[doi 10.1109%2FMAMI.2017.8307867] Kasturi, Kumari; Nayak, Manas Ranjan -- [IEEE 2017 2nd International Conference on Man and Machine Interfacing (MAMI) - Bhubaneswar, India (2

2017 2nd International Conference on Man and Machine Interfacing (MAMI)
Techno-Economic Analysis of conductor & capacitor
allocation in RDS using ICSA
Kumari Kasturi
Manas Ranjan Nayak
Dept. of Electrical Engg.
Siksha ‘O’ Anusandhan University
Bhubaneswar, 751030, Odisha, India
[email protected]
Dept. of Electrical Engg.
Siksha ‘O’ Anusandhan University
Bhubaneswar, 751030, Odisha,India
[email protected]
Abstract— In recent years, simultaneously the conductor and
capacitor allocation have been considered as a favorable
solution for reduction of real power loss, improvement of
voltage profile & stability, increase reserve capacity for
demand growth and maximize financial benefits in radial
distribution systems (RDS). A novel approach based on metaheuristic algorithm, known as Improved Cuckoo Search
Algorithm (ICSA) is to find the optimal allocation of the
system in 32-bus RDS. The suggested optimization technique is
used to minimize the objective function which includes (1) cost
of power losses, (2) cost of the installed conductors,(3) cost of
the installed capacitors . To validation of efficiency of
presented method, results are compared with previous similar
works.
Index Terms— Capacitor placement, Conductor selection,
Improved Cuckoo Search Algorithm (ICSA), Radial
distribution system (RDS)
I. INTRODUCTION
Due to the continuous growth in electrical demands with
respect to limited generation resources ,researchers are now
focused on methods used for conserving the electrical
energy. Out of that methods , reduction of power loss in
distribution network is considered as one of the most vital
way of conserving the generated energy. Power losses occur
in distribution networks during flow of power from
generating station to consumers [1]. Researchers have
explored many methodologies for reduction of power loss in
RDS out of which optimal selection of conductor sizes for
distribution system is a complex problem as it should take
into account many constraints. The power losses can be
reduced by decreasing the conductor resistance and
installation of shunt capacitors respectively. Power losses
can be reduced by selection of optimal conductor and
placement of capacitor. Both of these two loss reducing
methods require higher capital investment. Some authors
have published papers using each of these methods
separately. Simultaneously allocations of conductor
and capacitor in RDS have been considered by few authors
[2-3].
The problem of capacitor placement was solved
using analytical method in [4]. In [5], one different
approach for placement of capacitor are discussed. Optimal
placement of capacitor problems were solved by
using artificial intelligence in [6]. The placement and
sizing of shunt capacitors should also be investigated
carefully to avoid voltage rise problem. It has been
presented in some papers that the optimal placement of
shunt capacitor can reduce system power losses,
improve system voltage profile, relieve feeder loading [7].
M. Sreedhar et al. [8] have described fuzzy logic
based method for optimal size selection of conductor.
A novel approach is described in [9] to find out the best
conductors for different feeder of RDS.
The contribution of this paper is as follows:
(a) Optimal allocation of conductor associated with
capacitor in 32-bus RDS in order to minimize the power
losses cost, cost of the installed conductors and cost of the
installed capacitors as per the specified constraints.
(b) Improved Cuckoo Search Algorithm (ICSA) is used as
an optimization tool to achieve the minimum objective
function.
(c) Optimal planning is helped for transformer upgrade
deferral, demand charge management, electric service
reliability and voltage support in RDS.
The residue of this paper is assembled as follows:
in section II, modeling of distribution system with the
inclusion of shunt capacitors is described where as section
III present the problem formulation. In section IV,
ICSA is briefed and results and discussion is described in
section V. At last section VI concludes the paper.
