Design and spec harmonic filter

1. Design and Specification of Harmonic Filters for Variable Frequency Drives
Jesús A. Baez Moreno
ITESM (Departamento de Ingeniería Eléctrica)
Monterrey, NL. CP. 64849
ABSTRACT
This paper presents a method that can be applied to
design and specify low voltage harmonic filters for
variable frequency drives. The proposed methodology is
used to analyze an electrical distribution system feeding
a group of variable frequency drives.
1. INTRODUCTION
Generalized use of Variable Frequency Drives has
increased harmonic distortion at electrical distribution
systems. Some pieces of equipment, such as personal
computers, programmable controllers and
microprocessor-based instrumentation are very sensitive
to harmonic distortion. Proper application of harmonic
filters can help to keep harmonic distortion within
acceptable limits.
This paper describes a simple methodology that can be
applied to design harmonic filters for an electrical
system that will feed variable frequency drives. The
proposed methodology calculates the harmonic voltage
attenuation factor produced by filters [1]. Attenuation
factor is then used to estimate voltage harmonic
distortion at the point of connection and also the
harmonic currents injected into the system.
A computer program (EXCEL Macro) was developed
using Visual Basic for Application language to simulate
system performance. The application of this program to
the analysis of a electrical distribution system feeding a
group of VFDs is also presented.
2. SOLUTION METHODOLOGY
Figure 1 shows a one-line diagram of a electrical
distribution system feeding a Variable Frequency Drive
(VFD). The harmonic filter consists of a capacitor and
an inductor connected in series.
~
Utility
Nonlinear
Load (VFD)
Filter
Low Voltage Bus
Figure 1. One-line diagram of the electrical distribution
system feeding the VFD
A harmonic filter modifies all harmonic voltages at the
point of connection(Low Voltage Bus). Maximum
attenuation occurs for the voltage whose frequency is
equal or close to the resonant frequency of the filter. In
order to quantify how harmonic voltages are affected, we
will define the attenuation factor[1] as
( )
a h
V h
Vf h
n =
( )
( )
Where:
V(h): Harmonic voltage without the filter at the low
voltage bus.
Vf(h): The h-th Harmonic voltage with the filter at the
low voltage bus
an(h) : Attenuation factor of the harmonic voltage(h)
due to the (n-th) tuned filter.

2. Figure 2 illustrates the basic circuit used to calculate the
h-th harmonic attenuation factor produced by the n-th
harmonic filter. In this diagram, I(h) represents the h-th
harmonic injected by the variable frequency drive, Zs(h)
accounts for the system impedance and Zn(h) represents
the n-th harmonic filter impedance at the h-th harmonic.
I(h)
Zn(h)
Zs(h)
jh
SCKVA
−
j
h KVAn
j h
h KVAn
n
2
Figure 2. Circuit used for harmonic voltage calculation.
The n-th harmonic filter impedance at the harmonic
frequency (h) can be expressed in terms of the filter
kVAR(kVAn) and its tuning frequency (hn) as:
Z h
j
kVAn
h
h h
j
kVAn
h h
h h
n
n
( )
( )
= −





 =
−






2
2 2
2
1 n
n
The distribution system impedance seen by the low
voltage bus at the harmonic frequency (h) is related to
the low voltage bus short circuit kVA as follows:
Zs h
j h
SCkVA
( ) =
In order to simplify the calculation, the filter and the
system are represented by their admittance values.
Yn h
kVAn
j
h h
h h
Ys h
SCKVA
jh
( )
( )
=
−






=
n
2
n
2
2
The equivalent admittance seen by the VFD is calculated
by adding Yn(h) and Ys(h)
Yeq h
kVAn
j h
h h
h h
SCKVA
jh
( ) =
−





 +
2
2
n
2
n
2
[ ]
Yeq h
jh
kVAn SCKVA
( ) = +
1
δ
where:
δ =
−






h h
h h
2
2
n
2
n
2
The attenuation factor an(h) is then obtained as [1]:
[ ]
an h
V h
Vf h
Yeq h
Ys h
jh
kVAn SCKVA
SCKVA
jh
an h
kVAn
SCKVA
( )
( )
( )
( )
( )
( )
= = =
+
= +
1
1
δ
δ
When more than one filter is used, the attenuation
factor of the h-th harmonic voltage is given by
( )
( )
an h
kVA
SCKVA
kVA
SCKVA
h h
h h
n n N
n
k
n
k
N
k
( )
( ) ( )
( )
( )
= + + +










