# (522f) Benchmarking Stochastic and Deterministic MPC: A Case Study in Stationary Battery Systems

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Wednesday, November 13, 2019 - 2:05pm-2:24pm

In this work, we make the observation that certain types of disturbances cannot be adequately represented using summarizing statistics (e.g., most likely realization) and this can induce inconsistencies in the computation of the MPC control action. For instance, for a disturbance signal with zero mean or a discrete (e.g., ON/OFF) disturbance signal, the most likely realization will lead to misleading forecasts. To capture such disturbances, it is necessary to use an explicit characterization of the uncertainty space in the MPC formulation. In this work, we present a stochastic MPC framework that can capture diverse types of uncertainty characterizations [6]-[8]. We consider the scenario-based, two-stage stochastic MPC formulations that provide computational flexibility and achieve significant benefits over deterministic MPC. In a two-stage stochastic MPC, uncertainty of the disturbances is captured when computing the next immediate control action, and uses a receding horizon implementation to include new information and update the uncertainty description [9].

We present a computational framework that integrates disturbance forecasting, uncertainty quantification, and MPC to provide a critical assessment of deterministic and stochastic MPC [10]. Our framework focuses on a case study of the management of stationary battery systems providing frequency regulation (FR) services to the power grid while simultaneously mitigating peak monthly demand charge costs of a university campus [9],[10]. Real disturbance data and a rigorous benchmarking procedure are used to systematically compare performance of deterministic and stochastic MPC policies. We show that that FR dispatch signals from the power grid, which are zero-mean random signals (like white noise), cannot be properly captured by deterministic MPC formulations, and this results in ineffective control actions causing constraint violations and losses in performance. In a deterministic MPC, a back-off term that allocates battery reserve capacity can prevent the constraint violations, but this approach is ad hoc and prevents full utilization of the battery asset and thus decreasing its value. This indicates that feedback alone is insufficient to counteract certain types of disturbances. Stochastic MPC provides a more systematic framework to account for diverse disturbances, satisfy constraints, and maximize asset utilization and value. We show that stochastic MPC provides significant benefits over deterministic MPC in such cases. We also derive a quasi-stochastic MPC formulation using a coarse representation of the uncertainty space, and we show that this simple approach already avoids most of the limitations of deterministic MPC while decreasing the computational complexity of stochastic MPC.

References:

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[9] Kumar, R., Wenzel, M.J., Ellis, M.J., ElBsat, M.N., Drees, K.H. and Zavala, V.M., 2018. A stochastic model predictive control framework for stationary battery systems. *IEEE Transactions on Power Systems*, *33*(4), pp.4397-4406.

[10] Kumar, R., Jalving, J., Wenzel, M.J., Ellis, M.J., ElBsat, M.N., Drees, K.H. and Zavala, V.M., 2019. Benchmarking stochastic and deterministic MPC: A case study in stationary battery systems. *AIChE Journal*, p.e16551.