Design and Specification of Harmonic Filters for Variable Frequency Drives
Jesús A. Baez Moreno
ITESM (Departamento de Ingeniería Eléctrica)
Monterrey, NL. CP. 64849
ABSTRACT
2. SOLUTION METHODOLOGY
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.
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
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.
~
Low Voltage Bus
Nonlinear
Load (VFD)
Filter
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 n ( h) =
V ( h)
Vf ( h )
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.
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.
jh
SCKVA
h
Zs(h)
2
n
jh
KVAn
Zn(h)
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:
 h
1
j  h 2 − hn 2 
=
−




2
h  kVAn  h hn 2 
 (hn )
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 ) =
jh
SCkVA

kVAn  h h
 2
2 
j  h − hn 
Ys(h) =
1
δ kVAn + SCKVA
jh
[
]
 h 2 hn2 
δ= 2
2 
 h − hn 
The attenuation factor an(h) is then obtained as [1]:
[
1
δ kVAn + SCKVA
V (h) Yeq (h)
jh
an(h) =
=
=
SCKVA
Vf (h)
Ys(h)
jh
δ kVAn
an(h) = 1 +
SCKVA
When more than one filter is used, the attenuation
factor of the h-th harmonic voltage is given by
an(h) = 1 +
In order to simplify the calculation, the filter and the
system are represented by their admittance values.
Yn(h) =
Yeq (h) =
I(h)
Figure 2. Circuit used for harmonic voltage calculation.
j
kVAn
kVAn  h 2 hn2  SCKVA

+
j h  h 2 − hn2 
jh
where:
j
−
h KVAn
Z n ( h) =
Yeq (h) =
2
n
SCKVA
jh
The equivalent admittance seen by the VFD is calculated
by adding Yn(h) and Ys(h)
δ
kVAn (1)
δ kVAn ( N )
+ L+ N
SCKVA
SCKVA
1
where:
(
(
)
)
2
 2
(
k
)
h
h

n
δ k =
2
2−
 h hn ( k )






