Delay-dependent Wide-area Damping Controller Synthesis Approach Using Jensen's Inequality and Evolution Algorithm

A time-delay-dependent wide-area damping controller synthesis approach, based on Jensen's integral inequality and evolution algorithm, is developed to suppress the adverse effect of time delay on the supplemental control of high-voltage direct current (DC) transmission systems. Initially, the state-space model of hybrid AC/DC systems with time delay is derived and the delay-dependent criteria for the stability of the closed-loop system are provided based on Jensen's integral inequality. Subsequently, initial solutions are randomly generated to overcome the difficulty of solving the nonlinear matrix inequality. Finally, the time-delay stability upper bound of the controller is optimized using the differential evolution algorithm. In comparison to popular time-delay stable controller design methods, such as the free-weighting-matrix approach, the proposed method based on output feedback realization requires fewer decision variables and is more suitable for large-scale hybrid AC/DC systems. Three examples are introduced to verify the effectiveness of the proposed method.