In polar coordinates, a quantity at any time is repre- textbook Theory and Calculation of Alternating Current Phe- sented as a length and a time (with time being a repre- nomena (1908), where a whole chapter (VI, p. 42) is devoted sentation of angle for a periodic function.) It was obvious to comparing the polar diagram and the crank diagram. Stein- to Steinmetz that any periodic function could be repre- metz knew about our sort of phasor diagrams, and he thought sented in polar coordinates, and this is what he taught. them impractical. In his vector power discussion, he wrote: In Figure S2, a movable radius vector rotates with time, This limitation to sine waves appears to me as one starting from the abscissa at t = 0. (Approximately 100 years of the main reasons, why a standardization of the ago, there was much discussion on which way it should crank diagram could not fulfil the purpose of secur- rotate. Anticlockwise was settled on.) The moving radius ing uniformity of notation, by eliminating the polar vector traces out the circle in Figure S3. diagram, since the latter would still have to be used If the amplitude varied as a sine wave, a half cycle of when dealing with distorted waves, as for instance when working up oscillograph records, etc. the waveform could be represented by a circle. The direction of the diameter from the origin gives the phase of Of course, deep down, we know that the waves we deal with the sine wave. The phase thus determined would require are distorted. These days, we tend to overlook that truth. that the sign of the phase offset term in (1) be negative. For Further Reading The other half of the sine wave would be drawn right on C. P. Steinmetz, "Complex quantities and their use in elec- top of the first half. If the wave were known to be a sinu- trical engineering," presented at the Int. Electrical Congress, soid, the circle could be omitted and only the diameter Chicago, IL, 1893. drawn. The resemblance to our diagrams is then strong- but superficial. The phasor diagram (as we know it today, centered on the origin) is not the same. Our method, the crank diagram to Steinmetz, is not mentioned until the fourth edition of his The concept of the rotating phasor arises from the time dependence of the complex exponential which characterizes AC voltages and currents. Let us consider the following phasor representation for an AC voltage V (j~, t) = Vs e j (~t + z) . The concept of the rotating phasor does not, in fact, "arise from the time dependence of the complex exponential" of anything; it arises from a book written more than 100 years earlier by Lord Kelvin! Has the line phasor gone away entirely? Perhaps. In a 1997 book, Electrical Engineering, Mishra describes the location of some points on the complex plane, writing, "If we join these points to the origin, with arrow-heads directed toward the points, we obtain line segments i.e., OA , OB , and so on which are called phasors." I have seen nothing more recent referring to the phasor specifically as a line. Some authors-perhaps most- separate the argument of the exponent A. E. Kennelly, "Vector power in alternating-current circuits," presented at the 27th Annu. Conv. Amer. Institute Elect. Engineers, Jefferson, NH, 1910. C. P. Steinmetz, Theory and Calculation of Alternating Current Phenomena. New York: McGraw-Hill, 1908. Impact the Future of the Industry Get Involved with the IEEE Power & Energy Society's Technical Committees * Identify industry challenges * Develop new standards * Educate the industry Participation in technical activities is a great way to connect with a diverse group of peers from around the world to establish and grow your professional network. There is a PES technical committee or subcommittee for nearly every aspect of the electric power industry. GET INVOLVED TODAY Learn more and visit ieee-pes.org/technical-activities Digital Object Identifier 10.1109/MPE.2019.2957556http://www.ieee-pes.org/technical-activities

