Ash accumulation is a relevant problem due to the widespread use of coal-fired power plants and a very limited number of ash utilization technologies. Plasma processing of ash is a promising method of ash valorization for production of various useful products, which is limited by high energy consumption. In the current study, a mixture of waste ash from power plant and black carbon was processed using an original direct current plasma arc experimental setup in ambient air which allows lower energy consumption due to the absence of the vacuuming system. Four types of samples at different plasma exposure times were produced and together with the initial ash were studied by thermal analysis, X-ray diffractometry and scanning electron microscopy. The X-ray diffraction analysis identified the resulting phases of graphite, silicon carbide, and aluminum nitride in the synthesis products; at the same time, at the arc discharge energy increased from 26 to 105 kJ, the intensities of the maxima that correspond to metal and nonmetal oxides in the composition of the initial ash decreased to nearly zero. To remove graphite, the processed samples were annealed at 750 °C in air and studied. It was found that the applied approach made it possible to obtain a mixture of silicon carbide and aluminum nitride powders in direct current arc plasma initiated in ambient air, which reduced the energy consumption for ash processing by electric arc.