# Measurement of fundamental frequency component and carrier frequency component of voltage source PWM inverter

WT5000 Precision Power Analyzer

1. Introduction

Inverters using PWM control are widely used as drivers for rotating equipment such as motors and compressors (hereinafter collectively referred to as motors). These inverters control the drive frequency and torque to change the motor speed from low to high in response to DC or commercial frequency input. Voltage-source PWM inverters change the fundamental frequency component of voltage waveform by changing the duty of the pulse wave to change the motor behavior including output. In that process, the effect of the triangular wave contained in the current flowing through the motor differs depending on the frequency of the pulse waveform (carrier frequency). Therefore, higher frequencies are being used in order to make the current waveform closer to a sine wave and to miniaturize inverter systems.

2. Challenges

The inverter's fundamental frequency component, which is closely related to motor torque, can be measured relatively easily by using the harmonic measurement function built into a power analyzer. It can also be measured by using the filter function appropriately without using the harmonic measurement function.

For the carrier frequency component, a close value can be obtained simply by subtracting the fundamental frequency component from the power value of the entire measurement bandwidth.

However, in order to obtain the value of only the carrier frequency component, it is necessary to make full use of the harmonic measurement function. In particular, the harmonic measurement function has a frequency resolution due to its measurement principle, so a gap is created on the frequency axis and the function may not be able to measure carrier frequency components over the entire measurement bandwidth. These characteristics need to be considered when configuring the power analyzer settings. For recent digital sampling type power analyzers, appropriate filter settings are essential and measurement results may vary depending on the cutoff frequency setting. Additionally, the effect of aliasing based on the sampling theorem cannot be ignored.

3. WT5000 measurement principle and various line filter functions

Before explaining how to measure the inverter's fundamental frequency component and carrier frequency component, we will introduce the principle of power measurement using the Precision Power Analyzer WT5000. It can also be seen as the basic principle of power measurement using a digital sampling method, and it is especially important to accurately measure the period of the signal being measured. Understanding the power measurement principle is also useful for understanding the WT5000’s various filter functions essential for measuring fundamental frequency components and harmonic components.

1) Principle of WT5000 power measurement

The WT5000 performs power calculation using the digital sampling method. The digital sampling method samples input voltage and current waveforms at the same timing and obtains the power value by averaging the instantaneous power obtained by multiplying the two. At this time, measurement accuracy is ensured by obtaining the average value over several periods.

Figure 1. Principle of digital sampling type Power Analyzer

The important point here is to accurately measure the period of the input signal. Particularly in the power measurement of voltage source PWM inverters, it is difficult to accurately measure the period at the zero-crossing point because the voltage waveform is pulse-shaped and the current waveform  is a sine wave with a superimposed triangular wave of the carrier frequency of the pulse wave. Therefore, a frequency filter is provided to accurately measure the period. This frequency filter can be set not only to low-pass but also to high-pass, and also function as a band-pass filter by combining the two, making it useful for measuring the carrier frequency. In addition, a detection level can be set for the filter and zero-crossing point to measure the ON/OFF period even of burst waveforms with interrupted periods.

Figure 2. Input signal period detection

On the other hand, the WT5000 also includes a digital filter average method that measures power without requiring period detection. If you select this mode, basically you don’t need to turn on the frequency filter (however, it is preferable to turn it on if you want to measure the fundamental frequency with high accuracy).

Figure 3. Comparison of WT5000 period average method (upper) and digital filter average method (lower)

2) WT5000 line filter function

The WT5000 has multiple line filters. One of them is an anti-aliasing filter to avoid aliasing based on the sampling theorem. This is an analog filter with a cutoff frequency of 1 MHz that is effective for both normal and harmonic measurements. Another is a digital filter with a cutoff frequency that can be set from 300 kHz to 0.1 kHz in 0.1 kHz increments of resolution for normal measurement. Furthermore, a digital filter for harmonic measurement is available with the same specifications as for normal measurement. Since the two digital filters can be set independently for the same signal, it is possible to simultaneously measure harmonic components up to and including the required bandwidth, including the fundamental frequency component, while performing normal measurement over the entire measurement bandwidth.

