Rachid Dehini et. al. / International Journal of Engineering Science and Technology
Vol. 2(5), 2010, 1185-1193
Shunt Hybrid Active Power Filter
Improvement
Based On Passive Power Filters Synthesis
by Genetic Algorithm
Rachid DEHINI1*, Brahim BERBAOUI2, Chellali BENACHAIBA3 ,Otmane HARICI4
Faculty of the sciences and technology, Bechar University B.P 417 BECHAR (08000), ALGERIA
Abstract
This paper, a synthesizing a passive power filters (5th, 7th) method is presented based on optimization
by a Static Genetic Algorithm (SGA). Passive power filter parameters (C5 and C7) are optimized
simultaneously. Binary encoding method was proposed, in which an individual is represented by two
chromosomes describing the two parameters of the Passive power filters. The genetic operations of
crossover and mutation used in this genetic algorithm have been defined. This synthesis method has been
exploited in such a way that the passive power filter are simultaneously connected in parallel with (FAP) in
load side used to in order to achieve the percentage of (SAPF) apparent power (SF) compared to (Load)
apparent power (SL) Limited between 14% and 16% and become very reasonable. The studies have been
accomplished using simulation with the MATLAB-Simulink. The results show That (SHAPF) is more
effective and robust than (SAPF), and has lower cost.
Key Words: Genetic Algorithm optimization, Shunt active power filter, passive power filter; nonlinear loads,
Shunt hybrid active filter.
1. Introduction
Due to proliferation of power electronic equipment and nonlinear loads in power distribution systems, the
problem of harmonic contamination and treatment take on great significance .These harmonics interfere with
sensitive electronic equipment and cause undesired power losses in electrical equipment[1,2,3]. In order to solve
and to regulate the permanent power quality problem introduce by this Current harmonics generated by
nonlinear loads such as switching power factor correction converter, converter for variable speed AC motor
drives and HVDC systems, the resonance passive filters (RPF) have been used; which are simple and low cost.
However, the use of passive filter has many disadvantages, such as large size, tuning and risk of resonance
problems which decrease more the flexibility and reliability of the filter devices
Owing to the rapid improvement in power semiconductor device technology that makes high-speed,
high-power switching devices such as power MOSFETs, MCTs, IGBTs , IGCTS, IEGTs etc. usable for the
harmonic compensation modern power electronic technology, Active power filter (APF) have been considered
as an effective solution for this issue, it has been widely used.
One of the most popular active filters is the Shunt Active Power Filter (SAPF) [6, 7, 8, 9, 10, and 11].
SAPF have been researched and developed, that they have gradually been recognized as a workable solution to
the problems created by non-linear loads, unfortunately, because of the high cost operation, the (SAPF) is not a
cost-effective solution.
The disadvantages of (RPF) and (SAPF) orientate the researchers toward shunt hybrid active power filter
(SHAPF), consequently (SHAPF) has become more attractive [1]. The (SHAPF) involve a (RPF) connected in
parallel with (SAPF), this solution allows the use of (SAPF) in the large power system avoiding the expensive
initial cost and improves the compensation performance of passive filter remarkably.
The high cost and large capacity APFs, whereby form a very important role in determining the (ShAPF)
performance, leads that the design of PPF is a major effect which influences the general (ShAPF) performance.
It was noted that different approaches have been developed to optimize the passive filters sizes. Recently, to
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Vol. 2(5), 2010, 1185-1193
overcome this problem, some methods based on artificial intelligence have been applied. These methods
generally do not require the convexity of the objective function and have a high probability to converge towards
the global minimum.
The past decade has seen a dramatic increase in interest in simple Genetic algorithms (SGA) which are
search algorithms using efficient operations found in natural genetics for the determination of a function
extreme defined on a data space. (SGA) have proven their effectiveness in the optimization of objective
functions. In this work the application of genetic algorithm has been described to the problem of passive filters
sizing in an electric network affected by harmonic disturbances. The minimization of total voltage and current
harmonic distortion and cost of passive harmonic filters component has been used as objective function in order
to achieve the percentage of (SAPF) apparent power (SF) compared to (Load) apparent power (SL) Limited
between 14% and 16% and become very reasonable.
The functioning of (SAPF) is to sense the load currents and extracts the harmonic component of the load
current to produce a reference current Ir, a block diagram of the system is illustrated in Fig. 1. The reference
current consists of the harmonic components of the load current which the active filter must supply. This
reference current is fed through a controller and then the switching signal is generated to switch the power
switching devices of the active filter such that the active filter will indeed produce the harmonics required by the
load. Finally, the AC supply will only need to provide the fundamental component for the load, resulting in a
low harmonic sinusoidal supply.
3 phase
AC
iia , iib , iic V
Supply i , i , i
c
sa sb sc v sa , v sb , v sc
isa isb i sc
ira
Courrent irb
Detetction irc
Control
Circuit
S a Sb Sc
Lf
Lf
Lf
iia
iib
iic
iLa i Lb i Lc
Ls Ls
Vc
Pssive filter 7 eme order
Ls
RL
LL
Pssive filter 5eme order
Figure 1.Schematic diagram of shunt (SHAPF)
2. Mathematical Formulation of the Problem
The parallel passive filters were implemented since 1920, to compensate harmonics created by non
linear loads, provide the reactive power requested, and increase the capacity of transport of networks.
The basic shunt passive filtering principle is to trap harmonic currents in LC circuits, tuned up to the
harmonic filtering frequency ,and be eliminated from power system.
In single-tuned filter, the reactance of inductor is equal to that of capacitor at resonant frequency
fn
.The relationship among L, C, R, Q values are:
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C
n

