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Harmonic
Current Spectrum of Typical PWM Adjustable Frequency Drive with internal
dc bus reactor
Description of full load current waveform using individual frequency components
The following table shows the approximate values for each frequency component contained within the current pulses associated with the line current for a PWM adjustable frequency drive with an internal dc bus reactor. The components are not true harmonics, only a representation of individual waveforms whose areas equals the area under the original waveform or typical input power line current pulses.
It is important to keep in mind that the area under the input line current pulse or waveform is equal to the real power being transferred from the distribution system through the drive to the motor. With the PWM drive, are current flows forward and each contributes some portion of real power that will be used by the motor to perform work. There are no negative sequence currents as would be defined by a Fourier analysis of the waveform.
All current components contribute to the real power transferred. There is little or no reactive component and as such no current injected into the system as would be typical in linear, ie transformers and non linear load types which contain a reactive component in the current waveform.
Other types of non linear equipment such as electric
arc furnace controls, dc drives, and current source inverters inject distorted
reactive current into the electrical system and as such may increase the
current demand on a distribution system. The following table does not
describe the harmonic current spectrum for other types of non linear equipment.
|
Frequency Component (HZ) |
Equivalent Harmonic |
Theoretical % of Fundamental |
Typical % of Fundamental |
Current Sequence |
|
60 |
1st |
100 |
95.5 |
Positive |
|
300 |
5th |
20 |
23.5 |
Positive |
|
420 |
7th |
14.29 |
13.5 |
Positive |
|
660 |
11th |
9.09 |
8.5 |
Positive |
|
780 |
13th |
7.69 |
7.1 |
Positive |
|
1020 |
17th |
5.88 |
5.4 |
Positive |
|
1140 |
19th |
5.26 |
4.3 |
Positive |
|
1380 |
23rd |
4.35 |
3.4 |
Positive |
|
1500 |
25th |
4 |
2.8 |
Positive |
|
1740 |
29th |
3.45 |
2.4 |
Positive |
|
1860 |
31st |
3.23 |
2.1 |
Positive |
|
2100 |
35th |
2.86 |
1.8 |
Positive |
|
2220 |
37th |
2.7 |
1.6 |
Positive |
|
2460 |
41st |
2.44 |
1.2 |
Positive |
|
2580 |
43rd |
2.33 |
1.1 |
Positive |
|
2820 |
47th |
2.13 |
0.8 |
Positive |
|
2940 |
49th |
2.04 |
0.4 |
Positive |
|
3180 |
53rd |
1.89 |
0.25 |
Positive |
|
3300 |
55th |
1.82 |
0.12 |
Positive |
The preceding data is typical for a Pulse Width Modulated Adjustable Frequency Drive with an internal dc link choke or reactor. It is also typical for a PWM drive using ac line reactors rated for the output current of the drive and containing at least 3% impedance. Line reactors with a larger rating than the drive load must have a greater % impedance to limit the peak to rms value of the input current pulses. The larger the peak to rms value, the greater the percent distortion of the waveform.
Calculation of rms current
The rms value of the input line current waveform is determined by calculating
the square root of the sum of the squares of all frequency components.
The next table shows how the total transferred rms current is calculated.
Since the current waveform is in phase with the applied line to line voltage,
the power transferred is positive or real power.
|
Frequency Component (HZ) |
Value |
Value Squared |
|
1st |
.955 |
0.9120 |
|
5th |
.235 |
0.0552 |
|
7th |
.135 |
0.0182 |
|
11th |
.085 |
0.0072 |
|
13th |
.071 |
0.0051 |
|
17th |
.054 |
0.0029 |
|
19th |
.043 |
0.0019 |
|
23rd |
.034 |
0.0012 |
|
25th |
.028 |
0.0008 |
|
29th |
.024 |
0.0006 |
|
31st |
.021 |
0.0004 |
|
35th |
.018 |
0.0003 |
|
37th |
.016 |
0.0003 |
|
41st |
.012 |
0.0001 |
|
43rd |
.011 |
0.0001 |
|
47th |
.008 |
0.0001 |
|
49th |
.004 |
-- |
|
53rd |
.0025 |
-- |
|
55th |
.0012 |
-- |
|
|
SQRT of sum --> |
1.00 |
The value shown as the square root of the sum of the squares represents the rms value for current. That value of 1.00 and is equal to 100% of the power required to transfer power to the motor for full operation. Although the current waveform can be separated into many individual frequency components, each component contributes to the power that is transferred from the distribution system to the motor. Some components may contribute some additional heating to the distribution system, however that additional heating is minor and will not cause overloading of a distribution system that is designed to handle the same motor operating across the line or direct on line.
A key point is that PWM drives without an internal reactor or input ac line reactors will contribute larger distortion values. To limit peak currents, a minimum series impedance of 3% should be applied. If an existing distribution system is tuned to a specific frequency, it is possible that one of the frequency components contained within the current waveform may excite that existing system. It is important to note that if the system is not tuned to a specific frequency, the frequency components contained within the current waveform can not cause resonance to occur. Since the current flow is into the drive, no resonance can exist. The unidirectional characteristics of the PWM converter prevent current from flowing back into the distribution system.
Applying the recommendation
defined in IEEE-519 (1992) for current distortion
Changing the characteristics of the current waveform of a PWM drive with
the objective of meeting the recommendations defined in table 10.3 of
IEEE-519 (1992) is reasonable if no additional costs or additional energy
loss occurs. Most knowledgeable utilities and consultants recognize that
only more current places a greater demand on the distribution system.
Current distortion is not more current. It is only a representation of
the peak to rms value.
It is a fact that, compared to operating motors across the line, the current demanded from the distribution system when PWM drives are used is significantly less than the nameplate amps of the motor. Specifying IEEE-519 (1992) current distortion recommendations insure greater costs and higher energy losses for the sole reason of obtaining a "pretty" waveform. Current distortion is important when applied to some non linear motor equipment and electric arc furnaces. Also voltage distortion limits are important, although some types of voltage distortion, like flat topping, typically create no problems. Voltage notching and distortion about the zero crossover point of the voltage waveform can create problems with some types of power control.
What is important is that the peak of the current waveform not exceed the capabilities of the distribution system. In most cases, the use of series reactors solves that condition. Phase shifting the supply voltage also aids in keeping the peak of the current waveform, with respects to the rms value, to a reasonable value, however line to line voltage balance must be maintained to insure that currents are equal. In all cases, series impedance must exist to control the current peaks.
It is important to understand the characteristics of electrical equipment. To apply current distortion and voltage distortion limitations as a means to insure equipment operation only adds costs and losses to an electrical system. It does not guarantee that electrical problems will be eliminated.
