Integrating new technologies into existing thermal energy systems enables multigenerational production of energy sources with high efficiency. The advantages of multigenerational energy production are reflected in the rapid responsiveness of the adaptation of energy source production to current market conditions. To further increase the useful efficiency of multigeneration energy sources production, we developed an exergoeconomic machine-learning model of the integration of the hydrogen thermochemical Cu–Cl cycle into an existing gas-steam power plant. The hydrogen produced will be stored in tanks and consumed when the market price is favourable. The results of the exergoeconomic machine-learning model show that the production and use of hydrogen, in combination with fuel cells, are expedient for the provision of tertiary services in the electricity system. In the event of a breakdown of the electricity system, hydrogen and fuel cells could be used to produce electricity for use by the thermal power plant. The advantages of own or independent production of electricity are primarily reflected in the start-up of a gas-steam power plant, as it is not possible to start a gas turbine without external electricity. The exergy analysis is also in favour of this, as the integration of the hydrogen thermochemical Cu–Cl cycle into the existing gas-steam power plant increases the exergy efficiency of the process.