manual paladin armonicos

8/10/2019 MANUAL PALADIN ARMONICOS

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Harmonic Analysis

Power Analytics Corporation10805 Rancho Bernardo Road, Suite 270

San Diego, California 92127U.S.A.

U.S. Toll Free Phone: 800-362-0603Fax: 858-675-9724

www.PowerAnalytics.com

Copyright Power Analytics Corporation 2012All rights reserved
http://www.poweranalytics.com/http://www.poweranalytics.com/http://www.poweranalytics.com/


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Table of Contents

Whats New in Version 5.00.00....................................................................................................... 1I. FOREWORD ........................................................................................................................... 2

II. INTRODUCTION ..................................................................................................................... 2III. SOURCES OF HARMONICS ................................................................................................... 5

3.1 Harmonic Current Source Data ..................................................................................... 73.2 Harmonic Voltage Source Data..................................................................................... 83.3 FFT and Inverse FFT.................................................................................................. 103.4 Thyristor Converter Simulation .................................................................................... 113.5 Common Harmonic Sources ....................................................................................... 13

IV. NETWORK AND COMPONENT MODELS ......................................................................... 144.1 Long Feeder Model .................................................................................................... 154.2 Skin Effect .................................................................................................................. 16

4.3

Power Company Frequency Response ....................................................................... 16V. FREQUENCY SCAN ANALYSIS ........................................................................................... 18

VI. HARMONIC DISTORTION INDICES (THD, TIF ETC) ....................................................... 206.1 Bus Voltage Indices .................................................................................................... 226.2 Branch Current Indices ............................................................................................... 236.3 Transformer K-factor .................................................................................................. 236.4 Conduct Calculation ................................................................................................... 24

VII. FILTER DESIGN AND APPLICATION ............................................................................... 29

IMPORTANT NOTE: Power Analytics Corporations software products are tools intended to be usedby trained professionals only. They are not substitutes for your professional judgment or forindependent verification and testing of results as they pertain to your specific application. Use of all

Power Analytics Corporation software products is governed by the terms and conditions of the End-User License Agreement (EULA) you accepted when purchasing and installing the software. Youmust comply with these terms and conditions in applying the instructional material in this manual. Ifyou do not have or are unfamiliar with the contents of your EULA for this software, you should request, read, and understand a copy of yourEULA before proceeding.


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Whats Newin Version 5.00.00

In this version of the program, we implemented a new user interface based on feedback from ourusers. The calculation engine was also rewritten based on our latest power flow engine. Theprogram is now faster and more robust. The new user interface is more user friendly, making iteasier to conduct the analysis and select desired results.

For existing harmonic analysis projects built in a previous DesignBase version, they can be directlyopened and used in the current version. The harmonic device symbols (harmonic sources, filtersand PFR), however, need to be replaced by selecting Tools > Replace Old Harmonic Symbol asshown below. All the project data is automatically converted and untouched.

For conducting harmonic frequency scan, the following dialog box is involved and from here its

easy to make selections and view results graphically or in text shown in Crystal Report format.


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The text results generated in Crystal Report format can also be easily exported and saved in otherformats as shown below.

I. FOREWORD

This discussion assumes that the user is a Professional Engineer familiar with the issuessurrounding harmonics problems in electrical power systems. The program's assumptionsand definitions are consistent with standard analysis techniques. This document should beused in conjunction with other texts on the subject, and should not be used as the designer'ssole source of information on harmonic analysis.

Determination of validity of the results, and whether the program is applicable to asystem, is solely the responsibility of the user.

This program is undergoing continuous development and refinement. As with all its products,Power Analytics Corporation is committed to making the Harmonic Analysis program ascurrent, comprehensive and easy to use as possible. Any comments, suggestions or errorsencountered in either the results or documentation should be immediately brought to Power

Analytics Corporation's attention.

II. INTRODUCTION

The DesignBase Harmonic Analysis program has been designed to assist electricalengineers in solving harmonic problems. This program is capable of performing variousFrequency Scan Analysis and Harmonic Distortion Indices Analysis.

