Power System Harmonic
Fundamental Considerations:
Tips and Tools for Reducing
Harmonic Distortion in Electronic
Drive Applications
October 2011/AT313
by
Larry Ray, P.E.
Louis Hapeshis, P.E.
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Revision #1 10/11
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Power system harmonic fundamental considerations
Summary
Abstract ....................................................................................................... p 3
Introduction ................................................................................................. p 4
Harmonic Distortion Basics .......................................................................... p 5
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Voltage and Current Distortion ..................................................................... p 8
Harmonics and Power Factor – Displacement and Total ............................... p 11
Harmonic Mitigation – Two Passive Techniques ........................................... p 13
Common Harmonic Current Signatures ....................................................... p 15
Harmonic Distortion Simulation Methods...................................................... p 17
References .................................................................................................. p 22
AT313 | 2
Power system harmonic fundamental considerations
Abstract
This paper provides an overview of harmonic considerations for designing industrial and commercial electric
power distribution systems. These power systems must serve a combination of loads, many of which produce
non-sinusoidal current when energized from a sinusoidal AC voltage source. While conventional power
distribution systems accommodate a significant amount of non-sinusoidal current, the design engineer can
utilize existing IEEE guidelines and basic software tools to avoid some special circuit and load configurations
that exacerbate harmonic distortion problems.
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AT313 | 3
Power system harmonic fundamental considerations
Introduction
Power system harmonic distortion has existed since the early 1900s, as long as AC power itself has been
available. The earliest harmonic distortion issues were associated with third harmonic currents produced by
saturated iron in machines and transformers, so-called ferromagnetic loads. Later, arcing loads, like lighting
and electric arc furnaces, were shown to produce harmonic distortion as well. The final type, electronic
loads, burst onto the power scene in the 1970’s and 80’s, and has represented the fastest growing category
ever since.
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A better understanding of power system harmonic phenomena can be achieved with the consideration of
some fundamental concepts, especially, the nature of non-linear loads, and the interaction of harmonic currents
and voltages within the power system.
AT313 | 4
Power system harmonic fundamental considerations
Harmonic Distortion Basics
What’s Flowing on the Wire?
By definition, harmonic (or non-linear) loads are those devices that naturally produce a non-sinusoidal current
when energized by a sinusoidal voltage source.
Each “waveform” on the right, for example, represents the variation in instantaneous current over time for two
different loads each energized from a sinusoidal voltage source (not shown on the graph).
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Graph 1
For each load, instantaneous current at some point in time (at the start of the graph, for example) is zero.
Its magnitude quickly increases to a maximum value, then decreases until it returns to zero. At this point, the
current direction appears to reverse – and the maximum-to-zero-magnitude trend repeats in the negative
direction. This pattern is repeated continuously, as long as the device is energized, creating a set of largelyidentical waveforms that adhere to a common time period.
Both current waveforms were produced by turning on some type of load device. In the case of the current on
the left, this device was probably an electric motor or resistance heater. The current on the right could have
been produced by an electronic variable-speed drive, for example. The devices could be single- or threephase, but only one phase current waveform is shown for illustration. The other phases would be similar.
How to Describe What’s Flowing on the Wire?
Fourier Series
While the visual difference in the above waveforms is evident, graphical appearance alone is seldom sufficient
for the power engineer required to analyze the effects of non-sinusoidal loads on the power system. The
degree of non-linearity must be objectively established, and the method of quantifying the harmonic distortion
must also facilitate future analysis and mitigation.
AT313 | 5
Power system harmonic fundamental considerations
Graph 2
One method of describing the non-sinusoidal waveform is called its Fourier Series. Jean Fourier was a French
mathematician of the early 19th century who discovered a special characteristic of periodic waveforms. Periodic
waveforms are those waveforms comprised of identical values that repeat in the same time interval, like those
shown above.
Fourier discovered that periodic waveforms can be represented by a series of sinusoids summed together. The
frequency of these sinusoids is an integer multiple of the frequency represented by the fundamental periodic
waveform. The waveform on the left above, for example, is described entirely by one sinusoid, the fundamental,
since it contains no harmonic distortion.
