Well-functioning electricity systems are today crucial for maintaining essential functions such as healthcare, communication and water supply. Swedish electricity networks have long been stable and grid outages are rare, where the dependence on safety nets in the form of backup power plants has not been as great as in many other countries in the world. Unfortunately, there are several reports that paint a picture where more frequent extreme weather and increasingly stressed electricity networks could give rise to the need for more robust backup power plants.  Today, most of these plants are fossil-fueled, but with increasing environmental demands and technological advances, interest in more sustainable alternatives has increased significantly. One of these new plants is hybrid systems, which rely on multiple energy sources working together to provide plants with electricity, both in emergencies and in daily operations. However, their practical application also involves several electrotechnical challenges that need to be solved.  The purpose of this study was to analyze and model a hybrid system intended for backup power consisting of a Fuel Cell and a battery system, with a focus on its regulation and implications they entail, regarding voltage quality, response time and stability. The work was carried out in Simulink/Matlab, where a detailed model of a fuel cell-based hybrid system was constructed and simulated in several different operating scenarios.  The results showed that a well-dimensioned hybrid system could deliver stable voltage and frequency within applicable standards under both sudden and varying loads. The fuel cell showed surprisingly good performance while the battery system handled fast effects and improved the system's response time. At the same time, several challenges were encountered during the work that needed to be solved in each approach.   The study underlined the importance of not only assessing backup power systems by nominal effects, but also examining their dynamic behavior, control strategy and intended operating range.