Power system harmonics are not a new topic, but the proliferation of highpower
electronics used in motor drives and power controllers has necessitated increased
research and development in many areas relating to harmonics. For many years,
highvoltage direct current (HVDC) stations have been a major focus area for
the study of power system harmonics due to their rectifier and inverter stations.
Roughly two decades ago, electronic devices that could handle several kW up
to several MW became commercially viable and reliable products. This technological
advance in electronics led to the widespread use of numerous converter topologies,
all of which represent nonlinear elements in the power system.
Even though the power semiconductor converter is largely responsible for the
largescale interest in power system harmonics, other types of equipment also
present a nonlinear characteristic to the power system. In broad terms, loads
that produce harmonics can be grouped into three main categories covering (1)
arcing loads, (2) semiconductor converter loads, and (3) loads with magnetic
saturation of iron cores. Arcing loads, like electric arc furnaces and florescent
lamps, tend to produce harmonics across a wide range of frequencies with a
generally decreasing relationship with frequency. Semiconductor loads, such
as adjustablespeed motor drives, tend to produce certain harmonic patterns
with relatively predictable amplitudes at known harmonics. Saturated magnetic
elements, like overexcited transformers, also tend to produce certain "characteristic" harmonics.
Like arcing loads, both semiconductor converters and saturated magnetics produce
harmonics that generally decrease with frequency.
Regardless of the load category, the same fundamental theory can be used to
study power quality problems associated with harmonics. In most cases, any
periodic distorted power system waveform (voltage, current, flux, etc.) can
be represented as a series consisting of a DC term and an infinite sum of sinusoidal
terms as shown in Equation 1 where ω_{0} is the fundamental power frequency.
(eqn 1)
A vast amount of theoretical mathematics has been devoted to the evaluation
of the terms in the infinite sum in Equation 1, but such rigor is beyond the
scope of this chapter. For the purposes here, it is reasonable to presume that
instrumentation is available that will provide both the magnitude Fi and the
phase angle [theta]i for each term in the series. Taken together, the magnitude
and phase of the ith term completely describe the ith harmonic.
It should be noted that not all loads produce harmonics that are integer multiples
of the power frequency. These noninteger multiple harmonics are generally
referred to as interharmonics and are commonly produced by arcing loads and
cycloconverters. All harmonic terms, both integer and non integer multiples
of the power frequency, are analytically treated in the same manner, usually
based on the principle of superposition.
FIG. 1 Current waveform.
TABLE 1 Current Harmonic Magnitudes and Phase Angles
FIG. 2 Harmonic magnitude spectrum.
FIG. 3 Example of timevarying nature of harmonics.
FIG. 4 Example of timevarying nature of voltage THD.
In practice, the infinite sum in Equation 1 is reduced to about 50 terms;
most measuring instruments do not report harmonics higher than the 50th multiple
(25003000 Hz for 5060 Hz systems). The reporting can be in the form of a
tabular listing of harmonic magnitudes and angles or in the form of a magnitude
and phase spectrum. In each case, the information provided is the same and
can be used to reproduce the original waveform by direct substitution into
Equation 1 with satisfactory accuracy.
As an example, FIG. 1 shows the (primary) current waveform drawn by a small
industrial plant.
Table 1 shows a table of the first 31 harmonic magnitudes and angles. FIG.
2 shows a bar graph magnitude spectrum for this same waveform. These data are
widely available from many commercial instruments; the choice of instrument
makes little difference in most cases.
A fundamental presumption when analyzing distorted waveforms using Fourier
methods is that the waveform is in steady state. In practice, waveform distortion
varies widely and is dependent on both load levels and system conditions. It
is typical to assume that a steadystate condition exists at the instant at
which the measurement is taken, but the next measurement at the next time could
be markedly different. As examples, Figures 3 and 4 show time plots of
fifth harmonic voltage and the total harmonic distortion, respectively, of
the same waveform measured on a 115 kV transmission system near a 5 MW customer.
Note that the THD is fundamentally defined in Equation 2, with 50 often used
in practice as the upper limit on the infinite summation.
(eqn 2)
Because harmonic levels are never constant, it is difficult to establish utilityside
or manufacturing side limits for these quantities. In general, a probabilistic
representation is used to describe harmonic quantities in terms of percentiles.
Often, the 95th and 99th percentiles are used for design or operating limits.
FIG. 5 shows a histogram of the voltage THD in FIG. 4, and also includes a
cumulative probability curve derived from the frequency distribution. Any percentile
of interest can be readily calculated from the cumulative probability curve.
Both the Institute of Electrical and Electronics Engineers (IEEE) and the
International Electrotechnical Commission (IEC) recognize the need to consider
the timevarying nature of harmonics when deter mining harmonic levels that
are permissible. Both organizations publish harmonic limits, but the degree
to which the various limits can be applied varies widely. Both IEEE and IEC
publish "systemlevel" harmonic limits that are intended to be applied
from the utility pointofview in order to limit power system harmonics to
acceptable levels. The IEC, however, goes further and also publishes harmonic
limits for individual pieces of equipment.
