Motors operating under non-sinusoidal power supplies will experience many additional losses besides the normal losses generated by the fundamental frequency. These losses mainly manifest as increased stator copper losses, rotor copper losses, and iron losses, thus affecting the motor's efficiency.
1. Stator copper losses are caused by harmonic currents in the stator windings, which increase I²R.
When the skin effect is ignored, the stator copper loss under non-sinusoidal current is proportional to the square of the effective value of the total current. Experiments have shown that due to the presence of harmonic current and the corresponding leakage flux, the magnetic circuit saturation of the leakage flux increases, thus increasing the excitation current and consequently increasing the fundamental frequency component of the current.
2. At harmonic frequencies, the resistance of the stator winding can generally be considered constant for rotor copper losses.
For the rotor of an asynchronous motor, the AC resistance increases significantly due to the skin effect. This is especially pronounced in deep-slot squirrel-cage rotors. In contrast, for synchronous motors or reluctance motors powered by a sinusoidal wave, the losses in the rotor surface windings are negligible due to the very small stator space harmonic magnetomotive force.
When a synchronous motor operates under a non-sinusoidal power supply, the time harmonic magnetomotive force induces rotor harmonic currents, just like an asynchronous motor operating at near its fundamental synchronous speed.
Both the counter-rotating 5th harmonic magnetomotive force and the forward-rotating 7th harmonic magnetomotive force will induce a rotor current six times the fundamental frequency. When the fundamental frequency is 50Hz, the rotor current frequency is 300Hz. Similarly, the 11th and 13th harmonics induce a rotor current 12 times the fundamental frequency, i.e., 600Hz.
At these frequencies, the actual AC resistance of the rotor is much greater than its DC resistance. The actual increase in rotor resistance depends on the conductor cross-section and the geometry of the rotor slots through which the conductors are arranged. For a typical copper conductor with an aspect ratio of around 4, the AC resistance to DC resistance ratio is 1.56 at 50Hz, approximately 2.6 at 300Hz, and approximately 3.7 at 600Hz. At higher frequencies, this ratio increases proportionally to the square root of the frequency.
Motors operating under non-sinusoidal power supplies will experience many additional losses besides the normal losses generated by the fundamental frequency. These losses mainly manifest as increased stator copper losses, rotor copper losses, and iron losses, thus affecting the motor's efficiency.
3. Stator copper losses: Harmonic currents appearing in the stator windings increase I²R.
When the skin effect is ignored, the stator copper loss under non-sinusoidal current is proportional to the square of the effective value of the total current. Experiments have shown that due to the presence of harmonic current and the corresponding leakage flux, the magnetic circuit saturation of the leakage flux increases, thus increasing the excitation current and consequently increasing the fundamental frequency component of the current.
4. At harmonic frequencies, the resistance of the stator winding can generally be considered constant for rotor copper losses.
For the rotor of an asynchronous motor, the AC resistance increases significantly due to the skin effect. This is especially pronounced in deep-slot squirrel-cage rotors. In contrast, for synchronous motors or reluctance motors powered by a sinusoidal wave, the losses in the rotor surface windings are negligible due to the very small stator space harmonic magnetomotive force.
When a synchronous motor operates under a non-sinusoidal power supply, the time harmonic magnetomotive force induces rotor harmonic currents, just like an asynchronous motor operating at near its fundamental synchronous speed.
Both the counter-rotating 5th harmonic magnetomotive force and the forward-rotating 7th harmonic magnetomotive force will induce a rotor current six times the fundamental frequency. When the fundamental frequency is 50Hz, the rotor current frequency is 300Hz. Similarly, the 11th and 13th harmonics induce a rotor current 12 times the fundamental frequency, i.e., 600Hz.
At these frequencies, the actual AC resistance of the rotor is much greater than its DC resistance. The actual increase in rotor resistance depends on the conductor cross-section and the geometry of the rotor slots through which the conductors are arranged. For a typical copper conductor with an aspect ratio of around 4, the AC resistance to DC resistance ratio is 1.56 at 50Hz, approximately 2.6 at 300Hz, and approximately 3.7 at 600Hz. At higher frequencies, this ratio increases proportionally to the square root of the frequency.
5. The core loss in the motor is also increased due to the presence of harmonics in the power supply voltage; the various harmonics of the stator current establish time harmonic magnetomotive force in the air gap.
The total magnetomotive force at any point in the air gap is the synthesis of the fundamental and time-harmonic magnetomotive forces. For a three-phase six-step voltage waveform, the peak magnetic flux density in the air gap is about 10% larger than the fundamental value, but the increase in iron loss caused by the time-harmonic flux is very small. Stray losses caused by end leakage flux and skewed slot leakage flux will increase under the influence of harmonic frequencies, which must be considered in non-sinusoidal power supply. The end leakage flux effect exists in both the stator and rotor windings, mainly due to eddy current losses caused by leakage flux entering the end plates. Due to the change in phase difference between the stator and rotor magnetomotive forces, skewed slot leakage flux is generated in the skewed slot structure, with the magnetomotive force being the largest at the ends, causing losses in the stator and rotor cores and teeth.
6. The magnitude of harmonic losses in motor efficiency is significantly determined by the harmonic content of the applied voltage.
