## 1 Introduction  
Biogas is a relevant component of an increasingly renewable energy system in many countries. Biogas plants feature some specific properties compared to other renewable energy plants such as flexible provision of electricity and heat by gas storage, or possible contribution of energy to the transport sector. With anaerobic digestion (AD), the main transformation process from organic matter to biogas is a biological one. The complex processes of hydrolysis, acidogenesis, acetogenesis, and methanogenesis are well known and described [1]. AD works with various types of organic feedstock, such as municipal sludge from wastewater treatment plants, municipal solid waste, animal waste, algae, or energy crops. Some of those are constantly available, while others are subject to regional and seasonal restrictions. Main product of the anaerobic digestion is biogas, primarily methane and carbon dioxide (CO\({}_{2}\)). The side product is a nutrient-rich digestate. Biogas can be converted to different energy products, such as heat (by combustion), electricity and heat (combined heat and power plant: CHP), electricity (by turbines), natural gas (by the separation of CO\({}_{2}\)), or fuels (e.g., by increasing the methane fraction or CO\({}_{2}\)-assisted catalytic reforming) [2]. A common pathway for the energetic use of biogas is electricity and heat production in a CHP. The focus in many countries lies on the production of electricity. In Germany, for instance, the privileged feed-in of renewable electricity from biogas CHPs is regulated by the Renewable Energy Act [3]. In comparison to other renewable energy sources, electricity production from biogas is not weather-dependent. biogas plants can produce electricity flexibly according to demand, by utilizing the possibility of storing feedstock and biogas [4]. This provides a distinguished role for biogas plants in the energy sector. Furthermore, biogas can also participate in the supply of heat and fuel where the share of renewable energies, for example, in Germany, it is much lower than for electricity. The shares of renewable energies for electricity, heat, and transport in Germany in 2019 were 37.8, 13.9, and 5.6%, respectively [5]. Biogas plant operation needs continuous monitoring and process control because the AD process is based on microbiological activities that require a complex biocenosis of different microorganisms. This is where process modeling comes into focus. Biogas process modeling was originally developed for the prediction of possible biogas yields and optimization of the AD process (e.g., [6; 7; 8]), as well as for process control and staff training (e.g., [9; 10]). Those models--often assigned to the water sector--focus on a very detailed description of microbiological transformation. Early papers on AD modeling, for instance, go back to the 1970s [11; 12; 13]. Since 2002, the anaerobic digestion model (ADM1) has been a commonly used tool to model physical and biological processes within biogas fermenters. Biogas plants in energy systems are mostly investigated from an agricultural or energy economical point of view. Energy system modeling often regards biogas plants as black box models. They basically tend to be included as gas storage combined with a CHP unit (e.g., [14]). The modeling of biogas plants within future energy systems with high shares of renewable energies needs to look further into the biological process, though, in order to answer new questions due to the dynamic nature of energy supply and demand, such as:  
* How can electricity production be adjusted to electricity demand profiles? * How can biogas plants contribute to energy sector coupling? * Which pathway of biogas exploitation is most beneficial for the energy system? * Which pathway of biogas exploitation offers a business model for the operator?