Identification of Linear Power System Models Using Probing Signals R. Cardenas-Javier, F. A. Zelaya, M. R. A. Paternina National Autonomous University of Mexico - UNAM {rcardenasj,fzelaya223}@comunidad.unam.mx, mra.paternina@fi-b.unam.mx Felipe Wilches-Bernal Sandia National Laboratories fwilche@sandia.gov Abstract This paper compares the accuracy of two methods to identify a linear representation of a power system: the traditional Eigensystem Realization Algorithm (ERA) and the Loewner Interpolation Method (LIM). ERA is based on time domain data obtained using exponential chirp probing signals and LIM system identification method is based on frequency domain data obtained using sinusoidal probing signals. The ERA and LIM methods are evaluated with the noise produced by the nonlinear characteristics of the system, these characteristics are caused by increasing the amplitude of the applied probing signal. The test systems used are: the two-area Kundur system and a reduced order representation of the Northeastern portion of the North American Eastern Interconnection. The results show that the LIM method provides a more accurate identification than the ERA method. 1. Introduction System identification methods estimate a linear model from measurement data of an actual system. Traditionally, some of the most important indicators of system identification methods are the accuracy of the estimated models as well as how immune to noise the methods are. For this comparison, the frequency response obtained with the small signal analysis (SSA) of the complete model of the system is used, the lack of an adequate complete model due to the various uncertainties of a system have motivated the comparison using different identification methods [1]. Classical methods use the impulse/pulse time domain response of the system [2], or assume that the transient response after a perturbation can be represented as unit impulse response. However, sometimes the measurements used to identify the model do not contain enough dynamic information because the applied pulse may not sufficiently excite the range of modes to be identified. Thus to improve the identification made with the Eigensystem Realization Algorithm (ERA) in [3] the system is modulated with an exponential chirp signal, this type of signal better excites the modes of interest, providing better selectivity to the identification. The ERA method was initially developed in the aerospace community [4] but it has been successfully adapted and it is widely used in the power systems community [5, 6]. The Loewner Interpolation Method (LIM) was presented in [7] as a frequency-domain method to compute Frequency Dependent Network Equivalents (FDNEs) for electromagnetic transient (EMT) simulations. This method was first proposed by Antoulas et al. in [8] to generalize the identification problem, by fitting a descriptor system using sampling data from the transfer matrix of an actual system. The method has shown considerable advantages to modeling time domain macro-models from tabulated impedance, admittance or scattering parameters of Multiple-Input, Multiple Output (MIMO) systems [9, 10]. Furthermore, the LIM was recently used in [11] as an alternative for power system identification and model order reduction. However, that effort did not indicate the performance of the LIM method when noise is present in the measurements. This noise can be caused when the amplitude of the probing signal activates a limit in the nonlinear characteristics of the system. Therefore, in this article, the identification is carried out by gradually increasing the amplitude of the probing signal until the nonlinear characteristics of the system components are activated, then the system model is identified using ERA and LIM with similar criteria, and to evaluate which of these methods is more immune to noise. On the other hand, in [11] large sets of modulation frequencies and extremely long simulation times are required. This paper shows how by grouping measurements using different modulated inputs, the accuracy of the identified linear system is considerably improved. This method allows for reducing the set of frequencies as well as the simulation times. This paper is organized as follows. Section 2 summarizes ERA for system identification. Section 3 details the methodology of identification using LIM. Section 4 shows the results of using these system identification methods in two test power systems. Finally, Conclusions and Future Work are presented in Section 5. Proceedings of the 54th Hawaii International Conference on System Sciences | 2021 Page 3214 URI: https://hdl.handle.net/10125/71006 978-0-9981331-4-0 (CC BY-NC-ND 4.0)