ω A θ O figure 2. A rotating phasor, the projection of which on the horizontal axis is x(t) = A cos (~t+i). Le ng th =A Po Angular Velocity ω Radian/s sit Tim ion a et t cos pt, can be represented by the projection, on a fixed line, of a vector of constant length A supposed to revolve uniformly so as to complete one revolution in a time T given by the relationship pT = 2r. The angle between the revolving vector and the fixed line is pt at any instant t. In the first edition of Thomson and Tait's 'Natural Philosophy' (vol. 1, p. 38, § 58) it is shown any two simple harmonic functions of one period can be compounded to a single simple harmonic function of the same period, and that the vector, representing the compounded function, is obtained from those representing the component functions by the ordinary process of vector addition. This device has proved valuable for many purposes, but it has proved especially useful for ac problems. Its application to such cases was first clearly pointed out by T.H. Blakesley more than 12 years earlier. Thus, we see that, before 1900, methods of combining vectors were known and used in electrical engineering. The Blakesley work referred to is most likely his book Alternating Currents of Electricity, published in 1885. The word vector was used by power engineers by 1897, meaning the line last passed through its middle position in the positive direction. Although the word vector is not used directly in association with this figure, the expression radius-vector is used to describe the line from the center of the circle in other versions of the figure. In Figure 1, that line is OQ. At the time of this very early work, no thought was given to using the diagram or the idea of simple harmonic motion for electrical applications: the book considers mechanical things. However, it did not take long for electricians (as electrical engineers were then called) to appreciate the method. Electrical use was apparently "well known" in 1897 when W.E. Sumpner, in a paper at the Royal Society, referred back to T and T: It has been well known for many years that the variations of a simple harmonic function, such as A s an ωt i ad R at ion = 0 t i s Po me t Ti s dian θ Ra O Acos(ωt + θ) figure 3. A phasor diagram corresponding to Figure 2, as typically taught. In some books, this is known as an Argand diagram. 78 ieee power & energy magazine from the center of the circle of rotation to the point moving uniformly in a circle the projection of which gives the equation of simple harmonic motion. It is a double abstraction. First, we have to assume that the physical signal can be represented as a mathematical sine wave; then, we have to see that a vector (a rotating line) can be used to generate the sine wave. This use of the word to signify a line persisted unchanged until well after the suggestion to instead use the word phasor in 1944. Post-1944 Use Adopting the Word After 1944, the word phasor was adopted somewhat gradually. Its use was described in 1960 in a general-purpose electrical engineering textbook (Electrical Engineering Science, by Clement and Johnson) with the following words: For convenience in the mathematical treatment to be given in Chap. 11, we shall choose to project the arrow onto the horizontal axis. The arrow is termed a phasor. Somewhere along the way, the rotating line has gained an arrowhead, and the direction of projection changed, but it is still a line. There is a footnote that introduces the word sinor, apparently another term for the same thing. Sinor was used in some works published between 1945 and approximately 1955, but it was falling out of favor by then. In the 1952 book Analysis of Alternating Currents, W.R. LePage writes, "The term 'sinor' is to be interpreted as an abbreviation for the phrase 'symbolic representation for a sinusoid'," A footnote in the original adds the following, highlighting the idea of a line: A sinor does not represent a sinusoid in the sense that an ordinary variable represents a quantity. The directed line is quite different from a sinusoid. Therefore the word "symbolic" is important. LePage acknowledges the double abstraction. He continues with an explanation suggesting that the sinor includes only the magnitude and the angle in its symbolic representation. Perhaps because january/february 2020

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