Download harmonic treatment in industrial power systems

HARMONIC TREATMENT IN INDUSTRIAL
POWER SYSTEMS
Presented by
Stefanos Manias
1
IEEE PESC-02
JUNE 2002
CONTACT INFORMATION
Stefanos N. Manias
National Technical University of Athens
Phone: +3010-7723503
FAX: +3010-7723593
E-mail: [email protected]
Mailing Address
National Technical University of Athens
Department of Electrical and Computer Engineering
9, Iroon Polytechniou Str, 15773 Zografou
Athens, Greece
2
IEEE PESC-02
JUNE 2002
PLAN OF PRESENTATION
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3
DEFINITIONS
CATEGORIES OF POWER QUALITY VARIATIONS
HARMONIC DISTORTION SOURCES IN INDUSTRIAL POWER
SYSTEMS
EFFECTS OF HARMONICS ON ELECTRICAL EQUIPMENT
HARMONIC MEASUREMENTS IN INDUSTRIAL POWER SYSTEMS
HARMONIC STANDARDS
HARMONIC MITIGATING TECHNIQUES
GENERAL PASSIVE AND ACTIVE FILTER DESIGN PROCEDURES
DESIGN EXAMPLES
CONCLUSIONS
IEEE PESC-02
JUNE 2002
WHY HARMONIC ANALYSIS ?
When a voltage and/or current waveform is distorted, it causes
abnormal operating conditions in a power system such as:




4
Voltage Harmonics can cause additional heating in induction and
synchronous motors and generators.
Voltage Harmonics with high peak values can weaken insulation in
cables, windings, and capacitors.
Voltage Harmonics can cause malfunction of different electronic
components and circuits that utilize the voltage waveform for
synchronization or timing.
Current Harmonics in motor windings can create Electromagnetic
Interference (EMI).
IEEE PESC-02
JUNE 2002





5
Current Harmonics flowing through cables can cause higher
heating over and above the heating that is created from the
fundamental component.
Current Harmonics flowing through a transformer can cause
higher heating over and above the heating that is created by the
fundamental component.
Current Harmonics flowing through circuit breakers and switchgear can increase their heating losses.
RESONANT CURRENTS which are created by current harmonics
and the different filtering topologies of the power system can
cause capacitor failures and/or fuse failures in the capacitor or
other electrical equipment.
False tripping of circuit breakers ad protective relays.
IEEE PESC-02
JUNE 2002
HARMONIC SOURCES
a) Current Source nonlinear load
Thyristor rectifier for dc drives,
heater drives, etc.
Per-phase equivalent circuit
of thyristor rectifier
b) Voltage source nonlinear load
Diode rectifier for ac drives,
electronic equipment, etc
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IEEE PESC-02
Per-phase equivalent circuit
of diode rectifier
JUNE 2002
INPUT CURRENT OF DIFFERENT
NOLINEAR LOADS
TYPE OF
NONLINEAR LOAD
TYPICAL WAREFORM
THD%
1.0
80%
(high 3rd
component)
0.5
0.0
Current
1-φ
Uncontrolled
Rectifier
-0.5
-1.0
0
10
20
30
40
Time (mS)
1.0
0.5
0.0
Current
1-φ
Semicontrolled
Rectifier Bridge
2nd, 3rd, 4th ,......
harmonic
components
-0.5
-1.0
0
10
20
30
40
Time (mS)
1.0
0.5
0.0
-0.5
-1.0
7
80%
Current
6 –Pulse Rectifier
with output voltage
filtering and without
input reactor filter
0
10
20
30
40
5, 7, 11, ……….
Time (mS)
IEEE PESC-02
JUNE 2002
1.0
0.5
0.0
40%
5, 7, 11, ………..
Current
6 - Pulse Rectifier
with output voltage
filtering and with 3%
reactor filter or with
continues output
current
-0.5
-1.0
0
10
20
30
40
Time (mS)
1.0
0.5
0.0
Current
6 - Pulse Rectifier
with large output
inductor
28%
5, 7, 11, ………..
-0.5
0
10
-1.0
20
Time (mS)
30
40
1.0
0.5
0.0
15%
11, 13, ………..
Current
12 - Pulse Rectifier
-0.5
0
-1.0
8
10
20
Time (mS)
IEEE PESC-02
30
40
JUNE 2002
CURRENT HARMONICS GENERATED BY 6-PULSE CSI CONVERTERS
HARMONIC
P.U PULSE
1
5
7
11
13
17
19
23
1.00
0.2
0.143
0.09
0.077
0.059
0.053
0.04
CURRENT HARMONICS GENERATED BY 12-PULSE CSI CONVERTERS
9
HARMONIC
P.U PULSE
IEEE 519 std
1
5
7
11
13
THD
1.00
0.03-0.06
0.02-0.06
0.05-0.09
0.03-0.08
7.5%-14.2%
5.6%
5.6%
2.8%
2.8%
7.0%
IEEE PESC-02
JUNE 2002
RECENT CURRENT MEASUREMENTS TAKEN IN AN
INDUSTRIAL PLANT WITH 600 KVA, 20 KV/400 V
DISTRIBUTION TRANFORMER
Current waveform and its respective spectrum
at the inputs of a motor drive system
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JUNE 2002
Current waveform and its respective spectrum
at the inputs of a motor drive system
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IEEE PESC-02
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Current waveform and its respective spectrum
at the secondary of the distribution transformer
( i.e. at the service entrance)
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DEFINITIONS
f (t) = Fourier Series of a periodic function f (t) =

Co   Ch cos hωt  θ h 
h 1
1 T
Ch  A 2h  B2h
Co  o f ( t )dt,
T
2 T
A h  o f ( t ) cos(hωt )dt
T
2 T
Bh  o f ( t ) sin( hωt )dt
T
(1)
(2)
(3)
(4)
h = harmonic order
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IEEE PESC-02
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THD υ %  Percentage of the Total Harmonic Distortion of
a nonsinusoidal voltage waveform

 Vh2
h 2

THDi % 
V1
 100
Percentage of the Total Harmonic Distortion of
a nonsinusoidal current waveform


2
 Ih
h 2
I1
 100
(6)
Vh  hth
harmonic component of the voltage
I h  hth
harmonic component of the current
~
VH  RMS value of the voltage distortion 
14
(5)
IEEE PESC-02
~2
V
 h
h 2
JUNE 2002
~
IH 
RMS value of the current distortion 
~
I
RMS value of a nonsinusoidal current =
h 2

