IEC TR 61000-1-7:2016

IEC TR 61000-1-7 ®
Edition 1.0 2016-02
TECHNICAL
REPORT
Electromagnetic compatibility (EMC) –
Part 1-7: General – Power factor in single-phase systems under non-sinusoidal
conditions
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IEC TR 61000-1-7 ®
Edition 1.0 2016-02
TECHNICAL
REPORT
Electromagnetic compatibility (EMC) –

Part 1-7: General – Power factor in single-phase systems under non-sinusoidal

conditions
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.100.01 ISBN 978-2-8322-3196-8

– 2 – IEC TR 61000-1-7:2016 © IEC 2016
CONTENTS
FOREWORD .4
INTRODUCTION .6
0.1 Series overview .6
0.2 Purpose of this document .6
1 Scope .8
2 Normative references .8
3 Terms and definitions .8
4 General . 14
5 Electric power quantities under non-sinusoidal conditions . 15
5.1 Voltages and currents . 15
5.1.1 Instantaneous values . 15
5.1.2 Reference fundamental components . 16
5.1.3 Total distortion contents . 16
5.1.4 RMS values of the voltage and current . 16
5.1.5 RMS values of total distortion contents . 17
5.1.6 DC ratios . 17
5.1.7 Total distortion ratios . 17
5.2 Instantaneous power . 18
5.3 Definitions related to the active power . 18
5.3.1 Active power . 18
5.3.2 DC power . 18
5.3.3 Fundamental active power . 19
5.3.4 Distortion active power . 19
5.4 Definitions related to the apparent power . 19
5.4.1 Apparent power . 19
5.4.2 Fundamental apparent power . 20
5.5 Definitions related to the power factor . 20
5.5.1 Power factor . 20
5.5.2 Fundamental power factor . 21
5.5.3 Non-fundamental power factor . 21
5.6 Summary . 21
6 Electric power quantities with a sinusoidal voltage and a current distorted only
with harmonics . 22
6.1 Voltages and currents . 22
6.1.1 Instantaneous values . 22
6.1.2 Fundamental components . 22
6.1.3 Harmonic content of the current . 23
6.1.4 RMS values of the voltage and current . 23
6.1.5 RMS value of the harmonic content of the current . 23
6.1.6 Total harmonic ratio of the current . 24
6.1.7 Fundamental factor . 24
6.2 Instantaneous power . 24
6.3 Active power . 24
6.4 Definitions related to the apparent power . 25
6.4.1 Apparent power . 25

6.4.2 Fundamental apparent power . 25
6.5 Definitions related to the power factor . 25
6.5.1 Power factor . 25
6.5.2 Fundamental power factor . 26
6.5.3 Non-fundamental power factor . 26
6.6 Summary . 27
Annex A (normative) Electric power quantities under sinusoidal conditions . 28
A.1 Instantaneous values of the voltage and current . 28
A.2 Instantaneous power . 29
A.3 Active power . 30
A.4 Reactive power . 30
A.5 Apparent power . 30
A.6 Power factor . 30
Annex B (informative) Fundamental active factor . 32
B.1 Fundamental active factor and its use . 32
B.2 Consumer convention . 32
Bibliography . 34

Figure A.1 – Illustration of the displacement angle (φ) when the voltage leads the
current, φ > 0 . 28
Figure A.2 – Illustration of the displacement angle (φ) when the voltage lags the
current, φ < 0 . 29
Figure B.1 – Consumer sign convention of the fundamental active factor, fundamental
active power and fundamental reactive power . 33

Table 1 – Summary of the power quantities under non-sinusoidal conditions . 21
Table 2 – Summary of the power quantities with a sinusoidal voltage and a current
distorted only with harmonics . 27

– 4 – IEC TR 61000-1-7:2016 © IEC 2016
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTROMAGNETIC COMPATIBILITY (EMC) –

Part 1-7: General – Power factor in single-phase systems
under non-sinusoidal conditions

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
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with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an
international consensus of opinion on the relevant subjects since each technical committee has representation
from all interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
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between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
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5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
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6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC TR 61000-1-7, which is a Technical Report, has been prepared by subcommittee 77A:
EMC – Low frequency phenomena, of IEC technical committee 77: Electromagnetic
compatibility.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
77A/911/DTR 77A/920/RVC
Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 61000 series, published under the general title Electromagnetic
compatibility (EMC), can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.

