Abstract
To monitor, diagnose, and suppress the inter-turn short-circuit faults (ITSCFs) of a submersible motor, an approach for the on-line identification of its winding faults has been proposed based on monitoring the stator current. First, an ITSCF model with the global leakage referred to the stator is given. With this model, the detection parameter, which is equal to the ratio of the turns of the fault windings to the total turns of the windings in the healthy phase, can be derived. Second, a faulty model described by the fourth order state-space equation of the motor with a winding fault has been given. Based on sampled stator voltage and stator current, the detection parameter has been solved and used to estimate the location and the turns of inter-turn short-circuit windings of the motor in real time. The accuracy and the robustness of the proposed approach has been illustrated with a 1.5 kW motor that is fed by a 10 kW inverter. Experiment shows that the identification accuracy in terms of the number of the ITSCF windings of the motor stator is less than 3. It can give a reference for the on-line diagnose the ITSCFs of the stator windings of a submersible motor that works in 2 km deep well.
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Abbreviations
- \(\theta_{c}\) :
-
Localization angle between the faulty phase and the reference phase (phase b) (rad)
- \(R_{c}\) :
-
Rotor position (rad)
- \(R_{c}\) :
-
Impedance of the ITSCF winding (\(\Omega\))
- \(B_{c}\) :
-
Short-circuit winding
- \(n_{c}\) :
-
Turn number of the fault windings
- \(n_{s}\) :
-
Total turns in a healthy phase, \(n_{s}\) = 315
- \(\eta_{c}\) :
-
Detection parameter, \(\eta_{c} = n_{c} /n_{s}\)
- \(\eta_{ck}\) :
-
\(k = 1,2,3\) Detection parameters of phases a, b, and c
- \(n_{ck}\) :
-
\(n_{ck} = \eta_{ck} \cdot n_{s} { ,}k = 1,2,3,\) estimation turn of the ITSCF winding of phase a, phase b, and phase c
- \(\mu\) :
-
\(\mu = [\eta_{c1 \, } \, \eta_{c2 \, } \, \eta_{c3 \, } ]^{T}\), detection parameter set
- \(n_{c1}^{*}\) :
-
Actual turns of the artificial ITSCF windings of phase a of the experimental motor
- \(u_{ds} /u_{qs}\) :
-
d axis/q axis components of the stator voltage (V)
- \(u_{dqs}\) :
-
\(u_{dqs} = [u_{ds} \, u_{qs} ]^{T}\)
- \(\overline{u}_{ds} /\overline{u}_{qs}\) :
-
d Axis/q axis components of the stator voltage under ITSCF (V)
- \(\overline{u}_{dqs}\) :
-
\(\overline{u}_{dqs} = [\overline{u}_{ds} \, \overline{u}_{qs} ]^{T}\)
- \(i_{ds} /i_{qs}\) :
-
d Axis/q axis components of the stator current (A)
- \(i_{dqs}\) :
-
\(i_{dqs} = [i_{ds} \, i_{qs} ]^{T}\)
- \(\overline{i}_{dqc}\) :
-
Short-circuit current of the stator under ITSCF (A)
- \(\overline{i}_{dqck}\) :
-
\(k = 1,2,3\), Short-circuit currents of phases a, b, and c (A)
- \(i^{\prime}_{dqs}\) :
-
Equivalent current injected into the fault stator (A)
- \(i_{dqr}\) :
-
Equivalent current injected into the rotor (A)
- \(Q\left( {\theta_{c} } \right)\) :
-
Matrix depending on the short-circuit angle \(\theta_{c}\)
- \(P\left( {\theta_{r} } \right)\) :
-
Transformation matrix
- \(Q_{ck}\) :
-
\(k = 1,2,3\), Short-circuit elements of phases a, b, and c
- \(R_{s} /R_{r}\) :
-
Stator/rotor resistance (\(\Omega\))
- \(L_{f} /L_{m}\) :
-
Stator/mutual inductance (H)
- \(\phi_{ds} /\phi_{qs}\) :
-
d Axis/q axis components of the stator flux linkages (Wb)
- \(\phi_{dqs}\) :
-
\(\phi_{dqs} = [\phi_{ds} \, \phi_{qs} ]^{T}\)
- \(\phi_{dr} /\phi_{qr}\) :
-
d Axis/q axis components of the rotor flux linkages (Wb)
- \(\phi_{dqr}\) :
-
\(\phi_{dqr} = [\phi_{dr} \, \phi_{qr} ]^{T}\)
- \(\omega\) :
-
Rotor electrical frequency (rad/s)
- \(u_{abc}\) :
-
\(u_{abc} = [u_{a} ,u_{b} ,u_{c} ]\), sample voltage of the motor (V)
- \(i_{abc}\) :
-
\(i_{abc} = [i_{a} ,i_{b} ,i_{c} ]\), sample current of the motor (A)
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Funding
This research was funded by Open Foundation 2019 of China Electric Power Research Institute, Grant no [FXB51201901053].
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Appendices
Appendix 1
To further analyze the influence of the ITSCF on the stator current of the motor, the d axis and q axis components of the stator current \(i_{abc}\) have been derived by transforming the synchronized rotating coordinates based on Fig. 12. As can be seen in Fig. 23, when Fig. 23a is the stator current in condition, there is no ITSCF in the experimental motor. Meanwhile, when Fig. 23b is the stator current, the turns of the ITSCF windings are 12. Comparing Fig. 23b with Fig. 23a shows that the fault current includes a large number of harmonic components which can result in motor instability.
It should be noted that only the 12 turns short-circuit state of the ITSCF motor has been considered for emphasizing the distortion influence of the faulty current. Comparing Figs. 23b with 12b shows that the ITSCF significantly distorts the waveform of the stator current, which makes the motor invalid.
Appendix 2
As can be seen in Fig. 24, since the ESM woks in a wellbore with a length of about 2 km, it is difficult to achieve the on-line monitoring of ITSCFs caused by overheating and overpressure. Therefore, to extend the motor inspection period of oil wells it is necessary to develop an approach to localize and identify ITSCFs in real time.
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Wang, L., Feng, M., Tian, Z. et al. On-line identifying stator winding short-circuit approach for a submersible motor based on faulty current monitoring. J. Power Electron. 22, 1872–1884 (2022). https://doi.org/10.1007/s43236-022-00495-x
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DOI: https://doi.org/10.1007/s43236-022-00495-x