Minimum loss optimization of flywheel energy storage systems via distributed adaptive dynamic programming

In this article, a distributed controller based on adaptive dynamic programming is proposed to solve the minimum loss problem of flywheel energy storage systems (FESS). We first formulate a performance function aiming to reduce total losses of FESS in power distribution applications. Then we use the Hamilton–Jacobi–Bellman (HJB) equation to solve this optimal control problem. The solution of the HJB equation is approximated by neural networks. To achieve distributed control, we estimate the global variables in the HJB equation by using the dynamic average consensus algorithm. A barrier Lyapunov function and a saturation function are introduced to handle the issue of state and input constraints, respectively. Then the stability of the system is proved through the Lyapunov stability analysis. Finally the effectiveness of the proposed strategy is verified by simulations. Simulation results show that FESS can track the power command while minimizing total power losses by interacting with neighbors. The proposed algorithm leads to a loss reduction of compared to the equal power distribution strategy.