The application of energy storage (ES) in power system is limited due to the high cost of the ES device, which exponentially increases with its capacity. This paper is to improve the saturation-dependent stability of the power system equipped with the energy storage based damping controller (ESDC), and hence, reduce the required size of the ES. The phenomenon that the capacity of ES is smaller than the required value produced by the ESDC, is modeled as actuator saturation using the saturation function. The proposed method is to design an anti-windup compensator (AWC), which in the event of saturation, produces a signal based on the output difference between the ESDC and saturated ES and then augment the signal to the ESDC to alleviate the adverse effect of saturation. The AWC is designed with the reduced- order model of power system and linear matrix inequality. Detailed design procedure is introduced. Case studies based on a modified 4-machine 2-area power system and 10-machine New England power system are carried out to demonstrate the effectiveness of the AWC design method.