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International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
http://iraj.in
Volume-5, Issue-9, Sep.-2017
OPTIMUM CAPACITOR ALLOCATION IN THREE PHASE
UNBALANCED RADIAL DISTRIBUTION SYSTEM WITH
HARMONICS AND RESONANCE CONSIDERATION USING PSO
ALGORITHMS
1
AYUSTA LUKITA WARDANI, 2ONTOSENO PENANGSANG, 3RONY SETO WIBOWO
1,2,3
Electrical Engineering Department, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia
Email: [email protected], [email protected],[email protected]
Abstract - Distribution system connects between generation system and transmission system to the load. Power quality in
distribution system can affect the flow of electric distribution. Decrease in power quality can be caused of low power factor,
voltage drop, line loses and harmonic. Installation of capacitors can overcome the power quality problems when placement is
appropriate. In a distorted system the presence of a capacitor may aggravate the harmonic level and cause either parallel or
series resonance. In this research, capacitor placement and capacities are limited by minimum voltage, maximum reactive
power load, THD and resonance index. Resonance index based on limit of capacitor loading according to IEEE standard.
This scheme is tested on a distorted three-phase unbalanced distribution system which is have under voltage characteristics.
The simulation result shows the installation of capacitor using PSO algorithm by considering harmonics and resonance index
is capable to fulfill standard of THD that is 4.6929 % and decrease of active power loss equal to 19.74% and minimum
voltage 0.95 pu.
Keywords - line loses, resonance index, THD, PSO.
minimum voltage, maximum reactive power load,
THD and resonance index. Resonance index based on
limit of capacitor loading as in [2] and THD limit as
in [3]. PSO Algorithm is used to solve multi objective
problem.
I. INTRODUCTION
Distribution system is a vital component in the power
system. Radial distribution system (RDS) is the most
widely used system for power distribution because it
has a simple form and also low investment costs.
RDS system has many challenges about line loss,
unbalanced issues, and harmonic spread due to
increased use of power electronic devices. Power
losses and voltage drop are main problem in the
longest feeder in RDS. Line loss can be overcame
with the installation of capacitors but the allocation
must be appropriate to avoid aggravate the harmonic
level and cause either parallel or series resonance.
Harmonic effect can be divided into two term. Effect
in Immediate and medium/long term.
In immediate term can lead to overheating of
conductor, transformer, capacitors, and malfunction
of regulator devices. And in medium/long term can
be reason for reduction of live time for motor and
transformer.
Harmonic in RDS cannot be avoid but it can be
control by modify the frequency response of filters,
inductors or capacitor. Move a capacitor to a point on
the system with different short –circuit impedance or
higher losses as in [1] or change the capacitor size.
Not only reduce line losses but also can control IHD
and THD to fulfill IEEE standard. The capacitor has
standard loading to avoid heating, dielectric stress
and decrease of lime time and to avoid system from
resonance
In this research used 25 bus unbalance RDS data
which has low voltage characteristic. The system
have six harmonic sources from ASD. The size of
capacitor using standard capacitor available in
industry. The allocation of capacitor limited by
II. RESEARCH METHODS
A. Radial Power Flow Analysis
This research using network topology approach of
RDPF. To clarify RDPF algorithm, flowchart of
RDPF can be seen form figure 1 as follow:
Figure 1: Radial Distribution Power Flow flowchart.
Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using
PSO Algorithms
6
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
http://iraj.in
Network topology approach can determine the model
of network by using K-matrix. K-matrix is one part of
the graph theory which is also called branch-path
incidence matrix as in [4]. Values of the K-matrix
elements expressed as 1 if the branch is in the path of
the bus to the reference in the same direction and vice
versa, if the K-matrix elements will be -1 if the
branch is in the bus heading in the opposite direction
reference [5].
After distribution power flow is complete, the result
will be used to analyze the influence of harmonics.
Is
Ih
Volume-5, Issue-9, Sep.-2017
Capacitor Current
Harmonic Current
From this equation the number of capacitor must be
the same number with capacitor. The capacitor
number decided to six.