~
V

~2
 Ih

~2
 Ih
(7)
h 1
RMS value of a nonsinusoidal voltage =
~2
 Vh

(8)
h 1
THD υ %  HF 
Drive kVA
 100
SC kVA
(9)

HF  Harmonic Factor =
15
 h 2 I 2h / I1
h 5
IEEE PESC-02
(10)
JUNE 2002
Drive kVA  Full load kVA rating of the Drive system
SC kVA  Short Circuit kVA of the distribution system at
the point of connection
SINUSOIDAL VOLTAGE NONSINUSOIDAL CURRENT
~~
P  V Ii,1 cos φ1
(11)
~~
~~
Q  V Ii,1 sin φ1 , S  V I
D  Distortion VA  S2  P 2  Q2
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(12)
(13)
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

~ ~
~
D  S  V 2 Ii,21  V 2
2
2

~2
 Ii,h
(14)
h 2
P  Ii,1 
 cos φ1
λ  True Power Factor   
S  I 
(15)
 Distortion Factor  Displace ment Factor
NONSINUSOIDAL VOLTAGE AND NONSINUSOIDAL CURRENT


~ ~
~ ~
P   Vh Ih cos φ h , Q   Vh Ih sin φ h
h 1
D  Distortion Power
17
h 1

  Snm S*nm
n m
n m
IEEE PESC-02

(16)

*
S
S
 n m
(17)
n m
n m
JUNE 2002
S2  P 2  Q 2  D 2

(18)
  
~ 2~ 2
~~ 2 ~~
S   Vh Ih  V1 I1  V1 IH
h 1

~ ~
 VH IH

2
2  V~H~I1 2 
 S12  S2N
(19)
~~
S1  Fundamenta l Apparent Power  V1 I1
SN  Nonfundame ntal Apparent Power

 
 

~~ 2 ~ ~ 2 ~ ~ 2
S2N  V1 IH  VH I1  VH IH
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IEEE PESC-02
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~~
V1 IH  Current Distortion Power
(20)
~ ~
VH I1  Voltage Distortion Power
(21)
~ ~
VH IH  Harmonic Apparent Power
(22)
S2H  PH2  N 2H  Total Harmonic Active Power 
 Total Harmonic Non Active Power
(23)
XC  Reactance of the capacitor  VL-L 2 / VAR 3phase
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IEEE PESC-02
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Harmonic sequence is the phase rotation relationship with respect to
the fundamental component.
Positive sequence harmonics ( 4th, 7th, 10th , ……. (6n+1) th ) have
the same phase rotation as the fundamental component. These
harmonics circulate between the phases.
Negative sequence harmonics ( 2nd, 5th, 8th ……… (6n-1) th ) have
the opposite phase rotation with respect to the fundamental component.
These harmonics circulate between the phases.
Zero sequence harmonics ( 3rd, 6th, 9th, ….. (6n-3) th ) do not produce
a rotating field. These harmonics circulate between the phase and neutral
or ground. These third order or zero sequence harmonics, unlike positive
and negative sequence harmonic currents, do not cancel but add up
arithmetically at the neutral bus.
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IEEE PESC-02
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EXAMPLE 1
SINUSOIDAL VOLTAGE-NONSINIMUSOIDAL CURRENT
A periodic, sinusoidal voltage of instantaneous value v  200 2 sin ωt
Is applied to a nonlinear load impedance. The resulting instantaneous current is
given by:






i  2 20sin ωt  45o  10sin 2ωt  60o  10sin 3ωt  60o

Calculate the components P, Q, D of the apparent voltamperes and hence
calculate the displacement factor, the distortion factor and the power factor.
Solution
v  200 2 sin ωt






i  2 20sin ωt  45o  10sin 2ωt  60o  10sin 3ωt  60o

The presence of the nonlinearity causes frequency components of current (i.e. the
second and third harmonic terms) that are not present in the applied voltage.
The rms voltage and current at the supply are:
~
V  200V
~2
I  202  102  102
 6102 A2
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IEEE PESC-02
JUNE 2002
The apparent voltamperes at the input is therefore given by
~ 2~ 2
S  V I  2002  6 102  24 106 VA 2
2
In this example only the fundamental frequency components are common to
both voltage and current. Therefore, the real power P and the apparent
power Q are
~~
P  V I1 cos ψ1
ψ1 = displacement angle between the fundamental of
the voltage and the fundamental of the current
 200 20 cos 45o

4000
W
2
~~
Q  V I1 sin ψ1
 200 20 sin 45o

22
4000
VA
2
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JUNE 2002
~I  ~I 
~I  ~I 
 200 10  10   8 10 VA 
~
D2  V 2
~
 V2
2
2
1
2
3
2
2
2
2
6
2
~ ~
P2  Q2  D2  V2 I 2
~~
~
P V I1 cos ψ1  I1 
PF  power factor  
  cos ψ1 
~~
S
VI
 I
1
Displacement factor  cos ψ1 
 0.707
2
I
20
Distortion factor  1 
 0.817
I
600
Therefore, the power factor is
PF 
23
1 2
 0.577
2 6
IEEE PESC-02
JUNE 2002
EXAMPLE 2
NONSINUSOIDAL VOLTAGE-RL LOAD


A periodic, sinusoidal voltage given by v  2 200sin ωt  200sin 5ωt  30o
is applied to a series, linear, resistance-inductance load of resistance 4Ω and

fundamental frequency reactance 10Ω.
Calculate the degree of power factor improvement realizable by capacitance
Compensation when
f1  50HZ.
~
Solution. The rms terminal voltage V is given by
~ ~2 ~2
V  V1  V5
 200 2  200 2
Therefore
~
V  283V
Z1  4  j10
Z1  10.8
1  tan 1 10 / 4  68.2o
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IEEE PESC-02
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5  51  50
Z5  4  j50
Z5  50
 5  tan 1 50 / 4  85.4o
The instantaneous load current is given by