Ln
1
 (2    fn )2
fn
Rn 
(1)
is cut-off frequency
Ln  (2    fn )
Q
(2)
Where Q is the quality factor
After some calculations, it can lead
BP 
1
Q
(3)
Where Bp is the bandwidth of the RPF
When Q is very high, the bandwidth is narrow, is difficult to obtain the turning up. Indeed, the inductance
values and capacitance are given with manufacturing tolerance of rank ± 10%. Moreover, the capacity value
varies depending on temperature. To overcome these drawbacks, we must take:
Q  75 for inductors in air
Q  75 for the iron core inductors
2.1 reactive power compensation
Reactive power compensation at 50 Hz
U
2
n2

Q ( w0 ) 
Cw 0
Z ( w0 ) n 2  1
U
2
(4)
n= harmonic order fn/f1
U= nominal line-line voltage
W0= ( 2    f 1 ) angular frequency
PPF expect a high Compensation reactive power in power system. But reactive power can’t be
overcompensation though (
SF
* 100) is limited between 14% and 16%.
SL
above need is expressed by:
Q min 
Q
F
 Q max
(5)
After some calculations, it can lead
C min 
2.2
n
n2
C n  C max
2
1
(6)
Total harmonics distortion function
A suitable passive power filter shall have lower total harmonics distortion of current THDi which reflect
harmonics suppression effect.
Let the equivalent 5th, 7th harmonic impedance of single-tuned filters are
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Z
Z
 R5 
5
 R7 
7
 24
)
25 w
(7)
j
 48
(
)
C 7 49 w
(8)
j
C
(
5
The total impedance of system is introduced from above harmonic impedance, shown as
Z 
Z5Z 7
Z5Z 7Z S
 Z S Z 7  Z 5Z S
(9)
Therefore, total harmonics distortion function of current is given by
THD I 
Ij

j  5, 7  I1

2

 * 100 % 

 Z


j  5 , 7  kZ j

2
(10)

 * 100 %


3. Cost function
The problem statement is to minimize multiple objective functions interpreting the cost of passive filters
parameters and total voltage and current harmonic distortion associated with this nonlinear load. The objective
function of the economic cost of passive filters is presented as [13]:
F (C , L , R )  a1  C i  a 2 L i  a 3 R i
(11)
Where a ji , are the cost coefficients of each passive harmonic filter component, they are given.
F (C , L , R )  a1  C i  a 2 L i  a 3 R i
(12)
According to resonate theory, resistor and inductor in formula (8) can be transformed into capacitor. So
F (C i )  a1  C i  a 2
1
 a3
w i2 C i
1
wiC iQ
(13)
The function to minimize can be described as follows:

 n
min 
F ( C i , L i , R i )  10  5  THD I 

 i 1
(14)