The distorted (non-linear) waveform, however, deserves further scrutiny. This waveform meets the continuous,
periodic requirement established by Fourier. It can be described, therefore, by a series of sinusoids. This
example waveform is represented by only three harmonic components, but some real-world waveforms
(square wave, for example) require hundreds of sinusoidal components to fully describe them. The magnitude
of these sinusoids decreases with increasing frequency, often allowing the power engineer to ignore the effect
of components above about the 50th harmonic.
The concept that a distorted waveform (even a square wave!) can be represented by a series of sinusoids is
difficult for many engineers. But it is absolutely essential for understanding the harmonic analysis and mitigation
to follow.
It’s important for the power engineer to keep in mind a few facts:
The equivalent harmonic components are just a representation – the instantaneous current as described by the
distorted waveform is what’s actually flowing on the wire.
• This representation is necessary because it facilitates analysis of the power system. The effect of sinusoids
on typical power system components (transformers, conductors, capacitors) is much easier to analyze than
distorted signals.
• Power engineers comfortable with the concept of harmonics often refer to individual harmonic components
as if each really exists as a separate entity. For example, a load might be described as producing “30 A of
5th harmonic.” What’s intended is not that the load under consideration produced 30 A of current at 300 Hz,
but rather that the load produced a distorted (but largely 60 Hz) current, one sinusoidal component of which
has a frequency of 300 Hz with an rms magnitude of 30 A.
AT313 | 6
Power system harmonic fundamental considerations
• The equivalent harmonic components, while imaginary, fully and accurately represent the distorted current.
As one test, try summing the instantaneous current of the harmonic components at any point in time.
Compare this value to the value of the distorted waveform at the same time (see chart below). These values
are the same.
Graph 3
Total Harmonic Distortion
The series of harmonic components that represent a distorted waveform are often described by a single
number, total harmonic distortion. This number is calculated in two different ways, depending somewhat on the
engineer’s geographic location.
In the United States, total harmonic distortion is calculated as the sum of all the harmonic components (except
the fundamental), divided by the magnitude of the fundamental. This value is represented as THD (all upper
case). Or, in equation form:
Note that the components are summed vectorially, not algebraically, because they have different phase angles.
For a waveform represented by a fundamental current of 100 A, a 5th component of 20 A, and a 7th component
of 12 A, for example, Ih would equal the square root of (202 + 122), or 23 A, not (20 + 12) = 32 A. The THD is,
therefore, 23/100 = 0.23 or 23%.
It is possible for the US-convention THD to exceed 1.0 or 100%, since it is possible for the magnitude of
harmonic current to exceed the magnitude of fundamental current. This is the primary distinction between the
US and European convention. The European convention, thd (all lower case) equals the harmonic components
divided by the total rms current (harmonics plus fundamental). This thd value can never exceed 100%.
AT313 | 7
Power system harmonic fundamental considerations
Voltage and Current Distortion
Harmonic Current Flow
The current drawn by non-linear loads passes through all of the impedance between the system source and
load. This current produces harmonic voltages for each harmonic as it flows through the system impedance.
These harmonic voltages sum and produce a distorted voltage when combined with the fundamental. The
voltage distortion magnitude is dependent on the source impedance and the harmonic voltages produced.
Figure 4 illustrates how the distorted voltage is created. As illustrated, non-linear loads are typically modeled
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as a source of harmonic current.
Figure 4:
Creation of distorted current
With low source impedance the voltage distortion will be low for a given level of harmonic current. If harmonic
current increases, however, system impedance changes due to harmonic resonance (discussed below),
voltage distortion can increase significantly.
Circuit Impedance – Without Power Factor Correction
While the preceding discussion focused on distorted current waveforms, it is important to note that ac
voltage can also show the effects of harmonic distortion. The degree of distortion is determined by applying
the same techniques as described earlier for current. So, what is the relationship between voltage distortion
and current distortion?
Higher-frequency (harmonic) components of ac voltage and current follow the same power system rules as
60 Hz voltages and currents – Kirchoff’s Voltage and Current Laws, Ohm’s Law, etc. One basic principle is that
voltage and current are related by impedance. As with ac voltage and current, impedance is a complex term,
consisting of resistance, capacitance, and inductance. While resistance is largely independent of frequency,
impedance associated with capacitance and inductance changes as the frequency of the signal changes.
