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GUIDELINES FOR POWER FACTOR
IMPROVEMENT PROJECTS
Gregory W. Massey, P.E.
Electrical Engineer
Federal Bureau ofPrisons
ABSTRACT
KW is the real power output of the electrical
system, and
KVA is the apparent power consumed by the
electrical system in producing the real power
output.
Power factor is an indication of electrical system
efficiency. Low power factor, or low system efficiency,
may be due to one or more causes, including lightly
loaded transformers, oversized electric motors, and
harmonic-generating non-linear loads. Knowing the
cause of low power factor is essential to developing an
effective remedy.
Essentially, this expression of power factor is a
simple measure of efficiency: total output divided by
total input. The real power output, KW, is the useful
work performed in pumping fluids, moving air,
producing heat, producing light, etc. The apparent
power input, KVA, is the unique composite power
required from the utility by the distribution system
equipment and by the loads to produce the system­
specific power output in KW. Apparent power is
composed of real, reactive, and harmonic power.
If low power factor is caused by harmonic loads,
for example, the misapplication of capacitor banks
alone could create other, more significant problems.
Additionally, the goal of power factor improvement can
vary from the simple reduction of utility costs to the
complex elimination ofharmonic load currents.
Regardless of the cause of low power factor or
the goal in improving system efficiency, the
methodology in defining the solution is similar. This
paper discusses the critical issues involved in
developing a power factor improvement project Note:
The views expressed in this paper do not necessarily
represent the views of the United States of America,
the U. S. Department of Justice, or the Federal Bureau
ofPrisons.
Reactive power, expressed as Kilo-Volt Amperes
Reactive (KVAR), is the power consumed in
establishing and maintaining electric and magnetic
fields in induction machines such as motors and
transformers. Harmonic power, expressed as Kilo-Volt
Amperes-harmonic (KVAh), is the power consumed by
non-linear loads such as adjustable speed motor drives,
arc furnaces, and switch-mode power supplies, and, to
a lesser degree, by the inherent imperfections in linear­
type loads.
INTRODUCTION
Although power factor can be defined in several
different ways, the most useful definition of power
factor when dealing with energy-related concerns is the
ratio of real power, expressed as KiloWatts (KW), to
apparent power, expressed as Kilo-Volt Amperes
(KVA), as given by:
PF=KW
KVA
Kansas City, Kansas
Using Equation 1 as the basis for analyzing
electrical system. efficiency empirically, low power
factor is caused either by an excessive reactive power
requirement from lightly loaded or oversized motors
and transformers, by an excessive harmonic power
requirement from large or numerous non-linear loads,
or by a combination of both.
(1)
The pages that follow outline a methodology for
quantifying reactive power requirements of the system
and load, and for determining the cause of low power
factor, either from excessive reactive power or from
excessive harmonic power requirements.
where
PF is Power Factor,
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Rearranging Equation 1, and using the maximum
historical peak demand and the measured power factor
from utility bills gives the maximum peak apparent
power demand, KVAD:
QUANTIFYING REACTIVE POWER
REQUIREMENTS
As an overview, it is important to understand the
cyclic nature of electrical energy usage prior to
performing any type of energy audit. Except for 24
hour per day operations, electrical loads exhibit daily
and seasonal demand cycles.
KVAD=KWD
PF
Electrical usage is typically lower at night when
employees are away from work. As employees arrive,
electrical load builds on the system as lights,
computers, fans, heaters, coffee pots, radios, etc., are
turned on at the start of the work day. Electrical usage
drops off toward the end of the work day as employees
prepare to go home.
(2)
Because apparent, real and reactive power are
related by the Pythagorean Theorem through the
theoretical power triangle, the reactive power
requirement, KVARD, of the maximum peak demand
load is given by:
(3)
Similar to the daily cycling of electrical loads,
seasonal loading of electrical systems occurs.
Typically, summer months exhibit higher electrical
usage and energy demand because air conditioners are
in operation. Winter months represent lower electrical
usage and demand because most boilers and furnaces
operate on fossil fuels.
The peak demand reactive power requirement
determined by Equation 3 is the amount of reactive
capacitance used by the electrical distribution
equipment and loads to supply the peak real power
output of the system. It is also the amount of
compensatory capacitive reactance required to raise
power factor of the maximum historical peak demand
load to unity, or 1.00.
