 Open Access
 Total Downloads : 25
 Authors : M.Rama Mohana Rao, Akula Venkata Naresh Babu, Chintalapudi Venkata Suresh, Sirigiri Sivanagaraju
 Paper ID : IJERTCONV4IS07004
 Volume & Issue : ETE – 2016 (Volume 4 – Issue 07)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Optimal Power Flow Analysis using Two Stage Initialization based Flower Pollination Algorithm
1M.Rama Mohana Rao*
Assistant Professor,
Department of EEE, DVR & Dr.HS MIC College of Technology, Kanchikacherla,
India – 521 180.
2Akula Venkata Naresh Babu
Professor,
Department of EEE, DVR & Dr.HS MIC College of Technology, Kanchikacherla,
India – 521 180.
3Chintalapudi Venkata Suresh
Fulltime Research Scholar,
EEE Dept., University College of Engineering, JNTU Kakinada, India – 533003.
4Sirigiri Sivanagaraju
Professor & Head, EEE Dept., University College of Engineering, JNTU Kakinada, India 5 33003.
Abstract In this paper, a new approach to solve optimal power flow (OPF) problem in power systems is presented. In the proposed algorithm, a two stage initialization process have been adopted and also it gives optimal solution with less number of generations which results in the reduction of the computation time. The feasibility of the proposed algorithm is demonstrated for IEEE 30bus system with different objective functions. The OPF result of proposed algorithm is compared with existing algorithm. The results reveal better solution and computational efficiency of the proposed algorithm.
Keywords Two stage initialization, optimal power flow; optimization techniques; power system operation.

INTRODUCTION
the proposed algorithm gives better solution than existing algorithm .
The remaining portion of the paper is organized as follows: Section II discusses the OPF problem formulation with different objective functions. Section III gives the overview of the proposed algorithm . Section IV demonstrates the effectiveness of proposed algorithm through numerical example and finally, conclusion is drawn in Section V.

OPF PROBLEM FORMULATION
In its general form, the OPF problem can be mathematically represented as
In the optimal power flow problem, certain control variables are adjusted to minimize an objective function such as the cost of active power generation or emission or losses while satisfying operating limits on various control and
Minimize
f (x, u)
subjected to
g(x, u) 0
(1)
(2)
dependent variables. The solution of OPF problem must satisfy the network security constraints. In the past, conventional methods like Newtons method [13] and
where
hmin
h(x, u) hmax
(3)
Interior point method [46] were used to solve the OPF problem. But, in recent years, evolutionary methods are commonly used to solve the OPF problem than conventional methods because of their advantages like simple to implement, reduction in computation time, a fast and near global optimal solution .
An approach for the optimal power flow problem in a deregulated power market using Benders decomposition has been presented[79].The other methods to find the solution for OPF problem have been discussed [1013]. Based on the review above, it reveals that there is a single stage initialization process. But, in this paper the initialization is done in two stages and also it gives better solution with less
number of generations which results in the reduction of the
f (x, u) is the objective function.
x is the vector of dependent variables
u is the vector of independent variables g(x, u) represents equality constraints h(x, u) represents inequality constraints
In this article, minimization of fuel cost, emission and total power loss are considered as an objective functions to examine the performance of the proposed algorithm. The optimal solution must satisfy the equality and inequality constraints. The mathematical expressions for total fuel cost function, emission and total power loss are given in Eqn.(4)
(6) respectively.
ng
computation time. Numerical results are carried out on a
F (P ) (a b P c P2 ) $ / h
(4)
standard IEEE 30 bus system. The OPF results like bus voltages, active power generation, generation cost ,emission, power loss and computation time has been compared for
gi i i gi i gi i1
ng
TSIFPA and FPA. From the results, it can be observed that
E(P ) ( P P2 ) ton / h
(5)
gi i i gi i gi i1
nl 2 2 xt 1
xt

