Wide-area damping state feedback and output feedback controller design strategy considering time delays and actuator saturation based on parametric Lyapunov theory

Remote signal transmission time delays are the major factors to affect the performance of wide-area damping controller (WADC) and even deteriorate stability of large-scale power system. If the physical structure and the mathematical model of the system are different, the method of mathematically dealing with time delay is not the same. From the perspective of mathematical application engineering, there are two main ways to deal with the communication time delay: linear matrix inequalities (LMI) theory and conventional time-delay predictive compensation theory. Traditional time delay damping controller based on linear matrix inequalities (LMI) suffers relatively large conservatism and complexity. Traditional time delay damping controller based on time delay compensation has no clear relation between the control parameter and the time delay. On the other hand, the saturation of actuator leads to the deterioration of control performance and even threat system stability. The existing methods for saturation are negative feedback anti-saturation after the actuator is saturated, which is an afterwards control and it is difficult to well eliminate the influence of saturation. In this paper, a novel design strategy for wide-area time-delay damping controller based on parametric Lyapunov theory is derived. The explicit expression of the controller parameter value associated with the time delay is determined. This strategy can deal with arbitrary large time-vary delay theoretically and have extremely low controller dimension, which makes it have potential capability to be applied in large-scale inter-connected power systems. The control strategy is determined according to the system stability original definition (The system energy function is finite and positive and its first derivative is negative), which avoids complex matrix inequalities cyclic solution and reduces the conservatism of the controller. Moreover, it can directly give simple and explicit control law and specific control parameters, which enable this method to adjust its parameters online according to the exact time delay obtained by GPS. In the design process, the saturation characteristics of the actuator are taken into account in the linearization model of the closed-loop system. This makes it very adaptable to actuator saturation, so that the proposed design strategy can ensure the small signal stability of the closed-loop system considering time delays and actuator saturation. Case study is undertaken based on a New England ten-machine 39-bus power system, which stands for a large scale power system to verify the feasibility and effectiveness of the proposed design strategy. Compared with the free weight matrix damping controller (FWMC), which is a kind of LMI-based design strategy with excellent performance, the advantages and superiority of the proposed control strategy are verified. The proposed design strategy based on state feedback and output feedback has better control performance than FWMC.