Model of a Power-to-Gas System with Fuel Cell in a Mixed Integer Linear Program for the Energy Supply of Residential and Commercial Buildings

Abstract

In the field of energy supply for residential and commercial buildings, the optimal operation,system configuration and sizing of generation as well as storage technologies are essential stepsfor cost-efficient investments. In current research, flexibility options for electricity from growing renewableenergies attract attention. One of the considered options is the power-to-gas technology incombination with fuel cells. Linear Programs for optimal system operation exist for example for distributedenergy systems. In this study we propose a Mixed Integer Linear Program of a power-to-gasunit consisting of an electrolyzer, a fuel cell and a hydrogen storage. For the fuel cell a minimum loadand a non-linear efficiency curve is taken into account. The non-linear efficiency curve is approximatedby piecewise linearization. Bilinear products in the modeling of the efficiency curve are beingsubstituted to maintain full power plant sizing and operation functionality. Different fuels, such as naturalgas and hydrogen to be converted in the fuel cell, are implemented as well. As a result, we showthat a detailed model of the non-linear efficiency curve of a fuel cell leads to more accurate results concerningthe system operation. The configuration of system components in the observed energy systemchanges. Especially the battery system experiences a change in sizing and operation. However, solvingtime of the model is increasing dramatically. Our results demonstrate a valuable approach to comparethe results of a Linear Program to a Mixed Integer Linear Program. Hence giving the possibility toevaluate the necessity of detailed over simplified models regarding calculation of cost-effectiveness.