Harmonic Sources

7/29/2019 Harmonic Sources

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A short note on Harmonics in Power Systems, EDSA 2001

HARMONIC SOURCES

Fundamental causes for harmonic generation

Distortion due to magnetic saturation of materials Geometric configuration of electric machines

Repeated, periodic switching in electrical circuits

More specifically:

Electric Machines- Generators- Motors

Transmission and Distribution

- Transformers- HVDC converters- Static VAR compensators

Industrial Equipment- AC/DC- AC/AC, cycloconverters- Switching controls- Arc furnaces, arc welding

Residential and Commercial Equipment- Diode rectifier circuits- Thyristor controlled loads


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HARMONIC CONTENT

Any periodic signal can be seen as a sum of sines and cosines at frequenciesthat are multiples of the fundamental frequency:

s(t) =n

n M

=

=

1[ Ancos(nwot) + Bnsin(nwot) ]

where:wo is the fundamental frequency

An, Bn are coefficients (to be determined)t is time

If s(t) is an EVEN function, then only COSINE terms appear. If in addition s(t) = -s(T0/2 - t), then only ODD HARMONICS are present. That is often the case inpower systems.

HARMONIC GENERATION IN HVDC CONVERTERS

CHARACTERISTIC HARMONICS

The switching of thyristors "p" times per cycle generates harmonic currents:

AC Side:frequencies: f(k) = fo(k.p 1)magnitudes: I(k) = 1/k

DC Side:frequencies: f(k) = fo.k.p

magnitudes: I(k) 1/k2 for small firing angleI(k) 1/k for large firing angle

NON-CHARACTERISTIC HARMONICS

Non-characteristic harmonics are generated by unbalances, time lags inswitching, and persistent variations in firing angle. They are small compared to

the characteristic harmonics.

HARMONIC GENERATION IN STATIC VAR COMPENSATORS, FREQUENCYCONVERTERS AND RECTIFIERS

The static VAR compensator is a thyristor-controlled variable reactance. Thefrequency converter is also a power electronic device that generates highfrequency power signals (typically 400 Hz) from a fundamental-frequency


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source. A diode-bridge rectifier is similar to a HVDC converter, except that thefiring angle control of the thyristor is removed. Although these device's functionsand switching processes differ from those of the HVDC converter, their harmonicgeneration (AC side) is similar.

HARMONICS GENERATED BY CYCLOCONVERTERS

This is a frequency converter that generates low frequency power signals from afundamental-frequency source. It is used typically in variable-speed AC motordrives.

CHARACTERISTIC HARMONICS

Harmonics of the fundamental frequency are similar to those of the HVDCconverter. In addition, harmonics of the low-frequency signal are produced:

frequencies: f(k) = fi(k.p 1) + 2.fo.kmagnitudes: I(k): both components proportional to 1/k

COMMENT: The harmonic generation of a cycloconverter is difficult to predictbecause of its variable output frequency.

HARMONIC GENERATION IN ARC FURNACES

Harmonics are generated because of delays in arc ignition and because of thehighly nonlinear V-I characteristic of both the arc and the melting material. Thepower spectrum of the voltage and current signals vary widely depending on theprocess. Typically harmonics are superimposed on a continuous backgroundspectrum. The frequencies vary randomly, but they are usually clustered in arange of 0.1 to 30 Hz around each harmonic.

HARMONIC GENERATION IN RESIDENTIAL AND COMMERCIALEQUIPMENT

As in all consumer equipment, power consumption is low, but the cumulativeeffects of widespread use can result in significant harmonic generation.

DIODE RECTIFIER CIRCUITS: These are used as DC sources in consumerelectronics goods. In particular computers and television sets contribute to oddand even-ordered harmonics.

THYRISTOR CONTROLLED LOADS: These controls are found in variousdevices, such as light dimmers, heat controllers, etc.


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GAS DISCHARGE LAMPS: Ballasts (transformers) and the highly nonlinearcharacteristics of fluorescent lamps generate harmonics:

triple harmonics generated in particular by the ballast odd and even order harmonics are generated

resonance conditions can occur between ballasts and power factorcorrecting capacitors in long lighting circuits.

EFFECTS OF HARMONICS

The presence of harmonic currents and voltages degrades the systemperformance in various ways.

