Electrical Power and Energy Systems 45 (2013) 142–151
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
A novel approach to identify optimal access point and capacity of multiple
DGs in a small, medium and large scale radial distribution systems
Satish Kumar Injeti a,⇑, N. Prema Kumar b
a
b
Department of Electrical and Electronics Engineering, Sir C.R. Reddy College of Engineering, Eluru, West Godavari, Andhra Pradesh 534 007, India
Department of Electrical Engineering, A.U. College of Engineering, Andhra University, Visakhapatnam, Andhra Pradesh 530 003, India
a r t i c l e
i n f o
Article history:
Received 20 April 2012
Received in revised form 11 July 2012
Accepted 19 August 2012
Keywords:
Distributed generation
Large scale radial distribution system
Simulated annealing
Voltage
Stability index
a b s t r a c t
Distributed generation (DG) sources are predicated to play major role in distribution systems due to the
demand growth for electrical energy. Location and sizing of DG sources found to be important on the system losses and voltage stability in a distribution network. In this paper an efficient technique is presented
for optimal placement and sizing of DGs in a large scale radial distribution system. The main objective is
to minimize network power losses and to improve the voltage stability. A detailed performance analysis
is carried out on 33-bus, 69-bus and 118-bus large scale radial distribution systems to demonstrate the
effectiveness of the proposed technique. Performing multiple power flow analysis on 118-bus system, the
effect of DG sources on the most sensitive buses to voltage collapse is also carried out.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The features like radial structure, high R/X ratio and unbalanced
loads make radial distribution systems special. High R/X ratios in
distribution lines result in large voltage drops, low voltage stability
and high power losses. Traditional methods such as Newton
Raphson and Fast Decoupled Power Flow are effective for ‘‘well conditioned’’ power systems but tend to encounter convergence problems with distribution systems due to above mentioned features.
A more suitable algorithm for distribution systems such as ladder
technique (backward–forward sweep) or power summation must
be used. The radial distribution system (RDS) experiences sudden
voltage collapse due to the low value of voltage stability index at
most of its nodes under critical loading conditions in certain industrial areas. Recently, DGs are becoming increasingly attractive to
utilities and consumers because these units produce energy close
to the load, and are more efficient (less losses), easier to site and have
less environmental impact. DGs are primarily installed on the distribution and sub transmission level networks. Their main technical
benefits include [1]:
Reduced line losses.
Voltage profile improvement.
Improved reliability and security.
⇑ Corresponding author. Mobile: +91 9581371537.
E-mail addresses: [email protected] (S.K. Injeti), prem_navuri@yahoo.
co.in (N. Prema Kumar).
0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ijepes.2012.08.043
Reduced GHG emissions from central power plants.
Relieved T&D congestion.
Several optimization studies have been performed to quantify
these benefits and identify DG penetration threshold limits by
optimally locating and sizing DGs to improve a particular objective,
or a combination of objectives.
Authors in [2], considered an analytical expression to calculate
the optimal size and an effective methodology to identify the corresponding optimum location for DG placement for minimizing the
total power losses in primary distribution systems. Authors in [3],
considered a simple method for optimal sizing and placement of
DGs. A simple conventional iterative search technique along with
Newton Raphson method of load flow study is implemented.
Authors in [4], were to quantify the effect of DG on system reliability improvements, but did not use this to specifically allocate DG
optimally. In [5], author fixed the DG candidate locations, number
of available DGs, and total DG capacity before optimally allocating
binary encoded DGs of a predefined size to minimize real power
loss only. Authors in [6] combined two optimization methods, a
discrete form of PSO and GA operators, to perform optimal DG allocation using technical objectives but assigned costs to the objectives. But considering cost function in finding optimal location
and DG size may deviate from the original problem. Author in
[7], used the Harmony Search Algorithm as a new approach; however, the optimal penetration limit for DG is set by the user before
running the optimal allocation routine. Hung et al. in [8], combined
the loss sensitivity concept with optimal siting and sizing, but only
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S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Table 1
Summary of DG types [17].