Under the following constraints:
C
min
5
 C
5
 C
max
5
(15)
C
min
7
 C
7
 C
max
7
(16)
For the genetic algorithm application, the method of minimization under constraints has been used which
is the penalty method [14].
g i (C i )  0
i  5 ,7
(17)
These are the inequality constraints of type,
The problem is transformed into a penalty function, which is presented as follows:
F ( C i , r k )  F ( C i )  10
5
 THD
I
 rk

[
1
]2
g i (C i )
(18)
Where: rk is the coefficient of penalty.
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4. Simulation Result
The performance of the (SHAPF) was examined through simulations. The system model was implanted
in Matlab / Simulink environment. The (SAPF) was designed to compensate harmonics caused by nonlinear
loads when the network is strong relative to the load (Ssc / SL = 3000). The system model parameters are shown
in Table I.
Table 1. System parameters
Active Filter Parameters
Supply phase voltage U
220 V
Supply frequency fs
50 Hz
Filter inductor Lf
0.7 mH
Dc link capacitor Cf
0.768474 mF
Smoothing
inductor 70 μH
Lsmooth
A three-phase diode rectifier with an RL load was used as a harmonic producing load. The load
(resistance was 10/3 Ω and the inductance 60 mH.).
The genetic algorithm (SGA) which provides optimization of PPF is used only during the (PPF)
synthesis phase. It is no longer involved in the system during normal operation.
The main parameters chosen for SGA are shown in:
Initial population = 100;
Crossing probability = 0.8;
Probability of mutation = 0.2,
Maximum generation number = 120;
rk coefficient of penalty=100
x 10
Unit price of R a3=88¥/Ωμ
Unit price of C a1=4800¥/μF
Unit price of L a3=320¥/mH
Bound of C5 [125 , 190]
Bound of C7 [43.2 , 108]
6
Best: 1363113.5745
1.3637
Best Fitness
1.3636
1.3635
1.3634
1.3633
1.3632
1.3631
10
20
30
Generation
40
50
Table 2. the optimum Passive filters characteristics
order
5
7
R(Ω)
L(mH)
C(μF)
0.08354
5
0.11994
4
3.191216
127.00005686400706
3.272517
63.18619265054698
THDI
(%)
16.10%
THDV
(%)
0.20%
QC(VAR)
Cost(¥105)
6001.3609
9.1289
2926.1332
The waveform and spectrum character of phase-a supply current is presented in Fig. 13 ,system without
(SAPF), then the total harmonic distortion has been taken up to 2.5 kHz (THD2,5 kHz)
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(a)
200
ILa
100
0
-100
-200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time(s)
(c)
Fundamental (50Hz) = 167.8 , THD= 16.10%
Mag (% of Fundamental)
Mag (% of Fundamental)
(b)
Fundamental (50Hz) = 167.4 , THD= 26.85%
20
15
10
5
8
6
4
2
0
0
0
10
20
30
Harmonic order
40
50
0
10
20
30
Harmonic order
40
50
Figure 4. (a)1 Simulated phase-a the supply current waveforms Isa (A).(b) Harmonic spectrum of load current Phase ‘a’, without (RPF).(c)
Harmonic spectrum of supply current Phase ‘a’, with (RPF)
In second place, the two optimum resonant passive filters tuned up to the frequency 250Hz (h5) and
350Hz (h7) are simultaneously connected in parallel with (FAP) in load side at 0.4s.
(a)
200
Isa
100
0
-100
-200
0
0.1
0.2
0.3
0.4
Time(s)
0.5
0.6
0.7
0.8
(c)
Fundamental (50Hz) = 168.1 , THD= 0.62%
(b)
Fundamental (50Hz) = 172.4 , THD= 1.02%
Mag (% of Fundamental)
Mag (% of Fundamental)
0.15
0.8
0.6
0.4
0.2
0
0
10
20
30
Harmonic order
40
50
0.1
0.05
0
0
10
20
30
40
50
Harmonic order
Figure 5. (a)2 Simulated phase-a the supply current waveforms Isa.(b) Harmonic spectrum of supply current Phase ‘a’, with (SAPF).(c)
