Robust decentralized PID-based power system stabilizer design using an ILMI approach

Thanks to its essential functionality and structure simplicity, proportional-integral-derivative (PID) controllers are commonly used by industrial utilities. A robust PID-based power system stabilizer (PSS) is proposed to properly function over a wide range of operating conditions. Uncertainties in plant parameters, due to variation in generation and load patterns, are expressed in the form of a polytopic model. The PID control problem is firstly reduced to a generalized static output feedback (SOF) synthesis. The derivative action is designed and implemented as a high-pass filter based on a low-pass block to reduce its sensitivity to sensor noise. The proposed design algorithm adopts a quadratic Lyapunov approach to guarantee α-decay rate for the entire polytope. A constrained structure of Lyapunov function and SOF gain matrix is considered to enforce a decentralized scheme. Setting of controller parameters is carried out via an iterative linear matrix inequality (ILMI). Simulation results, based on a benchmark model of a two-area four-machine test system, are presented to compare the proposed design to a well-tuned conventional PSS and to the standard IEEE-PSS4B stabilizer.