200
 200

i  2
sin t  68.2o 
sin 5t  30o  85.4o 
50
 10.8

~
The rms load current I
is therefore given by
~ 2  ~ 2

~ 2 ~ 2 ~ 2  V1   V5 
I  I1  I5  



 Z1   Z5 
 18.52 2  4 2  359A 2
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IEEE PESC-02
JUNE 2002
Apparent voltamperes S at the load terminals in the absence of capacitance is
therefore
~ ~
2
S2  V 2 I 2  28.72 106 VA 
P
Average power
In this case is
n
~ ~
~~
~ ~
P   Vn In cos  L  V1 I1 cos 1  V2 I2 cos  2  ...
1
 200 18.52 cos 68.2o  200  4  cos85.4o
 1440W
The power factor before compensation is therefore
PF 
26
P
S

1440
28.72  10
6
 0.27
IEEE PESC-02
JUNE 2002
EXAMPLE 3
NONSINUSOIDAL VOLTAGE AND NONSINIMUSOIDAL CURRENT
A periodic, nonsinusoidal voltage with instantaneous value given by



The resulting current has an instantaneous value given by
i  2 20 sinωt  45   10 sin2ωt  60   10 sin3ωt  60 
v  2 200sin ωt  200sin 2ωt - 30o is applied to a nonlinear impedance.
o
L
o
o
SLR , SLX , SLD of the load apparent voltamperes
and compare thee with the classical values PL , QL , DL respectively.
Calculate the components
Solution.



2 20 sinωt  45   10 sin2ωt  60   10 sin3ωt  60 
v  2 200sin ωt  200sin 2ωt - 30o
iL 
o
o
o
Note that the presence of the load nonlinearity causes a frequency component
of load current (I.e. the third harmonic term) that is not present in the supply
voltage.
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IEEE PESC-02
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The rms voltage and current at the supply are given by
~
V2  2002  2002  8 104 V2
~2
IL  202  102  102  6 102 A2
~ and ~
The load apparent voltamperes SL therefore has a value defined in terms V
IL
~ ~
2
S2L  V 2 IL2  48 106 VA 
Instantaneous expressions of the hypothetical currents i R , i X , i D are given by


i R  2 20 cos 45o sin t  10 cos 300 sin 2t  30o

 
2
~2
 ILR
 20 cos 45o  10 cos 30o

2



11
10 2 A 2
4

i X   2 20 sin 45o cos ωt  10 sin 300 cos 2ωt  30o

 

2 10 sin 3t  60 
2
~2
 ILX
 20 sin 45o  10 sin 30o
iD 
2

9
 10 2 A 2
4
o
~2
 ILD
 10 2 A 2
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IEEE PESC-02
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Note that current components i R , i X contain only those harmonic terms which
are common to both voltage and current. These are therefore consistent with the
n1 terms.
~
~
~
The rms load current components ILR , ILX , ILD are found, as expected to sum
~
to the total rms load current IL
~2 ~2 ~2
~
 11 9 
ILD  ILR  ILD  10 2 1     6 10 2  IL2
4 4

Components
S
2
LR
S
2
LX
SLR , SLX , SLD
of the apparent voltamperes can now be obtained
~ 2 ~ 2 11 2
2
 V ILR  10  8 10 4  22 106 VA 
4
~ 2~ 2 9 2
2
 V ILX  10  8 10 4  18 106 VA 
4
~ ~2
2
S2LD  V 2 ILD
 10 2  8 10 4  8 106 VA 
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The component voltamperes are seen to sum to the total apparent voltamperes
S2LR  S2LX  S2LD  106 22  18  8
 48106 VA 2
 S2L
Components
PL , QL , DL of SL are found as follows:
n


~ ~
2

PL    Vn1 In1 cos ψ n1 
 1


2
 200  20  cos 45  200 10  cos 30
2

 100 20 2  10 3

 106 2 2 
30
3

2

o 2
o

2


 106 8  3  4 6  20.8 106  S2LR
IEEE PESC-02
JUNE 2002
2
n


~ ~
2

Q L    Vn1 In1 sin ψ n1 
 1

 200  20  sin 45o  200 10  sin 30o



2

 10 6 2 2  1  14.6  10 6  S2LX
D2L  S2L  PL2  Q2L
 48  20.8  14.6 106  12.6  106 VA 2  S2LD
From the possible compensation viewpoint it is interesting to note that SLX
and Q L differ by significant amount.
SLX could be defined as “that component of the load apparent voltamperes that
Is obtained by the combination of supply voltage harmonics with quadrature
Components of corresponding frequency load current harmonics”.
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IEEE PESC-02
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Similarly the definition of active voltamperes
SLR
could be given by “that
component of the load apparent voltamperes that is obtained by the combination
of supply voltage harmonics with in-phase components of corresponding
frequency load current harmonics”.
Both
SLR
and
SLX
are entirely fictitious and non-physical. The active
SLR Is not to be compares in importance with the average power
PL which is a real physical property of the circuit. Term SLR Is merely the
analytical complement of term SLX
voltamperes
Term
SLX
the energy-storage reactive voltamperes, is that component
of the load apparent voltamperes that can be entirely compensated (for sinusoidal
supply voltage) or minimized (for nonsinusoidal supply voltage) by energy-storage
methods.
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Voltage and current profiles in a
commercial building
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HARMONIC STANDARDS

