Analytical modelling of one cage rotor induction motor for electric submersible pumps

Abstract

A new hybrid analytical model (HAM) based on conformal mapping (CM) method and magnetic equivalent circuit (MEC) model is presented in this paper for electromagnetic modelling of cage rotor induction motors (CRIMs) used in electric submersible pumps (ESPs). For every operating point, the iron parts are modelled with a non-linear MEC model to calculate the equivalent virtual currents, which represent the influence of magneto motive force (MMF) drops and MMF sources in stator and rotor cores. The effects of the equivalent virtual currents on the air-gap magnetic field are then considered using the CM method and Hague's solution. This approach for calculating the air-gap field is also used to prepare a 3-D lookup table (3-D LUT) for each element of inductance matrix and derivative of inductance matrix in terms of rotor position. These LUTs are then used for transient modelling and analysis of CRIM under no-load and loading conditions. The accuracy of proposed HAM is validated by comparing the results obtained through HAM with corresponding results obtained from finite element method and experiment set-up. K E Y W O R D S conformal mapping (CM), hybrid analytical model (HAM), inductance, magnetic equivalent circuit (MEC) model, magnetic field, magnetic saturation This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Modified magnetic equivalent circuit model for magnetic field analysis of one cage‐rotor induction motor used in electric submersible pumps

“…To calculate the air‐gap magnetic field for every operating point, it is firstly necessary to calculate the distribution of scalar magnetic potential on the inner surface of stator and outer surface of rotor ( U s and U r ) [17]. These distributions are then translated into equivalent virtual currents on r = R s and r = R r as follows: $$$\left\{\begin{array}{c}{I}_{\mathrm{v}\mathrm{s}}(i)={U}_{\mathrm{s}}(i)-{U}_{\mathrm{s}}(i+1)\\ {I}_{\mathrm{v}\mathrm{r}}(j)={U}_{\mathrm{r}}(j)-{U}_{\mathrm{r}}(j+1)\end{array}\right.$$$ where R s and R r are, respectively, the inner radius of stator and outer radius of rotor.…”

“…To calculate the air-gap magnetic field for every operating point, it is firstly necessary to calculate the distribution of scalar magnetic potential on the inner surface of stator and outer surface of rotor (U s and U r ) [17]. These distributions are then translated into equivalent virtual currents on r = R s and r = R r as follows:…”

“…As shown, the proposed MMEC has more accuracy than the proposed HAM in ref. [17] because the air-gap region was modelled by conventional method [6] in ref. [17].…”

“…[17] because the air-gap region was modelled by conventional method [6] in ref. [17]. Figure 14 shows the distribution of air-gap magnetic field for a typical operating point under T L = 400 N.m. As shown in Figures 13 and 14, due to the overestimation of mutual air-gap permeances by classic method [17], B r and B t are overestimated and underestimated by proposed HAM in ref.…”

“…Multi-slice MEC model was used to quasi-3D model of one outer-rotor singlephase induction motor while considering the skewing effect of rotor slots [13]. In many HAMs based on CM method [14][15][16][17] and winding function theory [18][19][20], MEC model has been used to accurately consider the iron parts.…”