Electromagnetic compatibility (EMC) - Part 4-40: Testing and measurement techniques - Digital methods for the measurement of power quantities of modulated or distorted signals

IEC TR 61000-4-40:2020 which is a Technical Report, deals with the assessment of electrical power quantities (RMS voltage, RMS current and active power). It explains and compares two digital algorithms suitable for power quantity measurements in fluctuating or non-periodic loads. The examples are from 50 Hz or 60 Hz power systems. This document does not attempt to cover all possible digital implementations of the algorithms used for power quantity assessment in fluctuating loads, for example in the context of the EMC assessment described in several IEC documents. Rather, it compares averaging with one of the filtering algorithms. This document aims to highlight some examples of applications that illustrate how the presented algorithms work. Further, guidance is given for quantifying the accuracy of each approach.

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Publication Date
10-Mar-2020
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11-Mar-2020
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IEC TR 61000-4-40:2020 - Electromagnetic compatibility (EMC) - Part 4-40: Testing and measurement techniques - Digital methods for the measurement of power quantities of modulated or distorted signals
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IEC TR 61000-4-40
Edition 1.0 2020-03
TECHNICAL
REPORT
colour
inside
Electromagnetic compatibility (EMC) –
Part 4-40: Testing and measurement techniques – Digital methods for the
measurement of power quantities of modulated or distorted signals
IEC TR 61000-4-40:2020-03(en)
---------------------- Page: 1 ----------------------
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IEC TR 61000-4-40
Edition 1.0 2020-03
TECHNICAL
REPORT
colour
inside
Electromagnetic compatibility (EMC) –
Part 4-40: Testing and measurement techniques – Digital methods for the
measurement of power quantities of modulated or distorted signals
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.100.01 ISBN 978-2-8322-7907-6

Warning! Make sure that you obtained this publication from an authorized distributor.

® Registered trademark of the International Electrotechnical Commission
---------------------- Page: 3 ----------------------
– 2 – IEC TR 61000-4-40:2020 © IEC 2020
CONTENTS

FOREWORD ........................................................................................................................... 4

INTRODUCTION ..................................................................................................................... 6

1 Scope .............................................................................................................................. 7

2 Normative references ...................................................................................................... 7

3 Terms and definitions ...................................................................................................... 7

4 General ........................................................................................................................... 7

5 Modulated sine waveforms used in this document to compare measurement

algorithms ....................................................................................................................... 9

5.1 General ................................................................................................................... 9

5.2 Half-wave rectification ........................................................................................... 10

5.3 Full-wave rectification ........................................................................................... 10

5.4 Multi-cycle symmetrical control ............................................................................. 11

5.5 Random on-off control .......................................................................................... 12

6 Measurement algorithms ............................................................................................... 12

6.1 General ................................................................................................................. 12

6.2 Averaging algorithms ............................................................................................ 12

6.2.1 General ......................................................................................................... 12

6.2.2 Performance of the averaging algorithm ........................................................ 13

6.2.3 Instrumental errors of the averaging algorithm ............................................... 18

6.3 Smoothing filter algorithm ..................................................................................... 19

6.3.1 Frequency and step response ........................................................................ 19

6.3.2 Verification of the smoothing filter algorithm .................................................. 21

6.3.3 Instrumental errors of the filtering algorithm ................................................... 25

7 Conclusions ................................................................................................................... 25

Annex A (informative) Smoothing filter studied in this document .......................................... 27

A.1 Algorithm .............................................................................................................. 27

A.2 General C++ class program code .......................................................................... 31

Bibliography .......................................................................................................................... 34

Figure 1 – Typical resistive load current and supply voltage waveform of half-wave

rectification ........................................................................................................................... 10

Figure 2 – Typical full-bridge rectifier current and supply voltage waveforms ........................ 11

Figure 3 – Current and voltage patterns in an MCSC circuit, (left) 1/3 MCSC and

(right) 2/3 MCSC ................................................................................................................... 11

Figure 4 – Amplitude of 50 Hz current with on and off periods varying within a 1 min to

2 min range .......................................................................................................................... 12

Figure 5 – Step response of an algorithm in Formula (6) with a half-cycle, 1-cycle and

10-cycle measurement interval ............................................................................................. 14

Figure 6 – RMS current and active power for half-wave rectification ..................................... 15

Figure 7 – Sliding average RMS current and active power of a device controlled with a