The IEEE limits are covered in two documents, IEEE 5191992 and IEEE 519A
(draft). These documents suggest that harmonics in the power system be limited
by two different methods. One set of harmonic limits is for the harmonic current
that a user can inject into the utility system at the point where other customers
are or could be (in the future) served. (Note that this point in the system
is often called the point of common coupling, or PCC.) The other set of harmonic
limits is for the harmonic voltage that the utility can supply to any customer
at the PCC. With this twopart approach, customers insure that they do not
inject an "unreasonable" amount of harmonic current into the system,
and the utility insures that any "reasonable" amount of harmonic
current injected by any and all customers does not lead to excessive voltage
distortion.
Table 2 shows the harmonic current limits that are suggested for utility customers.
The table is broken into various rows and columns depending on harmonic number,
short circuit to load ratio, and voltage level. Note that all quantities are
expressed in terms of a percentage of the maximum demand current (IL in the
table). Total demand distortion (TDD) is defined to be the rms value of all
harmonics, in amperes, divided by the maximum (12 month) fundamental frequency
load current, IL, with this ratio then multiplied by 100%.
The intent of the harmonic current limits is to permit larger customers, who
in concept pay a greater share of the cost of power delivery equipment, to
inject a greater portion of the harmonic current (in amperes) that the utility
can absorb without producing excessive voltage distortion. Furthermore, customers
served at transmission level voltage have more restricted injection limits
than do customers served at lower voltage because harmonics in the high voltage
network have the potential to adversely impact a greater number of other users
through voltage distortion.
Table 3 gives the IEEE 5191992 voltage distortion limits. Similar to the
current limits, the permissible distortion is decreased at higher voltage levels
in an effort to minimize potential problems for the majority of system users.
Note that Tables 2 and 3 are given here for illustrative purposes only;
the reader is strongly advised to consider additional material listed at the
end of this chapter prior to trying to apply the limits.
The IEC formulates similar limit tables with the same intent: limit harmonic
current injections so that voltage distortion problems are not created; the
utility will correct voltage distortion problems if they exist and if all customers
are within the specified harmonic current limits. Because the numbers suggested
by the IEC are similar (but not identical) to those given in Tables 2 and
3, the IEC tables for systemlevel harmonic limits given in IEC 100036
are not repeated here.
FIG. 5 Probabilistic representation of voltage THD.
TABLE 2 IEEE519 Harmonic Current Limits
TABLE 3 IEEE 5191992 Voltage Harmonic Limits
While the IEEE harmonic limits are designed for application at the threephase
PCC, the IEC goes further and provides limits appropriate for singlephase
and threephase individual equipment types.
The most notable feature of these equipment limits is the "mA per W" manner
in which they are pro posed. For a wide variety of harmonicproducing loads,
the steadystate (normal operation) harmonic currents are limited by prescribing
a certain harmonic current, in mA, for each watt of power rating.
The IEC also provides a specific waveshape for some load types that represents
the most distorted cur rent waveform allowed. Equipment covered by such limits
include personal computers (power supplies) and singlephase battery charging
equipment.
Even though limits exist, problems related to harmonics often arise from single,
large "point source" harmonic loads as well as from numerous distributed
smaller loads. In these situations, it is necessary to conduct a measurement,
modeling, and analysis campaign that is designed to gather data and develop
a solution. As previously mentioned, there are many commercially available
instruments that can provide harmonic measurement information both at a single "snapshot" in
time as well as continuous monitoring over time. How this information is used
to develop problem solutions, however, can be a very complex issue.
Computerassisted harmonic studies generally require significantly more input
data than load flow or short circuit studies. Because high frequencies (up
to 23 kHz) are under consideration, it is important to have mathematically
correct equipment models and the data to use in them. Assuming that this data
is available, there are a variety of commercially available software tools
for actually performing the studies.
Most harmonic studies are performed in the frequency domain using sinusoidal
steadystate techniques. (Note that other techniques, including full timedomain
simulation, are sometimes used for specific problems.) A power system equivalent
circuit is prepared for each frequency to be analyzed (recall that the Fourier
series representation of a waveform is based on harmonic terms of known frequencies),
and then basic circuit analysis techniques are used to determine voltages and
currents of interest at that frequency. Most harmonic producing loads are modeled
using a current source at each frequency that the load produces (arc furnaces
are sometimes modeled using voltage sources), and network currents and voltages
are determined based on these load currents. Recognize that at each frequency,
voltage and current solutions are obtained from an equivalent circuit that
is valid at that frequency only; the principle of superposition is used to "reconstruct" the
Fourier series for any desired quantity in the network from the solutions of
multiple equivalent circuits. Depending on the software tool used, the results
can be presented in tabular form, spectral form, or as a waveform as shown
in Table 1 and Figures 1 and 2, respectively. An example voltage magnitude
spectrum obtained from a harmonic study of a distribution primary circuit is
shown in FIG. 6.