AT313 | 8
Power system harmonic fundamental considerations
For the typical industrial power system, the impedance as seen by the loads is dominated by inductance. Since
inductive reactance is directly proportional to the frequency of the current, the system impedance approximates
a straight line, as illustrated below.
1.50
Typical system impedance
(without power factor
correction capacitors)
Impedance, Ω
1.20
0.90
0.60
0.30
0.00
0
300
600
900
1200
1500
Frequency (Hz)
Graph 4
For this typical power system, the impedance encountered by the 300 Hz (5th harmonic) component of
current is approximately five times the impedance encountered by the 60 Hz (fundamental) component. With
this type of power system, the amount of voltage distortion can be estimated by summing the voltage drop
at each harmonic component, as summarized in the following table. The table assumes that the circuit load
is represented by the single harmonic source shown earlier, with a total Irms = 102.7 A, and ITHD = 23%, with a
nominal system voltage of 480 Vrms.
Table 1
Harmonic
Current, Irms
Impedance,
Ohms
Voltage Drop,
Vrms
1
100
0.01
1.00
5
20
0.05
1.00
7
12
0.07
0.84
Total Vh drop
1.3
Resulting VTHD
0.27%
Resulting Vrms
478
Circuit Impedance – With Power Factor Correction
Power factor correction capacitors are often utilized in industrial and commercial power systems to reduce
power factor penalties, release circuit capacity, improve voltage regulation and reduce resistive heating losses
in circuit conductors. While power factor correction capacitors do not inject harmonic distortion (that is, PFC’s
are linear loads – they produce a sinusoidal current waveform when energized from a sinusoidal voltage
source), their presence on a power system dramatically changes the circuit impedance. These impedance
changes can adversely affect power system components, and worsen harmonic distortion concerns.
AT313 | 9
Power system harmonic fundamental considerations
Graph 5
When power factor correction capacitors are installed, a frequency of high impedance known as the resonance
point results from the new combination of inductive and capacitive reactance. This resonance point is limited
in magnitude only by the amount of resistance in the circuit, and is often many times the value of the inductive
impedance at that frequency. The more capacitance added to the circuit, the lower the frequency at which
this resonance point occurs.
This high-impedance point, coupled with the operation of harmonic-producing loads, can result in much
higher levels of voltage distortion than the circuit without capacitors. That’s why it is so important to closely
evaluate the addition of power factor correction capacitors on a power circuit serving harmonic loads. The
example estimate below shows the distortion estimate associated with the same 103 A, 23% THD
load shown earlier, except that the impedance at the 7th harmonic is assumed to be ten times its non-PFC
value (a resonance point at or near 420 Hz). Note that this change results in nearly a tenfold increase in
voltage distortion.
Table 2
Harmonic
Current, Irms
Impedance,
Ohms
Voltage Drop,
Vrms
1
100
0.01
1.00
5
20
0.05
1.00
7
12
0.7
8.40
Total Vh drop
8.5
Resulting VTHD
1.26%
Resulting Vrms
471
AT313 | 10
Power system harmonic fundamental considerations
Harmonics and Power Factor –
Displacement and Total
As discussed, harmonic distortion and power factor correction are seldom considered as separate topics.
This is due to the dramatic effect on system impedance at harmonic frequencies that can result from the
addition of conventional power factor correction capacitors. The relationship, unfortunately, does not end there.
Due to their non-linear nature, the presence of harmonic loads can sometimes fool the power engineer into
considering unnecessary power factor correction in the first place!
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Power Factor of a PWM Drive – An Extreme Example?
The pulse-width-modulated (PWM) variable frequency drive (VFD) produces a characteristic current waveform
when energized from a sinusoidal voltage source. This three-phase device produces a voltage and current
waveform for one phase that resembles the following graphic:
Graph 6
If the power parameters (real, reactive, and apparent) associated with this PWM device are measured
with a true-rms meter, the typical values would show a relationship of real (kW) to apparent power (kVA) of
approximately 0.6. The engineer might conclude from this knowledge that the power factor of the device is
poor, and that a circuit containing many of these PWM drives (not uncommon) would require power factor
correction capacitors.