DG type
p.f
Capable of injecting
Example
1
2
3
4
0 < p.fDG < 1
0 < p.fDG < 1
p.fDG = 1
p.fDG = 0
Real power and reactive power
Real power but consuming reactive power
Real power only
Reactive power only
Synchronous generator
Wind turbine
PV, MT and FC with PE interface
Synchronous compensator
studies the real and reactive power loss reduction objectives. However, the authors did execute a rigorous comparison of the IA
method with the bench mark ELF method lending credibility to
their work. Authors in [9], used an energy savings goal based on
emission reduction, which are typically highly specific to the region and power supply mix, and can be difficult to quantify accurately. In [10], a GA based algorithm was used to determine the
optimum size and location of multiple DGs to minimize the losses
and the power supplied by the grid. In [11], DGs were placed as at
the most sensitive buses to voltage collapse. The DGs had the same
capacity and were placed one by one. In [12], a GA–PSO based algorithm was presented to find optimal location and sizing of multiple
DGs to minimize multi objective function. All mentioned research
installing DGs with unity power factor in small and medium distribution systems. And many authors did not mention the run time of
implemented methods. In [13], a PSO–GA was used to find the
optimal location of a fixed number of DGs with specific total capacity such that the real power loss of the system is minimized and
the operational constraints of the system are satisfied. In this paper
fast and novel computation technique is proposed to evaluate the
optimal siting and sizing of multiple DGs with unspecified power
factor (p.f) in a large scale radial distribution system with an objective of minimizing real power loss and improvement in voltage
profile. The first stage in the technique presented in this paper is
optimal siting by applying the loss sensitivity factor (LSF). The
advantage of relieving SA from determination of optimal location
of DGs is to reduce the search space and to improve convergence
characteristics and less computation time. The top most nodes
are ranked to create a candidate nodes list, and within this list
the top ranked index values represented optimal DG locations after
which optimal sizing was then performed using Simulated Annealing. The proposed technique was applied to large scale 118-bus radial distribution system [14] without tie-lines. It is capable of
finding optimum solution with in very short simulation time, in
the range of a few seconds. A multiple power flow analysis is carried out to determine the effect of DGs on the voltage stability. The
entire technique is built in MATLAB platform.
3. Types of distributed generation
Table 1 gives information about various types of DGs. It should
be noted that although utilities, manufacturers and the researchers
agree that reactive power support is useful by-product of DG
installation. If utilities infrastructure is equipped with two-way
communication between small DG and utility’s control operations
center, then it is easy to manage reactive power. Therefore, the current practice is to maintain DG at unity power factor. The developed algorithm can handle all types of DG at various load levels.
The present studies were run with Type 1 (0.866 p.f) and Type 3
(Unity p.f) DGs only.
4. Problem formation
Optimal DG placement in a radial distribution system is to find
best locations of radial network that gives minimum power loss
while satisfying certain operating constraints. The operating constraints are voltage profile of the system, current capacity of the
feeder and radial structure of the distribution system. The objective
function for the minimization of power loss is described as follows:
F ¼ minðPT;Loss Þ . . . with DGs
Subjected to:
Power balance constraint:
PDGi ¼ PDi þ PLoss
ð1Þ
Voltage limits:
V imin 6 V i 6 V imax
ð2Þ
Thermal limit:
Ii;iþ1 6 Ii;iþ1max
ð3Þ
Real power generation limits
PDGimin 6 PDGi 6 PDGimax
ð4Þ
Reactive power generation limits
Q DGimin 6 Q DGi 6 Q DGimax
2. Load model
Distribution system loads are characterized by voltage sensitivity, and most distribution load flow programs offer the following
standard models:
Constant Power – The real and reactive power stays constant as the voltage changes.
Constant Current – The current stays constant as the voltage changes.
Constant Impedance – The impedance is constant as the
voltage changes.