The greatest resource for documenting the daily
and seasonal loading of the electrical system under
analysis is the utility company providing electric
service to the facility. A little research into the
historical energy usage provides tremendous insight in
developing the scope of work.
The method of determining the amount of
capacitive reactance required to raise power factor to
some value other than unity takes three steps. First,
Equation 2 must be solved for the apparent power
required for the target power factor. Second, that value
is substituted for the apparent power in Equation 3.
And third, that result is used in the following equation
with the peak demand reactive power requirement of
the load at unity power factor:
Utility Bill Database
Most utility companies provide a wealth of
information on the customer's bill. Many times peak
demand and power factor are included, along with
energy usage, for industrial and commercial energy
customers. This information can be used to determine
the reactive power requirements of the distribution
system up to the point of utility connection.
KVARD-.. ~(KVARDoId)-(KVARD...,.)
To develop a representative energy consumption
database, a minimum of 36 months of the most recent
utility bills are required to account for periods of mild
weather during summer or winter months. It is helpful
to graph the peak demand over time to visualize the
seasonal cycles of electrical loading.
(4)
where:
KVARD comp is the required compensatory
capacitive reactance required to raise the power
factor from the original value to the new target
value,
KVARD DId is the capacitive reactive power
required by the system and loads with the original
low power factor, and
KVARD.... is the capacitive reactive power
required by the system and loads with the new
target power factor.
Using the utility bills as a guide, the maximum
reactive power required by any given system is derived
from the peak demand information. Utility companies
typically define peak demand as the maximum
electrical demand during any given 15 minute period
during the billing cycle.
Given the cyclic nature of loads as previously
discussed, installing capacitive reactance to achieve
unity power factor for the peak load could create
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voltage stability problems during times of light loading.
In short, too much capacitive reactance causes a
voltage increase above the nominal voltage that can
cause equipment misoperation and failure, along with
overvoltage conditions system-wide.
Harmonic Resonance
While inductive impedance increases with
frequency, capacitive impedance decreases with
frequency. For any given electrical distribution system,
the capacitive reactance will equal the inductive
reactance at a specific frequency, essentially canceling
both. This condition, when the only impedance to
current flow is the pure resistance of circuit conductors,
is referred to as resonance.
Typically, every power factor improvement
project involves some quantity of static, or unswitched,
reactive power compensation. Given the inherent
cyclic operation of electrical systems, some method of
controlling the amount of reactive power compensation
must be incorporated into the design to prevent leading
power factor.
Harmonic resonance is characterized by large
magnitudes of voltage and current within the system.
The result of resonance varies from equipment
malfunction to catastrophic failure. It is important to
determine the likelihood of a resonant condition prior
to installing capacitors on a distribution system.
DesiKD Alternatives
Several approaches to improving power factor to
acceptable levels while preventing a leading power
factor are available.
The following equations, common in literature,
are useful in determining whether the installation of
capacitors on a distribution system might lead to a
resonant condition. The short circuit KVA available
from the utility must be determined first., and is given
by:
One method is to design improvement to some
level below unity. Improving power factor to 0.95, for
example, would ensure some tolerance for fluctuating
load levels, but would not necessarily prevent leading
power factor during times of light system loading.
Alternatively, automatically switched capacitor
banks can be used to control capacitive reactive power
connected to the system. Depending upon the levels of
capacitance that are switched, automatic capacitor
banks can introduce voltage transients into the
distribution system. Depending upon the presence of
harmonic load currents, automatic capacitor banks can
also introduce a resonant condition.
(5)
where
KVA.c is the available short circuit KVA from
the utility,
V L-L is the system operating voltage, and
I sc is the available short circuit current.
Synchronous motors can be connected to the
distribution system with automatic controls for its
operation as a reactive power compensator.
Synchronous condensers provide an excellent method
for "seamless" power factor improvement and
harmonic power control, as no switching occurs.
Synchronous motors, however, are relatively large and
are not practical for use on smaller distribution
systems.
