Dynamic modelling and control system development of a Brayton-based Carnot battery: Impact of thermal energy storage–induced delays

Carnot batteries are increasingly investigated as a promising solution for large-scale electricity storage. As power systems increasingly rely on intermittent renewable energy sources, the load-regulation capability of Carnot batteries becomes essential. Yet, their dynamic response and controllability under rapid power transients remain largely unexplored in the literature. This work presents a comprehensive dynamic modelling framework for a Brayton-based Carnot battery, together with the development of a dedicated control system. A high-fidelity dynamic model is implemented in the Modelica language, accounting for shaft dynamics, actuator behaviour, and fluid-dynamic propagation delays introduced by the thermal energy storage. The control system is progressively developed, ranging from conventional proportional-integral and proportional–integral–derivative controllers to advanced architectures incorporating anti-windup protection, Smith predictor-based delay compensation, and reference shaping. The model is validated against reference results from the literature, and a sensitivity analysis highlights the critical influence of rotational inertia and actuator dynamics on transient performance. In addition, a statistical correlation is proposed to estimate the inertia coefficient of Brayton-based systems as a function of rated power. Results indicate that, when coupled with an optimised control system, a 10 MW Carnot battery can increase its output from 60% load to full load in approximately 6.2 s, exhibiting a power undershoot and overshoot of 10% and 1.8%, respectively, while keeping the frequency deviation below 6%. These results show that Brayton-based Carnot batteries can provide fast and stable power regulation, provided that thermal-energy-storage-induced delays are explicitly considered in the control system design.