Fast scenario-based decision making in unbalanced distribution networks

In this paper we consider the problem faced by a distribution network operator that is required to guarantee, with high probability, the satisfaction of operational constraints of the grid in the presence of stochastic disturbances caused by fluctuating loads and intermittent microgeneration. We formulate this problem as a chance-constrained decision problem, and we employ a scenario-based approach in order to convert it into a large-scale deterministic decision problem. In order to make this latter problem computationally tractable, we approximate the nonlinear power flow equations via a sparse, implicit linear model. This approach results in an accurate and fast decision making strategy, that we validate in simulations on the IEEE 13-bus three-phase test feeder.