Regardless of the presentation format of the results, it is possible to use
this type of frequencydomain harmonic analysis procedure to predict the impact
of harmonic producing loads at any location in any power system. However, it
is often impractical to consider a complete model of a large system, especially
when unbalanced conditions must be considered. Of particular importance, however,
are the locations of capacitor banks.
FIG. 6 Sample magnitude spectrum results from a harmonic study.
When electrically in parallel with network inductive reactance, capacitor
banks produce a parallel resonance condition that tends to amplify voltage
harmonics for a given current harmonic injection.
When electrically in series with network inductive reactance, capacitor banks
produce a series resonance condition that tends to amplify current harmonics
for a given voltage distortion. In either case, harmonic levels far in excess
of what are expected can be produced. Fortunately, a relatively simple calculation
procedure called a frequency scan, can be used to indicate potential resonance
problems. FIG. 7 shows an example of a frequency scan conducted on the positive
sequence network model of a distribution circuit. Note that the distribution
primary included the standard feeder optimization capacitors.
A frequency scan result is actually a plot of impedance vs. frequency. Two
types of results are avail able: driving point and transfer impedance scans.
The driving point frequency scan shown in FIG. 7 indicates how much voltage
would be produced at a given bus and frequency for a 1 A current injection
at that same location and frequency. Where necessary, the principle of linearity
can be used to scale the 1 A injection to the level actually injected by specific
equipment. In other words, the driving point impedance predicts how a customer's
harmonic producing load could impact the voltage at that load's terminals.
Local maximums, or peaks, in the scan plot indicate parallel resonance conditions.
Local minimums, or valleys, in the scan plot indicate series resonance.
A transfer impedance scan predicts how a customer's harmonic producing load
at one location can impact voltage distortions at other (possibly very remote)
locations. In general, to assess the ability of a relatively small current
injection to produce a significant voltage distortion (due to resonance) at
remote locations (due to transfer impedance) is the primary goal of every harmonic
study.
Should a harmonic study indicate a potential problem (violation of limits,
for example), two categories of solutions are available: (1) reduce the harmonics
at their point of origin (before they enter the system), or (2) apply filtering
to reduce undesirable harmonics. Many methods for reducing harmonics at their
origin are available; for example, using various transformer connections to
cancel certain harmonics has been extremely effective in practice. In most
cases, however, reducing or eliminating harmonics at their origin is effective
only in the design or expansion stage of a new facility. For existing facilities,
harmonic filters often provide the leastcost solution.
Harmonic filters can be subdivided into two types: active and passive. Active
filters are only now becoming commercially viable products for highpower applications
and operate as follows. For a load that injects certain harmonic currents into
the supply system, a DC to AC inverter can be controlled such that the inverter
supplies the harmonic current for the load, while allowing the power system
to supply the power frequency current for the load. FIG. 8 shows a diagram
of such an active filter application.
FIG. 7 Sample frequency scan results.
===
FIG. 8 Active filter concept diagram.
 Power frequency current
 Current harmonics
 Power frequency current plus harmonics
 Harmonic producing load
 Active filter
===
For high power applications or for applications where power factor correction
capacitors already exist, it is typically more cost effective to use passive
filtering. Passive filtering is based on the series resonance principle (recall
that a low impedance at a specific frequency is a seriesresonant characteristic)
and can be easily implemented. FIG. 9 shows a typical threephase harmonic
filter (many other designs are also used) that is commonly used to filter fifth
or seventh harmonics.
It should be noted that passive filtering cannot always make use of existing
capacitor banks. In filter applications, the capacitors will typically be exposed
continuously to voltages greater than their ratings (which were determined
based on their original application). 600V capacitors, for example, may be
required for 480V filter applications. Even with the potential cost of new
capacitors, passive filtering still appears to offer the most cost effective
solution to the harmonic problem at this time.
In conclusion, power system harmonics have been carefully considered for many
years and have received a significant increase in research and development
activity as a direct result of the proliferation of highpower semiconductors.
Fortunately, harmonic measurement equipment is readily available, and the underlying
theory used to evaluate harmonics analytically (with computer assistance) is
well understood. Limits for harmonic voltages and currents have been suggested
by multiple standardsmaking bodies, but care must be used because the suggested
limits are not necessarily equivalent.
Regardless of which limit numbers are appropriate for a given application,
multiple options are avail able to help meet the levels required. As with all
power quality problems, however, accurate study on the "front end" usually
will reveal possible problems in the design stage, and a lowercost solution
can be implemented before problems arise.
The material presented here is not intended to be allinclusive. The suggested
reading provides further documents, including both IEEE and IEC standards,
recommended practices, and technical papers and reports that provide the knowledge
base required to apply the standards properly.
FIG. 9 Typical passive filter design.
