TECHNICAL NOTE
PowerMonic Measurement of Harmonics and Interharmonics
Introduction
PowerMonic PM40 measurements comply with IEC Standard 61000-4-7
“Electromagnetic compatibility (EMC - part 4-7: Testing and measurement techniques -
General guide on harmonics and interharmonics measurements and instrumentation
for power supply systems and equipment connected thereto”.
1st
harmonic
fundamental
1st
interharmonic
2nd
harmonic
B
i
n
4
6
2
B
i
n
4
6
3
B
i
n
4
6
4
B
i
n
4
6
5
B
i
n
4
6
6
B
i
n
4
6
7
B
i
n
4
6
8
B
i
n
4
6
9
B
i
n
4
7
0
B
i
n
4
7
1
B
i
n
4
7
2
B
i
n
4
7
3
2295 Hz
2300 Hz
2305 Hz
2310 Hz
2315 Hz
2320 Hz
2325 Hz
2330 Hz
2335 Hz
2340 Hz
2345 Hz
2350 Hz
2355 Hz
2360 Hz
2365 Hz
3rd
interharmonic
46th
harmonic
47th
interharmonic
47th
harmonic
B
i
n
4
7
4
B
i
n
4
7
5
B
i
n
4
7
6
B
i
n
4
7
7
B
i
n
4
7
8
B
i
n
4
7
9
B
i
n
4
8
0
B
i
n
4
8
1
2405 Hz
B
i
n
4
6
1
2400 Hz
B
i
n
4
6
0
2395 Hz
B
i
n
4
5
9
2390 Hz
B
i
n
2
8
2385 Hz
B
i
n
2
7
2380 Hz
B
i
n
2
6
2375 Hz
B
i
n
2
5
2370 Hz
B
i
n
2
4
140 Hz
B
i
n
2
3
135 Hz
B
i
n
2
2
130 Hz
B
i
n
2
1
125 Hz
B
i
n
2
0
120 Hz
90 Hz
2nd
interharmonic
B
i
n
1
9
115 Hz
B
i
n
1
8
110 Hz
B
i
n
1
7
105 Hz
B
i
n
1
6
95 Hz
B
i
n
1
5
100 Hz
B
i
n
1
4
85 Hz
B
i
n
1
3
80 Hz
B
i
n
1
2
75 Hz
B
i
n
1
1
70 Hz
B
i
n
1
0
65 Hz
40 Hz
B
i
n
9
60 Hz
B
i
n
8
55 Hz
B
i
n
7
50 Hz
B
i
n
6
45 Hz
B
i
n
5
35 Hz
10 Hz
B
i
n
4
30 Hz
DC
DC
B
i
n
3
25 Hz
B
i
n
2
20 Hz
B
i
n
1
15 Hz
B
i
n
0
5 Hz
The PM40 uses a Discrete Fourier Transform (DFT) to calculate harmonics and
interharmonic components of the voltage and current waveforms. The DFT input is 10
cycles of the input waveform, and the DFT output bins are spaced at 5 Hz intervals.
The first bin (Bin 0) is centered at 0 Hz (DC), the 10th bin is centered at 50 Hz and the
Nth bin is centered at 5N Hz. Only the first 482 bins are used, so the last bin (number
481) is centered at 2405 Hz.
48th
interharmonic
48th
harmonic
Figure 1 ‐ Graphical representation of harmonics and interharmonics
Harmonic Amplitudes and Phases
The harmonic amplitudes are calculated as
Hn 
1
C
i  1
2
10 n i
where C10 n i is the Root Mean Square output of the 10n  i th bin, centered at
frequency 50n  5i Hz .
The first harmonic or fundamental is therefore combined from the values of the 9th,
10th & 11th bins, with center frequencies of 45, 50 & 55 Hz respectively.
GridSense, Inc.
2568 Industrial Blvd., Ste. 110
West Sacramento, CA 95691
CHK GridSense PTY Ltd.
Tel: 916-372-4945
Fax: 916-372-4948
Suite 102, 25 Angas Street
Meadowbank, NSW 2114, Australia
Tel: +61 2 8878-7700
Fax: +61 2 8878-7788
gridsense.com
The harmonic phase angle of the n th harmonic is the phase angle of the 10n th bin,
relative to the phase angle of fundamental (or first harmonic) of the phase A voltage
(bin 10).
This phase angle can be used in harmonic power calculations.
Interharmonic Amplitudes
The interharmonic amplitudes are calculated as
IH N 
2
C
i  8
2
10 N i
where C10 N i is the RMS output of the (10N+i) th bin, centered at frequency
50 N  5i Hz .
The first interhamonic therefore includes bins 2 through 8, with center frequencies of
10 Hz through 40Hz.
The second interharmonic uses bins 12 through 18, with center frequencies of 60 Hz
through 90 Hz.
PowerView can display interharmonics as absolute values (Volts or Amps) or as relative
values, where the fundamental is assumed to have a magnitude of 100%.
Total Harmonic Distortion
IEC Standard 61000-4-7 defines Total Harmonic Distortion (THD) as the ratio of the
Root Mean Square (RMS) sum of all the harmonic components to the RMS value of the
first harmonic or fundamental.
Total Harmonic Distortion - Fundamental
In the PM40, this value is known as THD_F and is calculated as
H 
THD _ F    n 
n 2  H1 
48
2
THD_F is normally expressed as a percentage.
Graphical representation of harmonics and interharmonics
2
Total Harmonic Distortion - RMS
When there is severe distortion on the waveform, the total harmonic distortion relative
to the RMS value of the waveform is often a more useful measure.
In the PM40, this measurement is known as THD_R, and is calculated as:
 H
THD _ R    n
n  2  V RMS
48



2
THD_R is normally expressed as a percentage.
Converting between THD_F and THD_R
To calculate THD_F from THD_R use the following formula:
THD _ F 
THD _ R
1  THD _ R 
2
To calculate THD_R from THD_F use the following formula:
THD _ R 
THD _ F
1  THD _ F 
2
Graphical representation of harmonics and interharmonics
3