Design and Specification of Harmonic Filters for Variable Frequency Drives

Jesús A. Baez MorenoITESM (Departamento de Ingeniería Eléctrica)

Monterrey, NL. CP. 64849

ABSTRACT

This paper presents a method that can be applied todesign and specify low voltage harmonic filters forvariable frequency drives. The proposed methodology isused to analyze an electrical distribution system feedinga group of variable frequency drives.

1. INTRODUCTION

Generalized use of Variable Frequency Drives hasincreased harmonic distortion at electrical distributionsystems. Some pieces of equipment, such as personalcomputers, programmable controllers andmicroprocessor-based instrumentation are very sensitiveto harmonic distortion. Proper application of harmonicfilters can help to keep harmonic distortion withinacceptable limits.

This paper describes a simple methodology that can beapplied to design harmonic filters for an electricalsystem that will feed variable frequency drives. Theproposed methodology calculates the harmonic voltageattenuation factor produced by filters [1]. Attenuationfactor is then used to estimate voltage harmonicdistortion at the point of connection and also theharmonic currents injected into the system.

A computer program (EXCEL Macro) was developedusing Visual Basic for Application language to simulatesystem performance. The application of this program tothe analysis of a electrical distribution system feeding agroup of VFDs is also presented.

2. SOLUTION METHODOLOGY

Figure 1 shows a one-line diagram of a electricaldistribution system feeding a Variable Frequency Drive(VFD). The harmonic filter consists of a capacitor andan inductor connected in series.

~ Utility

NonlinearLoad (VFD)

Filter

Low Voltage Bus

Figure 1. One-line diagram of the electrical distributionsystem feeding the VFD

A harmonic filter modifies all harmonic voltages at thepoint of connection(Low Voltage Bus). Maximumattenuation occurs for the voltage whose frequency isequal or close to the resonant frequency of the filter. Inorder to quantify how harmonic voltages are affected, wewill define the attenuation factor[1] as

( )a hV h

Vf hn =( )

( )

Where:

V(h): Harmonic voltage without the filter at the lowvoltage bus.Vf(h): The h-th Harmonic voltage with the filter at thelow voltage busan(h) : Attenuation factor of the harmonic voltage(h)due to the (n-th) tuned filter.

Figure 2 illustrates the basic circuit used to calculate theh-th harmonic attenuation factor produced by the n-thharmonic filter. In this diagram, I(h) represents the h-thharmonic injected by the variable frequency drive, Zs(h)accounts for the system impedance and Zn(h) representsthe n-th harmonic filter impedance at the h-th harmonic.

I(h)Zn(h)Zs(h)

jh

SCKVA

−j

h KVAn

j h

h KVAnn2

Figure 2. Circuit used for harmonic voltage calculation.

The n-th harmonic filter impedance at the harmonicfrequency (h) can be expressed in terms of the filterkVAR(kVAn) and its tuning frequency (hn) as:

Z hj

kVAn

h

h h

j

kVAn

h h

h hnn

( )( )

= −

=

−

2

2 2

2

1 n

n

The distribution system impedance seen by the lowvoltage bus at the harmonic frequency (h) is related tothe low voltage bus short circuit kVA as follows:

Zs hj h

SCkVA( ) =

In order to simplify the calculation, the filter and thesystem are represented by their admittance values.

Yn hkVAn

j

h h

h h

Ys hSCKVA

jh

( )

( )

=−

=

n2

n22

The equivalent admittance seen by the VFD is calculatedby adding Yn(h) and Ys(h)

Yeq hkVAn

j h

h h

h h

SCKVA

jh( ) =

−

+

2

2n2

n2

[ ]Yeq hjh

kVAn SCKVA( ) = +1

δ

where:

δ =−

h h

h h

2

2n2

n2

The attenuation factor an(h) is then obtained as [1]:

[ ]an h

V h

Vf h

Yeq h

Ys h

jhkVAn SCKVA

SCKVA

jh

an hkVAn

SCKVA

( )( )

( )

( )

( )

( )

= = =+

= +

1

1

δ

δ

When more than one filter is used, the attenuationfactor of the h-th harmonic voltage is given by

( )( )

an hkVA

SCKVA

kVA

SCKVA

h h

h h

n n N

n k

n k

N

k

( )( ) ( )

( )

( )

= + + +

=−

1 1

22

22

1δ δ

δ

L

where:

Harmonic currents flowing into the tuned filters and intothe system(utility) with the connected filter(s) can becalculated as follows:

In hV h

Zn h( )

( )

( )= ; Is h

I h

an h( )

( )

( )=

I(h)Zn(h)Zs(h)Is(h) If(h)

+

V(h)

-

Figure 3. Harmonic filter and system current calculation

Once these currents have been calculated, it is possibleto get filter’s specifications with the aid of the worksheetfilter.xls [3]

The above procedure is summarized in the flowchartshown in Figure 4.

