Lyapunov-global-Lanczos algorithm for model order reduction and adaptive PI controller of large-scale electrical systems

Mathematical modeling of complex electrical systems has led us to linear mathematical models of higher order. Consequently, it is difficult to analyze and to design a control strategy for these systems. Order reduction is an important and effective tool to facilitate the handling and designing of a control strategy. In this paper, we firstly present a reduction method, which is based on the Krylov subspace and Lyapunov techniques, called Lyapunov-Global-Lanczos. This method minimizes the H1 norm error and absolute error, and preserves the stability of the reduced system. It also provides a better reduced system of order 1, with closer behavior to the original system. This first order system is used to design PI (Proportional-Integral) controller. Secondly, we implement an adaptive digital PI controller in a microcontroller. It calculates the PI parameters in real time, referring to the error between the desired and measured outputs and the initial values of PI controller, that are determined from the first order system. Two simulation examples and a real-time experimentation are presented to show the effectiveness of the proposed algorithms.