Stochastic Tube Model Predictive Control of Medium Voltage Grids with Distributed Resources

The uncertainties associated with load and generation forecasts, as well as voltage measurement, present significant challenges for voltage control strategies that employ Model Predictive Control (MPC) in its deterministic formulation. This paper presents a Stochastic Model Predictive Control (SMPC) formulation for the voltage control of distribution grids that uses information on the probability distribution of the uncertainties to frame the control problem. The proposed SMPC applies a tube-based approach, which is capable of handling arbitrary probability distributions, can jointly evaluate different uncertainty sources, and allows for the formulation of the uncertainty as an additive disturbance. The test results show a significant reduction in voltage violations across the majority of uncertainty realizations with regard to both amplitude and frequency of these occurrences.