=
−
1 1
2
2
2
2
1
δ δ
δ
L
where:
Harmonic currents flowing into the tuned filters and into
the system(utility) with the connected filter(s) can be
calculated as follows:
In h
V h
Zn h
( )
( )
( )
= ; Is h
I h
an h
( )
( )
( )
=

3. 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 possible
to get filter’s specifications with the aid of the worksheet
filter.xls [3]
The above procedure is summarized in the flowchart
shown in Figure 4.
Read system data
UtilitySCMVA,XFMR(ZandkVA)
Drive KVA, Harmonic Spectra (%I(h)),
Displacement power factor
Filter(s) kVAr, Detuning Factors(α)
MaximumallowedTHDV(THDVmax)
Evaluate harmonic Voltages
and THDV without filters
V h I h h
DrivekVA
SCKVA
( ) [% ( )][ ]
=






Calculate attenuation factors an(h),
resulting harmonic voltages and THDV
( )
Vf h
V h
a h
n
( )
( )
= [ ]
THDV Vf h
h
=
=
∑ ( )
2
5
43
[ ]
THDV V h
h
=
=
∑ ( )
2
5
43
THDV<THDVmax?
Modify
filter(s) kVAr
Calculate harmonic
filter loading and harmonics
flowing into the system
Calculate filter specs
using spredasheet filters.xls
NO YES
In h
V h
Zn h
( )
( )
( )
=
SCMVA
13.8 kV 50
5.75% 1000 kVA
12903.2 SCKVA 480 V
THDV 3.58%
472.50 233.62
0.031911 Ω
Ω A RMS 0.03256 Ω
Ω A RMS
500kVAr 250kVAr
@ 600V @ 600V
5-th 7-th
900 kVA
6-pulse 250 HP 480-V CSI VFD(measured)
~
Generate Report
*Voltage/current distortion
* Filter sepecifications)
I s h
I h
an h
( )
( )
( )
=
;
an h
kVA
SCKVA
kVA
SCKVA
n n N
N
( )
( ) ( )
= + + +
1 1 1
δ δ
L
Figure 4. Flowchart for the proposed solution methodology

4. 3. COMPUTER PROGRAM
The computer program was developed in an Excel
Workbook (VFD.XLS), using Visual Basic for
Applications Language[2].
Harmonic Spectra of Variable Frequency Drives is
stored in one worksheet within the same workbook. To
add harmonic spectra of a non listed VFD(or group of
VFDs), the user types in this worksheet a name for this
load and its harmonic spectra.
Simulation results are stored into the following
Worksheets:
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 plain
capacitors(no tuning reactor)
3) CURRENTS: Harmonic currents flowing into the
system with and without filters, and filter currents
4) FILTER-5: 5th harmonic filter design
specifications
5) FILTER-7: 7th harmonic filter design
specifications
The program was written under the following
assumptions:
1)This application was developed for VFDs operating at
240V and 480 V systems. For applications at 240V, 480
V capacitor banks are used, and the total KVAR rating
is adjusted to the next multiple of 25 kVAR
For applications at 480V , 600 V capacitor banks are
used and the total KVAR rating is adjusted to the next
multiple of 50 kVAR For example, if the user chooses a
300 kVAR bank at 480 V, the required kVAR rating at
600 V is 300(600/480) ^2 = 468.75 kVAR. The bank
kVAr rating is adjusted to 500 kVAR.
2) Load at the low voltage bus consists only of VFDs and
the resistive effect is neglected
3) 5th
and 7th
harmonic voltage distortion at the high
voltage side is given a as 2%. (This value can be
modified 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 electrical
distribution system depicted in figure 5.
UTILITY
5th
7th
SCMVA=50
~
Z (%) = 5.75
1000 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 frequency
drives with a total load of 900 kVA operating at 0.9(-)
displacement power factor. This loading condition
results in a very high harmonic current and voltage
distortion.
The proposed methodology was used to analyze the
effect of connecting two harmonic filters on low voltage
bus harmonic distortion levels.
Filter 1: 300 kVAR, 5-th harmonic filter tuned at
hn=4.75
Filter 2: 150 kVAR, 7-th harmonic filter tuned at
hn=6.65
The computer program calculates harmonic voltage and
current distortion with and without filters and also
calculates harmonic filter loading. A summary of the
simulation results is presented in figure 6 (actual
program output).
The effect of these harmonic filters on harmonic
voltages and currents distortion is presented in Tables 1
and 2.
Total harmonic current distortion (THDI) is reduced
from 35% to 7.5% and total harmonic voltage distortion
is reduced from 15.76 to 4.56 %.
Figure 7 shows the 5-th harmonic filter spec sheet.

