ESL-IE-97-04-36
VARIABLE FREQUENCY MOTOR DRIVES:
HARMONICS, POWER FACTOR,
AND ENERGY EFFICIENCY
Gregory W. Massey, P.E.
Electrical Engineer
Federal Bureau of Prisons
Kansas City, Kansas
the energy used under partial load can be greatly
reduced, compared to mechanical devices like inlet
vanes or water valves. The primary benefit of
VFD's is economic; significant energy savings result
in a relatively quick payback on capital expenditures.
An additional benefit is reduced wear and tear on
motors, pumps, fans, pulleys, etc., which run at
lower RPMs.
ABSTRACT
Variable frequency motor drives (VFD's) have
been on the market for many years. Early versions
were unreliable and prone to failure. Relatively
recent developments in Pulse-Width Modulated
(PWM) waveform technology have improved VFD
reliability and efficiency. This paper provides an
overview of PWM variable frequency drive theory
and operation. The second portion of the paper
provides an overview of the impact of installing
VFD's within the electrical distribution system,
including concerns regarding harmonics and power
factor. 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 of Prisons.
Variable frequency motor drives are non-linear
loads and can create problems within the electrical
distribution system. Power quality for both the
customer and the utility is a critical design
consideration when installing VFD's. When the
implications of installing variable frequency drives
are fully considered, a proper balance between
energy efficiency and power quality can be achieved.
INTRODUCTION
The use of variable frequency AC motor drives
has grown at an exponential rate in recent years.
VFD's increasingly have become an element of
mechanical and electrical systems design in industrial
and commercial projects. Some new and retrofit
applications include conveyors, chemical processes,
manufacturing, wastewater treatment, and HVAC
systems.
VARIABLE FREQUENCY DRIVES:
AN
OVERVIEW
Motor speed is dictated by the frequency of the
source. Typical 60 Hz AC motors display nominal
nameplate speeds of 1,200 rpm, 1,800 rpm, and
3,600 rpm for six-, four-, and two-pole motors,
respectively. Connection to a 60 Hz source will
result in approximately these motor speeds under no­
load conditions. The characteristics of the load and
the individual motor, however, will influence the
actual speed that the motor will rotate under load.
The development of advanced power electronic
switching devices has enabled high-frequency
switching operation and has improved the
performance of PWM inverters for driving AC
motors (5). Using solid-state technology provides an
efficient, effective, and economical method for
controlling motor speed. Variable frequency drives
are solid-state power converters that can vary the
voltage and frequency delivered to three-phase motors
to produce specific motor speeds.
To maintain the rated torque of the motor,
voltage must be kept proportional to frequency (8).
For example, if a motor is operated at 30 Hz, or one­
half speed, the voltage must also be reduced by one­
half of the rated value. If voltage is not reduced
proportionately to frequency, the motor will overheat
from excessive load currents.
The result is that motor speed can be matched
to the application requirements. For HVAC systems,
this means varying motor speed to control the amount
of water pumped through a pipe, air through a duct,
or refrigerant through a compressor. In each case,
Pulse Width Modulation is the present state-of­
the-art method used to control both voltage and
frequency. PWM variable frequency drives consist
of three sections; a rectifier, a DC bus, and an
inverter. The AC source voltage is converted to DC
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ESL-IE-97-04-36
by the rectifier. In the DC bus, large capacitors
charge to the peak of the RMS voltage waveform of
the source.
where:
BHP 1 is the initial horsepower,
N. is the initial fan speed,
BHPz is the reduced horsepower, and
N z is the reduced fan speed.
The DC is then "inverted," into a solid-state
controlled square-wave output by the inverter. The
logic programmed into the inverter determines the
width and polarity of the DC pulses, thereby
controlling the voltage and frequency, respectively, of
the output. The inductance of the motor and motor
branch circuit conductors resists the rapid switching
of the voltage and smoothes out the DC voltage
pulses. The motor accepts the inverter output as a
three-phase sine wave.
While fan speed is proportional to airflow, input
power has a cubic relationship to motor speed. A
15% reduction in fan speed, for example, results in
a 15 % reduction in airflow, while horsepower is
reduced by 39 % to approximately 61 % of the original
power required from the motor:
BHP2 =BHP1
Variable frequency drives are typically
classified according voltage and horsepower, based
upon the motor they will serve (8). Small, low­
voltage motors generally are rated 250 horsepower or
less and operate at or below 600 volts AC. Medium­
voltage motors are larger than 250 horsepower and
operate above 600 volts AC. Where a motor is large
but operates at low voltage, the horsepower rating
typically dictates its classification.