C. Algorithm PSO
PSO as an optimization method has several steps to
run the algorithm. The algorithm can be divided into
several points as follows:
1. Initialization of uniform distributed agent
populations (particles) in a search field
2. Evaluate each position of the particle against
objective function
3. If the current particle position is better than the
previous best position then update the best
position
4. Determine the best particles according to the best
position of the particle
5. Update the velocity of each particle according to
the equation:
B. Harmonic Power Flow Analysis
This research using backward/forward sweep based
harmonic analysis method for distribution system [6].
To clarify HPF algorithm, flowchart of HPF can be
seen form figure 2 as follow:



Vi k 1 Vi k  c1rand1 x Pbestik  X ik  c2rand2 x Gbest k  X ik

(2)
Where
Vi k
individual velocity i on iteration k
w
parameter weight
c1, c2
acceleration coefficient
rand1, rand2random number between 0 and 1
Xi k
individual position i on iteration k
Pbesti kPbest individual i to iteration k
Gbesti k Gbestgroup until iteration k
6.
7.
Move the particle to its new position according
to the equation (2)
Repeat the algorithm in the second step until the
desired criteria are met.
III. PROBLEM FORMULATION
The allocation capacitor is a nonlinear integer
optimization which limited by power constraint and
quality constraints.
Objective Function: minimize fundamental real
power loss and harmonic real power loss.
Figure 2: Harmonic Power Flow flowchart
=∑
HA matrix is used to find the presence of harmonic
sources. Harmonic source in this research are six
ASD. It will inject harmonic source to the system.
The harmonic components of capacitor current can be
calculate by
Is = (HLF^-1)*(-HAsh)* (Ih)
( )
+∑
∑
( )
(3)
Where
P_loss
Nb
ho
hmax
(1)
total power loss (kw)
the branch number
harmonic order to 1
maximum harmonic order
And the limits used are the boundaries of equality and
inequality. The equality boundary is the limitation
used by non- linear power flow calculations whereas
Where
Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using
PSO Algorithms
7
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
http://iraj.in
inequality limits are used to limit bus voltages,
magnitude of THD and amount of reactive power
being compensated. Here are the constrainthat must
be met.
Volume-5, Issue-9, Sep.-2017
Harmonic source will be placed in six location to
equalize the amount of capacitor. In that way
capacitor harmonic current can be calculate.
Harmonic source will be placed in according to table
4.
1. Voltage Bus
IV. SIMULATION AND DATA ANALYSIS
≤| |≤
(4)
This research used 25 bus unbalanced three phase
radial distribution system. As figure 3.
Where the lower limit of the voltage is
0.95 pu and the upper limit of the voltage is 1.05 pu
so it is still within the range of 5% of the nominal
voltage.
2. THD level
≤ 5%
(5)
THD limit for bus voltage below 69kV is 5%.
3. Reactive Power
∗
≤
(6)
The maximum reactive power that is
compensated by using capacitors is limited by the
total reactive power demand of the load.
4. Capacitor Loading limits
Capacitor limit as resonance index will be used in
case number 3 and 4. The result will be compare with
case number 1 and 2 to get the best result which
fulfill the constraint.
Index
Description
Limit
S
Apparent power of the
capacitor
RMS voltage of the
capacitor
Peak voltage of the
capacitor
RMS current of the
capacitor
135%
Vrms
Vpeak
Irms
Figure3: Single Line Diagram 25 Bus Unbalance System
From radial distribution power flow the voltage
profile are
110%
120%
180%
Table 1 : Standard Capacitor Loading Indices and Limits
Branch
Bus
Voltage
(kV)
I
J
Current(A)
Losses
(kW)
1
4.16
1
2
588.24
24.15
1
4.16
1
2
594.16
25.13
1
2
4.16
1
2
594.24
24.89
4.02
2
3
315.93
3.48
2
4.02
2
3
320.85
3.66
Table 4: The result from RDPF
The data of harmonic source are from ASD which
only used orde 5, 7, 11, and 13 because as in [7] it
was observed that in their vicinity, resonances close
to the fifth or the seventh harmonic order occurred.
