Simulation and Optimization of Gas and Water Supply Networks

Beschreibung

In this work, we consider the simulation and optimization of gas and water supply networks. In particular, we are dealing with the daily operation of both types of networks. First, we describe a mathematical model for gas and water supply networks, which consists of partial and ordinary differential equations as well as algebraic equations. Supplemented with initial and boundary conditions, these can be solved by applying appropriate discretization schemes. For this purpose, we have developed a software framework for problems on networks, which allows the application of different schemes for each type of equations and which takes care of the correct coupling. A matter of particular importance is the treatment of the underlying hyperbolic partial differential equations. Here, we apply an implicit box scheme as well as explicit central schemes. For both methods, we give a profound stability analysis in a well-known setting. The next step after the solution of simulation tasks is the computation of sensitivity information. Here, we follow an adjoint approach. The resulting gradient information can directly be applied in three state-of-the-art optimization tools, for which we provide interfaces in our software. In practice, the optimization tasks in the daily operation of gas and water supply networks also involve discrete decisions for switching certain network elements on or off. To handle mixed integer problems, we follow two approaches. First, we present a heuristic penalization strategy, and secondly, we have developed an adaptive linearization technique for the treatment of the underlying nonlinear problems with mixed integer linear programming methods. Finally, numerical results for a real-life gas and water supply network are presented as well as for a representative test network provided by one of our industry partners.
In this work, we consider the simulation and optimization of gas and water supply networks. In particular, we are dealing with the daily operation of both types of networks. First, we describe a mathematical model for gas and water supply networks, which consists of partial and ordinary differential equations as well as algebraic equations. Supplemented with initial and boundary conditions, these can be solved by applying appropriate discretization schemes. For this purpose, we have developed a software framework for problems on networks, which allows the application of different schemes for each type of equations and which takes care of the correct coupling. A matter of particular importance is the treatment of the underlying hyperbolic partial differential equations. Here, we apply an implicit box scheme as well as explicit central schemes. For both methods, we give a profound stability analysis in a well-known setting. The next step after the solution of simulation tasks is the computation of sensitivity information. Here, we follow an adjoint approach. The resulting gradient information can directly be applied in three state-of-the-art optimization tools, for which we provide interfaces in our software. In practice, the optimization tasks in the daily operation of gas and water supply networks also involve discrete decisions for switching certain network elements on or off. To handle mixed integer problems, we follow two approaches. First, we present a heuristic penalization strategy, and secondly, we have developed an adaptive linearization technique for the treatment of the underlying nonlinear problems with mixed integer linear programming methods. Finally, numerical results for a real-life gas and water supply network are presented as well as for a representative test network provided by one of our industry partners.

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Oliver Kolb

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