LONG TERM EFFECTS

electromagnetic effects:o

hysterisis and eddy current losseso skin effecto inductive interferenceo interferes with the operation of control, protection,o electronic and communication equipment

degrades dielectrics prematurelyo high frequency effectso increase in peak voltageo increased copper losses and heating, reduced efficiency

INSTANTANEOUS EFFECTS

contributes to voltage drops on weak systems results in false measurements resonance conditions can cause failures, malfunctions or can force downgraded operation.

EFFECTS OF HARMONICS ON ROTATING MACHINES

For both synchronous and induction machines, the main problems causes byharmonics are:

increased iron and copper losses, heating and reduced efficiency the introduction of oscillating motor torques (usually small) increased noise level


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EFFECTS OF HARMONICS ON TRANSFORMERS

The main problems associated with harmonics are

increased iron and copper losses, heating and reduced efficiency

further distortion of waveforms increased stress on insulation formation of hot spots in the tank circulation of excessive triplen currents in delta windings

EFFECTS OF HARMONICS ON CAPACITOR BANKS, LINES AND CABLES


increased losses and heating degradation of the dielectric, in capacitor banks and cables

appearance of corona due to higher peak voltages corrosion in aluminum cables due to DC currents.

EFFECT OF HARMONICS ON CONVERTER EQUIPMENT


current switching causes notches in voltage waveforms, which may affectthe synchronizing of other converter equipment.

voltage notching causes misfiring of thyristors harmonic voltages can cause the firing of gating circuits at other than the

required instants

EFFECTS OF HARMONICS ON THE SYSTEM AS A WHOLE PROBLEM

The presence of capacitors in a system made up predominantly of inductivepower apparatus can and often does result in resonance conditions.

Harmonic currents can be forced through high impedance networks resulting inover voltages, or harmonic voltages can be fed into low impedance networks,resulting in high currents.

This can contribute to the degradation of network elements or to persistent fuseblowing.

EFFECTS OF HARMONICS ON PROTECTIVE RELAYS

Protective devices are usually designed to act upon information contained insignals at fundamental frequency. Electromechanical relays filter out many of thehigher order harmonics, and so are immune to their effects.


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Waveform distortions caused by lower order harmonics can have detrimentaleffects.

General conclusions on the effects of harmonics:

relays exhibit a tendency to operate slower and/or at higher pickup values. over current, over voltage and under frequency relays are susceptible to

substantial changes in operating characteristics distance relaying can be difficult without filtering relaying intelligence based

on crest values or zero crossing can be degraded by excessive harmonic content. Under normal conditions however, with low harmonic magnitudes, improper

operation is unlikely.

EFFECTS OF HARMONICS ON SWITCHGEAR

Besides the additional losses and heating, effects on circuit interruption areunclear at this point.

EFFECTS OF HARMONICS ON METERING

Most metering devices are calibrated on pure sinusoidal currents. Subsequently,distorted waveforms lead to errors.

ELECTROMAGNETIC DEVICES

o Effects vary greatly from one device to anther.o Devices exhibit uneven frequency responses.o DC and harmonics degrade the ability of the meter to measure

fundamental power.o It appears that harmonics cause high readings.

SOLID STATE DEVICESo Solid-state meters have a filtering capability, and can measure

power irrespective of waveform.

EFFECTS OF HARMONICS ON RESIDENTIAL AND COMMERCIALEQUIPMENT

Here are the effects on some important types of equipment:

Computers: sensitive to threshold voltages of digital circuits. Manufacturersimpose limits on supply-voltage harmonic distortion.

Television: Distorted waveforms cause fluctuations in TV picture size andbrightness.


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Converters (rectifiers, inverters, etc.) are sensitive to voltage distortion andzero crossings.

Fluorescent and mercury arc lighting: a harmonic voltage can excite thelamps resonant frequency.

EFFECTS OF HARMONICS ON COMMUNICATIONS

The presence of transmission lines in close proximity to telephone lines causesinterference on the telephone signal. Fundamental frequency noise is barelytransmitted, but noise due to harmonic frequencies can seriously degrade thetransmitted information.

The important factors are:

Power system: content of audio frequency harmonics, their relativemagnitudes and the degree of unbalance of the phases.