Next, the building or facility distribution system
short circuit capacity must be estimated. Because
transformers represent the majority of impedance
within the system., the facility short circuit capacity can
be approximated by:
(6)
Installing static capacitors directly at and
switched on and offwith the offending load is another
solution, but can be costly simply from the number of
locations that may be required.
where
KVA.r. is the short circuit capacity of the
secondary electrical system.,
KV~ is the KVA rating of the system
transfonner(s),
KVA.c is the available short circuit KVA from
the utility, and
Z, is the impedance of the system transfonner(s).
Finally, harmonic filters may be required if low
power factor is contributable in whole or in part to
significant harmonic loads. Caution must be exercised
when capacitors designed for 60 Hz operation are
installed on a system with significant harmonic load
currents to prevent harmonic resonance.
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Finally, the resonant harmonic of the distribution
system under analysis is given by:
hr =
One-Line
The first step is to examine a one-line diagram of
the facility to determine concentrations of typical low
power factor loads, such as induction motors.
Additionally, the KVA ratings of transformers in the
system should be swnmed to determine the percentage
of their loading during the peak demand.
(7)
Manufacturers of large mechanical equipment,
such as chillers, typically offer power factor
improvement capacitors as an option at the time of
purchase. Moreover, a power factor improvement
project may have been completed in the past.
Consequently, it is important to determine the locations
and ratings of any existing capacitors or synchronous
condensers on the system.
where
11, is the resonant hannonic,
KVA,y. is the available short circuit KVA from
the distribution system,
KVA",., is the available short circuit KVA from
any motor contribution, and
KVARc is the sum of capacitor KVAR ratings.
When Equation 7 indicates a relatively low
resonant harmonic, and spectrum analyses indicate that
the magnitude of harmonic currents are significant at or
near the resonant frequency, harmonic filters may be
required to provide the necessary capacitive or
harmonic reactance power while protecting the
capacitor bank from failure.
Interviews
The next step is to interview maintenance
personnel to verify the accuracy of the one-line
diagram. These interviews will also provide insight
into the level of maintenance that will be performed on
any new equipment installed, which may affect the
design.
Low power factor may in fact be entirely due to
harmonic currents generated by non-linear loads. In
those instances, power factor may be improved by
installing filters alone. In most cases, however, a
combination of harmonic filters along with capacitors
designed to operate at the fundamental frequency are
required to improve power factor to acceptable levels
in systems with harmonic currents present.
Site Survey
The final step is to tour the facility and to take
direct measurements at the loads. Gathering
preliminary data may involve measuring the power
consumption of any distribution feeders that are
suspected of supplying significant or numerous low­
power factor loads. Low power factor loads may be
concentrated on only a portion of the distribution
system, enabling the elimination of one or more areas
of the system from the survey.
Given the cyclic nature of electrical loading, and
given the unique makeup of each electrical distribution
system, the optimal technical solution will consist of
two or more of the alternatives outlined above. The
next step in refining the scope of work is to locate the
cause of low power factor.
Significant low power factor loads should be
individually monitored in order to identify significant
reactive power conswnption in relation to real power
output. Examples of individual loads that should be
monitored separately include any large motors, any
concentrations of small motors on a motor control
center, any large non-linear loads such as adjustable
speed motor drives, and any significant concentrations
of non-linear loads such as computer room branch
circuit or distribution panelboards.
DETERMINING TIlE CAUSE OF LOW POWER
FACTOR
As previously mentioned, every electrical system
is unique. The loads, the distribution system
equipment and the interconnection of the distribution
circuiting all combine into a type of system
"fingerprint."
The duration of this phase of the project is
dependent upon the complexity of the system.
Recording power quality analyzers, including hannonic
voltage and current measuring capabilities, are
recommended to be installed for a minimum of 24
hours at each location. Measurements should be taken
From an engineering standpoint, it is imperative
to dissect the electrical system to determine cause of
low power factor before applying an inexpensive,
cookbook type solution that addresses symptoms but
ignores the root cause of the problem.
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during periods of peak seasonal loading based upon
historical records, which are typically from July
through September for facilities with significant air­
conditioning loads.