Frequency Scan Analysis

The reason for harmonics problems in power systems is that there are harmonic sourcespresent and the system is in resonance condition (with high impedance). This program iscapable of calculating the impedance frequency responses (Frequency Scan) of all buseswith respect to a harmonic source at a given location (bus) and with respect to positive,negative and zero sequence networks to identify possible resonance situations. The


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frequency scan results can be plotted or viewed in crystal report format. The unit is Ohms forthe magnitude, degrees for the angle and Hz or pu for the frequency.

Harmonic Distortion Indices

The main index for measuring the harmonics problems of a power system is the TotalHarmonic Distortion (THD). The Telephone Interference Factor (TIF) is used to measure theseverity of the noise problems in the phone system due to induced harmonic componentwhen telephone lines are in parallel with power lines that contain harmonic current. Thisprogram can calculate bus voltage THD and TIF for all buses, and branch current THD, TDD(Total Demand Distortion) and TIF for all branches of a power system when one or severalharmonic sources are presented. Also bus voltage RAM, kVT, branch current RMS, kITvalues and transformer K-factors are calculated. The simulation results are presented in time-domain waveform and in frequency-domain spectrum. They can be displayed in text orgraphics.

The program is designed in a user friendly way. It can help you in performing a "What if" typeof analysis quickly and easily by permitting you to match the same network description todifferent filter designs and harmonic source sets. It gives you the choice of describingharmonic sources in either the time-domain or frequency domains. It maintains a library ofstandards and user defined harmonic sources for quick inclusion into analysis.

After building a DesignBase project, click the Harmonics Analysis button as shown below

There are three icons to choose: Options, Frequency Scan and Harmonic Indices.


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The Options dialog box:

Options

Frequency Scan

Harmonic


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The Frequency Scan dialog box:

The Harmonic Distortion Indices dialog box:

III. SOURCES OF HARMONICS

When there is a nonlinear device in a power system it will generate harmonics. Nonlineardevices may be modeled as harmonic voltage sources or harmonic current sources. For


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power system harmonics studies nonlinear devices are usually treated as harmonic currentsources. Both harmonic current and voltage sources are available for harmonic studies.Figure 1 shows a harmonic source current waveform and spectrum.

Figure 1: Harmonic Current Waveform and Spectrum

A harmonic current can be specified in time-domain by a set of waveform sampling points, orin frequency-domain by its spectrum: individual harmonic magnitude and angle. To facilitateFast Fourier Transformer (FFT) operation, the sampling points need to be 2n(32, 64, 128,

256, ).

The Following pictureFigure 2 shows the symbols of harmonic current and voltage sources.Figure 3 shows a harmonic current source attached to node 0019. The harmonic currentsource editor dialog box appears by double clicking the current source symbol. Harmonicvoltage source is similar to harmonic current source with extra impedance data.

Figure 2: HarmonicCurrent and Voltage Source Symbols


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Figure 3: A Harmonic Current Source Attached to Node 0019

3.1 Harmonic Current Source Data

By double-clicking a harmonic current source symbol in a network, the editor dialog box willopen, as shown below.

Harmonic source current data can be directly attached to a bus of a network or added to theharmonics source library for general usage. They can be in frequency-domain format ofharmonic in percent with respect to the fundamental current and phase angle, or in time-domain format of waveform sampling points. Source data are entered by direct screen editingin spreadsheet form or copy from a spreadsheet data. The data can be saved with just one


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click into the library. There are both frequency domain and time domain data libraries andthey can be easily transformed to each other.

