A Schaum's Outline of the period adopted a different approach when it opened a section on phasors by noting that By definition a phasor is a complex number associated with a phase-shifted sine wave such that, if the phasor is in polar form, its magnitude is the effective (rms) value of the voltage or current and its angle is the phase angle of the phase-shifted sine wave. For example, V = 3+45c V is the phasor for = 3 2 sin (377t + 45c) V. By 2005, however, one could imagine ways to combine the idea of a rotating phasor and a complex number. Moura and Darwazeh, in Introduction to Linear Circuit Analysis and Modeling, discussed the rotating and stationary phasors, opening with these words: Revit Integration ® An efficient bi-directional data integrator between Autodesk® Revit® and EasyPower power system analysis. This new stand-alone module automatically and instantly creates a one-line (single-line) diagram in EasyPower with one mouse-click in Revit. · Map Revit families and properties to EasyPower equipment · Save time using EasyPower's powerful Auto-Design tool for sizing equipment · Bring EasyPower analysis results back in Revit Autodesk EasyPower Revit Model System One-line kV T-SCV 500 kVA .48-0.48 kV 4% 3-#250, 1#250, 1-#6 8 .4 3-#1, 1#1, 1-#8 3-#1, 1#1, 1-#8 PANEL Analysis and Auto-Design CURRENT IN AMPERES X 100 AT 480 VOLTS 1000 .5 .6 .8 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 100 2 3 4 5 6 7 8 9 1000 Bus kV Sym Amps X/R Ratio Mult Factor Asym Amps 4' - 0" Equi Type 0.480 19480.3 3.69 1.19 23188.3 LVPCB MCC-1 0.480 20032.6 3.55 1.18 23640.9 LVPCB 0.48 MCC-2 0.480 19779.7 3.43 1.17 23181.0 LVPCB 1' - 0" 10597.4 PNL-1 0.480 3.73 1.19 PNL-2 0.208 5961.4 2.11 1.07 6377.3 SWG-4 0.480 24127.6 6.18 1.33 31990.4 8882.5 Hazard Boundary inches 2 at 18 Amps pants or arc cal/cm Duty cal/cm2 at 18 inches arc rated 6.0 shirt and - Arc Flash Incident d Arc-rated Energy 19480.3 when cover is remove Hazard 0.48 kV Shock kV Shock Hazard 20032.6ch when cover is removed 3' - 6" Limited Approa ch Limited Approach Approa 1' - 0" Restricted Restricted Approach 19779.7 (Fed By: 27B) A N ONLY Equipment URATIO Name: MCC-23 Name: SWG-4 8882.5 LVPCB (Fed By: 18A) Equipment SYSTEM CONFIG VALID FOR NORMAL NORMAL SYSTEM CONFIGURATION VALID FOR 5961.4 LVPCB ONLY 6.0 0.15 4 3 2 Short Circuit Calculations 24127.6 18.71 3 .1 1.90 40 30 20 17.58 8 8 6 5 4 3 2 1 1 .8 BL-3 GE MVT-9 T-9 Sensor = 800 Plug = 800 Cur Set = 0.5 0.5 5 (400A) LT Band = 1 Inst = 4 (3200A) .6 .5 .4 .3 .2 .6 .5 BL-5 Cutler H Hammer Series C am mmer er Serie HFD Frame e = 225A (150AT) (150A Trip = 150 .06 .05 .04 .03 .4 BL-1 18627A .3 C-6 1 - 400 kcmil CU TX-2 1000 / 1288 kVA INRUSH .1 .08 .06 .05 .04 .03 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 100 2 3 4 Automated Protective Device Coordination .02 BL-5 20574A .8 .2 .1 BL-3 29249A .02 .5 .6 80 10 BL-5 C-H HFD 225/150 .8 .08 .01 300 200 100 60 50 BL-3 GE AKR-30H 800/400 .4 M-1 3' - 6" LVPCB 400 BL-1 GE AKR-50 1600/1760 19 TIME IN SECONDS Total Fault Fault 3 PHASE Fault M-1 Bus Name BL-1 MVT-Plus GE MVT MV T-Plus Sensor = 1600 Plug = 1600 Cur Set = 1.1 (1760A) LT Band = 1 STPU = 2.5 .5 (4400A) ST Delay = Int Int ST Delay I²t = Out Override = 50000A 8 6 5 rd k Risk Haza and Shoc Arc Flash and Shock Arc Flash iate PPE Required ropr Equipment Duties App Appropriate PPE Risk Hazard Required t Energy Boundary Flash4' Inciden coverall - 0" Flash Hazard - Arc rated Flash 5 6 7 8 9 10000 1000 TX-2 1 / 1.288 MVA 13.8 - 0.48 kV 6% 24 SWG-4 40 30 10 Vpu = 1.00 4 800 TX-2 -2 kVA 1000 / 1288 k VA 6% 20 EasyPower 10.4.0.198 10/11/2018 10:00:07 AM C:\...\Protection-1..dez EasyPower LLC Comments: 3 600 500 80 60 50 LV Momentary Report 2 TX-2 FLA 800 600 500 400 300 200 100 TIME IN SECONDS The Changing Meaning In 1981, a power textbook (T. Wildi and P. McNeill, Electrical Power Technology) described a phasor as "a straight line whose length is proportional to the effective voltage or effective current it represents." Even angle is not mentioned. By 1990, a further change in meaning had occurred. Scharf and Behrens, in their book A First Course in Electrical and Computer Engineering, describe a "conceptual leap from the complex number e ji to the phasor e j^~t + ih f" According to these authors, the phasor is no longer a line, it is an exponential expression. They were likely not the first to make a further abstraction. kV 3-#250, 1#250, 1-#3 .4 8 T-SCV-S 3-#350, 1#350, 1-#4 "everybody knew" that the frequency of the power system was constant, the fact that a sinusoid had a frequency was fading from awareness. All you needed to know were the angle and magnitude, and you had completely characterized the power system voltage or current. Perhaps in recognition of that, some textbooks of the period added a new term, one seemingly coming from the mathematics community. Instead of the original use of phasor, the term stationary phasor was identified with the line representing the sinusoid. We can at least draw a stationary phasor. The sinusoid in (1), a function of time, is given by the projection of the phasor (i.e., the line) on the horizontal axis, as seen in Figures 2 and 3. However, these figures can be thought of as snapshots of a rotating line (the phasor) at a particular time. In Figure 3, t = 0. For example, Clement and Johnson state that "if ~ is known, the stationary phasor ... represents the function f (t) = A cos (~t + i) . " (The italics are in the original.) In other words, although the stationary phasor is not the whole story, it represents the whole story because we all know the frequency. The stationary phasor gives us the amplitude and the phase. In practice, the word stationary is frequently omitted in writing, particularly in the writing of power engineers. Furthermore, the curved arrow showing angular velocity is generally omitted from phasor diagrams, and the rotation speed ~ is not written down. 5 6 7 8 9 1000 2 3 4 .01 5 6 7 8 9 10000 CURRENT IN AMPERES X 100 AT 480 VOLTS Explore more online and request a free demo copy at: www.EasyPower.com/Revit ® Power made easy.http://www.EasyPower.com/Revit

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