Coupling between power and communication circuits.

o loop inductiono longitudinal electromagnetic inductiono longitudinal electrostatic inductiono conduction

Electrical characteristics of the communication circuit (susceptive ness).

o response to different interfering frequencieso balance of the communication circuito shielding effects of cable sheaths

HARMONIC MEASUREMENT AND ANALYSIS

High fidelity measurement of signals is essential for the analysis and control ofharmonic pollution. Measurement equipment is required for two specific tasks:

Monitoring levels of harmonic distortiono in voltageo in current

Measuring the harmonic impedance of a network

Analysis of the recorded signals then allows extracting harmonic information.This can be achieved using analog or digital instruments:

Analog, filters


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Digital, discrete Fourier transform (DFT) and fast Fourier transform (FFT)

HARMONIC MEASUREMENT

Harmonic measurements require high fidelity probes, transducers, etc. over therange of desired frequency measurement (typically, up to 3 kHz).

A good measure of the fidelity of a measuring device is its frequency response.Ideal conditions:

Linear response over its entire range Constant gain No phase shift

In practice, non-ideal characteristics of a measurement device can be

compensated.

HARMONIC MEASUREMENT - CURRENT TRANSFORMERS

The most common type of current transformer is the toroidally wound transformerwith ferromagnetic core.

Characteristics:

Usually have a single turn on the primary Low leakage impedance Low primary winding resistance Operates in linear portion of magnetization curve Models with an air gap maintain linearity over a wide range Limitations in frequency response determined by inter-turn, inter-winding

and stray capacitance Present CT's can measure up to the 50th harmonic without distortion

HARMONIC MEASUREMENTS - VOLTAGE TRANSFORMERS

Voltage transformers can be connected directly to low voltage distribution circuits(up to 12 kV). Cascaded transformers or voltage dividers are required at highervoltages.

VOLTAGE TRANSFORMER

Characteristics:

Limitations in frequency response determined mostly by inter-turn, interwinding and stray capacitance, which are more important than in CTs.


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Linear response can often be obtained up to 1 kHz. The precise response is dependent on the burden.

VOLTAGE DIVIDERS TYPES

Resistive divider: frequency response is influenced by stray capacitance andskin effect. Improvements are possible to some extent by providing anearthen screen around the device, parallel capacitors.

Capacitive divider: better frequency response, but is subject to ringing. Lowvoltage capacitor is screened and resistors are placed in parallel withcapacitors.

Capacitive divider with amplifier: The amplifier acts as a buffer circuit,providing a fixed burden to the divider on one side and to the communicationlink or PT on the other.

Series RC divider: A resistance is part of the divider stack.

HARMONIC MEASUREMENTS - DATA TRANSMISSION

Measured signals are usually transmitted from the instrumentation site to acontrol room through a noisy environment. Precautions must be taken to protectthis information. Ideas:

encoded data digitized data isolation amplifiers coaxial cables optical fiber links shielding:

o electrostatic: earthen screen, guard circuito electromagnetic: magnetic shield, careful design

HARMONIC ANALYSIS

Signal processing instruments are available to extract harmonic information fromrecorded power system signals. Although both analog and digital processingmethods are presently available, digital methods are now recommended, forflexibility, ease of use, extended features and cost.

ANALOG INSTRUMENTS, such as filters DIGITAL INSTRUMENTS, based on the FFT implementation of the discrete

Fourier transform (DFT).


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HARMONIC ANALYSIS - FEATURES OF A GOOD ANALYZER

Here are some of the main features in a digital harmonic analyzer presentlyavailable:

measures harmonic components up to the 50th harmonic (3kHz) simultaneously samples 7 or more input channels:

high resolution A/D conversion calculations:

o power and harmonic powero RMS voltage and currento THD and IT producto Telephone Interference Factor (TIF)

system impedance (magnitude and phase) at harmonic frequencies real-time or deferred time analysis with programmable sampling and time

windows

output of waveforms or frequency spectra in graphical or tabular form data storage facility user friendly, convenient, easy to set up, portable

LIMITATIONS ON HARMONIC CONTENT

Three criteria are emphasized for setting standards:

To protect equipment against harmful over voltages, limits are set on both:

o total harmonic distortion of voltageo individual voltage harmonics

To limit current injections and subsequent propagation into the network,limits are set on both:

total harmonic distortion of current

o individual current harmonics

Restrictions on both harmonic voltages and currents, as a function ofdevice ratings


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STANDARDS FOR LIMITATION OF HARMONICS

There are 2 broad categories of national standards:

1) Sets voltage/current distortion levels at the power system/customer interface

without setting allowable limits for individual consumers.