II. MODEL OF DISTRIBUTION SYSTEM WITH INCLUSION OF
SHUNT CAPACITORS
A. Load Flow Solution
Fig. 1. RDS with capacitor installation
978-1-5386-2989-5/17/$31.00 ©2017 IEEE
Load flow solution is done in RDS as shown in Fig.1
using the backward and forward update methods [10].
Where R ij and X ij is resistance & reactance of the branch
between buses i and j . Pi and Q i are real & reactive
power flowing out of bus i . P j and Q j are real & reactive
power flowing out of bus j . P Li and Q Li are real &
reactive power load connected at bus i . P Lj and Q Lj are
real & reactive power load connected at bus j . V i and V j
are voltage of bus i & j , I ij is current in branch between
buses i and j .
Real power loss, Voltage deviation, Voltage stability
index and load balancing index are computed as given
below, which are derived from the RDS as shown in Fig.1.
(1) Total real power loss ( PT , Loss ) :
ij =1
PLoss
where
2
ij =
(2)
branch number , R ij = resistance of the
ij th branch, I ij = current at ij th branch , PLoss , ij = power
th
loss of ij branch and
system.
n
is the total number of bus in the
=
n
 (V
i =1
i,nom
−V
i
)
2
(3)
Where V i , nom is nominal voltage of bus i and V i voltage of
bus i .
(3) Voltage stability index ( VSI ) :
The index of voltage stability will affected by allocation of
conductor & capacitor in RDS.The voltage stability index at
bus j is calculated as [11]:
2
2
4
L j = V i − 4  P j X ij − Q j R ij  − 4  P j R ij + Q j X ij  V i
(4)
=
m
a
x
(
)
j
=
2
,
3,
...
n
,
(5)
L m ax
L j


(6)

 L m ax 
Where P j and Q j are real & reactive power flowing out of
VSI = 
where I ij,avg
1
bus j , X ij is reactance of the branch between
(4) Load balancing index ( LBI) :
ij th .
2
(7)
1 n−1
 I ij
n −1 ij =1
=
(8)
B. Modelling of capacitors and conductors
Cross sectional area, impedance and maximum
permissible carrying current (Imax) are some special features
of different types of conductors used in the RDS. The
electrical properties of conductors are given in the Table 1.
The shunt capacitors are modeled as a negative ‘Q’ load
delivering reactive power to the RDS. The amount of
reactive power injected to RDS at i th bus is expressed as
follows:
(9)
Q i = Q Cap − Q L
i
Q Ca p is the reactive power generation of the
i
capacitor connected at bus i , Q Li is the reactive power
load connected at bus i .Different types of conductors with
specification is given in Table I. The finite number of
standard sizes of capacitors along with cost are available in
the market as given in Table II.
TABLE I. ELECTRICAL PROPERTIES OF CONDUCTORS
Type of conductor
(2)Voltage deviation ( VD ) :
VD
LBI =
Where
(1)
, ij
= R ij I ij
, ij
 I ij 
 

ij = 1
 I ij ,a v g 
n −1
i
n −1
PT , Loss =  PLoss
The load balancing index makes reserve capacity for
demand growth. The index is written as
Squirrel
Weasel
Rabbit
Raccon
Electrical properties of conductors [8]
Area
Resistance
Reactance
(mm2)
(ohm/km)
(ohm/km)
12.90
1.3760
0.3896
19.35
0.9108
0.3797
32.26
0.5441
0.3673
48.39
0.3657
0.3579
Imax
(A)
115
150
208
270
TABLE II. AVAILABLE CAPACITOR SIZES AND COST
Size
(kVAr)
Cost
(₹/kVAr)
Capacitor size and cost available in the market
150
300
450
600
750
900
31.32
21.92
15.85
13.78
17.29
11.46
1050
1200
14.28
10.65
III. PROBLEM FORMULATION
A. Objective Function
An economic optimization has been applied to select
optimal conductors for different feeder of 32-bus RDS, and
obtain optimal allocation of capacitors in distribution
