Uncertainties associated with the loads and the output power of distributed generations create challenges in quantifying the integration limits of distributed generations in distribution networks, i.e., hosting capacity. To address this, we propose a distributionally robust optimization-based method to determine the hosting capacity considering the voltage rise, thermal capacity of the feeders and short circuit level constraints. In the proposed method, the uncertain variables are modeled as stochastic variables following ambiguous distributions defined based on the historical data. The distributionally robust optimization model guarantees that the probability of the constraint violation does not exceed a given risk level, which can control robustness of the solution. To solve the distributionally robust optimization model of the hosting capacity, we reformulated it as a joint chance constrained problem, which is solved using the sample average approximation technique. To demonstrate the efficacy of the proposed method, a modified IEEE 33-bus distribution system is used as the test-bed. Simulation results demonstrate how the sample size of historical data affects the hosting capacity. Furthermore, using the proposed method, the impact of electric vehicles aggregated demand and charging stations are investigated on the hosting capacity of different distributed generation technologies.
Optimal PV Inverter Control in Distribution Systems via Data-Driven Distributionally Robust Optimization