(
0.85) 3 =BHP1 (0.614)
1.0
(2)
Traditionally, mechanical means, such as guide
vanes and dampers, have been employed in restricting
airflow and reducing energy consumption. Because
of the cubic relationship between fan speed and
power, energy savings from installing variable
frequency drives surpasses guide vanes, dampers, and
similar mechanical means of energy consumption.
ENERGY EmCIENCY
POWER QUALITY CONCERNS: HARMONICS
AND POWER FACTOR
The main reason that systems operate much
more efficiently with the ability to vary motor speed
is because mechanical systems are inherently
oversized for their application. HVAC systems, for
example, are based on an area's weather extremes.
An HVAC system designed to handle extreme
summer and winter temperatures requires only a
portion of its full capacity on an average day.
Harmonics are produced by VFD's because the
current is not drawn from the source in a sinusoidal
form, but in pulses. These pulses occur when the
AC source is at a higher voltage than the DC bus of
the drive, during which time the rectifier bridge
diodes are forward biased and conduct (3).
Actual air-volume requirements for any given
HVAC system tend to follow a normal distribution
curve (2). Approximately 87% of the time, any
given HVAC system requires less than 70 % of its
maximum air flow. VFD's can reduce motor speed
and motor wear by more closely matching the actual
load.
Harmonic currents flow from the load toward
the utility, seeking a low impedance path to ground,
and causing a voltage drop through the distribution
system according to Ohm's Law. Harmonic voltages
combine with the fundamental source voltage
producing voltage distortion throughout the power
system.
Other equipment is affected by the
harmonic-laden system voltage and may inject even
more harmonic currents into the system.
Additionally, harmonic distortion can result in low
power factor.
Moreover, VFD's can result in significant
energy savings by allowing fans and pumps to
approach the ideal performance described by fan
laws, which state that fan or pump horsepower, is
reduced by the cube of the flow rate (2), as given by
the following equation:
Most variable frequency motor drives will have
a negligible effect on displacement power factor
because the current lag associated with a diode bridge
is relatively small.
Conversely, if significant
harmonic currents are present and the utility measures
true power factor, or the ratio of real power divided
by the total apparent power comprised of real,
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ESL-IE-97-04-36
TPF can be low due to high harmonic power
consumption as well as high reactive power
consumption. The resulting high apparent power in
the denominator results in lower TPF. TPF is always
lower than DPF when harmonics exist.
With
significant harmonic currents present, power factor
can be improved by installing harmonic filters.
Installing capacitor banks by themselves on a
harmonically loaded distribution system may result in
a resonant condition.
reactive, and harmonic power, power factor will be
lower than displacement power factor.
Power Factor
Based upon the Power Triangle model, real
power, expressed as KW, reactive power, expressed
as KV AR, and apparent power, expressed as KVA,
are related through the Pythagorean Theorem as
given below:
KVA=JKW2+KVAR2
(3)
Harmonic Resonance
Inductance increases in proportion to frequency,
as given by:
Power factor is defined as the cosine of the
power factor angle, but can also be determined
through trigonometric identities:
PF=Cos(8) = KW
-KVA
(6)
where
(4)
XL is the inductive reactance,
f
is the fundamental frequency of the system in
Hertz,and
L is the finite, constant value of inductance in
Henries.
Power factor, in the classical power triangle
representation, is more appropriately referred to as
Displacement Power Factor (DPF). DPF is that
portion of power factor that is attributable to phase
displacement between source voltage and load current
at the fundamental frequency. The Power Triangle
models real and reactive power at the fundamental
frequency of the electrical power system. Harmonic
currents cannot be modeled vectorially along with the
fundamental current. As such, displacement power
factor does not consider that portion of power factor
attributable to harmonic load current.
Impedance due to inductive reactance increases
with frequency, which tends to damp higher order
harmonics.
Meanwhile, capacitive reactance
decreases in proportion to frequency as given by:
X=
1
c 21tfC
(7)
where
Xc is the capacitance,
and
C is the finite, constant value of the capacitance
in Farads.
True Power Factor
True Power Factor (TPF) can be defined by
revisiting the definition of power factor as the ratio of
real power to apparent power. TPF is the ratio of
real power to total power consumed in the system as
given by:
TPF= __KW
__
KVAt;ot;al
Impedance due to capacitive reactance decreases
with frequency, which does not tend to attenuate
higher order harmonics.
At a specific frequency, the inductive reactance
is equal to the capacitive reactance, which is the
definition of resonance. During series resonance, the
impedance of the composite transformer(s) and
capacitor bank(s) is minimized, essentially cancelling
each other. The only impedance to current flow is
the pure resistance of the distribution circuit, which
is normally low.
