5
20
25
30
35
40
45
50
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Power Factor, PF
Line Current % Change
0
50
100
150
200
250
300
350
400
450
500
Line Loss, W
a
tts
DID YOU KNOW ?
Heinrich Rudolf Hertz (1867-1894) discovered electromagnetic waves cira 1887. Clark Maxwell proposed the existence of
such waves in 1864. Heinrich Hertz was only 37 years old when he died. His research was instrumental in ushering in the age
of radio communication and unit of frequency (cycles per second) was named the Hertz in his honor.


Current Modules Measure Power Factor

Preamble
The power factor of AC systems or components is the
cosine of the angle by which the AC current leads or lags
the applied AC excitation voltage. The physics of
inductance and capacitance behavior establishes the
voltage-current relationship, which depends on both the
AC excitations amplitude and time rate of change (i.e.
derivative wrt time). This behavior causes a phase shift
phenomena between voltage and current, which increases
line losses, thereby increasing the supply line current
required to produce a given amount of useful output
power. Utility companies often charge a penalty for a
customers unacceptable power factor. It is important for
the consumer of electrical energy to be aware of power
factor and the available methods for correction. See Ref 2,
Dataforths Application Note AN109, for a review of
single AC circuit behavior.

Practical Illustrations
Figure 1 shows a single-phase inductive load with a
supply voltage wiring resistance, which is responsible for
undesirable line losses and lowered load voltage, VL.




















Figure 1
Inductive Load Showing Current Phasors
The current phasors shown in Figure 1 illustrate that an
inductive reactive load component creates a 90-degree
lagging phase shift between the applied load voltage and
the input line current. The power dissipated in the
resistive component of a given load is responsible for
useful work and is RL*IRL
2
. Loads containing either
inductive or capacitive reactive components (PF <1), have
line currents greater than that (IRL) required for
producing the useful output, RL*IRL
2
. This means larger
line losses, lower load voltages, and higher utility costs.

Figure 2 illustrates the effect on line current and
associated line losses caused by changing the power
factor of a 5 horsepower single-phase 208 VAC motor
delivering a constant output power (requires small speed
changes). This example assumes a total of 0.50-ohm line
resistance, 0.25 ohms in each wire.



















Figure 2

Line Current Change & Line Losses vs Load PF
5 Horsepower 208 VAC Motor with 0.50-ohm line

Clearly, power factors (PF) can have a costly impact on
electrical utility costs.
AN111
Dataforth Corporation

Page 2 of 3


XL
RL
Load 1
VL
IL
ILine
VL
(reference)
IXL
IRL
IXL
IRL
PF Angle
a
b
A
d
d
R
e
s
i
st
i
ve E
l
em
e
n
t
Rx
Ix
Ix
ILine
IL
27
18
14
A
D
C
B
A
B
E
Kilowatts, (KW)
K
i
l
o
w
a
t
t
s-
R
e
act
i
v
e
(
K
V
AR)
K
ilo
w
a
tts
-R
e
a
c
tiv
e
(
K
VAR)
Appar
ent Po
wer, (K
VA)
Apparent Power, (KVA) 3c
3b
3a

Any load or section of a facility can be represented by its
power triangle. Figure 3 shows some typical power
triangle examples. The accepted convention plots the total
KW resistive power (line losses plus useful output) on the
positive x-axis and reactive power (KVAR) on the y-axis.
Inductive KVAR is defined as positive and capacitive
KVAR as negative. Surprisingly, KVAR does no useful
work! Applied voltage multiplied by input line current is
the apparent power, KVA, and is the vector sum of KW
and KVAR.


















Figure 3
Power Triangle Examples
Figure 3a Inductive Load, KVAR ( B-C)
Figure 3b Capacitive KVAR (C-D) Reduces
Inductive Load, KVAR (B-C)
Figure 3c Capacitive Load, KVAR (B-E)


Power Triangles illustrate the following useful
relationships;

1.

Reactive Power (KVAR), which does no useful
output work, is the sum of Inductive and Capacitive
reactive power and can be tailored by adding external
capacitance.
2.

Line current is equal to the supplied apparent power
(KVA) divided by the supply voltage (Vs). Note:
Line current is reduced when the reactive power
(KVAR) is reduced, which in turn reduces the power
factor angle.

Suggestions
In many situations, it is cost effective to analyze system
cells, load groups, and individual loads to determine
existing power factors and if there is a return on the
investment needed to improve them. Utility companies
have resources and personnel available to do on-site
investigations. Plant personnel can conduct their own
electrical system studies with commercially available
equipment.
Figure 4 illustrates a scheme whereby one can make three
AC current measurements with standard off-the-shelf AC
current transformers (CTs) and Dataforths line of
isolated true rms signal conditioning modules to develop a
measurement scheme for either on-line real time or
individual stand-alone measurements.





















Figure 4
Simple Measurement Scheme for Determining PF

The scheme shown in Figure 4 requires three current
measurements; load current, line current, and the current
flowing in an external resistor. This external resistive
element can simply be a configuration of incandescent
bulbs or a resistive heating element selected such that the
external current (Ix) is in the neighborhood of 10% of the
rated load current. Equation 1 gives a relationship for
calculating the power factor (PF) magnitude from RMS
measurements of the currents; Iline, IL, and Ix shown in
Figure 4.

2
2
2
Iline - IL - Ix
PF =
, Cos (PFangle)
2*IL*Ix
Eqn. 1.

Combinational calculation errors generated by using
Eqn.1 are unavoidable. The difference of squared
numbers divided by the product of numbers produces a
result with tolerance errors larger than those associated
with the tolerance error in each individual number. For
the example shown in Figure 2, results from 200 random
calculations of Eqn. 1 show a
± 5% tolerance in PF using
± 0.25% accuracy in the measured currents. Precise
measurements are necessary to minimize combinational
calculation errors.
Volume 1

Page 3 of 3


Dataforth Isolated True RMS AC modules are well suited for implementing measurement techniques such as those shown
above. Dataforth RMS modules measure RMS values of AC voltages (0 -300 Vrms) directly or RMS values of AC currents
(0-5 Arms) using conventional current transformers (CT). These RMS modules have a DC voltage output representing RMS
values with a linear scale factor. Note that a RMS to DC scale factor has no effect in Eqn.1, since the scale factor appears in
both numerator and denominator.

Figure 5 illustrates Dataforths SCM5B33

True RMS Isolated Signal Conditioning Module circuit topology, designed for
measuring RMS values over a frequency range of 45 Hz up to 20kHz and is available in 5B or Din Rail Modules. See Ref. 1,
Dataforth website catalog for complete specifications.

A Word of Caution:
When making current measurements with conventional current transformers (CT) never leave the current transformer
secondary leads open circuit. Current transformers are usually torrid in shape and the high current (primary) side has only a
few turns (generally 1) whereas the secondary has many turns in order to reduce the secondary current down to an industry
standard level. For example, a 500-amp current transformer would have a 5-amp output for 500-amp input, a current
reduction of 100, but the voltage has a step-up factor of 100. It is possible to have an open circuit current transformer
secondary with the primary side connected into a 440 Vac system, resulting in 44000 volts on the open secondary. Properly
designed CTs have built in protection; however, it is wise to assume the worst and always take appropriate safety
precautions.




Figure 5
Dataforths SCM5B33

True RMS Isolated Input Module



Dataforth References

1.

Dataforth Corp Website
http://www.dataforth.com

2.

Dataforth Corp., Application Note AN109
http://www.dataforth.com/technical_lit.html