Interharmonics

APPLICATION NOTE
INTERHARMONICS
Z. Hanzelka, A. Bien
December 2015
ECI Publication No Cu0151
Available from www.leonardo-energy.org

Publication No Cu0151
Issue Date: December 2015
Page i
Document Issue Control Sheet
Document Title: Application Note – Interharmonics
Publication No: Cu0151
Issue: 03
Release: Public
Author(s): Z. Hanzelka, A. Bien
Reviewer(s): Roman Targosz, David Chapman
Document History
Issue Date Purpose
1 July 2004 Initial publication
2 February
2012
Adapted and updated for adoption into the Good Practice Guide
3 December
2015
Review by Stefan Fassbinder
Disclaimer
While this publication has been prepared with care, European Copper Institute and other contributors provide
no warranty with regards to the content and shall not be liable for any direct, incidental or consequential
damages that may result from the use of the information or the data contained.
Copyright© European Copper Institute.
Reproduction is authorised providing the material is unabridged and the source is acknowledged.

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CONTENTS
Summary ........................................................................................................................................................ 1
Introduction.................................................................................................................................................... 2
Definitions...................................................................................................................................................... 2
Interharmonic frequency........................................................................................................................................2
Voltage or Current Interharmonic..........................................................................................................................2
Sources .......................................................................................................................................................... 3
Arcing loads ............................................................................................................................................................3
Electric motors........................................................................................................................................................4
Static frequency converters....................................................................................................................................5
Indirect frequency converters..................................................................................................................5
Current-source load commutated inverters ............................................................................................5
Voltage-source inverters ........................................................................................................................................7
Integral cycle control of thyristor switch................................................................................................................7
Mains signalling voltage in power systems ............................................................................................................9
Effects of the presence of interharmonics .................................................................................................... 11
Voltage fluctuations and flicker............................................................................................................................11
Measurement............................................................................................................................................... 13
Standardization ............................................................................................................................................ 14
Standardised factors.............................................................................................................................................14
Standardised method of measurement................................................................................................................14
Compatibility limits...............................................................................................................................................16
Provisions of International Electrotechnical Commission (IEC) .............................................................16
CENELEC (Standard EN 50160) ...............................................................................................................17
Subharmonic and interharmonic emission limits [13] ...........................................................................18
Mitigation of interharmonics and reduction of their effects ......................................................................... 19
Conclusion .................................................................................................................................................... 21
References.................................................................................................................................................... 22
Appendix 1 ................................................................................................................................................... 23
Appendix 2 ................................................................................................................................................... 28

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SUMMARY
Interharmonics are voltages or currents with a frequency that is a non-integral multiple of the fundamental
supply frequency, while each harmonic frequency is an integral multiple of the supply frequency.
Interharmonics, always present in the power system, have recently become of more importance since the
widespread use of power electronic systems results in an increase of their magnitude.
Interharmonics are caused by the asynchronous switching of semiconductor devices in static converters such
as cycloconverters and pulse width modulation (PWM) converters, or by rapid changes of current in loads
operating in a transient state.
This Application Note discusses the background, origin and measurement of interharmonics.

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INTRODUCTION
Harmonics are voltages or currents with a frequency that is an integral multiple of the fundamental supply
frequency. Interharmonics are voltages or currents with a frequency that is a non-integral multiple of the
fundamental supply frequency. The knowledge of electromagnetic disturbance associated interharmonics is
still developing and currently there is a great deal of interest in this phenomenon. Interharmonics, always
present in the power system, have recently become of more importance since the widespread use of power
electronic systems results in increase of their magnitude.
DEFINITIONS
Harmonics and interharmonics of an analyzed waveform are defined in terms of the spectral components in a
quasi-steady state over a defined range of frequencies. Table 1 provides their mathematical definitions.
Harmonic 1nff  where n is an integer greater than zero
DC component 1nff  for n = 0
Interharmonic 1nff  where n is greater than zero
Subharmonic 0f Hz and 1ff 
f1 - voltage fundamental frequency (basic harmonic)
Table 1 - Spectral components of waveforms (of frequency f).
The term „subharmonic” does not have any official definition - it is a particular case of interharmonic of a
frequency less than the fundamental frequency. However, the term has appeared in numerous references and
is in general use in the professional community.
IEC-61000-2-1 standard defines interharmonics as follows:
Between the harmonics of the power frequency voltage and current, further frequencies can
be observed which are not integer multiples of the fundamental. They can appear as discrete
frequencies or as a wide-band spectrum.
For the purpose of further considerations the following detailed definitions apply.
INTERHARMONIC FREQUENCY
Any frequency which is a non-integer multiple of the fundamental frequency. By analogy to the order of a
harmonic, the order of interharmonic is given by the ratio of the interharmonic frequency to the fundamental
frequency. If its value is less than unity, the frequency is also referred to as a subharmonic frequency.
According to the IEC recommendation, the order of interharmonic is denoted by the letter ”m” (according to
IEC 61000-2-2).
VOLTAGE OR CURRENT INTERHARMONIC
A sinusoidal voltage or current of a frequency between the harmonics, i.e. a frequency which is not an integer
of the fundamental component frequency.