Large harmonic components increase motor losses and reduce efficiency. However, most static inverters do not generate harmonics below the 5th order, and the amplitude of higher-order harmonics is relatively small. Voltage waveforms of this type do not significantly reduce motor efficiency. Calculations and comparative tests on medium-capacity asynchronous motors show that their full-load effective current increases by approximately 4% compared to the fundamental value. If the skin effect is ignored, the motor's copper losses are proportional to the square of the total effective current, with harmonic copper losses accounting for 8% of the fundamental loss. Considering that the rotor resistance can increase by an average of 3 times due to the skin effect, the motor's harmonic copper losses should be 24% of the fundamental loss. If copper losses account for 50% of the total motor losses, then harmonic copper losses increase the overall motor losses by 12%. The increase in iron losses is difficult to calculate because it is affected by the motor structure and the magnetic materials used.
7. If the high-order harmonic components in the stator voltage waveform are relatively low, such as in a 6th-order staircase waveform, the increase in harmonic iron loss will not exceed 10%.
If iron loss and stray loss account for 40% of the total motor losses, then harmonic loss accounts for only 4%. Friction loss and wind resistance loss are unaffected, so the total increase in motor losses is less than 20%. If the motor efficiency is 90% with a 50Hz sinusoidal power supply, the efficiency will only decrease by 1% to 2% due to the presence of harmonics. If the harmonic components of the applied voltage waveform are significantly greater than those of the 6th-order staircase waveform, the motor's harmonic losses will increase significantly, and may even exceed the fundamental frequency loss.
When using a 6-step waveform power supply, a low-leakage reactance reluctance motor may absorb a large harmonic current, causing a 5% or greater decrease in motor efficiency. In this case, a 12-step waveform inverter or a six-phase stator winding should be used for satisfactory operation. The motor's harmonic current and harmonic losses are practically independent of the load; therefore, the magnitude of time harmonic losses can be determined by comparing sinusoidal and non-sinusoidal power supplies under no-load conditions. This allows for the determination of the approximate range of efficiency reduction for a particular type or structure of motor.
8. The core loss in the harmonic iron loss motor also increases due to the presence of harmonics in the power supply voltage; the various harmonics of the stator current establish time harmonic magnetomotive force in the air gap.
The total magnetomotive force at any point in the air gap is the synthesis of the fundamental and time-harmonic magnetomotive forces. For a three-phase six-step voltage waveform, the peak magnetic flux density in the air gap is about 10% larger than the fundamental value, but the increase in iron loss caused by the time-harmonic flux is very small. Stray losses caused by end leakage flux and skewed slot leakage flux will increase under the influence of harmonic frequencies, which must be considered in non-sinusoidal power supply. The end leakage flux effect exists in both the stator and rotor windings, mainly due to eddy current losses caused by leakage flux entering the end plates. Due to the change in phase difference between the stator and rotor magnetomotive forces, skewed slot leakage flux is generated in the skewed slot structure, with the magnetomotive force being the largest at the ends, causing losses in the stator and rotor cores and teeth.
9. The magnitude of harmonic losses in motor efficiency is significantly determined by the harmonic content of the applied voltage.
Large harmonic components increase motor losses and reduce efficiency. However, most static inverters do not generate harmonics below the 5th order, and the amplitude of higher-order harmonics is relatively small. Voltage waveforms of this type do not significantly reduce motor efficiency. Calculations and comparative tests on medium-capacity asynchronous motors show that their full-load effective current increases by approximately 4% compared to the fundamental value. If the skin effect is ignored, the motor's copper losses are proportional to the square of the total effective current, with harmonic copper losses accounting for 8% of the fundamental loss. Considering that the rotor resistance can increase by an average of 3 times due to the skin effect, the motor's harmonic copper losses should be 24% of the fundamental loss. If copper losses account for 50% of the total motor losses, then harmonic copper losses increase the overall motor losses by 12%. The increase in iron losses is difficult to calculate because it is affected by the motor structure and the magnetic materials used.
10. If the high-order harmonic components in the stator voltage waveform are relatively low, such as in a 6th-order staircase waveform, the increase in harmonic iron loss will not exceed 10%.
If iron loss and stray loss account for 40% of the total motor losses, then harmonic loss accounts for only 4%. Friction loss and wind resistance loss are unaffected, so the total increase in motor losses is less than 20%. If the motor efficiency is 90% with a 50Hz sinusoidal power supply, the efficiency will only decrease by 1% to 2% due to the presence of harmonics. If the harmonic components of the applied voltage waveform are significantly greater than those of the 6th-order staircase waveform, the motor's harmonic losses will increase significantly, and may even exceed the fundamental frequency loss.
When using a 6-step waveform power supply, a low-leakage reactance reluctance motor may absorb a large harmonic current, causing a 5% or greater decrease in motor efficiency. In this case, a 12-step waveform inverter or a six-phase stator winding should be used for satisfactory operation. The motor's harmonic current and harmonic losses are practically independent of the load; therefore, the magnitude of time harmonic losses can be determined by comparing sinusoidal and non-sinusoidal power supplies under no-load conditions. This allows for the determination of the approximate range of efficiency reduction for a particular type or structure of motor.
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