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Harmonic Measurements in Industrial Power Systems
Article in IEEE Transactions on Industry Applications · February 1995
DOI: 10.1109/28.363032 · Source: IEEE Xplore
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 1, JANUARY/FEBRUARY 1995
175
Harmonic Measurements in Industrial Power Systems
Peter E. Sutherland, Member, IEEE
Abstract- Harmonic measurements are made in industrial
power systems in order to: (a) aid in the design of capacitor or
filter banks, (b) verify the design and installation of capacitor or
filter banks, (c) verify compliancewith utility harmonic distortion
requirements, and (d) investigate suspected harmonic problems.
The results of these measurements are used in design calculations,
verification, comparison with standards, and system modeling.
Each of these objectives will affect the choice of a measurement
approach. The selection of the measured quantities,measurement
points in the system, and the types of instrumentsand transducers
should be based upon the measurement objective. Once measurements are taken, additional calculations must be made to put
the results into a useful form. The measurement results will then
provide a firm basis for further engineering work.
current injections from standard power conversion equipment,
such as six- and twelve-pulse drives, may be estimated without
measurement. However, the loading and diversity factors may
not be known. In addition, the wide variety of harmonic producing equipment in a facility may make estimation difficult.
The harmonic measurements should be taken at times when
the largest harmonic sources are in steady-state operation at
maximum loading. Harmonic measurements are also needed
to determine the distortion present from the utility system.
This factor can only be determined by measurement. The
harmonic measurement data are then used to calculate the
expected harmonic currents and voltages to be experienced
by the proposed capacitor or filter bank.
I. INTRODUCTION
H
ARMONIC analysis studies of industrial power systems
require measurement data. An approximate calculation
may be made using estimates of harmonic magnitudes derived
from equipment nameplate data, but this might not reflect
operating conditions. IEEE Standard 519-1992 [I] contains
recommended practices for performing harmonic measurements. The harmonic measurement process begins with the
choice of equipment and techniques that will determine the
validity of the results. General purpose spectrum analysis
instruments provide a wide variety of possible measurement
modes, from which the proper settings for power system
measurements must be chosen. Special-purpose power system
harmonic analyzers exist which have fewer choices of measurement modes available, and thus require an understanding
of when and how they can be used. Transducers that provide
the low voltage input for instruments are a critical link in
the measurement process. Measurement points in the system
depend upon what analysis is to be done with the measurement
results.
11. PURPOSES OF HARMONIC
MEASUREMENT
B. Harmonic Filter and Capacitor Bank Installation
After the design process is completed, and a capacitor or
filter bank has been installed, it should be checked to determine
whether the desired results have been obtained and that the
bank has been applied within its design limits. Power factor
measurements and fundamental frequency voltage and current
measurements provide initial confirmationof correct operation.
Measurements of the harmonic voltages at, and currents into,
the bank should be compared with the specified harmonic
voltage and current capabilities of the bank. These measurements are a baseline for tracking the future performance of the
device. Additional measurements should be taken when when
any significant change is made in the power system. A bank
that has been properly designed for one set of conditions may
fail when subjected to conditions not envisioned at the time
of installation.
Harmonic current and voltage levels at a common bus can
vary with not only the magnitude, but the phase angle of
the harmonic sources. For this reason, a single measurement
alone may not indicate worst case conditions. Harmonic measurements should always be evaluated in conjunction with
harmonic calculations.
A. Harmonic Filter Design and Capacitor Bank Application
Before power factor correction capacitors are applied in a
facility where significant sources of harmonic currents andor
voltages are present, it is usually necessary to perform a
harmonic analysis to determine whether a capacitor bank may
be used, or whether a harmonic filter is needed. Harmonic
Paper ICPSD 94-14, approved for publication by the Power Systems Protection Committee of the IEEE Industry Applications Society for presentation
at the 1994 IEEEAAS Industrial & Commercial Power Systems Technical
Conference, Irvine, CA, May 1-5. Manuscript released for publication July
20, 1994.
The author is with GE Industrial & Power Systems, Installation and Service
Engineering, General Electric Company, Albany, NY 12205 USA.
IEEE Log Number 9406625.
C. Compliance with Utility and IEEE 519 Requirements
The requirements specified by an electric utility company
for harmonic injection by industrial customers may be checked
by measurements, but additional calculations are often needed.
IEEE Standard 5 19 [ 11 specifies allowable levels of harmonic
currents at the “point of common coupling.” Harmonic measurements, coupled with harmonic analysis of both the worst
case conditions and of the effects of the addition of power
factor correction capacitors or harmonic filters, will indicate
whether or not a possible harmonic problem exists, and can
also serve to verify the correctness of the solution.
