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

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.

General Information

• Status: Published
• Publication Date: 10-Mar-2020
• ICS: 33.100.01 - Electromagnetic compatibility in general
• Technical Committee: SC 77A - EMC - Low frequency phenomena
• Drafting Committee: WG 1 - TC 77/SC 77A/WG 1
• Current Stage: PPUB - Publication issued
• Start Date: 11-Mar-2020
• Completion Date: 13-Mar-2020

Standards Content (Sample)

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
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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

– 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

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
th
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
th
Figure 15 – Output of the 10 order smoothing filter used to calculate the active
power of a signal with a step change . 21
th
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

– 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
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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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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.

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.

– 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.

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:

– 8 – IEC TR 61000-4-40:2020 © IEC 2020
τ+kT
U = u(t) dt
[ ] (1)
∫
kT
τ
τ+kT
1 2
I = i(t) dt
[ ]
(2)
∫
kT
τ
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)
∫
kT
τ
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.
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.
– 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
measurement of the power of this waveform in half-cycle intervals is not usually used for general
power quantity assessment, the analysis of this waveform over a half-cycle interval can highlight
the need for correct synchronisation for the averaging measurement algorithm.

Figure 1 – Typical resistive load current and supply
voltage waveform of half-wave rectification
5.3 Full-wave rectification
Full-wave rectification is used in DC power supplies of various common electronic devices. An
interesting feature of these power supplies is the concentration of current conduction near the
peak of the voltage. When the energy is concentrated in a small part of the period, a larger
number of samples covering that part is required to reduce the instrumental errors.
For the purposes of this document, voltage and current in a real item of equipment based on
full-wave rectification were measured using a 100 kHz sampling frequency. The results were
then normalised to give an RMS current of 1 A and a power of 100 W (see Figure 2).

Figure 2 – Typical full-bridge rectifier current and supply voltage waveforms
5.4 Multi-cycle symmetrical control
The multi-cycle symmetrical control (MCSC) technique enables regulation of the power
delivered to a load. An MCSC circuit connects or disconnects the load for one or more half-
cycles of the power system frequency. Two basic patterns, which can be combined to give other
waveform patterns, are illustrated in Figure 3. In the first pattern the load is connected during
one half-cycle per each three consecutive half-cycles of the mains frequency. This pattern is
called 1/3 MCSC. Conversely, in the second pattern the load is connected during two half-
cycles per each three consecutive half-cycles. This is the 2/3 MCSC pattern. Other commonly
used patterns are 1/2 MCSC and 1/5 MCSC. Here "symmetrical" means that there is an equal
number of half-cycles in the positive and negative parts of the repeating waveform pattern; this
is necessary to avoid direct currents (DC), which are undesirable for distribution systems.
Each of the two patterns illustrated in Figure 3 is periodic, with a period equal to three cycles
of the mains frequency. Equipment controlled by MCSC can produce varying currents having
long periods, up to several seconds, with intermediate constant power levels for fractions of the
overall control cycle. As patterns are combined to maintain the desired temperature, control
cycles can vary from one second to the next. Only the two basic patterns are studied in this
document with the aim of showing how these signals can be assessed with various
measurement algorithms.
1/3 MCSC 2/3 MCSC
Figure 3 – Current and voltage patterns in an MCSC circuit,
(left) 1/3 MCSC and (right) 2/3 MCSC

– 12 – IEC TR 61000-4-40:2020 © IEC 2020
5.5 Random on-off control
Some control circuits, such as those used in thermostats, turn equipment on and off during
several seconds as required by their application. For example, a high-pressure die-casting
machine in an industrial environment would typically turn its motor on for approximately 20 s
during the moulding process and then disconnect it until the start of the next process. Other
examples include refrigerators and older air conditioning systems with motors energised at
random times.
When the application requires the measurement of an average power, or current, of such
devices over a long period of time, the 10 min averaging technique suggested in
IEC 61000-4-30 to obtain the power quantities at the point of common coupling (PCC) can be
sufficient. To illustrate both algorithms described in Clause 6, a 50 Hz current with periods
randomly varying between 1 min and 2 min was artificially generated. Figure 4 shows the RMS
values of a signal alternating between 0 A and √2 A, the average of which gives a result of 1 A
when evaluated over 30 min intervals, assessed using 10-cycle contiguous RMS windows.