Bus
Voltage
(kV)
2
Branch
I
J
Current
(A)
Losses (kW)
4.02
2
3
320.32
3.62
Order
Magnitude (%)
Angle
3
3.99
3
4
128.28
0.57
5
23.520
111
3
3.99
3
4
139.48
0.69
7
6.080
109
3
3.99
3
4
122.14
0.53
11
4.570
-158
4
3.97
4
5
27.96
0.07
13
4.200
-178
4
3.97
4
5
32.78
0.10
4
3.97
4
5
26.66
0.07
Table 3: Harmonic Injection
Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using
PSO Algorithms
8
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
http://iraj.in
Volume-5, Issue-9, Sep.-2017
5
3.97
2
6
272.31
6.87
19
3.93
18
20
52.58
0.41
5
3.96
2
6
273.34
6.96
20
3.94
18
21
18.93
0.05
5
3.97
2
6
273.92
6.97
20
3.94
18
21
22.00
0.07
6
3.97
6
7
217.60
4.38
20
3.94
18
21
24.33
0.09
6
3.96
6
7
223.44
4.65
21
3.93
21
22
33.11
0.16
6
3.96
6
7
225.34
4.72
21
3.94
21
22
26.91
0.11
7
3.92
6
8
32.88
0.20
21
3.93
21
22
28.27
0.12
7
3.92
6
8
28.06
0.15
22
3.92
4
23
78.53
0.46
7
3.92
6
8
26.75
0.13
22
3.93
4
23
82.63
0.51
8
3.95
7
9
105.81
1.04
22
3.92
4
23
76.74
0.44
8
3.95
7
9
102.27
0.97
23
3.96
23
24
51.83
0.20
8
3.95
7
9
105.92
1.04
23
3.96
23
24
49.83
0.19
9
3.90
9
10
105.81
1.04
23
3.96
23
24
48.74
0.18
9
3.89
9
10
102.27
0.97
24
3.95
24
25
32.98
0.16
9
3.89
9
10
105.92
1.04
24
3.95
24
25
25.64
0.10
10
3.87
10
11
83.46
0.39
24
3.95
24
25
26.82
0.11
10
3.87
10
11
79.91
0.36
25
3.94
10
3.87
10
11
83.54
0.39
25
3.94
11
3.86
11
12
27.40
0.05
25
3.94
11
3.86
11
12
28.75
0.06
11
3.86
11
12
33.70
0.08
12
3.86
11
13
22.44
0.04
12
3.86
11
13
22.45
0.04
3.85
11
13
22.46
3.86
7
14
62.68
0.36
13
3.86
7
14
65.84
0.40
13
3.86
7
14
68.96
0.44
14
3.91
14
15
24.51
0.03
14
3.90
14
15
19.10
After getting the results from the RDPF then proceed
HPF to get the Ploss harmonics and the amount of
THD early.
0.04
13
0.02
14
3.90
14
15
22.22
0.03
15
3.90
7
16
27.02
0.07
15
3.90
7
16
33.23
0.10
15
3.90
7
16
28.37
0.07
16
3.91
14
17
19.10
0.04
16
3.91
14
17
24.55
0.07
16
3.91
14
17
22.23
0.05
17
3.90
3
18
168.97
2.64
17
3.90
3
18
159.65
2.38
17
3.90
3
18
174.18
2.82
18
3.95
20
19
40.89
0.15
18
3.95
20
19
40.90
0.16
18
3.95
20
19
48.62
0.22
19
3.94
18
20
55.13
0.44
19
3.94
18
20
45.83
0.31
143.71
Bus
THD R
THD S
THD T
Bus
THD R
THD S
THD T
2
2.27
2.26
2.46
14
3.02
2.90
3.13
3
2.29
2.28
2.48
15
3.07
2.90
3.13
4
2.30
2.29
2.49
16
3.06
2.98
3.23
5
2.30
2.29
2.50
17
3.07
2.99
3.24
6
2.47
2.46
2.68
18
2.31
2.30
2.51
7
2.67
2.66
2.90
19
2.32
2.31
2.52
8
2.65
2.64
2.87
20
2.32
2.30
2.51
9
2.79
2.77
3.00
21
2.32
2.31
2.52
10
2.92
2.87
3.10
22
2.33
2.31
2.52
11
2.99
2.93
3.16
23
2.31
2.30
2.50
12
2.99
2.93
3.17
24
2.31
2.30
2.51
13
2.99
2.93
3.17
25
2.32
2.31
2.51
Table 5: The result from HPF
From table number 5 the biggest THD is 3.24 % and
the lowest is 2.26%.
