Harmonic analysis

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Robert Ellis, P Eng , Member, IEEE
Allen-Bradley Canada Ltd
135 Diindas Street
Cambridge, Ontario
NI R 5x1
:lbstmcl- When large harmonic producing loads are added to
an industrial plant power system it is good engineering practice
to analyze the impact on the power system by performing
harmonic modeling analysis of the system at the design stage.
Such a study can identify any potentially hannful resonances or
other harmonic levels that are predicted to be in excess of IEEE
5 19 recommended limits and suggest corrective measures (if
necessary). This paper discusses the impact of the harmonic
limits of IEEE 519-1992 on the: industrial power consumer and
addresses the differences between the 1992 and 1981 versions of
the standard. Harmonics produced by variable frequency drives
are discussed The data required to conduct a harmonic study,
the types of analyses that can be performed, and some of the
mitigating measures that can be taken to alleviate a potential
harmonic problem are detailed. A case study is presented basetd
on a typical paper mill where a large variable frequency drive
was added to the power system.
Power system harmonics is an area that is receiving a
great deal of attention recently This is primarily due to the fact
that non-line,ar loads are comprising a larger and larger portion
of the total connected load for a typical industrial plant. If
power factor correction capacitors are applied to a power systerm
the results coluld be disastrous in some instances without due
consideration to natural frequencies of the system and harmonic
producing loads. If a reso:nanc:e occurs there is a potential for
capacitor hsle blowing or premature equipment failure, or
transformer or motor overheatling.
Harmonics are a mathematical way of describing
distortion to a voltage or current waveform, are a continuous,
steady state phenomenon, and should not be confused with
spikes. surges or other forms of power system transients.
Fourier theory tells us thai. any repetetive waveform can be
esprcssed as the summation 01 a number of sinusoids of various
frequencies. Harmonics, by definition, are components of a
waleform which are integer multiples of the fundamental
to address harmonic concems prior to the addition of large
non-linear loads by performing harmonic modeling analysis.
IEEE 5 19- 1092, the major standard that governs harmonic
limits is also interpreted for the reader.
The: intent of this paper is to give an overview of how
IEEE Standard 519-1992 entitled "IEEE
Recommended Practices and Requirements for Harmonic
Control in Electric Power Systems" has been officially released
and put into effect. There have been some significant changes
made to this document since it was first published in I98 1. The
main emphasis i n these changes has been to establish an
approach to set harmonic limits on individual power consumers
that will result in reasonable harmonic voltage distortion on the
utility power system. An oveniew of the major changes to this
harmonic standard follows [ 11.
Response Characteristics." The section addresses. in some
detail, the factors that influencc the response of a power system
to harmonics. Some of the factors discussed arc: short circuit
capacity, capacitors, cables, system loads, system unbalances,
and parallel and series resonance. Some useful assumptions for
typical distribution, transmission. and industrial systems are
also outlined.
A separate section has been added that gives
information on the harmonics produced by sis pulse rectifiers,
arc furnaces, static VAR compensators, three phase inverters,
electronic phase control, cycloconverters. switch-mode power
supplies, and pulse-width modulated drives. The 198 1 standard
quoted typical harmonic magnitudes that were :;upposed to be
representative of any six-pulse converter. The 1992 standard
contains curves which take into account the impedance of the
power system and the amount of DC ripple in the current to
more accurately characterize the harmonic currents that will be
generated by particular converter on a given power system.
More information has been added regarding the effects
of harmonics on various types of equipment such as motors,
cables, capacitors, electronic equipment, metering, switchgear
and relays, telephones, and static converters.
The portion of IEEE-5 19 that has the most impact on
an industrial plant is the "Recommended Pract.ices for
Individual Consumers." Substantial changes have been made i n
this section compared to the 1981 version. IEEE 519-1981
stated 5% total harmonic distortion as a recommended limit for
voltage distortion on a general power system. 'The 198 1
standard did not recommend limits for individual consumers.
This left some gray areas between utility and consumer
responsibilities. The new version makes the responsibilities of
the individual consumer and the utility clearer The guiding
philosophy has not changed much in the 1992 standard in that
the goal is to limit voltage distortion at the point of common
coupling (PCC) to 5%. The PCC is generally defined as the
A new section has been created entitled "System
0-7803-2(p28-X-6/94 $4.00 Q 1994 IEEE
utilit!-/customer connection point. On a smaller scale, the PCC
within ;in industrial plant can tie used. for example, as an
artificial interface between mill di\.isions to address specific
concerns about harmonic distoilion.
