Atmospheric pressure cold plasmas have recently been the subject of intense research and applications for solving problems in the fields of energy, environmental engineering, and biomedicine. Non-thermal atmospheric pressure plasma sources, with dielectric barrier discharges, plasma jets, and arc discharges, are non-linear power loads. They require special power systems, which are usually designed separately for each type of plasma reactor, depending on the requirements of the plasma-chemical process, the power of the receiver, the type of process gas, the current, voltage and frequency requirements, and the efficiency of the power source. This paper presents non-linear phenomena accompanying plasma generation in the power supply plasma reactor system, such as harmonic generation, resonance, and ferroresonance of currents and voltages, and the switching of overvoltages and pulse generation. When properly applied, this can support the operation of the above-mentioned reactors by providing improved discharge ignition depending on the working gas, thus increasing the efficiency of the plasma process and improving the cooperation of the plasma-generation system with the power supply.