Read system dataUtility SCMVA, XFMR(Z and kVA)Drive KVA, Harmonic Spectra (%I(h)),Displacement power factorFilter(s) kVAr, Detuning Factors(α)Maximum allowed THDV(THDVmax)

Evaluate harmonic Voltages and THDV without filters

V h I h hDrivekVASCKVA

( ) [% ( )][ ]=

Calculate attenuation factors an(h),resulting harmonic voltages and THDV

( )Vf hV ha hn

( )( )

= [ ]THDV Vf hh

==∑ ( )

2

5

43

[ ]THDV V hh

==

∑ ( ) 2

5

43

THDV<THDVmax?Modifyfilter(s) kVAr

Calculate harmonicfilter loading and harmonics flowing into the system

Calculate filter specs using spredasheet filters.xls

NO YES

In hV hZn h

( )( )( )

=

SCMVA13.8 kV 50

5.75% 1000 kVA

12903.2 SCKVA 480 V

THDV 3.58%

472.50 233.620.031911 ΩΩ A RMS 0.03256 ΩΩ A RMS

500kVAr 250kVAr@ 600V @ 600V

5-th 7-th900 kVA

6-pulse 250 HP 480-V CSI VFD(measured)

~

Generate Report*Voltage/current distortion

* Filter sepecifications)

I s hI h

an h( )

( )( )

=;

an hkVA

SCKVA

kVA

SCKVAn n NN( )

( ) ( )= + + +1 1 1δ δ

L

Figure 4. Flowchart for the proposed solution methodology

3. COMPUTER PROGRAM

The computer program was developed in an ExcelWorkbook (VFD.XLS), using Visual Basic forApplications Language[2].

Harmonic Spectra of Variable Frequency Drives isstored in one worksheet within the same workbook. Toadd harmonic spectra of a non listed VFD(or group ofVFDs), the user types in this worksheet a name for thisload and its harmonic spectra.

Simulation results are stored into the followingWorksheets:1) SUMMARY : Summary of the results obtained in

the simulation (THDV, Filter specs)2) VOLTAGES: Harmonic voltages in the low voltage

bus without filters, with filters and with plaincapacitors(no tuning reactor)

3) CURRENTS: Harmonic currents flowing into thesystem with and without filters, and filter currents

4) FILTER-5: 5th harmonic filter designspecifications

5) FILTER-7: 7th harmonic filter designspecifications

The program was written under the followingassumptions:

1)This application was developed for VFDs operating at240V and 480 V systems. For applications at 240V, 480V capacitor banks are used, and the total KVAR ratingis adjusted to the next multiple of 25 kVARFor applications at 480V , 600 V capacitor banks areused and the total KVAR rating is adjusted to the nextmultiple of 50 kVAR For example, if the user chooses a300 kVAR bank at 480 V, the required kVAR rating at600 V is 300(600/480) ^2 = 468.75 kVAR. The bankkVAr rating is adjusted to 500 kVAR.

2) Load at the low voltage bus consists only of VFDs andthe resistive effect is neglected

3) 5th and 7th harmonic voltage distortion at the highvoltage side is given a as 2%. (This value can bemodified in Worksheets FILTER-5 and FILTER-7

4) Voltage at the low voltage bus is assumed constant(1.0 pu).

4. SIMULATION RESULTS

The proposed methodology and the computer program(VFD.XLS) were used to simulate the sample electricaldistribution system depicted in figure 5.

UTILITY

5th 7th

SCMVA=50~

Z (%) = 5.751000 KVA

150-HP PWM VFDs TOTAL LOAD =900 KVA

300 kVAR 150 kVAR

α=0.95 α=0.95

. . .

13.8 kV

480 V

Figure 5. One-line diagram of the electrical system

This system feeds a group of PWM variable frequencydrives with a total load of 900 kVA operating at 0.9(-)displacement power factor. This loading conditionresults in a very high harmonic current and voltagedistortion.

The proposed methodology was used to analyze theeffect of connecting two harmonic filters on low voltagebus harmonic distortion levels.Filter 1: 300 kVAR, 5-th harmonic filter tuned athn=4.75Filter 2: 150 kVAR, 7-th harmonic filter tuned athn=6.65

The computer program calculates harmonic voltage andcurrent distortion with and without filters and alsocalculates harmonic filter loading. A summary of thesimulation results is presented in figure 6 (actualprogram output).

The effect of these harmonic filters on harmonicvoltages and currents distortion is presented in Tables 1and 2.Total harmonic current distortion (THDI) is reducedfrom 35% to 7.5% and total harmonic voltage distortionis reduced from 15.76 to 4.56 %.

Figure 7 shows the 5-th harmonic filter spec sheet.

