Utilización del vatímetro electrodinámico estándar para la medición de potencia armónica

Alejandro Fabio Veyrat Durbex; Yaki Nachajon Schwartz; Hernán Tacca

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

aveyrat@fi.uba.ar

ynachajon@fi.uba.ar

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

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.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

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

) and to a lesser extent in

the first multiple of this (2.f

), being totally negligible for

3.f

. 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)

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

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.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

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

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

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.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

Fig. 17. PULLIN wattmeter error with PWM voltage as a function of load

for different frequencies.

Fig. 18. YOKOGAWA wattmeter error with PWM voltage as a function of

load for different frequencies.

In this case, the accuracy of the readings is limited by the

instability of the measurement. To minimize the observer's

error, the hold function of the digital instrument was used, in

synchronization with the photographic capture of the

measurement scale of the analog instrument.

From the analysis of the results, it can be affirmed that the

errors are higher than those committed by the instruments at

a frequency of 50Hz; even so they do not reach 2 %. And, in

the case of the YOKOGAWA wattmeter (Fig. 18) it does not

deviate much from 0.5 % original error. It is also observed

that the maximum deviations occur for low carrier

frequencies, 4 kHz in the case of the WESTON and

YOKOGAWA wattmeters, and 2 kHz in the case of the

PULLIN wattmeter. Regarding the trend of variation of the

error with the load, the three wattmeters reproduce the

behavior at 50Hz, where it was seen that the readings had

tendency to over-measure for higher load values.

E. PWM polyharmonic measurement for different cos φ

Using (C) setup, the measurement made by the ED

YOKOGAWA wattmeter was compared with the digital

power meter reading when PWM voltage is applied and the

current has low harmonic distortion, and varying the phase

shift between them, that is, cosφ, where φ is the angle

between the current and the fundamental of the switched

voltage. To do this, a three-phase phase shifter is used to

whose primary a WEG CFW 09 converter is connected and

to whose secondary a pure resistive load is connected.

Measurements were carried out for the drive's four

configurable carrier frequencies: 1.25 kHz, 2.5 kHz, 5 kHz,

and 10 kHz. As the secondary emf remains constant for a

given load, the current also remains constant. Then, by

manually turning the rotor the desired phase shifts are

obtained. This scenario allows testing the wattmeter in the

combined presence of reactive power and distortion power.

Fig. 19. YOKOGAWA wattmeter error with PWM for different FP

depending on the carrier frequency.

In Fig. 19 the results are plotted, verifying that the

measurements with the electrodynamometer wattmeter differ

from those obtained with the digital power meter in the order

of 0.5% of the full scale reading.

This scenario that involves the measurement of power with

a polyharmonic voltage waveform and a current waveform

with low harmonic distortion, out of phase with each other,

can be seen in figure 20.

Fig. 20. Above: Current and voltage waveform. Bottom: Image shows

voltage and current harmonic content from a PWM measurement.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

F. Unitary PF PWM Polyharmonic Measurement

In Section III it was said that the electrical quantity with

the narrowest harmonic distortion bandwidth determines the

final bandwidth of the power signal. Power measurements

made with PWM voltage waveforms and current waveforms

with low distortion show low errors in ED instruments. To

verify the response of the ED wattmeters with the PWM

voltage and current polyharmonic waveform, measurements

were made with frequencies up to 10kHz with resistive load,

but for these frequencies, the load bank made with nichrome

wire wounded on ceramic cores have an inductive component

that distorts the test. As an alternative, the measurement of a

fixed load of 400W obtained with three star-connected

halogen lamps was carried out. Three readings were made for

each carrier frequency available in the drive (1.25 kHz, 2.5

kHz, 5 kHz, 10 kHz).

The figure 21 shows the error increase when the drive

switching frequency increases.

Fig. 21. YOKOGAWA wattmeter error with PWM voltage and current

waveform for different frequencies.

Fig. 22. Current harmonic content from a unitary PF PWM measurement.