Harmonic spectrum of supply current Phase ‘a’, with (SHAPF)
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Vol. 2(5), 2010, 1185-1193
(a)
400
300
200
Vsa(V)
100
0
-100
-200
-300
-400
0
0.1
0.2
0.3
0.4
Time(s) 0.5
0.7
0.8
0.9
1
(c)
-3
x 10 Fundamental (50Hz) = 311.1 , THD= 0.30%
2.5
4
Mag (% of Fundamental)
Mag (% of Fun dam ental)
(b)
-3
x 10 Fundamental (50Hz) = 311.1 , THD= 0.30%
0.6
3
2
1.5
2
1
1
0.5
0
0
0
10
20
30
Harmonic order
40
0
50
10
20
30
Harmonic order
40
50
Figure 6. (a)3 Simulated phase-a the supply voltage waveforms Vsa(A).(b) Harmonic spectrum of supply voltage Phase ‘a’, with (SAPF).(c)
Harmonic spectrum of supply voltage Phase ‘a’, with (SHAPF)
4
(b)
(a)
x 10
60
9
8
50
7
Sf
SL
40
(Sf/SL)%
S (V A)
6
5
4
30
20
3
2
10
1
0
0
0.2
0.4 Time(s) 0.6
0.8
0
1
0
0.2
0.4
0.6
Time(s)
0.8
1
Figure 7. (a) (SAPF) apparent power (Sf) and (Load) apparent power (SL).(b) The percentage of (SAPF) apparent power compared to
(Load) apparent power
(b)
(a)
60
100
40
50
Iinj(A)
Iinj(A)
20
0
0
-20
-50
-40
-100
0.2
0.21
0.22
0.23
Time(s)
0.24
0.25
(Peak) Iinj = 88.56,( 35.5 rms)
0.26
-60
0.8
0.81
0.82
0.83
Time(s)
0.84
0.85
(Peak) Iinj =58.01,(19.33 rms)
Figure 8.(a)4 Simulated phase-a the injected current waveforms Iinja (A) with (SAPF).(b)5 Simulated phase-a the injected current
waveforms Iinja (A) with (SHAPF)
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Vol. 2(5), 2010, 1185-1193
(a)
100
IF5
50
0
-50
-100
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
Time(s)
0.5
0.6
0.7
0.8
0.9
1
0.5
0.6
0.7
0.8
0.9
1
40
IF7
20
0
-20
-40
Time(s)
Figure 9.(a)6 Simulated phase-a the passive filter current waveforms IF5 with (SHAPF).(b)7 Simulated phase-a the passive filter current
waveforms IF7 with (SHAPF)
(a)
(b)
4
0.2
Impedance(ohms)
Impdance(ohms)
3
2
1
0
0
500
1000
1500
Frequency (Hz)
2000
2500
0.15
0.1
0.05
0
0
100
200
300
Frequence(Hz)
400
500
Figure 10.(a)network impedance with (5h, 7h, 11h, 13h, and 17h high-pass).(b)network impedance with (SAPF)and resonant passive filter
(5h ,7h)
4.1 Discussions
According to the simulation results, the optimized passive power filters (5h, 7h) which are connected
with APF filter at 0.4 sec have improved both the power quality by reducing the total distortion harmonic and
the cost of hybrid shunt power active filter.
In figure 6, the supply current THD has been decreased considerably from 1.02 to 0.62%. Moreover, the
hybrid shunt active’s cost has been reduced as shown in figure 7 when the SAPF apparent power (SF) compared
to the load apparent power (SL) has diminished from 30% to 15% which signifies lower cost by 50%
approximately.
The key for currents harmonics compensation for power electrical network using (SAPF) is almost
costly. But the optimized system with Genetic algorithm has demonstrated it’s effective in reducing current
harmonic with acceptable cost.
5. Conclusions
For the structure (HSAPF) under consideration, the simulation results with genetic algorithm confirm to
be more effective than primary system. The well adjusted (SHAPF) consists of passive filter with larger rated
power is used to filter the low order harmonics and one active filter with low power rating to filter the other high
order harmonies.
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So the compensating performance and the lower cost of hybrid SAPF can reply the requirements of
power system. Also, the proposed GA can be widely applied to many fields.
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