Analysis of Control Methods for the Traction Drive of an Alternating Current Electric Locomotive
Abstract
:1. Introduction
- -
- Scalar.
- -
- Vector.
- -
- With direct torque control.
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- Selection of a mathematical model of a traction motor, which allows us to investigate the operation of the motor in the presence of asymmetry in its windings and in the presence of asymmetry in the power supply system.
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- Simulation of the control system of the output converter with scalar and vector control.
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- Received starting characteristics for scalar and vector traction drive control system for normal operation.
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- The starting characteristics were obtained for the scalar and vector traction drive control system for the emergency (asymmetric) mode: (1) in the traction motor; (2) in the output converter; (3) simultaneously in the traction motor and the output converter.
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- The comparison of the obtained starting characteristics.
2. Materials and Methods
3. Results of the Analysis of Control Methods for the Output Converter of the Traction Drive of an AC Electric Locomotive
3.1. Justification of the Choice of a Mathematical Model of an Induction Motor
3.2. Simulation of the Control System of the Output Converter with Scalar and Vector Control
3.3. Simulation Results
4. Discussion
- -
- The asymmetry in the power supply system has a greater effect on the torque ripple and the imbalance of the stator phase currents than the asymmetry of the stator windings. With a deviation of the phase voltage of one of their phases by 2%, the torque ripple coefficient for a scalar control system was 40%, the unbalance coefficient of the stator phase currents was 14%. With a vector control scheme, the torque ripple coefficient was 34.5%, and the unbalance coefficient of the stator phase currents was 17%. With a deviation of the impedance of one of the phases by 10%, similar parameters for scalar control were: torque ripple coefficient—18%, stator phase current imbalance coefficient—4.5%. With vector control: torque ripple factor—15, 5%, unbalance factor of stator phase currents—1.5%.
- -
- With the same damages with a vector control scheme, less ripple of the torque occurs, and with a scalar one, a smaller imbalance of phase currents.
5. Conclusions
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- With an asymmetry of the power supply system, the ripple coefficient of the motor torque is 2.3 times greater than with the asymmetry of the stator windings with scalar control and 2.2 times more with vector control; the current imbalance coefficient is 3 times higher with scalar control and 11 times higher with vector control.
- -
- With the same damages with a vector control scheme, less ripple of the torque occurs, and with a scalar one, a smaller imbalance of phase currents.
6. Patents
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Indicators | Value |
---|---|
Number of locomotive axles N, pcs. | 4 |
Starting traction FT, N | 27,523 |
Restrictions | By current |
Traction motor type | AD914U1 |
Electric locomotive weight m, kg | 90,000 |
Wheel radius R, m | 0.6 |
Gear ratio μ, p.u | 4.105 |
Gearbox efficiency ηr,% | 96 |
Indicators | Value |
---|---|
Power P, kW | 1200 |
Current value of line voltage Unom, V | 1870 |
Effective value Inom, A | 450 |
Rated frequency of the supply voltage f, Hz | 55.8 |
Number of phases n, pcs. | 3 |
Number of pole pairs pp | 3 |
Nominal rotation frequency nr, rpm | 1110 |
Efficiency η, % | 95.5 |
Power factor cosφ, per unit | 0.88 |
Active resistance of the stator winding rs, Ω | 0.0226 |
The active resistance of the rotor winding reduced to the stator winding r’r, Ohm | 0.0261 |
Stator winding leakage inductance Lσs, Hn | 0.00065 |
Reduced to the stator winding leakage inductance of the rotor winding, L’σr, Hn | 0.00045 |
Total inductance of the magnetizing circuit Lμ | 0.0194336 |
Motor moment of inertia J, kg·m2 | 73 |
Base Values | ||
---|---|---|
Base value for voltages, V | Ub = √2·Unom | 1527 |
Basic value for currents, A | Ιb = √2·Ιnom | 450 |
Base value for corner frequencies, 1/s | Ωb = 2·π·fnom | 349.345 |
Base value for electrical angles, rad | θb = 2·π | 6.283 |
Basic value for resistances, Ohm | Ib = Ub/Inom | 3.393 |
