Concurrent Placement of Distributed Generation
Resources and Capacitor Banks in Distribution
Systems
Milad Doostan, Shashank Navaratnan, Saeed Mohajeryami, Valentina Cecchi
Energy Production and Infrastructure Center (EPIC)
Electrical and Computer Engineering Department
University of North Carolina at Charlotte
Charlotte, NC, USA
Email: {mdoostan, snavarat, smohajer, vcecchi}@uncc.edu
Abstract—In this paper, a new approach for placement of
both Distributed Generation (DG) units and capacitor banks
in distribution systems is proposed. The goal is to 1) reduce
the total real and reactive power losses, 2) improve the voltage
profile, and 3) improve the power factor for the total demand. The
method uses a bus-ranking scheme based on a weighted sum of
indices representative of the impacts that a DG unit or capacitor
bank would have in terms of the three aforementioned objectives.
Moreover, the introduced indices provide a quantitative measure
to identify whether placing a DG unit or a capacitor bank is more
beneficial at each bus. In order to assess the performance of the
proposed method, a 49-bus distribution system is introduced.
The method is applied on the test system and best locations for
allocation of DG units and capacitor banks on each branch are
identified. Besides, a comparison between the performance of DG
units and capacitor banks at each bus is noted. At the end, by
examining the resulting real and reactive power losses, voltage
profile and power factor, it is demonstrated that the proposed
method successfully accomplishes its objectives.
Index Terms—DG placement; capacitor placement; loss reduction; voltage profile improvement; power factor improvement
I. I NTRODUCTION
In recent decades, the traditional energy resources have
increasingly become identified with serious environmental
problems. In addition, the growing electricity demand is
presenting challenges to the operation of the conventional
power system [1]. Consequently, the electricity industry is
seeking for alternative solutions to address the aforementioned
environmental and operational issues. One effective answer is
the integration of DG units into the power system [2]. DG
units are commonly known as the electric power generation
technologies that could be integrated within the distribution
systems [3], [4].
DG units offer various advantages over the traditional power
generation. The operational advantages include loss reduction,
congestion alleviation, interruption and transients alleviation,
reactive power support, voltage profile improvement, resiliency
improvement, providing electricity for remote areas, improving efficiency, and etc [3] , [5]–[10]. Furthermore, DG units,
by employing the renewable resources, could offer better
environmental protection.
On the other hand, should the wrong settings be selected
for the DG units, sundry challenges would be posed to the
safe and reliable operation of the power systems. For instance,
as DG technologies, specifically renewable resources, mainly
depend on the weather conditions or the owner’s decision in
order to generate electricity, the concerns of reliability and
maintaining adequate generation reserve’s margins might come
to the fore [3], [11], [12]. Also, another important issue,
caused due to the high penetration of DG units, is voltage
problem in low-voltage secondary distribution networks. For
example, the authors in [6] have found that if DG units are not
placed properly, there might be unwanted low/high voltages
at specific loads. Additionally, with high penetration of DG
units in the distribution system, the voltage level increases. If
the voltage rise is significant, it could violate the maximum
voltage criteria, specifically in light loading conditions [13].
In order to avoid the aforesaid problems and maximize the
benefits of the integration of DG units, it is critical to correctly
size and locate them [14]. There is a plethora of research
conducted to address the problems of DG units’ sizing and
placement. Reference [15] carries out an extensive review of
various methods employed for this purpose.
Traditionally, shunt capacitors have widely been used as
a major source of the reactive power support in distribution
networks. Capacitors are employed for various purposes such
as reducing power losses and improving the voltage profile
[16]. Almost all the methods explained in [15] could be
employed for sizing and placement of capacitors in distribution
networks.
In recent distribution systems, high penetration of DG units
as well as presence of capacitor banks, have prompted the
researchers to study and propose approaches for the simultaneous placement of DG units and capacitor banks. Indeed, it
is critical to present a holistic approach in the selection of DG
units and capacitor banks in order to avoid unwanted problems
such as the imbalance between the generated reactive power by
DG units and capacitor banks, and the reactive power needed
by the grid [17].