system, which minimizes investment (fixed) costs of feeders
& capacitors and the operation (variable) costs in the form
of energy losses, subject to the system constraints. Thus, the
objective function (total annual cost) is written as
C = M in im iz e
( C fix e d + C
v a r ia b le
)
Q
(10)
(1)Fixed costs ( C fixed )
Fixed cost of the conductor without allocation of capacitor
in RDS is given by
,i
max
≤ Q Cap
(19)
,i
where, P SUB & Q SUB are active & reactive power injection
of substation ; P T , Loss & Q T , Loss are total active & reactive
min
power loss; V i
max
& Vi
are minimum & maximum value
max
voltage magnitude of bus ; I ij
ij= 1
feeder between buses i and j ; PFmin &
(11)
Fixed cost of the conductor with allocation of capacitor in
distribution system is given by
n-1
J
C fixed =   λ × A ( k ) × Cost ( k ) × Len ( ij)  +  K ic Q ic
i =1
ij=1
(12)
where λ = interest and depreciation factor i.e 0.1; A( k ) =
Cross sectional area of k type of conductor in mm2 ;
Cost ( k ) = Cost of k type of conductor in Rs/mm2/km = 500
Rs/mm2/km ; Len ( ij) = Length of branch ij in km ; K ic =
c
Annual cost of capacitor at bus i in kVAr ; Qi = Size of
capacitor at bus i in kVAr ; j = Buses in which the
capacitors are installed.
(2)Variable costs ( C var iable )
The annual cost for the energy loss in feeder ij with k
type conductor and shunt capacitor size placed at bus j is
given by
n-1
C var iable
=
 Ploss (ij,k) × [ Kp + Ke × Lsf × T ]
(13)
where Ploss (ij,k) = Peak real power loss of feeder ij under
peak load condition with k type conductor for 32- bus RDS
[12], Kp = Annual demand cost per unit of power loss (Rs. /
kW ) = 2500 Rs /kW ; Ke = Annual demand cost per unit of
energy loss ( Rs. / kWh ) = 0.5 Rs /kWh ; Lsf = Loss factor
= 0.2; T = Time period in hours (8760 hr).
B. System operational constraints
The solution of the optimization problem considers the
following constraints :
n
P S U B =  P L i + P T , L o ss
i =1
n
n
Q SUB +  Q C ap , i =  Q Li + Q T , Loss
i =1
≤V
i
m ax
≤V
i =1
m ax
i
I ij ≤ I ij
P Fm in ≤ P Fsys ≤ P Fm ax
(14)
is maximum current in
PFmax are
minimum & maximum power factor; PFsys is power factor
min
max
at swing bus; Q Cap
,i & Q Cap ,i are lower and higher limit of
reactive power generation of the Capacitor connected at bus
i.
IV. IMPROVED CUCKOO SEARCH ALGORITHM
Cuckoo search algorithm is derived from the behavior of
cuckoos of manipulating the host to raise their offspring
instead of the host’s young ones. This leech behavior
enhances the probability of continuation of the cuckoos’
genes without any need to waste any energy upbringing the
offspring. However, on discovering the fact that the eggs are
not their own, the host bird destroys those eggs. The natural
behavior of Cuckoos is utilized in this search algorithm in
order to traverse the search space and find optimal solutions.
Three idealized rules are applied in this algorithm, which
are as follows: [12]
•
•
•
ij=1
m in
i
≤ Q Cap
n -1
C fix e d =   λ × A ( k ) × C o s t ( k ) × L e n ( ij ) 
V
min
Cap , i
Each cuckoo lays one egg at a time in a randomly
selected nest.
The off springs will come out of high quality eggs
of best nest.
The number of available host nests is fixed, and the
probability of discovering the cuckoo’s eggs by the
host bird with is Pa ∈ [0, 1] where the host bird
can either throw the egg away or desert the nest,
and build a completely new nest.