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SOURCES
There are two basic mechanisms for the generation of interharmonics.
The first is the generation of components in the sidebands of the supply voltage frequency and its harmonics
as a result of changes in their magnitudes and/or phase angles. These are caused by rapid changes of current
in equipment and installations, which can also be a source of voltage fluctuations. Disturbances are generated
by loads operating in a transient state, either continuously or temporarily, or, in many more cases, when an
amplitude modulation of currents and voltages occurs. These disturbances are of largely random nature,
depending on the load changes inherent in the processes and equipment in use.
The second mechanism is the asynchronous switching (i.e. not synchronized with the power system frequency)
of semiconductor devices in static converters. Typical examples are cycloconverters and pulse width
modulation (PWM) converters. Interharmonics generated by them may be located anywhere in the spectrum
with respect to the power supply voltage harmonics.
In many kinds of equipment both mechanisms take place at the same time.
Interharmonics may be generated at any voltage level and are transferred between levels, i.e. interharmonics
generated in HV and MV systems are injected into the LV system and vice versa. Their magnitude seldom
exceeds 0.5% of the voltage fundamental harmonic although higher levels can occur under resonance
conditions.
Basic sources of this disturbance include:
 arcing loads
 variable-load electric drives
 static converters, in particular direct and indirect frequency converters
 ripple controls
Interharmonics can also be caused by oscillations occurring in the systems comprising series or parallel
capacitors and transformers subject to saturation and during switching processes.
The power system voltage contains a background Gaussian noise with a continuous spectrum. Typical levels of
this disturbance are in the range (IEC 61000-2-1):
 40-50 mV (ca. 0.02 % UN ) when measured with a filter bandwidth 10 Hz
 20-25 mV (ca. 0.01 % UN ) when measured with a filter bandwidth 3 Hz
where UN is the nominal voltage 230 V.
ARCING LOADS
This group includes arc furnaces and welding machines. Arc furnaces do not normally produce significant
interharmonics, except where amplification occurs due to resonance conditions. Transient operation, being a
source of interharmonics, occurs most intensively during the initial phase of melting (Figure 1).

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Figure 1 - Typical arc furnace voltage flicker measured at the supply transformer secondary.
Welding machines generate a continuous spectrum associated with a particular process. The duration of
individual welding operations ranges from one to over ten seconds, depending on the type of welding
machine.
ELECTRIC MOTORS
Induction motors can be sources of interharmonics because of the slots in the stator and rotor iron,
particularly in association with saturation of the magnetic circuit (so-called „”slot harmonics“„). At the steady
speed of the motor, the frequencies of the disturbing components are usually in the range of 500 Hz to
2000 Hz but, during the startup period, this range may expand significantly. Natural asymmetry of the motor
(rotor misalignment, etc.) can also be a source of interharmonics – see Figure 2.
Figure 2 – Results of the spectral analysis of the motor phase current and voltage at the motor terminals.

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Motors with variable-torque loading, i.e. forge drives, forging hammers, stamping machines, saws,
compressors, reciprocating pumps, etc., can also be sources of subharmonics. The effect of variable load is also
seen in adjustable-speed drives powered by static converters.
In wind power plants the effect of the variation in turbine driving torque, resulting, for example, from the
”shadow effect“ of the pylon, can modulate the fundamental voltage component, thus becoming the source of
undesirable, low-frequency components.
STATIC FREQUENCY CONVERTERS
INDIRECT FREQUENCY CONVERTERS
Indirect frequency converters contain a dc-link circuit with an input converter on the supply network side and
an output converter (usually operating as an inverter) on the load side. In either current or voltage
configurations the dc-link contains a filter which decouples the current or the voltage of the supply and load
systems. For that reason the two fundamental (the supply and the load) frequencies are mutually decoupled.
But ideal filtering does not exist, and there is always a certain degree of coupling. As a result, current
components associated with the load are present in the dc-link, and components of these are present on the
supply side. These components are subharmonic and interharmonic with respect to the power system
frequency.
CURRENT-SOURCE LOAD COMMUTATED INVERTERS
Due to the semiconductor devices switching technique, these are classified as line commutated indirect
frequency converters. A frequency converter (Figure 3) consists of two three-phase bridges P1 and P2 and a
dc-link with reactor of inductance Ld. One of the bridges operates in the rectifier mode and the other in the
inverter mode, although their functions could be interchangeable.
Figure 3 – Indirect frequency converter with a load commutated inverter.
The presence of two rectifier bridges supplied from two systems of different frequencies results in the dc-link
current being modulated by two frequencies – f1 and f2. Each of the converters will impose non-characteristic
components on the dc link, which will appear as non-characteristic harmonics on the ac side, both in the load
and in power supply system.
Components in the dc-link:
from system 1: fd1 = p1kf1 k = 0, 1, 2, ...
from system 2: fd2 = p2nf2 n = 0, 1, 2, ...
where:
p1, p2 pulse number, respectively of converter P1 and P2

