An optimal modal approximation method for model reduction of linear power system models

A number of recent studies have examined the problem of modal reduction of large-scale power system linear models. In this paper, an optimal model reduction strategy for the analysis and control of inter-area oscillations in power systems that uses concepts from proper orthogonal decomposition and modal analysis and preserves exactly the input–output properties of the original system is presented. The technique uses a new projection matrix that minimizes the error between the states of the original system and the states of its reduced-order model, and is suitable for analyzing large power system models described by differential–algebraic equation (DAE) systems.Based on this theoretical framework, an efficient algorithm for model reduction is proposed which combines the ease of use of linear modal analysis, with the flexibility of extracting relevant behavior that statistical multivariate methods can offer. Methods for analysis of reduced system representations using linear approximations are critically reviewed and compared. The proposed technique is tested on a 50-machine, 145-bus, and 453-line test system. The effects of system dimension, accuracy of the approximations to capture inter-system oscillations, and the generality of the techniques are discussed in detail in the parametric study. Accuracy of the solution and weaknesses of the model reduction are also investigated. Direct numerical simulation of the power system dynamic model is performed to investigate the accuracy and robustness of the method.

► Combines linear analysis with statistical multivariate methods.
► Determines efficient reduced-order dynamic models for large-scale systems.
► Critical system features and structure are retained.
► Preserves the stability and passivity of the system.
► Applicable to the analysis and control of inter-area oscillations.