Power Management in Active Distribution Systems Penetrated by Photovoltaic Inverters: A Data-Driven Robust Approach

Under the smart grid paradigm, distribution systems with large penetrations of photovoltaic-based power generation are called to optimize their operational resources to achieve a more efficient and reliable performance. In this context, this paper proposes a multiperiod mixed integer second order cone formulation to optimize distribution feeders operation. The model takes into account the feeder physical behavior; discrete control equipment (tap changers and capacitors banks) with a maximum allowable daily switching operation number; photovoltaic inverters operation; and the uncertain nature of solar energy and loads. A two-stage robust optimization framework is used to include the uncertainty into the model, where discrete and continuous control actions are assumed to be part of the first and second stage of this model, respectively. The conservativeness level of the robust model is controlled by an polyhedral uncertainty set whose vertexes are adaptively adjusted in a data-driven fashion in order to better capture complex spatiotemporal dependencies among uncertain parameters. Extensive computational experiments are performed utilizing modified versions of various IEEE test feeders. The performance of the proposed data-driven model is contrasted against traditional deterministic and robust budget-constrained models, using a rolling horizon out-of-sample evaluation methodology. When compared to the deterministic model, the data-driven approach yields a reduction in power losses of approximately 15% and a reduction up to 98% in hourly voltage violations. Results also suggests that the proposed approach exhibits better performance in terms of both average and conditional-value-at-risk metrics in comparison to budget-constrained models.