0093-9994/95$04.00 0 1995 IEEE
I76
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 1, JANUARYIFEBRUARY 1995
INCOMING L I N E
MAIN BUS
VOLTAGE
:CAE:AKER
L
i
I
I
I
I
OPEN FOR
HARMONIC
C C n
\
mn
@
o
+
r:
4
HARMONIC CURRENT
ME4SUREMENT P O I N T
HARMONIC V O L T A G E
MEASUREMENT P O I N T
1 - Incoming Line
Voltage a n d C u r r e n t
Incoming Main Breaker
Voltage and Current
3 - Feeder Breaker Current
4
Low Voltage Substation
Main Breaker Voltage
a n d Current
5
Harmonic Source Current
6
Capacitor Bank Current
~
~
~
Fig. 1. One-line diagram of typical industrial power system showing locations for harmonic measurements.
111. MEASUREMENT
POINTS
A. Harmonic Filter Design and Capacitor Bank Application
The harmonic measurement data needed for design calculations consist of harmonic source currents and voltages. Load
equipment, such as rectifiers and variable speed drives, are
modeled as harmonic current sources in the calculations. The
incoming harmonics from elsewhere in the power system, e.g.,
the utility interfaces, are modeled as voltage sources.
Harmonic current measurements at feeders and at substation
main breakers may be used to trace harmonic currents to their
sources.
Current measurements in a substation should be made at
feeder breakers in preference to the main breaker (see Fig. 1
and 2). If some of the feeders go to impedance loads, such as
motors, then measurements should be made on the feeder(s) of
interest. The reason for this is that the harmonic currents will
divide between the transformer and the motors. Measurements
may be made at the main breaker as a check. The sum of the
feeder harmonic currents as measured should not be expected
to be the same as the harmonic currents measured at the
main breaker, because the phase angles of the currents are
not measured. If power factor correction capacitors are present
anywhere in the system, they should be disconnected during
the measurements to avoid resonance effects.
Current measurements should be made on all three phases
if possible, because harmonic currents may be unbalanced.
Voltage measurements at the point of common coupling are
necessary for the harmonic calculations. As with the current
data, all three phases should be measured.
Fig. 2. One-line diagram of a substation with power factor correction
capacitors and dc drives.
B. Harmonic Filter and Capacitor Bank Installation
Measurements taken after installation do not need to be as
extensive as those made earlier. The harmonic content of the
capacitor current, bus voltage, and of the current and voltage
at the utility tie point should be checked. Harmonic voltage
measurements at substation buses will help to locate problem
resonances. These measurements should be made with all
existing capacitors connected.
C. Compliance with Utility and IEEE 519 Requirements
Industrial facilities should not supply more than the allowed
amount of harmonic current to the utility. The point of
common coupling is not always where the metering is located,
as is shown in Fig. 3. Due to the expense of high voltage
metering equipment, metering is sometimes performed at
the secondary level (Fig. 3(b)), and the utility billing is
corrected for the losses in the transformer. When harmonic
measurements must be made at the secondary level, they too
must be corrected.
IV. HARMONIC
MEASUREMENT
TECHNIQUES
A. Transducers
Current Transformers: It is preferable for safety reasons to
make current measurements at locations where current transformers (CT’s) are already present for relaying or metering
purposes. A clamp-on current probe is normally attached to
the CT secondary leads. This may be done at the back of a
relay, or at ammeter or ammeter switch.
CT accuracy is usually specified only for 60 Hz. According
to the IEEE Standard 519-1992 [l], CT’s have an accuracy in
the range of 3% at frequencies up to 10 kHz [ 2 ] .The frequency
response characteristics of a CT circuit are a function of the
internal impedances of the CT and its burden. This is illustrated
in Fig. 4 and 5. More work needs to be done on the accuracy
of CT circuits at harmonic frequencies.
The impedances are defined as follows:
Primary Impedance. This is not a factor in CT
2,
error.
SUTHERLAND: HARMONIC MEASUREMENTS IN INDUSTRIAL POWER SYSTEMS
INCOMING LINE
P U I N T OF
COMMON
CDUPLING
~
9
L
A
I I
T
Le
ICs
Lb
(a)
(b)
INCOMING LINE
Fig. 4. Current measurement (a) circuit and (b) equivalent circuit [2].
I
POINT O F
COMMON
COUPLING
CT RATIO CORRECTION FACTOR
1.01 -
/*
1.m.~
1.008
~.
1.007
..
