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

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:

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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

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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
