IEEE Power & Energy Magazine - January/February 2020 - 82

into two parts: e j (~t + z) = e j~t e jz and deal
with only the part that is not time dependent as "the phasor."
Therefore, the phasor started life as a
vector, a line rotating around the origin.
It became an arrow, then was written in
an exponential form, and then split into
a stationary and a rotating part. The
confusion continues, as we shall see.

Phasor Measurement
A new term has recently been introduced: synchrophasor was added to the
vocabulary by the standardization of
the method of measuring phase angles
in power systems. With the invention of
the phasor measurement unit (PMU),
routine measurement of the angle of
any part of a system (with respect to a
global reference) became possible.
The PMU works by taking digital
samples of the analog voltage (or current)
signals at its input and examining them
within a measurement time window. For
each window, the values of the parameters of (1) are found. It is acknowledged
that the parameters might be changing

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(typically, will be changing) so that, ideally, the value at the center of the window
is to be reported.
The window can be as short as two
cycles of the input waveform, or it may
be longer, depending on the type of PMU
and its settings. It is, I think, a tribute to
the designers of such equipment that accurate values of the parameters can be measured from such short sample sequences.
Performance requirements are spelled out
in the IEEE standards, the latest of which
is C37.118.1-2011, with an amendment
in 2014. I was a member of the working
group that developed the 2011 standard.
If the parameters are changing, the
signal is not representable by a sinusoid
because a sinusoid has constant values
for all time. The equation is normally
thought of as requiring the addition of a
term representing a rate of change of frequency, and the PMU is supposed to report
this value. (The parameter is, however,
hard to measure when there is noise or
distortion on the signal. It is what mathematicians call an "ill-posed problem.")
Most commercial PMUs work by
performing a discrete Fourier transform
on the windowed signal. The usual assumption of the Fourier transform is that
the signal is infinite in time. In the PMU,
that translates to the assumption of a periodic signal, with a period integrally
related to the window duration. Because
that is not always true (because the period may be off nominal), the window
is shaped by tapering down at the beginning and end to reduce what is called
spectral leakage.
The measured results are termed
a synchrophasor, signifying a synchronized phasor. According to the
IEEE standard, the term actually applies only to the magnitude and angle
data, not the frequency. However, for
some applications, the frequency is the
most important parameter being measured. To add to the confusion, the word
synchrophasor has come to mean both
the reported measurement results and the
device that delivers them (i.e., the PMU).
As we can see, the reports coming from a
PMU may be synchronized, but they do
not describe a phasor, whichever meaning is applicable.

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Conclusions
For almost a century, the meanings of the
words vector, and then phasor, did not
change. These terms meant a line rotating about the origin in the complex plane.
Then a change took place. The word
phasor began to mean only the complex
number representation and then just the
part that was not time dependent.
It seems regrettable to me that there is
confusion over the meaning. Communication suffers as a result, and there is a deep
problem underlying the lack of clarity regarding wording. The vector and phasor,
as rotating lines, were clearly conceptual
notions that could help form ideas about
the physical world. The separation of the
conceptual and the physical has been an
important part of the development of science and engineering. The rotating line on
the Argand diagram (Figures 2 and 3). with
its amplitude and phase shown and with a
curved arrow showing the frequency, captured all three parameters of a sinusoidal
signal without seeming to be "like" the
sinusoidal signal. With the move to exponential notation, users begin to equate the
conceptual idea (the notion of a signal represented by a sinusoid) with the physical.
The process began a long time ago.
In a 1954 article, Hermont wrote, "The
process of measuring electrical phasors,
quite naturally, may be subdivided into
two parts." The statement implies a kind
of muddy thinking that continues today.
One does not measure a phasor, one
measures a signal that one assumes to
be representable by a sinusoid, and one
represents the sinusoid by a phasor. Only
the signal is a physical thing, the phasor
is a conceptual thing, a mental construct.
The distinction between the physical
and the conceptual is at least as old as
the vector idea. As James Clerk Maxwell noted near the end of his 1870 address to the British Association,
I shall only make one more remark
on the relation between mathematics and physics. In themselves, one
is an operation of the mind, the
other is a dance of molecules.
Even the IEEE Standards Dictionary
is not completely honest in this regard; it
(continued on p. 88)

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IEEE Power & Energy Magazine - January/February 2020

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