The paper provides an economic model for the assessment of hydrogen production at the site of an existing thermal power plant, which is then integrated into the existing gas grid. The model uses projections of electricity prices, natural gas prices, and CO2 prices, as well as estimates of the cost of building a power-to-gas system for a 25-year period. The objective of this research is to calculate the yellow hydrogen production price for each lifetime year of the Power-to-gas system to evaluate yellow hydrogen competitiveness compared to the fossil alternatives. We test if an incentive scheme is needed to make this technology economically viable. The research also provides several sensitivity scenarios of electricity, natural gas, and CO2 price changes. Our research results clearly prove that yellow hydrogen is not yet competitive with fossil alternatives and needs incentive mechanisms for the time being. At given natural gas and CO2 prices, the incentive for hydrogen production needs to be 52.90 EUR/MWh in 2025 and 36.18 EUR/MWh in 2050. However, the role of hydrogen in the green transition could be very important as it provides ancillary services and balances energy sources in the power system.