With Burden
1.03 --
8 1.005 --
~
U 1.004 -1 . m --
c
4-
WilhoutBurden
/
~
-
- - -
/ / /
1.m
ID31
-:
--
1.
i
~
~
~
~:
~,
,
~
Fig. 3 . One-line diagrams showing point of common coupling: (a) primary
metering and (h) secondary metering.
ZCS
2,
Secondary winding capacitance.
Excitation Impedance. This frequency dependent
inductance forms a parallel resonant circuit with
zcs .
Secondary winding impedance. This is smaller
than Z,, resulting in a very high resonant
frequency.
Burden Impedance. This may have frequency
zb
dependence as well, which is not modeled here.
The Ratio Correction Factor may be calculated from the
formula [2]:
2,
RCF = 1
+ 2 s + zb + -2..g + zb
~
zcs
z e
(1)
The resonant frequency of 2, and ZCSis well above the range
of interest. If resistance is neglected, the resonant frequency
of L and C is:
1
f=T
2"
If the inductance is frequency dependent,
L
L = O
d7
(3)
then the resonant frequency becomes:
(4)
For values of LO = 8, and C = 1 nF for a CT tested by
Douglass [2], the resonant frequency is approximately 21.6
kHz. This is well above the range of interest.
The percentage error as compared to the fundamental may
be calculated using (1). For the CT [2] and burden combination
shown, the maximum error at the 50th harmonic of 60 Hz is
less than 1.0%. This is illustrated in Fig. 5 . If similar data
was available for other CT's, and if burden impedances versus
frequency were known, the accuracy of actual measurement
situations could be evaluated.
178
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 1, JANUARYEBRUARY 1995
for easy attachment to the circuit being investigated. A small
burden resistance (typically 5 R) is attached to the CT
output. It is selected so as not to cause saturation, but to
provide sufficient input voltage for the instrument. Frequency
response specifications and/or curves should be available
I
J
from the manufacturer to aid in selection. Clamp-on CT’s are
available in many styles, current ranges, frequency ranges,
and accuracies. Many CT’s designed for use at 60 Hz have an
accuracy that falls off rapidly at the higher harmonics, while
CT’s designed for higher frequencies may not be accurate at
60 Hz. Suitable current probes have an accuracy of 0.5 to 2%
over a frequency range of 50-10,000 Hz.
Hall Effect Probes: Hall effect current probes are similar
to clamp-on current transformers in their manner of usage.
The semiconducting Hall effect device allows dc currents to
be measured as well as ac currents. The specified accuracy for
Icput
Le Zcs
z
m
Zb
CJrcult
typical commercial probes is 2 to 5% over a frequency range
(b)
of dc to 500 or 1000 Hz. Hall effect probes have not been
Fig. 6. Voltage transformer, burden and harmonic analyzer input: (a) circuit generally used for harmonic measurements in power systems.
and (b) equivalent circuit [3].
Voltage Probes: Voltage probes used for harmonic measurement serve two functions: to reduce the measured voltage
Voltage Transformers: Magnetic type voltage transformers to one unsable by the instrument, and to minimize disturbance
(VT’s) are typically used in Industrial Power Systems. The to the system being measured. Standard oscilloscope probes
typical accuracy of a VT [l] is within 3% for harmonics less generally have been used for harmonic measurements. The
than 5 kHz [3]. A typical VT measurement circuit is shown two major characteristics of an oscilloscope probe are high
resistance (typically 10 MR) and low capacitance (typically
in Fig. 6. The Ratio Correction Factor (RCF) [3] is:
10-100 pF for a l o x probe and 2 pF for a lOOx probe) [4].
The inductance is negligible. Probe frequency response is in
the hundreds of MHz. Care should be taken not to exceed the
where
voltage rating of the probe.
Winding Impedance. This includes a series R-L
The ground lead of the probe is a critical part of the meaZ,,
term, and a primary-secondary capacitance.
surement circuit. If a differential input amplifier is available,
z b
Burden Impedance.
two probes may be used, and the ground leads removed from
ZCS Secondary capacitance to ground.
the probes. Where a single-ended measurement must be made,
Excitation Impedance. This varies with frequency the ground lead may be connected to the grounded side of the
Ze
in a similar manner to the CT impedance.
circuit being measured only i f the voltage is first measured
Impedance of the measurement circuit.
