IEEE Power & Energy Magazine - January/February 2020 - 77
Early Use
A
Q
P
O
A′
figure 1. A simple harmonic motion
figure based on the work by Thomson
and Tait.
75 years before then, and phasor has
been the word since. For 75 years, people knew what a vector was. It is phasor
whose meaning has changed and is no
longer fundamental, logical, and clear as
Stockman and Hok hoped it would be.
It is the process of the changes in meaning that we will examine in this article.
First, let us look at the original meaning.
Readers may be surprised.
Power system quantities are usually
described by sinusoidal equations, as
in (1). This is the same equation that
Stockman and Hok were interested in,
although they were concerned with
modulating the two terms that were not
amplitude. In a power system, the x (t)
might represent a voltage or a current, t
is the time, ~ is the angular frequency,
A is the magnitude of the waveform,
and i is the angle between the signal
being observed and some reference evaluated at time 0:
x (t) = A cos (~t + i) .
(1)
This sinusoidal equation is familiar to
engineers everywhere (see "Steinmetz
Preferred Polar Coordinates"). The
same kind of equation describes what is
called simple harmonic motion, for example, the motion of a pendulum with
very small deflection. It is a description
of motion (not voltage or current) in a
book from 1867 (Treatise on Natural
Philosophy by Thomson and Tait) that
gave us our model. Thomson was the
person who went on to become Lord
Kelvin, and Tait was a long-time colleague of his. The book was immensely
well known, and was called simply T and
T. Figure 1 is redrawn from the original.
The following description is given in association with the figure:
When a point Q moves uniformly in a circle, the perpendicular
QP drawn from its position at
any instant to a fixed diameter
AA' of the circle, intersects the
diameter in a point P, whose position changes by a simple harmonic motion.
The text goes on to describe the motion and the terms used. For example,
phase is described as follows:
The Phase of a simple harmonic
motion at any instant is the fraction of the whole period which has
elapsed since the moving point
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IEEE Power & Energy Magazine - January/February 2020
Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - January/February 2020
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