The impact of frequency converters on motors and their efficiency during variable frequency speed control: Regardless of the control method used, the voltage pulses output to the motor terminals during variable frequency speed control are non-sinusoidal. Therefore, analyzing the operating characteristics of ordinary asynchronous motors under non-sinusoidal conditions involves understanding the impact of variable frequency speed control on the motor. This mainly includes the following aspects:
Motor losses and efficiency: Motors operating under non-sinusoidal power sources will experience many additional losses in addition to the normal losses generated by the fundamental wave. These losses are mainly manifested in increased stator copper losses, rotor copper losses, and iron losses, thus affecting the motor's efficiency.
1
The stator copper loss is caused by harmonic currents appearing in the stator windings, which increases I²R. When the skin effect is ignored, the stator copper loss under non-sinusoidal current is proportional to the square of the total effective value of the current. If the number of stator phases is m1, and the stator resistance per phase is R1, then the total stator copper loss P1 is given by substituting the total effective value of the stator current, including the fundamental current, into the above equation. The second term in the equation represents the harmonic loss. Experiments have shown that the presence of harmonic currents and the corresponding leakage flux increases the magnetic saturation of the leakage flux, thus increasing the excitation current and consequently increasing the fundamental component of the current.
2
At harmonic frequencies, rotor copper losses can generally be considered as constant due to the constant resistance of the stator windings. However, for asynchronous motors, the AC resistance of the rotor increases significantly due to the skin effect, especially in deep-slot squirrel-cage rotors. In synchronous motors or reluctance motors operating under sinusoidal power, the stator space harmonic magnetomotive force is very small, and the losses in the rotor surface windings are negligible. When a synchronous motor operates under a non-sinusoidal power supply, the time harmonic magnetomotive force induces rotor harmonic currents, similar to those of an asynchronous motor operating near its fundamental synchronous speed.
Both the counter-rotating 5th harmonic magnetomotive force and the forward-rotating 7th harmonic magnetomotive force induce rotor currents six times the fundamental frequency. At a fundamental frequency of 50Hz, the rotor current frequency is 300Hz. Similarly, the 11th and 13th harmonics induce rotor currents twelve times the fundamental frequency, or 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. 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.
3
The core loss in a 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 6-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 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 when the power supply is not sinusoidal: 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 plate. Due to the change in the phase difference between the stator magnetomotive force and the rotor magnetomotive force, 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.
4
The magnitude of harmonic losses in motor efficiency is significantly determined by the harmonic content of the applied voltage. Larger 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 three 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.
If the higher harmonic components in the stator voltage waveform are relatively low, as in a 6th-step waveform, the increase in harmonic iron losses will not exceed 10%. If iron losses and stray losses account for 40% of the total motor losses, then harmonic losses will only account for 4% of the total motor losses. Friction losses and windage losses 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 with a 6th-step waveform, the motor's harmonic losses will increase significantly, possibly exceeding the fundamental loss. Even with a 6th-step waveform power supply, a low-leakage-reluctance motor may absorb a large harmonic current, causing the motor efficiency to decrease by 5% or more. In this case, for satisfactory operation, a 12th-step waveform inverter or a six-phase stator winding should be used. The harmonic current and harmonic losses of a motor are actually 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 us to determine the approximate range of efficiency reduction for a certain type or structure of motor.