Z,
between the instrument’s ground (usually the case, which is
The input circuit consists of the resistance and inductance of connected to the third wire of the 120 V plug for safety) and
the system forming a low-pass filter with the input capacitance the point where the ground lead is to be attached, and found
of the VT. This does not affect the response in the frequency to be within acceptable limits. It is often the case in a power
range considered here. The internal resonant frequencies of system that the ground of Voltage Transformers in switchgear
the VT may be analyzed in a similar manner to those of the is not the same as the ground of nearby receptacle outlets. If
CT. These resonance also are above the frequency range of these two grounds are not the same, applying the ground lead
interest for harmonic measurements.
may cause a short circuit to occur, which may be dangerous
Direct Connections: Direct connection may be made to to personnel and damaging to equipment.
Low Voltage circuits in cases where CT’s and VT’s are
Newer instruments use special purpose voltage probes denot available. Voltage measurements may be performed using signed for power system use.
a 100:1 Oscilloscope probe with sufficient voltage rating.
Current measurements may be made by attaching a clampon Current Probe around a cable or busbar. For all direct C. Instrument Input Integace
measurements, the connection should only be made while
Impedance: The input impedance of an instrument is
the circuit is de-energized, locked Out and grounded. The characterized by a resistance and a capacitance. Typically,
grounds must be removed, and the circuit re-energized before harmonic analyzers have a l - M ~input resistance that is
the measurement is made.
compatible with scope probe inputs. The input capacitance of
B. Probes
Clamp-on Current Transformers: The clamp-on transformer contains a split-core in a hinged structure that allows
an instrument may be in the range of 10-100 pF. This is too
small to have a noticeable effect for harmonic measurements.
If a probe is used, its input resistance and capacitance apply,
not those of the instrument.
179
SUTHERLAND HARMONIC MEASUREMENTS IN INDUSTRIAL POWER SYSTEMS
Voltage: The inputs of instruments are only able to withstand a small voltage. Overvoltages will cause measurement
errors and possibly equipment damage. Because of this, the
use of a lOOx oscilloscope probe is recommended.
The input range selection should be carefully noted.
Whether the input has manual or auto-ranging, the best
accuracy is obtained when the amplitude signal being
measured is near the top of the range being used.
D. Harmonic Analyzers
Types: Harmonic measurements may be made with any
of several types of measurement systems. Almost all harmonic analyzers now use the Fast Fourier Transform (FFT)
calculation procedure 191 for sampled data.
Spectrum Analyzers combine the functions of data input,
calculation, and presentation of harmonic data, usually
on an oscilloscope screen. These are available in both
laboratory and portable types. A wide variety of frequency
ranges and accuracy levels are available, some of which
are suitable for power system use.
Portable Computers may be fitted with analog input
boards and used as a spectrum analyzer. The FFT may be
performed in software or on a digital signal processing
board.
Power System Harmonics Analyzer. Special purpose instruments are available to measure power system harmonics. Harmonic analysis capability is also available as
a feature on other types of instrument, such as power and
disturbance analyzers.
Digital Storage Oscilloscopes [ 5 ] may be used to gather
sampled data, which is then transferred to a computer for
processing.
Minimum Specijcations: Frequency Range. The frequency
range to be measured depends upon the purpose of the
measurement. For capacitor and harmonic filter design and
application, only those harmonics which have sufficient magnitude to affect the current and voltage rating of the device
need to be considered. Typically, measurements may be made
up to the 25th harmonic. The requirements of IEEE Standard
519-1992 [ l ] include limitations on harmonics above the 35th
order. Instruments measuring up to the 50th harmonic (3000
Hz in a 60-Hz system) may be used. In many situations,
harmonic magnitudes above the 25th are so low that they
have no practical effect.
Accuracy. It is recommended in IEEE Standard 519-1992
[ 11, that the harmonic analyzer used have an accuracy of 5% of
the harmonic limit specified in that standard. For example, the
limit for current harmonics supplied from a distribution system
at the point of common coupling is 0.3% of the fundamental
for odd harmonics of order greater than 35. An error of 5%
in measuring 0.3% means that the overall accuracy must be
0.015% of the fundamental. For even harmonics, the limit is
25% of this, or 0.00375%. In many practical cases, measurement may be limited to the first 25 odd harmonics, resulting in
an accuracy requirement of 0.075% of the fundamental. When
the instrument accuracy is specified in percentage of a fullscale reading, and the signal being measured is at the upper
limit of the measurement range, then these figures may be
compared with the instrument’s specifications. Otherwise, the
instrument must be more accurate. If an accuracy of 0.015% is
required of a signal where the fundamental is 80% of the input
range, then the instrument accuracy should be at least 0.012%.
Noise in the instrument input circuit may be specified as an
additional source of error in harmonic analyzers. This should
be well below the level of the input signal. In order to minimize
errors caused by noise, the input voltage to the instrument
should be well above the lower limit of the input range. If
time averaging is available, this can also be used to cancel
out random noise.
