Using the Standard Electrodynamometer
Wattmeter for Harmonic Power Measurement
Utilización del vatímetro electrodinámico estándar para la medición de potencia
armónica
A. Veyrat Durbex
†*1
, Y. Nachajon Schwartz
†2
y H. Tacca
†3
†
Laboratorio de Control de Accionamientos Tracción y Potencia (LABCATYP), Departamento de Electrónica, Facultad de
Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV, Buenos Aires, Argentina
.
1
aveyrat@fi.uba.ar
2
ynachajon@fi.uba.ar
3
htacca@fi.uba.ar
*
Departamento de Energía, Facultad de Ingeniería, Universidad de Buenos Aires
Paseo Colón 850, C1063ACV, Buenos Aires, Argentina
Abstract— Historically, for the measurement of electrical
power, the wattmeter electrodynamometer was used, but when
dealing with frequencies higher than those of power line, it was
necessary to develop special equipment. Digital power meters
are currently used.
This work studies the use of the electrodynamometer
wattmeter in a very frequent application such as power
measurement at the output of a frequency converter.
Measurements are made by comparing the readings of this
instrument with those of digital instruments in different
scenarios, depending on the frequency, cosφ, load, etc., to
determine under which conditions it is useful.
Keywords: electrodynamometer wattmeter; frequency
converter; power measurement; power harmonics; power
electronics.
Resumen— Históricamente para la medición de potencia
eléctrica se utilizó el vatímetro electrodinámico, pero cuando
involucraba frecuencias superiores a las industriales se debían
desarrollar equipos especiales. En la actualidad se utilizan
medidores digitales de potencia.
En este trabajo se estudia la utilización del vatímetro
electrodinámico en una aplicación muy frecuente como es la
medición de potencia a la salida de un convertidor de frecuencia.
Se realizan mediciones comparando la lectura de este
instrumento con la de instrumentos digitales en distintos
escenarios, en función de la frecuencia, el cosφ, la carga, etc.,
para determinar en qué condiciones es de utilidad.
Palabras clave: Vatímetro electrodinámico; convertidor de
frecuencia; medición de potencia; potencia de armónicas;
electrónica de potencia.
I. INTRODUCTION
The ability to accurately measure electrical power is
essential to determine the operating range of electrical
equipment, its efficiency and reliability. Currently, the search
for sustainable resource management drives the replacement
of fossil fuels with electric power. It is in this scenario that
the need to develop high-efficiency motors and controllers
increases.
In these cases, pulse width modulation (PWM) techniques
at high frequency and with high currents are widely used.
The power measurement in the aforementioned conditions
is carried out with electronic instruments based on analog-
digital conversion, which from the sampling of the analog
variables at very high frequency allows the digital
reconstruction of the magnitudes so that they can be
processed by a DSP (digital signal processor) or another type
of microcontroller, in order to obtain the value of the power
by numerical calculation.
For many years, when high-power measurements were
made at power frequencies, electrodynamometer (ED)
wattmeters were used. Due to their popularity, it is common,
even today, to find instruments of this type in most
laboratories, especially in technical schools, academic
institutions and state scientific laboratories in developing
countries. In addition, because they do not have electrolytic
capacitors, do not depend on auxiliary sources, have a very
long useful life and are inherently robust against noise, ED
wattmeters are still in use in some applications (such as in
nuclear power plants). As a result, ED wattmeters are still
being manufactured in some countries today [1], [2], [3], [4].
For this reason, it is interesting to study their response
when used in measuring circuits with the presence of
harmonic powers with frequencies higher than power line
frequencies. In this work, the usefulness of these ED
wattmeters for measurements at frequencies up to 16 kHz is
analyzed.
II. THE ED WATTMETER AT 50HZ
This instrument is made up of a fixed system formed by a
coil generally divided into two sections, to produce a uniform
magnetic field that allows the mobile system to be housed in
the middle of said field. The load current flows through this
coil which is generally called the “current” coil.
The mobile system, made up of the “pressure” o “voltage”
coil and the pointer, is mounted on a shaft with minimal
friction. It is completely surrounded by the fixed coil. It is
made of thin conductors, with an air core, and has high
Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)
ISSN 2525-0159
19
Recibido: 29/03/23; Aceptado: 06/06/23
Creative Commons License - Attribution-NonCommercial-
NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
https://doi.org/10.37537/rev.elektron.7.1.177.2023
Education Article
resistance. The moving coil is connected between the load
terminals in such a way that it is passed through by a current
proportional to the load voltage.