For implementation each egg in a nest is assumed to
represent a candidate solution. The target is to use the new
solutions (eggs) with higher potential to replace poor
solutions (eggs). The concept of Levy flights is incorporated
to improve the algorithm which is distinguished by a
variable step size punctuated by 90-degree turns. [13-14].
Step 1: Cuckoo search parameters such as number of
nests ( n) , step size parameter (α ) , discovering probability
( Pa ) and maximum number of generation are set.
(15)
Step 2: Initial nests are generated by assigning a set of
random values to variables of each nest as follows:
(16)
nest((i0, )j ) = x j , min + rand ( x j , max − x j , min )
(17)
(18)
(20)
( 0)
where nest( i , j ) is the initial value of the jth variable of ith
and x j , max
x j , min represents the maximum and
minimum allowable values for jth variable.
4
Step 3: New cuckoo eggs are produced with Levy flights
which replaces eggs in other nests apart from the best one
based on their quality. Formulation process of new cuckoo
eggs can be given as follows:
nesti( g +1)
g
= nestig + . S .(nestig − nestbest
). r
g
th
nesti is the current position of i nest,
α
(21)
where
α is the step
size parameter, ‫ ݎ‬is a random number from a standard
5.2
u
(22)
1
5
4.8
4.6
4.4
g
is the position of the best
normal distribution and nestbest
nest so far and ܵ is a random walk based on Levy flights and
can be calculated as follows:
S=
x 10
5.4
Total cost (Rs.)
nest;
Case II : Optimal conductor selection simultaneously with
capacitor placement & sizing
The objective function (total annual cost) variation for case
I & II are shown in Fig.2 and 3 respectively.
4.2
0
4.4
where β is a parameter between [1,2] ; ‫ ݑ‬and ‫ ݒ‬are drawn
from normal distribution as follows:
1
β

πβ 
 Γ(1 + β ).sin( ) 

2 
σu = 
β −1  , σ v = 1
 Γ 1 + β .β .2 2 
  2 

(24)
Step 4: The alien eggs discovery is modeled by replacing a
fraction of total number of eggs in nests by new random
solutions. Generally eggs (solutions) those are replaced are
with lower fitness values.
Step 5: Generation of new cuckoo eggs and alien egg
discovery process are performed alternatively until a
termination criterion is met. Here the termination criterion is
the maximum no. of generations.
V. RESULTS AND DISCUSSION
The proposed ICSA optimization technique was tested in
32- bus radial distribution systems in India[15]. The
parameters of ICSA used in simulations are number of nests
as 100 and net discard probability as 0.35. Then 10 trial
runs are made using this set of parameters and best result
obtained is reported. Power flow calculation is performed
using base value 100MVA and 11 kV. The bus voltages are
limited to 0.95p.u. to 1.05p.u. . The conductor replacement
and three capacitors (i.e. inject reactive power) installations
are done simultaneously in to the system. To test the
effectiveness of the ICSA, the following cases are
considered.
Base case : Without optimal conductor selection and
capacitor placement & sizing
Case I
: Only optimal conductor selection
60
80
100
120
No of Iterations
140
160
180
200
x 10
4
4.2
Total cost ( Rs.)
(23)
40
Fig. 2. Obj. function (Total annual cost) variation for case - I in 32 bus
RDS
vβ
u ~ N (0, σ u2 ), v ~ N (0,σ v2 )
20
4
3.8
3.6
3.4
3.2
3
0
20
40
60
80
100
120
No of Iterations
140
160
180
200
Fig. 3. Obj. function (Total annual cost) variation for case - II in 32 bus
RDS
In Case I & II (After Optimization), the
reconductoring is necessary with respect to base case for all
the branches except branch no. 7,10,12,19 & 27 in Case I
and branch no. 7,10,14,20 & 30 in Case II which are shown
in Table III. The optimal place and size of capacitors for
Case - II are given in Table IV. The comparisons of results
for base case, Case I and Case II are shown in Table IV.
From the result it is noticed that the solutions found in Case
II is minimum as compared with other cases. It is also
evident that the proposed ICSA technique is superior than
MDE[16] & FEP[8].