- limits on harmonic voltage only, Country: U.S.A- limits on both harmonic voltage and current, Countries:- U.K. and Australia

2) Sets voltage/current distortion levels at the power system/customer interfaceand sets allowable limits for individual consumers as a function of loading.

- limits on harmonic voltages only, Countries: France, Sweden,Switzerland

- limits on harmonic currents only, Country: Netherlands- limits on both harmonic voltage and current, Countries: Finland,Germany

Conditions specified in the various standards usually reflect concerns proper toconditions in that country.

RESTRICTIONS ON TOTAL HARMONIC CONTENT TAKEN FROMSTANDARDS

USA:- THD limited to 5% at voltages from 2.4 to 69 kV

1.5% at voltages of 115 kV and up

UK:- THD limited to 5% at voltages of 415 V and less

4% at voltages of 6.6 and 11 kV3% at voltages of 33 and 66 kV

1.5% at 132 kV

SWEDEN:- THD limited to 4% at voltages of 430 V and less

3% at voltages between 3.3 and 24 kV2% at voltages between 33 and 72 kV1% at voltages beyond 84 kV

IN GENERAL:The highest permissible THD is of the order of 5% at low voltage levels and 1%at high voltage levels.


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RESTRICTIONS ON INDIVIDUAL HARMONIC CONTENT TAKEN FROMSTANDARDS

Here are some examples of limitations on individual voltage harmonic content:

UK: - Vn/V1 at common coupling point limited to4% (odd) and 2% (even) at 415 V3% (odd) and 1.75% (even) at 6.6 - 11 kV2% (odd) and 1% (even) at 33 - 66 kV1% (odd) and .5% (even) at 132 kV

GERMANY:- Vn/V1 at common coupling point limited to

5% for 5th

and 7th

harmonics3% for 11th and 13th harmonics

decreases to 1% at 100

th

harmonic according to a defining curve.

RESTRICTIONS ON HARMONIC CURRENTS FOR ANY ONE CUSTOMER

Such restrictions exist in the UK and the Netherlands. Again in the UK, limits areset for the different voltage levels. For example, at 415 V:

Harmonic RMS Current in Amps

2 483 344 22

5 566 1119 6

RECOMMENDATIONS MADE FOR STANDARDS

Here is a summary of recommendations in a paper by Dr. A.M. Sharaf made atthe second International Conference on Harmonics in Power Systems:

Limitations on THDv and individual Vn, odd and even harmonics

Limitations on THDi and individual In, odd and even harmonics Limitations on IT and possibly KVT Limitations on voltage pulsations and notching Equal allocation of permissible harmonic limits per customer whether large or

small Three voltage levels: transmission, distribution and utilization Limited access to the network of large nonlinear loads Limited access to the network of devices generating even harmonics


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Distinction between steady state and transient harmonics Standard harmonic measurements are proposed Maximum rating of industrial converters based on short circuit level

MITIGATION TECHNIQUES TO REDUCE HARMONIC CONTENT

Here is a partial list of solutions to reduce the harmful effects of harmonics. Eachsolution is particular to a given problem, and cannot be considered general.

Relocation of capacitor banks Reconfigure 3-phase transformer Transposition of conductors to reduce inductive effects Improve grounding Neutral reactor Filters

Phase reversal Single phase vs. 3-phase Geographic separation Improved insulation Reducing fault current Balancing 3-phase operation Shielding


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Harmonics Analysis Techniques

Harmonic analysis is required when devices that generate harmonics, such asrectifiers, arc furnaces, AC/DC drives etc, are present or anticipated to be addedto the power system. Frequent failure of power system components may also

justify the undertaking of harmonic studies. Another important reason may be toarrive at harmonic filter specifications. The response of an electric power systemto harmonics can be studied by any of the following techniques:

Hand-Calculations: Manual calculations are restricted to small-size networkssince it is not only very tedious but quite susceptible to errors as well.

Transient Network Analyzer (TNA): TNA is also restricted to rather smallnetwork sizes because it is, generally found to be expensive and timeconsuming.

Field measurements: Harmonic measurements are often used to determinethe level of harmonic pollution of the power system. It is widely recognized,

however, that undertaking harmonic measurements in a systematic fashion,can be quite expensive and time consuming. Harmonic measurements,although quite useful in many cases, can be of limited validity because theyreflect only the system topology they have been taken at. Moreover,measurements can be in error due to inaccuracies of measuring instrumentsor erroneous utilization. Field measurements are used effectively to validateand refine system modeling for digital simulations.