In short feeders’ power loss is of great concern and for large
feeders voltage stability is great importance. Modeling all loads
as constant current is a good approximation for many circuits
while modeling all loads as constant power is conservative for voltage profile analysis [15,16]. In this context it is more relevant to assume all loads are constant power loads.
ð5Þ
where Vi is the voltage magnitude of bus i, Vmin and Vmax are bus
minimum and maximum voltage limits, respectively. Ii,i+1max is the
maximum loading on branch i, i + 1. Ii is the current flowing through
the ith branch, which is dependent on the locations and sizes of the
DGs. A set of simplified feeder-line flow formulations is employed.
Considering the single-line diagram depicted in Fig. 1, the recursive
Eqs. (6)–(8) are used to compute the power flow.
Because of the complexity of the large scale distribution system,
network is normally assumed as symmetrical system and constant
loads. Therefore, the distribution lines are represented as series
impedances of the value (Zi,i+1 = Ri,i+1 + jXi,i+1) and load demand as
constant and balanced power sinks SL = PL + jQL.
The real and reactive power flows at the receiving end of branch
i + 1, Pi+1, and Qi+1, and the voltage magnitude at the receiving end,
|Vi+1| is expressed by the following set of recursive equations:
Piþ1 ¼ Pi P Liþ1 Ri;iþ1 P2i þ Q 2i
jV i j2
ð6Þ
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Table 2
Assigned values for various SA parameters.
Parameter
Value
Population size
Initial temperature
Final temperature
Cooling rate factor
Boltzmann constant
30
1.0
1e8
0.9
1.0
Fig. 1. Single-line diagram of a main feeder.
ward update is expressed by the following set of recursive
equations:
Pi1 ¼ Pi þ PLi þ Ri;iþ1 P 2i þ Q 2i
ð7Þ
jV i j2
2
2
jV iþ1 j ¼ jV i j 2ðRi;iþ1 Pi þ X i;iþ1 Q i Þ þ ðR2i;iþ1 þ X 2i;iþ1 Þ P2i þ Q 2i
jV i j2
ð8Þ
Eqs. (5)–(7) are known as the distinct flow equations. Hence, if P0,
Q0, V0 at the first node of the network is known or estimated, then
the same quantities at the other nodes can be calculated by applying the above branch equations successively. This procedure is
referred to as a forward update. Similar to forward update, a back-
02
P02
i þ Qi
ð10Þ
jV i j2
jV i1 j2 ¼ jV i j2 2ðRi1;i P 0i þ X i1;i :Q 0i Þ þ ðR2i1;i þ X 2i1;i Þ P 0i
ð9Þ
jV i j2
Q i1 ¼ Q i þ Q Li þ X i;iþ1 Fig. 2. Single line diagram of a two-bus distribution system.
Q iþ1 ¼ Q i Q Liþ1 X i;iþ1 02
P02
i þ Qi
02
P 02
i þ Qi
jV i j2
Q 0i
where ¼ P i þ P Li and
¼ Q i þ Q Li .
Note that by applying backward and forward update schemes
successively one can get a power flow solution. The power loss of
the line section connecting between buses i and i + 1 is computed
as:
PLoss ði; i þ 1Þ ¼ Ri;iþ1 02
P02
i þ Qi
jV i j2
ð11Þ
The total power loss of the feeder PF,Loss is determined by summing
up the losses of all line sections of the feeder, which is given by
Fig. 3. SA perturbation process.
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Table 3
Performance analysis of the 33- bus RDS after DG installation at different system power factors
Method
PLoss (MW)
GA [12]
Critical bus/S.I. value/voltage (p.u)
Bus no.