Dynamic Range. [ 101 The dynamic range of the instrument
should be checked to ensure that the smallest detectable
variations are not larger than the resolution required. The
binary word length of the Analog to Digital Converter (ADC)
provides the dynamic range. In order to resolve a signal
variation of 0.015% of full scale, a dynamic range of 76 dB
is needed. This may be provided by a 14 bit ADC. ADC
specifications also include a linearity error on the order of
f l Least Significant Bit. This ADC error is included in the
overall instrument specification.
Aliasing occurs when signals of frequencies higher than the
upper limit of the spectrum displayed are sampled and included
as if they were lower frequency spectral lines. Aliasing may
cause measurement errors when signals are present in the system which have a higher frequency than the highest frequency
being measured. This effect is minimized by anti-alising
filters, present in all harmonic analyzers. Because aliasing is
caused by outside signals, its effect cannot be included in the
percentage error of the instrument. The specification which
describes aliasing is the steepness of the anti-aliasing filter.
Aliasing is a consequence of the sampling process, and
operates on the same principles as the sampling of a frequency
within the range desired. For an N point sample, frequencies
from 0 to N / 2 - 1 cycles per sample period are captured, and
the FFT will display them at the correct frequency. When the
signal frequency is between N / 2 and N cycles per sample
period, two or fewer samples per cycle are taken Aliasing
occurs when the FFT maps these frequencies into the range
of 0 to N / 2 - 1. The amplitude level of the signals, so that a
signal of frequency 1 is mirrored at N - 1. When the FFT is
calculated, the magnitudes of the lines from 0 to N / 2 - 1 are
doubled, and the higher order lines are dropped.
Let the sampled signal be expressed as a function of the
sample number, n:
f ( n ) = sin
where h is the harmonic order, N is the number of samples,
and 0 is the phase angle of the signal. If h is expressed as a
function of N / 2 and a, where a is the order of the aliasing:
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 1, JANUARY/FEBRUARY 1995
180
Aliasing o f 6 5 t h H a r m o n i c
VT RATIO CORRECTION FACTOR
1
5
9
13
17
21
25
29
33
37
41
45
49
128 S a m p l e s
HAR MONK
(a)
Fig. 7. Voltage transformer, burden and harmonic analyzer input: frequency
response curves [3], using the data of Fig. 6. The burden resistance is 2960
R, and the inductance is 1.52 H.
Aliasing o f 65th Harmonic
1,
This may be expressed as the product of a cosine wave of
frequency N/2 and a sine wave of frequency a:
f ( n ) = cos
(
7
. I). sin (
2.1r.n
N
2.1r.n.a
p)
0.8 ..
1
._ 0.6 -~
c
0.4
..
(d
N
0.2 ~.
This product models the modulation effect shown in Fig. 8(a),
and may be expressed as two sidebands on N/2:
0
16
32
64
48
80
96
112
Harmonic
(b)
- s i n 2( .T7 r( . T
n -N
a)
-6)).
(9)
Fig. 8. (a) Time plot of the effect of sampling a signal of a frequency N/2+1
cycles per sampling period. Here, N = 128 and a = 1. (b) The result of the
FFT of this signal, showing aliasing to N / 2 - 1 cycles.
The FFT produces both of the above terms in an N-line output.
An example is shown in Fig. 8(b). This is reduced to N/2 lines,
with the values doubled, in the final output. If a is negative,
then the signal is within the range of the FFT and the aliasing
is at the higher frequency of N - a cycles.
A harmonic analyzer that samples 128 times, as in Fig. 8,
may have a display that goes to the 50th harmonic. The 78th
harmonic would be aliased to the 50th with a magnitude 1/n
of 0.0128, causing a 64% error in the measurement of the 50th
harmonic of magnitude 0.02. Anti-aliasing filters are used to
reduce this error.
50
60
70
80
90
100 110 120
Anti-aliasing filters are steep rolloff analog or digital filters
H a rmonic
placed in the instrument before sampling takes place. The filter
rolloff starts below the frequency N/2. Typical starting points Fig. 9. Anti-aliasing filter rolloff at -130 dB/decade starting at the 50th
are 50 out of 64 and 400 out of 512 cycles per sampling harmonic. For a @-point FFT,harmonics beyond the 78th would be aliased.
period. A typical value of rolloff is -130 dB per decade. For
the example of Fig. 8, the attenuation would be:
frequency that can appear in the display is 3120 Hz, or the
52nd harmonic. At -130 dB/decade starting at 2000 Hz, the
Atten. = 1301og
attenuation at 3120 Hz is 25.1 dB, as in the example above.
