Dealing with various sources of uncertainty in the operational control of water systems using ensemble based MPC with convex optimization

Model Predictive Control (MPC) can be an effective tool for the operational control of water systems, but there are still many open questions about how this technique can effectively take into uncertainties of forecasts, initial states or the model setup. Moreover, computational cost and robustness often prohibit the use of existing methods in practice. We here report recent developments in the open source RTC-Tools software framework that allow representing these uncertainties through ensembles and computing the optimal control strategy with convex optimization techniques in combination with lexicographical goal programming. Convex optimization is required to have robust mathematical solutions within the short computation times that are feasible in operational practice. Goal programming is here used to facilitate straightforward optimization of competing objectives with results understandable for end-users. Adaptations of Raso’s Tree-Based MPC (e.g. Raso et al., 2014) are used to represent the possibilities offered in future control steps, permitting a realistic moving horizon control strategy while not being excessively conservative.

The developments are illustrated with applications in different water systems using methods for convex optimization of linear Mixed Integer problems as well as quadratically constrained problems with both open source and commercial solvers. We also demonstrate how RTC-Tools build-in methods can be used for linearization of system equations and objectives. The applications were evaluated in controlled experiments to learn about strengths and weaknesses in comparison with other ensemble and deterministic MPC methods.

Exploration of the added value of selected uncertainty representation techniques within MPC solutions is presented in a separate contribution (Smoorenburg et al. 2020, session HS4.3 “Ensemble hydrological forecasting: Decision making under uncertainty”).

Raso, L., D. Schwanenberg, N. C. van de Giesen, and P. J. van Overloop. 2014. “Short-Term Optimal Operation of Water Systems Using Ensemble Forecasts.” Advances in Water Resources 71 (September): 200–208.