Unfortunately, this line of reasoning is incorrect and can lead to disastrous results. While the kW/kVA
relationship indicated above is accurate, 0.6 is not the power factor of the device. At least, it is not the
complete picture of the power factor.
Further measurements would reveal that the displacement angle between voltage and current for this device
is 0. That is, the current and voltage are in phase with each other. Or, more accurately, the fundamental (60 Hz)
component of voltage and the fundamental (60 Hz) component of current are in phase, as shown below.
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Power system harmonic fundamental considerations
Graph 7
Since harmonic loads like PWM drives are able to consume power in a non-linear fashion; that is, by turning
on and off in a manner not proportional to the applied instantaneous voltage, their kW/kVA relationship is not
equal to the phase angle between fundamental voltage and current.
This peculiarity, in fact, has required the establishment of two power factor definitions. These two power
factors are equal for undistorted (sinusoidal) voltages and currents.
Displacement Power Factor (dPF) – Cosine of the phase angle between fundamental voltage and
fundamental current.
Total (sometimes referred to as “True”) Power Factor (tPF) – Real power (kW) divided by apparent
power (kVA).
Power factor correction capacitors primarily affect the displacement power factor for a circuit. If PFC’s are
applied on a circuit that already has a high dPF, then the fundamental current component could be shifted
into a leading relationship to fundamental voltage. This situation can result in voltage regulation and distortion
problems for the circuit.
In addition, the addition of large PFCs on a PWM circuit can also increase the likelihood of harmonic resonance
problems, and the resulting excessive voltage distortion issues introduced earlier.
AT313 | 12
Power system harmonic fundamental considerations
Harmonic Mitigation – Two
Passive Techniques
Harmonics Attenuation
The earlier voltage and current distortion discussion, and voltage distortion estimates assume that the current
distortion remains unchanged regardless of the circuit impedance, but this is not entirely true. Harmonic current
distortion is affected by the amount of circuit impedance. In fact, an engineer will discover that placing the
same harmonic producing load at two different nodes in a power system will result in two different levels of load
current distortion.
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Power system designers can utilize this effect, called attenuation, as one method of passive harmonic
mitigation. The current waveforms below show the effects of introducing a series line reactor (“choke”) at the
terminals of a 100 hp pulse-width-modulated (PWM) adjustable-speed drive (ASD). The current total harmonic
distortion associated with the ASD drops from about 81% to 38%.
Graph 8
Graph 9
AT313 | 13
Power system harmonic fundamental considerations
This attenuation effect is often employed to reduce the harmonic distortion associated with three-phase ASD’s.
The ASD operation is not adversely affected, provided the line reactor chosen for the application does not
exceed about 5% impedance (relative to the drive base).
Harmonics Cancellation
In addition to attenuation, harmonic current distortion can be reduced by cancellation. Cancellation occurs
because individual harmonic components of a distorted current are affected differently when passing through
normal power system transformers. The magnitude of harmonic currents, like the 60 Hz component, increases
or decreases consistent with the transformer turns ratio.
The phase angle of harmonic components, however, is influenced by the type of connection of the three
phase transformer. The 5th and 7th components, for example, experience a 30° phase angle shift through a
power system transformer connected delta-wye, as compared with the same current components transmitted
through a wye-wye or delta-delta connected transformer.
This phase-angle effect can be used with multiple ASD’s to reduce the current distortion on the circuit feeding
the drives. As demonstrated in the diagram below, the alternating combination of delta-wye and wye-wye
connections can produce much lower harmonic distortion for similarly-sized and similarly-loaded drives.
The combination of line reactors and delta-wye transformers produces a similar cancellation effect.
Graph 10
AT313 | 14
Power system harmonic fundamental considerations
Common Harmonic
Current Signatures
IEEE 519a (Draft) Table
Despite the preponderance of electronic loads, there are surprisingly few categories required to characterize
the major harmonic-producing devices in industrial and commercial facilities. Electronic machines that
share similar rectifier configurations create similar characteristic harmonic current signatures, as the table
below demonstrates.