International Electrotechnical Commission (IEC) European
Standards.
- EN 61000-3-2 Harmonic Emissions standards were first published
as IEC 55-2 1982 and applied only to household appliances. It was
revised and reissued in 1987 and 1995 with the applicability
expanded to include all equipment with input current  16A per
phase. However, until January 1st, 2001 a transition period is in
effect for all equipment not covered by the standard prior to 1987.
- The objective of EN 61000-3-2 (harmonics) is to test the equipment
under the conditions that will produce the maximum harmonic
amplitudes under normal operating conditions for each harmonic
component. To establish limits for similar types of harmonics current
distortion, equipment under test must be categorized in one of the
following four classes.
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IEEE PESC-02
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CLASS-A: Balanced three-phase equipment and all other equipment
except that stated in one of the remaining three classes.
CLASS-B: Portable electrical tools, which are hand held during normal
operation and used for a short time only (few minutes)
CLASS-C: Lighting equipment including dimming devices.
CLASS-D: Equipment having an input current with special wave shape
( e.g.equipment with off-line capacitor-rectifier AC input
circuitry and switch Mode power Supplies) and an active
input power 600W.
- Additional harmonic current testing, measurement techniques and
instrumentation guidelines for these standards are covered in IEC
1000-4-7.
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IEEE PESC-02
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•
IEEE 519-1992 United States Standards on harmonic limits
-
IEEE limits service entrance harmonics.
The IEEE standard 519-1992 limits the level of harmonics at the
customer service entrance or Point of Common Coupling (PCC).
With this approach the costumer’s current distortion is limited based
on relative size of the load and the power supplier’s voltage
distortion based on the voltage level.
IEEE 519 and IEC 1000-3-2 apply different philosophies, which
effectively limit harmonics at different locations. IEEE 519 limits
harmonics primarily at the service entrance while IEC 1000-3-2 is
applied at the terminals of end-user equipment. Therefore, IEC limits
will tend to reduce harmonic-related losses in an industrial plant
wiring, while IEEE harmonic limits are designed to prevent
interactions between neighbors and the power system.
36
IEEE PESC-02
JUNE 2002
POWER QUALITY STANDARDS –
IEEE 519-1992 STANDARDS
TABLE I
CURRENT DISTORTION LIMITS FOR GENERAL DISTRIBUTION SYSTEMS
(120-69000 V)
37
Isc/IL
<11
11<h<17 17<h<23 23<h<35
35<h
TDD
<20*
4.0
2.0
1.5
0.6
0.3
5.0
20<50
7.0
3.5
2.5
1.0
0.5
8.0
50<100
10.0
4.5
4.0
1.5
0.7
12.0
100<1,000
12.0
5.5
5.0
2.0
1.0
15.0
>1,000
15.0
7.0
6.0
2.5
1.4
20.0
Source: IEEE Standard 519-1992.
Note: Even harmonics are limited to 25 percent of the odd harmonic limits above.
Current distortions that result in a direct current offset; for example, half wave
converters are not allowed.
Table I is for 6-pulse rectifiers. For converters higher than 6 pulse, the limits for
characteristic harmonics are increased by a factor o f q/6 , where q is the pule number,
provided that the
amplitudes of noncharacteristic harmonics are less than 25 percent.
*All power generation equipment is limited to these values of current distortion, regardless of
actual ISC/IL.
Where ISC =
Maximum short circuit at PCC.
And IL
=
Average Maximum demand load current (fundamental frequency
component at PCC).
IEEE PESC-02
JUNE 2002
TABLE II
LOW VOLTAGE SYSTEM CLASSIFICATION AND DISTORTION LIMITS
IEEE 519-1992 STANDARTS
Special
Applications
General
System
Dedicated
System
Notch Depth
10%
20%
50%
THD (Voltage)
3%
5%
10%
Notch Area
(AN)*
16,400
22,800
36,500
Source: IEEE Standard 519-1992.
Note:
The value AN for another than 480Volt systems should be
multiplied by V/480 .
The notch depth, the total voltage distortion factor (THD) and
the notch area limits are specified for line to line voltage.
In the above table, special applications include hospitals and
airports. A dedicated system is exclusively dedicated to converter load.
*In volt-microseconds at rated voltage and current.
38
IEEE PESC-02
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TABLE III
LIMITS OF THD%
IEEE 519-1992 STANDARDS
39
SYSTEM
Nominal Voltage
Special
Application
General
Systems
Dedicated
Systems
120-600V
3.0
5.0
8.0
69KV and below
-
5.0
-
IEEE PESC-02
JUNE 2002
TABLE IV
PROPOSED IEC 555-2 CLASS D STANDARDS for power from 50 to 600W
40
Harmonic
Relative limits
Milliamps/Watt
Absolute Limits
Amps
3
3.4
2.30
5
1.9
1.14
7
1.0
0.77
9
0.5
0.40
11
0.35
0.33
13
linear
extrapolation
0.15 (15/n)
IEEE PESC-02
JUNE 2002
METHODOLOGY FOR
COMPUTING DISTORTION
Step 1: Compute the individual current harmonic distortion at each
dedicated bus using different Software programs (i.e. SIMULINK,
SPICE, e.t.c.) or tables that provide the current distortion of
nonlinear loads.
Step 2: Compute the voltage and current harmonic content at the Point of
Common Coupling (PCC) which is located at the input of the
industrial power system.
- Each individual harmonic current at the PCC is the sum of
harmonic current contribution from each dedicated bus.
- The load current at PCC is the sum of the load current
contribution from each dedicated bus.
- The maximum demand load current at PCC can be found by
computing the load currents for each branch feeder and multiply
by a demand factor to obtain feeder demand. Then the sum of all
feeder demands is divided by a diversity factor to obtain the
maximum demand load current.
41
IEEE PESC-02
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Step 3: Choose a base MVA and base KV for the system use the following
equations in order to compute individual and total current and
voltage harmonic distortions at PCC and any other point within the
power system.
3
MVA

10
b
Ib= Base current in Amps 
(24)
Amps
3kVb
Zs = System impedance =
MVAb= Base MVA,
MVA b
MVA sc
p.u.
(25)
MVAsc= short circuit MVA at the point of interest
VH= Percent individual harmonic voltage distortion =
I
 h h  Zs   100 Volts
Ib
42
IEEE PESC-02
(26)
JUNE 2002
  2
  Vh  12


THD υ %  h 2 
100
V1
THD i % 
2


2
  Ih 
h  2 
I1
 100
(27)
h = harmonic order
Ih
 100
IH = Percent individual harmonic distortion =
IL
(28)
Isc = Short Circuit current at the point under consideration.
IL = Estimated maximum demand load current
Isc MVA sc