Before DGs
After DG
Before DGs
After DGs
0.2109
0.10630
18/0.6672/0.90377
25/0.9258/0.98094
PSO [12]
0.10535
30/0.9247/0.98063
GA/PSO [12]
0.10340
25/0.9254/0.98083
LSFSA
0.08203
14/0.8768/0.96767
LSFSA
0.02672
25/0.9323/0.98266
DG size
11
29
30
13
32
8
32
16
11
6
18
30
6
18
30
p.f
PDG (MW)
QDG (Mvar)
1.5000
0.4228
1.0714
0.9816
0.8297
1.1768
1.2000
0.8630
0.9250
1.1124
0.4874
0.8679
1.1976
0.4778
0.9205
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.6915
0.2759
0.5315
Unity power factor
0.866
Table 4
Performance analysis of the 69- bus RDS after DG installation at different system power factors.
Method
PLoss (MW)
GA [12]
Critical bus /S.I. value/voltage (p.u)
Locations
Without DG
With DG
Without DG
With DG
0.2247
0.0890
65/0.6833/0.90919
57/0.9736/0.99360
PSO [12]
0.0832
65/0.9609/0.99007
GA/PSO [12]
0.0811
65/0.9703/0.99249
LSFSA
0.0771
61/0.9655/0.98115
LSFSA
0.01626
61/0.9678/0.9885
PT;Loss ¼
n1
X
PLoss ði; i þ 1Þ
ð12Þ
21
62
64
61
63
17
63
61
21
18
60
65
18
60
65
PLineloss ½q ¼
i¼0
where the total system power loss PT,Loss is the sum of power losses
of all feeders in the system.
5. Optimal location and sizing of DGs
The technique consists of two parts. The first part in the technique presented in this paper is optimal siting by applying the
power loss sensitivity factor (LSF). The second part in the comprehensive technique finds the optimal size of DGs at the feasible locations by applying a Meta heuristic optimization algorithm,
Simulated Annealing.
Q Lineloss ½q ¼
DG size
p.f
PDG (MW)
QDG (Mvar)
0.9297
1.0752
0.9925
1.1998
0.7956
0.9925
0.8849
1.1926
0.9105
0.4204
1.3311
0.4298
0.5498
1.1954
0.3122
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.3175
0.8635
0.1803
ðP2eff ½q þ Q 2eff ½qÞR½k
ðV½qÞ2
ðP2eff ½q þ Q 2eff ½qÞX½k
ðV½qÞ2
Unity power factor
0.866
ð13Þ
ð14Þ
where Peff [q], Qeff[q] are total effective active and reactive power
supplied beyond the node ‘q’.
After mathematical process, the loss sensitive factors can be obtained as follows:
@PLineloss 2 R½k Q eff ½q
¼
@Q eff
ðV½qÞ2
ð15Þ
5.1. Loss sensitivity factors
@Q Lineloss 2 X½k Q eff ½q
¼
@Q eff
ðV½qÞ2
ð16Þ
The locations for the placement of DGs are determined using
loss sensitivity factors. The estimation of these locations basically
helps in reduction of the search space for the optimization procedure. Consider a distribution line with an impedance of R + jX
and a load of Peff. + jQeff, connected between ‘p’ bus and ‘q’ bus as
given in Fig. 2.
Active power loss in the kth line is given by, ½I2k R½k which can
be expressed as,
The loss sensitivity factors (oPlineloss/oQeff) are calculated from
the base case load flows and the values are arranged in descending
order for all the lines of the given system or according to Eq. (15),
buses will be ranked and some buses are locations as the one
which have the most sensitivity for DG placement in order to have
the best effect on loss reduction. A vector bus position ‘bpos[i]’ is
used to store the respective ‘end’ buses of the lines arranged in
descending order of the values (oPlineloss/oQeff). The descending
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S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Fig. 4. Convergence characteristics of objective function.