1/3 MCSC circuit ................................................................................................................... 15

Figure 8 – Worst case 1/3 MCSC circuit active power calculation variation ........................... 16

Figure 9 – Example of a 10 min sliding average power calculation for a load having a

92 s period ............................................................................................................................ 17

Figure 10 – Active power of randomly fluctuating load averaged over a sliding 10 min

interval ................................................................................................................................. 18

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IEC TR 61000-4-40:2020 © IEC 2020 – 3 –

Figure 11 – Sensitivity of the full-bridge rectifier RMS current and active power

measurement to time interval error of single-cycle sliding average calculation ...................... 19

Figure 12 – Comparison of the first and the 10 order filters used to estimate RMS

current of a step signal ......................................................................................................... 20

Figure 13 – Filter frequency responses ................................................................................. 20

Figure 14 – Filter step responses .......................................................................................... 20

Figure 15 – Output of the 10 order smoothing filter used to calculate the active

power of a signal with a step change .................................................................................... 21

Figure 16 – Delay and response time of a 10 order filter used to assess the

sinusoidal current of a sinusoidal waveform .......................................................................... 22

Figure 17 – Measurement of the current and power of a half-wave rectified signal

using a smoothing filter with a 10 Hz cut-off frequency .......................................................... 22

Figure 18 – Power quantities in full wave rectification assessed using a smoothing

filter with 16,667 Hz cut-off frequency ................................................................................... 23

Figure 19 – MCSC 1/3 pattern power quantities filtered with approximately 5,556 Hz

cut-off frequency ................................................................................................................... 23

Figure 20 – Active power of a load having a 92 s period measured with different

algorithms ............................................................................................................................. 24

Figure 21 – Active power of randomly fluctuating load measured using different

algorithms ............................................................................................................................. 25

Table 1 – Calculated power of 2/3 MCSC for different measurement windows ....................... 16

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– 4 – IEC TR 61000-4-40:2020 © IEC 2020
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTROMAGNETIC COMPATIBILITY (EMC) –
Part 4-40: Testing and measurement techniques –
Digital methods for the measurement of power quantities
of modulated or distorted signals
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,

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preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with

may participate in this preparatory work. International, governmental and non-governmental organizations liaising

with the IEC also participate in this preparation. IEC collaborates closely 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

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3) IEC Publications have the form of recommendations for international use and are accepted by IEC National

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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is

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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 61000-4-40, which is a Technical Report, has been prepared by subcommittee SC77A:

EMC – Low frequency phenomena, of IEC technical committee TC 77: Electromagnetic
compatibility.
The text of this Technical Report is based on the following documents:
Enquiry draft Report on voting
77A/1055/DTR 77A/1065/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.
---------------------- Page: 6 ----------------------
IEC TR 61000-4-40:2020 © IEC 2020 – 5 –

This document 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 document will remain unchanged until the

stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to

the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates

that it contains colours which are considered to be useful for the correct understanding

of its contents. Users should therefore print this document using a colour printer.

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– 6 – IEC TR 61000-4-40:2020 © IEC 2020
INTRODUCTION
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 several parts, published either as International Standards,

Technical Specifications or Technical Reports, some of which have already been published as

sections. Others are and will be published with the part number followed by a dash and a second

number identifying the subdivision (example: IEC 61000-6-1).

This document gives the rationale for the assessment of electrical power quantities (RMS

voltage, RMS current and active power) under non-stationary conditions. It explains and

compares two digital methods that can be used in digital measurement instrumentation to either

average or filter the signals when measuring fluctuating loads, and algorithms for the realization

of both methods. The examples relate to 50 Hz or 60 Hz power systems because power quantity

assessments are predominantly required for these systems.

The digital averaging or integration algorithm is evaluated for fluctuating, or non-stationary,

conditions, as is a digital filtering algorithm that emulates the traditional analogue power meter.

This document aims to illustrate the application of the two measurement algorithms given above

to characterize existing, and commonly found, non-stationary loads, which have been selected

to help interpret the measurement results obtained using both algorithms.
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IEC TR 61000-4-40:2020 © IEC 2020 – 7 –
ELECTROMAGNETIC COMPATIBILITY (EMC) –
Part 4-40: Testing and measurement techniques –
Digital methods for the measurement of power quantities
of modulated or distorted signals
1 Scope

This part of IEC 61000, which is a Technical Report, deals with the assessment of electrical

power quantities (RMS voltage, RMS current and active power). It explains and compares two

digital algorithms suitable for power quantity measurements in fluctuating or non-periodic loads.