Figure 4. Line filters installed in WT5000

4. Measurement of fundamental frequency component of inverter output

1) Measurement method using harmonic measurement function

Using the WT5000's harmonic measurement function, you can easily measure the fundamental frequency component of the inverter output.

The harmonic measurement function can be synchronized to the fundamental frequency related to the motor's rotational frequency using the PLL method, so set the PLL source to voltage or current.

The PLL source can be set separately from the synchronization source for normal measurement. Since both sources use the results of the frequency measurement circuit, you need to first make sure that the frequency of the input PLL source (and synchronization source) can be measured stably and accurately.

Figure 5. WT5000 PLL circuit

According to the sampling theorem, frequency components exceeding 1/2 of the sampling frequency (10 MS/s for WT5000) will appear aliased. For this reason, turn on the anti-aliasing filter with a cutoff frequency of 1 MHz if the influence of components in higher frequency bands is expected. In addition, turn on the line filter for harmonic measurement to eliminate the effect of resampling during harmonic measurement. In this case, it is desirable to set the cutoff frequency at about 100 times the fundamental frequency to minimize the effect on the fundamental frequency component. Note that the cutoff frequency often needs to be adjusted as the line filter directly affects measured values.

2) Measurement of fundamental frequency component by performing normal measurement with the line filter

Turn on the line filter to remove the carrier frequency component and perform the measurement using the value of the fundamental frequency component measured with the above harmonic measurement function as a reference.

Figure 6. Setting of line filter cutoff frequency

The cutoff frequency of the line filter should be set to about 1/5 of the carrier frequency to avoid being affected by the carrier frequency component. At this time, turn on the anti-aliasing filter with a cutoff frequency of 1 MHz.

Figure 7. shows an example of actual measurement. The upper half of the screen shows the normal measurement results, and the lower half shows the harmonic measurement results. The cutoff frequency for harmonic measurement is 6 kHz (100 times the fundamental frequency), and the cutoff frequency for normal measurement is 3 kHz (1/5 of the carrier frequency) since the fundamental frequency is 60 Hz and the carrier frequency according to the inverter settings is 15 kHz. It can be seen that the voltage and power values from the normal measurement are close to the fundamental frequency component of the harmonic frequency.

Figure 7. Example of normal measurement and harmonic measurement with the line filter OFF (upper) and ON (lower)

1) Subtract the power value of the fundamental frequency component from the power value of the entire measurement bandwidth

The simplest way to measure the carrier frequency component is to subtract the power value of the fundamental frequency component from the power value of the entire measurement bandwidth. The carrier frequency component can be given by obtaining the fundamental frequency component using the measurement method described earlier and subtracting it from the power value of the entire measurement bandwidth. However, the difference is not necessarily the value of only the carrier frequency component.

Figure 8. Calculation of carrier frequency components based on the measured values of the entire measurement bandwidth by normal measurement and the measured values of fundamental frequency components by harmonic measurement
Fundamental frequency: 60 Hz & carrier frequency: 2 kHz (upper) Fundamental frequency: 190 Hz & carrier frequency: 5 kHz (lower)

The power value of the entire measurement bandwidth includes a DC component. It also includes harmonic components of the fundamental frequency and of the carrier frequency component. Additionally, it may contain high frequency components that exceed the carrier frequency, which can be considered a noise  region. Generally, it is better to remove them with a line filter. In fact, their effect cannot be said to be zero.

With the above components taken into account, the method for measuring only the carrier frequency component is explained below.

2) Power measurement of carrier frequency components

The carrier frequency component of the inverter is measured using the harmonic measurement function. As mentioned earlier, the harmonic measurement has a frequency resolution. By increasing the resolution, it is possible to measure only the components in a certain bandwidth, but a gap may appear in the measurement bandwidth depending on the settings.

Specifically, when the WT5000 is used for the measurement and the fundamental frequency is 60 Hz and the number of FFT points is set to 8192, the window width will be 8 waveforms. Therefore, the frequency resolution will be “the fundamental frequency x 1/8 Hz” and there is a gap between harmonic orders where no measurements are made.