S.C. Ratio = Short circuit Ratio 
I L MVA D
(29)
MVAD = Demand MVA
43
IEEE PESC-02
JUNE 2002
K Factor = Factor useful for transformers design and
specifically from transformers that feed
Adjustable Speed Drives


 h 
h 1
2
 Ih 
  
 IL 
2
(30)
ONCE THE SHORT CIRCUIT RATIO IS KNOWN, THE IEEE CURRENT
HARMONIC LIMITS CAN BE FOUND AS SPECIFIED IN TABLE I OF
THE IEEE 519-1992 POWER QUALITY STANDARDS
USING THE ABOVE EQUATIONS VALUES OF IDIVINDUAL AND
TOTAL VOLTAGE AND CURRENT HARMONIC DISTORTION CAN
BE COMPUTED AND COMPARED WITH THE IEEE LIMITS
44
IEEE PESC-02
JUNE 2002
Step 4: If the analysis is being performed for CSI-type drives then the area
of the voltage notch AN should also be computed.
- At this point an impedance diagram of the under analysis
industrial power system should be available.
- The Notch Area AN at the PCC can be calculated as follows.
AN = AN1 + AN2 + …………. V . microsec
(31)
AN1 , AN2 , …… are the notch areas contribution of the different busses
A N1 
Source inductance
A NDR1
Source inductance  the sum of inductance s from PCC to the drive
(32)
ANDR1 : Notch area at the input of the drive
45
IEEE PESC-02
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Step 5: Determine preliminary filter design.
Step 6: Compute THDv and THDi magnitudes and impedance versus
frequency plots with filters added to the system, one at a time.
SIMULINK or PSPICE software programs can be used for final
adjustments.
Step 7: Analyze results and specify final filter design.
46
IEEE PESC-02
JUNE 2002
EXAMPLE OF A SYSTEM ONE LINE
DIAGRAM
47
IEEE PESC-02
JUNE 2002
System impedances diagram which can be used to
calculate its resonance using PSPICE or SIMULINK
programs
48
IEEE PESC-02
JUNE 2002
TYPES OF FILTERS
1) Parallel-passive filter for current-source nonlinear loads
• Harmonic Sinc
• Low Impedance
• Cheapest
• VA ratings = VT (Load Harmonic current + reactive current of the filter)
49
IEEE PESC-02
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2) Series-passive filter for voltage-source nonlinear loads
• Harmonic dam
• High-impedance
• Cheapest
• VA ratings = Load current (Fundamental drop across filter + Load Harmonic Voltage)
50
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3) Basic parallel-active filter for current source in nonlinear loads
51
IEEE PESC-02
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4) Basic series-active filter for voltage-source in nonlinear loads
52
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5) Parallel combination of parallel active and parallel passive
6) Series combination of series active and series passive
53
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JUNE 2002
7) Hybrid of series active and parallel passive
8) Hybrid of parallel active and series passive
54
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9) Series combination of parallel-passive and parallel-active
10) Parallel combination of series-passive and series-active
55
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11) Combined system of series-active and parallel-active
12) Combined system of parallel-active and series-active
56
IEEE PESC-02
JUNE 2002
A SIMPLE EXAMPLE OF AN INDUSTRIAL
POWER DISTRIBUTION SYSTEM
57
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HARMONIC LIMITS EVALUATION WHEN
POWER-FACTOR-CORRECTION CAPASITORS
ARE USED
-
-
As it can be seen from the power distribution circuit the power-factorcorrection capacitor bank, which is connected on the 480 Volts bus, can
create a parallel resonance between the capacitors and the system
source inductance.
The single phase equivalent circuit of the distribution system is shown
below.
Rtot
Ltot
IS
If
C
VS
Ih
AC Source
Harmonic
Load
Z in
Using the above circuit the following equations hold:
58
IEEE PESC-02
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2
kVLL

 X 
R sys 
 cos tan 1  ,
MVA sc
 R 

2
kVLL
 1 X 
Xsys 
 sin tan   ,
MVA sc
 R 

R sys 
Xsys 
R sys
α
2
Xsys
α
2
(33)
(34)
α = The turns ratio of the transformer at PCC
2
1000  kVLL
R tr  R pu 
kVA tr
2
1000  kVLL
X tr  X pu 
kVA tr
59
IEEE PESC-02
(35)
(36)
JUNE 2002
R tot  Rsys  R tr
(37)
X tot  Xsys  X tr
Xc 
2
1000  kVcap
C
(39)
kVAR cap
1
ωX c
Xc 
(40)
1
ωC
X tot
L tot 
ω
60
(38)
(41)
X tot

2 πf
IEEE PESC-02
(42)
JUNE 2002
The impedance Z looking into the system from the load, consists of the
in
parallel combination of source impedance R
 jX tot and the
tot
capacitor impedance
Zin

R tot  jωL tot    j / ωC

1
R tot  jωL tot  j
ωC
1
1
ωo L tot 
,
fo 
ωo C
2πωo
(43)
(44)
The equation for Zin can be used to determine the equivalent system
impedance for different frequencies. The harmonic producing loads can
resonate (parallel resonance), the above equivalent circuit. Designating
the parallel resonant frequency by ωo (rad/sec) or f o (HZ) and equating
the inductive and capacitive reactances.
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IEEE PESC-02
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-
Harmonic current components that are close to the parallel resonant frequency are amplified.
Higher order harmonic currents at the PCC are reduced because the capacitors are low
impedance at these frequencies.
The figure below shows the effect of adding capacitors on the 480 Volts bus for power factor
correction.
This figure shows that by adding some typical sizes of power factor correction capacitors will
result in the magnification of the 5th and 7th harmonic components, which in turns makes it
even more difficult to meet the IEEE 519-1992 harmonic current standards .
- Power factor correction capacitors should not be used without turning reactors in case the
adjustable speed drives are >10% of the plant load.
62
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EXAMPLE
Let us examine an industrial plant with the following data:
Medium voltage = 20KVLL
Low voltage = 0.4 KVLL
Utility three phase short circuit power = 250 MVA
For asymmetrical current, the X ratio of system impedance  2.4
R
The Transformer is rated:
1000 KVA, 20 KV-400 Y/230 V
Rpu = 1%, Xpu = 7%
- The system frequency is: fsys = 50 HZ.
- For power factor correction capacitors the following cases are examined:
a.
200 KVAR
b.
400 KVAR
c.
600 KVAR
d.
800 KVAR
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IEEE PESC-02
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The parallel resonant frequencies for every case of
power factor correction is calculated as follows:

20

 sintan
250

2.4  1.4769Ω
202
R sys 
 cos tan 12.4  0.6154Ω
250
2
Xsys
α
1
20
 50
0.4
R sys  0.6154 502  0.000246Ω
Xsys  1.4769 502  0.000591Ω
1000  0.42
R tr  0.01
 0.00160Ω
1000
1000  0.42
X tr  0.07 
 0.0112Ω
1000
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R tot  0.000246  0.0016  0.001846Ω
X tot  0.000591 0.0112  0.011791Ω
0.011791
L tot 
 37.55  10 6 H
2  π  50
Case a:
1000  0.42
Xc 
 0.8 Ω
200
1
C 
 3.98  103 F
2 π  50  0.8
fo 
1
2 π  37.50  10 6  3.98  103
 412.18HZ
For 200 KVAR, the harmonic order at which parallel resonance occurs is:
h  412.18 50  8.24
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IEEE PESC-02
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Case b:
1000  0.42
Xc 
 0.4 Ω
400
C  7.96 103 F
f o  291.45HZ
h  5.83
Case c:
1000  0.42
Xc 
 0.267 Ω
600
C  11.94 103 F
f o  237.97HZ
h  4.76
66
IEEE PESC-02
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Case d:
1000  0.42
Xc 
 0.2 Ω
800
C  15.92 103 F
f o  206.08HZ
h  4.12
It is clear for the above system that in the 600 KVAR case, there
exists a parallel resonant frequency f o close to the 5th harmonic.
67
IEEE PESC-02
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POWER FACTOR CORRECTION AND
HARMONIC TREATMENT
USING TUNED FILTERS
-
Basic configuration of a tuned 3-φ capacitor bank for power factor
correction and harmonic treatment.
Simple and cheap filter
 Prevents of current harmonic magnification

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IEEE PESC-02
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-
-
IN ORDER TO AVOID HARMONIC MAGNIFICATION WE CHOOSE A
TUNED FREQUENCY < FITH HARMONIC (i.e 4.7)
The frequency characteristic of the tuned filter at 4.7 is shown below
As it can be seen from the above figure significant reduction of the 5th
harmonic is achieved. Moreover, there is some reduction for all the other
harmonic components.
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The single phase equivalent circuit of the power distribution system
with the tuned filter is shown below
Using the above circuit the following equations hold:
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f os 
1
1
= Resonant frequency of the series filter (45)
2πLf  C  2
2
f

1000
kV
1
2πf  X c
cap
Lf 


C  2πf os 2 2πf os 2 2π  f os 2  kVAR cap


(46)
The new parallel combination is having resonant frequency when
1
ωo L tot  ωo Lf 
0
ωo C
fo 
(parallel resonance)
1
1
2πL tot  Lf   C 2
= resonance frequency of the
(47)
equivalent distribution circuit
Also
R tot  jωL tot
If  I h 
R tot  jωL tot  ωL f  1 ωC
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(48)
JUNE 2002
Is  I h 
j ωLf  1 / ωC 
R tot  j ωL tot  ωLf  1 ωC
Vh  Is  R tot  jωLtot 
(49)
(50)
R tot  jωL tot    jωLf  j
1 

ωC 

Zin 

1
R tot  jωL tot  jωLf  j
ωC
R tot  jωL tot    jωLf
1 

ωC 


1 

R tot  j  ωL tot  ωL f 

ω
C


72
j
IEEE PESC-02
(51)
JUNE 2002
As it was discussed before Selecting f o  235HZ or 4.7 th harmonic
With
Lf 
KVcap= 0.4 ,
2
50 1000  0.4 
2  π  2352  600
KVARcap= 600
 68.45 10 6 H  38.45μH
The new parallel combination is having resonant frequency:
fo 
with
fo 
1
2 π
L tot  Lf   C
Ltot  37.55 106 H
Lf  38.45 106 H
C  11.94 103 F
1
2  π  76 106 11.94 103
h  167.16 / 50  3.43
73
we have
 167.16HZ
(without Lf was 4.76)
IEEE PESC-02
JUNE 2002
The following table shows the variation of Parallel resonant frequency
With and without resonant inductor
Parallel Resonant f0
74
KVAR
C(mF)
Without Lf
200
3.98
8.80
115.3μH
4.08
400
7.96
6.22
57.7μH
3.66
600
11.94
5.08
38.45μH
3.43
800
15.92
4.40
29.5μH
3.08
IEEE PESC-02
With Lf
JUNE 2002
SIMULATED RESULTS USING
MATLAB/SIMULINK
T1
i
-
+
C
motor
.
+
v
-
380kw/490rpm
V
compens
Bus Bar (horiz)2
T
Ground (input)
Gnd
+
v
-
200m cable 4x240
50m cable 4x1
V1
Ground (output)1
-
Current Measurement4
i
+
v
-
+
Voltage Measurement3
voltage
Series RLC Branch
Scope3
Scope1
+
i
Source
itot
Scope2
+
i
-
Scope4
Scope
Current Measurement6
Bus Bar (horiz)3
Source1
chock2%5
chock2%3
chock2%1
AC Voltage Source
Ground (input)8
Ground (input)4
Ground (input)5
Ground (output)
Current Measurement5
i
-
+
+
i
-
Current Measurement3
Bus Bar (horiz)7
AC Current Source7
Bus Bar (horiz)5
AC Current Source4
Series RLC Branch3
Series RLC Branch2
AC Current Source5
AC Current Source8
AC Current Source6
AC Current Source3
Bus Bar (horiz)6
Bus Bar (horiz)4
Ground (input)2
-
i
Current Measurement1
+
Ground (input)3
Bus Bar (horiz)1
AC Current Source1
AC Current Source2
Series RLC Branch1
AC Current Source
Bus Bar (horiz)
Ground (input)1
75
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SIMULINK RESULTS
76
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SIMULINK RESULTS
77
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ACTIVE FILTERING
Parallel type
78
Series type
IEEE PESC-02
JUNE 2002
RESULTS OF ACTIVE FILTERING
2500
1500
25
500
20
[% I1]
I
[A]
30
-500
15
10
-1500
5
-2500
0
0
5
10
15
20
25
Time [ms]
30
35
2
40
5
8
11
14
17
Harmonics
20
23
Input current of a 6-pulse Rectifier driving a DC machine without any input filtering
35%
30%
2500
25%
[%I1]
I Dynacomp [A]
5000
0
20%
15%
10%
-2500
5%
-5000
0%
0
10
20
30
40
Time [ms]
Input current with Active Filtering
79
IEEE PESC-02
2
5
8
11
14
17
20
23
Harmonics
JUNE 2002
1000
14
12
10
[% U1]
U [V]
500
0
8
6
4
-500
2
-1000
0
0
5
10
15
20
25
Time [ms]
30
35
40
2
5
8
11
14
17
Harmonics
5
8
11
14
17
Harmonics
20
23
Typical 6-pulse drive voltage waveform
1000
14
12
10
[% U]
U [V]
500
0
8
6
4
-500
2
-1000
0
0
5
10
15
20
25
Time [ms]
30
35
40
2
20
23
Voltage source improvement with active filtering
80
IEEE PESC-02
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SHUNT ACTIVE FILTERS
By inserting a parallel active filter in a non-linear load location we can
inject a harmonic current component with the same amplitude as that of
the load in to the AC system.
LF
C
Equivalent circuit
81
IEEE PESC-02
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ADVANTAGES OF THE SHUNT OR PARALLEL
ACTIVE FILTER

Low implementation cost.