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f1 fundamental frequency of system 1 (supply network) [Hz]
f2 fundamental frequency of system 2 (load) [Hz].
The operation of converter P1 will cause characteristic current harmonics to occur in the supply network,with
the following frequencies:
  11, 1 fkpf charhh  k = 1, 2, ...
caused by the converter P1 operation will occur in the supply network.
Also components associated with the components occurring in the direct current of orders nd2 will occur,
where
1
2
2
f
f
n d
d 
with respect to the supply system frequency, which is due to the converter P2 operation.
A complete set of frequencies of the supply network current components could be expressed in general form
by:
𝑓𝑠 = (𝑘𝑝1 ± 1)𝑓1 ± 𝑝2 𝑛𝑓2
where
fs = frequency components in the supply current
k = 0, 1, 2, ...
n = 0, 1, 2, ...
Assuming n = 0, for k = 0, 1, 2,... we obtain orders of characteristic harmonics for a given configuration of the
converter P1. Components determined for k = constant and n  0, are the sidebands adjacent to the inverter
characteristic frequencies. Thus each characteristic harmonic, e.g. for a six-pulse bridge, of order n1 = 1, 5, 7,...
has its own sidebands as illustratively shown for the 5th harmonic in Figure 4.
Figure 4 – Indirect frequency converter with a load commutated inverter.
The first pair of interharmonics, occurring in the vicinity of the fundamental component, i.e. with frequencies
f1  p2 f2, has the largest amplitude. The inductance of the reactor in the dc-link has significant influence on the
interharmonics level. An example of the electric drive configuration containing a current-source inverter is the
static slip recovery drive.

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VOLTAGE-SOURCE INVERTERS
Figure 5 – Schematic diagram of a voltage source frequency converter.
In the voltage source converter (Figure 5) also, the characteristic harmonics of converter P1 are predominant.
Sidebands, with frequencies determined by the number of pulses of converter P2, occur around the
characteristic P1 frequencies, i.e.:
𝑓𝑠 = (𝑘𝑝1 ± 1)𝑓1 ± 𝑝2 𝑛𝑓2
where
fs = frequency components in the supply current
k = 0, 1, 2, ...
n = 0, 1, 2, ...
In most cases non-characteristic harmonics are a very small portion of the supply current.
Numerical determination of the supply current harmonics and interharmonics values requires precise analysis
of a particular frequency converter including the load, or information from the manufacturer.
Some converters comprise an active input rectifier operating at a switching frequency that is not an integer of
the line frequency. This frequency may be constant or variable, depending on the design of the converter
control.
Voltage-source frequency converters with a PWM modulated input rectifier emit current components at the
semiconductor device switching frequency and their harmonics, which are not synchronized with the line
frequency. Normally they are within the range from several hundred Hertz to several tens kHz.
INTEGRAL CYCLE CONTROL OF THYRISTOR SWITCH
This kind of control allows a full cycle of current to flow through a semiconductor switch. Thus the current is
not distorted as a result of the control – it is either sinusoidal (for a linear load) or it is zero.
Figure 6 shows an example of semiconductor switches control in a three-phase configuration. Switching a
three-phase load at zero-crossing of phase voltages results in a current flow in the neutral conductor in a four-
wire system. For simultaneous switching in phases and a resistive load there is no current flow in the neutral
conductor but, in the case of an inductive load, transients associated with switching processes occur.

Page 8
Figure 6 – Waveforms of currents in a three-phase 4-Wire configuration for integral cycle control.
Figure 7 – Alternating current controller in a three-phase (a) and single-phase (b) configuration.
The analysis for a configuration as in Figure 7a (with neutral conductor) can be restricted to a single-phase
circuit (Figure 7b). A single-phase, resistive load, as the most common practical application, will be further
considered.
A full control cycle comprises N cycles of conduction within an integer number of cycles M (Figure 8). The
average power supplied to a load is controlled by means of controlling the value of the ratio N/M. As a basis
for Fourier analysis, the period of the current waveform repeatability should be assumed to be Mf1
-1
, where f1
is the frequency of the supply voltage and M is the number of cycles.
The first component is the interharmonic at a frequency of (1/M)f1, which is the lowest frequency component
of the current. In the example from Figure 8, where N = 2, M = 3, the value of this subharmonic is one third of
the supply voltage frequency. Frequencies of the other components are multiples of it.
Figure 8 – Waveform of a load current in the integral cycle controlled system: N = 2, M = 3.

