Thermal Stress Control of a Two-Stage Steam Turbine System via Efficient NMPC Strategies

Steam turbines are one of the key components of thermal power units, and any additional improvement in their efficiency has an important economic significance. In the case of concentrated solar plants, the steam turbines experience rapid fluctuations in working conditions as they are subject to multiple start-ups that lead to considerable thermal stress in the rotor region. A two-stage system, comprised of a series of a high-pressure (HP) and a low-pressure (LP) turbine, is here investigated and optimized. The proposed nonlinear model predictive control (NMPC) algorithms have a two-fold objective, that is, the optimal regulation of the total generated electric power and the simultaneous limitation of thermal stress on both turbines. The proposed formulations incorporate time-varying constraints and nonlinear disturbances that fluctuate within the prediction horizon of the controller's dynamic module. A suitable collocation method is derived and compared with a traditional multiple-shooting approach. The adoption of slack variables is also investigated, but the peculiar benefits prove to be negatively compensated by higher computational times. As a final result, the collocation method without slacks demonstrates the most efficient solution to solve the considered optimal control problem.