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)
I ( h)
; Is ( h ) =
Zn(h)
an( h )
]
Once these currents have been calculated, it is possible
to get filter’s specifications with the aid of the worksheet
filter.xls [3]
+
Is(h)
Zs(h)
Zn(h)
If(h)
I(h)
V(h)
The above procedure is summarized in the flowchart
shown in Figure 4.
-
Figure 3. Harmonic filter and system current calculation
Read system data
Utility SCMVA, XFMR(Z and kVA)
Drive KVA, Harmonic Spectra (%I(h)),
Displacement power factor
Filter(s) kVAr, Detuning Factors(α)
Maximum allowed THDV(THDVmax)
Calculate harmonic
filter loading and harmonics
flowing into the system
V(h)
I (h)
In(h) =
I s (h) =
Zn(h) ;
an(h)
Evaluate harmonic Voltages
and THDV without filters
 DrivekVA
V (h) = [%I(h)][h] 
 SCKVA 
THDV =
Calculate filter specs
using spredasheet filters.xls
43
[V (h)]2
∑
h 5
=
Calculate attenuation factors an(h),
resulting harmonic voltages and THDV
an(h) = 1 +
δ 1 kVAn (1)
δ kVAn ( N )
+ L+ N
SCKVA
SCKVA
Generate Report
*Voltage/current distortion
* Filter sepecifications)
~
13.8 kV
5.75%
Vf (h) =
V (h)
an (h)
THDV =
43
∑[Vf (h)]
12903.2 SCKVA
SCMVA
50
1000 kVA
480 V
2
THDV
h=5
3.58%
472.50
A RMS
0.031911 Ω
0.03256 Ω
500kVAr
@ 600V
250kVAr
@ 600V
5-th
Modify
filter(s) kVAr
NO
YES
900 kVA
6-pulse 250 HP 480-V CSI VFD(measured)
THDV<THDVmax?
Figure 4. Flowchart for the proposed solution methodology
233.62
A RMS
7-th
3. COMPUTER PROGRAM
4. SIMULATION RESULTS
The computer program was developed in an Excel
Workbook (VFD.XLS), using Visual Basic for
Applications Language[2].
The proposed methodology and the computer program
(VFD.XLS) were used to simulate the sample electrical
distribution system depicted in figure 5.
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
assumptions:
was
written
under
the
UTILITY
~
480 V
...
150-HP PWM VFDs
TOTAL LOAD =900 KVA
13.8 kV
SCMVA=50
1000 KVA
Z (%) = 5.75
5th
300 kVAR
α=0.95
7th
150 kVAR
α=0.95
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.
following
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).
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.
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
Table 2 . Harmonic currents flowing into the system and harmonic filters loading
FUNDAMENTAL
5
7
11
13
17
19
23
25
29
31
35
37
41
43
HARM. CURRENT
RMS CURRENT
THDI (%)
XFMR(NO FILTERS) XFMR(FILTERS) 5TH FILTER 7TH FILTER
I(AMPS)
I(AMPS)
I(AMPS)
I(AMPS)
1082.5
982.62
402.75
196.90
364.8
60.54
347.45
43.18
11.8
1.54
1.60
8.66
79.8
31.26
21.50
27.02
37.9
15.86
10.24
11.78
37.9
16.81
10.20
10.88
22.7
10.23
6.11
6.39
17.3
7.93
4.64
4.75
15.2
6.98
4.05
4.12
8.7
4.02
2.31
2.33
9.7
4.54
2.60
2.61
6.5
3.04
1.73
1.73
5.4
2.53
1.44
1.44
4.3
2.03
1.15
1.14
3.2
1.53
0.86
0.86
379.2
1147.0
35.0%
73.85
985.39
7.52%
348.55
532.63
55.01
204.44
Low Voltage Filter Calculations:
Example Filter Design Spreadsheet
SYSTEM INFORMATION:
Filter Specification:
5 th
Capacitor Bank Rating(Available)
Rated Bank Current:
Nominal Bus Voltage:
Power System Frequency:
500 k V A r
481 Amps
480
Capacitor Current (actual):
384.9 Amps
Filter Tuning Harmonic:
4.75
Capacitor Rating:
60 H z
Derated Capacitor:
600 Volts
60 H z
320 k V A r
Total Harmonic Load:
900 k V A
Filter Tuning Frequency:
285 H z
Cap Impedance (wye equivalent):
0.7200 Ω
Cap Value (wye equivalent):
3684.1 uF
Reactor Impedance:
0.0319 Ω
Reactor Rating:
0.0846 m H
Filter Full Load Current (actual):
Filter Full Load Current (rated):
Transformer Nameplate:
(Rating and Impedance)
402.8 Amps
503.4 Amps
1000
5.75
Supplied Compensation:
Load Harmonic Current:
86.54 % F u n d
Load Harmonic Current:
348.6 Amps
67.8 Amps
Max Total Harm. Current:
416.4 Amps
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
Utility Harmonic Current:
335 k V A r
Utility Side Vh:
(Utility Harmonic Voltage Source)
2.00 % T H D
CAPACITOR DUTY CALCULATIONS:
CAPACITOR LIMITS: (IEEE Std 18-1980)
Peak Voltage:
Current:
KVAr:
RMS Voltage:
<−−−−−−>
<−−−−−−>
<−−−−−−>
<−−−−−−>
120%
180%
135%
110%
FILTER CONFIGURATION:
101%
120%
103%
85%
XL =>
0.0319 Ω
500 kVAR
600 V
FILTER REACTOR DESIGN SPECIFICATIONS:
Reactor Impedance:
Fundamental Current:
0.0319 Ω
402.8 Amps
Reactor Rating:
Harmonic Current:
Figure7. 5th Harmonic filter specifications
0.0846 m H
416.4 Amps
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 # 932, 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.