Digital simulation: Digital computer simulation is the most convenient, andperhaps more economical, way of tackling the problem of harmonic analysis.The reason is that the advent of computer technology has made availablequite sophisticated computer programs featuring a large array of systemcomponent models to be used in a variety of cases. Computer simulations,are centered on system-wide approaches utilizing the notions of systemimpedance and/or admittance matrices, backed by elegant and powerfulnumerical calculation techniques.

Power System Components Modeling

Harmonic modeling differ somewhat from the system modeling as far as short-circuit, load flow and transient stability studies are concerned. The reason is thatthe behavior of the system equipment must be predicted for frequencies wellabove the fundamental. This section summarizes system modeling for harmonicanalysis.

Generator Model: Generators of relatively modern make produce no harmonicvoltages, therefore they can be represented by shunt impedance connected toground. A reactance derived from either sub-transient or negative sequencereactances is often used (both having similar values). Impedance measurementsfor small units agree to within 15% as compared with that of the sub-transientimpedance. In the absence of a better model, and until more results are reported,


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a series RL circuit representing the sub-transient reactance with X/R ratioranging between 15-50 can be used. However, the generator resistance shouldbe corrected due to skin effect. The following equation is suggested:

R = Rdc ( 1.0 + A hB

)

where Rdc is the armature DC resistance and h is the harmonic order.Coefficients A and B have typical values of 0.1 and 1.5 respectively.

Transformer Model: an ideal transformer in series with the nominal leakageimpedance can model a transformer. The leakage reactance varies linearly withfrequency but proper resistance modeling must account for skin effect. A similarexpression to the one used for the generator resistance can be used. Manyvariants for the transformer leakage impedance are recommended by CIGRE.More complex models, recommend considering the inter-winding transformercapacitances. These models are very complex, cumbersome, data intensive, and

have questionable practical value for the range of frequently considered powersystem harmonics.

Induction Motor Model: A model for an induction consists of stator impedance,a magnetization shunt branch and the rotor impedances. Motor slip is a functionof harmonic order and varies as follows:

Sh = ( h 1 ) / h

where Sh is the harmonic slip. At higher frequencies, harmonic slip approachesunity. If the magnetization impedance is ignored, one can model an inductionmotor by its locked-rotor impedance only. Despite the fact that this is still a verypopular model, it very often pays to consider the complete motor model.

Load Model: Various models have been proposed for the representation of loadsfor harmonic studies. Since these loads, may consist of several load types (static,rotating, solid state etc), different models have been devised to cater forindividual load components as compared to the ones meant to addressaggregate models. In general, a model derived from the active and reactivepower consumed can be represented by a parallel or series combination of aresistance and a reactance. This model is, almost invariably, used for static loadrepresentation.

Transmission line and Cable Models: A short line or cable can be represented

by a series RL circuit reflecting the line series resistance and reactance. Theresistance must be corrected to take into account skin effect for higherfrequencies. For longer lines, modeling of the line shunt capacitance becomesnecessary. The distributed parameter model is an adequate model to usebecause the line length notion is dependent on the frequency the line is studiedat. The following approximate formula for skin effect can be used:

R = Rdc ( 0.035 X2

+ 0.938 ) for X < 2.4


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R = Rdc ( 0.35 X + 0.3 ) for X >= 2.4

where X = 0.001585 ( f/Rdc ) and f is frequency in Hertz and Rdc inOhms/Miles.

Filter Models: Filters, by definition, exhibit small impedances at tunedfrequencies. At the fundamental frequency their impedance is mostly ofcapacitive nature, thereby supplying reactive power to electrical network. Manytypes of filters are applied in power systems, for different purposes. Filters , mostcommonly used for harmonic mitigation, are illustrated in figure 1. A single-tunedfilter has an impedance characteristic shown in figure 2, and is used to suppressa specific harmonic. A double-tuned filter basically consists of two single-tunedones, but, arranged in an equivalent circuit to reduce their physical dimensions.High pass filters can be of first, second or third order. The second order is widelyused. A more recent type of high pass filter, called C-type filter, is becomingpopular due to its smaller losses at the fundamental frequency. Impedance plots

of second order and a C-type filter are shown in figures 3 and 4 respectively.Application of filters is one of the commonly employed solutions to limit theeffects of harmonics. Other remedial measures such as moving the disturbingloads to a higher voltage levels, reinforcing the system and detune capacitors areoften used. In any case, economics will dictate the most appropriate solution.Recent studies, advocate the utilization of active filtering in an effort to counterthe injected harmonics. These techniques, however, are still in the researchstage and have not yet attained neither maturity nor industry wide acceptance.


