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Because the optimal operation trajectory obtained under a fixed freshwater demand and known operational conditions could not achieve cost savings when these parameters change uncertainly over time, in this paper, a real time operational optimization method based on rolling prediction of hourly freshwater demand is proposed. First, via analysis of the historical data of hourly water consumption in a seawater desalination system, a new method for predicting the daily water demand in the next 24 h is proposed, and the predicted trajectory is continuously corrected and updated with present freshwater consumption. Then, with the well-established seawater desalination system model combined with the dynamics of a storage tank, a real time optimal operational problem with the strategy for its solution is given to minimize the daily operational cost. The optimization problem with differential and algebraic equations is discretized into a nonlinear programming problem by finite element collocation, and then a rolling optimization solution strategy based on simulation is used. Finally, a case study is used to verify the proposed method. The results show that the proposed optimal operation method can achieve significant cost savings and can also overcome the water level violation problem under a fixed freshwater demand or via the conventional method.

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The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.