•The proposed method can limit equipment damage in different scenarios.•Damage can be reduced 40% with a revenue loss of less than 1%.•Different damage mechanisms in the equipment can be included in the method.•Variable uncertainty in power demand and price can be included.•Adequate selection of material design temperature reduces deterioration. Renewable energy sources have been the focal point to decarbonise the power sector. The large deployment of these intermittent power generation units requires mechanisms to balance the grid. Thermal power plants can provide this service by increasing the number of start-ups, shut-downs, and intraday ramps at the expense of higher deterioration in critical equipment, including high-pressure steam drums, turbine rotors and blades, and high-temperature heat exchangers and pipes. This work proposes a method to formulate the power generation scheduling of thermal power plants as a stochastic optimisation problem with limitations on the maximum damage in critical components. This method models the uncertainty associated with intermittent power generation from renewable sources with a scenario-tree whilst computing the deterioration of the equipment in each scenario to limit the maximum damage. Scheduling of a flexible natural gas combined cycle demonstrated how this methodology can reduce the deterioration of the superheating heat exchanger of the power plant with minimum detriment in power generation and revenue. Furthermore, the effect of the design temperature of the material on the total damage was analysed for a broad range of temperatures and operating profiles, showing how adequate selection of design temperature can reduce the deterioration of the equipment and enhance its lifetime.