TABLE III. AVAILABLE CAPACITOR SIZES AND COST
Method
Base case
MDE[16]
ICSE
ICSE
Type of conductor and branch number
Weasel-1 to 31
Case I
Raccon-1 to 5, 9, 17, 23 to 25; Rabbit-6, 18, 26;
Weasel-7, 10, 12, 19, 27
Squirrel-8, 11, 13 to 16, 20 to 22, 28 to 31
Raccon-1 to 5, 9, 17, 23 to 25;
Rabbit-6, 18, 26 ;
Weasel-7, 10, 12, 19, 27
Squirrel-8, 11, 13 to 16, 20 to 22, 28 to 31
Case II
Raccon-1 to 5, 12, 17, 22 to 26; ;
Rabbit-6, 9, 18 to 19;
Weasel-7, 10, 14, 20, 30
Squirrel-8, 11 ,13 ,15 to 16, 21, 27 to 29, 31
The improved voltage profile & voltage stability index for
base case, case I and case II are shown in Fig.4 & Fig.5
respectively. From the presented figures one can noticed
that the proposed method is succeeded in minimizing
overall system cost with an improvement in system voltage
profile as well as voltage stability index.
Stability Index (pu)
1.1
TABLE IV. OPTIMIZATION RESULTS FOR BASE CASE WITH
CASE I & CASE II
Optimal
Capacitor
placement
Bus
Optimal
capacitor
Size(kVAr)
Min.
Voltage
magnitude
(p.u.)
Real power
Loss(kW)
Voltage
deviation
(VD) in
p.u.
Voltage
stability
index(VSI)
in p.u.
Load
Balancing
Index(LBI)
Optimal
Total
annual cost
(₹/year)
Net Saving
(₹/year)
% Benefit
of total
annual cost
%
Reduction
in real
power loss
Base Case
-
FEP[8]
Case I
MDE
0.9901
0.9903
0.9904
25.37
10.4
10.376
10.373
7.12
0.0050
-
-
0.0014
0.0004
1.0733
-
-
1.0394
1.0243
76.9947
-
76.9929
69.04
90588.66
44004
42974
42973.59
31777.92
-
46584.66
47614.66
47615.07
58810.74
-
51.42
52.5613
52.5618
64.92
-
59.006
59.101
59.113
71.93
Voltage Magnitude (pu)
0.985
Fig. 4. Voltage profile of 32-bus RDS
30
25
30
35
Base Case
Case I
Case II
5
0
5
10
15
20
Branch No
25
30
Fig. 6. Power loss variation for 32-bus RDS
VI. CONCLUSION
In this paper, a techno-economic optimization has been
studied for determine the location & size of the capacitors
and the selection of conductor type using ICSA. The
proposed technique has been applied to 32 bus RDS with
adequate and comparable results to other papers. To increase
the reserve capacity for demand growth, the proposed
algorithm can find out minimum total cost in addition to
reduction in power loss, voltage profile improvement,
voltage stability improvement and reduction in load
balancing index.As shown in the results, the bus voltages are
in the permissible limits and current flowing through
branches below the current capacity of the conductors. The
above results showed the techno-economic advantage of the
proposed power management strategy with the ICSA.
Case II
25
20
10
0
0.99
15
20
Bus No
15
15
0.995
10
10
From the Fig.6. it is observed that installation of capacitor
with conductor selection can significantly reduce the power
loss in RDS.
0.9825
Case I
5
Fig. 5. Voltage stability index of 32-bus RDS
300,
300,
600
0.9940
Base Case
0
Bus No
Case II
ICSA
8,26,4
ICSA
-
5
1.02
1
1
0
1.04
After Optimization
1.005
0.98
1.06
R e a l p o w e r lo ss ( k W )
Parameters
Before
Optimization
Base Case
Case I
Case II
1.08
35
35
REFERENCES
[1] V. N .Varivodov, “Technological aspects of loss reduction in
main equipment of electrical networks,” Electric Power’s
News, no. 1, pp. 11–16, January 2010.