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The first column of the table describes the type of electronic device. A “single-phase power supply,” for
example, indicates the typical switch-mode power supply inside a conventional personal computer. The
second column shows the typical current signature, or waveform, that the device produces when energized
from a low-impedance, sinusoidal voltage source. For three phase loads, only one phase current is shown.
The other phases are similar in form, and separated in phase angle by 120°.
The third column shows the typical ITHD associated with the waveform. Note that third and fourth entries
represent the PWM drive – with and without line reactor – discussed earlier.
The fourth and final column requires a bit more explanation. This column represents a weighting factor
associated with each load type intended to facilitate simple harmonic assessments. The weighting factor for
individual loads can be used to estimate the total weighted power requirement of all the harmonic loads in the
facility. This weighted power requirement could then be compared against the system short circuit capacity to
evaluate the likelihood of adverse effects associated with harmonic distortion.
If the weighted power requirement of the harmonic loads, for example, could be shown to be less than 0.1% of
the short-circuit capacity, then the likelihood of harmonic problems is low. A fuller discussion of this weighting
factor is included in IEEE 519a, and in IEC Standard 61000-3-6.
AT313 | 15
Power system harmonic fundamental considerations
Table 3
Type of Load
Typical Waveform
Current
Distortion
Weighing
Factor (W i )
Single-phase power supply
80% (high 3rd)
2.5
Semiconverter
High 2nd, 3rd, 4th
at partial loads
2.5
Six pulse converter, capacitive
smoothing, no series inductance
80%
2
Six pulse converter, capacitive
smoothing, with series
inductance > 3%, or DC drive
40%
1
Six pulse converter with large
inductor for current smoothing
28%
0.8
12 pulse converter
15%
0.5
AC voltage regulator
Varies with
firing angle
0.7
Fluorescent lighting
0.05
0.5
AT313 | 16
Power system harmonic fundamental considerations
Harmonic Distortion
Simulation Methods
The weighting factor method for evaluating the likelihood of harmonic problems is applicable to only a small
power system with few harmonic loads and no power factor correction capacitors. Most power systems do not
fall into this category, so other, more sophisticated methods must be employed to evaluate harmonic concerns.
Computer Techniques
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Simple radial networks can sometimes be analyzed utilizing hand calculations (as performed earlier for the
small 103-A harmonic load). In most cases, however, these calculations quickly become tedious as the circuit
size increases beyond a few nodes and devices. The most common computer techniques are based on nodal
admittance equations for the network. These equations are usually stated in the form: I = Y * E, where I is the
injected current at each node, Y is the circuit admittance matrix, and E are the node voltages.
This Y matrix is built at each frequency, and the resulting equations are solved for the node voltages, E. The
solution is carried out by either matrix inversion, Gaussian Elimination, or some other technique. Computers are
especially suited for this solution task.
Commercially-available software tools, like the HI_WAVE module of Power*Tools for Windows® (SKM Systems
Analysis, Inc.; www.skm.com), facilitate harmonic analysis of complex systems and loads. These tools provide
graphical interface to build a variety of circuit types, including radial, loop systems, and multiple independent
systems of different voltage levels. They also contain a large library of conductor, transformer, capacitor, motor,
and harmonic load types. The library eliminates the need to enter individual harmonic waveforms, for example,
by offering the ability to use characteristic models already listed.
Variable-Frequency Drive Applications
Another software tool, called HarmCalc,™ has been developed to facilitate a common harmonic evaluation task:
Application of variable frequency drives (VFD) to an existing low-voltage radial power system. While this tool is
not accurate for complex systems, or for systems with power factor correction capacitors or harmonic filters,
it is widely applicable for evaluating VFD applications. Many consulting engineers and end-users who specify
VFD designs accept this tool as a suitable means of estimating VFD effect on a power system, and as a means
of evaluating certain mitigating devices like line reactors and drive-isolation transformers, delta-wye transformer
connections and broadband filters.
VFD’s and IEEE 519
IEEE Standard 519 is frequently quoted in consulting engineer specifications associated with VFD installations.
The gist of these specifications is that the VFD vendor assumes responsibility for supplying VFD’s that “comply
with IEEE 519.” This specification requirement is clearly outside the original intent of the standard, and often
unnecessarily increases the cost of a VFD installation.