The authors in [16] propose a probabilistic formulation
for capacitor placement in distribution networks with high
penetration of DG units. In their work, Genetic Algorithm
(GA) has been used to solve the optimization problem. Their
results show that with proper capacitor placement in a system
with high penetration of DG units, a significant reduction in
cost associated with the electricity losses could be achieved.
In another attempt, the authors in [18] study the optimal
placement of DG units and the proper allocation of capacitor
banks simultaneously in distribution systems. The objective
function defined in their work consists of three indices: active
loss, reactive loss and voltage profile. The objective function
is minimized employing GA. Also, the effectiveness of the
proposed method is evaluated by comparing the voltage profile
of buses for both cases of prior and after the implementation.
In [19], the authors propose a new approach to minimize the
loss in the system with the presence of DG units and capacitor
banks at the same time. Bacterial Foraging Optimization
Algorithm (BFOA) is employed to minimize the objective
function. The results demonstrate that simultaneous DG and
capacitor placement is more effective in minimizing power
losses and improving the voltage profile.
In this paper, a new approach for simultaneous allocation of
capacitor banks and DG units is proposed. The advantage of
the proposed method over the aforesaid works is that it provides a quantitative measure to identify whether placing a DG
unit or a capacitor bank is more beneficial at each bus in order
to attain the objectives. Besides, unlike the aforementioned
works, which neglect the impact of unit allocation on power
factor, the proposed method attempts to make improvement on
power factor as one of its objectives.
The organization of the paper begins with introducing
the approach in section II. Afterwards, a 49-bus distribution
system is introduced in section III. This section, also, provides
a case study to evaluate the performance of the proposed
method. Moreover, the results are presented and discussed.
Section IV closes the paper by drawing conclusions.
II. M ETHODOLOGY
The allocation of capacitor banks and DG units in the
distribution system could be made to accomplish different
goals. They include power loss reduction, voltage profile
improvement, power factor correction, load balancing, and etc.
In this paper, the goal is to concurrently place capacitor banks
and DG units such that 1) total real and reactive losses of the
system are reduced, 2) voltage profile is improved, and 3) the
power factor for the total demand is improved. To carry out
such task, six indices are defined as in (1) to (6).
• Real and reactive power loss indices for DG unit and
capacitor bank, respectively:
P LDGi
P IDGi =
(1)
PL
QIDGi =
P ICi =
QLDGi
QL
(2)
P LCi
PL
(3)
QICi =
•
QLCi
QL
(4)
Voltage profile index for DG unit and capacitor bank:
V P Ii = max (1 − |Vj |)
(5)
j=1 to n
•
Power factor index for DG unit and capacitor bank:
P F Ii = max (1 − P F )
(6)
Where:
PL
Total real loss before DG/Cap. placement
Total real loss after DG placement at bus i
PLDGi
QL
Total reactive loss before DG/Cap. placement
Total reactive loss after DG placement at bus i
QLDGi
Total real loss after Cap. placement at bus i
PLCi
Total reactive loss after Cap. placement at bus i
QLCi
Voltage magnitude of bus j
|Vj |
n
Total number of buses
PF
Power factor percentage of the total demand
Indices that are defined in (1), (2) and (5) were previously
introduced in [20].
Two overall indices are defined from the aforementioned
indices as in (7) and (8).
OIDGi = w1 ·P IDGi +w2 ·QIDGi +w5 ·V P Ii +w6 ·P F Ii
(7)
OICi = w3 · P ICi + w4 · QICi + w5 · V P Ii + w6 · P F Ii (8)
Where, wi is weight coefficient assigned to indices and sum
total of the weights is one. The weight coefficients are to be
selected based on the priorities of objectives.
These indices are used to evaluate the impact of DG and
capacitor placement on real, reactive power losses, voltage
profile and power factor percentage of the total demand. It is
obvious that a lower value for each index is desirable. The
overall indices presented in (7) and (8) are a combination
of active loss, reactive loss, voltage profile and power factor
indices and are used to determine the best locations for
placement of units. Moreover, they are employed to identify
whether placing a DG unit or a capacitor bank is more
beneficial at each bus (i.e for each bus i, if OIDGi < OICi ,
placing a DG unit at that bus would be more beneficial in
terms of reducing losses, improving voltage profile and power
factor for total demand).
