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 s Meets FAA Specifications! Color - Size - Shape! - International Orange s Tested and approved by major power companies! s Thousands still in service after 40 years s Universal attaching! Fits any wire .1" to 1"! s Installs in 5 minutes! s Withstands hail! s No maintenance! Does not slip, oscillate, chafe, cause electrolysis or harmonic vibration. s Ships in halves nested. 9, 12, 20, 24, 30, and 36" balls & special sizes available Call now 573-796-3812 ext. 2001 Fax 573-796-3770 www.tanawiremarker.com TANA WIRE MARKERS (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. P.O. Box 370, California, MO 65018 634276_Tana.indd 1 23/03/13 10:38 AM 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)http://www.tanawiremarker.com

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