Page 9
This kind of control is a source of subharmonics and interharmonics, but it is not a source of higher harmonics
of the fundamental component. When N = 2, M = 3, as in Figure 8, amplitudes of the harmonics are zero for
n = 6, 9, 12.... . The spectrum of the current for this case is shown in Figure 9. As seen from the figure, major
components are harmonic of the supply voltage frequency and subharmonic of frequency (2f)/3. Amplitudes of
harmonics are equal to zero.
Figure 9 – Spectrum of the current for N = 2, M = 3.
MAINS SIGNALLING VOLTAGE IN POWER SYSTEMS
The public power network is intended primarily for supplying electric power to customers. However the
supplier often uses it for transmitting system management signals, e.g. for controlling certain categories of
loads (street lighting, changing tariffs, remote loads switching, etc.) or data transmission.
From the technical point of view these signals are a source of interharmonics occurring with a duration of 0.5-
2 s (up to 7 s in earlier systems) repeated over a period of 6-180 s. In the majority of cases the pulse duration is
0.5 s, and the time of the whole sequence is about 30 s. The voltage and frequency of the signal are pre-
agreed and the signal is transmitted at specified times.
Four basic categories of these signals are specified in Standard IEC 61000-2-1:
ripple control signals. Sinusoidal signals in the range 110-2200 (3000) Hz with 110-500 Hz preference
in new systems. Mainly used in professional power systems (sometimes also in industrial power
systems) at LV, MV and HV levels. Magnitude of the sinusoidal voltage signal is in the range 2-5% of
the nominal voltage (depending on local practices). Under resonance conditions it may increase to
9%.
Medium frequency power-line-carrier signals. Sinusoidal signals in the range 3-20 kHz, preferably, 6-
8 kHz. Mainly used in professional power systems. Signal magnitude up to 2% UN.
Radio-frequency power-line-carrier signals: 20-150 (148.5) kHz (up to 500 kHz in some countries).
Used in professional, industrial and communal power systems, also for commercial applications
(equipment remote control, etc.).
Mains-mark systems. Non-sinusoidal marks on the voltage waveform in the form of:

Page 10
long pulses (voltage notch of duration 1.5-2 ms, preferably at the voltage zero-crossing
point);
short pulses, duration 20-50 s;
pulses with 50 Hz frequency and duration equal one or a half of the mains voltage cycle.
Figure 10 – FFT results for the voltage during emission of data transmission signal (Uih = 1.35%, f(Uih) = 175Hz).
Figure 10 shows an example of the voltage spectrum for a system using data transmission at a frequency of
175 Hz (Uih = 1.35 %). In the illustrated case, there are other interharmonics generated by interaction with
harmonic frequencies. Components above the second harmonic are unimportant (they will not disturb loads),
while interharmonics below 200 Hz may cause problems.

Page 11
EFFECTS OF THE PRESENCE OF INTERHARMONICS
Interharmonic currents cause interharmonic distortion of the voltage depending on magnitudes of the current
components and the supply system impedance at that frequency. The greater the range of the current
components’ frequencies, the greater is the risk of the occurrence of unwanted resonant phenomena, which
can increase the voltage distortion and cause overloading or disturbances in the operation of customers'
equipment and installations. Among the most common, direct, effects of interharmonics are:
a) Thermal effects
b) Low-frequency oscillations in mechanical systems
c) Disturbances in fluorescent lamps and electronic equipment operation. In practice, the operation of
any equipment that is synchronized with respect to the supply voltage zero-crossing or crest voltage
can be disturbed (Figure 11)
d) Interference with control and protection signals in power supply lines. This is now the main harmful
effect of the interharmonics
e) Overloading passive parallel filters for high order harmonics
f) Telecommunication interference
g) Acoustic disturbance
h) Saturation of current transformers
The most common effects of the presence of interharmonics are variations in rms voltage magnitude and
flicker.
Figure 11 – Multiple zero-crossing of the voltage waveform as a result of distortion.
VOLTAGE FLUCTUATIONS AND FLICKER
The supply voltage can be expressed as:

h
hhi tUtmtUtu )sin()]sin(1)[sin()( 11 
)]sin(1[)sin()sin()( 11 tmtUtUtu i
h
hh  








 
where
11 2 f 
m is the index of modulation signal with frequency ii f 2 .

Page 12
The above equations represent possible sources of voltage fluctuations caused by modulation of the
fundamental component with integer harmonics. The second case is of small practical significance.
With only the fundamental component taken into account, the equation becomes:
    tt
mU
tUtmtUtu iii   11
1
1111 coscos
2
sin)]sin(1)[sin()(
In this equation, besides the fundamental component, there are two components with frequencies associated
with the modulating signal frequency located symmetrically on each side of the fundamental frequency
component. Periodic variations of the voltage could be considered as variations of the rms (or peak) value, or
as a result of the presence of the sideband interharmonics, which modulate the supply voltage.
For instance, for )2sin()2sin()( tfmfttu i  (assumed U1 = 1), the maximum variation of voltage amplitude is
equal to the amplitude of the interharmonic, whereas the variation of the rms value depends on both the
amplitude and frequency of the interharmonic. Figure 12 shows maximum percentage variation of the voltage
rms value, determined over several cycles of the fundamental waveform, caused by interharmonics of
different frequencies but of a constant amplitude m = 0.2% of the fundamental component voltage.
Figure 12 – Dependence of maximum rms voltage variation on the frequency of an interharmonic of constant
amplitude (0.2% of the fundamental component amplitude) [10].
As seen from Figure 12 the influence of interharmonics of frequencies higher than twice the power supply
frequency is small compared to the influence of components of frequencies lower than the second harmonic
frequency (100 Hz). In case of interharmonics there is a risk of voltage fluctuations causing flicker if the level
exceeds, for a given frequency, certain limit values. Hence, if 1ffi  , and particularly for if near to the
fundamental frequency Hzf 15( 1  ), modulation of the fundamental component causes fluctuations of rms
voltage magnitude and therefore it is a source of flicker. This phenomenon can be observed both for
incandescent and fluorescent lamps, however the mechanism and frequency range, and also permissible
amplitudes of disturbing components are entirely different.
A particular source of flicker can be the power line signaling systems discussed earlier. Despite their small
magnitude, these signals can sometimes give rise to flicker in case of very sensitive lighting devices such as
energy-saving compact fluorescent lamps, particularly with inductive ballasts. This kind of disturbance seldom
occurs for light sources with electronic ballasts.