The instantaneous torque that generates the angular
deflection of the mobile system can be found from the energy
of the field formed by both coils:
𝜏
= 𝑖
∙ 𝑖
∙
, (1)
Where 𝑖
is the current flowing through the fixed coil and
𝑖
through the moving one, 𝑑𝑀 𝑑𝜃
⁄
is the derivative of the
mutual inductance M with respect to the deflection angle 𝜃.
Considering that the time constant of the system is much
greater than the period of the electrical variables and that the
measurement reaches equilibrium when the mean deflecting
torque becomes equal to the restoring torque 𝑇
= 𝑘 ∙ 𝜃
where k is the spring constant, one obtains:
𝜃 =
∙
∫
𝑖
∙ 𝑖
∙ 𝑑𝑡 , (2)
Assuming, ideally, that the moving coil is purely resistive,
and substituting the current 𝑖
by 𝑢
𝑅
⁄
in (2) it is
concluded that the deflection is proportional to the power of
the circuit in which it is measured.
For the sinusoidal case with 𝑖
(
)
=
√
2 ∙ I
sin
(
𝜔𝑡 − 𝜑
)
and 𝑖
()
=
√
2 ∙ U
𝑅
sin
(
𝜔𝑡
)
substituting in (2):
𝜃 = 𝑘
∙ I
∙ U
∙ 𝑐𝑜𝑠𝜑 = 𝑘
∙ 𝑃 , (3)
Which allows to see that the deflection is proportional to
the active power.
The sources of error in electrodynamometer wattmeters
have been extensively studied. In [5] they are broken down
between errors due to voltage or current separately, those that
affect the product of both and those that affect the angle.
Among the former are magnetic impurities in the mobile
system that can cause deflections with currents only in the
fixed coil, induced or capacitive currents in the moving
system that increase with the square of the magnitude and
frequency of the current through the fixed coil. The errors due
to the U.I product, called errors at unity power factor,
generally are discarded as being negligible at frequencies up
to 3 kHz. In the case of phase angle dependent errors, the
causes include eddy currents in the fixed coils or skin effect.
Also, errors may be caused by capacitive couplings in the
fixed coils and by phase errors in the voltage circuit due to a
phase difference between the current that flows through the
mobile coil and the voltage applied to it.
Similarly, in [6], the analysis of audio frequency
measurements with electrodynamometer wattmeters is
carried out, emphasizing the shielding needs of the fixed and
mobile system to prevent external magnetic fields from
exerting a torque on the mobile system. The benefits of
shielding with a compensation capacitor and the use of
double shielding are evaluated.
In [7] the design and construction of an ED wattmeter for
accurate measurements in the range of direct current to 20
kHz is discussed. The main effort in the construction of this
instrument was devoted to obtain a sufficient torque with low
number of turns in the current and potential windings, paying
attention to their shapes and physical arrangement to
minimize the interaction effects of the moving and fixed coil
fields. To reduce capacitive influences at high frequencies,
the potential coils were wound with paper inserts. The current
coils are made with individually twisted and lacquered
conductors to avoid eddy currents.
Another design can be found in [8]. Where the moving
system of the comparator is in the form of a transverse
horizontal beam, acting as a balance, on the edges of which
plane coils of two identical electrodynamic transducers are
fastened, while their fixed coils are connected rigidly to a
beam parallel to the base of the comparator, the suspension
of the mobile system takes the form of four tension wires, the
electrodynamic transducer is in the form of flat coils. This
comparator is an extremely sensitive measuring instrument.
This enable only a small number of windings to be used in
the transducers and consequently it will have a low
inductance, giving the instrument a wide range of
measurement values and frequencies.
This brief review of history accounts for the effort to
optimize the system, make compensations and corrections in
order to increase the frequency range of electrodynamometer
type wattmeters. Without these improvements, the
instruments only guarantee the class of accuracy within the
kHz range. In Fig. 1 the percentage change in the reading due
to the frequency, presented by a manufacturer, can be
observed.
Fig. 1. Error increase with increasing frequency [Source: Yokogawa
Portable Wattmeters 2041, 2042].
It can be noted that a class 0.5 instrument, for example,
will measure at frequencies of the order of 2 kHz but with an
accuracy of the order of 1% of the full scale value.
III. THE ED WATTMETER WITH POLYHARMONICS
When it is required to measure power in systems with
distorted voltages and/or currents [9], power can be
expressed as:
𝑃 = 𝑈
∙ 𝐼
+
∑
𝑈
∙ 𝐼
∙ cos
𝜑
− 𝜑
, (4)
Where 𝑈
and 𝐼
are the DC components of the voltage
and current respectively, 𝑈
is the rms value of the k-order
harmonic component of the voltage, 𝐼
is the rms value of
the k-order current component, and 𝜑
, 𝜑
are the phases of
the components of order k of the voltage and current
respectively. The cross products between voltage and current
harmonics of different frequencies are zero due to
orthogonality between sinusoidal functions that are multiples
of the same frequency.