L xt g
(8)
P g (V
V 2VV
cos(
)) MW
(6)
i i i *
loss k i j i j i j k 1
where L ~
sin / 2 1
where
xt Solution vector x
S1+
at iteration t
a , b & c
are cost coefficient of ith
generator. i i
i i i
g* Current best solution
, & are emission coefficient of ith
generator.
i i i
gi
gi
P is the generation of the ith generator.
ng is the number of generator buses.
Standard Gamma function
Due to physical proximity and other factors such as wind, local pollination can have a significant fraction p in the overall pollination activities.
nl is the number of lines.
xt 1
xt

xt xt
(9)
k
k
g is the conductance of k th
line.
x
x
where
i i j k


OVERVIEW OF PROPOSED ALGORITHM
t and xt
are pollen from different flowers of the same
k
k
j
j
plant species. This essentially mimics the flower constancy in
x
x
x
x
j
j
k
k
In this paper, a two stage initialization[14] based flower pollination algorithm (TSIFPA) has been presented. It tries to
a limited neighborhood. Mathematically if t and t
approach the target in an optimal manner for finding the optimal solution to any mathematical optimization problem. The major stages of the proposed algorithm are briefly described as follows:
The population is generated by using the following equation
come from the same species or selected from the same population, this equivalently becomes a local random walk if
is drawn from a uniform distribution in [0,1].

