Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC for Battery Scheduling Under Forecast Uncertainties

Chance constrained stochastic model predictive controllers (CC-SMPC) trade off full constraint satisfaction for economical plant performance under uncertainty. Previous CC-SMPC works are over-conservative in constraint violations leading to worse economic performance. Other past works require a-priori information about the uncertainty set, limiting their application to real-world systems. This paper considers a discrete linear time invariant system with hard constraints on inputs and chance constraints on states, with unknown uncertainty distribution, statistics, or samples. This work proposes a novel adaptive online update rule to relax the state constraints based on the time-average of past constraint violations, for the SMPC to achieve reduced conservativeness in closed-loop. Under an ideal control policy assumption, it is proven that the time-average of constraint violations converges to the maximum allowed violation probability. The time-average of constraint violations is also proven to asymptotically converge even without the simplifying assumptions. The proposed method is applied to the optimal battery energy storage system (BESS) dispatch in a grid connected microgrid with PV generation and load demand with chance constraints on BESS state-of-charge (SOC). Realistic simulations show the superior electricity cost saving potential of the proposed method as compared to the traditional MPC (with hard constraints on BESS SOC), by satisfying the chance constraints non-conservatively in closed-loop, thereby effectively trading off increased cost savings with minimal adverse effects on BESS lifetime.