Reducing greenhouse gases (GHG), especially CO2, is necessary to counteract climate change. The European steel industry currently corresponds to 5.7% of the total EU emissions and must therefore minimize their GHG fractions in the future. One of the most promising technologies to eliminate CO2 emissions while directly reducing iron ore to steel in a single step is the hydrogen plasma smelting reduction. The stability of the plasma arc, which is determined by the properties and geometry of the graphite electrode, has a substantial impact on the process’ economic feasibility. To study the arc stability concerning the graphite quality, tip geometry, and electrode gap, a series of experiments is conducted. The results are evaluated to create stability maps and fields to identify stable process parameters. The geometry of the graphite cathode shows the primary influence on arc stability. Tips with a flat end (standard version) offering the most unstable and a machined step on the graphite cathode providing the most stable conditions. However, an additional coating to prevent side arcing leads to the deterioration of the arc. The two graphite grades tested, with different maximum grain sizes and price classes, show no great relevance to the stability of the arc.