Instrumentation & Measurement Magazine 24-3 - 11

Measurement of Voltage, Current
and Power at Distorted Waveforms
Branislav Djokic´ and Harold Parks

E

lectric power systems have been designed to operate under sinusoidal voltage and current conditions
at power frequencies, mainly 50 Hz and 60 Hz, and
by far most electrical energy transmission occurs at 50 Hz and
60 Hz. Electric utilities are responsible for providing a sinusoidal voltage to their residential, commercial and industrial
customers. The customers are, on their side, responsible for
not causing excessive distortion of the voltage and current in
the system. Since voltage and current, in practice, are periodical but not exactly sinusoidal, they contain higher frequency
components-harmonics-in addition to the fundamental frequency component (50 Hz or 60 Hz).
Due to their negative effects, harmonics have to be monitored and controlled according to national and international
standards. Harmonic management includes different limits
for harmonic distortion at different voltage levels. Although
harmonics are present in the transmission system, they are
more pronounced in the distribution system because of an
increasing penetration of power electronics loads. Some
standards, e.g., [1], are related to tests and measurements of
harmonics.
To measure harmonics and other power quality parameters, it is necessary to scale down voltage and current from
their transmission and distribution levels to the levels that can
be processed by electrical instrumentation. A harmonic-measurement capability is present in numerous revenue meters,
e.g. in Smart Meters, in a number of digital protective relays
and in power analyzers. Therefore, the evaluation of harmonic measurements should entail the whole measurement
chain, with traceable calibrations of both instrument transformers operating at high primary voltages and currents and
harmonic-measuring instruments connected to the instrument
transformers' low secondary voltages and currents.
This paper describes the calibrations of high-voltage and
high-current transformers and recent developments in the calibration of power instrumentation at the National Research
Council (NRC) Canada, undertaken to increase the frequency
range and accuracy of harmonics calibrations at higher frequencies [2].

May 2021	

Measurements in the Presence of
Harmonics at the NRC
The role of national measurement institutes is to provide the
technical means for ensuring the quality of measurements
through low measurement uncertainties (a non-negative parameter characterizing dispersion of the values attributed to
a measured quantity) and their traceability to SI (a property of
the measurement result or the value of a standard whereby
it can be related to stated references, usually national or international measurement standards, through an unbroken
chain of comparisons all of which have stated uncertainties). Type A evaluation of uncertainty is performed by the
statistical analysis of series of observations, whereas Type B
evaluation of uncertainty is performed by means other than
the statistical analysis of series of observations, using available knowledge of the measurement method and means. In
this process, standard uncertainties, i.e., uncertainties of the result of a measurement expressed as standard deviations are
evaluated. Combined standard uncertainty of the measurement
result is obtained as the square root of a sum of the squares of
standard uncertainties of the quantities that the result depends
on, weighted according to how the measurement result varies
with changes in these quantities. Expanded uncertainty U is obtained by multiplying the combined standard uncertainty by a
coverage factor k. The result of a measurement is then expressed
as Y = y ± U, where y represents the best estimate of the value
attributable to the measurand Y. For the coverage factor of k =
2, the uncertainty U represents a level of confidence of approximately 95% that Y is within the interval [y - U, y + U]. Detailed
discussion with definitions and examples is provided in the
Guide to the Expression of Uncertainty in Measurement (available
at https://www.bipm.org). Most national measurement institutes have implemented quality systems that are compliant
with ISO/IEC Standard 17025.
Research in power measurements in the presence of
harmonics at the NRC have been driven by interest in the performance of revenue meters, and related instrumentation,
at nonsinusoidal conditions. In addition to practical considerations, there have also been theoretical considerations

IEEE Instrumentation & Measurement Magazine	11
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https://www.bipm.org
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