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Figure 1: Harmonic Filters

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00

Freq(PU)

0.00

3.00

6.00

9.00

12.0

15.0

18.0

21.0

24.0

27.0

30.0 Z Ohm

1

1

1:5-TH HARMONIC SINGLE TUNED FILTER

IMPEDANCE PLOT FOR SINGLE TUNED FILTER

Figure 2: Impedance Plot for single tuned filter


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1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00

Freq(PU)

0.00

3.00

6.00

9.00

12.0

15.0

18.0

21.0

24.0

27.0

30.0 Z Ohm

1

1

1:5-TH HARMONIC HIGH-PASS FILTER

IMPEDANCE PLOT FOR HIGH-PASS FILTER

Figure 3: Impedance Plot for High-pass filter

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00

Freq(PU)

0.00

3.00

6.00

9.00

12.0

15.0

18.0

21.0

24.0

27.0

30.0 Z Ohm

1

1

1:5-TH HARMONIC C-TYPE FILTER

IMPEDANCE PLOT FOR C-TYPE FILTER

Figure 4: Impedance Plot for C-type filter


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Network Modeling and solution techniques: Power system networks aremodeled as sets of frequency-dependent models of the various, abovedescribed, system components. For every frequency of interest, an admittancematrix is built for the whole system. Sparse-matrix and vector techniques areused to solve for the equivalent system impedances at the various points of

interest, for all the frequency range, thus completing the so called frequencyscanning. When harmonic current sources are included in the network, harmonicvoltages will be calculated. Numerical techniques, such as the matrix InversionLemma are also used for fast re-calculation of the system impedances, undersingle or multiple contingencies.

Harmonic analysis for industrial systems: The following summarizes thenecessary steps, normally required for a harmonic study in the industrialenvironment:

1. Prepare system one-line diagram.2. Gather equipment data and rating.3. Obtain from the utility company the relevant data and requirements at

the point of common coupling. These must include: Minimum and maximum fault levels or preferably system impedances

as a function of frequency for different system conditions. Permissible limits on harmonics including distortion factors and IT

factor. The criteria and limits vary considerably from country tocountry. Typical values for different voltage levels are given in IEEE519 standard.

4. Carry out harmonic analysis for the base system configuration bycalculating the system impedances at the harmonic source bus bars aswell as all shunt capacitors locations.

5. Compute harmonic voltage distortion factors and IT value at the pointof common coupling.

6. Examine the results and, eventually, go back to step 1 or step 4,depending on whether the network data or only the parameters of theanalysis need to be modified.

7. Compare the composite (fundamental plus harmonic) loadingrequirements of shunt capacitor banks with the maximum ratingpermitted by the standards. Reference [..] has defined the followingoperating limits:

Continuous operating voltage


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9. Add filters if the harmonic distortion factors and IT values at the pointof common coupling exceed the limit imposed by the utility.

The above steps should be carried out for the base system configuration as wellas for system topologies resulting from likely contingencies. Any future system

expansion and utility short-circuit level changes should also be considered.

Example:

In the above example, filter is not part of the initial (base) network. 6-pulseconverter harmonic data is as follows:

Harmonic order Current (Amp) Phase Angle (Degrees)

5 190 0

7 107 180

11 34 180

13 22 0

17 14 0


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The impedance plot at Main bus shows that the system is resonating at afrequency close to 300 Hz (fifth harmonic). Harmonic voltage distortion factorsare summarized in table 2. Result of a case where the capacitor bank (installedat Main bus) has been modified to include a tuning reactor (tuned to 300 Hertzi.e., a 5

thharmonic filter) is also shown for comparison.

LocationHarmonic Voltage DistortionFactor (%), Capacitor bankonly

Harmonic Voltage DistortionFactor (%), Capacitorconverted to Filter

Utility 0.70 0.08Main bus 6.09 0.79Converter 9.69 7.11

Aux1 6.10 0.83Aux2 6.09 0.79

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Harmonic Sources