An analysis of an LQR design for a hybrid power plant’s load-sharing problem

This paper analyzes the design of a Linear Quadratic Regulator (LQR) for a hybrid power plant providing Frequency Containment Reserve (FCR). The analysis focuses on the selection of the LQR’s weighting coefficients aiming to achieve the highest possible turbine stress reduction by distributing the hybrid plant’s gross power between a turbine and energy storage. In this study, the LQR was formulated to approximate the constrained optimization problem related to load sharing. To find the weighting coefficients of the LQR, an approach is presented that utilizes the optimal solution of the load-sharing problem. The evaluation revealed that the weight selection principle can be presented in an analytic form containing the important parameters related to the hybrid plant operation. The analytic solution was validated with numerical methods. The simulations verified that the best attainable turbine stress reduction can be obtained with the proposed design.