The examples are from 50 Hz or 60 Hz power systems.

This document does not attempt to cover all possible digital implementations of the algorithms

used for power quantity assessment in fluctuating loads, for example in the context of the EMC

assessment described in several IEC documents. Rather, it compares averaging with one of

the filtering algorithms. This document aims to highlight some examples of applications that

illustrate how the presented algorithms work. Further, guidance is given for quantifying the

accuracy of each approach.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the cited edition applies.

For undated references, the latest edition of the referenced document applies, including any

amendments.

IEC TR 61000-1-7:2016, Electromagnetic compatibility (EMC) – Part 1-7: General – Power

factor in single phase systems under non-sinusoidal conditions
3 Terms and definitions

For the purposes of this document, the terms and definitions given in IEC TR 61000-1-7 apply.

ISO and IEC maintain terminological databases for use in standardization at the following

addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
4 General

IEC TR 61000-1-7:2016, 3.1, defines the root-mean square (RMS) value of a time-dependent

quantity as a positive square root of the mean value of the square of the quantity taken over a

given time interval.

IEC TR 61000-1-7:2016, 5.1.4, further states that the RMS value of the voltage U (current I) is

defined as the positive square root of the mean value of the square of the voltage u(t) (current

i(t)) taken over an integer number of periods kT of the AC power supply system:
---------------------- Page: 9 ----------------------
– 8 – IEC TR 61000-4-40:2020 © IEC 2020
τ+kT
U = u(t) dt
[ ] (1)
τ+kT
1 2
I = i(t) dt
[ ]
(2)
where
T is the reciprocal of the reference fundamental frequency;
k is an integer number;
τ is the time when the measurement starts.

Similarly, the active power is defined in IEC TR 61000-1-7 as the mean value, taken over an

integer number of periods kT, of the instantaneous power p(t) = u(t) i(t):
τ+kT
P = p(t) dt (3)

In digital instrumentation, the assessment of the RMS value of voltage or current is performed

by first obtaining the squares of the sampled values of the signal. Similarly, for the assessment

of active power the products of each pair of the instantaneous voltage u(t) and current i(t)

samples are obtained. Then the instrument performs the integration of the squared or multiplied

samples over the measurement time interval. To adhere to IEC TR 61000-1-7, the measurement

time interval is normally set to an integer multiple of the period of the power system fundamental

frequency, but many instruments permit the user to select arbitrary time intervals. Further, for

AC power systems, such as 50 Hz or 60 Hz public supply networks, the values of non-active

power and apparent power can be derived from the obtained RMS values of current, voltage

and active power.

For a sinusoidal signal, the multiplication of voltage and current, or the squaring operation,

gives a function whose period is half of the period of the sine wave. This function contains a

zero-frequency (DC) component that is equal to the active power or the square of the RMS

value. In addition to the desired DC component, there is also an AC component at twice the

frequency of the sine wave that it is essential to remove, or at least heavily attenuate, to retrieve

the DC value.

Historically, instruments for the measurement of power quantities were implemented in an

analogue form, using certain characteristics of thermal, magnetic or electrical components. In

moving iron meters, for example, the squaring step is realised through a magnetic force applied

to a vane made of iron. This magnetic force, proportional to the square of the current, is

generated by a current flowing in a coil. When measuring a sinusoidal signal, the force oscillates

at twice the frequency of the sine wave and causes the vane with its attached pointer to vibrate

at the same frequency. To produce a stable reading, the assembly is mechanically damped (a

smoothing function). The damper is analogous to a low-pass filter, decreasing oscillations

caused by the alternating current. The measured RMS value is indicated on a non-linear scale

devised according to the electromechanical properties of the meter.

Since the RMS value of an electric signal represents a heating effect, another analogue

approach, implemented using thermal converters, is to heat a resistor (heater) with a voltage

or a current applied across its terminals. The heater temperature is then measured with a

thermocouple producing a DC voltage proportional to the square of the RMS current passing

through the resistor. The thermal medium of the thermal converter smoothes the temperature

measured by the thermocouple. Thus this thermal smoothing effect also behaves like a low-

pass filter.
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IEC TR 61000-4-40:2020 © IEC 2020 – 9 –

Further modifications of these techniques, with two coils (electrodynamic wattmeters) or two or

more thermal converters (thermal wattmeters and thermal power comparators), enable the

measurement of active power in stationary conditions.