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MEASUREMENT
Most instruments that perform measurements in the frequency domain work correctly when only harmonics
are present in the measured signal. These instruments employ a phase locked loop to synchronize the
measurement with the fundamental component frequency and sample the signal during one or several cycles
in order to analyze it using Fast Fourier Transformation (FFT). Due to the phase locked loop, the ”single-cycle“
samples can give an accurate representation of the waveform spectrum only when it does not contain
interharmonics. If other than harmonic frequencies (in relation to the measuring period) do occur and/or the
sampled waveform is not periodic in this time interval, difficulties with interpretation of results arise.
The fundamental analysis tool is the Fourier transformation (FT). In practice the signal is analyzed in a limited
time interval (measuring window of time Tw) using a limited number of samples (M) of the actual signal.
Results of Discrete Fourier Transform (DFT) depend on the choice of the Tw and M values. The inverse of Tw is
the fundamental Fourier frequency, fF. DFT is applied to the actual signal within the time-window; the signal
outside the window is not processed but is assumed to be identical to the waveform inside the window. In this
way, the actual signal is substituted with a virtual one, which is periodic with a period equal to the window
width. In the analysis of periodic waveforms there is no problem synchronizing the analysis time with the
fundamental waveform period (also with harmonics). However, with interharmonics analysis the problem
becomes more difficult. The frequencies of interharmonic components are non-integer multiples of the
fundamental frequency, and often they are time-varying, which makes the measurement additionally difficult.
Because of the presence of both harmonic and interharmonic components the Fourier frequency, which is the
greatest common devisor of all component frequencies contained in the signal, is different from the supply
voltage fundamental frequency and is usually very small. There are two problems:
 Minimum sampling time can be long and the number of samples large
 It is difficult to predict the fundamental Fourier frequency because not all the component frequencies
of the signal are known a priori
This can be illustrated by the following examples:
The signal to be analyzed is a sum of the fundamental component (50 Hz), an interharmonic (71.2 Hz) and a
harmonic (2500 Hz). The fundamental Fourier frequency is 0.2 Hz and is much lower than the frequency of the
fundamental component. The corresponding period is 5 s and consequently the permissible minimum
sampling time is also 5 s. Assuming the sampling frequency is 10 kHz, which is practically the minimum
applicable value resulting from the Nyquist criterion (Appendix 2), the minimum required number of samples
M is 50,000. If there were no interharmonic component (71.2 Hz), the minimum time measurement would be
20 ms and the number of samples would be 200.
The signal to be analyzed is a sum of the fundamental component (50 Hz) and a harmonic (2500 Hz), the
amplitude of each of them sinusoidally varying with frequency 0.1 Hz and 5 Hz respectively. The effect of these
modulations is four interharmonics at frequencies of: 49.9 Hz, 50.1 Hz, 2495 Hz and 2505 Hz. The fundamental
Fourier frequency is 0.1 Hz, and the minimum sampling time 10 s and M = 100,000.
In practical applications, due to the equipment and software limitations, the number of samples M cannot be
greater than a certain maximum number and consequently the measurement time is limited. Use of a
measurement time different from the fundamental Fourier period results in a discontinuity between the signal
at the beginning and the end of the measuring window. This give rise to errors in identification of the
components known as spectrum leakage. A possible solution of this problem is the use of the “weighted” time-
window to a time-varying signal before FFT analysis. In practice two kinds of measuring windows are applied:
the rectangular and Hanning window (Appendix 1).

