) is crucial for ensuring stable and economical operation of distribution grids and electric vehicle charging stations (EVCSs). We propose a computationally efficient and privacy-preserving decentralized DSO-CSO coordination framework for robust operation of distribution grids and EVCSs under uncertainties in active unbalanced distribution systems. A centralized model predictive control (MPC) is developed based on distributionally robust optimization (DRO), which characterizes the uncertainties in photovoltaic generation outputs, loads, and electricity prices using the Wasserstein metric. Two scalable optimization approaches are presented to address the high computation time requirement of the proposed centralized DRO-based MPC method through the reduction of constraints: i) a robust optimization method including a distributionally robust bound on the uncertainties, and ii) a bi-level optimization method that determines critical buses associated with voltage violations. Furthermore, to preserve data privacy of electric vehicles, the centralized DRO-based MPC problem is transformed through an alternating direction multiplier method into a decentralized DRO-based MPC problem comprising the DSO and CSO problems. The efficiency and scalability of the proposed DSO-CSO coordination framework are analyzed using the IEEE 37-bus and IEEE 123-bus systems.