Harmonic source data used in the program are in frequency-domain with fundamental being100%. Therefore, if the original data are in time-domain, the data will be transformed into

frequency domain stored in the project file. The absolute frequency spectrum values aredepending on the source KVA and power factor. The current magnitude and angle arecalculated by using the following equations:

I(1) =oltageBusSystemVx3

SourceKVAx1000 (3.1)

Angle(V(1),I(1)) = arccos (SourcePF) (3.2)

Harmonic currents in a power system may be in positive sequence, negative sequence or

zero sequence. The relationship between harmonics, frequency and sequence is shown inthe following table:

Table 1: Harmonic Sequence

Harmonic Frequency(Hz) Sequence1 60 +

2 120 -

3 180 0

3n-1 60(3n-1) -3n 60(3n) 0

3n+1 60(3n+1) +

Note: n=1,2,

3.2 Harmonic Voltage Source Data

The harmonic voltage source editor dialog box:


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Compared with harmonic current source, harmonic voltages source has the additional data ofseries impedance and shunt admittance. For the series impedance, it may change accordingto the frequency in a way that can only be measured. The program provides the facility (twoextra columns of series R and X) to handle just that. Otherwise, leave the two columns of theseries R and X being 0. The following shows the voltage waveform and the spectrum of thedefined harmonic voltage source.


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3.3 FFT and Inverse FFT

A periodic waveform (60 or 50 Hz for most electrical power systems) can be defined in time-domain by a set of sampling points, or in frequency-domain by its spectrum. The Fast Fourier

Transform (FFT) algorithm is used to find the spectrum of a time-domain waveform or inverseFFT to find the waveform of a frequency-domain spectrum.

The FFT algorithm may be based on cosine function or sine function. On the HarmonicAnalysis Option dialog box, user can select FFT Basis: cosine or sine for his/her application.FFT operation the sampling points have to be 2n. Users can choose 32, 64, 128, 256, 512 points.

If the Graph button on the harmonic current source dialog box as shown below is clicked,

the program will transform the spectrum to waveform by inverse FFT and plot both.


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If the Import time domain data button on the harmonic current source dialog box is clicked,the program transforms the spectrum to waveform and show the waveform data in thespreadsheet in the Time Domain Data dialog box as shown below. You can save the datainto the time domain source data library or enter or copy from other sources to thespreadsheet. If OK is clicked, the waveform data will be transformed to spectrum back.

3.4 Thyristor Converter Simulation

Thyristor converter circuits used in AC/DC conversion are one of the major harmonic sourcesin power systems. The program provides a converter simulation module, which calculates the

AC currents in a converter circuit with six thyristors and then it automatically transfers theresulting AC line current to the main program (harmonics source library or a bus).Figure 4shows the converter circuit.


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Figure 4: Equivalent Network for a Converter Circuit

Click the Converter button on the harmonic current source dialog box to generate theharmonic current source data as shown below.


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The converter model is based on reference [1]. The characteristic harmonics (h) currentgenerated by a converter having p pulses are of the order:

h = p k 1,

Where k is an integer starting from k=1,2,... For example the harmonic orders generated bya 6-pulse converter are:

5, 7, 11, 13, 17, 19 and a 12-pulse converter generates: 11, 13, 23, 25

The harmonic current order Ihis computed according to the following:

4/])2)2())(2([))](2()2(([ SINSINjCOSCOSA

)1/()])(1(())1(([)1/())])(1(())1((([ hhCOShCOShhCOShCOSB

hhhSINhSINhhSINhSINj /2/))1/()])(1(())1(([)1/())])(1(())1((([

1*I

A

BI

h

Where is the firing angle and is the extinction (overlap) angle and I 1is the fundamentalcurrent.

3.5 Common Harmonic Sources

The following are commonly encountered harmonic sources in power systems:

Thyristor-Controlled Equipment, Diode Bridges, etc.

Since this type of equipment imposes cyclical changes in impedance in a power sourcecircuit, it is a source of harmonics. Static VAR sources, Cycloconverters (frequencyconverters), Rectifiers, Inverters, Motor Speed Controllers, and Voltage Controllers forindustrial heating, induction melting, lighting control are all examples of harmonic sources.


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Transformers

When the applied primary voltage is above the transformer rated voltage, or when thetransformer is saturated (nonlinear relation between the magnetizing force and the magneticflux in the iron), harmonics are generated.

Arc Equipment

The nonlinear voltage current characteristic of power arcs generates harmonics.

Rotating Machinery

Variation in magnetic reluctance caused by slots in the machine's starter, or rotor, are theprinciple source of harmonics in rotating machinery.