The major difference in the recommended practices is
the introduction of current distortion limits. There are differenl
current distortion limits depending on which one of fi ~c
categories the particular power system falls; into. On the one
extreme of this spectrum is a power system that serves 1 or 2
large customers. The other end of the spcctrum is a power
systeni that sen'es many small custorners. Different current
distortion limits are assigned based on which category a
particular power system falls into. The idea behind this is to
allou individual power consumers their fair share of harnioiiic
current distortion while assuring that voltage distortion at the
PCC does not esceed 5% THD (barring a significant parallel
resonance at ;I harmonic frequency). The a~ctual basis for
categorizing a power system is the ratio of maximum short
circuit current to maximum demand load current at the PU' .
Rat10 =Isc/Il
Isc =maximum short-circuit current at PCC
11 =niawnum demand load current at PCC
Indi\.idual and total currelit harmonic distortion limits are
expressed as 21 percentage of thc maximum demand load current
(not the fundamental current of a particular harmonic
producing load) and is rcferrl:d to as total demand distortion
(TDD). Most large industrial power systems seem to fall into
the categor) that limits current distortion (TDD) to 5% with
additional, lower limits on individual harmonic currents. One
of the main factors that will decide whether the limits will be
esceeded is the relative current of the harmonic producing loads
i n comparison to the total load for the plant.
The harmonic current limits in thc tables of this
scction applj. for six-pulse rectifiers. The benefit of
implementing rectifiers wiih higher pulse numbers has been
recognimd and the limits have been relaxed on the
characteristic harmonics as. long as tlie non-characteristic
harmonics are 25% or less of ihe six-pulse limits. Using a
twelvc-pulse rectifier as an example. the lirnits on the 1 lth.
13th. 23rd. 25th. 35th. 37111, -17th. & 49th harmonics are
increased b), a factor of 1.414 This :issum(:s that the 5th. 7111,
17th. 19th. 29th. 1lst. -1lst. & 43rd harmonics do not esceed
25Y0 of the limits in the tables What this means is that a larger
twelve-pulse rectifier could be used compared to a six-pulse
rectifier v,hilc niaintaining thc limits specilied.
reached on the point of coninion coupling. The closer the PCC
is to the input terminals of the non-linear loads the more
difficult 11 uill beto nieet these reconiniendations without
adding cost to the installation of the system.
Befor-e applying 1EE:E 5 19 an agreement must be
The pulse number of the rectifier is the determining
factor in nhat the characteristic power system harmonics will be
for a pwticular tinkc The harrtionics produced by a six-pulse
rectifier will be the 5th, 7th, 11 th, 13th, 23rd. 25th. etc. Their
magnitudes are roughly the in\ erse of the harmonic order tinics
the magnitude of the hndamental (e.g., the 5th harmonic is
about one fifth of the fundamental current). A Iwelvc-pulse
drive will exhibit harmonics at the 1 ltli. 13th. 2.3rd. 25th. etc.
Twelve-pulse drives will produce small amount:; of 5th. 7th.
17th. and 19th harmonics (typically on the order of 10 perccnt
of the levels for a six-pulse drive).
the inverter to the motor. These harmonics are typically
multiples of the inverter operating frequency (not the power
supply frequency) but no generalization can be made about their
magnitude since this varies greatly with the typc of drive and
the switching algorithm for the inverter semiconductors.
and the output waveforms. Interharnionics do rlot f i t tlie
classical definition of harmonics since they are not strictly
integer multiples of the fundamental frequency, Intcrliarnionics
can be a result of rectifier harmonics showing up on the output
or inverter harmonics appearing at the input. Harmonics can
occur on the input that are at the pouer system frequency plus
or minus the inverter operating frequency but are normally
small i n magnitude. The inverter output can contain harmonics
that are the rectifier pulse number tinies the power sj stem
frequency plus or minus the inverter operating frequency anid
can be significant in magnitude. These output interharmonics
are related to the ripple in the DC link current c'r voltage
Drives also produce harmonic currents on the output of
Some interharmonics may also be prescnt in the input
Comuonents which need to be included in the model
All but the simplest of power systems will require a
computer simulation program to perform a ineaiiingful
harmonic study in a reasonable amount of time. Most
information that is required to model an industrial plant power
system is available from the overall one-line diagram for the
system 12],[3].
equivalent (i.e., short circuit MVA, and per unil 60 Hz
inductance, and resistance). I t is generally sufficient to iissunie
that the harmonic impedance of the utility systein will be the
harmonic number times the furidamental impedmce and that
the X/R ratio of the system is constant for all frt,quencies. I n
some cases, the utility may have measured and documented the
impedance of the power systemat a number of frequencies
which is referred to as the harnioiiic envelope. 'The utility's
harmonic envelope should be used when available instead of
making assumptions about the harmonic imped;inces as stated
All power factor correction capacitors must be incl~uded
in the model. This applies to large capacitor baitlks applied to a
bus as well as capacitors that are switched with individual
motors. Capacitors in combination with the sys'leminductance
will determine the resonant frequencies of the system.
from tlie nameplate. The actual X / R ratio of tlir: transformer
should be used if readily available. An X/ R rati3 of 10 can Ibe
assumed for most distribution transformers if th.: actual ratilo is
The utility should be modeled as its short-circuit
Transformers are modeled using percentage impedance
not available. The resistance of a transformer will change with
frequency and often the X/ R ratio is assumed to be constant as
frequency changes for the purposes of harmonic modeling. The
winding connection configuration (delta or wye) should also be
taken into account since a 30 degree phase shift will occur
between delta and sqe windings.