Similar to summing the individual loads,
harmonic current magnitudes can be summed at any
common points of connection. The combined
harmonic profiles of the individual loads at common
busses will result in greater magnitudes of harmonic
currents than would be measured at the utility meter
because of inherent load cycling and cancellation
effects. This provides a "worse-than-worst-case"
profile of harmonics present in the system, and ensures
a conservative design.
Additionally, it is important to verify the
condition and operation of any existing capacitors on
the system. An existing capacitor that has
malfunctioned may be an indication of harmonic load
currents and/or harmonic resonance. The cause of any
previous capacitor malfunction or failure must be
determined in order to prevent a similar or more
significant problem with new equipment
If measured and summed harmonic load currents
are either significant or exist near the resonant
frequency of the distribution circuit as determined by
Equation 7, at least a portion of the capacitive
reactance installed should be in the form of a harmonic
filter.
As the site survey and load monitoring
progresses, one interesting fact should become readily
apparent; the cyclic nature of electrical loads extends
past the utility meter into the distribution system. As a
result, the peak demand of the distribution system as
measured by the utility will most likely be less than the
sum ofpeak demand measured at the individual loads.
Harmonic Filters
Harmonic filters "capture" harmonic currents by
diverting them through a specially designed series
resonant, or low impedance, shunt path to ground.
Harmonic filters are an effective and economical way of
minimizing harmonic current and voltage distortion and
to improve power factor in an electrical environment
rich in harmonic load currents.
In short, an intensive program of metering
individual feeders and loads within a system will reveal
that the sum of the parts is greater than the whole
because individual loads peak at different times. This
fact provides the basis for a conservative and effective
design.
Active Harmonic Filters
Active filters have the ability to cancel harmonics
in the current waveform by injecting energy into the
gaps that are created by non-linear loads. This
technology is still developing and not competitive for
general use.
Once the system has been adequately dissected,
the next step in the development of the project is to
manipulate the data measured during the site survey
and to confirm the empirical data available from the
utility database.
Passive Harmonic Filters
Passive harmonic filters are more commonly
used. Passive filters are constructed of one or more
tuned resonant circuits. To compensate for capacitor
aging over time, the actual resonant frequency of the
harmonic filter is designed to be below the target
harmonic. For this reason, a nominal Sth harmonic
filter is normally designed for the 4.7th harmonic.
REFINING THE SCOPE OF WORK
Using the measured results from the site survey,
the maximum and minimum levels of the individual
loads should be determined using Equations 2 and 3. It
is important to note any cycling of the individual loads.
Whether a load runs constantly or has short,
sporadic periods of operation affects the method of
improving the power factor for that load. A large,
lightly loaded motor that typically runs for 10 minutes
every hour, for example, is a good candidate for a
capacitor that is connected on the load side of the motor
controller and is switched on and offwith the motor.
To prevent the filter from trapping harmonics
from the utility grid, a decoupling reactor should be
installed as part of the filter. Technical literature is
replete with examples of damage caused to harmonic
filters installed without a decoupling reactor.
Additionally, harmonic filters should have
internal protection similar to capacitor banks, such as
fuses, along with fault indicators for blown fuses or
capacitor failure.
After examining the individual loads, the next
step is to place this information into the context of the
facility one-line diagram by separately summing the
maximum power requirements of the individual loads,
along with the associated harmonic profiles, at the
conunon points of connection.
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Capacitors experience terminal voltage in excess
of rated voltage when installed in a harmonic filter.
The following equation expresses the percent of
voltage rise that capacitors experience as a function of
the harmonic number at which the filter is tuned:
Harmonic filters on the market are designed as an
assembly. although it is possible to specify components
for field assembly into a harmonic filter. Upgrading an
existing capacitor bank to make a shunt filter can also
be performed, provided several issues are addressed.
Capacitors. for example. have definite limitations
that must be taken into consideration during normal
operation as well as during operation as an integral
component of a harmonic filter. Capacitor rating
limitations include a maximum of 180% of rated
current. a maximum of 110% of rated voltage, and a
maximum of 135% of rated reactive power.
(10)
where
% VR is the percent ofvoltage rise above
nominal, and
h is the tuned harmonic.
To account for the extra duty required of a
capacitor to operate as a harmonic filter. an additional
15-20% increase in capacitor line-to-neutral voltage
rating is reconunended.