It can be noted that the total power within a given
bandwidth is the sum of the DC power plus the sum of the
active powers due to each harmonic frequency, which means
that the electrical magnitude with the narrower harmonic
distortion bandwidth determines the final bandwidth of the
power signal.
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http://elektron.fi.uba.ar
A very frequent situation is the need to measure power
with sinusoidal voltage applied from the electrical grid and
with nonlinear current load. Another case would involve
converters used for electrical machines that use PWM
voltage with sinusoidal currents. Note that in these cases,
ideally, the necessary bandwidth would be the same as for
power frequency measurement.
In [10] comparative power measurements were made
between an electrodynamometer wattmeter, an electronic
wattmeter with analog operating principle and an energy
meter, connected to the input of a half-wave rectifier (where
a DC component is present) and with a thyristor controlled
rectifier, with load R, R-L and R-C. From this comparative
test, the author concludes that the electrodynamometer
instrument measures accurately. However, even when the
harmonic content of the variables has frequencies greater
than 50 Hz, it is much lower than the harmonic content
present in PWM inverters.
In practice, none of the variables is perfectly sinusoidal,
but the harmonic distortion can be very low. For example, in
frequency converters used in induction motors with carriers
of a few kHz in voltage, the greater the inductances of the
machine and the higher the switching frequency, the lower
the current distortion will be (Fig. 2).
Fig. 2. Pulse Width Modulated (PWM) voltage and current drawn by an
induction motor.
It is not an easy task to determine what will be the
necessary bandwidth in each case. The distribution of the
losses in the frequency spectrum depends on the fundamental
frequency, the switching frequency, the type of drive control,
the geometry of the machine and the laminations used, the
state of load, etc.
The phenomenon of losses in machines using converters
has been studied using different approaches, with
computational techniques based on finite elements such as
[11], [12]; using analytical models [13] or empirical methods
[14].
Due to this, the standards do not have a single criterion for
the treatment of the subject either. They consider the increase
in motor losses due to the use of the converter, but there is no
standard that specifies the test procedure to evaluate the
efficiency of the system [15].
The NEMA MG1 Part 30 [16] standard considers a power
derating factor to avoid overheating using the converter,
depending on the harmonic content of the PWM voltage. IEC
60034-17 [17] proposes as an example a motor with a 315
frame with 95.3% efficiency and breaks down the
components of the increase in losses due to the use of a drive,
which are 15% higher than rated losses.
If this example is considered to determine the necessary
bandwidth in power measurement and taking into account
that this increase in losses occurs in the switching frequency
bands and their multiples, since the difference between the
losses in the band of the fundamental frequency of a 50Hz
sinusoidal excitation and a PWM excitation is marginal [11],
it is expected that the reduction in accuracy suffered by the
electrodynamometer wattmeter at high frequencies affects
only that additional 15% of power. In addition, although the
measurement error increases with frequency, the power loss
decreases, according to [11] these losses are found mainly in
the switching frequency band (f
sw
) and to a lesser extent in
the first multiple of this (2.f
sw
), being totally negligible for
3.f
sw
. Considering this, and assigning an average error of 10%
of the wattmeter in the high part of the spectrum, this would
introduce an error of 1.5% in the measurement of the total
power loss 𝑝
(9), and if the measurement is made on the
input power of the machine 𝑃
, the error is negligible (10).
Separating the losses in the fundamental band, from those
due to the harmonic components (which are indicated by the
subscript HF for high frequency):
𝑝
= 𝑝
+ 𝑝
(5)
𝑝
= 𝑃
∙
(
1 − 0.953
)
= 𝑃
∙ 0.047
(
±𝜀
)
, (6)
𝑝
= 𝑝
∙ 0.15
(
±𝜀
)
, (7)
𝜀
= 𝑝
∙ 0.15 ∙ 0.1 = 𝑝
∙ 0.015 , (8)
Replacing (7) in (5):
𝑝
= 𝑝
(
±𝜀
)
+ 𝑝
∙ 0.15 (±𝜀
)
If the contribution to the error of the harmonic power
measurement is the only one considered (that is, the error at
50 Hz is not taken into account):
𝑝
= 𝑝
∙
(
1 + 0.15
)
𝜀
= 𝑝
∙ 0.015 = 𝑝
∙
.
(
.
