Optimal planning of thermal energy systems in a microgrid with seasonal storage and piecewise affine cost functions

Abstract

The optimal design of microgrids with thermal energy system requires optimization techniques that can provide investment and scheduling of the technology portfolio involved. In the modeling of such systems with seasonal storage capability, the two main challenges include the low temporal resolution of available data and the non-linear cost versus capacity relationship of solar thermal and heat storage technologies. This work overcomes these challenges by developing two different optimization models based on mixed-integer linear programming with objectives to minimize the total energy costs and carbon dioxide emissions. Piecewise affine functions are used to approximate the non-linear cost versus capacity behavior. The developed methods are applied to the optimal planning of a case study in Austria. The results of the models are compared based on the accuracy and real-time performance together with the impact of piecewise affine cost functions versus non-piecewise affine fixed cost functions. The results show that the investment decisions of both models are in good agreement with each other while the computational time for the 8760-h based model is significantly greater than the model having three representative periods. The models with piecewise affine cost functions show larger capacities of technologies than non-piecewise affine fixed cost function based models.