Maximizing Robust and Risk-averse Hosting Capacity for Unbalanced Distribution Network with Volt/Var Control

The rapid integration of distributed energy resources, especially photovoltaics (PVs), has triggered the evolution of active distribution networks. This evolution necessitates the assessment of hosting capacity (HC) to determine the maximum allowable PV power generation while ensuring network operating constraints. Firstly, this paper defines a robust HC under the worst case of uncertainty realization and a risk-averse HC that can reduce the risk of inadequate assessment. Then, this paper proposes robust and risk-averse HC maximization methods with inverter-based Volt/Var control (VVC) for a three-phase unbalanced distribution network. The proposed robust or risk-averse HC can be used as an objective function in optimization models. A linearized branch flow model for the network operation and a compatible ZIP load modeling for voltage-dependent loads is developed. Finally, a Latin hypercube sampling method is adopted to model the uncertainty for the optimization models. Numerical simulations are conducted on an extensive and unbalanced distribution network. Simulation results validate the accuracy of the models with an error of less than 1% and the effectiveness of the robust and risk-averse HC maximization methods in assessing robustness and the risk control of unexpected HC realizations.