If the number of FFT points is set to 1024, the resolution and accuracy will be lower, but the window width will be1 wave. This means that the resolution will be “the fundamental frequency x 1 Hz” and there will be no gap in the measurement bandwidth between orders. Therefore, 1024 FFT points is recommended for harmonic component measurement.

Figure 9. Measurement gap between orders when the number of FFT points is 8192

Figure 10. Measurement between orders when the number of FFT points is 1024

Alternatively, it is also possible to roughly measure the carrier frequency component by setting the fundamental frequency to be exactly an integer fraction of the carrier frequency. However, under very special conditions, carrier frequency components may be dispersed, so there is a possibility that some of the components may be missed.

When the number of FFT points is 1024, the resampling frequency for harmonic measurement is “the fundamental frequency x 1024 Hz”. When the fundamental frequency is low, there is a high possibility that the resampling frequency will not be high enough to capture carrier frequency components completely. Therefore, when measuring carrier frequency components, it is necessary to set the fundamental frequency as high as possible and increase the resampling frequency.

Next, we consider the line filter settings for harmonic measurement. As mentioned above, the harmonic measurement function is used, so turn on the anti-aliasing filter with a cutoff frequency of 1 MHz. It is desirable to set the cutoff frequency for resampling to about 1/10 of the resampling frequency.

Carrier frequency components may not be measured accurately with the proposed cutoff frequency as the difference between the resampling frequency related to the fundamental frequency and the carrier frequency is small. In this case, it is necessary to obtain the carrier frequency component by subtracting the power value of the fundamental frequency component from the power value of the entire measurement bandwidth.

In actual measurement, it is also necessary to measure and sum the power dispersed near the carrier frequency since the inverter's pulse wave may not be exactly at the carrier frequency.

Below are examples of actual measurement.

Figure 11. Measurement results when the No. of FFT points is  to 1024 (component observed near 68th order ≒ 4 kHz)
(Fundamental frequency: 60
Hz, carrier frequency: 2 kHz, harmonic measurement cutoff frequency: 6 kHz)

Figure 12. Measurement results when the No. of FFT points is set to 8192 (carrier frequency component cannot be observed)
(Fundamental frequency: 60
Hz, carrier frequency: 2 kHz, harmonic measurement cutoff frequency: 6 kHz)

Figure 13. Measurement results when the No. of FFT points is set to 1024 (component observed near 54th order ≒ 10.3 kHz)
(Fundamental frequency: 190
Hz, carrier frequency: 5 kHz, harmonic measurement cutoff frequency: 19 kHz)

Figure 14. Measurement results when the No. of FFT points is set to 8192 (carrier frequency component cannot be observed)
(Fundamental frequency: 190 Hz, carrier frequency: 5 kHz, harmonic measurement cutoff frequency: 19 kHz)

6. Summary

Table 1 summarizes the methods for measuring the fundamental frequency component and carrier frequency component of a motor drive inverter using the WT5000 as an example.

Table 1. Setting examples for measuring inverter fundamental  frequency component and carrier frequency component

Meas.
Mode
Frequency
filter
settings
Line filter settings Harmonic
meas.
settings
Anti-
aliasing
Filter
Individual line filter FFT
points
Fundam.
Frequency component
meas.
Normal
meas
ON
cut off
frequency:
2 kHz or less
ON ON
cut off
frequency:
frequency
Harmonic
meas.
Same as above ON ON
cut off
frequency:
frequency
1024
Career Frequency
Component
meas.
Harmonic
meas.
Same as above ON Same as above 1024

There are several measurement methods, and it is difficult to say which one is the best. These measurement methods give relatively similar results of fundamental frequency component, however, result in a large variation in carrier frequency component. In particular, the value of carrier frequency component changes greatly depending on the cutoff frequency setting of the line filter, so it is necessary to finely adjust the settings using the method that seems most appropriate.

 WT5000 Precision Power Analyzer lWorld's highest power accuracy lFlexible expandability provided by its modular architecture lUp to 10 MS/s, 18 bit sampling lSimultaneous power measurement of up to 7 inputs lEvaluation of up to 4 motors (optional) l10.1-inch color LCD (WXGA) with touch screen lCurrent Sensor Element for direct connection with a current sensor lWaveform data streaming at up to 2 MS/s (optional)

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