)
= 𝑝
∙ 0.013 , (9)
If it is evaluated how much the error of the ED wattmeter
affects the measurement of the input power:
𝜀
= 𝑃
∙ (1 − 0.953) ∙ 0.15 ∙ 0.1
=𝑃
∙ 0.000705 , (10)
The proportion of losses caused by harmonics when using
PWM depends on many variables: The load condition of the
machine, the fundamental frequency, the modulation index,
the modulation strategy, etc.
Assuming a machine with low efficiency of the order of
80%, and losses increased by harmonics by 50%, the error of
the wattmeter in the measurement of the total loss power will
be 3.33%, while for the input power it will be 1%.
In general:
𝜀
= 𝑝
∙
(
)
∙ 𝜀
, (11)
𝜀
= 𝑃
∙ (1 − ) ∙ k ∙ 𝜀
, (12)
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Where k is the increase in losses in per unit due to the use
of the drive,
is the rated efficiency for 50Hz sinusoidal and
𝜀
the average estimated error of the wattmeter at harmonic
frequencies.
It is interesting to note that to determine the efficiency of
a motor, estimation methods are sometimes used, for
example "slip method" or "current method" [18], which
provide greater errors than those mentioned. More complex
methods [19] produce errors of the same order. If the
intention is to measure power losses by some segregation
method [20], the accuracy will not be sufficient. It will be
necessary to evaluate in each particular case whether the
resulting errors are acceptable or not.
IV. LABORATORY MEASUREMENTS
The experimental results were obtained using three setups
for power measurement under different conditions.
The first setup (A) can be seen in Fig. 3. An Agilent 6834B
AC Power Source/Analyzer 4500VA with a power
measurement error of [0.15% + 3 W] is used to power a three
phase resistive load bank and a three phase inductive load
bank connected in parallel. The tested wattmeters are
connected individually and their reading is compared with
the one provided by the power source, which has an external
sensing feature to measure the voltage on the load.
Fig. 3. Measurement setup A.
Fig. 4 shows the simplified circuit of the test bench used
for power measurement with harmonic content
(configuration B) [21], [22]. A frequency converter (Siemens
Micromaster440) drives a 3kW 220/380V 18.4/10.6A
715rpm “Mocbos” induction motor that is mechanically
coupled to a “Motortech” 5.5KW 220V DC generator. This
is connected to the power grid through a non-autonomous
inverter (Mocbos ST 3630 controlled rectifier) to allow the
regeneration of the energy used during the tests. The
measurement with the tested ED wattmeters is carried out at
the drive output, comparing the readings with a Yokogawa
WT200 Digital Power Meter whose bandwidth is 50 kHz and
whose error at 50 Hz is ± (0.15% of rdg + 0.1% of rng) and
about double at 10 kHz.
The third setup (C), graphed in Fig. 5, allows testing the
wattmeters with PWM voltage and, in turn, with variation of
cosine φ. To do this, a three-phase rotor induction phase
shifter is used (2 kVA Siemens-Schuckert, 225 V 7.8 A /
110V 10.6 A) whose primary is connected to a WEG model
CFW 09 converter while its secondary is connected to a pure
resistive load. The voltage connection of the instruments is
made on an input phase and the current of the corresponding
secondary phase flows through the current circuit of the
instruments.
Fig. 4. Measurement setup B.
In all cases, “short connection” is used, that is, the
instruments measure, in addition to the power dissipated in
the load, the power consumed by the voltage circuit, but no
correction is made since the instrument used for comparison
measures the same power.
Then, the difference between the reading of the ED
wattmeter and the reference wattmeter is calculated and the
percentage that it represents with respect to the full scale (FS)
value of the tested instrument is plotted.
Fig. 5. Measurement setup C.
Three electrodynamometer wattmeters with markedly
different date of manufacture were tested.
A Weston model 310 No. 11499 dating from the year 1946
from the USA, whose class originally is 0.25 and at 50 Hz it
verifies that the deviations are within 0.25% of the full scale
value with respect to the measurements made with the
standard. Even so, it cannot be affirmed that it is in class,
since an evaluation of the uncertainty of the calibration is not
carried out, considering that the standard does not have a
sufficiently better accuracy than the instrument. However,
the comparison is useful to evaluate how the errors evolve
later when testing it under different harmonic conditions.
A Pullin N°S50232 of English origin dating from 1962.
Original class 0.6, although it is verified that at 50 Hz the
error doubles the 0.6% of the full scale reading.
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A Yokogawa No. 80AN0167 from the year 2010 that
retains its original Class 0.5.
A. 50Hz sinusoidal measurement
The first tests were carried out with (A) setup (Fig. 3).
The results show that in all three cases the wattmeters
measure with an increasing error trend as a function of power.
