Chance constrained stochastic model predictive controllers (CC-SMPCs) tradeoff 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 article considers a discrete linear time-invariant (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 (MG) with photovoltaic (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 with the traditional economic model predictive control (EMPC) without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints nonconservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime.

Monthly demand charges form a significant portion of the electric bill for microgrids with variable renewable energy generation. A battery energy storage system (BESS) is commonly used to manage these demand charges. Economic model predictive control (EMPC) with a reference trajectory can be used to dispatch the BESS to optimize the microgrid operating cost. Since demand charges are incurred monthly, EMPC requires a full-month reference trajectory for asymptotic stability guarantees that result in optimal operating costs. However, a full-month reference trajectory is unrealistic from a renewable generation forecast perspective. Therefore, to construct a practical EMPC with a reference trajectory, an EMPC formulation considering both non-coincident demand and on-peak demand charges is designed in this work for 24 to 48 h prediction horizons. The corresponding reference trajectory is computed at each EMPC step by solving an optimal control problem over 24 to 48 h reference (trajectory) horizon. Furthermore, BESS state of charge regulation constraints are incorporated to guarantee the BESS energy level in the long term. Multiple reference and prediction horizon lengths are compared for both shrinking and rolling horizons with real-world data. The proposed EMPC with 48 h rolling reference and prediction horizons outperforms the traditional EMPC benchmark with a 2% reduction in the annual cost, proving its economic benefits.

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.

The recent increase in the intermittent variable renewable energy sources (VRES) results in mismatches between demand and supply that can cause grid instability. These issues can be mitigated with battery energy storage systems (BESS). However, BESS are generally dispatched conservatively to manage uncertainties in VRE forecast. Therefore, this paper proposes an online adaptive stochastic model predictive control (A-SMPC) based approach that minimizes electricity costs by expanding the BESS state of charge (SOC) limits beyond the nominal range of 20% – 80%. Allowing the SOC limits to expand, results in violation of the nominal SOC constraints. Chance constraints are implemented in the proposed A-SMPC method that guarantee that the probability of violating nominal SOC constraints remains below a desired value. Furthermore, the A-SMPC cost function includes time-of-use demand charges that have not been considered before in this type of model. Simulations based on historical load and PV generation data from the Port of San Diego for January 2019 shows that the proposed formulation outperforms the traditional MPC formulation, that does not include nominal SOC constraint violation, by reducing the monthly electricity costs by 7%. The proposed A-SMPC method results in 8% higher BESS utilization which translates to about 1 extra charging/discharging cycle during the analyzed month which is unlikely to have a significant impact on BESS lifetime.

This work proposes a novel EV forecasting technique that predicts each EV’s arrival time (AT), energy demand (ED) and plug duration (PD) over the course of a calendar day using a hybrid machine learning (ML) forecast. The ML forecasts as well as persistence forecasts are then input in a model predictive control (MPC) algorithm that minimizes the electricity costs incurred by the charging provider. The MPC with the hybrid ML forecast reduced peak loads and monthly electricity costs over a base case scenario that determined costs for uncontrolled L2 charging: Reductions in weekday mean peak load during a 30 day summer time case study were 47.0% and 3.3% from the base case to ML MPC and persistence to ML MPC, respectively. Reductions in utility costs during the summer case study were 22.0% and 1.4% from base case to ML MPC and persistence to ML MPC respectively. Results are similar for a 30 day winter case study.