Again, high magnitudes of
harmonic currents at or near the resonant frequency
can flow unimpeded through the distribution system.
(5)
where
TPF is the true power factor,
KW is the real power consumed by the
electrical system, and
KVA.c..J is the total apparent power composed
of real, reactive, and harmonic power.
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ESL-IE-97-04-36
During parallel resonance, the impedance of the
composite transformer(s) and capacitor bank(s) is
maximized and harmonic currents at or near the
resonant frequency can create high harmonic voltages
across the high parallel impedance.
installation of capacitors on an electrical distribution
system might lead to a resonant condition. The short
circuit KVA available from the utility must be
determined first, and is given by:
Non-Linear Loads and Harmonics
A resonant distribution circuit is aggravated
because non-linear loads, such as variable frequency
drives, generate harmonic currents, operating on the
60 Hertz source voltage and returning harmonic-rich
load current to the distribution system (7). The load
current is distributed across the harmonic spectrum
by non-linear loads, significantly increasing the
likelihood of a resonant circuit between inductance
and capacitance within the distribution system.
where
KV A." is the available short circuit KVA from
the utility,
VL-L is the system operating voltage, and
Isc is the available short circuit current.
Next, the building or facility distribution system
short circuit capacity must be calculated, as given by:
Harmonic related problems are well documented
in literature and include overheating equipment,
blown fuses, and equipment failure.
Excessive
harmonic voltages and current in capacitors results in
increased losses in iron, insulation, and conductors
with a corresponding increase in temperature. Life
expectancy of electrical equipment is reduced when
exposed to excessive heat generated by harmonics.
where
KV A..:t. is the short circuit capacity of the
secondary electrical system,
KV A. is the KVA rating of the substation
transformer(s),
KVA." is the available short circuit KVA from
the utility, and
~ is the impedance of the
substation
transformer(s).
Unwanted harmonic currents can be prevented
from flowing back through the power system by
installing line impedance to "de-tune" the distribution
circuit or by installing harmonic filters. Additional
line impedance will increase the harmonic order of
the resonant frequency. Since inductive reactance
increases with frequency, the magnitudes of higher
order harmonics are inherently attenuated by
inductive reactance.
Unfortunately, too much
inductive reactance will increase voltage distortion to
levels above those found in IEEE 519-1992 (4).
Finally, the resonant harmonic of
distribution system under analysis is given by:
hI
Alternatively, 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 true power factor.
=
the
(10)
where
h,. is the resonant harmonic,
KV A..:t. is the available short circuit KVA from
the distribution system,
KV A.a: is the available short circuit KVA from
motor contribution, and
KV ARc is the sum of capacitor KVAR ratings.
Under special circumstances, existing capacitor
banks can be reconfigured into harmonic filters by
adding series reactance, keeping the voltage, current,
and reactive power limitations of the capacitor in
When Equation 10 indicates a relatively low
resonant harmonic, and spectrum analyses indicate
that the magnitude of harmonic currents are
significant at or near the resonant frequency, the most
likely solution wi)) be to install harmonic filters. In
fact, low true power factor may be entirely due to
harmonic currents generated by the load (6). In those
mind.
The following series of equations, common in
literature, are useful in determining whether the
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ESL-IE-97-04-36
instances, TPF may be improved by installing filters
or traps alone. In most cases, a combination of
harmonic filters along with capacitors designed to
operate at the fundamental frequency are required to
improve TPF to acceptable levels in systems with
harmonic currents present.
5 % will increase voltage distortion and voltage drop
in accordance with Ohm's Law. The drive may not
be able to operate under high harmonic distortion or
low voltage, depending upon the sensitivity of the
VFD. As such, a 3 % reactor is typically used for
individual drive applications.
Harmonic Mitigation/Improving Power Factor
There are two schools of thought on dealing
with power system harmonics. The first perspective
is management of harmonic load currents.
Conductors are oversized. Panelboards have double­
capacity neutrals. Transformers are derated or are
K-rated. Motors, generators, and switchgear are
oversized to compensate for harmonic currents. In
short, equipment is oversized to handle harmonic­
induced heating effects.
If harmonic load currents are significant, either
in magnitude or harmonic order, it may be necessary
to remove these currents from the distribution system
for safe operation.
Harmonic Filters
Active filters have the ability to cancel
harmonics in the current waveform by injecting
energy into the gaps that are created by rectifier
loads (3). In some cases special transformers or
input choppers are used. This technology is still
developing and not competitive for general use.