order of (oPlineloss/oQeff) elements of ‘bpos[i]’ vector will decide the
sequence in which the buses are to be considered for compensation. This sequence is purely governed by the (oPlineloss/oQeff) and
hence the proposed loss sensitive factors become very powerful
and useful in DG Placement. At these buses of ‘bpos[i]’ vector, normalized voltage magnitudes are calculated by considering the base
case voltage magnitudes given by (norm[i] = V[i]/0.95). Now for the
buses whose norm[i] value is less than 1.01 are considered as the
locations requiring the multiple DG Placement. These candidate
buses are stored in ‘rank bus’ vector. It is worth note that the ‘Loss
Sensitivity factors’ decide the sequence in which buses are to be
considered for compensation placement and the ‘norm[i]’ decides
whether the buses needs compensation or not. If the voltage at a
bus in the sequence list is healthy (i.e., norm[i] > 1.01) such bus
needs no compensation and that bus will not be listed in the ‘rank
bus’ vector. The ‘rank bus’ vector offers the information about the
possible potential or locations for DG placement. The sizing of DGs
at buses listed in the ‘rank bus’ vector is done by using Simulated
Annealing, i.e., locations determined by loss sensitivity factors are
given as input. So the objective function is now only dependent on
the sizes of the DGs at these locations.
growing since mid 1980s [18]. SA is not new to power system
optimization; it was already implemented in distribution system
reconfiguration problem [19]. Application of SA algorithm to optimal sizing of multiple distributed generators is new. There are three
most important parameters of the SA technique require solving any
optimization problem as follows:
The annealing temperature, this parameter permits the SA not
to be entrapped in local minima though the use of Boltzmann’s
function.
The number of iterations at constant temperature. A low number of iterations will result in being trapped in local.
Cooling strategy, if the annealing temperature is decreased too
fast the algorithm will be trapped in the local.
6.2. SA components
6.2.1. Initialization
The initial solution or configuration of a DG size is set with their
upper and lower limits which are determined by
X i ¼ roundðU ðX max X min ÞX min Þ
ð17Þ
6.1. SA algorithm principle
where Xi is the size of DG number i, U is a uniform randomly generated number between 0 and 1, and Xmin and Xmax are the lower
limit and upper limit of the location, respectively.
A technique to obtain near-to-optimum solution of optimization
problems entitled SA was proposed by Kirk Patrik, Gelatt and Vecchi
in 1983. SA has been tested in several optimization problems showing great ability for not been trapped in local minima. Due to its
implementation simplicity and good results shown, its use has been
6.2.2. Perturbation process
The trial neighborhood solution matrix is generated by perturbing the current solution matrix as shown in Fig. 3.
Where Nl is the size of DG, XNl (k) is the size of DG at iteration k,
ðkþ1Þ
and X Nl
is the size of DG at the next iteration
6. Simulated Annealing
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S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Table 5
Performance analysis of the 118 bus RDS after DG installation at different system power factors.
Type
PLoss (kW)
Reduction in PLoss (kW)
% Loss reduction
Bus no.
DG size (MW/Mvar)
Comp. time (s)
75
116
56
36
103
75
116
56
36
103
88
48
75
116
56
36
103
75
116
56
36
103
88
48
2.1318/0.00
0.7501/0.00
1.1329/0.00
4.5353/0.00
4.9452/0.00
2.8246/0.00
0.4606/0.00
3.6739/0.00
7.4673/0.00
5.0803/0.00
2.2979/0.00
0.7109/0.00
2.9296/1.6896
1.5465/0.8930
1.4841/0.8570
4.4551/2.5725
5.9126/3.4140
2.7544/1.5904
0.5076/0.2931
4.3123/2.4900
6.1109/3.5285
5.3350/3.0805
0.6262/0.3616
2.1778/1.2575
23.6635
Before DG’s
After DG’s
1296.3604
858.8133
437.5471
33.75
With 7DG’s at Unity p.f Type 1
900.1885
396.1719
30.56
With 5DG’s at 0.866 p.f Type 3
684.0282
612.3322
47.23
With 7DG’s at 0.866 p.f Type 3
638.9684
657.3920
50.71
With 5DG’s at Unity p.f Type 1
25.2920
23.9703
25.3011
Fig. 5. Voltage profile of 118-bus radial distribution system.
6.2.3. Schedule of cooling
Cooling schedule is an annealing process with rate of cooling.