Base value for flux linkages, Wb | ψb = Ub/Ωb | 4.371 |
Base value for inductances, H | Lb = ψb/Inom | 0.009713 |
Base value for powers, W | Pb = 2·Ub·Inom/3 | 1,030,725 |
Basic value for mechanical angular velocities, 1/s | Ωbmech = Ωb/ppole | 116.448 |
Basic value for moments, N⋅m | Mb = Pb/Ωbmech | 8851 |
Base value for time | Tb = 1/Ωb | 0.002862 |
Basic value for moments of inertia, kg⋅m2 | Tb = Mb·ppole/(Ωb)2 | 0.218 |
Additional parameters of AM in p.u. | ||
Magnetizing inductance | L*m = Lm/Lb | 1.334 |
Magnetizing inductance | L*s = Ls/Lb | 1.401 |
Rotor phase total inductance | L*r = Lr/Lb | 1.38 |
R*s = Rs/Rb | 0.00666 | |
R’*r = R’r/Rb | 0.07692 | |
Rotor moment of inertia | J*en = Jen/Jb | 335.507 |
Additional dimensionless parameters of AD | ||
Total dissipation coefficient | σ = 1 − (L*m)2/(L*s·L*r) | 0.08 |
Dimensionless stator time constant | χ*s = L*s/R*s | 210.314 |
Dimensionless rotor time constant | χ*r = L*r/R*r | 179.434 |
Controller parameters | ||
Current loop tuning factor X | aIx | 2 |
Current loop tuning factor Y | aIy | 2 |
Flow loop adjustment factor | aIμ | 2 |
Speed loop tuning factor | aω | 2 |
Uncompensated time constant | χ*μ = 10/(6·τPWM) | 0.361 |
Proportional coefficient of the current regulator X in the absence of an EMF compensation unit | KpIx = (R*s·σ·χ*s)/(aIx·χ*μ) | 0.155 |
Integral coefficient of the current regulator X in the absence of an EMF compensation unit | KiIx = (R*s + (χ*μ)2/(χ*r·L*r))/(aIx·χ*μ) | 0.019 |
Proportional coefficient of the current regulator Y | KpIy = (R*s·σ·χ*s)/(aIy·χ*μ) | 0.155 |
Integral coefficient of the current regulator Y | KiIy = R*s/(aIx·χ*μ) | 0.00922 |
Proportional coefficient of the rotor magnetizing current regulator | KpIμ = χ*r/(aIx·aIμ·χ*μ) | 124.226 |
Integral coefficient of the rotor magnetizing current regulator | KiIμ = 1/(aIx·aIμ·χ*μ) | 0.692 |
Proportional coefficient of the speed controller | Kpω = J*en·kj/(aIy·aω·χ*μ) | 6736 |
Integral coefficient of the speed controller | Kiω = 0 | 0 |
Parameter | Parameter Value | |||
---|---|---|---|---|
Experiment 1 | Experiment 2 | Experiment 3 | Experiment 4 | |
Maximum torque, N·m | 1745.5 | 2047 | 2857 | 3060 |
Minimum torque value, N·m | 1745.25 | 1433 | 618.4 | 425.9 |
Average torque, N·m | 1745.375 | 1740 | 1403.3 | 1357.05 |
Ripple frequency, Hz | 60 | 60 | 60 | 60 |
Stator phase current A, A | 151.1 | 163.6 | 159.1 | 168.4 |
Stator phase current B, A | 151.1 | 158.4 | 138.2 | 139.2 |
Stator phase current C, A | 151.1 | 156.5 | 158.9 | 161.2 |
Engine speed, rpm | 600 | 600 | 600 | 600 |
Transient end time, s | 90 | 90 | 90 | 90 |
Torque ripple factor, kpT, % | 0.002 | 17.64 | 40 | 48.5 |
Unbalance factor of stator phase currents, knbI | 0 | 4.4 | 13.7 | 18.7 |
Parameter | Parameter Value | |||
---|---|---|---|---|
Experiment 5 | Experiment 6 | Experiment 7 | Experiment 8 | |
Maximum torque, N·m | 1744.2 | 2009 | 2942 | 3090 |
Minimum torque value, N·m | 1743.5 | 1472 | 541.7 | 417.7 |
Average torque, N·m | 1743.85 | 1740.5 | 1741.85 | 1753.85 |
Ripple frequency, Hz | 60 | 60 | 60 | 60 |
Stator phase current A, A | 133 | 138.6 | 141.8 | 146.8 |
Stator phase current B, A | 133 | 133.1 | 118.9 | 116.9 |
Stator phase current C, A | 133 | 132.3 | 140.9 | 140.6 |
Engine speed, rpm | 600 | 597.8 | 597.6 | 597.3 |
Transient end time, s | 90 | 90.3 | 90.51 | 90.65 |
Torque ripple factor, kpT, % | 2 | 15.4 | 34.5 | 38.0 |
Unbalance factor of stator phase currents, knbI | 0 | 1.6 | 17.1 | 22.1 |
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Goolak, S.; Tkachenko, V.; Šťastniak, P.; Sapronova, S.; Liubarskyi, B. Analysis of Control Methods for the Traction Drive of an Alternating Current Electric Locomotive. Symmetry 2022, 14, 150. https://doi.org/10.3390/sym14010150
Goolak S, Tkachenko V, Šťastniak P, Sapronova S, Liubarskyi B. Analysis of Control Methods for the Traction Drive of an Alternating Current Electric Locomotive. Symmetry. 2022; 14(1):150. https://doi.org/10.3390/sym14010150
Chicago/Turabian StyleGoolak, Sergey, Viktor Tkachenko, Pavol Šťastniak, Svitlana Sapronova, and Borys Liubarskyi. 2022. "Analysis of Control Methods for the Traction Drive of an Alternating Current Electric Locomotive" Symmetry 14, no. 1: 150. https://doi.org/10.3390/sym14010150
APA StyleGoolak, S., Tkachenko, V., Šťastniak, P., Sapronova, S., & Liubarskyi, B. (2022). Analysis of Control Methods for the Traction Drive of an Alternating Current Electric Locomotive. Symmetry, 14(1), 150. https://doi.org/10.3390/sym14010150