The second perspective is removal of harmonic
currents from the electrical system through filtering
or cancellation technology. Large non-linear loads
can be individually filtered to reduce or remove
harmonic load currents from the system. Zig-zag or
multiple-secondary winding transformers cancel
balanced harmonic load currents.
Every electrical distribution system is unique.
It is important to recognize that the most economical
approach to dealing with harmonic load current may
come from either perspective. The electrical system
under consideration will prescribe its own cure.
Passive harmonic filters are more commonly
used. Passive filters are constructed of one or more
tuned resonant circuits. The filters most commonly
used with VFD applications consist of individual
circuits tuned for the 5th, 7th, and 11th harmonics
plus, in a few cases, a high pass filter tuned near the
17th harmonic (3). 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 5th harmonic
filter is normally designed for 4.7th harmonic.
Inductive Reactance
From the perspective of managing harmonics,
harmonic currents can be controlled by placing
additional line inductance ahead of the variable
frequency drive (2). If the line impedance is too
low, transient voltage spikes or interruptions can
create excessive current spikes that will cause
nuisance input fuse blowing and may cause damage
to the drive power structure.
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.
Installing line reactors slows the rate at which
the drive can draw current. Instead of drawing
current in short, spike-like bursts with a high peak
current, the drive draws current more slowly, with a
much lower, broader peak. Line reactors or drive­
isolation transformers, if a voltage change is
required, can be specified to provide the inductance
required to achieve this.
A harmonic analysis should be performed to
determine the existing and potential harmonic
currents and voltage levels resulting from installing
variable frequency drives.
Once a model is
complete, an approach to mitigating harmonics and
improving power factor can be developed.
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
In most cases, line impedance should not exceed
5 % because of voltage distortion and voltage drop at
the terminals of the drive. Impedance in excess of
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ESL-IE-97-04-36
are addressed. Capacitors have definite limitations
that must be taken into consideration during normal
operation and during operation as an integral
component of a harmonic filter.
When a capacitor bank rated 240 volts is
installed on a 208 volt system, for example, its
reactive power rating must be derated to 75 %:
Capacitor Ratings
Two industry standards govern the
characteristics of capacitors: ANSllIEEE Standard
18-1980, and NEMA CPI-1973 (9). 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.
KVARActual=KVARRated(
(12)
The margins dictated by the standards are
required to allow for overvoltage due to harmonics,
switching surges, and fundamental overvoltage at the
capacitor terminals; for excessive reactive power
demand due to harmonics, switching surges,
overvoltage at the capacitor terminals; and for
excessive capacitance from manufacturing tolerances.
KVARAcual =KVARRaCed (0.75)
(13)
Applying a capacitor rated 240 volts on a
208 volt system without derating the KVAR capacity
to 75 % may result in an improved power factor
lower than expected.
The system may require
additional capacitance to improve power factor to
satisfactory levels.
Normally, the 180% of rated current limitation
is less restrictive than the reactive power and voltage
limitations outlined above (9). Observing capacitor
ratings ensures a reasonable life expectancy, realizing
that any increase in the applied voltage over the
capacitor rating will result in shortened capacitor life.
To account for this extra duty an additional 15­
20 % increase in capacitor line-to-neutral voltage
rating is recommended (1). The capacitors within a
harmonic filter are typically rated for the next higher
nominal voltage than the system to which it is
connected.
Capacitors installed as an integral harmonic
filter component operate at a steady-state overvoltage
due to the existence of harmonic voltages.
Additionally, installing a capacitor bank on a system
other than its nominal voltage requires derating of its
rated reactive power to ensure adequate overload
capacity for harmonics and surges. The following
equation, common in literature, illustrates reactive
power derating for any derivation from rated voltage:
VTT7I D
.I\.
VTT7I D
vn.n.Actual =.1\. v.ru;"Rated
(
~~~) 2
A capacitor bank with a nominal voltage rating
and an actual operating terminal voltage of 480 V
should not be upgraded into a harmonic filter because
the steady-state overvoltage from harmonic currents
will most likely exceed the 110% voltage limitation,
and may exceed the 135 % reactive power limitation.
Harmonic filter capacitors connected to a 480 V bus
are typically rated for 600 V operation, a 25%
increase in line-to-neutral voltage rating.
VActual()lt1)
V Rated
where,
KVAR Ratm is the KVAR rating of the capacitor,
is the calculated KVAR
KVARAduaJ
capacity of the derated
capacitor,
V!laUd
is the voltage rating of the
capacitor, and
VA<XlaI
is the operating voltage of the
capacitor as installed.
Sizing for Reactive Power Requirements
Sizing KVAR requirements for power factor
improvement, either through the installation of
capacitor banks or harmonic filters, is the similar (6).
