Cogeneration sources play a very important role in the power industry with dispersed renewable sources with forced generation (e.g., photovoltaics and wind generators). They also fit into the circular economy by increasing the efficiency of fuel use, including biogas from agricultural or livestock waste. The aim of our research was to develop an effective source of electricity powered by agricultural biogas. The most important features of such a source are: operation in on-grid and off-grid mode, as well as a low cost of the device and uncomplicated operation. In addition, in Europe, the source of electricity connected to the power grid must meet the technical requirements of the “Network Codes Requirements for Generators” (NC RfG) network code. The appropriate certificate is easier to obtain using a power converter system for the source. For this purpose, an induction generator with a converter system and a small battery was planned. A converter system was developed and built, and then tests were carried out in various operating modes. During the measurements, it was confirmed that the requirements for the quality of electricity for off-grid and on-grid operation modes were met. The assumed maximum time of voltage recovery after changing the operating mode, amounting to 40 ms, was not exceeded. Furthermore, the limit values of phase voltages with unsymmetrical load, amounting to ±10% of the rated voltage, were not exceeded. In the battery usage off-grid mode, the time after a step change in the load power was not longer than 2 s.