– 6 – IEC TR 61000-1-7:2016 © IEC 2016
INTRODUCTION
0.1 Series overview
IEC 61000 is published in separate parts, according to the following structure:
Part 1: General
General considerations (introduction, fundamental principles)
Definitions, terminology
Part 2: Environment
Description levels
Classification of the environment
Compatibility levels
Part 3: Limits
Emission limits
Immunity limits (in so far as they do not fall under the responsibility of the product
committees)
Part 4: Testing and measurement techniques
Measurement techniques
Testing techniques
Part 5: Installation and mitigation guidelines
Installation guidelines
Mitigation methods and devices
Part 6: Generic standards
Part 9: Miscellaneous
Each part is further subdivided into sections which are to be published either as international
standards, technical specifications, or as technical reports.
These standards and reports will be published in chronological order and numbered
accordingly (for example, 61000-6-1).
0.2 Purpose of this document
The prevalence of loads drawing non-sinusoidal current from power systems requires
clarification of such concepts as power and power factor, in order to avoid confusion due to

implied assumptions of sinusoidal voltage and current. This document specifically addresses
the terms related to the power factor of equipment that are applicable regardless of the
voltage and current waveforms.
When voltages and currents on power supply networks are perfectly sinusoidal, cos ϕ
corresponds to the power factor. But this is not true anymore when electric quantities are
distorted. In some existing documents, cos ϕ is still used as power factor, leading to an
incorrect assessment of the equipment impact to supply networks.
The purpose of this Technical Report is to give clear information on both components in the
power factor:
• the fundamental power factor, which is due to the phase difference between the voltage
and current at the fundamental frequency (cos ϕ ), and
• the non-fundamental power factor, which is related to the distortion of the voltage and/or
current.
– 8 – IEC TR 61000-1-7:2016 © IEC 2016
ELECTROMAGNETIC COMPATIBILITY (EMC) –

Part 1-7: General – Power factor in single-phase systems
under non-sinusoidal conditions

1 Scope
This part of IEC 61000, which is a Technical Report, provides definitions of various electrical
power quantities and the relationship between them under non-sinusoidal conditions, in order
to give clear information on both components in the power factor: the fundamental power
factor, which is due to the phase difference between the voltage and current at the
fundamental frequency, and the non-fundamental power factor, which is related to the
distortion of the voltage and/or current. This Technical Report is applicable only to single-
phase systems.
This Technical Report provides definitions for the three following cases:
• the general case where the voltage and current are both distorted (Clause 5),
• the case where the voltage is assumed to be sinusoidal and the current is only distorted
with harmonic components (Clause 6),
• the particular case where the voltage and current are both sinusoidal (Annex A).
Annex B gives information on the fundamental active factor, which is used to describe the
behaviour of a piece of equipment as a load or a generator.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document
and are indispensable for its application. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
Void.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
root-mean-square value
r.m.s. value
effective value
for a time-dependent quantity, positive square root of the mean value of the square of the
quantity taken over a given time interval
Note 1 to entry: The root-mean-square value of a periodic quantity is usually taken over an integration interval
the range of which is the period multiplied by a natural number.
Note 2 to entry: For a sinusoidal quantity a(t) = Âcos(ωt +ϑ ), the root-mean-square value is A = Â/√2.
0 eff
Note 3 to entry: The root-mean-square value of a quantity may be denoted by adding one of the subscripts eff or
rms to the symbol of the quantity.

