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


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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.



Edited by:

Jörg Franke, Sven Kreitlein, Gunther Reinhart, Christian Gebbe, Rolf Steinhilper and Johannes Böhner




N. Ebell et al., "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", Applied Mechanics and Materials, Vol. 871, pp. 11-19, 2017

Online since:

October 2017




* - Corresponding Author

[1] D. I. W. Berlin, Stromüberschüsse aus Wind- und Solarkraft sind ein lösbares Problem, (2013).

[2] BMWi, Energiekonzept für eine umweltschonende, zuverlässige und bezahlbare Energieversorgung, (2010).

[3] C. Milan et al., Modeling of non-linear CHP efficiency curves in distributed energy systems, in: Applied Energy, volume 148, (2015), pp.334-347.

[4] T. Beck et al., Optimal operation, configuration and sizing of generation and storage technologies for residential heat pump systems in the spotlight of self-consumption of photovoltaic electricity, in: Applied Energy, volume 188, (2017).


[5] G. F. Schneider, Optimization of Distributed Energy Supply Systems by Branch-and-Price, Englisch, Masterthesis, Aachen: RWTH Aachen, (2014).

[6] Integriertes Energetisches Quartierskonzept Stadt Langenhagen Wiesenau, tech. rep., Stadt Langenhagen, (2013), p.185.

[7] PVWatts, ඎඋඅ: http: /pvwatts. nrel. gov.

[8] T. Beck et al., Assessing the influence of the temporal resolution of electrical load and PV generation profiles on self-consumption and sizing of PV-battery systems, in: Applied Energy, volume 173, (2016), pp.331-342.


[9] B. Maschler, A. Bott, Generation of coherent, synthetic thermal and electric load profiles for residential and non-residential buildings in Germany, Internal Research Study 4664, Robert Bosch GmbH, (2016), p.125.

[10] ix35 Fuel Cell - Hyundai Motor Deutschland GmbH, ඎඋඅ: http: /www. hyundai. de/Modelle/ Alle-Modelle/ix35-Fuel-Cell. html.