Loewner matrix approach for modelling FDNEs of power systems

• The Loewner matrix (LM) approach is a non-iterative method having a system theoretic interpretation which fits accurate state space descriptor models without any convergence issues. It doesn’t need any starting poles.
• A simple matrix implementation for LM formation, MATLAB based stable model extraction is proposed. Model order can be exactly identified for lumped systems and a probable system order for distributed systems.
• It has been shown that the data splitting step of the LM approach has significant impact on accuracy. Even and odd samples data splitting is found to be comparable to vector fitting with respect to accuracy, stability and passivity.

This paper proposes a new approach for modelling frequency dependent power system network equivalents (FDNE) using tangential interpolation framework based on Loewner matrix (LM) pencil. The Loewner matrix based tangential interpolation technique has been recently proposed for modelling of large multi-port VLSI circuits. The LM approach fits accurate state space descriptor system models from the frequency response measurements. Singular value decomposition based LM approach has been investigated in this paper for modelling of FDNEs. The proposed method's performance is compared to the widely used vector fitting approach using four power system examples. A simple matrix implementation for LM formation and a MATLAB based stable model extraction approach is proposed. It has been shown that the data splitting step of the LM approach has significant impact on the accuracy of the fitting. The LM method is shown to be comparable to vector fitting in terms of accuracy, stability and passivity. It does not require any starting poles and has no convergence issues because it is a non-iterative method. It also gives an indication of the system order which is a unique advantage.