Note 4 to entry: In electrical technology, the root-mean-square values of electric current i(t) and voltage u(t)are
usually denoted I and U, respectively.
[SOURCE: IEC 60050-103:2009, 103-02-03]
3.2
direct component
mean value of a quantity taken over a given time interval
[SOURCE: IEC 60050-103:2009, 103-06-05, modified – definition extended to quantities
containing interharmonic components.]
3.3
sinusoidal, adj.
pertaining to an alternating quantity represented by the product of a real constant and a sine
or cosine function whose argument is a linear function of the independent variable
Note 1 to entry: The real constant may be a scalar, vector or tensor quantity.
Note 2 to entry: Examples are a(t) = Âcos(ωt +ϑ ) and a(x) = Âcos[k(x –x )].
0 0
[SOURCE: IEC 60050-103:2009, 103-07-01]
3.4
initial phase
phase angle
ϑ
value of the phase of a sinusoidal quantity when the value of the independent variable is zero
Note 1 to entry: For the quantity a(t) = Âcos(ωt +ϑ ), the initial phase is ϑ .
0 0
[SOURCE: IEC 60050-103:2009, 103-07-05]
3.5
periodic conditions
state of an electric circuit element or electric circuit that is characterized by the electric
currents and voltages all being periodic functions of time with the same period T
[SOURCE: IEC 60050-131:2002, 131-11-27, modified – addition of symbol T for the period.]
3.6
sinusoidal conditions
state of a linear electric circuit element or electric circuit that is characterized by the electric
currents and voltages all being sinusoidal functions of time with the same frequency
[SOURCE: IEC 60050-131:2002, 131-11-28]
3.7
instantaneous power
p(t)
for a two-terminal element or a two-terminal circuit with terminals A and B, product of the
voltage u between the terminals and the electric current i in the element or circuit
AB
p(t) = u (t)⋅i(t)
AB
where u is the line integral of the electric field strength from A to B, and where the electric
AB
current in the element or circuit is taken positive if its direction is from A to B and negative if
its direction is from B to A
– 10 – IEC TR 61000-1-7:2016 © IEC 2016
Note 1 to entry: The direction of electric current is as defined in IEC 60050:2002, 131-11-29.
Note 2 to entry: In circuit theory the electric field strength is generally non-rotational and thus u = v – v ,
AB A B
where v and v are the electric potentials at terminals A and B, respectively.
A B
Note 3 to entry: The coherent SI unit of instantaneous power is watt, W.
Note 4 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2013, 131-11-30, modified – in note 2, the term irrotational is
replaced by non-rotational and a new note 4 has been added.]
3.8
apparent power
S
product of the r.m.s. voltage U between the terminals of a two-terminal element or two-
terminal circuit and the r.m.s. electric current I in the element or circuit
S = UI
Note 1 to entry: The coherent SI unit for apparent power is voltampere, VA.
Note 2 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2013, 131-11-41, modified – the existing note 1 has been removed
and a note 2 has been added.]
3.9
active power
P
under periodic conditions, mean value, taken over one period T, of the instantaneous power
p(t)
T
P= p(t)dt
∫
T
Note 1 to entry: The coherent SI unit for active power is watt, W.
Note 2 to entry: When the voltage or current contain interharmonic components, often their waveforms are no
more periodic. In this document, the active power is approximated by the mean value of the instantaneous power,
taken over an integer number of periods of the a.c. power supply system (see 5.3.1 and 5.1.4). This definition is
also used under periodic conditions in this document (see 6.3 and Clause A.3).
[SOURCE: IEC 60050-131:2013, 131-11-42, modified – the existing note 1 has been removed
and a note 2 has been added.]
3.10
non-active power
Q~
for a two-terminal element or a two-terminal circuit under periodic conditions, quantity equal
to the square root of the difference of the squares of the apparent power S and the active
power P
2 2
Q~= S − P
Note 1 to entry: The coherent SI unit for non-active power is voltampere, VA. The special name "var" and its
symbol "var" are also used. See IEC 60050-131:2013, 131-11-45.
Note 2 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2013, 131-11-43, modified – the existing note 1 has been removed
and a note 2 has been added.]
3.11
reactive power
Q
for a linear two-terminal element or two-terminal circuit, under sinusoidal conditions, quantity
equal to the product of the apparent power S and the sine of the displacement angle φ
Q = Ssinϕ
Note 1 to entry: The coherent SI unit for reactive power is voltampere, VA. The special name var and its symbol
var are also used. See IEC 60050-131:2013, 131-11-45.
Note 2 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
Note 3 to entry: When the conditions are not sinusoidal, there is no international consensus on a definition of the
reactive power. Instead, several definitions of the reactive power exist. In some documents, the reactive power is
taken as the non-active power, but there are many other formulae.
[SOURCE: IEC 60050-131:2013, 131-11-44, modified – the existing note 1 has been removed
and notes 2 and 3 have been added.]
3.12
power factor
λ
ratio of the absolute value of the active power P to the apparent power S
P
λ=
S
Note 1 to entry: Under sinusoidal conditions, the power factor is the absolute value of the active factor.
[SOURCE: IEC 60050-131:2002, 131-11-46, modified – definition extended to quantities
containing interharmonic components.]
3.13
displacement angle
phase difference angle
φ
under sinusoidal conditions, phase difference between the voltage applied to a linear two-
terminal element or two-terminal circuit and the electric current in the element or circuit
Note 1 to entry: The cosine of the displacement angle is the active factor.
Note 2 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2002, 131-11-48, modified – a note 2 has been added.]
3.14
active factor
for a two-terminal element or a two-terminal circuit under sinusoidal conditions, ratio of the
active power to the apparent power
Note 1 to entry: The active factor is equal to the cosine of the displacement angle, and can vary from –1 to +1.
Note 2 to entry: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2002, 131-11-49, modified – a note 2 has been added.]
3.15
fundamental component
fundamental
sinusoidal component of the Fourier series of a periodic quantity having the frequency of the
quantity itself
– 12 – IEC TR 61000-1-7:2016 © IEC 2016
[SOURCE: IEC 60050-103:2009, 103-07-19]
3.16
reference fundamental component
conventionally chosen sinusoidal component of a quantity, to the frequency of which all the
other components are referred
Note 1 to entry: The term is used when, for a periodic quantity, the chosen component differs from the
fundamental component, or when the quantity is not periodic due to interharmonic components.
Note 2 to entry: In this document, the component having the frequency of the a.c. supply system is chosen as the
reference fundamental component.
[SOURCE: IEC 60050-103:2009, 103-07-20, modified – definition extended to quantities
containing interharmonic components and a note 2 added.]
3.17
fundamental frequency
frequency of the fundamental component of a periodic quantity
[SOURCE: IEC 60050-103:2009, 103-07-21]
3.18
reference fundamental frequency
frequency of the reference fundamental component
Note 1 to entry: The term is used when, for a periodic quantity, the reference fundamental component differs from
the fundamental component, or when the quantity is not periodic due to interharmonic components.
[SOURCE: IEC 60050-103:2009, 103-07-22, modified – definition extended to quantities
containing interharmonic components.]
3.19
harmonic frequency
frequency which is an integer multiple greater than one of the fundamental frequency or of
the reference fundamental frequency
Note 1 to entry: When a reference fundamental frequency is defined, it is used in place of the fundamental
frequency.
Note 2 to entry: In this document, the harmonic frequencies are always related to the frequency of the a.c. power
supply system.
[SOURCE: IEC 60050-551:2001, 551-20-05, modified – addition of notes 1 and 2.]
3.20
interharmonic frequency
frequency which is a non-integer multiple of the reference fundamental frequency
[SOURCE: IEC 60050-551:2001, 551-20-06]
3.21
harmonic component
sinusoidal component of a quantity having a harmonic frequency
[SOURCE: IEC 60050-551:2001, 551-20-07, modified – definition extended to quantities
containing interharmonic components.]