The proposed approach, which is illustrated in Fig.1, includes the following steps.
1) Power flow analysis is carried out and bus voltages are
computed;
2) Buses are ranked according to the voltage profile from
the lowest to the highest;
3) Buses with voltage below the limit are selected.If all
buses have voltage above the limit, then buses with
voltage less than the average voltage are selected.Indeed,
this selection will reduce the search space for the purpose of decreasing the computational burden;
4) A capacitor with initial value of 1 p.u (reactive power) is
placed at the selected buses one at a time, and the OICi
Start
Run the Power Flow
Step1
Rank buses according
to voltage magnitude
Step2
Yes
No
Are there buses with
Vi <Vmin?
Step3
Select buses with
Vi < Vmin
Select buses with
Vi < Vavg
Add DG unit to bus i and
calculate OIDGi
Add capacitor to bus i
and calculate OICi
Fig. 2: Schematic of the test system
DG unit
and
Capacitor
Allocation
Step4
base kVA is 10 kVA. Also, the current carrying capacity of
branches 1-5 is 400A, 32-35 and 38-45 is 300A and for all
other branches is 200A. The complete line and load data for
the test system is provided in appendix A.
Capacitor
or DG unit
Decision
Sort the buses according to their
OICi and OIDGi values
Step5
Yes
Based on the limits on numbers of
units, place DG or capacitor for
achieved locations in each branch
Increase the size of
units
OIDGi < OICi
DG is better
option for bus i
No
Capacitor is
better option
for bus i
No
Are Constraints
satisfied?
Yes
End
Fig. 1: Algorithm for the proposed method
is calculated. Similarly, a DG unit with unity power
factor and initial value of 1 p.u (real power) is placed
at the selected buses one at a time, and the OIDGi is
computed;
5) The buses are sorted according to their OICi and OIDGi
values. The buses with the lowest overall index value
in each branch have the highest priority for capacitor
and DG unit placement. Also, at this step, it could be
determined which of the capacitor bank or DG unit
provides a better result by comparing the OIDGi and
OICi values;
6) Based on the constraints on costs or number of allowed
capacitor banks or DG units, the number of units is
decided and the placement is performed;
7) The size of DG units and capacitor banks are adjusted
until all electrical requirements are satisfied.
III. M ETHOD I MPLEMENTATION
In what follows, for representation and validation purposes,
the method is applied on a test system.
A. Test system
A modified version of the system introduced in [21] is used
to perform the analysis. The schematic of the modified system
is demonstrated in Fig 2. The system is a 49-bus system. The
substation (S/S) voltage is assumed to be 12.66kV and the
B. Case Study
In order to apply the proposed method on the test system,
the algorithm is implemented in MATLAB. As it was discussed, the first step is to carry out the power flow analysis
to obtain voltage profile for all buses. Hence, the test system
is simulated in the software and the power flow is performed.
The resulting voltage profile for all buses is illustrated in Fig.
3.
The buses, then, are ranked based on their voltage magnitude from the lowest to the highest values, and buses with the
voltage magnitude less than the minimum are selected. In this
case study, V min is assumed to be 0.98 p.u. Table I shows the
buses with voltages less than 0.98 p.u. According to Table I, it
is observed that there are 25 buses that have voltage magnitude
less than the minimum.
Fig. 3: Voltage profile for test system
TABLE I: BUSES WITH VOLTAGE LESS THAN V min
Bus No.
45
44
43
42
41
18
17
16
15
14
13
12
11
Voltage (p.u.)
0.922511
0.922992
0.924914
0.925157
0.935629
0.960723
0.960741
0.96096
0.96117
0.961176
0.962317
0.962325
0.963133
Bus No.
10
9
49
48
40
8
47
46
7
39
6
38
Voltage (p.u.)