AT313 | 17
Power system harmonic fundamental considerations
The original intention of IEEE Standard 519 was to introduce harmonic current and voltage distortion guidelines
for electric utilities and their customers. The objective was to establish acceptable levels of current distortion
that an individual customer could generate without adversely affecting other electric utility customers sharing
the same distribution system. Further, this standard provided recommended limits for electric utility control of
voltage distortion that could result from customer harmonic current injection
Despite the misapplication, this specification requirement has become so widespread that IEEE 519 has
effectively become the consensus equipment standard for VFD applications. Given that backdrop, use of
HarmCalc and other tools in evaluating VFD installations requires further exploration, and definition of terms
associated with IEEE 519.
Point-of-Common Coupling
As discussed, the circuit node at which harmonic current and voltage limits were to be evaluated was that
point on the electric utility system at which other customers could be served. This so-called point-of-commoncoupling, or PCC is described graphically, as shown above. Often, VFD specifications that require 519
compliance will also designate the PCC. Generally, the closer this PCC is to the VFD terminals, the more
costly the compliance requirements will be.
Graph 11
Voltage Distortion Limits
The voltage distortion limits in IEEE 519 are fairly straightforward, as reproduced below. There are only three
levels recommended, the first intending to address sub-transmission and distribution circuits on the electric
utility system. The voltage distortion, by the way, is calculated using the nominal voltage as the “fundamental”
component (in the denominator of the THD calculation.
Table 4
Bus Voltage at PCC (Vn ) Individual Harmonic
Voltage Distortion (%)
Total Voltage
Distortion – THDVn (%)
Vn ≤ 69 kV
3.0
5.0
69 kV < Vn ≤ 161 kV
1.5
2.5
Vn > 161 kV
1.0
1.5
AT313 | 18
Power system harmonic fundamental considerations
The assumptions behind establishment of the voltage distortion limits may be useful in determining whether
or not to invest in harmonic mitigation at low-voltage circuits. The 519 Working Group established 5% voltage
distortion as the limit at electric utility distribution circuits under the assumption that customer harmonic loads
would drive the VTHD higher at customer low voltage busses. The 5% THD limit was selected to allow lowvoltage busses to be maintained at 8% VTHD; a value that is acceptable to most linear and non-linear loads.
Current Distortion Limits
Determining current distortion limits is a more involved than voltage. This is due to the fact that the degree to
which one customer’s harmonic loads might affect another’s is dependent on the utility’s system impedance at
the PCC node. A relatively weak source impedance point in a utility’s system would reach the voltage distortion
limit at a much lower harmonic current injection level than a stiffer point.
That’s why the current distortion table requires a little more information in order to apply it correctly. Specifically,
the short-circuit value at the PCC, ISC, needs to be determined. For PCCs on the electric utility circuit, the utility
usually provides this number. The second required value is the estimated or measured demand current of the
customer’s total load, IL.
TDD – A Valuable Quantity to Learn and Apply
Another useful term needs to be defined at this juncture – TDD, or, more accurately, ITDD. Note that the current
distortion limits below are given in TDD, not THD. ITDD is similar to the definition of ITHD introduced earlier, with
one important difference: The denominator is IL; that is, the total customer 60 Hz demand current. Recall that
the ITHD denominator is the fundamental current of the distorted waveform, whether small or large relative to
other loads on the circuit.
The difference between the two quantities boils down to this: ITDD more accurately reflects the amount of
harmonic current a power system can absorb than ITHD. Since ITDD is the amount of harmonic current compared
to the customer’s total fundamental load current, it is a better predictor of the circuit’s ability to transmit the
harmonic current without adverse effects.
TDD is also an extremely valuable term to utilize throughout harmonic distortion evaluation and analysis, not
just IEEE 519 assessment. ITHD, on the other hand, is often a misleading value.
Suppose, for example, that a harmonic measurement indicates ITHD = 47%. Will this circuit experience harmonic
problems? The ITHD value alone cannot be used to answer this question. If the 47% THD measurement
is actually 0.47 A of harmonic current and 1.0 A of fundamental current, and the circuit in question has an
ampacity of 1600 A, harmonic problems are unlikely.
