Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

In this paper a mixed integer linear programming (MILP) model is developed to facilitate the design of a solar domestic hot water system. The MILP model does so by optimising the area of roof mounted flat plate solar thermal collectors and the volume of thermal energy storage that are required to minimise the annual capital and operational cost of the overall energy system. A new formulation of the MILP is presented in which the model is decomposed into two sub-modules that are iteratively solved. One module determines the optimal sizing of the solar thermal collectors and storage tank. The other module optimises the hourly energy production of the solar collectors based on the impact that the collector inlet stream temperature has on the collector efficiency. This iterative formulation is compared to both a conventional MILP formulation and a dynamic simulation model to determine if the iterative formulation results in a design tool that is able to accurately represent the dynamic behaviour of a solar domestic hot water system, while maintaining the computational tractability and scalability of the model. The novel iterative MILP formulation is applied to a case study of an apartment building in Rheinfelden, Switzerland. The results indicate that conventional MILP formulations overestimate the amount of energy that solar thermal collectors are able to produce, resulting in an oversizing of the required thermal storage tank. However, the iterative MILP model more accurately predicts the energy production of the solar collector, leading to the more realistic sizing of the component technologies. This result is important when evaluating the financial feasibility of solar thermal collector systems in comparison to other renewable generation technologies, as an overestimation of the generation potential of solar thermal collectors may result in an incorrect assessment of their investment attractiveness.