HARMONIC ANALYSIS OF [NDUSTRIAL POWER SYSTEMS

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.

INTRODlJCTlON

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

frequency.

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 519 AND ITS IMPACT ON THE INDUSTRIAL

POWER CONSUMER

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

116

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

where.

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

HARMONlCS PRODUCEBY V A R l A m

FRE 0 I J EN C Y DRIVES

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

KEY ELEMENTS IN HARMONIC MODEL=

ANALYSIS

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

above.

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

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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

loads.

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

resonance.

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

currents.

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

elements.

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

interference.

CASE STUDY - PAPER MILL - APPLICATION OF

LARGE HORSEPOWER MEDIUM VOLTAGE DRIVE

Backmound

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

operation.

Results

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

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12th harmonics were causing amplification of the nearby

harmonics.

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

PLANT POWER FACTOR CORRECTION STRATEGIES

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

SUB I 4

41s-E64 I

FIGURE I: POWER SYSTEM MODEL

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

capacitors.

CONCLUSIONS

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

119

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.

REFERENCES

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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