3.22
interharmonic component
sinusoidal component of a quantity having an interharmonic frequency
[SOURCE: IEC 60050-551:2001, 551-20-08, modified – definition extended to quantities
containing interharmonic components.]
3.23
harmonic order
ratio of the frequency of any sinusoidal component to the fundamental frequency or the
reference fundamental frequency
Note 1 to entry: The harmonic order of the fundamental component or the reference fundamental component is
one.
Note 2 to entry: When a reference fundamental frequency is defined, it is used in place of the fundamental
frequency.
[SOURCE: IEC 60050-551:2001, 551-20-09, modified – addition of note 2.]
3.24
total distortion content
quantity obtained by subtracting from a quantity its direct component and its fundamental
component or its reference fundamental component
Note 1 to entry: The total distortion content includes harmonic components and interharmonic components if any.
Note 2 to entry: When a reference fundamental frequency is defined, the reference fundamental component is
used in place of the fundamental component.
Note 3 to entry: The total distortion content is a time function.
[SOURCE: IEC 60050-551:2001, 551-20-11, modified – definition extended to quantities
containing interharmonic components and note 4 deleted.]
3.25
harmonic content
sum of the harmonic components of a quantity
Note 1 to entry: The harmonic content is a time function.
[SOURCE: IEC 60050-551:2001, 551-20-12, modified – definition extended to quantities
containing interharmonic components and notes 2 and 3 deleted.]
3.26
total harmonic ratio
total harmonic distortion
THD
ratio of the r.m.s. value of the harmonic content to the r.m.s. value of the fundamental
component or the reference fundamental component of a quantity
Note 1 to entry: When a reference fundam
...