The capacitor provides the reactive power
required by the reactor in the filter along with
providing reactive power for the distribution system.
Additionally, the reactive power that a capacitor
delivers is dependent upon terminal voltage. As such,
the capacitor's reactive power output is as given by
Equation 11:
A capacitor bank: with a nominal voltage rating
and an operating temUnal voltage of 480 V. for
example. should not be upgraded into a harmonic
filter. The steady-state overvoltage from harmonic
currents will most likely exceed the 11 00/0 voltage
limitation of the capacitor, and may exceed the 135%
reactive power limitation. Capacitors within a
harmonic filter connected to a 480 V bus are typically
rated for 600 V operation, a 25% increase in line-to­
neutral voltage rating, to prevent equipment damage.
KV.4 R .
--"fill.,
2
=(VL_U
X -X
C
(11)
L
where
KV~tcr is the KVAR output of the filter,
VL-L is the applied system voltage,
Xc is the capacitive reactance of the filter, and
XL is the inductive reactance of the filter.
Uperadine an Existine Capacitor into a Harmonic
Filter
The following equations can be used to size an
in-line reactor needed to upgrade an existing capacitor
bank into a harmonic filter:
Finalizing the Scope of Work
All of the information required to finalize the
scope of work has been gathered, beginning with the
macroscopic utility database and ending with the
microscopic data measured during the site survey.
Modeling of the measured data using the one-line
diagram as a guide will provide the framework for
making decisions for improving power factor at
individual loads, and, subsequently, for improving the
power factor for the entire system.
(8)
and
(9)
Static Capacitance
The minimum reactive power requirements of the
facility as determined from Equation 4 using the target
power factor and using the minimum measured power
requirements will establish the amount of static, or
unswitched, capacitive reactance to install on the
system. The location of static capacitance will vary,
based upon the configuration of the distribution system.
Typical locations are any conunon points of connection
for equipment. such as branch circuit panelboards,
where
Xc is the capacitive reactance of the filter,
VL-L is the rated voltage of the capacitor bank,
KVAR 3_pbue is the ratedKVAR of the capacitor
bank,
h is the tuned harmonic, and
XL is the inductive reactance of the filter.
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distribution panelboards, motor control centers, service
entrance switchboards, etc.
numerous low-power factor loads for further study. A
systematic method of measuring actual power
requirements offeeders and loads can be used to
establish the framework for understanding the
quantities calculated base upon the utility database.
Harmonic Filters
The power requirements of any non-linear loads
as determined from measured data will pro~de the
basis for establishing the amount, configuration and
location of harmonic filters to install on the system.
Typical locations are at any large non-linear loads, or at
any common points of connection for non-linear loads.
Whether any harmonic filters are switched or are static
will be determined by the operational nature of the non­
linear loads.
Placing the measured power requirements of the
individual loads into the context of the system one-line
diagram brings the project scope of work into focus.
The nature and location of significant reactive power
consuming loads will help to determine the optimal
engineering solution.
Automatically Switched Capacitance
The amount of automatically switched capacitive
reactance required to improve power factor is
determined by the maximum reactive power
requirements of the system, minus the minimum
reactive power requirements, and minus the harmonic
reactive power requirements of the system.
Automatically switched capacitance may take one
of several forms outlined above, including one or more
static capacitor banks switched by the controller of a
large motor, one or more automatically switched
capacitor banks connected to a common bus, or a
synchronous condenser.
The location and configuration ofcapacitive
reactance is governed by technical concerns and
economics. It is more economically feasible to group
the capacitance required for several small motors at the
common point of connection, namely a motor control
center or distribution panel, than to install individual
power factor capacitors at each motor.
Because economics frequently dictate that a
combination ofstatic and automatically switched
.capacitance be installed at the same location, capacitor
manufacturers typically offer this combination as a
standard product.
CONCLUSION
Every electrical distribution system is unique in
composition and in operation. Using a cookbook
approach to power factor improvement that neglects
the inherent characteristics of the distribution system
equipment and loads can result in more significant
problems than low power factor.
The historical database available from utility bills
can be used to determine the peak magnitude of
reactive power consumed by the electrical system. The
system one-line diagram can be used to identify large or
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