If, on the other hand, the 47% ITHD represents 470 A of harmonic and 1000 A of fundamental current on the
same 1600 A circuit, harmonic problems are highly probable and should be investigated at once.
For this reason, many power engineers prefer to calculate ITDD for a circuit in question, even if IEEE 519
compliance is not an issue. For low-voltage circuits within a facility, for example, they will often utilize the circuit
ampacity, or some other reasonable estimate of the circuit’s capacity, for the denominator.
AT313 | 19
Power system harmonic fundamental considerations
HarmCalc
Background
To facilitate VFD application into power systems that utilize IEEE 519 guidelines, Square D and Electrotek
Concepts co-developed an executable software program called HarmCalc. This software tool is available free
of charge at Square D’s Design Resource Center; follow the “Consulting Engineer” link under the “Customers
and Markets” listing at www.squared.com/us to “software tools” and download the file.
The HarmCalc tool includes an electronic tutorial and help documentation, but the following example can
illustrate its usefulness in evaluating VFD applications and some basic mitigating options. Note that HarmCalc
also includes capabilities for exporting the solution information to two third-party software tools intended
to facilitate additional analysis. Web links to these tools, SuperHarm™ and TOP,™ are available with the
HarmCalc installation.
Example
The simple power system shown below was configured to serve as an example of the program and its use.
There is a 1000 kVA transformer serving an MCC at 480 V. The electric utility system has been defined by its
available-fault-current and X/R ratio (values typically available from the utility). The MCC already serves about
300 hp in induction motor load (“linear load”). Two Square D® VFDs are being added, and IEEE 519 compliance
has been specified.
The VFD’s specified are identical Square D model Altivar 66 VT, 100 hp each. These VFD’s (as described in
the “Help” screen associated with VFD selection) are variable-torque devices, meaning that they are intended
for application on variable-torque motor loads like centrifugal pumps or fans. The VFD’s chosen here are
configured with 6-pulse diode rectifiers, although these VFDs are also available in 12- and 18-pulse versions.
Three options have been considered; as summarized in the table below. Note that the unmitigated addition
of the VFD’s would result in an ITDD slightly above the IEEE 519 current distortion limit, although the VTHD value
is slightly below 5%. The 519 limits can be readily met if the VFD’s are equipped with 3%-impedance line
reactors. While the delta-wye configuration for one drive results in the lowest harmonic distortion, this option is
likely to be less cost effective. In addition, line reactors provide other benefits, including reducing the tendency
of nuisance VFD tripping on electric utility power factor correction capacitor switching transients.
Table 5
Harmonic Mitigation
VTHD
at PCC2
ITHD
at PCC2
IEEE 519
Compliance?
None
4.85%
8.92%
No
3% line reactors only
2.23%
4.06%
Yes
Delta-wye/delta-delta only
1.97%
1.69%
Yes
AT313 | 20
Power system harmonic fundamental considerations
Screen Capture 1
ReactiVar AccuSine® PCS
Another useful software tool for the harmonic-mitigation designer is available on the Square D website. This
spreadsheet-based tool facilitates sizing and application of the Square D ReactiVar AccuSine active harmonic
filter. The active filter is the state-of-the-art method for harmonic current mitigation. It works by sensing the
amount and type of harmonic current being required by the loads (through the “CT,” or current transformer,
shown below), then injects harmonic current of the proper magnitude and frequency to cancel the load
harmonics. The resulting current returning to the “source” is low in current distortion. This and other harmonic
mitigation, power quality and power factor correction products and services are also available.
Graph 12
AT313 | 21
Power system harmonic fundamental considerations
References
1.IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems,
ANSI/IEEE Std. 519-1992.
2.IEEE Guide for Applying Harmonic Limits on Power Systems – Unpublished Draft , IEEE Std P519.1™/D9a,
January, 2004.
3.Electrical Power System Harmonics Design Guide, R.C. Dugan, M.F. McGranaghan, E.W. Gunther,
Electrotek Concepts, Inc., Knoxville, TN, 1992.
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AT313 | 22
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Document Number AT313
October 2011
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