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STANDARDIZATION
STANDARDISED FACTORS
Table 2 gives some numerical factors of interharmonics content used in various standardisation documents.
Factor Definition
Magnitude of the interharmonic with respect to the
fundamental component (current or voltage) 1Q
Qi
Total Distortion Content 2
1
2
QQTDC 
Total Distortion Ratio
1
2
1
2
1 Q
QQ
Q
TDC
TDR


Total Interharmonic Distortion Factor
1
1
2
Q
Q
TIHD
n
i
i

Total Subharmonic Distortion
1
1
2
Q
Q
TSHD
S
i
i

Q total rms value representing either current or voltage
Q1 rms value of the fundamental component
Qi rms value of the interharmonic
i running number of interharmonic
n total number of considered interharmonics
S total number of considered subharmonics.
Table 2 – Harmonic distortion factors applied in Standards.
STANDARDISED METHOD OF MEASUREMENT
The measurement of interharmonics is difficult with results depending on many factors, hence the attempts to
develop a measurement method, which will simplify the measurement process and produce repeatable
results. Standard [6] suggests a method of interharmonics measurement based on the concept of the so-called
“grouping”. Its basis is Fourier analysis performed in a time-window equal to 10 cycles of the fundamental
frequency (50 Hz), i.e. approximately 200 ms. Sampling is synchronized with the power supply frequency by
means of a phase-locked loop. The result is a spectrum with 5 Hz resolution. The standard defines the method
of processing of individual 5 Hz lines in order to determine so-called harmonic or interharmonic groups, to
which recommendations of standards and technical reports are referred.
Groups of harmonics and interharmonics are calculated according to equations in Figure 13.
Definitions related to the concept of grouping:
RMS value of a harmonic group
The square root of the sum of the squared amplitudes of a chosen harmonic and its adjacent spectral
components in the observation window.

Page 15
RMS value of a harmonic subgroup
The square root of the sum of the squared amplitudes of a chosen harmonic and the two adjacent
spectral components. The aim is to include voltage fluctuation during voltage surveys. A subgroup of
output components of the DFT is obtained by summing the energy contents of the frequency
component directly adjacent with the harmonic itself.
RMS value of an interharmonic group
The rms value of all interharmonics components in the interval between two consecutive harmonic
frequencies (see Figure 13).
RMS value of an interharmonic centered subgroup
The rms value of all interharmonic components in the interval between two consecutive harmonic
frequencies, excluding frequency components directly adjacent to the harmonic frequencies (see
Figure 13).
Figure 13 – Illustration of the principle of the harmonics and interharmonics groups.
More detailed information concerning this concept of measurement can be found in the standard [6]. On the
basis of these definitions, measurements can be performed for any interharmonic group, as well as for total

Page 16
interharmonic distortion, and referred to the fundamental component, total rms value or other reference
value. These values are the basis for determining limit values.
This method is attractive for monitoring purposes in the event of complaints and for compatibility tests,
because the limit levels can be defined on the basis of total distortion and they do not refer to the
measurement of particular frequencies. The method is not adequate for diagnostic purposes.
COMPATIBILITY LIMITS
The interharmonics standardization process is in its infancy, with knowledge and measured data still being
accumulated.
The limit level 0.2% for interharmonic voltages is widely applied, chiefly because of the lack of a better
suggestion. It has been introduced with regard to load sensitivity in the mains signalling systems but its
application to other cases, not taking into account the possible physical effects, may lead to very costly
solutions e.g. expensive passive filters. Provisions of several example documents are quoted below, but
inconsistency and significant variations are apparent.
PROVISIONS OF INTERNATIONAL ELECTROTECHNICAL COMMISSION (IEC)
According to the IEC recommendations the voltage interharmonics are limited to 0.2% for the frequency range
from dc component to 2 kHz.
The Standard [7] gives immunity test levels for interharmonics in various frequency ranges. Depending on the
equipment class the voltage levels are contained within 1.5% U1 (1000-2000 Hz). Test levels for interharmonics
above 100 Hz are within 2-9%.
Figure 14 – Compatibility levels for interharmonics relating to flicker (beat effect) [5].
In the document [5] compatibility levels are formulated only for the case of the voltage interharmonics with
frequencies near to the fundamental component, which result in modulation of supply voltage and flicker.
Figure 14 shows the compatibility level for a single interharmonic voltage, expressed as a percentage of the
fundamental component amplitude, as a function of beat frequency of two combining components whose
interaction results in the interharmonic. The characteristic is referred to as the flicker severity Pst = 1 for 230 V
incandescent lamps.

Page 17
More detailed recommendations with regard to limit values of the mains signaling voltage in power systems
are given below:
Ripple control signals. The level of these signals shall not exceed values of the odd harmonics being a
non-multiple of 3 for the same frequency band ([5], Table 3). For practical systems this value is
contained in the range 2-5 % UN.
Medium frequency power-line-carrier signals. Signal value up to 2 % UN.
Radio-frequency power-line-carrier signals. Compatibility levels under consideration; should not
exceed 0.3 %.
Mains-mark systems. The equipment manufacturers shall guarantee compatibility with working
environment.
Harmonic order 5 7 11 13 4917  h
rms harmonic value (% of fundamental
component)
6 5 3.5 3 27.0)/17(27.2 hx
Table 3 – Values of harmonics as the basis for determining the interharmonics compatibility levels [5].
In some countries the so-called Meister curve, shown in Figure 15 is officially recognized.
Figure 15 – Meister curve for ripple control systems in public networks (100 Hz do 3 000 Hz) [5].
CENELEC (STANDARD EN 50160)
Over 99% of a day, the three-second mean of signal voltages shall be less or equal to the values given in Figure
16.

