Model predictive approaches for real-time reservoir flood control under uncertainty

Abstract

Climate change is making flood prediction and management increasingly important. In 2020, South Korea suffered severe flood damage in areas downstream of multipurpose reservoirs, primarily due to unexpected heavy rainfalls occurring in quick succession. All multipurpose reservoirs in Korea are managed by K-water, which follows an operating procedure that analyzes scenarios using real-time observation data and weather forecasts. Although there are existing operating rules, these rules are often based on common-sense practices that can be bypassed in critical situations, allowing decision-makers to adjust reservoir operations flexibly based on Flood Water Level (FWL), Flood season Restricted Water Level (FRWL), and Normal High Water Level (NHWL). This method works well when flood predictions are accurate or when experienced decision-makers are present. However, accurate rainfall prediction remains a challenge. Thus, systematic and model-based approaches are necessary to help determine water release amounts, especially when rainfall forecasts have high uncertainty.

Real-time reservoir flood control has traditionally relied on simulation models, but time constraints often prevent the review of extensive scenarios, potentially missing optimal and explicitly risk-aware options. While optimization approaches offer alternatives, practical implementation faces several challenges. First, operational objectives are rarely specified clearly in legal/operational guidelines, and when expressed as nonlinear formulas, the problem becomes computationally intractable. Second, operators' preferences regarding the relative importance of objectives change with flood conditions. Multi-objective optimization approaches that generate Pareto fronts could help visualize the trade-offs between competing objectives, but generating these Pareto sets at each time step requires optimizing the parameters that capture these dynamic preferences and system constraints. To address these challenges, a Model Predictive Control (MPC) framework incorporating practical objectives often overlooked in theoretical studies, such as minimizing the magnitude and frequency of changes in outflow schedules, is presented. We integrate a model-based learning concept for dynamic optimization of weights and parameters, which converts the originally intractable multi-objective nonlinear optimization problem into parameterized linear MPC problems.

However, system nonlinearity combined with these dynamic preferences results in optimization problems that are still computationally expensive and impractical during rapidly evolving flood events. Due to the computational challenges of real-time operation of Parameterized Dynamic Model Predictive Control (PD-MPC), we propose two data-driven approaches: (1) an explicit MPC using deep neural networks to directly determine optimal outflow schedules, and (2) a switched MPC that combines data-driven models that produce optimal weights based on hydrological conditions with linear MPC. Both methods leverage offline learning from the PD-MPC framework to dramatically reduce computation time from approximately 10 minutes to less than one second, enabling prompt decision-making during rapidly evolving flood events. The explicit MPC demonstrates reliable performance for conditions similar to its training data, while the switched MPC maintains robustness across diverse scenarios due to its receding time horizon optimization process.

Although the above approaches work well as deterministic control tools, more advanced stochastic optimization-based MPC can offer ways to explicitly handle uncertainty. Uncertainty management with stochastic control requires the generation of a sufficiently large number of representative scenarios for inflows. However, traditionally used scenario generation models struggle to capture temporal dependencies or generate scenarios without requiring explicit probability distributions. From this perspective, a Bayesian Neural Network (BNN) model can successfully capture temporal dependencies in inflow time series with high accuracy for short prediction horizons, without requiring explicit probability distributions of variables to be known in advance. Although we can generate a large number of required scenarios with a BNN to assure we sufficiently represent the uncertainty in inflow, it would make stochastic optimization difficult as computational time scales nonlinearly with the number of scenarios. We therefore need scenario reduction approaches that preserve representativeness while reducing the number of scenarios significantly. However, existing scenario reduction approaches themselves lack appropriate distance measures optimally suited for hydrological applications. Therefore, this thesis investigates four distance measures with corresponding reduction algorithms, which are widely used in references: Manhattan with the K-median, Euclidean with the K-mean, Wasserstein with a one-step forward selection, and energy distances with a one-step forward selection algorithm. While the energy distance best preserves statistical characteristics of the original scenario set, the Euclidean distances have significantly lower computational costs. Additionally, the Manhattan and Euclidean distances retain extreme scenarios, which is crucial for flood control, in terms of a tailored performance measure that represents the size of the envelope of a scenario set (using l1-norm), ensuring the reduced sets retain the range of maximum and minimum flows of the original scenarios.

Finally, this thesis combines these advanced scenario reduction methods to define a risk-constrained MPC problem using Conditional Value-at-Risk (CVaR) to reflect changes in operator risk-averseness by changing a confidence level. Traditional chance constraints in stochastic MPC only consider exceedance probability, while CVaR, which quantifies the expectation of exceedance, remains underutilized in reservoir flood control despite its proven value in risk minimization. By incorporating CVaR as soft constraints, operators can specify risk thresholds that reflect practical considerations rather than relying solely on physical limits that are rarely activated during typical flood events. A stochastic MPC with CVaR outperforms a deterministic counterpart in terms of reflecting the operator's risk-averseness and robustness to inflow uncertainty. Moreover, scenario reduction based on the Euclidean distance is more effective than energy distance-based reduction for real-time flood control applications, considering both closed-loop performance and computational efficiency.
Each proposed framework is validated through numerical experiments for the Geum River and Daecheong Reservoir in South Korea. Intractability in a nonlinear multi-objective optimization problem due to dynamic preferences can be effectively addressed by a PD-MPC framework and its explicit and switched extension based on data-driven models. In addition, stochastic MPC with CVaR incorporating scenario generation and reduction proves beneficial for managing hydrological uncertainty and operators' risk-averseness. We believe the proposed approaches offer sufficient flexibility to accommodate region-specific constraints and objectives, suggesting their potential utility for addressing water resource management challenges in diverse geographical contexts. We anticipate this research will contribute to expanding the application possibilities of real-time optimal reservoir flood control and lay the foundation for practical implementation. The presented methodology is not intended to replace manual operation but rather to provide tools for reducing operator stress in critical situations and ultimately enhancing decision-making capabilities.