As above, this will result in a 3.5% error in the 33rd harmonic
= 25.1 dB
for l / h amplitude distributions.
= 5.56%.
Windowing is used in spectrum analyzers to provide filtering
Thus the aliased signal is .0556/78 = 0.000712 per unit, in the time domain and bandwidth control in the frequency
causing a 3.6% error in the 0.02 per unit 50th harmonic. The domain. Windowing in an FFT spectrum analyzer performs
slope of this anti-aliasing filter is illustrated in Fig. 9.
the same function as bandpass filtering did in earlier spectrum
For another example, suppose that the spectral lines are analyzers which used analog electronics. In the time domain,
spaced every 5 Hz, and 400 lines are displayed, the maximum discrepancies due to changes in the signal during the sampling
harmonic shown is the 33rd, and the maximum frequency period are removed. Windowing is performed by multiplying
is 200 Hz. With 512 b in the FFT, samples are taken up the sampled data by a window function, which is zero at each
to 2560 Hz, just below the 43rd harmonic. The first aliased ' end of the time record.
):(
SUTHERLAND: HARMONIC MEASUREMENTS IN INDUSTRIAL POWER SYSTEM[S
A signal should have exactly the same voltage at the
beginning of each consecutive sampling interval [8]. This may
be accomplished if the system is in a steady-state condition
with only integral order (characteristic) harmonics and the
sampling interval, T , is an integral multiple of the fundamental
cycle time, l / f . Under these conditions, each spectral line
of the FFT contains information on the magnitude of its
respective harmonic only. For N samples, N / 2 lines are
generated, giving a maximum harmonic order of
181
Third Harmonic x 1.01
1
0.8
0.6
0.4
0
:.
0.2
0
3 -0.2
-0.4
-0.6
-0.8
1
If 1024 samples are taken in 0.2 s, h,,
= 42. The spectral
lines are spaced U0.2 or 5 Hz apart. In order to detect
noncharacteristic harmonics, a frequency resolution of less
than 60 Hz is required. The amount of resolution between
characteristic harmonics depends upon the length, T , of the
sampling interval. The bandwidth of the measurement is
usually wider than the resolution due to windowing.
The N samples of the waveform being measured are assumed by the FFT to be exactly repeated over all time. If
there is a discrepancy in the endpoints, then errors will occur
where signals from the one frequency are added to those at
another frequency in the result. This is called spectral leakage.
Suppose that the sampled signal has a small frequency error,
E , in comparison with the sample period, T :
f ( t )= sin(w. t . m(1 + E ) )
03
C, cos(w . t . n + 4,)
where
= Abs 2ns::m~)
+
0 1 2 3 4 5 6 7 8 9 10111213
Harmonic Order
(b)
Fig. IO. Illustration of spectral leakage. (a) Third harmonic signal with
1% frequency error. (b) Magnitude of leakage for lower order harmonic
frequencies.
(13)
n=O
{
magnitude
Third Harmonic x 1.01 showing leakage.
(12)
where w = 2 . K . f , and m is an integer. The Fourier Series
of this function is:
~ ( t=)
128 Sampler
+ +
and a = m ( l E ) - n, b = m ( l E )
n. Notice that
m is the original harmonic order of the measured signal,
while n is the harmonic order of the calculated harmonic.
This equation may be used to calculate the leakage error
for a small frequency deviation between the frequency being
measured and the sampling rate of the instrument. As an
example, a third harmonic signal measured with d frequency
error of 1% gives a second harmonic component as follows:
m = 3, n = 2, E = 0.01, a = 1.03,b = 5.03, Cn = 0.023. The
second harmonic leakage component is thus 2.3% of the third
harmonic signal. This example is illustrated in Fig. 10.
If the error, E , goes to zero, then C, also goes to zero
unless m = n. When m = n,
sampling period to the power system frequency. This is valid
as long as neither the frequency nor the harmonic content
change during the sampling interval.
In the general case, the approach that is used is to multiply
the data by a window function that forces it to zero at each
end of the sampling interval [6], [7]. This can only be done
accurately if several cycles of the fundamental are included in
the sample interval. Twelve or more cycles are usually taken.
The window function that provides the best measurement
accuracy is the Flat Top or P201 window, developed by R. W.
Potter [6]. This window has an accuracy of 1% or better for
signals within the passband, and has minimal ripple outside,
resulting in very little leakage.