In analogue devices the processed signal is smoothed with the internal time constant of the

meter, which allows for a steady reading of the result to be made for stationary input signals.

Even with fluctuating loads, when the needle of the meter is not completely stable, it is often

possible to determine the average value by observing where the variation is centred.

To obtain a similar result, the manufacturers of digital instruments usually add digital filtering

to their measuring algorithms, which helps stabilize and/or average the readings. In the simplest

form, the filtering is based on averaging over multiple periods of the signal. As the power system

frequency is usually quite accurate, digital measurement instruments often use a constant

measurement time interval corresponding to a multiple of the nominal period of the power

system. For example, the 200 ms time interval specified in IEC 61000-4-7 corresponds to

10 cycles of a 50 Hz signal and 12 cycles of a 60 Hz signal. Further filtering can be obtained

by using a digital implementation of the low-pass filter function. For example, in IEC 61000-4-7

a low-pass filter with a 1,5 s time constant was selected, partly because it reproduces the typical

behaviour of a moving coil instrument.

When the period of the signal does not correspond to the nominal 50 Hz or 60 Hz power system

frequency, readings from instruments that use a constant measurement time interval often show

fluctuating results. For example, multi-cycle symmetrical control (MCSC) used in water heaters

produces current waveforms with periods that are longer than the fundamental frequency period

of the power system voltage feeding the device. Additionally, these MCSC controls can vary

the control cycle from one instant to another as required, to maintain water temperature under

different flow conditions. Another example is fluctuating loads, such as refrigerators, where

compressor motors can be energised at random times, producing non-periodic currents. It is

also noted that supply voltage frequency variations are common, for example, in isolated power

systems having no electrical connections to a large interconnected system, such as is common

in remote communities served by small generation sources.

To characterise the performance of various devices, many documents require the determination

of reference current or power. Additionally, for various voltage quality assessments, specific

measurement time intervals have been defined by IEC documents, such as half-cycle, 10 or

12 cycles for 50 Hz or 60 Hz power systems, 3 s, 10 min and 2 h.

Stable readings are often a prerequisite in order to obtain comparable results. In the case of

fluctuating loads these are sometimes difficult to achieve using conventional voltage, current

and power meters. In these situations the current and voltage can be recorded by data loggers

and post-processed using, for example, spreadsheet software. Smoothing functions

corresponding to the fluctuation rates can then be implemented as required. As data logger

recordings are often limited in their duration, fast-settling filters are desirable.

This document compares one averaging and one filtering algorithm used to assess the power

quantities for four typical groups of waveforms. For simplicity, the amplitude of the current

waveform used in the study was adjusted to give an RMS current of 1 A. The voltage was also

adjusted at the appropriate level to obtain an active power of 100 W.
5 Modulated sine waveforms used in this document to compare measurement
algorithms
5.1 General

For an ideal sine wave with constant amplitude and frequency, most measurement algorithms

would produce accurate results within the capabilities of the measuring instrument. The

situation becomes more complicated if the sine wave is randomly modulated and/or contains

distortion, as found in uncontrolled environments. Some examples of current waveforms

produced by real-life equipment that challenge the assessment of power quantities are

described in Clause 5. There exist even more complex situations that are not addressed in this

document.
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– 10 – IEC TR 61000-4-40:2020 © IEC 2020
5.2 Half-wave rectification

Half-wave rectification occurs when the equipment is connected only during one polarity of the

cycle (e.g. the current of a hair dryer, illustrated in Figure 1). In this case there are, in principle,

two possible measurement time intervals of interest.

The half-wave rectified current waveform is asymmetrical with a period of around 16,667 ms in

a 60 Hz power system. Therefore, the first appropriate measurement time interval to select is

one or more whole cycles of the power line frequency. If the current varies, a stable

measurement can only be obtained, if desired for the application, by the use of a measurement

time interval containing a larger number of periods.

Secondly, to assess instantaneous voltage fluctuation d(t), as required by IEC 61000-4-15 for

flicker assessment, the measurement time interval should be equal to one half-cycle. Whilst

measu
...

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