This paper deals with the control problem of a hybrid power plant consisting of six gas turbines and a battery energy storage system. The peculiarity of the plant is that it is designed to provide an ancillary service only, namely Automatic Frequency Restoration Reserve (aFRR). When the plant’s aFRR reserve capacity is not activated, the turbines remain idle (non-spinning) and are activated (spinning) only when needed during the aFRR activation. Thus, the control is responsible for switching the turbines between non-spinning and spinning reserves without affecting the quality of service. The control problem of unit commitment and subsequent economic dispatch is formulated as an optimisation problem. To ensure the robustness of the solution, the paper proposes an efficient method that prevents a non-robust solution through the use of lazy constraints. The approach is validated by experimental results using a digital twin of a real power plant, and the paper discusses the additional costs and benefits associated with the proposed robust strategy.