Cable impedances within a plant are not usually
significant for harmonic modeling purposes. Cables will have
the effect of slightly dampening the system response at or near a
resonant frequency. Analyzing ithesystem without modeling
the cables is the worst case. It is usually not practical or
worthwhile to collect data on exact lengths and sizes of all
cables in the system.
Significant motor loads, should be modeled by their
subtransient reactance which cainbe approximated based on
locked rotor current if reactance is not readily available. Large
motors should be modeled individually while smaller motors
may be lumped together as a single impedance. Motors have
the effect of raising the parallel resonant frequency of the power
system since the inductance is in parallel with the system
inductance and tlie resonant frequency is inversely proportional
to the system inductance.
multiple current sources (one for each characteristic harmonic
frequency). As mentioned previ,ously, IEEE 5 19 contains some
very useful information to deterimine analytically the harmonic
currents generated by a number of different types of non-linear
inductive and resistive component. The inductive component of
the load will have the effect of raising the natural frequency of
the system. The resistive component will lower the peak of a
Harmonic producing loads are generally modeled as
Other loads on the system should be modeled as an
Types o f analyses which can be performed
Voltape and current distortiianalvsis
The computer mocleling software used must be able to
provide predicted total harrnonic distortion of voltage and
current for each bus or branch of the system. The calculations
are usually performed by creating a system of “n“ equations of
‘‘n’’ unknowns, applying Ohm’s and Kirchoff s Laws, and using
sparse matrix techniques to sol\.e for the unknown voltages and
compared to the recommended practices of IEEE 5 19. A high
distortion levcl in a particular portion of the system may
indicate a resonance condition. The software package should
also calculate the magnitude of individual voltage and current
harmonics. Analysis of individual harmonics can help in
predicting a resonance pricir to energizing the system.
The voltage and current distortion figures can be
Impedance ainalpsis
Impedance versus frequencj for each bus of the system
in a tabular and/or graphical format IS another useful feature in
a modeling system. A self impedance plot gives a quick visual
indication of the natural frequencies at a specific bus. A peak in
the impedance plot indicates a parallel resonant frequency and a
valley indicates a series resonant frequency.
The effect of a parallel resonance is to amplifq one or
more current harmonics if they fall at or near a natural
frequency of the system. Similarly, a series resotrance can cause
amplification of harmonic voltages. The height of the peak or
depth of the valley gives an indication of the expccted
amplification of a harmonic that is close to a resonant
frequency. The resistive impedances i n the system \+i l l
deterniine the amount of amplification that OCCUI’S i n ii
resonant condition. The greater the amount of resistance. the
lower the amplification of the harmonics. Therefore. i f analysis
of harmonic amplification is of great importance in the study,
particular attention should be paid to accurately iinodel resistive
Telephone Influence (I. T produca
In some cases it may be beneficial to have ;in
indication of the expected level of telephone influence in the
branch of the system that connects to the utilitl. Telephone
interference is not generally a problem within a plant ;I long as
appropriate segregation of wiring classes is impleniented.
Telephone influence can occur where there are Icing, parallel
runs of utility power cables and telephone cables The most
common way to express telephone interference is the I T
product. The 1.T product takes into account the rms value of
each injected harmonic current as well as a weighting factor for
each frequency since certain frequencies 1iaL.ea greater effect on
telephone circuits than others. IEEE 5 19 contains some rough
guidelines on 1.T levels that are likely or not likcly to cause
A harmonic modeling study was performed i n
conjunction with the addition of a 1250HP, 2300V. medium
voltage. variable frequency drive system. The utilit) feed to the
mill was at 69KV and the main transformer for the system was
20 MVA. The primary elements in the power s>.stein model
were transformers, large induction motors, power factor
correction capacitors, and the drive as a harmonic current
source (see Fig. 1). For the purposes of the stud) i t was assumed
that all motors operated continuously. and simultaneously. I n
reality, there niay be times when only some of the motors are in
Most of the predicted harmonic levels’ were within the
recommendations of IEEE 5 19 except for tlie vciltage distortion
at Bus 8 (Fig. 1) which was expected to be about G.8?4, THD.