The lack of a window is a window itself, called the uniform
window [8]. The passband of the uniform window is the same
shape as the Fourier Transform of a rectangular pulse. This is
called the Dirichlet kernel, and crosses the horizontal axis at
integral multiples of 1/T. All of the signals within any of the
lobes are reported in the FFT as part of the harmonic being
measured.
E. Output Formats
which goes to 1 if E goes to zero. One method of making
m = n is to use a phase-locked loop circuit to lock the
Data Storage Requirements: Because of the large amount
of measurement data collected, the harmonic analyzer should
have sufficient nonvolatile data memory. Bubble memory was
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 1, JANUARYEBRUARY 1995
182
used in earlier analyzers. Some newer instruments use removable solid-state memories called PCMCIA (Personal Computer
Memory Card International Association) cards. Many of these
use “Flash” memories, a form of electrically erasable programmable read-only memory (EEPROM). Memory cards
which use RAM, on the other hand, contain a small battery.
Floppy disk data storage may be used if the environment
permits.
Printed Results: The measurement results may be printed
with both time and frequency plots alongside the tabulated
harmonic magnitudes, as shown in Fig. 11. These results may
be printed automatically by the use of a computer or printer
which interfaces with the harmonic analyzer.
A STORE0
RANGE
RAEKON-A
B STORED
TREKON-A
-51 OBV
STATUS
I
”Jolt
5
m V o 1t
/DIV
I
-20
v . EVALUATION
OF RESULTS
PAUSED
X
6 0 HZ
Y
9 644 m v r m s
A. Additional Calculations Needed
The result of a harmonic measurement consists of a millivolt
level for each frequency on each phase. This can be converted
to system volts or amperes by multiplying by the CT or
VT ratios and by taking into account transducers and burden
resistors. It is important that all necessary data be recorded
in the field. A typical data recording form is shown in Fig.
12. This also contains spaces for recording data directly if an
instrument with memory is not available.
If the power system is to be modeled with a one-line
equivalent circuit, the harmonic magnitudes from all three
phase should be averaged. The harmonics should be converted
to a percentage of the fundamental, as well as to system
amperes and volts. The total harmonic distortion (THD) and
total demand distortion (TDD) [l] must also be calculated.
Harmonics are evaluated on a steady-state basis, meaning
that design values are constant for periods of one hour or
more [l]. Thus it may be necessary to average several measurements taken at different times. This may be done within
the instrument, or later when the data is being analyzed.
Careful measurement procedure should eliminate this added
complication in most cases.
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00
21 .oo
22.00
23.00
24.00
25.00
26.00
27.00
28.00
29.00
30.00
31.00
32.00
33.00
RSS
B. Use of Results
THD
Vsurn
-
=
=
60
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
1020
1080
1140
1200
1260
1320
1380
1440
1500
1560
1620
1680
1740
1800
1860
1920
1980
9.643840
0.172385
0.111622
0.031441
2.228435
0.010796
0.406912
0.031028
0.160509
0.021 196
0.838977
0.014817
0.247742
0.050962
0.165291
0.020547
0.516714
0.014085
0.126692
0.021903
0.149194
0.016943
0.320812
0.019600
0.102153
0.039994
0.151095
0.023227
0.274789
0.017199
0.022349
0.021852
0.119536
100 .oooo
1.7875
1.1574
0.3260
23.1073
0.1119
4.2194
0.3217
1.6644
0.2198
8.6996
0.1536
2.5689
0.5284
1.7140
0.2131
5 :3580
0.1460
1.3137
0.2271
1.5470
0.1757
3.3266
0.2032
1 .0593
0.4147
1.5668
0.2409
2.0494
0.1783
0.2317
0.2266
1.2395
9.9768 mV
26.5054 X
16.1146 mV
The harmonic analysis program should first be used to
(b)
model the existing system as a base case. As many case
Fig. 1 1 . (a) Example of harmonic time and frequency plots. (b) Example of
conditions as necessary should be used to model all switching harmonic measurement results in tabular format.
configurations in the system. From this the maximum harmonic current magnitudes can be determined for the PCC and
compared with the limits specified in IEEE Standard 5 19-1992 should be done for all case conditions, and for all permutations
[ 11, or other standard as required. This will aid in determining of component tolerances within each case condition.
When appropriate capacitor and/or filter sizes and locations
whether a harmonic filter is necessary. The harmonic currents
and voltages at existing capacitors and harmonic filters may have been determined, the current and voltage calculations performed originally should be repeated. Using the design values,
be calculated and compared with their ratings.