0.966257
0.968919
0.971294
0.971295
0.971323
0.971605
0.974477
0.974478
0.974531
0.975105
0.975556
0.977851
TABLE II: VALUE OF THE WEIGHTS
Weight
Value
w1
0.33
w2
0.22
w3
0.33
w4
0.22
w5
0.33
w6
0.11
TABLE III: INDEX VALUES FOR DG PLACEMENT
Bus
45
44
43
42
41
18
17
16
15
14
13
12
11
10
9
49
48
40
8
47
46
7
39
6
38
PIDGi
0.7277
0.7181
0.7169
0.7169
0.7570
0.9102
0.9084
0.8994
0.8952
0.8952
0.8922
0.8922
0.8922
0.8958
0.8982
0.9072
0.9072
0.8952
0.9012
0.9108
0.9102
0.9090
0.9084
0.9120
0.9180
QIDGi
0.7500
0.7396
0.7383
0.7383
0.7759
0.9028
0.9015
0.8950
0.8924
0.8924
0.8898
0.8898
0.8898
0.8924
0.8937
0.9002
0.9002
0.8782
0.8963
0.9028
0.9028
0.9015
0.8937
0.9028
0.9041
VPIi
0.0583
0.0582
0.0605
0.0609
0.0637
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0748
0.0728
0.0748
0.0748
0.0748
0.0748
0.0736
0.0748
0.0743
PFIi
0.1811
0.1812
0.1812
0.1812
0.1810
0.1800
0.1800
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1801
0.1800
0.1800
0.1800
OIDGi
0.4488
0.4433
0.4433
0.4434
0.4661
0.5490
0.5481
0.5436
0.5417
0.5417
0.5401
0.5401
0.5401
0.5419
0.5430
0.5474
0.5474
0.5378
0.5445
0.5491
0.5489
0.5483
0.5459
0.5495
0.5517
0.62
0.59
OICi
OIDGi
0.56
Overall Index Value
The algorithm continues with placement of one capacitor
bank with the initial value of 1p.u at each bus one at a time.
PICi , QICi , VPI i , PFI i and OICi indices are then calculated.
As it was mentioned, for the purpose of calculating the overall
index value, the weights (wi ) are to be selected based on the
priorities of objectives. The values of weights for this case
study are presented in Table II.
Next, the same procedure is followed for DG unit and
PIDGi , QIDGi , VPI i ,PFI i and OIDGi are computed. The
complete results for all indices for both cases of DG unit and
capacitor bank placements are presented in Tables III and IV.
For illustration purpose, the overal indices’ values achieved
for DG units and capacitor banks at each bus are shown and
compared in Fig.4
By sorting the buses according to their overall index values
for both capacitor banks and DG units the locations having
high priority for placement are determined. Table V sorts the
overall index values (multiplied by 100) for capacitor and DG
units. The values are scaled (i.e. multiplied by 100).
According to Tables III, IV and V, the following observations can be made.
• DG units provide lower overall index values for all buses
in comparison with capacitor banks; as a result, DG units
deliver better overall performance.
• DG units show better results for real and reactive power
loss reduction and voltage profile improvement as their
PIDGi , QIDGi and VPI i indices’ values are lower compared to that for capacitor banks.
• Capacitors deliver better performance for power factor
0.53
0.5
0.47
0.44
0.41
0.38
0.35
45 44 43 42 41 18 17 16 15 14 13 12 11 10 9 49 48 40 8 47 46 7 39 6 38
Bus Number
Fig. 4: Illustration of overal index values for different buses
improvement as their PFI i is lower compared to this
value for DG units.
• The best place for DG placement is bus 44, while the
best location for capacitor bank placement is bus 42.
• In the longest branch (buses 1 to 18), the best location for
DG unit placement is bus 13, whereas for the capacitor
bank placement, the best location is bus 8.
• Although a considerable voltage drop is observed in bus
18, this bus gets low priority for adding DG units and
capacitor banks.
