Model Predictive Control applied to the Dutch delta, a probabilistic safety analysis

Abstract

As many areas in The Netherlands are located below or slightly above mean sea level, or adjacent to large rivers, a lot of effort is put into ensuring the Dutch keep dry feet. The prevention of flooding is the most important and internationally well-known layer in the Dutch water safety policy. Nowadays this takes place by means of taking physical measures, i.e. making sure flood defences (e.g. dikes, barriers) are of adequate height and strength, or allowing enough space for the river to store water in case of extreme discharges. Though very robust, taking physical measures for flood prevention is generally also very expensive. Another method to prevent flooding, currently hardly applied in The Netherlands, is anticipatory: the optimization of the control of the large (controllable) flood defence structures in the Dutch water system. This is explored in this thesis in the form of the application of Optimal Control, which utilizes Model Predictive Control. This is the only control method which can deal with large interconnected systems, anticipation on predictions, conflicting goals, and constraints. It is a methodology that originates in the process industries and is throughout the world applied to all sorts of systems and processes. More recently it has found its way into water management. A major benefit of this method is that the costs of realisation, operation and maintenance of such a system are estimated to be orders of magnitude lower than taking (extensive) physical measures. In previous studies the influence of the application of Model Predictive Control on the water safety in The Netherlands has been determined for specific cases. However, a probabilistic analysis, which can provide a more complete picture of the profit of this technology in general, i.e. the effect on overall system behaviour, and is required by Dutch law for any measure in order to be considered a potential solution for safety against flooding, has not been possible thus far. In this research a computing platform which allows for parallel calculation is used which makes this analysis possible. In this research, a model framework has been set up allowing for such a probabilistic water safety analysis of The Netherlands using Model Predictive Control. This framework consists of: - a high resolution Sobek Rural model of the rivers, lakes and estuaries of The Netherlands (LSM) which is used to simulate the real world; - Optimal Control in Matlab, which includes an internal model, an objective function and constraints; - Hydra-Zoet probabilistic model to account for the probabilistic analysis. During this research improvements and adaptations have been made to the models used. Using this framework the probabilistic approach has been followed in order to determine the effect of the application of Model Predictive Control. Additionally five structures, selected considering existing plans for the water system and the effect these structures can have on the water distribution, have been added to these models to further investigate possibilities within the system. The effect of Model Predictive Control in this research is determined largely by a minimization of the objective function which includes many locations, structures and goals, each made explicit by weights set in the controller. Before results could be obtained, an iterative process (trial and error) has been gone through in order to determine a best suiting set of weights to be used for this research. The required model calculations for the probabilistic analysis used in this research consist of a limited set of 108 calculations determined by previous research of HKVLIJN IN WATER, these are considered to be representative for the overall system behaviour. This set consist of nine river discharge levels, combined with six storm levels combined with possible (dependant) failing of the Maeslant barrier and Hartel barrier. What can be concluded from the results is that, when applying Optimal Control, clear effects can be expected in certain cases, while in other cases differences with current control are minimal. As a result, the effect on the overall system behaviour (normative water levels) is minimal as all scenarios are considered and effects are levelled out. In the upper rivers water system no differences can be observed as in this water system (almost) no structures exist to influence the water distribution. When the new structures are added to the model, more extensive differences can be observed. The effects of these structures are clear when considering individual cases, however the results in terms of differences in normative water levels are not in line with results obtained from individual cases. More detailed inspection of the results obtained from different parts in the model framework revealed some inconsistencies in the outcomes of the Sobek-calculations, which are probably the cause of the deviating results in terms of normative water levels. Due to the complexity of the model framework and enormous amount of data output such inconsistencies can be easily overlooked. Considering this the results displayed in this research should not be considered representative for the differences in overall system behaviour when the new structures are added to the system. Possibly some inconsistencies still exist for the calculations with current control and Optimal Control without new structures as well. Recommendations have been made for improvements of the model framework and further research, most importantly the addition of the new structures to the objective function.