Figure 4 – Amplitude of 50 Hz current with on and off periods varying
within a 1 min to 2 min range
6 Measurement algorithms
6.1 General
The focus is set on two very commonly used groups of smoothing algorithms, averaging and
filtering algorithms. Numerous filtering algorithms exist, but it is not the aim of this document to
cover all of them. Instead, the aim is to explain the limitations of the two major algorithm
categories.
6.2 Averaging algorithms
6.2.1 General
Digital measurement systems approximate the integral in the definition for active power in
IEC TR 61000-1-7, by summing the instantaneous power samples obtained during the selected
measurement interval. The sum is then divided by the number of samples N contained in the
measurement time interval N∆t. The result is a time-dependent function which is the average of
the instantaneous power samples over the selected measurement time interval. A similar
algorithm is used for calculation of the RMS values of voltage and current.

N−1
P t = u tn− Δt ⋅−i tn Δt
() ( ) ( ) (4)
∑
N
n=0
N−1
(5)
U(t=) u (t− n Δt)
∑
N
n=0
N−1
(6)
I(t) = i (t− n Δt)
∑
N
n=0
For stationary signals, and when the measurement interval equals an integer number of periods
of the AC power supply:
NΔt = kT , (7)
the averaging algorithm returns a constant reading. In many other cases, when the energy
contained within each measurement interval is not constant, the averaging algorithm reflects
this by returning fluctuating readings.
6.2.2 Performance of the averaging algorithm
As follows from Formulae (4) to (6), subject to instrumental errors which can be caused, for
example, by insufficient number of samples N, the averaging algorithm always returns a true
value of the average energy contained in the measurement period. Therefore, when the signal
to be measured varies throughout the measurement interval, selecting different measurement
intervals can well lead to varying results, and better understanding the measurand helps in
selecting the most appropriate measurement interval for the application and in the interpreting
of the results. To illustrate this, Figure 5 shows an example of waveform averages calculated
over a sliding window, applied with different measurement time intervals and varying
synchronization with the measured signal. Generally, an instrument based on the averaging
algorithm produces only one value per assessed measurement time interval. Thus the output
of the instrument contains equidistant samples taken from the curves shown in Figure 5.
Figure 5 shows how the averaging algorithm calculates the RMS current values of a 50 Hz
symmetrical current waveform starting at 0 A, rising to a peak current of 1,41 A (RMS current
1 A) and then falling to a peak value of 1,13 A (RMS value of 0,8 A). When the measurement
interval, containing N samples, equals one half-cycle, the output of Formula (6) rises from zero
to 1 A in a half-cycle. It also reduces from 1 A to 0,8 A in a half-cycle. Similarly, when Formula
(6) is used to compute the RMS values over 1 cycle and 10 cycles, the rise and fall times are
respectively 1 cycle and 10 cycles.

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

Whole test sequence Detail
Figure 5 – Step response of an algorithm in Formula (6) with a half-cycle,
1-cycle and 10-cycle measurement interval
As can be seen, averaging is very accurate for the determination of the RMS value of a periodic
and sinusoidal waveform provided the samples contain an integer number of cycles. The results
are available immediately upon completion of the measurement interval (10 ms for a half-cycle,
or 200 ms for the 10-cycle average).
The measurement time interval equal to one half-cycle is used to analyse the fast fluctuation of
voltages in the context of the directly measured parameters d , d(t), d and T when
c max max
performing flicker assessment. For this reason IEC 61000-4-15 specifies a half-cycle
measurement between zero-crossings of the voltage.
In the extreme case, when the measurand is a half-wave rectified waveform so that a half-cycle
measurement interval is mandatory, the synchronization of the measurement interval with the
zero-crossing of the signal is very important, as the measurement interval is only half of the
actual period of the current. If the measurement time interval is exactly synchronized to start
and end at the zero-crossing of the voltage, the calculated values of the RMS current and active
power alternate between 0 A and 1 A, or 0 W and 100 W, respectively, for the consecutive
values calculated at the end of the measurement interval. The sliding average shown in Figure
6 gives these values at time instants indicated by circles.
In contrast, if the measurement time interval is synchronized to end at the positive and negative
peaks of the voltage, then the RMS current and active power calculations produce constant
values of 0,707 A and 50 W, respectively; this can be seen, for example, at time instants of
5 ms and 15 ms which are indicated by triangles in Figure 6. Between these two extreme cases
of synchronisation, fluctuating values that are neither zero nor 1 A or 100 W are observed.
Therefore, when measuring signals based on half-wave rectification, a measurement interval
equal to one or more full cycles should be used.