Typical data for 7 types of commonly encountered harmonic sources are build-in the program'ssource library; Users can use these typical data or have the choice of inputting their own fieldtested data and add them to the library.

Harmonic current source library:

IV. NETWORK AND COMPONENT MODELS

It is assumed that the power network being studied is linear: all components are lineardevices, except the harmonic sources. The network is represented by its bus admittancematrix Y which is built at each frequency of harmonic current with respect to the harmonicsequence. For positive sequence harmonics the program uses positive sequence Y-matrix,for negative sequence harmonics the program uses negative sequence Y-matrix, and for


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zero sequence harmonics the program uses zero sequence Y-matrix. The bus voltages arefound by solving the following equation:

I = YV (4.1)

where I: bus injection current vectorY: bus admittance matrixV: bus voltage vector

Load at the fundamental frequency can be modeled as constant power, constant current,constant impedance or mixed load. Load at harmonic frequencies is treated as impedance. Itcan be grounded or ungrounded (selected in the load editor dialog box).

Before running harmonic analysis program, make sure power flow converged for the network(see the power flow program users guide). In the harmonic analysis option dialog box, usercan select the equivalent impedance parameter of generators and motors of the network.Load impedance can be parallel or series. Harmonic source can override or add to anexisting bus load if the source is attached to the load. User can define the minimum feederlength for the feeders being modeled using long feeder model. Considering skin effect forgenerators, motors and branches is selective. Also FFT setting and the TelephoneInterference Factor Weighting are here to view, select or edit.

4.1 Long Feeder Model

Feeders in the analysis are modeled generally by circuit. For feeders that their length isequal or greater than the minimum length defined on the harmonic analysis option dialog box,they are represented with a model based on an equivalent circuit derived from the solution ofthe second order differential equations describing wave propagation along long transmissionlines. This model is referred to as equivalent circuit as shown in the following equations andFigure.


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Z h

Z YZ

YZ

sinh

(4.2)

Y h

Y YZ

YZ

tanh

(4.3)

where Z and Y are the total admittance and impedance of the nominal circuit.

Figure 5: Feeder Wave Model

Long lines are usually more than 150 miles or 250 km. They can be modeled using oneequivalent circuit or by cascading several circuit. Its worthwhile to cascade sections ofeither model to produce harmonic voltage profile along the line.

4.2 Skin Effect

For synchronous machines, induction machines, transformers and Line/Cable, user canchoose including skin effect or not. According IEEE Std 399 (reference [3]), the followingformula are used in considering skin effect:

For synchronous machines, induction machines, and transformers:

R(h) = Rdc (1.0 + A * hB)

where Rdc is the DC resistance and h is the harmonic order. Coefficient A and B havetypical values of 0.1 and 1.5, respectively.

For lines and cables:

R(h) = Rdc (0.35 X2

+ 0.938) for X < 2.4R(h) = Rdc (0.35 X2+ 0.3) for X >= 2.4

where X = 0.001585 * (f / Rdc)0.5and f is frequency in Hertz and Rdc in Ohms/Meter.

4.3 Power Company Frequency Response


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Utility/power companies are represented in the analysis by impedance, which is dependenton its short circuit KVA and X/R ratio. The resistance is constant and the reactance isproportional to the frequency. If power company frequency response (PFR) is available, thefrequency response can be entered into the program and used to represent the powercompany. The program has a library facility for the power company frequency response data

to assist the data management.

The following screen picture shows a PFR symbol connected to a utility bus. Double click thePFR to edit the data in s spreadsheet format.

PFR data spreadsheet and library.


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V. FREQUENCY SCAN ANALYSIS

Frequency scan refers to scanning the network for impedance characteristics as a function offrequency over a range of frequencies with respect to a driving point. There are twoimpedance calculations: driving point and transfer impedances. The driving point impedance

is defined as the voltage calculated at bus i divided by current injected at the same bus. Thetransfer impedance is the voltage measured at bus j due to a unit current injected at adifferent bus i. The two impedances are expressed in equations as follows:

i

i

I

V

iiz (5.1)

i

j

I

V

ijz (5.2)

WhereZiiis the driving impedance at bus iZijis the transfer impedance to bus i

Viis the voltage measured at bus iViis the voltage measured at bus jIiis the current injected at bus i.

