Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC

TL;DR

This paper introduces an adaptive relaxation method for chance constrained stochastic MPC that reduces conservativeness and improves economic performance in uncertain systems without prior knowledge of uncertainty distribution.

Contribution

It proposes a novel adaptive online update rule for relaxing constraints based on past violations, with proven asymptotic convergence under ideal control policies.

Findings

Achieves reduced conservativeness in constraint satisfaction.

Demonstrates significant cost savings in microgrid BESS dispatch.

Maintains minimal adverse effects on BESS lifetime.

Abstract

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. This paper considers a discrete LTI 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, to achieve reduced conservativeness in closed-loop. Under an ideal control policy assumption, it is proven that the time-average of constraint violations asymptotically converges to the maximum allowed violation probability. The method is applied for 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 economic MPC without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints non-conservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime.