Harmonics Consequences on Drive Systems with Induction Motor
Abstract
:1. Introduction
2. Methodological Aspects
2.1. Mathematical Model of the IM
2.2. Modeling and Simulation of the IM in Harmonics
- The initial reference situation is that when the IM stator is supplied with a symmetrical system of sinusoidal voltages, at the network frequency, the motor is running stable at a determined constant torque and speed.
- The voltage waves applied to the stator are deformed, by superposing over the fundamental of a single harmonic, with orders from the series k ∊ {5, 7, 11, 13, 17, 19}, and having percentage levels among the values γVk ∊ {5%, 10%, 15%, 20%, 25%, 30%}, above the rated value of the voltage.
- Solving the situations considered above on the physical model of the IM, the levels of the harmonics of the stator current, corresponding to those of the injected voltage, are followed. Moreover, the total harmonic distortion (THD) of the stator current, of the electromagnetic torque and its THD, the PF, and the IM efficiency are monitored as well.
3. Results
4. Discussion
4.1. THD of the Stator Current
4.2. The Electromagnetic Torque of the IM
4.3. THD of the IM Electromagnetic Torque
4.4. Power Factor of the IM
4.5. The Efficiency of the IM
5. Conclusions
- Deformation of the voltage waves applied to the stator, by overlaying a single harmonic, with different orders and percentage levels, so that the total RMS value of the voltage is less than or equal to the rated value.
- Introduction of two or even more harmonics into the harmonic content of the voltage wave simultaneously.
- The study of the IM behavior in harmonics at different percentage loads such as 25%, 50%, and 75%.
- Adaptation of the current physical model of the IM to track the effects of saturation on the current harmonics developed in the motor. The present study is a reference to assess the consequences of saturation.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | Parameter | Value |
---|---|---|
Pn | Rated power | 4 kW |
Vn,RMS | Rated line-to-line voltage | 400 V |
f | Frequency | 50 Hz |
Nn | Rated speed | 1430 rpm |
Rs | Stator resistance | 1.405 Ω |
Lls | Stator leak inductance | 0.005839 H |
Rr’ | Rotor resistance | 1.395 Ω |
Llr’ | Rotor leak inductance | 0.005839 H |
Lm | Mutual inductance | 0.1722 |
J | Inertia | 0.0131 kgm2 |
F | Friction factor | 0.002985 Nms |
p | Pole pairs | 2 |
PFn | Rated power factor | 0.82 |
ηn | Rated efficiency | 88.5% |
Parameter | Motor Load, % | |||
---|---|---|---|---|
25% | 50% | 75% | 100% | |
Stator Current—IS,RMS, A | 4.44 | 5.29 | 6.5 | 7.94 |