Do not create displacement power factor problems and utility loading.

Supply inductance LS, does not affect the harmonic compensation of
parallel active filter system.

82
Simple control circuit.

Can damp harmonic propagation in a distribution feeder or between
two distribution feeders.

Easy to connect in parallel a number of active filter modules in order to
achieve higher power requirements.

Easy protection and inexpensive isolation switchgear.

Easy to be installed.

Provides immunity from ambient harmonic loads.
IEEE PESC-02
JUNE 2002
WAVEFORMS OF THE PARALLEL ACTIVE
FILTER
Source voltage
Load current
Source current
A. F. output current
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PARALLEL ACTIVE FILTER EQUATIONS
IC  GI L
G1  0
IS 
(52)
G h 1
ZL
VS
 I LH 
Z
Z
ZS  L
ZS  L
1 G
1 G
ZL
1
VS
1 G
IL 
 I LH 

ZL
1  G Z  ZL
ZS 
S
1 G
1 G
If
ZL
 ZS h
1 G h
(53)
(54)
(55)
Then the above equations become
I C  I Lh
(56)
ISh  1  G I LHh  1  G 
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IEEE PESC-02
VSh
0
ZL
(57)
JUNE 2002
I Lh  I LHh 
VSh
ZL
(58)
Equation (55) is the required condition for the parallel A.F. to cancel
the load harmonic current. Only G can be predesign by the A.F. while
Zs and ZL are determined by the system.
For pure current source type of harmonic source ZL  ZS
and consequently equations (53) and (55) become
IS
I LH
 1  G 
(59)
1  G h  1
(60)
ZS = Source impedance
I LH = Is the equivalent harmonic current source
ZL = Equivalent load impedance
G = equivalent transfer function of the active filter
Equation (59) shows that the compensation characteristics of the A.F. are not
influenced by the source impedance, Zs. This is a major advantage of the A.F.
with respect to the passive ones.
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VdC
C
• The DC bus nominal voltage, VdC, must be greater than or equal to line voltage
peak in order to actively control i C .
• The selection of the interface inductance of the active filter is based on the
compromise of keeping the output current ripple of the inverter low and the same
time to be able to track the desired source current.
• The required capacitor value is dictated by the maximum acceptable voltage
ripple. A good initial guess of C is:

2
VdC  Vφn
t
max i Cdt
3
Also
LF 
0
di φL
C
max
Δv Cmax

dt
nφV = peak line-neutral voltage

CdV = DC voltage of the DC bus of the inverter
Lφ i = Line phase current
xamCvΔ = maximum acceptable voltage ripple,
C i = Phase current of the inverter
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P-Q THEORY
For identifying the harmonic currents in general the method of computing
instantaneous active and reactive power is used.
Transformation of the three-phase voltages v u , v v and v w and the threephase load currents i Lv , i Lu and i Lw into α-β orthogonal coordinate.
 vα 
v  
 β
i Lα 
i  
 Lβ 
87
2 1

3 0
 1/ 2
2 1

3 0
 1/ 2
3/2
3/2
IEEE PESC-02
 vu 
 1/ 2   
  vv 
 3 / 2
 v w 
 i Lu 


i
 Lv 
 3 / 2 
i Lw 
 1/ 2
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Then according to p - q theory, the instantaneous real power p L and the
instantaneous imaginary (reactive) power q L are calculated.
p L   v α
q     v
β
 L 
vβ  i Lα 
v α  i Lβ 
where
88

pL  pL  pL  ~
pL 
DC + low frequency comp. + high freq. comp.

q L  qL  q L  ~
qL 
DC + low frequency comp. + high freq. comp.
IEEE PESC-02
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~
The conventional active power is corresponding to p L, the conventional reactive
~
power to q L and the negative sequence to the 2 f components of p L and q L .
The commands of the three-phase compensating currents injected by the
shunt active conditioner, iCu , iCv and iCware given by:
 iCu 
  
 i Cv  
i 
 Cw 
 1
2 
 1/ 2

3
 1 / 2
0

 vα

3/2  
- vβ

 3 / 2
1
v β   p 
v α  q 
p = Instantaneous real power command
q = Instantaneous reactive power command
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Substituting
p  ~
pL 

  Current Harmonics compensation is achieved

~
q  qL 


p  ~
pL

  Current Harmonics and low frequency variation


~
Components of reactive power compensation
q  q L  qL 


p  pL  ~
pL 

Current Harmonics and low frequency variation



Components of active and reactive power compensation
q  q L  ~
qL 


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HARMONIC DETECTION METHODS
i)
Load current detection iAF= iLh
It is suitable for shunt active filters which are installed near
one or more non-linear loads.
ii)
Supply current detection iAF= KS iSh
Is the most basic harmonic detection method for series
active filters acting as a voltage source vAF.
iii) Voltage detection
It is suitable for shunt active filters which are used as
Unified Power Quality Conditioners. This type of Active
Filter is installed in primary power distribution systems. The
Unified Power Quality Conditioner consists of a series and a
shunt active filter.
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SHUNT ACTIVE FILTER CONTROL
a) Shunt active filter control based on voltage detection
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Using this technique the three-phase voltages, which are detected at the point of
installation, are transformed to v d and vq on the dq coordinates. Then two first
~
order high-pass filters of 5HZ in order to extract the ac components vd and ~
vq
from v d and vq
. Next the ac components are applied to the inverse dq
transformation circuit, so that the control circuit to provide the three-phase
harmonic voltages at the point of installation. Finally, amplifying each harmonic
voltage by a gain Kv produces each phase current reference.
iAF  K V  vh
The active filter behaves like a resistor 1/KV ohms to the external circuit for
harmonic frequencies without altering the fundamental components.