The biggest THD is in the phase T and the lowest in
the phase S. Ploss harmonic is 0.0658 kW. So the
total loss of active power is 143.7716 kW.
Profile THD
3.3
3
THD (%)
12
Total Losses
2.7
2.4
2.1
1.8
1 3 5 7 9 11 13 15 17 19 21 23 25
Bus
Table 6 Profile THD
Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using
PSO Algorithms
9
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
http://iraj.in
In this research have 4 study cases.
1. Case no 1 only limited Voltage and reactive
power compensation.
2. Case no 2 limited Voltage, reactive power
compensation and THD.
3. Case no 3 limited Voltage, reactive power
compensation and RI.
4. Case no 4 limited voltage, reactive power
compensation, THD and RI.
no 3 doesn’t meet IEEE THD standard. So case
number 3 cannot be used.
Bus
2
3
4
5
6
7
8
9
10
11
12
13
From the simulation the results from study case no 1
the THD profile is describe by table number 6.
Bus
2
3
4
5
6
7
8
9
10
11
12
13
THD R
5.94
5.99
6.01
6.02
6.45
6.95
6.91
7.29
7.63
7.84
7.89
7.89
THD S THD T
2.78
3.39
2.81
3.42
2.82
3.43
2.82
3.43
3.02
3.67
3.25
3.95
3.23
3.93
3.35
4.09
3.45
4.23
3.52
4.31
3.52
4.34
3.53
4.35
Bus
14
15
16
17
18
19
20
21
22
23
24
25
THD R THD S THD T
7.99
3.54
4.35
8.07
3.54
4.37
8.05
3.62
4.46
8.07
3.62
4.47
6.05
2.83
3.45
6.07
2.84
3.46
6.06
2.84
3.46
6.07
2.84
3.46
6.09
2.85
3.47
6.03
2.83
3.44
6.05
2.83
3.45
6.06
2.84
3.45
Bus
2
3
4
5
6
7
8
9
10
11
12
13
From case number 1 allocation kapasitor are in bus
11 R 450 kVAR, bus 12 R 150 kVAR, 12 S 450
kVAR , 12 T 450 kVAR, 14 S 450 kVAR and 15 T
350 kVAR. The biggest THD is 8.07 %and the lowest
is 2.78 %. Case no 1 does not meet IEEE THD
standard. So case number 1 cannot be used.