The magnitude of power factor problem can be
ascertained from utility data. Once the target power
factor is set, capacitor manufacturer tables can be
used to calculate the KVAR requirement for the
system. Generally, only a portion of the total KVAR
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ESL-IE-97-04-36
required will be used for harmonic filtering. That
portion will be determined when filters are sized to
match the non-linear portion of the system load,
including any adjustments to the capacitor ratings.
derated in accordance with Equation 11 based upon
the extent of steady-state overvoltage that the
capacitor endures as a harmonic filter component.
The capacitor provides the reactive power
required by the reactor along with providing reactive
power for the distribution system. As such, the
addition of the reactor to the capacitor in making a
filter further reduces the capacitor's reactive power
output, as given by:
Reference (6) recommends sizing harmonic
filters between 0.30 and 0.40 times the drive
horsepower rating for variable frequency drives with
SCR front ends. For VFD's with diode bridge front
ends, (most PWM drives), the filter should be sized
between 0.25 and 0.30 times the drive horsepower.
(17)
Upgrading an Existing Capacitor into a Harmonic
Filter
The following series of equations can used to
size an in-line reactor needed to upgrade an existing
capacitor bank into a harmonic filter (1):
Where
KVARrow 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.
(14)
CONCLUSIONS
where
Variable frequency drives can reduce an
electrical system's energy consumption significantly.
It is important to remember that a drive may affect
other mechanical and electrical components in the
system. If improperly applied, the drive can generate
harmonic distortion that can have serious negative
effects on components in a building's electrical
distribution system and other equipment.
Xc is the capacitive reactance of the filter,
VL-L is the rated voltage of the capacitor bank,
and
KVAR}.pbue is the rated KVAR of the capacitor
bank.
(15)
Harmonics and power factor become
interrelated when non-linear loads are installed in the
electrical environment. High harmonic currents
result can result in low true power factor, although
displacement power factor may be near unity. Proper
application of capacitors, either alone or as harmonic
filters, can safely improve power factor and mitigate
harmonic distortion.
where
h is the tuned harmonic, and
XL is the inductive reactance of the filter,
Recall that capacitors experience terminal
voltage in excess of rated voltage when installed as a
harmonic filter component. 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 (1):
%VR=(~)Xl00
2
h -1
REFERENCES
1.
(16)
where
%VR is the percent of voltage rise above
nominal, and
h is the tuned harmonic.
2.
Andrews, D., Bishop, M., Witte, 1.,
"Harmonic Measurements, Analysis, and Power
Factor Correction in a Modem Steel
Manufacturing Facility," IEEE Transactions on
Industry Applicmions, May/June 1996
Beck, P., "Adjustable-Frequency Drives
Reduce HVAC Costs", Consulring-Specifying
Engineer, June 1992.
Recall that reactive power that a capacitor
delivers is dependent upon terminal voltage. Actual
reactive power generated by the capacitor must be
Proceedings from the Nineteenth Industrial Energy Technology Conference, Houston, TX, April 23-24, 1997
236
ESL-IE-97-04-36
3.
4.
5.
6.
7.
8.
9.
Gray, J., Haydock, F., "Industrial Power
Quality Considerations When Installing
Adjustable Speed Drive Systems,· IEEE
Transactions on Industry Applications,
May/June 1996.
IEEE Standard 519-1992: IEEE Guide for
Harmonic Control and Reactive Compensation
of Static Power Converters.
Jouanne, A., Enjeti, P., and Gray, W.,
•Application Issues for PWM Adjustable Speed
AC Motor Drives, " IEEE Industry Applications
Magazine, September/October 1996.
Lowenstein, Michael Z., ·Power Factor
Improvement for Non-Linear Loads,· 1991
Annual Technology Conference of the Textile,
Fiber, and Film Industry Committee, the
Industry Applications Society of the IEEE,
Greenville, South Carolina, May 1991.
Massey, G., ·Power Factor Improvement
Capacitors:
The Balance Between Power
Quality and Energy Efficiency, • PowerSystems
World,
Power Quality
'96, Imenec
International, Las Vegas, Nevada, September
1996.
Nicholas, D., ·Understanding the Twists and
Turns of Adjustable-Frequency Drives, •
Consulting-Specifying Engineer, November
1993.
Rice, D., •Adjustable Speed Drives and Power
Rectifier Harmonics - Their Effect on Power
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Industry Applications, JanuarylFebruary 1986.
Proceedings from the Nineteenth Industrial Energy Technology Conference, Houston, TX, April 23-24, 1997
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