Rotor Current—IR,RMS, A | 1.94 | 1.74 | 3.1 | 9.38 |
Rotor Speed—N, rpm | 1484 | 1468 | 1452 | 1435 |
Electromagnetic Torque—Te, Nm | 7.13 | 13.81 | 20.47 | 27.15 |
Active Power—P, kW | 1.2 | 2.28 | 3.39 | 4.53 |
Reactive Power—Q, kVAr | 2.83 | 2.86 | 2.96 | 3.12 |
Power Factor—PF | 0.39 | 0.62 | 0.75 | 0.82 |
Efficiency—η, % | 86.11 | 89.75 | 89.68 | 88.54 |
Harmonic Order k | Parameter | Voltage Harmonics Level of Fundamental, γVk, % | |||||
---|---|---|---|---|---|---|---|
5% | 10% | 15% | 20% | 25% | 30% | ||
5 | Stator current—IS,RMS, A | 7.96 | 8.04 | 8.17 | 8.34 | 8.56 | 8.82 |
THDIS, % | 8.01 | 16.04 | 24.05 | 32.05 | 40.05 | 48.03 | |
Rotor current—IR,RMS, A | 9.4 | 9.46 | 9.55 | 9.69 | 9.85 | 10.07 | |
Electromagnetic harmonic torque—Tek, Nm | 2.51 | 5.01 | 7.51 | 10.01 | 12.515 | 15.02 | |
Electromagnetic torque—THDTe, % | 9.22 | 18.44 | 27.66 | 36.87 | 46.09 | 55.31 | |
Active power—P, kW | 4.53 | 4.54 | 4.56 | 4.58 | 4.61 | 4.65 | |
Reactive power—Q, kVAr | 3.14 | 3.2 | 3.31 | 3.47 | 3.66 | 3.91 | |
Power factor—PF | 0.82 | 0.81 | 0.79 | 0.77 | 0.75 | 0.72 | |
Efficiency—η, % | 88.48 | 88.28 | 87.96 | 87.51 | 86.93 | 86.24 | |
7 | Stator current—IS,RMS, A | 7.95 | 7.99 | 8.05 | 8.14 | 8.25 | 8.39 |
THDIS, % | 5.74 | 11.49 | 17.24 | 22.99 | 28.74 | 34.5 | |
Rotor current—IR,RMS, A | 9.39 | 9.42 | 9.47 | 9.54 | 9.64 | 9.75 | |
Electromagnetic harmonic torque—Tek, Nm | 1.82 | 3.64 | 5.46 | 7.28 | 9.1 | 10.92 | |
Electromagnetic torque—THDTe, % | 6.7 | 13.4 | 20.11 | 26.81 | 33.51 | 40.22 | |
Active power—P, kW | 4.53 | 4.53 | 4.54 | 4.55 | 4.57 | 4.59 | |
Reactive power—Q, kVAr | 3.13 | 3.18 | 3.26 | 3.37 | 3.51 | 3.68 | |
Power factor—PF | 0.82 | 0.81 | 0.8 | 0.79 | 0.77 | 0.75 | |
Efficiency—η, % | 88.51 | 88.41 | 88.25 | 88.02 | 87.73 | 87.38 | |
11 | Stator current—IS,RMS, A | 7.94 | 7.96 | 7.98 | 8.02 | 8.07 | 8.13 |
THDIS, % | 3.66 | 7.32 | 10.98 | 14.64 | 18.3 | 21.96 | |
Rotor current—IR,RMS, A | 9.39 | 9.4 | 9.43 | 9.45 | 9.49 | 9.54 | |
Electromagnetic harmonic torque—Tek, Nm | 1.04 | 2.285 | 3.425 | 4.57 | 5.71 | 6.85 | |
Electromagnetic torque—THDTe, % | 4.21 | 8.41 | 12.62 | 16.82 | 21.03 | 25.23 | |
Active power—P, kW | 4.53 | 4.53 | 4.53 | 4.54 | 4.54 | 4.55 | |
Reactive power—Q, kVAr | 3.13 | 3.16 | 3.21 | 3.28 | 3.37 | 3.48 | |
Power factor—PF | 0.82 | 0.81 | 0.81 | 0.8 | 0.79 | 0.77 | |
Efficiency—η, % | 88.53 | 88.49 | 88.42 | 88.32 | 88.2 | 88.06 | |
13 | Stator current—IS,RMS, A | 7.94 | 7.95 | 7.97 | 8 | 8.03 | 8.07 |
THDIS, % | 3.09 | 6.19 | 9.29 | 12.39 | 15.49 | 18.59 | |
