There is a real need to use various efficient energy supply systems that are not aggressive with the world's environment ambient. Hydrogen has been seen in different research papers presented in the Literature as an essential fuel to generate energy in various energy storage systems. As is well known, using electrolysis, it is possible to generate renewable electricity. The hydrogen produced can be sold as fuel for various systems, most notably its use in solid oxide fuel cells and a host of modern applications today. Current low-temperature fuel cells are ideal for hydrogen operation but are not suitable for hydrogen mixtures. In this article, the mathematical analysis was carried out to generate electrical energy in a fuel cell, fed with synthesis gas from the residual biomass gasification process; our primary interest is the generation of electrical energy, we analyze solid oxide fuel cell (SOFC), which operate at the temperature of the gas at the outlet of the gasifier. We show the practical efficiency obtained and the theoretical results of the operation of the SOFC.