To perform frequency scan analysis, select one or more buses in the drawing and then clickthe Frequency Scan icon. There is no need for harmonic sources presented in the network.If they are, they will be not considered in the calculation. In the following screen picture, bus1020 is selected, after click Frequency Scan icon, the frequency scan options dialog boxappears.

Select bus1020 andthen click Frequency


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User can choose the frequency range and the total points, can select a different driving busand buses for report here, can select frequency unit used in the report and can choose curveresult or text report. The following screen pictures show the curves and partial text report.


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The above result shows that there is a peak around the 11th harmonic. The resonancefrequency is around 660Hz. If there is a 11th harmonic current component generated by non-linear load connected to this bus, it will produce high 11th harmonic voltage to cause overvoltage problems. This may result in the failure of the capacitor. These resonancefrequencies, if close to harmonic frequencies, are the major causes of system problems.

VI. HARMONIC DISTORTION INDICES (THD, TIF ETC)

There are two areas one needs to be concerned about: the first is the effect of harmonics onprotection devices, metering and control equipment, in which cases, errors could occur inmeasuring, operation of devices and interference with utility measuring devices. The secondimportant area is the effect of harmonics on equipment and plant. In this case, high harmoniccurrents and voltages will cause equipment damage and disturb the plant operation. Ofparticular concern is the effect of harmonics on transformers, rotating machines, switchgear,capacitor banks, and on system voltages and currents.

Harmonic producing loads can affect other loads if significant voltage and current distortion iscaused. The distortion is a function of both the amount of harmonic current injected and thesystem impedance characteristics. Voltage distortion is the major cause of failure of capacitor

banks.

The program calculates all major harmonic distortion indices and also generates violationreport based on the standard the user selected or defined in the option dialog box. Theharmonic standard selection is as shown in the following screen picture.


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For telephone interference factor calculation, a weighting factor table related to hearingsensitivity is applied and the factor table can be viewed and edited from the Options dialogbox, as shown below.


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6.1 Bus Voltage Indices

The most commonly used index for harmonics problem measurement is the bus voltage TotalHarmonic Distortion (THD), which is defined as follows:

THDv =1

22

3

2

2 ...

V

VVVh

(6.1)

where: VhVV ,...,, 32 are the individual harmonic voltages;

V1 is the fundamental frequency voltage.

The total RMS value is calculated as

1

2

h

hrms VV (6.2)

The telephone interference factor (TIF) based on bus voltage is calculated as

rms

h

hh

V

Vw

TIF

1

2)(

(6.3)

Where hw is the weighting factor defined in the Options dialog box.

The VT product index is another measure of the harmonic interference in audio circuits andis calculated as

1

2)(

h

hhVwTV (6.4)


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6.2 Branch Current Indices

Branch current THD calculation is based on equation (6.5), where current values are usedinstead of voltage, as follows:

THDi =1

22

3

2

2 ...

I

IIIh

(6.5)

Branch current RMS value is calculated according to:

22

2

2

1 ... hrms IIII

(6.6)

Because the heating loss of a feeder is dependent on the Irms, not on the I1, feeders should besized according to Irmsunder harmonics condition.

The telephone interference factor (TIF) based on current is calculated as

rms

h

hh

I

Iw

TIF

1

2)(

(6.7)

Where hw is the weighting factor defined in the Options dialog box.

The IT product index is calculated as

1

2)(

h

hhIwTI (6.8)

Total Demand Factor (TDD) is

TDD =L

h

I

III

22

3

2

2 ... (6.9)

where ILis the rated current.