NOTE The voltage and currents are measured using half-cycle measurement intervals synchronized with the
voltage zero-crossings (circles) and voltage peaks (triangles).
Figure 6 – RMS current and active power for half-wave rectification
The selection of the measurement time interval becomes even more critical for assessing the
power quantities of equipment controlled by an MCSC circuit, a common technique to control
devices with a heating element such as water heaters. As shown in 5.4, the 1/3 and 2/3 MCSC
patterns have a period of three cycles of the fundamental mains frequency. Therefore, the
energy consumed over one cycle is not constant. Selecting a measurement interval of one cycle
would show this, and selecting a multiple of three cycles would give a constant value
corresponding to the average power of the device over the MCSC period. MCSC devices can
utilise different patterns within one device. For example, for a ceramic hob with a six-position
control, the control period can be longer than 3 cycles. When the selected measurement time
interval is not equal to one or more of the control periods of the current, fluctuations in the
obtained values are observed. For example, the values obtained using a 10-cycle interval to
assess pure 1/3 or 2/3 patterns can have about 15 % peak-to-peak variation; see Figure 7 and
Figure 8.
Figure 7 – Sliding average RMS current and active power
of a device controlled with a 1/3 MCSC circuit
NOTE Figure 7 shows the different results for 1-, 3- and 10-cycle measurement intervals.
If all consecutive results from the sliding 10-cycle average measurements are smoothed with a
1,5 s low-pass filter, the peak variation of the filtered active power estimate is less than 0,03 %
from the nominal value of 100 W. IEC 61000-4-7 recommends that the signal to be filtered is
not the sliding average that is calculated after measuring every new sample but the average
value updated after each measurement time interval, that is, one measurement per ten periods
of 50 Hz or twelve periods of 60 Hz. When these values, having a 200 ms averaging interval,
are filtered by the 1,5 s low-pass filter, variation up to 1 % is possible as shown in Figure 8.
Therefore, the sliding average with a 1,5 s smoothing filter is more appropriate for the
measurements of MCSC waveforms.

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

NOTE This shows the result when a 10-cycle interval average is calculated every 200 ms and subsequently digitally
filtered using a low-pass filter with a 1,5 s time constant.
Figure 8 – Worst case 1/3 MCSC circuit active power calculation variation
The situation with the 2/3 MCSC is similar to that with 1/3 MCSC but the variations with a
10-cycle measurement interval are about half of those in the 1/3 MCSC case. Table 1 shows
the calculated power values for consecutive measurement windows for the 2/3 MCSC in a 50 Hz
system. As the name implies, the control turns the power "on" for 2 out of every 3 half-cycles.
So, for a 30 ms measurement window, consecutive windows show the exact same value. For
non-multiples of 30 ms, consecutive measurement windows show different values, with the
differences decreasing as the measurement window becomes longer. When averaged over
approximately 10 s, the calculated power value shows negligible differences versus the
theoretical average power, irrespective of the measurement window. For the 200 ms
measurement window in accordance with IEC 61000-4-7, the power over two consecutive
measurement windows differs by 7,692 %, simply because one 200 ms window includes 14
half-cycles that are "on" while the next one includes 13 half-cycles that are "on". Much like with
the 1/3 MCSC, the 1,5 s smoothing filter would largely remove the differences, approximating
the power over the MCSC period.
Table 1 – Calculated power of 2/3 MCSC for different measurement windows
Power calculation for 2/3 MCSC pattern with nominal 100 W (100 % "on") power
Measurement Minimum Maximum Average of two Delta Average of all
window time T power power consecutive (difference %) time windows
(ms) (W) (W) windows between over 10 s
(W) consecutive (W)
windows
30 666,667 666,667 666,667 0,000 666,667
50 600,000 800,000 700,000 33,333 666,700
60 666,667 666,667 666,667 0,000 666,667
100 600,000 700,000 650,000 16,666 7 666,700
180 666,667 666,667 666,667 0,000 666,667
200 650,000 700,000 675,000 7,692 666,675
300 666,667 666,667 666,667 0,000 666,667
1 000 660,000 670,000 665,000 1,515 666,670
3 000 666,667 666,667 666,667 0,000 666,667
All examples presented so far assume that a constant period of the signal exists, allowing the
selection of the measurement time interval to be exactly one or more control periods to assess
accurately the values of power quantities by averaging the samples. When the control circuit
randomly switches the load on and off, no particular period can be identified. One approach is
to calculate a 10/12-cycle interval average and process the obtained power quantity values
using the 1,5 s low-pass filter as recommended in IEC 61000-4-7.

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