In this paper, two DG units and one capacitor bank are
employed to show the improvements compared to the base
case. Although, as it was demonstrated, DG units deliver
better overall performance than capacitor banks at all buses,
due to possible limitations such as availability of DG units,
it is decided to use at least one capacitor bank. Also, it is
worth mentioning that cost of units could be a major concern;
nevertheless, in this paper, selection of the units is based on
the defined overall index values, which does not include cost
evaluation. The DG units are allocated to buses 44 and 13 and
the capacitor bank is placed at bus 8. As a matter of fact, as it
TABLE IV: INDEX VALUES FOR CAP. PLACEMENT
Bus
45
44
43
42
41
18
17
16
15
14
13
12
11
10
9
49
48
40
8
47
46
7
39
6
38
PICi
0.8318
0.8282
0.8264
0.8258
0.8491
0.9640
0.9622
0.9533
0.9491
0.9491
0.9449
0.9449
0.9443
0.9425
0.9413
0.9461
0.9461
0.9335
0.9401
0.9449
0.9449
0.9431
0.9413
0.9449
0.9473
QICi
0.8497
0.8419
0.8393
0.8393
0.8601
0.9533
0.9520
0.9455
0.9430
0.9430
0.9404
0.9404
0.9391
0.9378
0.9365
0.9404
0.9404
0.9235
0.9365
0.9391
0.9391
0.9378
0.9326
0.9391
0.9391
VPIi
0.0688
0.0699
0.0711
0.0713
0.0723
0.0762
0.0762
0.0761
0.0761
0.0761
0.0761
0.0761
0.0761
0.0761
0.0761
0.0761
0.0761
0.0751
0.0761
0.0761
0.0761
0.0761
0.0755
0.0761
0.0758
PFIi
0.1352
0.1353
0.1353
0.1353
0.1342
0.1309
0.1309
0.1310
0.1311
0.1311
0.1310
0.1310
0.1310
0.1308
0.1306
0.1304
0.1304
0.1305
0.1305
0.1302
0.1302
0.1302
0.1302
0.1301
0.1299
OICi
0.5040
0.5015
0.5007
0.5006
0.5132
0.5731
0.5722
0.5678
0.5658
0.5658
0.5638
0.5638
0.5634
0.5625
0.5617
0.5642
0.5642
0.5559
0.5613
0.5635
0.5635
0.5626
0.5607
0.5635
0.5641
TABLE V: COMPARING OVERALL INDEX VALUES FOR DG/CAPS.
Bus
44
43
42
45
41
40
13
15
10
9
16
8
39
49
17
7
46
18
47
6
38
OIDGi
44.33060769
44.33828213
44.34881399
44.88158179
46.61267613
53.78752192
54.01530568
54.17261688
54.19256501
54.30114282
54.36982435
54.45582105
54.59965553
54.74429115
54.81186157
54.83028785
54.89896938
54.90049124
54.91891752
54.95770267
55.1701715
Bus
42
43
44
45
41
40
39
8
9
10
7
11
6
47
13
38
49
15
16
17
18
OICi
50.06218
50.07686
50.15478
50.40921
51.32272
55.59956
56.07022
56.13844
56.17945
56.25035
56.26363
56.34121
56.35115
56.35226
56.38994
56.41819
56.42317
56.58826
56.78435
57.22902
57.31765
was demonstrated, bus 44 is the best place for DG placement;
therefore, one of the available DG units would be placed at
this bus. Moreover, as it was explained earlier, by looking at
the longest branch (buses 1 to 18), it is understood that the
best location for DG placement is bus 13. Hence, the second
available DG unit will be placed at this bus. For the capacitor
bank, the best location for placement is bus 42; furthermore, in
the longest branch bus 8 has the highest priority. It is decided
to place the capacitor in the longest branch; consequently, it
is placed at bus 8.
Finally, the values for all units are adjusted until all
electrical requirements (i.e. voltage, current and power flow)
are satisfied. The results of rating and location for units
are summarized in Table VI. Considering the total load in
the system and ratings of units provided in Table VI, DG
penetration would be 55.3%.
