Gradient-based hybrid model predictive control using Time Instant Optimization for Dutch regional water systems

Abstract

Many areas in the Netherlands can be characterized as low-lying polder systems. In order to keep our feet dry, a lot of effort is put into ensuring the safety of the physical structures that protect us from flooding, such as dams and dikes. To control the water quantity and quality within the polders, hydraulic structures such as pumps and gates are in place. These can be operated to meet different requirements. Some of these structures are operated manually, but often the control has been automated. The operation of such structures is in many cases done by rule-based (if-then) operators, which base their control actions on a comparison of the current state (e.g. water levels) with the desired state. The field of operational water management aims at optimizing the control of these automated structures.Model Predictive Control (MPC) is an anticipatory control technique that originated in the process industries, and found its way into water management over the last one or two decades. This methodology uses a mathematical model of the controlled process and forecasts of future process states and external disturbances to determine the optimal sequence of control actions over a finite prediction horizon. The trade-off between different, often conflicting objectives of a controller is described mathematically in an objective function. At every time step, an optimization problem has to be solved by minimizing the objective function subject to constraints. Only the first control step is implemented, and the optimization starts again with updated measurements and predictions at the new time step.This thesis focusses on Dutch regional water systems. These systems are often low-lying polder-belt canal systems, where many pumps are needed to meet different requirements regarding water quantity and quality. The control of a complex water system, consisting of continuous dynamics (evolution of water flow and levels) and discrete elements (e.g. barriers and pumps that are operated on or off) can be optimized using a so-called hybrid Model Predictive Controller. However, particularly the optimization of the combination of discrete and continuous elements requires extensive computational effort. Even with the ongoing increase in computational power, computational time remains an issue for the optimization of large hybrid systems in real-time control applications.Time Instant Optimization MPC has been proposed in literature as an alternative to the computationally more demanding Mixed Logical Dynamical models. TIO-MPC involves the Master of Science ThesisBart Dekens ii optimization of a (a priori determined) number of time instants, which are the moments that a discrete variable changes its state. The rationale behind this approach is that in many cases, it is undesirable to have too many switching of controllers. This significantly reduces the amount of optimization variables, as the controller does not have to decide at every time step whether or not to switch the state of discrete variables. The latter would normally l...

Potential of model predictive control of a polder water system including pumps, weirs and gates

“…The second goal is an often-used end-point goal to avoid the water levels increasing in the end of the horizon. With the minimization of the pumping costs as the third goal the solutions are preferred where excess water can be discharged without 2 Suppose that the optimization problem (12) finds as optimal value p * , then the goal programming routing of RTC-Tools will add the extra constraint…”

“…[10] use stochastic model predictive control on a reservoir-pump-wind-turbine system, but the dynamics of the pumps are not taken into account. One way to overcome the heavy computational burden is to not minimize the energy used by the pumps directly, but the number of switching intervals [11] or total on-time of the pumps [12]. [13] used a similar approach for a water distribution system (modeled by system identification) in which the number of pumps turned on was minimized.…”

How to Choose Suitable Physics‐Based Models Without Tuning and System Identification for Model‐Predictive Control of Open Water Channels?

“…For instance, MPC is used to keep the water level of reservoirs within bounds by controlling releases based on inflow forecasts (Anghileri et al., 2016; Raso et al., 2019), or to optimize hydropower production (Doan et al., 2013). MPC has also been applied for controlling water quality (Aydin et al., 2016; Galelli et al., 2015) by flushing, for controlling the water level of inland waterways (Segovia et al., 2019), and in drinking water networks (Ocampo‐Martínez et al., 2009), sewer networks (Joseph‐Duran et al., 2015), irrigation systems (Fele et al., 2014; Hashemy Shahdany et al., 2012) and drainage systems (Dekens, 2013; Horváth et al., 2019).…”

Convex Modeling of Pumps in Order to Optimize Their Energy Use

“…Dorini et al () describes convex modeling and optimization of pumps, supposing they are always on. Another way to reach the optimum without having to solve a mixed‐integer problem is to use time as the optimization variable to determine the start and length of the pump operation (Dekens et al, ; Price & Ostfeld, ). This approach provides a mathematical solution to the problem that leads to global optimum; however, it becomes very complex when it is combined with other elements of the water system, because the objective of the other elements might not be expressible using time as optimization variable.…”