RESULTS AND DISCUSSIONS
x x min rand ( 0, 1) (x max x min ) (7)
i, j j j j
In this section, a standard IEEE 30bus system [17] has
where
i 1, 2,.., ps ; j 1, 2,.., ncv.
been considered to demonstrate the effectiveness and
ps = population size.
ncv = number of control variables.
robustness of proposed TSIFPA. In 30bus test system, bus 1 is considered as slack bus, while bus 2, 5, 8, 11 and 13 are
j
j
x min & x
max
j
are the lower and upper bounds of
j th
taken as generator buses and other buses are load buses. A MATLAB program is implemented for the test system on a
control variable.
rand ( 0,1 ) is a uniformly distributed random number between 0 and 1.
The two stage initialization process provides better probability of detecting an optimal solution to the power flow equations that would globally minimize a given objective function. In the first stage, initial population is generated as a multidimensional vector of size (spv Ã— ncv). Evaluate the value of objective function for each string in the population vector and select the best string from the population vector corresponding to minimum function value. Repeat the procedure for number of population vectors (n). In the second stage, combine all the best strings to form multidimensinal vector of size (n Ã—ncv) and this new population is used for evolutionary operations. In flower pollination algorithm (FPA) proposed by Xin She Yang[15,16], each flower changes its position according to its constancy and the previous positions in the problem space. The individual best and global best is calculated during iterative process till the stopping criteria satisfied. The flower constancy is updated using the Eqn.(8)(9).
Local pollination and global pollination is controlled by a switch probability p [0, 1].
In the global pollination step, flower pollen gametes are carried by pollinators such as insects, and pollen can travel over a long distance because insects can often fly and move in a much longer range. The inertia weight is updated by using the following equation
personal computer with core2duo processor and 2 GB RAM. An analysis has been carried out to study the effect of algorithm parameters on the solution of a power flow problem. Based on the analysis, the input parameters of FPA and TSIFPA for the test system are given in Table I.
The solution for the OPF problem with different objective functions are obtained using FPA and TSIFPA. Table II summarizes the OPF results of both the methods for cost minimization. The OPF results of both the methods for emission and losses minimization are given in Table III and Table IV respectively. The convergence characteristics comparison of the test system using FPA and TSIFPA for cost, emission and losses minimization are shown in Fig.1 Fig.3 respectively.
TABLE I. INPUT PARAMETERS FOR IEEE 30 BUS SYSTEM
Optimization Method
Parameters
Quantity
FPA
& TSIFPA
Population size
50
Number of iterations
100
Probability vector
0.8
lambda
1 3
From Table II Table IV, it is observed that the control variables obtained using proposed TSIFPA is superior than FPA. Also, the computing time obtained using proposed algorithm is less than FPA. Further, the iterative process
begins with minimum function value and the change in function value from initial to final is less which indicates convergence rate is fast for proposed TSIFPA method than FPA as shown in the Fig.1 to Fig.3. This is because of best strings selected during the initialization which is known as two stage initialization adopted in the proposed method and evolutionary operations are performed on these best strings.
TABLE II. COMPARISION OF OPF SOLUTION FOR COST MINIMIZATION
Control Variables
FPA
TSIFPA
PG1(MW)
178.695
177.87
PG2(MW)
52.281
48.450
PG5(MW)
20.109
21.067
PG8(MW)
16.975
21.925
PG11(MW)
12.253
11.114
PG13(MW)
12.599
12.134
VG1(p.u.)
1.1
1.1
VG2(p.u.)
1.081
1.018
VG5(p.u.)
1.055
1.058
VG8(p.u.)
1.049
1.081
VG11(p.u.)
1.019
1.1
VG13(p.u.)
1.022
0.962
TAP69(p.u.)
0.920
0.973
TAP610(p.u.)
1.051
0.931
TAP412(p.u.)
0.944
0.9
TAP2827(p.u.)
1.001
0.932
QC10(MVar)
15.464
20.781
QC24(MVar)
19.926
13.856
Cost($/h)
801.692
800.834
Emission(ton/h)
0.371
0.368
PLoss (MW)
9.512
9.160
Time (Sec)
21.092
13.772
Fig.1 Comparison of convergence characteristics for cost minimisation.
TABLE III. COMPARISION OF OPF SOLUTION FOR EMISSION MINIMIZATION
Control Variables
FPA
TSIFPA
PG1(MW)
69.878
62.792
PG2(MW)
66.09
70.722
PG5(MW)
50
49.472
PG8(MW)
31.366
34.820
PG11(MW)
30
30
PG13(MW)
40
40
VG1(p.u.)
1.018
0.9687
VG2(p.u.)
1.015
0.9
VG5(p.u.)
1.019
0.942
VG8(p.u.)
1.1
1.052
VG11(p.u.)
0.9
1.045
VG13(p.u.)
1.1
1.098
TAP69(p.u.)
0.932
0.978
TAP610(p.u.)
0.9
0.948
TAP412(p.u.)
0.927
0.922
TAP2827(p.u.)
0.931
0.908
QC10(MVar)
26.403
22.417
QC24(MVar)
5
22.895
Cost($/h)
939.054
949.876
Emission(ton/h)
0.206
0.205
PLoss (MW)
3.933
4.406
Time (Sec)
24.718
14.872
PLoss (MW)
Control Variables
FPA
TSIFPA
PG1(MW)
53.854
51.998
PG2(MW)
78.483
79.623
PG5(MW)
50
50
PG8(MW)
34.909
35
PG11(MW)
29.516
30
PG13(MW)
39.958
40
VG1(p.u.)
1.092
1.051
VG2(p.u.)
1.021
1.047
VG3(p.u.)
1.062
1.028
VG8(p.u.)
1.056
1.035
VG11(p.u.)
0.921
1.051
VG13(p.u.)
1.086
1.082
TAP69(p.u.)
1.005
0.970
TAP610(p.u.)
1.057
0.954
TAP412(p.u.)
1.02
0.995
TAP2827(p.u.)
1.024
0.945
QC10(MVar)
15.113
16.597
QC24(MVar)
14.767
6.678
Cost($/h)
963.715
967.139
Emission(ton/h)
0.207
0.207
3.322
3.221
Time (Sec)
23.109
12.399
Control Variables
FPA
TSIFPA
PG1(MW)
53.854
51.998
PG2(MW)
78.483
79.623
PG5(MW)
50
50
PG8(MW)
34.909
35
PG11(MW)
29.516
30
PG13(MW)
39.958
40
VG1(p.u.)
1.092
1.051
VG2(p.u.)
1.021
1.047
VG3(p.u.)
1.062
1.028
VG8(p.u.)
1.056
1.035
VG11(p.u.)
0.921
1.051
VG13(p.u.)
1.086
1.082
TAP69(p.u.)
1.005
0.970
TAP610(p.u.)
1.057
0.954
TAP412(p.u.)
1.02
0.995
TAP2827(p.u.)
1.024
0.945
QC10(MVar)
15.113
16.597
QC24(MVar)
14.767
6.678
Cost($/h)
963.715
967.139
Emission(ton/h)
0.207
0.207
PLoss (MW)
3.322
3.221
Time (Sec)
23.109
12.399
TABLE IV. COMPARISION OF OPF SOLUTION FOR POWER LOSS MINIMIZATION
REFERENCES
Fig.2 Comparison of convergence characteristics for emission minimisation.
Fig.3 Comparison of convergence characteristics for loss minimization.

CONCLUSION
In this paper, a two stage initialization based flower pollination algorithm has been proposed to solve optimal power flow problem with different objective functions. The OPF results obtained for test system using the proposed TSIFPA and existing FPA are compared. The observations reveal that the control variables obtained using proposed TSIFPA is superior than FPA. Because of two stage initialization, the computing time obtained using proposed algorithm is less than FPA. Further, the iterative process begins with minimum function value and the change in function value from initial to final is less which indicates convergence rate is fast for proposed TSIFPA method than FPA.

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IEEE 30bus system data available at http://www.ee.washington.edu/research/pstca.