The schedule can be determined by
6.2.4. Probability of acceptance
The probability (P) is designed for decision movement of the
current solution (Sc), and it is given by
T k ¼ r T ðk1Þ
P ¼ exp
ð18Þ
where Tk is the temperature at iteration k, and r is the reduction
rate.
ðFðSÞt FðSÞc Þ
KbTk
ð19Þ
where St is the trial Solution, Sc is the current solution, Tk is the temperature, and kb is the Boltzmann constant. When P is higher than
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S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Table 6
Summary of critical bus & its stability index value for 118-bus system.
System
Bus no.
Voltage (p.u)
Angle (°)
S.I.
Without DG (base case)
With 5DG’s at unity p.f.
With 7DG’s at unity p.f.
With 5DG’s at 0.866 p.f.
With 7DG’s at 0.866 p.f.
77
54
111
54
111
0.86880
0.91905
0.93249
0.93765
0.94689
0.09541
0.55204
2.40942
0.49115
1.55736
0.5700
0.7165
0.7561
0.7733
0.8044
the uniform randomly generated (0, 1), the St is accepted as the next
current solution (Stþ1
c ).
6.3. Implementation of SA algorithm to solve optimal DG sizes
Step 1: Read the system data, power factor and constraints
Step 2: Run base case radial load flow
Step 3: Identify the locations for DG placement using Loss Sensitivity Factors
Step 4: Input identified locations to SA
Step 5: Set the temperature (T), iteration (K), (Ko), and the
reduction rate (r)
Step 6: Generate the initial solution and set it as the current
solution (Sc).
Step 7: Set the best solution found so far Sb = Sc.
Step 8: Generate trial solutions (St) around the best solutions
Step 9: If F(St) < F(Sb), set Sb = St. Otherwise,
If exp (F(St) F(Sc)/kbTk) > random (0–1), set Sb = St,
Else Sb is not updated. Set Ko = Ko + 1.
Step 10: If K0 > K0max, go to step11. Otherwise, go to step 8
Step 11: reduce temperature by Eq. (18).
Step 12: Check the stopping criterion. If satisfied, terminate the
search, else set K = K + 1, and go to step (6).
7. Implementation and numerical results
To validate the proposed method, it is initially tested on 33-bus
and 69-bus distribution systems, later implemented on 118-bus
large scale radial distribution system. The first system is a radial
distribution system with total load of 3.72 MW, 2.3 Mvar and the
real and reactive power losses in the system is 210.998 kW and
143 kvar [20]. The second system is a radial distribution system
with total load of 3.80 MW and 2.69 Mvar and the real and reac-
tive power losses in the system is 224.7 kW and 102.13 kvar
[21]. The third system is 118-bus large scale radial distribution
test system without tie lines and the base values used are
100 MVA and 11 kV. The total power loads are 22.709 MW and
17.041 Mvar. After load flow, real and reactive power losses at
its initial structure without tie lines are 1296.3 kW and
978.36 kvar. The detailed data of the test system is given in [14].
Maximum penetration of DG is considered in a range of 0–70%
of total load plus losses. In this study, it is considered that the
DG is operated at unity and other than unity power factor, unlike
the situation has commonly been used in literature. The maximum
number of DGs is restricted to three for 33-bus and 69-bus systems and seven for 118-bus system in this study, but developed
technique can accept any number of DGs. In fact, the number of
DGs is purely dependent on size of the test system, because inserting as many DGs in the system sometimes may result higher
power loss. The first bus is considered as sub-station bus and the
remaining buses of the distribution system except the voltage controlled buses are considered for the placement of DGs of given size
from the range considered. The real and reactive power loads were
modeled as being voltage dependent. A number of trails on the
performance of the proposed technique have been carried out on
the test systems to determine the most suitable SA parameters.