Page 18
Figure 16 – Voltage levels of signals used in public MV distribution systems [11].
SUBHARMONIC AND INTERHARMONIC EMISSION LIMITS [13]
In the United Kingdom, for example, it is assumed that ripple control systems are not used and therefore a
customer’s load may be connected without assessment, if the individual interharmonic emissions are less than
the limit values in Table 4. Limits for particular interharmonic frequencies between 80 Hz and 90 Hz may be
interpolated linearly from the limits given in Table 4.
Sub-harmonic or interharmonic frequency in Hz < 80 80 90 > 90 and < 500
Voltage distortion as % of the fundamental 0.2 0.2 0.5 0.5
Table 4 – Sub-harmonic and interharmonic emission limits.

Page 19
MITIGATION OF INTERHARMONICS AND REDUCTION OF THEIR EFFECTS
Methods of eliminating the effects of interharmonics include:
 Reducing the emission level
 Reducing the sensitivity of loads and
 Reducing coupling between power generating equipment and loads.
The methods used are the same as for harmonics.
Additional factors should be taken into account in the design of passive filters. For example, resonance
between filters and the power system interharmonics can be amplified and cause significant voltage distortion
and fluctuations. Filters need to be designed with a higher damping factor.
Figure 17 shows an example of the source impedance characteristics of a passive filter (3, 5, 7 and 12
harmonics) seen from input terminals of the converter supplying a large dc arc furnace installation. The fine
line corresponds to undamped filters. There was a real risk of resonance for the interharmonics adjacent to
120 Hz and 170 Hz. Damped 3rd and 7th harmonics filters reduced the danger of resonance occurring. The
filter design process sometimes requires a compromise between the accuracy of tuning and power losses,
which involves choosing the filter quality factor.
Figure 17 – Example of impedance seen from converters' terminals [10].
The design of a narrow pass-band filter presents several problems. The normal power system frequency
deviation may be important, especially when combined with changes in tuning frequency due to component
tolerance, ageing and temperature variation and changes in the impedance of the supply.
The resulting variation in the filter resonant frequency, considering the very narrow pass-band of the filter, can
significantly reduce the efficiency of the filtering, even if the change is small. It sometimes requires the choice
of a reduced quality factor, which widens the bandwidth and so is also advantageous in terms of filtering
interharmonics.

Page 20
Disturbances caused by the mains signaling systems can be eliminated by applying series filters, tuned to
desired frequencies and correctly located in the system. Other solutions involve increasing the immunity level
of the equipment in use or using active filters.

Page 21
CONCLUSION
The above review of the presence of interharmonics, their basic sources and the characteristic features of the
continuous and discrete spectrum allows the formulation of several conclusions of a general nature.
Firstly, in the vast majority of cases the values and frequencies of interharmonic currents and voltages are
stochastic quantities, which depend on numerous complex parameters of transient processes.
Secondly, assessment of the value and frequency of an interharmonic is possible for a particular, considered
process.
Thirdly, there are no coherent standardization regulations concerning the interharmonics, yet the practical
need of them exists.

Page 22
REFERENCES
1. Arrillaga J., Watson N.R., Chen S.: Power system quality assessment. Wiley, 2000.
2. Gunther E.W.: Interharmonics in power systems. UIEPQ-9727
3. Interharmonic Task Force Working Document – IH0101 20001 IEEE.
4. IEC 1000-2-1: 1990 - Electromagnetic compatibility (EMC) Part 2: Environment – Section 1: Description
of the environment – Electromagnetic environment for low-frequency conducted disturbances and
signalling in public power supply systems.
5. IEC 61000-2-2: 2002 - Electromagnetic compatibility (EMC) Part 2: Environment – Section 2:
Compatibility levels for low-frequency conducted disturbances and signalling in public low-voltage
power supply systems. (also materials used in preparation of the standard, obtained from the authors)
6. IEC 61000-4-7: 2002 Electromagnetic compatibility (EMC) Part 4: Testing and measurement
techniques Section 7: General guide on harmonics and interharmonics measurements and
instrumentation, for power supply systems and equipment connected thereto.
7. IEC 61000-4-13: 2002 Electromagnetic compatibility (EMC) Part 4: Testing and measurement
techniques Section 13: Harmonics and interharmonics including mains signalling at a.c. power port,
low frequency immunity tests (also materials used in preparation of the standard, obtained from the
authors)
8. Kloss A.: Oberschwingungen. vde Verlag. ISBN 3-8007-1541-4.
9. Materials used in preparation of standard IEC 61000-2-4 (obtained from the authors).
10. Mattaveli P., Fellin L., Bordignon P., Perna M.: Analysis of interharmonics in DC arc furnace
installations. 8
th
International Conference on Harmonics and Quality of Power, Athens, Greece,
October 14-16, 1998
11. EN 50160: 1999 - Voltage characteristics of electricity supplied by in public distribution systems.
12. Staudt V.: Effects of window functions explained by signals typical to power electronics. 8
th
International Conference on Harmonics and Quality of Power, Athens, Greece, October 14-16, 1998.
13. Engineering Recommendation G5/4. Electricity Association, Feb. 2001.