IEEE Power & Energy Magazine - January/February 2020 - Cover1

IEEE Power & Energy Magazine - January/February 2020 - Cover2

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

IEEE Power & Energy Magazine - January/February 2020 - 2

IEEE Power & Energy Magazine - January/February 2020 - 3

IEEE Power & Energy Magazine - January/February 2020 - 4

IEEE Power & Energy Magazine - January/February 2020 - 5

IEEE Power & Energy Magazine - January/February 2020 - 6

IEEE Power & Energy Magazine - January/February 2020 - 7

IEEE Power & Energy Magazine - January/February 2020 - 8

IEEE Power & Energy Magazine - January/February 2020 - 9

IEEE Power & Energy Magazine - January/February 2020 - 10

IEEE Power & Energy Magazine - January/February 2020 - 11

IEEE Power & Energy Magazine - January/February 2020 - 12

IEEE Power & Energy Magazine - January/February 2020 - 13

IEEE Power & Energy Magazine - January/February 2020 - 14

IEEE Power & Energy Magazine - January/February 2020 - 15

IEEE Power & Energy Magazine - January/February 2020 - 16

IEEE Power & Energy Magazine - January/February 2020 - 17

IEEE Power & Energy Magazine - January/February 2020 - 18

IEEE Power & Energy Magazine - January/February 2020 - 19

IEEE Power & Energy Magazine - January/February 2020 - 20

IEEE Power & Energy Magazine - January/February 2020 - 21

IEEE Power & Energy Magazine - January/February 2020 - 22

IEEE Power & Energy Magazine - January/February 2020 - 23

IEEE Power & Energy Magazine - January/February 2020 - 24

IEEE Power & Energy Magazine - January/February 2020 - 25

IEEE Power & Energy Magazine - January/February 2020 - 26

IEEE Power & Energy Magazine - January/February 2020 - 27

IEEE Power & Energy Magazine - January/February 2020 - 28

IEEE Power & Energy Magazine - January/February 2020 - 29

IEEE Power & Energy Magazine - January/February 2020 - 30

IEEE Power & Energy Magazine - January/February 2020 - 31

IEEE Power & Energy Magazine - January/February 2020 - 32

IEEE Power & Energy Magazine - January/February 2020 - 33

IEEE Power & Energy Magazine - January/February 2020 - 34

IEEE Power & Energy Magazine - January/February 2020 - 35

IEEE Power & Energy Magazine - January/February 2020 - 36

IEEE Power & Energy Magazine - January/February 2020 - 37

IEEE Power & Energy Magazine - January/February 2020 - 38

IEEE Power & Energy Magazine - January/February 2020 - 39

IEEE Power & Energy Magazine - January/February 2020 - 40

IEEE Power & Energy Magazine - January/February 2020 - 41

IEEE Power & Energy Magazine - January/February 2020 - 42

IEEE Power & Energy Magazine - January/February 2020 - 43

IEEE Power & Energy Magazine - January/February 2020 - 44

IEEE Power & Energy Magazine - January/February 2020 - 45

IEEE Power & Energy Magazine - January/February 2020 - 46

IEEE Power & Energy Magazine - January/February 2020 - 47

IEEE Power & Energy Magazine - January/February 2020 - 48

IEEE Power & Energy Magazine - January/February 2020 - 49

IEEE Power & Energy Magazine - January/February 2020 - 50

IEEE Power & Energy Magazine - January/February 2020 - 51

IEEE Power & Energy Magazine - January/February 2020 - 52

IEEE Power & Energy Magazine - January/February 2020 - 53

IEEE Power & Energy Magazine - January/February 2020 - 54

IEEE Power & Energy Magazine - January/February 2020 - 55

IEEE Power & Energy Magazine - January/February 2020 - 56

IEEE Power & Energy Magazine - January/February 2020 - 57

IEEE Power & Energy Magazine - January/February 2020 - 58

IEEE Power & Energy Magazine - January/February 2020 - 59

IEEE Power & Energy Magazine - January/February 2020 - 60

IEEE Power & Energy Magazine - January/February 2020 - 61

IEEE Power & Energy Magazine - January/February 2020 - 62

IEEE Power & Energy Magazine - January/February 2020 - 63

IEEE Power & Energy Magazine - January/February 2020 - 64

IEEE Power & Energy Magazine - January/February 2020 - 65

IEEE Power & Energy Magazine - January/February 2020 - 66

IEEE Power & Energy Magazine - January/February 2020 - 67

IEEE Power & Energy Magazine - January/February 2020 - 68

IEEE Power & Energy Magazine - January/February 2020 - 69

IEEE Power & Energy Magazine - January/February 2020 - 70

IEEE Power & Energy Magazine - January/February 2020 - 71

IEEE Power & Energy Magazine - January/February 2020 - 72

IEEE Power & Energy Magazine - January/February 2020 - 73

IEEE Power & Energy Magazine - January/February 2020 - 74

IEEE Power & Energy Magazine - January/February 2020 - 75

IEEE Power & Energy Magazine - January/February 2020 - 76

IEEE Power & Energy Magazine - January/February 2020 - 77

IEEE Power & Energy Magazine - January/February 2020 - 78

IEEE Power & Energy Magazine - January/February 2020 - 79

IEEE Power & Energy Magazine - January/February 2020 - 80

IEEE Power & Energy Magazine - January/February 2020 - 81

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

IEEE Power & Energy Magazine - January/February 2020 - 83

IEEE Power & Energy Magazine - January/February 2020 - 84

IEEE Power & Energy Magazine - January/February 2020 - 85

IEEE Power & Energy Magazine - January/February 2020 - 86

IEEE Power & Energy Magazine - January/February 2020 - 87

IEEE Power & Energy Magazine - January/February 2020 - 88

IEEE Power & Energy Magazine - January/February 2020 - 89

IEEE Power & Energy Magazine - January/February 2020 - 90

IEEE Power & Energy Magazine - January/February 2020 - 91

IEEE Power & Energy Magazine - January/February 2020 - 92

IEEE Power & Energy Magazine - January/February 2020 - 93

IEEE Power & Energy Magazine - January/February 2020 - 94

IEEE Power & Energy Magazine - January/February 2020 - 95

IEEE Power & Energy Magazine - January/February 2020 - 96

IEEE Power & Energy Magazine - January/February 2020 - Cover3

IEEE Power & Energy Magazine - January/February 2020 - Cover4

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091020

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070820

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050620

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030420

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010220

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111219

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091019

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070819

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050619

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030419

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010219

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111218

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091018

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070818

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050618

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030418

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010218

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111217

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091017

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070817

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050617

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030417

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010217

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111216

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091016

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070816

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050616

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030416

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010216

https://www.nxtbook.com/nxtbooks/ieee/powerenergy_010216

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111215

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091015

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070815

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050615

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030415

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010215

https://www.nxtbook.com/nxtbooks/pes/powerenergy_111214

https://www.nxtbook.com/nxtbooks/pes/powerenergy_091014

https://www.nxtbook.com/nxtbooks/pes/powerenergy_070814

https://www.nxtbook.com/nxtbooks/pes/powerenergy_050614

https://www.nxtbook.com/nxtbooks/pes/powerenergy_030414

https://www.nxtbook.com/nxtbooks/pes/powerenergy_010214

https://www.nxtbookmedia.com