Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

Abstract

This article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half-order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation of the half-order derivatives by the Grünwald–Letnikov definition, a state-space equation system was solved. For both models, a computational program written in Matlab® software was used. For the purpose of time domain simulation, the machine models were connected to an electric load composed of an RL circuit. To validate and compare both models, simulation results of a three-phase short-circuit and a no-load voltage recovery were compared with corresponding measurements performed on a solid salient-pole synchronous generator of 125 kVA.

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…The resulting asymptotic model has no physical meaning, in the sense that it does not describe a real-world system. However, expressions (18)(19)(20) fit well the experimental data and, as we shall demonstrate, give a reliable description of the measurements.…”

“…In the field of electromagnetism, the tools of FC were applied successfully to describe the behavior of electric machines [19][20][21] and other devices [12,22]. Specifically for modeling inductors, Schäfer and Krüger [1,2] showed that fractional models are suitable for describing hysteresis losses in the inductor core.…”

Development of an emulation platform for synchronous machine power generation system using a nonlinear functional level model

“…The rated data of the studied SG and the identified equivalent circuit parameters can be found in Appendix. The parameter identification process was carried out based on data from the standstill frequency response (SSFR) test and the least-squares problem procedures [21,22].…”

Solid-Rotor Induction Motor Modeling Based on Circuit Model Utilizing Fractional-Order Derivatives

“…where: N-number of measurement points, f-stator current frequency, L s -spectral inductance of the winding determined on the basis of the electromagnetic field distribution using the finite element method, and L s *-spectral inductance of the winding determined from the dependence (15) with p = jω = j2πf, w i being weight coefficients. The Levenberg-Marquardt method implemented in the Matlab [34] environment was used to solve the Equation (18). As a result of optimization, the following values of the sought vector χ coefficients were obtained: L m = 0.298 H, R k = 0.8548 Ω, L σk = 0.000012 H, T e = 0.13547 s, α = 0.4682 Figure 6 shows the obtained frequency characteristics of the spectral inductance L s (jf).…”

“…To achieve the required approximation accuracy, a sufficiently large number of rotor equivalent circuits must be used, but then numerical identification of the parameters of the equivalent scheme is very difficult. An alternative solution [16][17][18], presented in this paper, is to represent the skin effect in a solid rotor by means of resistance and inductance with fixed values and fractionalorder inductance depending on the frequency of induced eddy currents. This model more accurately reflects the physical phenomena occurring in a solid rotor.…”