5. Figure 6. Simulation Results (summary)
Table 1. Voltage at the low voltage bus with and without filters connected
NO FILTERS FILTERS
h %I(h) % V(h) a(h) % Vf(h)
5 33.7 11.753 6.03 1.9504
7 1.09 0.5322 7.66 0.0695
11 7.37 5.6546 2.55 2.2158
13 3.5 3.1736 2.39 1.3287
17 3.5 4.1501 2.25 1.8409
19 2.1 2.783 2.22 1.2526
23 1.6 2.5668 2.18 1.1759
25 1.4 2.4413 2.17 1.1247
29 0.8 1.6182 2.15 0.7513
31 0.9 1.946 2.15 0.906
35 0.6 1.4648 2.14 0.6848
37 0.5 1.2904 2.14 0.6042
41 0.4 1.1439 2.13 0.537
43 0.3 0.8998 2.13 0.4228
THDV(%) 15.176 4.5581

6. Table 2 . Harmonic currents flowing into the system and harmonic filters loading
XFMR(NO FILTERS) XFMR(FILTERS) 5TH FILTER 7TH FILTER
I(AMPS) I(AMPS) I(AMPS) I(AMPS)
FUNDAMENTAL 1082.5 982.62 402.75 196.90
5 364.8 60.54 347.45 43.18
7 11.8 1.54 1.60 8.66
11 79.8 31.26 21.50 27.02
13 37.9 15.86 10.24 11.78
17 37.9 16.81 10.20 10.88
19 22.7 10.23 6.11 6.39
23 17.3 7.93 4.64 4.75
25 15.2 6.98 4.05 4.12
29 8.7 4.02 2.31 2.33
31 9.7 4.54 2.60 2.61
35 6.5 3.04 1.73 1.73
37 5.4 2.53 1.44 1.44
41 4.3 2.03 1.15 1.14
43 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%

7. 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 Ω
Ω Cap Value (wye equivalent): 3684.1 uF
Reactor Impedance: 0.0319 Ω
Ω Reactor Rating: 0.0846 mH
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 Ω
Ω
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 Ω
Ω Reactor Rating: 0.0846 mH
Fundamental Current: 402.8 Amps Harmonic Current: 416.4 Amps
Figure7. 5th
Harmonic filter specifications

8. 5. CONCLUSIONS
The filter design iterative procedure can be greatly
simplified using the equations presented in this paper
along with the program developed.
Using the proposed methodology, it is possible to
determine the required rating of the filters to keep
harmonic distortion (voltage and current) within
acceptable limits and also define filters specifications.
ACKNOWLEDGEMENT
The author wishes to acknowledge the support received
from Electrotek Concepts Inc., which allowed me to
develop this project.
REFERENCES
[1] Peeran S.M. and Cascadden C. “Application, Design
and Specification of harmonic filters for Variable
Frequency Drives”, IEEE Trans. Ind. Applicat., vol. 31,
pp. 841-847, July/August 1995
[2] Boonin Elisabeth, Using Excel Visual Basic for
Applications, QUE, 1995
[3] ELECTROTEK, Harmflo+ Tech Notes, Issue # 93-
2, September, 1993
Jesus Baez. Received his BSEE in 1987, his Master of
Engineering degree in Electric Power Engineering in
1990 and his Master of Sciences Degree in Control
Engineering in 1995 from ITESM, Campus Monterrey.
He is professor of the Electrical Engineering Department
at ITESM since 1992. His research interest is simulation
and analysis of distribution and industrial power
systems.