[2] M.Vahid, N.Manouchehr, S. D Hossein, and A.Jamaleddin,
“Combination of optimal conductor selection and capacitor
placement in radial distribution systems for maximum loss
reduction”, Proc. IEEE Int. Conf. on Industrial Technology
(ICIT 2009), February 2009.
[3] M.Vahid, A.A Hossein, and M.Kazem, “Maximum loss
reduction applying combination of optimalconductor selection
and capacitor placement in distribution systems with
nonlinear loads”, Proc. 43rd Int. Universities Power
Engineering Conf. (UPEC 2008), September 2008.
[4] N. M. Neagle and D. R Samson, “Loss reduction from
capacitors installed on primary feeders,” AIEE Trans., vol.
75,pp. 950–959, Oct. 1956.
[5] M. M. A. Salama, E. A. A. Mansour , A. Y. Chikhani and R.
Hackam, “Control of reactive power in distribution systems
with an end-load and varying load conditions,” IEEE Trans.
Power Apparatus and Systems, vol. 104, no. 4,pp. 941–947,
Apr. 1985.
[6] I.V.Zhezhelenko, A. V. Gorpinich and M.T.Khalil, “Optimal
Capacitor Placement in Distribution System Considering
Mutual Coupling, Load Unbalancing and Harmonics,” The
20th International Conf. on Electricity Distribution, session 5,
paper no. 0441. 8-11 June 2009, Prague.
[7] R.A. Gallego, A.Monticelli, R.Romero, “Optimal capacitor
placement in radial distribution network, IEEE Trans Power
Syst Vol.16, no. 4, pp. 630 – 637,2001.
[8] M.Sreedhar, N.Visali, S.Sivanagaraju and V.Sankar, “A
Novel Method for Optimal Conductor Selection of Radial
Distribution
Feeders
Using
Fuzzy
Evolutionary
Programming” ,International Journal of Electrical Power
Engineering Vol. 2, No. 1, pp. 6-10, 2008.
[9] Z .Wang, H.Liu, D.Yu, X.Wang and H.Song, “A Practical
Approach to the Conductor Size Selection in Planning Radial
Distribution Systems”, IEEE Transactions on Power delivery,
Vol. 15, No. 1,January 2000.
[10] M.harkravorty, D.Das, ‘‘Voltage stability analysis of radial
distribution networks,” International Journal of Electrical
Power and Energy Systems. Vol. 23, No. 2, pp. 129-135,
2001.
[11] P. N. Vovos, J.W.Bialek,‘‘Direct incorporation of fault level
constraints in optimal power flow as a tool for network
capacity analysis ’’, IEEE Trans Power Syst, Vol. 20, No. 4,
pp.2125-34, 2005.
[12] X.S.Yang and S. Deb, "Cuckoo search via Lévy flights." In
Nature & Biologically Inspired Computing, 2009, World
Congress on, pp. 210-214. IEEE, 2009.
[13] X.-S. Yang and S.Deb, “Engineering Optimisation by Cuckoo
Search.” In International Journal of Mathematical Modelling
and Numerical Optimisation 1(4), pp.330-343, 2010.
[14] M.Gutowski ,“Lévy flights as an underlying mechanism for
global optimization algorithms.” Optimization, pp.1-8, 2001.
[15] R.S.Rao, K.Satish, S.V.L. Narasimham, “Optimal Conductor
Size Selection in Distribution Systems Using the Harmony
Search Algorithm with a Differential Operator” , Electric
Power Components and Systems, Vol. 40, pp.41-56, 2012.
[16] M.B.Kalesar,‘‘Conductor Selection optimization in Radial
Distribution System considering load growth using MDE
algorithm’’,World Journal of Modeling and Simulation, Vol.
10, No. 3, pp.175-184, 2014.