That is to say, the wattmeters under-measure for low loads,
but as the current increases (at constant voltage), this
tendency is reversed and reading becomes an over-measure.
These deviations occur within the rated error of the
WESTON wattmeter (Fig. 6) and the YOKOGAWA (Fig. 8),
but the PULLIN (Fig. 7) exceeds the rated error in excess,
doubling it.
Fig. 6. WESTON wattmeter error with 50 Hz sinusoidal voltage as a
function of load.
Fig. 7. PULLIN wattmeter error with 50Hz sinusoidal voltage as a
function of load.
Fig. 8. YOKOGAWA wattmeter error with 50 Hz sinusoidal voltage as a
function of load.
B. 5kHz sinusoidal measurement
Making use of the 5 kVA three-phase source in single-
phase mode, using a sinusoidal waveform and with a pure
resistive load, the three wattmeters are tested at frequencies
of 2 kHz, 4 kHz and 5 kHz.
Fig. 9. WESTON wattmeter error with sinusoidal voltage as a function of
the load for different frequencies.
Fig. 10. PULLIN wattmeter error with sinusoidal voltage as a function of
the load for different frequencies.
Fig. 11. YOKOGAWA wattmeter error with sinusoidal voltage as a
function of the load for different frequencies.
An unexpected result is obtained. Despite the existence of
a dispersion in the error values with respect to the
measurements at 50 Hz, these remain within the same order
of magnitude as at 50Hz. The Yokogawa wattmeter (Fig. 11)
remains within its class of accuracy. It shows a change in
trend at around 2 kHz (similarly to the WESTON wattmeter,
see Fig. 9) since at that frequency the measurement error
(which is an under-measurement) reaches its maximum value,
whereas for higher frequencies the trend changes and the
error becomes an over-measurement. In the case of the
PULLIN wattmeter (Fig. 10) the same change in trend occurs
at 4 kHz instead of at 2 kHz. A possible explanation would
be the following: as the frequency increases, the applied
voltage in the potential coil cannot maintain the same current,
since the inductance grows linearly with the frequency, and
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as a result the instrument measures less. For higher
frequencies, the errors due to parasitic and capacitive currents,
which depend on the square of the frequency, have a greater
influence compared to the previous effect, resulting in an
over-measurement.
C. 2kHz polyharmonic measurement
A more demanding test involves square wave voltage and
current measurement at 50 Hz and an approximately square
wave polyharmonic with fundamental at 2 kHz (Fig. 12)
performed with (A) setup.
Fig. 12. Above: Polyharmonic current and voltage waveform with 2 kHz
fundamental. Bottom: Voltage spectrum.
The results can be seen in the graphs (Fig. 13-14-15). The
measured power (with 50 Hz square wave voltage and current)
shows a variation in the error with respect to that obtained
with 50 Hz sinusoidal due to the presence of polyharmonics.
However, the difference is not significant, as the errors are of
the same order.
Fig. 13. WESTON wattmeter error with squared voltage (approx.) as a
function of load for different frequencies.
Fig. 14. PULLIN wattmeter error with squared voltage (approx.) as a
function of load for different frequencies.
Fig. 15. YOKOGAWA wattmeter error with squared voltage (approx.) as a
function of load for different frequencies.
On the other hand, it can be seen that the measured power
with polyharmonic voltage and current (with a fundamental
at 2 kHz) shows a significant deviation with respect to the
readings of similar power measurements at 50 Hz. This trend
in the YOKOGAWA wattmeter (Fig. 15) shows an error that,
in the worst case, practically triples the class of accuracy at
50 Hz. Something similar occurs with the WESTON
wattmeter (Fig. 13). In figure 12 it can be seen that the
voltage contains odd harmonics of appreciable magnitude,
the 11th (22 kHz) having an amplitude of approximately 30%
of the fundamental frequencies. Even so, in all cases the error
remained below 2% of the full scale value.
D. PWM polyharmonic measurement
The most relevant case results from the measurement of a
PWM-type polyharmonic voltage (common in converters)
and current with low distortion (due to the filtering effect of
the electric machine, which in this case is a 3kW induction
motor with four pairs of poles). It can be seen in (B) setup
that the converter used is a Siemens Micromaster 440 model
with the ability of configuring the switching frequency
between 2 kHz and 16 kHz in steps of 2 kHz. The
measurement of the errors committed by the three wattmeters
under four load conditions and for five carrier frequencies
was carried out. The readings obtained were compared with
those obtained with the digital power meter YOKOGAWA
WT200 which has a bandwidth of 50 kHz.
Fig. 16. WESTON wattmeter error with PWM voltage as a function of
load for different frequencies.
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