6.3 Transformer K-factor


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Under harmonic conditions transformer current may be different on primary and secondarysides, because zero sequence current may not go through Y- connected transformers.Therefore, the program calculates all transformer current indices for all sides. For two windingtransformers, it is the primary and secondary sides and for three winding transformers, its theprimary, secondary and tertiary sides. Transformer K-factor is calculated according to:

K-factor =

1

2

1

1

2

1

2

h

h

h

h

I

I

I

Ih

(6.10)

6.4 Conduct Calculation

To conduct harmonic distortion indices calculation, it needs at least one harmonic source inthe studied network. User selects desired buses and branches on the drawing and then clickHarmonic Indices buttonas shown below.

After clicked the Harmonic Indices, harmonic calculation was executed and the harmonicanalysis Reports dialog box opened. User can select desired buses and branches on thedrawing before selecting the Harmonic Indicesicon, or they may be selected in the dialog

box after selecting the icon.

Need at least one harmonicsource to run harmonicdistortion indices analysis.


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The program provides bus harmonic voltages and branch harmonic currents in plotting (selectbuttons of Bus Harmonic Voltage and Branch Harmonic Current on the Reports dialogbox) and text (Harmonic Voltage/Current button). The following screen pictures show oneharmonic voltage curve, one harmonic current curve and a portion of the text report.

Harmonic voltage in waveform and spectrum at bus Busbar:

Harmonic current in waveform and spectrum through Switch 1:


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Portion of harmonic voltage at different frequency text report:

Portion of harmonic current at different frequency text report:


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Select the Total Harmonic Indices to view the total harmonic indices text report. Thefollowing shows a portion of the report.

Selecting THD Violations button on the Reports dialog box provides a report of the busesand branches that have higher THD numbers than the standard limits defined. IEEE Std.519-1992 suggests the following values as maximum recommended limits for voltagedistortion:


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Table 6.1 Maximum Voltage Distortion Limits

Voltage at PCC Individual Component VoltageDistortion

Total Voltage Distortion(THDF)

V69 kV 3.0% 5.0%

69 kV < V161 kV 1.5% 2.5%

V> 161 kV 1.0% 1.5%

These values are to be considered as worst-case scenarios applicable to operatingconditions lasting at least one hour. For momentary conditions such as load start-ups,switching and other non-steady state circumstances, these limits may be exceeded by50%.

For current distortion Limits, the following IEEE Std. 519-1992 table indicates that theamount of harmonic current a customer is allowed to inject back into the PCC depends onthe size of the customer's load relative to the system's short circuit capacity.

Table 2: Maximum Current Distortion Limits

Maximum Harmonic Current Distortion in % of Fundamental (< 69 kV)

ISC/IL Harmonic Order (Odd Harmonics) % TDD %

h < 11 11


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VII. FILTER DESIGN AND APPLICATION

The common solution to harmonic problems is to use harmonic filters. In the simulation,Filters can be added to any bus in a power network. For a selected bus, it can beconnected to with many filters, for example, 3rd, 5th, 7th and high-pass filters. Six types offilters can be simulated in the program, as shown in the following harmonic filter editordialog box:

Filter types included:

Single tuned filter double tuned filter

1storder high-passfilter

2ndorder high-pass filter 3rdorder high-pass filter3rdorder high-passC-type filter


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The R, L and C parameters are entered into the program in ohms at the fundamentalfrequency or mH, H, F, mF ... at user's choice. There are also Design, Graph and VI-Cal buttons to assist filter design as shown in the screen picture below.

In the current version, the Design is only available for single tuned filter. When clicking it,the following dialog box opens:

This is the frequency impedance curve of the designed single tuned filter:

This is a 5th

single tuned filter


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Clicking VI-Cal button gets the filter P, Q consumption, V and I of each element:


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REFERENCES

1. E. W. Kimbark, "Direct Current Transmission", vol. 1, John Wiley & Sons,1971.

2. "IEEE Recommended Practice and Requirements for Harmonics Control in Electrical

Power Systems", IEEE Standard 519-1992.

3. "IEEE Recommended Practice for Industrial and Commercial Power SystemsAnalysis, IEEE Standard 399-1997.

4. Jos Arrillaga and Neville R. Watson, "Power System Harmonics", 2nd edition, JohnWiley & Sons 2003


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