# Optimal Power Flow Analysis using Two Stage Initialization based Flower Pollination Algorithm

DOI : 10.17577/IJERTCONV4IS07004

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#### 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

Full-time 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 30-bus 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.

1. 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.

2. 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 [1-3] and

where

hmin

h(x, u) hmax

(3)

Interior point method [4-6] 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[7-9].The other methods to find the solution for OPF problem have been discussed [10-13]. 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 co-efficient of ith

generator. i i

i i i

g* Current best solution

, & are emission co-efficient 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

3. 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].

4. 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 30-bus 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 30-bus 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 multi-dimensional 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 multi-dimensinal 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 TAP6-9(p.u.) 0.920 0.973 TAP6-10(p.u.) 1.051 0.931 TAP4-12(p.u.) 0.944 0.9 TAP28-27(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 TAP6-9(p.u.) 0.932 0.978 TAP6-10(p.u.) 0.9 0.948 TAP4-12(p.u.) 0.927 0.922 TAP28-27(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 TAP6-9(p.u.) 1.005 0.970 TAP6-10(p.u.) 1.057 0.954 TAP4-12(p.u.) 1.02 0.995 TAP28-27(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 TAP6-9(p.u.) 1.005 0.970 TAP6-10(p.u.) 1.057 0.954 TAP4-12(p.u.) 1.02 0.995 TAP28-27(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.

5. 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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