Figure 6. Simulation Results (summary)

Table 1. Voltage at the low voltage bus with and without filters connectedNO FILTERS FILTERS

h %I(h) % V(h) a(h) % Vf(h)5 33.7 11.753 6.03 1.95047 1.09 0.5322 7.66 0.0695

11 7.37 5.6546 2.55 2.215813 3.5 3.1736 2.39 1.328717 3.5 4.1501 2.25 1.840919 2.1 2.783 2.22 1.252623 1.6 2.5668 2.18 1.175925 1.4 2.4413 2.17 1.124729 0.8 1.6182 2.15 0.751331 0.9 1.946 2.15 0.90635 0.6 1.4648 2.14 0.684837 0.5 1.2904 2.14 0.604241 0.4 1.1439 2.13 0.53743 0.3 0.8998 2.13 0.4228

THDV(%) 15.176 4.5581

Table 2 . Harmonic currents flowing into the system and harmonic filters loading

XFMR(NO FILTERS) XFMR(FILTERS) 5TH FILTER 7TH FILTERI(AMPS) I(AMPS) I(AMPS) I(AMPS)

FUNDAMENTAL 1082.5 982.62 402.75 196.905 364.8 60.54 347.45 43.187 11.8 1.54 1.60 8.6611 79.8 31.26 21.50 27.0213 37.9 15.86 10.24 11.7817 37.9 16.81 10.20 10.8819 22.7 10.23 6.11 6.3923 17.3 7.93 4.64 4.7525 15.2 6.98 4.05 4.1229 8.7 4.02 2.31 2.3331 9.7 4.54 2.60 2.6135 6.5 3.04 1.73 1.7337 5.4 2.53 1.44 1.4441 4.3 2.03 1.15 1.1443 3.2 1.53 0.86 0.86

HARM. CURRENT 379.2 73.85 348.55 55.01 RMS CURRENT 1147.0 985.39 532.63 204.44

THDI (%) 35.0% 7.52%

Low Voltage Filter Calculations: Example Filter Design Spreadsheet

SYSTEM INFORMATION:

Filter Specification: 5 th Power System Frequency: 60 Hz

Capacitor Bank Rating(Available) 500 kVAr Capacitor Rating: 600 Volts Rated Bank Current: 481 Amps 60 Hz Nominal Bus Voltage: 480 Derated Capacitor: 320 kVAr

Capacitor Current (actual): 384.9 Amps Total Harmonic Load: 900 kVA

Filter Tuning Harmonic: 4.75 Filter Tuning Frequency: 285 Hz

Cap Impedance (wye equivalent): 0.7200 ΩΩ Cap Value (wye equivalent): 3684.1 uF

Reactor Impedance: 0.0319 ΩΩ Reactor Rating: 0.0846 m H

Filter Full Load Current (actual): 402.8 Amps Supplied Compensation: 335 kVAr Filter Full Load Current (rated): 503.4 Amps Transformer Nameplate: 1000 Utility Side Vh: 2.00 % T H D (Rating and Impedance) 5.75 (Utility Harmonic Voltage Source)

Load Harmonic Current: 86.54 % Fund Load Harmonic Current: 348.6 Amps

Utility Harmonic Current: 67.8 Amps Max Total Harm. Current: 416.4 Amps

CAPACITOR DUTY CALCULATIONS:

Filter RMS Current: 579.3 Amps Fundamental Cap Voltage: 502.3 Volts

Harmonic Cap Voltage: 103.9 Volts Maximum Peak Voltage: 606.1 Volts

RMS Capacitor Voltage: 512.9 Volts Maximum Peak Current: 819.1 Amps

CAPACITOR LIMITS: (IEEE Std 18-1980) FILTER CONFIGURATION:

Peak Voltage: 120% <−−−−−−> 101%Current: 180% <−−−−−−> 120% XL => 0.0319 ΩΩ

KVAr: 135% <−−−−−−> 103%RMS Voltage: 110% <−−−−−−> 85% 500 kVAR

600 V

F I L T E R R E A C T O R D E S I G N S P E C I F I C A T I O N S :

Reactor Impedance: 0.0319 ΩΩ Reactor Rating: 0.0846 m H Fundamental Current: 402.8 Amps Harmonic Current: 416.4 Amps

Figure7. 5th Harmonic filter specifications

5. CONCLUSIONS

The filter design iterative procedure can be greatlysimplified using the equations presented in this paperalong with the program developed.

Using the proposed methodology, it is possible todetermine the required rating of the filters to keepharmonic distortion (voltage and current) withinacceptable limits and also define filters specifications.

ACKNOWLEDGEMENT

The author wishes to acknowledge the support receivedfrom Electrotek Concepts Inc., which allowed me todevelop this project.

REFERENCES

[1] Peeran S.M. and Cascadden C. “Application, Designand Specification of harmonic filters for VariableFrequency Drives”, IEEE Trans. Ind. Applicat., vol. 31,pp. 841-847, July/August 1995

[2] Boonin Elisabeth, Using Excel Visual Basic forApplications, QUE, 1995

[3] ELECTROTEK, Harmflo+ Tech Notes, Issue # 93-2, September, 1993

Jesus Baez. Received his BSEE in 1987, his Master ofEngineering degree in Electric Power Engineering in1990 and his Master of Sciences Degree in ControlEngineering in 1995 from ITESM, Campus Monterrey.He is professor of the Electrical Engineering Departmentat ITESM since 1992. His research interest is simulationand analysis of distribution and industrial powersystems.