V. CONCLUSIONS

Power measurements made with ED instruments involving

voltages and currents with harmonic components of

frequencies higher than the power grid frequency deviate

from wattmeter readings made at 50Hz with sinusoidal

voltage and current. These deviations in readings for

frequencies of up to 5 kHz are similar to the deviations

obtained at 50 Hz with cosφ=1 with a sinusoidal waveform.

When power measurements made with ED instruments

involve voltages and currents with high harmonic content

(greater than 20 kHz), significant deviations are recorded

with respect to measurements of equal power made at a

frequency of 50 Hz. In all cases the tendency was to over-

measure, this deviation reached, in some instruments, three

times the class error.

For the very common case involving converters, of PWM

voltage and quasi-sinusoidal current, the errors (compared to

the 50Hz case) are minimal when the converter uses high-

frequency carriers, and increase slightly when the converter

uses low frequency carriers. Regarding the variation of error

with load, ED instruments have a tendency to over-measure

as load increases, such as occurs at 50Hz.

When both the voltage and current waveforms have high

harmonic content, the error grows significantly.

In short, if an accurate measurement of the losses of a

converter-driven machine is required, it will be necessary to

evaluate if the errors obtained with the use of ED wattmeters

are acceptable, or whether to resort to an expensive high-

bandwidth digital wattmeter. If an estimate of the losses or

efficiency of the machine is required, the ED wattmeter will

suffice, more so if only a measurement of the input power

supplied by the converter to the machine is required.

ACKNOWLEDGMENT

This work has received funding from the University of

Buenos Aires with funds from the UBACYT grant

20020170100386BA. “New structures and simulation and

control techniques for static converters and pulse generators”.

REFERENCES

[1] (2023) Standard Electric Works Co. LTD. webpage. [Online].

Available: http://www.sew.com.tw/front/bin/ptdetail.phtml?Part=1-

13-01-05&Category=431933

[2] (2023) Mahesh Electrical Instruments webpage. [Online]. Available:

http://www.meinstruments.in/portable-meters-electrical-laboratory-

meters--767151.html

[3] (2023) MECO-G webpage. [Online]. Available:

http://www.goliyainstruments.com/product-details/ANALOG-

ELECTRODYNAMOMETER-TYPE-PORTABLE-WATT-VAR-

POWER-FACTOR-METERS

[4] (2023) TESCA webpage. [Online]. Available:

https://www.tescaglobal.com/categories/analog-portable-meters

[5] J.H. Park, A.B. Lewis, “standard electrodynamic wattmeter and AC-

DC transfer instrument”, National Bureau of Standards, U.S.

Department of Commerce, research paper RP1344, vol 25, november

1940.

[6] A. H. M. Arnold, “Audio Frequency Power Measurements by

Dynamometer Wattmeters”, paper No 1653 M, April 1954.

[7] R. Friedl and G. Wolf, “Precision Mesuring Equipment for Electrical

Power in the Range of Audio Frequencies”, IEEE Transactions on

Instrumentation and Measurement, VOL. IM-15, Nº 4, December,

1966.

[8] A. I. Nefed’ev, “A new method of constructing electrodynamic

voltage, current, and power comparators”, Measurement Techniques,

Vol. 50, Nº 3, 2007.

[9] S. Yoshizaki, “Bandwidth and Phase Characteristic Requirementsfor

High-Precision Power Measurement of High Frequency and High-

Current PWM Control Inverters”, Yokogawa Test&Measurement

Corporation, June 2021.

[10] George C. Laventure Jr., “Measuring Accurately Single-phase

Sinusoidal and Non-sinusoidal Power”, Thesis, University of

Colorado, 1983.

[11] C. A. Hernandez-Aramburo, T. C. Green and S. Smith, "Assessment

of power losses of an inverter-driven induction machine with its

experimental validation," in IEEE Transactions on Industry

Applications, vol. 39, no. 4, pp. 994-1004, July-Aug. 2003, doi:

10.1109/TIA.2003.813744.

