Induction Machine with Anisotropic Multilayer Rotor Modelling the Electromagnetic and the Electrodynamic States of a Symmetrical Machine with Deep Bar Cage in Solid Iron Rotor Core

The Novel Rotor Flux Estimation Scheme Based on the Induction Motor Mathematical Model Including Rotor Deep-Bar Effect

“…Figure 1a presents the T-type equivalent circuit corresponding to the IM classical mathematical model expressed in the Laplace-domain (p-domain), in which the rotor resistance R 2 and leakage inductance L σ2 are represented by parameters varying as a function of slip frequency ω 2 . The variability of rotor electromagnetic parameters resulting from the rotor deep-bar effect can be modeled in the rotor equivalent circuit by a two-terminal network with constant parameters [16][17][18][19][20][21][22][23][24][25]. The electromagnetic parameters of such an IM mathematical model can be determined based on the p-domain motor inductance:…”

“…The p-domain inductance L 1δ (p) can be derived from a solution of Maxwell's differential system of equations which are formulated, for instance, on the basis of an IM multi-layer model [17]. However, the p-domain inductance L 1δ (p) is not directly applicable in an analysis of IM transients due to the lack of possibility for inverse transformation of a Laplace transform including this inductance.…”

“…The above-mentioned difficulty can be circumvent by the partial fraction decomposition of the inverse p-domain inductance L 1δ (p), which is an irrational function with an infinite number of negative real poles. This, in turn, leads to the rotor mathematical model in the form of a two-terminal network with constant R 2(n) , L σ2(n) parameters [17]:…”

“…An exact approximation of the reference p-domain inductance L 1δ (p) is obtained with an infinite number of poles of an approximative rational function (an infinite number of parallel connected two-terminals in the rotor mathematical model). For the sake of the desired simplicity of the IM mathematical model, the number of parallel connected two-terminals in the rotor equivalent circuit is limited to N two-terminals, and for achieving the required approximation accuracy of the irrational function L 1δ (p), the (N + 1)th residual two-terminal with parameters R 2(0) , L σ2(0) is included ( Figure 2) [17]:…”

“…The variability of rotor electromagnetic parameters resulting from the rotor deep-bar effect can be modeled by the IM mathematical model with rotor multi-loop representation [16][17][18][19][20][21][22][23][24][25]. Nevertheless, an estimation scheme of the rotor flux space vector which algorithm would be formulated on the basis of such IM mathematical models has not been developed so far.…”