Rotor current—IR,RMS, A | 9.38 | 9.4 | 9.41 | 9.43 | 9.46 | 9.49 | |
Electromagnetic harmonic torque—Tek, Nm | 0.975 | 1.95 | 2.92 | 3.895 | 4.87 | 5.84 | |
Electromagnetic torque—THDTe, % | 3.59 | 7.17 | 10.76 | 14.34 | 17.93 | 21.52 | |
Active power—P, kW | 4.53 | 4.53 | 4.53 | 4.53 | 4.54 | 4.54 | |
Reactive power—Q, kVAr | 3.12 | 3.15 | 3.19 | 3.25 | 3.33 | 3.42 | |
Power factor—PF | 0.82 | 0.81 | 0.81 | 0.8 | 0.79 | 0.78 | |
Efficiency—η, % | 88.53 | 88.5 | 88.46 | 88.39 | 88.3 | 88.2 | |
17 | Stator current—IS,RMS, A | 7.94 | 7.94 | 7.96 | 7.97 | 7.99 | 8.02 |
THDIS, % | 2.36 | 4.73 | 7.1 | 9.47 | 11.85 | 14.22 | |
Rotor current—IR,RMS, A | 9.38 | 9.39 | 9.4 | 9.41 | 9.43 | 9.45 | |
Electromagnetic harmonic torque—Tek, Nm | 0.74 | 1.48 | 2.22 | 2.96 | 3.7 | 4.44 | |
Electromagnetic torque—THDTe, % | 2.72 | 5.45 | 8.17 | 10.89 | 13.62 | 16.34 | |
Active power—P, kW | 4.53 | 4.53 | 4.53 | 4.53 | 4.53 | 4.54 | |
Reactive power—Q, kVAr | 3.12 | 3.14 | 3.17 | 3.22 | 3.28 | 3.35 | |
Power factor—PF | 0.82 | 0.81 | 0.81 | 0.8 | 0.79 | 0.78 | |
Efficiency—η, % | 88.54 | 88.52 | 88.49 | 88.45 | 88.4 | 88.34 | |
19 | Stator current—IS,RMS, A | 7.94 | 7.94 | 7.95 | 7.96 | 7.98 | 8 |
THDIS, % | 2.12 | 4.24 | 6.36 | 8.48 | 10.6 | 12.72 | |
Rotor current—IR,RMS, A | 9.38 | 9.39 | 9.4 | 9.41 | 9.42 | 9.44 | |
Electromagnetic harmonic torque—Tek, Nm | 0.665 | 1.33 | 1.995 | 2.66 | 3.325 | 3.99 | |
Electromagnetic torque—THDTe, % | 2.45 | 4.90 | 7.35 | 9.80 | 12.24 | 14.69 | |
Active power—P, kW | 4.53 | 4.53 | 4.53 | 4.53 | 4.53 | 4.53 | |
Reactive power—Q, kVAr | 3.12 | 3.14 | 3.17 | 3.21 | 3.26 | 3.33 | |
Power factor—PF | 0.82 | 0.81 | 0.81 | 0.8 | 079 | 0.78 | |
Efficiency—η, % | 88.54 | 88.52 | 88.5 | 88.47 | 88.43 | 88.38 |
Harmonic Order k | THDIS/γVk |
---|---|
5 | 1.600 |
7 | 1.149 |
11 | 0.732 |
13 | 0.619 |
17 | 0.473 |
19 | 0.424 |
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Beleiu, H.G.; Maier, V.; Pavel, S.G.; Birou, I.; Pică, C.S.; Dărab, P.C. Harmonics Consequences on Drive Systems with Induction Motor. Appl. Sci. 2020, 10, 1528. https://doi.org/10.3390/app10041528
Beleiu HG, Maier V, Pavel SG, Birou I, Pică CS, Dărab PC. Harmonics Consequences on Drive Systems with Induction Motor. Applied Sciences. 2020; 10(4):1528. https://doi.org/10.3390/app10041528
Chicago/Turabian StyleBeleiu, Horia Gheorghe, Virgil Maier, Sorin Gheorghe Pavel, Iulian Birou, Constantin Sorin Pică, and Pompei Cosmin Dărab. 2020. "Harmonics Consequences on Drive Systems with Induction Motor" Applied Sciences 10, no. 4: 1528. https://doi.org/10.3390/app10041528