Analysis of the field current after three-phase sudden short-circuit of turbogenerators using equivalent circuits

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

“…The dynamic state of a solid-rotor induction motor with a fractional-order impedance ( 6) is described by the stator voltage differential equation and the rotor differential equation containing the derivative of the fractional order In the work [26], on the basis of the analysis of the electromagnetic field in the cylindrical coordinate system, an analytical dependence was derived for the spectral inductance of the stator, in which the Bessel functions of the complex argument occur. Using the expansion of the function into a power series, the expression for the rotor operational impedance of the following form was obtained…”

“…The paper [23] presents an analysis of the transient states of a solid-rotor turbogenerator, where the rotor circuit was represented by the fractional-order operational inductance. In order to more accurately reproduce the skin effect in ferromagnetic elements or in the bars of the rotor cage, hybrid elements should be used [24][25][26]. These elements are a series connection of integer and noninteger order elements.…”

“…These elements are a series connection of integer and noninteger order elements. The equivalent circuit of a coil with ferromagnetic core in paper [24] as well as the equivalent circuit of the rotor cage in paper [25] are shown as a series connection of resistance and fractional order inductance.Based on a simplified analysis of the electromagnetic field, using the expansion of the Bessel function into the Taylor series, it was shown in [26] that the solid-rotor circuit of a synchronous machine can be replaced by the resistance and inductance with lumped constants and the fractional inductance.…”

“…The conversion from the operational transfer function form to the time form for the fractional-order operational transmittances is difficult. In the paper [27], for the operational transmittance containing fractional-order derivatives (the coefficients of the polynomial of the numerator and denominator of the Laplace operator p are multiples of 0.5), the field current waveform of a synchronous generator at a sudden short-circuit was determined, using the error function erfc of the complex argument. On the other hand, the analysis of the dynamic states of induction and synchronous machines with the use of a fractional-order equivalent circuit model for a variable rotational speed of the rotor is performed using the Grünwald-Letnikow method to solve equations with fractional-order derivatives [19,20].…”