The control parameters of SA are furnished in Table 2. The results
of applying the proposed method to the systems under consideration and the results given in [12] through applying the GA, PSO
and GA/PSO are given in Tables 3 and 4. It must be noted that
the run time of SA algorithm 1.6 s for 33-bus and 2.4 s for 69bus radial distribution systems, which relatively very short time
is. After successful implementation of proposed method on small
and medium scale distribution systems the same has been applied
to 118-bus large scale radial distribution system in addition voltage stability analysis is also carried out. As shown in Fig. 4, the
objective function converges to global optimum solution within
a reasonable computing time of about 24 s with 5 DGs and 25 s
with 7 DGs on an INTEL Core 2 Duo processor, 2.93 GHz with
1.96 GB of RAM. All evaluations were carried out with self developed MATLAB codes. The developed code has an ability to find
optimal placement and sizing of any number of DGs at any power
factor.
The effect of optimal access point and capacity of Type-1 and
Type-3 DGs on the real power loss of the 118-bus system, percentage loss reduction and computation time are given in Table 5. It is
Fig. 6. Variation of voltage magnitude and stability index value at critical bus of the 118-bus system with increasing load power.
S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Fig. 7. Variation of voltage magnitude and stability index value at critical bus of the 118-bus system with increasing load power including Type-1 5 DGs.
Fig. 8. Variation of voltage magnitude and stability index value at critical bus of the 118-bus system with increasing load power including Type-3 5 DGs.
Fig. 9. Variation of voltage magnitude and stability index value at critical bus of the 118-bus system with increasing load power including Type-1 7 DGs.
149
150
S.K. Injeti, N. Prema Kumar / Electrical Power and Energy Systems 45 (2013) 142–151
Fig. 10. Variation of voltage magnitude and stability index value at critical bus of the 118-bus system with increasing load power including Type-3 7 DGs.
shown that the Type-1 DGs caused less loss reduction compared to
Type-3 DGs. The reason is improved node voltage due to Type 3
DGs will give reactive power support to the system. And the overall
time taken for computation is almost same for the Type 1 and Type
3 DGs. The effect of inserting DGs on the voltage profile of the system is shown in Fig. 5, improvement in voltage profile under Types
1 and 3 DGs is possible. It is clear that with Type 3 DGs improvement in voltage profile is very significant. It is observed that, from
Table 3 percentage line loss reduction is significant in case of 5 DGs
than 7 DGs operating at unity p.f. But, it is not same with the case
of Type-3 7DGs operating at 0.866 p.f. The results of critical bus
analysis with Type 1 and Type 3 DGs are presented in Table 6.
Using the voltage stability indicator developed in [22], each node
or bus stability index (S.I) values are calculated, and the bus which
has minimum stability index value is recorded as the critical bus,
which is most sensitive to voltage collapse. Running multiple
power flow program developed in [23] for the test system with
and without DGs, in which each node or bus power is multiplied
by a load factor (k) as P = kPb and then P–V curves has been recorded. Bus 54 for 5 DGs case and bus 111 for 7 DGs case are weakest buses, showed a great improvement in the maximum loading
and hence in the voltage stability margin for buses in both cases.
From Figs. 6–10 it is observed that the variation of the critical
bus voltage magnitude and stability index value with increase of
load active power from the base case to the maximum loading
point for 118-bus system. Hence the improvement in critical loading point of the test system beyond which a small increment of
load causes the voltage collapse is also observed.
8. Conclusion
In the paper combined fast technique was proposed to solve
optimal access point (location) and capacity (size) for DGs. In this
technique, LSF and SA were used to determine the location and
to calculate the size of DGs respectively. Developed technique
was implemented for 33-bus, 69-bus and 118-bus large scale radial
distribution systems to minimize the losses, to improve the voltage
profile and to increase the voltage stability margin and maximum
loading. The results showed that the proposed technique is simple
in nature and capable of solving optimal placement and sizing
problem of DGs run at any power factor very quickly (less compu-
tation time). It is concluded that the proposed technique can be
implemented for any size of system. Inclusion of real time constraint and discrete DG sizes into proposed technique is the future
scope of this work.
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