[12] K. Yamazaki, A. Suzuki, M. Ohto and T. Takakura, "Harmonic Loss

and Torque Analysis of High-Speed Induction Motors," in IEEE

Transactions on Industry Applications, vol. 48, no. 3, pp. 933-941,

May-June 2012, doi: 10.1109/TIA.2012.2191252.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

[13] Y. Liu and A. M. Bazzi, "A General Analytical Three-Phase Induction

Machine Core Loss Model in the Arbitrary Reference Frame," in

IEEE Transactions on Industry Applications, vol. 53, no. 5, pp. 4210-

4220, Sept.-Oct. 2017, doi: 10.1109/TIA.2017.2695442.

[14] L. Aarniovuori, A. Kosonen, M. Niemelä and J. Pyrhönen,

"Frequency converter driven induction motor losses," IECON 2013 -

39th Annual Conference of the IEEE Industrial Electronics Society,

2013, pp. 2881-2886, doi: 10.1109/IECON.2013.6699588.

[15] Motores de inducción alimentados por convertidores de frecuencia

PWM, Guía Técnica, WEG, 01/2016.

[16] Performance Standards Applying to All Machines – Part 30:

Application Considerations for Constant Speed Motors Used on a

Sinusoidal Bus with Harmonic Content and General Purpose Motors

Used with Adjustable Voltage or Adjustable Frequency Controls or

Both, Application Considerations, ANSI/NEMA MG1-2016

(Revised 2018).

[17] Rotating electrical machines – Part 17: Cage induction motors when

fed from converters – Application guide, Ed. 4, IEC 60034-17, May

2006.

[18] A. Jurado, J. P. Robbiano, F. Ferreyra, “Determinación in situ de la

eficiencia de un motor eléctrico,” Encuentro Latinoamericano de Uso

Racional y Eficiente de la Energía - ELUREE2013. Buenos Aires,

Argentina – 25, 26 y 27 de Septiembre de 2013. GT04 – Eficiencia en

la Industria y Generación Eléctrica. ISBN: 978-987-1527-71-1.

Croquis SRL.revista Electrotécnica AEA.

[19] V. Sousa Santos, E. C. Quispe, J. R. Gómez Sarduy, P. R. Viego, N.

Lemozy, A. Jurado and M. Brugnoni, “Bacterial Foraging Algorithm

Application for Induction Motor Field Efficiency Estimation under

Harmonics and Unbalanced Voltages,” IEEE International electric

machines and drives conference, Chicago, EEUU. 12-15 de mayo

2013 ISBN: 978-1-4673-4975-8; p. 1174-1177. IEEE.

[20] IEEE Standard Test Procedure for Polyphase Induction Motors and

Generators, IEEE Std 112-2017 (Revision of IEEE Std 112-2004),

pp.1-115, 14 Feb. 2018, doi: 10.1109/IEEESTD.2018.8291810.

[21] Y. Nachajon, P. Witis, G. Bongiovanni, H. Tacca, and F. Ferreira,

“Banco de ensayos para algoritmos de control para motores de

inducción trifásicos”, SAAEI, Guijón-España, 2006.

[22] A. F. Veyrat Durbex, “Cargas activas para un banco de ensayos de

control de motores de inducción trifásicos,” Thesis, Universidad de

Buenos Aires, march of 2015.

Revista elektron, Vol. 7, No. 1, pp. 19-27 (2023)

ISSN 2525-0159

Enlaces de Referencia

Por el momento, no existen enlaces de referencia

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Revista elektron, ISSN-L 2525-0159
Facultad de Ingeniería. Universidad de Buenos Aires
Paseo Colón 850, 3er piso
C1063ACV - Buenos Aires - Argentina
revista.elektron@fi.uba.ar
+54 (11) 528-50889

Nombre de usuario
Clave
Recordar mis datos