The next step is to analyze the system for resonances, using currents and voltages should be calculated for all permutations
existing or recommended capacitors as necessary. Calculations of component tolerance during all case conditions. The worst
performed usually include determining amplification factors case results should then be used in specifying the components.
for injected currents, and impedance magnitudes and angles. The current values at the PCC should be compared with the
Both of these calculations produce plots of harmonic scans limits given in IEEE Standard 519-1992 [l], or other required
across the frequency range of interest. These calculations standard, and with base case values. The harmonic currents
183
SUTHERLAND HARMONIC MEASUREMENTS IN INDUSTFUAL POWER SYSTEMS
When the measurements have been completed, they may be
used in harmonic calculations to design filters and to check
compliance with standards. If the measurements have been
performed with their final use in mind, the final result will be
both accurate and useful.
ACKNOWLEDGMENT
The author would like to thank Randall Schlake of General
Electric Company, who developed some of the test procedures
described here, including the document shown in Fig. 12.
The author would also like to thank Louie Powell of General
Electric Company for his many helpful suggestions.
REFERENCES
,
I
I
I
Fig. 12. Example of a harmonic measurement data collection form.
should be reduced to an acceptable level in the final result.
VI. CONCLUSION
By careful selection of equipment and techniques, useful
harmonic measurements may be made in industrial power
systems.
The accuracy of the various portions of the measurement
system may be estimated as follows, in percentage of the
measured harmonic:
Instrument Transformers 0.1-1%
Current Probes
0.5-2%
5%
Harmonic Analyzer
Aliasing
0 - 3.6%
Windowing
1-1 %
Leakage
0-5%.
Overall measurement error should be on the order of 10%
of the harmonic magnitude. If a harmonic is measured which
is 0.3% of the fundamental, the overall accuracy required is
0.03%. The instrument accuracy should then be 0.015% of the
fundamental or better. The least expensive way to improve
accuracy is to use the spectrum analyzer function selections
wisely. Current probe selection is also of critical importance.
The use of probes not designed for use above 60 Hz can result
in far greater inaccuracies.
View publication stats
IEEE Recommended Practices and Requirements for Harmonic Control
in Electrical Power Systems, IEEE Standard 519-1992, 1993.
D. A. Douglas, “Current transformer accuracy with asymmetric and
high frequency fault currents,” IEEE Trans. Power Apparatus and Syst.,
vol. 100, no. 3, pp. 1006-1011, March 1981.
-,
“Voltage transformer accuracy at 60 Hz voltages above and
below rating and at frequencies above 60 Hz,” IEEE Trans. Power
Apparatus and Syst., vol. 100, no. 3, pp. 1370-1375, March 1981.
ABC’s of Probes, Tektronix, Inc., Beaverton, OR, 1989.
J. K. Winn, Jr. and D. R.Crow, “Harmonic measurements using a digital
storage oscilloscope,” IEEE Trans. Ind. Applicat., vol. 25, no. 4, pp.
783-788, July/Aug. 1989.
Dick Benson, Techniquesfor Signal and System Analysis, PN 363-010001, Tektronix, Inc., Beaverton, OR, 1991.
The Fundamentals of Signal Analysis, Application Note 243, HewlettPackard, Palo Alto, CA, 1985.
F. J. Harris, “On the use of windows for harmonic analysis with the
discrete Fourier transform,” in Proc. IEEE, vol. 66, no. 1, pp. 51-83.
Jan. 1978.
W. T. Cochran and J. W. Cooley, “What is the fast Fourier transform?“
in Proc. IEEE, vol. 55, no. 10, pp. 1664-1674, Oct. 1967.
“Fundamentals of sampled data systems,” in Application Note AN-282,
Applications Reference Manual, Analog Devices, Inc., Norwood, MA,
1993.
Peter E. Sutherland (M’83) received the A S .
degree in electrical engineering technology in 1979
and the B.S. degree in electrical engineering in
1983 from the University of Maine, Orono. In
1986, he received the M.Sc.E. degree in electrical
engineering from the University of New Brunswick,
Canada.
He has worked as a Test Engineer and a Disign Engineer for Accutest Corporation, Chelmsford, MA, a manufacturer of automatic test equipment for the semiconductor industry. For a short
time, he worked as a Planning Engineer for an electric utility company.
In 1987, he joined General Electric Company, and has been employed
as an Engineer in the Industrial Power Systems Engineering Operation,
Schenectady, NY, as an instructor in the Training and Development Center,
and as a Power Systems Engineer in Albany, NY. He is currently enrolled
as a part-time student In the Ph.D. program in electric power engineenng at
Rensselaer Polytechnic Institute, Troy, NY.
Mr. Sutherland is a member of Eta Kappa Nu and Tau Beta Pi. He is a
Registered Professional Engineer in Maine and New York.