After reviewing the impedance plot for Bus 8 and re\iewing the
individual harmonic levels for this portion of the system i t was
apparent that resonances were at the root of tlie excessive
voltage distortion. The 7th. 1 Ith. and 13th harmonic currents
were predicted to be higher in this branch of thc system than the
levels produced at the input to the drive. I t was evident from
the impedance plot that parallel resonances around the 8th and
12th harmonics were causing amplification of the nearby
combination of the system inductance and the 4.8 MVar
capacitor bank on the 12.47 KV bus. The 12th harmonic
resonance was due to the system inductance in parallel with the
550 KVar power factor correction capacitors on Bus 8. The
capacitance on this bus actually consisted of 2-250 KVar
capacitors and 1-50 KVar capacitor switched with 3 different
motors that added up to 2750 HP. Some analysis was done to
investigate the effect removing the capacitors on this bus. With
the 550 KVar of capacitance omitted from the power system
model the voltage distortion at Bus 8 was predicted to be3.9%.
Th~s represented a significant improvement over the 6.8%
distortion expected with the capacitors in the circuit. It was
also noted that harmonic levels at most other busses in the
system were predcted to decline. The recommendation was
made to disconnect the capacitors from the three induction
The 8th harmonic resonance was due to the parallel
There are tradeoffs in planning a power system for
acceptable power factor while avoiding harmonic resonance
problems [4]. If a single large capacitor bank is implemented at
the main bus on the system the number of resonances is
minimized but if a resonance does occur near a harmonic
frequency, the amplification can be lugh since there is very little
resistance to provide dampening. If multiple capacitors are
switched with individual motors, then power system natural
frequencies will constantly bechanging, malung it d~fEicult to
analyze a harmonic problem if one should occur. The
resistance between the individual capacitors and the system
inductance will be lugher, however, which means that less
harmonic amplification would occur compared to using a
single, larger capacitor bank on an upstream bus. A tlurd
possible power factor correction strategy would be to implement
tuned capacitors. By adding a reactor in series with the
41s-E64 I
motor starters in question. The customer decided that the
benefit of avoiding possible harmonic resonance problems
outweighed the drawback of losing a small portion of the plant
power factor correction and disconnected these capacitors.
Harmonic filtering is another option that could have been
considered in this case. Adding one or more series LC filter
legs at the input to the drive would limit the amount of
harmonic current injected back into the power system. The
filter would also provide some power factor correction. A
medium voltage vacuum contactor would be necessary to switch
the filter with starting or stopping of the dnve so that a leading
power factor would not occuf with the drive energzed but not
running. The benefit of improving the power factor would
have to be weighed against the cost of designing and
manufacturing a filter.
power system since the addition of this medium voltage drive.
The drive has been in operation for about two years.
It is difficult to perform analysis of every possible
resonant condition on a system such as this because of thefact
that a new set of resonances OCCUT every time an induction
No harmonic related problems have arisen on the
capacitor, the bank may be tuned to a specific frequency
(typically just below the first si gdi cant harmonic frequency).
This approach has the benefits of nailing down the resonant
frequencies in the system where no harm can be done as well as
providing some harmonic filtering effect. Where: synchronous
generators or motors are present in the plant it is sometimes
feasible to correct the plant power factor without the use of
Harmonics is an issue that is not going i o go away any
time in the near future. IEEE 5 19-1992 imposes more rigid
harmonic limitations than in the past. Although the likelihood
of harmonic problems is low, the instances in wbch they do
occur can result in reducing the reliability of the power system
and potentially affect plant output. When adding large non-
linear loads to a power system, performing analysis up front
may reduce any surprises during commissioning.
was presented that allows one to determine at the design stage if
An approach to harmonic modeling of a power system
motodpower factor correction capacitor is switched on or off, hannonic mitigation techmques may be required to avoid a
resonance or keep harmonic levels within those imposed by the
utility and/or IEEE 5 19.
A case study was presented that gives an example of
hartnonic modeling and one approach to harmonic reduction
Alternative plant power factor correction strategies
were presented with their pros and cons. I t is not feasible to
single out one strategy as being superior in all cases.
LUDBROOK, A., "IEEE Standard 5 19, Its Effect on Equipment
Manufacturers, Users, and Utilities", Canadian ElectriciQ
Forum, I9913Power QualityA'ower Harmonics Forum, Toronto.
DEWINTER F.D.. "A Practical Approach to Solving Large
Drive Harnionic Problems at the Design Stage", IEEE Paper
NO. PCIC-89-42 (1989).
HUNEAULT, DR. M.. "Comiputer Methods for Harmonic
Analysis". ~Canadian Electricity Forum. 1993 Power
QualityPower Harmonics Forum, Toronto.
LOWENSTEIN, M.Z., "Improving Power Factor in the
Presence of Harmonics IJ sing Low-Voltage Tuned Filters",
IEEE Transactions on Induslry Applications, (May/J une 1993).

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