Gaussian Process Supported Stochastic MPC for Distribution Grids

Abstract

The efficacy of control systems for distribution grids can be influenced by different sources of uncertainty. Stochastic Model Predictive Control (SMPC) can be employed to compensate for such uncertainties by integrating their probability distribution into the control problem. An efficient SMPC algorithm for online control applications is the stochastic tube SMPC, which is able to treat the evaluation of the chance constraints analytically. However, this approach is efficient only when the calculation of the constraint back-off is applied to a linear model. To address this issue, this work employs Gaussian Processes to approximate the nonlinear part of the power flow equations based on offline training, which is integrated into the SMPC formulation. The resulting SMPC is first validated and then tested on a benchmark system, comparing the results with Deterministic MPC and SMPC that excludes Gaussian Processes. The proposed SMPC proves to be more efficient in terms of cost minimization, reference tracking and voltage violationreduction.