Page 23
APPENDIX 1
Fourier transformation is the most popular method of spectral analysis of a signal. The fundamental theory of
spectral analysis assumes that the analysis is performed over a time interval from - to +. Discrete Fourier
Transform (DFT), or its variant Fast Fourier Transform (FFT), may introduce unexpected spectral components
of the analyzed signal. This effect occurs because DFT and FFT operate over a finite number of samples, i.e. on
a portion of the real signal. The determined and actual spectrum will be identical only when the signal is
periodic, and the time over which it is analyzed, contains an integer number of the signal cycles. This condition
is very difficult to satisfy in practical implementations.
Figure A1 1 – Modula of the signal spectrum, exactly 4 cycles have been used for analysis.
Figure A1 2 – Modula of the signal spectrum, 4.1 cycles have been used for analysis.
Results presented in Figure A1 1 and Figure A1 2 illustrate how the actual spectrum may look. Different spectra
have been obtained for the same signal while the observation time in Figure A1 2 was 2.5% longer. In the

Page 24
bibliography this effect is called spectral leakage. It could be said that part of the energy from the main
spectral line is transferred to the side lines. The following interpretation of this phenomenon has been
proposed. Sampling for DFT analysis can be compared to multiplication of the actual signal of infinite duration
by a rectangular window corresponding to the time of observation, Figure A1 3.
Figure A1 3 – Acquisition of samples for DFT analysis.
To limit the spectrum leakage it is necessary that values of the analyzed signal do not change rapidly at the
origin and the end of the sampling interval.
Figure A1 4 shows how the time window should be used for signal analysis.

Page 25
Figure A1 4 – Time windows used for the signal spectrum analysis.
Figure A1 5 shows how the presented methods have influenced the spectrum from the Figure A1 2 example.
The Hanning window has been used for the purpose of this example. The effect is a reduction in the number of
non-zero spectral lines, and the spectrum approaches the correct one, as shown in the Figure A1 1.

Page 26
Figure A1 5 – An example of Hamming window application to DFT analysis.
A number of DFT analysis windows are known in the current bibliography. The most popular are (Figure A1 6):
 Triangular window similar to Barlett window
 Hanning window
 Window lifted cosine or Hann, or Hamming window
Figure A1 6 – Exemplary time windows: triangular, Hanning, Hamming.

Page 27
These windows are the most often used in measuring instruments. Their use does not eliminate spectral
leakage problems but limits significantly the effect of finite observation time. This is particularly evident as an
improvement of the spectrum resolution.

Page 28
APPENDIX 2
The greatest difficulty associated with sampling a continuous signal is the problem of ambiguity. The essence
of the problem is illustrated in Figure A2 1. It follows from the figure that the same set of sampled data may
describe several waveforms, indistinguishable by measuring equipment.
Figure A2 1 – Ambiguity.
The principle of frequency analysis is the representation of an arbitrary waveform by the sum of a series of
sinusoidal signals. Such a method of presentation allows the analysis of the problem of ambiguity
quantitatively. For this purpose, consider the waveform shown in Figure A2 2
Figure A2 2 – Analysis of ambiguity
A signal x(t) is sampled in equal intervals of time h, determining the instants of sampling, for which values of
the measured signal are indicated in the figure. Assume that that function x(t) is sinusoidal with frequency f0.
The same points could also represent sinusoids with frequencies f1 or f2, which are multiples (not necessarily
integer multiples) of frequency f0. These various frequencies are obviously associated with the sampling
period. The frequency f0 is referred to as the fundamental frequency.
It could be stated, without presentation of the mathematical proof, that the range of frequencies for which the
effect of ambiguity does not occur extends from f0 = 0 to f0 = fN, where fN, the maximum frequency, is referred
to as the Nyquist frequency. It determines the limit frequency of data sampling, the so-called Shannon limit,
beyond which a unique reconstruction of a continuous signal is not possible. Thus, if the signal being analyzed
does not contain any component frequencies greater than fN, then the minimum sampling frequency
necessary to allow the sampled signal to represent the real signal is given as:

Page 29
NS ff 2 , or because
h
fS
1
 , then
h
fN
2
1
 .
This is the so-called sampling theorem. It follows that, for a given spectrum of frequencies, the components
situated between f0 = 0 and f0 = fN can be considered separately. If the signal contains components of
frequencies f > fN, these components will not be distinguished.
Therefore it is necessary to limit the bandwidth of the measured signal to reduce a direct consequence of the
ambiguity during its sampling. That implies the need to filter the signal to be measured through a low-pass
filter before sampling, in order to eliminate all frequencies greater than fN.

Interharmonics

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