After allocation of the units in the proposed locations,
again, the power flow analysis is performed. The results of
voltage profile, real and reactive power losses and power factor
percentage value for total demand are compared with the base
case in Figs. 5 through 7, respectively. Based on Fig. 5, it
is observed that the proposed placement scheme significantly
improves the voltage profile. Moreover, there is a dramatic
decrease in real and reactive losses after employment of the
proposed method as demonstrated in Fig.6. Finally, according
to Fig. 7, the power factor value for total demand is increased
from 0.82 to 0.915. Hence, it is concluded that the proposed
method is able to effectively select appropriate buses for DG
unit and capacitor bank placement.
TABLE VI: RATING AND LOCATION FOR SELECTED UNITS
Unit
DG
DG
Capacitor Bank
Bus
44
13
8
Rating
1600 kW
500 kW
1000 kvar
Fig. 5: Comparing voltage profile before and after implementation of the
method
Fig. 6: Comparing losses before and after implementation of the method
Fig. 7: Comparing power factor before and after implementation of the
method
IV. C ONCLUSION
In this paper, a new method for concurrent placement of
DG units and allocation of capacitor banks was proposed. The
objective was to reduce the total real and reactive power losses,
improve the voltage profile and power factor. Moreover, the
method was developed such that it is capable of indicating
which of DG unit and capacitor bank is a better option to
be allocated to any bus in the system. In order to propose
the method, eight indices were defined and an algorithm
was developed. For representation and validation purposes the
method was applied on a 49-bus distribution system. Then, the
algorithm was followed step by step and the best locations for
installing the DG units and capacitor banks on each branch
were determined. Moreover, the indices defined for DG units
and capacitor banks were compared with each other and for
each bus it was indicated which of DG unit or capacitor bank
delivers better performance for each objective. Then, two DG
units and one capacitor bank were placed and sized such that
all electrical constraints were satisfied. Finally, by analyzing
and comparing the results of voltage profile, power losses, and
power factor for base case and proposed method, the desirable
performance of the method was demonstrated.
As a future study, the authors have plan to define an index
for cost and include it in the overall index for both DG units
and capacitor banks, and investigate its effects on the results.
A PPENDIX A
The complete line and load data (sending end and receiving
end buses, impedance and load values) for the test system is
provided in Table VII.
TABLE VII: DATA FOR THE TEST SYSTEM
Sending
End
S/S
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
19
20
21
22
23
1
25
26
27
28
29
30
2
32
33
34
4
36
5
38
39
40
41
42
43
Receiving
End
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
R
(Ω)
0.001
0.0015
0.7721
0.0922
0.0493
0.819
0.1872
0.7114
1.03
1.044
1.2546
0.3744
0.0047
0.8798
0.014
0.5054
1.0577
0.1732
0.0044
0.064
0.819
0.839
1.708
1.474
0.0044
0.064
0.1357
0.0018
1.0793
0.1181
0.0009
0.0034
0.0851
0.2898
0.0822
0.0928
0.3319
0.174
0.203
0.2842
2.9692
0.8936
0.0974
0.8555
X
(Ω)
0.0024
0.0036
0.4099
0.047
0.0251
0.2707
0.0619
0.2351
0.34
0.345
0.4146
0.1238
0.0016
0.2902
0.0046
0.1671
0.3496
0.0572
0.0108
0.1565
0.2707
0.2816
0.5646
0.4873
0.0108
0.1565
0.1585
0.0021
1.261
0.1489
0.0012
0.0084
0.2083
0.7091
0.2011
0.0473
0.1114
0.0886
0.1034
0.1447
1.0406
0.3757
0.0496
0.4357
Receiving End Load
P
Q
(kW)
(kVar)
0
0
0
0
40.4
30
75
54
30
22
28
19
145
104
145
104
8
5
8
5.5
45.5
40
60
35
60
35
114
81
5
3.5
28
20
14
10
14
10
26
18.6
26
18.6
0
0
14
10
19.5
14
6
4
26
18.55
26
18.55
24
17
24
17
6
4.3
39.22
26.3
39.22
26.3
0
0
79
56.4
385
275
385
275
40.5
28.3
3.6
2.7
4.35
3.5
26.4
19
24
17.2
100
72
1244
888
32
23
227
162
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