THD T
2.23
2.25
2.26
2.26
2.42
2.61
2.59
2.68
2.76
2.80
2.81
2.80
Bus
14
15
16
17
18
19
20
21
22
23
24
25
THD R
4.19
4.23
4.25
4.25
4.54
4.88
4.87
5.07
5.25
5.37
5.42
5.42
THD S THD T
3.42
2.66
3.45
2.69
3.46
2.70
3.47
2.70
3.71
2.89
4.00
3.11
3.98
3.10
4.19
3.21
4.38
3.31
4.48
3.37
4.54
3.37
4.55
3.38
Bus
14
15
16
17
18
19
20
21
22
23
24
25
THD R THD S THD T
5.43
4.54
3.38
5.48
4.54
3.38
5.47
4.60
3.47
5.48
4.62
3.48
4.27
3.48
2.71
4.29
3.49
2.72
4.28
3.49
2.72
4.29
3.49
2.72
4.30
3.50
2.73
4.26
3.47
2.70
4.27
3.48
2.71
4.28
3.49
2.72
Table 8: THD Profile from Case Number 2
Table 6: THD Profile from Case Number 1
Bus THD R THD S
2
3.48
3.69
3
3.52
3.72
4
3.53
3.74
5
3.53
3.74
6
3.78
4.00
7
4.07
4.31
8
4.05
4.29
9
4.33
4.54
10
4.59
4.77
11
4.73
4.91
12
4.76
4.90
13
4.75
4.95
Volume-5, Issue-9, Sep.-2017
THD R
3.05
3.07
3.08
3.09
3.31
3.56
3.55
3.75
3.94
4.02
4.03
4.05
THD S
2.45
2.47
2.48
2.49
2.66
2.86
2.85
3.02
3.18
3.28
3.28
3.28
THD T
3.42
3.46
3.47
3.47
3.71
4.00
3.98
4.26
4.53
4.69
4.69
4.69
Bus
14
15
16
17
18
19
20
21
22
23
24
25
THD R THD S THD T
4.10
3.28
4.66
4.13
3.28
4.66
4.12
3.30
4.66
4.13
3.31
4.67
3.10
2.49
3.49
3.11
2.50
3.50
3.11
2.50
3.50
3.11
2.50
3.50
3.12
2.51
3.51
3.10
2.49
3.48
3.10
2.50
3.49
3.11
2.50
3.49
Table 9: THD Profile from Case Number 1
From case number 4 allocation kapasitor are in bus
11 R 350 kVAR, 10 R 150kVAR, 14 T 150 kVAR,
11 S 450 kVAR, 10 T 450 kVARdan 15 S150 kVAR.
The biggest THD is 4.62 %and the lowest is 2.45 %.
Case no 4 meet IEEE THD standard. So case number
4 can be used.
THD R THD S THD T
4.76
4.94
2.80
4.76
4.94
2.81
4.75
4.99
2.89
4.77
5.00
2.90
3.55
3.75
2.27
3.56
3.77
2.28
3.56
3.76
2.28
3.56
3.77
2.28
3.57
3.77
2.29
3.54
3.75
2.27
3.55
3.76
2.27
3.56
3.76
2.28
Compare
Before
After Allocation
Allocation Case 1 Case 2 Case 3 Case 4
Losses (kW)
143.67
113.53 115.88 115.38 115.30
Total Losses (kW)
143.77
113.63 115.98 115.44 115.40
Maximal THD
3.24
8.07
5.00
5.48
4.69
Reduction Total Ploss (%)
-
20.98
19.34
19.69
19.75
Total Capasitor (kVAR)
2300.00 2150.00 2250.00 2250.00
Table 10: Comparison of Capacitor Optimization Results
Before And After Capacitors.
Table 7: THD Profile from Case Number 1
From the table the best case which fulfil the equality,
inequality and the biggest reduction Ploss is case no
4.
From case number 2 allocation kapasitor are in bus
10 R 150 kVAR, bus 11 R 600 kVAR, 11 S 150
kVAR , 12 T 600 kVAR, 13 S 600 kVAR and 16 R
150 kVAR The biggest THD is 5 % and the lowest is
3.69 %. Case no 2 meet IEEE THD standard. So case
number 2 can be used.
CONCLUSION
From the simulation results on the distribution system
of 25 unbalanced three-phase bus, the following
conclusions are obtained:
1. The unbalanced three-phase bus distribution
system has a significant under voltage characteristic
of nearly 40%. And the maximum voltage is 0.97 pu.
From case number 3 allocation kapasitor are in 7 R
600 kVAR, 10 R 150kVAR, 12 R 150 kVAR, 12 S
600 kVAR, 12 T 600 kVARdan 150 kVAR.. The
biggest THD is 5.48 %and the lowest is 2.66 %. Case
Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using
PSO Algorithms
10
International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084
Volume-5, Issue-9, Sep.-2017
http://iraj.in
[7] IEEE Recommended Practices and Requirements for
2. Without considering the THD and the resonance
Harmonic
Control
index proven to cause 8% THD which is exceed the
in Electrical Power Systems, IEEE Standard 519, 1992
limit IEEE. Although it can reduce the loss of active
[8] Cheng T-H., dan Yang N-C, “Three-Phase Power-Flow by
power by 20.97%
Direct Zbr Method for Unbalanced Radial Distribution
Systems”, IET Gener.Transm.Distrib., Vol3, Iss.10, hal. 9033. Resonance index cannot stand alone because it will
910. (2009),
cause the system is not effective so it needs to be
[9] Saadat, Hadi, “Power System Analysis (Second Edition)”,
added consider THD proven by achieving maximum
McGraw-Hill Education (Asia), Singapura, hal. 189THD of 4.69% and can reduce the loss of active
240.(2004),
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11
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