The current control circuit compares the reference current i AF with the actual
current of the active filter i AF and amplifies the error by a gain KI . Each phase
voltage detected at the point of installation, v is added to each magnified error
signal, thus constituting a feed forward compensation in order to improve current
controllability. As a result, the current controller yields three-phase voltage

references. Then, each reference voltage v i is compared with a high frequency
triangular waveform to generate the gate signals for the power semiconductor
devices.
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b) Reference current calculation scheme using source currents (is),
load currents (iL) and voltages at the point of installation (vS).
94
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3-φ HYBRID ACTIVE-PASSIVE FILTER
Compensation of current harmonics and displacement power
factor can be achieved simultaneously.
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In the current harmonic compensation mode, the active filter improves the
filtering characteristic of the passive filter by imposing a voltage harmonic
waveform at its terminals with an amplitude
VCh  KISh
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If the AC mains voltage is pure sinusoidal, then
ISh
ZF

I Lh K  ZF  ZS
THD i 


ZF

I
  Lh K  Z  Z 
F
S
h  2
IS1
• THDi decreases if K increases.
• The larger the voltage harmonics generated by the active filter a better filter
compensation is obtained.
• A high value of the quality factor defines a large band width of the passive
filter, improving the compensation characteristics of the hybrid topology.
• A low value of the quality factor and/or a large value in the tuned factor
increases the required voltage generated by the active filter necessary to
keep the same compensation effectiveness, which increases the active
filter rated power.
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Displacement power factor correction is achieved by controlling the voltage
drop across the passive filter capacitor.
VC  βVT
Displacement power factor control can be achieved since at fundamental
frequency the passive filter equivalent impedance is capacitive.
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HYBRID ACTIVE-PASSIVE FILTER
Single-phase equivalent circuit
99
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Single-phase equivalent circuit
for 5th Harmonic
JUNE 2002
This active filter detects the 5th harmonic current component that flows
into the passive filter and amplifies it by a gain K in order to determine its
voltage reference which is given by
vAF  K  i F5
As a result, the active filter acts as a pure resistor of K ohms for the 5th
harmonic voltage and current. The impedance of the hybrid filter at the 5th
harmonic frequency, Z5 is given by
Z5  j5ωL F 
K0
The active filter presents a negative resistance to the external
Circuit, thus improving the Q of the filter.
K  rF
100
1
 rf  K
j5ωC F
VBUS5  0 ,
IEEE PESC-02
IS5 
1
VS5
j5ωL T
JUNE 2002
CONTROL CIRCUIT
The control circuit consists of two parts; a circuit for extracting the
5th current harmonic component from the passive filter iF and a circuit
that adjusts automatically the gain K. The reference voltage for the
active filter

v AF  K  i F5
HARMONIC-EXTRACTING CIRCUIT
The extracting circuit detects the three-phase currents that flow into
the passive filter using the AC current transformers and then the α-β
coordinates are transformed to those on the d-g coordinates by
using a unit vector (cos5ωt, sin5ωt) with a rotating frequency of
five times as high as the line frequency.
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SERIES ACTIVE FILTERS
By inserting a series Active Filter between the AC source and the load
where the harmonic source is existing we can force the source current to
become sinusoidal. The technique is based on a principle of harmonic
isolation by controlling the output voltage of the series active filter.
Equivalent Circuit
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- The series active filter exhibits high impedance to harmonic current
and consequently blocks harmonic current flow from the load to the
source.
VC  Output vol tage of the A.F.  KGI S
IS 
ZL I L
VS

ZS  ZL  KG ZS  ZL  KG
(61)
(62)
G = Equivalent transfer function of the detection circuit of
harmonic current, including delay time of the control
circuit.
G1  0
103
,
G h 1
IEEE PESC-02
(63)
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K = A gain in pu ohms
The voltage distortion of the input AC source VSh is much smaller
than the current distortion.
K  ZL h
If
and
K  ZS  ZL h
(64)
Then
VC  ZLILh  VSh
IS  0
104
(65)
(66)
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HYBRID SERIES AND SHUNT
ACTIVE FILTER
At the Point of Common Coupling provides:
• Harmonic current isolation between the sub transmission and the
distribution system (shunt A.F)
• Voltage regulation (series A.F)
• Voltage flicker/imbalance compensation (series A.F)
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SELECTION OF AF’ S FOR SPECIFIC APPLICATION CONSIDERATIONS
AF Configuration with higher number of * is more preferred
Compensation for
Specific Application
106
Active Filters
Active
Series
Active
Shunt
Hybrid of
Active Series
and Passive
Shunt
Hybrid of
Active Shunt
and Active
Series
Current Harmonics
**
***
*
Reactive Power
***
**
*
Load Balancing
*
Neutral Current
**
Voltage Harmonics
***
Voltage Regulation
***
Voltage Balancing
***
Voltage Flicker
**
***
Voltage Sag&Dips
***
*
*
IEEE PESC-02
*
**
*
**
*
**
*
*
**
*
JUNE 2002
CONCLUSIONS












107
Solid State Power Control results in harmonic pollution above the tolerable limits.
Harmonic Pollution increases industrial plant downtimes and power losses.
Harmonic measurements should be made in industrial power systems in order (a) aid
in the design of capacitor or filter banks, (b) verify the design and installation of
capacitor or filter banks, (c) verify compliance with utility harmonic distortion
requirements, and (d) investigate suspected harmonic problems.
Computer software programs such as PSPICE and SIMULINK can be used in order to
obtain the harmonic behavior of an industrial power plant.
The series LC passive filter with resonance frequency at 4.7 is the most popular filter.
The disadvantages of the the tuned LC filter is its dynamic response because it cannot
predict the load requirements.
The most popular Active Filter is the parallel or shunt type.
Active Filter technology is slowly used in industrial plants with passive filters as a
hybrid filter. These filters can be used locally at the inputs of different nonlinear loads.
Active Filter Technology is well developed and many manufactures are fabricating
Active filters with large capacities.
A large number of Active Filters configurations are available to compensate harmonic
current, reactive power, neutral current, unbalance current, and harmonics.
The active filters can predict the load requirements and consequently they exhibit very
good dynamic response.
LC tuned filters can be used at PCC and the same time active filters can be used
locally at the input of nonlinear loads.
IEEE PESC-02
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REFERENCES
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ACTIVE HARMONIC TREATMENT TECHNIQUES
H. Akagi, ΄΄New trends in active filters for Power conditioning΄΄,
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IEEE PESC-02
JUNE 2002