System reduction of optimal control problems with seasonal storage
The control and structural expansion of decentralized energy systems are very challenging due to the volatility of renewable energies and progressive structural changes. For balancing out seasonal fluctuations, conversions into heat or gas in combination with seasonal storage are frequently discussed approaches. In context of an optimal conceptual synthesis of such systems, investigations regarding the operation and design require a large time period of at least one year. In order to solve such optimal control problems, an immense calculation time is required. This contribution presents a multistep approach which determines the optimal operation strategy in an iterative way and is capable of reducing the calculation effort. In the first step, a rough optimization incorporating a low modeling depth is performed. Especially in combination with a rough time discretization, dynamic short-term storage (e.g. electrical batteries) can become irrelevant from an optimization point of view. Therefore, the considered system can be virtually reduced by several state and control variables resulting in a significantly reduced computation time. In this contribution, a method to analyze optimal control problems with respect to this kind of system reduction is presented. Using the results of the first optimization, a second fine optimization is performed to solve the full optimal control problem. While in the first step, the dynamic programming is utilized to solve the optimal control problem in one instance, the second step uses the mixed integer linear programming to solve multiple short time periods of the optimal control problem in a sequential way.