1. AEEICB-2016
PAPER ID- 187
Voltage Stability Enhancement and Voltage Deviation Minimization Using Ant-Lion Optimizer Algorithm
Indrajit N. Trivedi 1 Siddharth A. Parmar 2 R. H. Bhesdadiya 3 Pradeep Jangir 4
GEC Gandhinagar, Gujarat 1
L.E. College Morbi, Gujarat 2,4
School of Engineering, RK University, Rajkot, Gujarat 3 1

2. OUTLINE Previous Paper Concept Problem Formulation Proposed System
Ant-Lion Optimizer Algorithm
Results & Discussion
Conclusion
References

3. Previous Paper Concept
The objective of the OPF problem is to determine the optimal settings of control variables of a power system by optimizing a particular objective while satisfying certain operating constraints [1].
Earlier deterministic optimization techniques [2] :
Gradient Based Methods
Linear Programming
Interior Point Methods
Newton Based Methods
Highly non-linear and multi-modal optimization problem [3].
No criterion to decide whether a local solution is also the global solution.
Need of development of Stochastic optimization techniques.
One of them is Antlion Optimizer technique.

4. Set of Equality Constraints Set of Inequality Constraints
4. Problem Formulation
The OPF problem can be formulated as a non-linear constrained optimization problem as follows[1]:
Minimize J(x, u)
Vector of
State Variables
Vector of
Control Variables
Subject to
g(x, u) = 0
&
h(x, u) ≤ 0
Set of Equality Constraints
Set of Inequality Constraints

5. Standard IEEE 30-Bus Test System
The standard IEEE 30-bus test system selected in this work has the following characteristics[4]:
six generators at buses 1,2,5,8,11 and 13.
four transformers with off-nominal tap ratio at lines 6-9,6-10,4-12 and
nine shunt VAR compensation buses at buses 10,12,15,17,20,21,23,24 and 29.
The Maximum and Minimum Limits of Generators, Transformers and Compensators are shown in Table 5 [4].
Fig. 1 Standard IEEE 30 Bus Test System

6. Control Parameters Used In Ant Lion Optimizer
Table 1 : Control Parameters used in Ant Lion Optimizer
Sr. No.
Parameters
Value 1
Population (No. of Ants) (N) 50 2
Maximum iterations count (t)
500 3
No. of Variables (dim) 6 4
Random Number
[0,1]

7. Ant-Lion Optimizer Algorithm
The Ant Lion Optimizer was developed by Seyedali Mirjalili in 2015.ALO based on the hunting mechanism of ant lions in nature. Five main steps of hunting prey such as the random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are implemented [5].

8. Pseudo Code of Antlion Algorithm
Initialize the first population of ants and antlions randomly
Calculate the fitness of ants and ant lions
Find the best antlions and assume it as the elite (determined
optimum)
while the end criterion is not satisfied
for every ant
Select an antlion using Roulette wheel
Update c and d using equations Equation 𝑐 𝑡 = 𝑐 𝑡 𝐼 and 𝑑 𝑡 = 𝑑 𝑡 𝐼
Create a random walk and normalize it using Equation X(t)=[0,
cum sum(2r( 𝑡 1 )-1),cum sum(2r( 𝑡 2 )-1),…,cum sum(2r( 𝑡 𝑛 )-1)]
and 𝑥 𝑖 𝑡 = ( 𝑥 𝑖 𝑡 − 𝑎 𝑖 )∗( 𝑑 𝑖 − 𝑐 𝑖 𝑡 ) ( 𝑑 𝑖 𝑡 − 𝑎 𝑖 ) + 𝑐 𝑖
Update the position of ant using Equation 𝐴𝑛𝑡 𝑖 𝑡 = 𝑅 𝐴 𝑡 + 𝑅 𝐸 𝑡 2
end for
Calculate the fitness of all ants
Replace an ant lion with its corresponding ant it if becomes
fitter Equation 𝐴𝑛𝑡𝑙𝑖𝑜𝑛 𝑗 𝑡 = 𝐴𝑛𝑡 𝑖 𝑡 𝑖𝑓 𝑓 𝐴𝑛𝑡 𝑖 𝑡 >𝑓( 𝐴𝑛𝑡𝑙𝑖𝑜𝑛 𝑗 𝑡 )
Update elite if an antlion becomes fitter than the elite
end while
Return elite

9. RESULTS ALO 799.1545 Ant Lion Optimizer Method Cost Method description
Case 1: Minimization of Generation Fuel Cost:
The objective function J represents the total fuel cost of all generator units and it is expressed as follows[1]:
J= 𝑖=1 𝑁𝐺 𝑓 𝑖 ($/ℎ) (1)
Where, 𝑓 𝑖 is the fuel cost of the 𝑖 𝑡ℎ generator.
𝑓 𝑖 , can be expressed as follow:
𝑓 𝑖 = 𝑎 𝑖 + 𝑏 𝑖 𝑃 𝐺𝑖 + 𝐶 𝑖 𝑃 𝐺𝑖 2 ($/ℎ) (2)
Where, 𝑎 𝑖 , 𝑏 𝑖 and 𝐶 𝑖 are cost coefficient.
Table 2 : Optimal Values for Case 1.
Method
Cost
Method description
ALO
Ant Lion Optimizer FA
Firefly Algorithm
PSO
Particle Swarm Optimization
BHBO [2]
Black-Hole-Based Optimization

10. RESULTS Method Voltage Deviation Method description ALO 0.1222
Case 2:Voltage Deviation Minimization
Here the goal is to increase voltage profile simultaneously by reducing the voltage deviation of PQ buses from 1.0 p. u. Hence, the objective function may be calculated as given below [1]:
(3)
Where, w is an appropriate weighting factor.
(4)
(5)
Table 3 : Optimal Values for Case 2.
Method
Voltage Deviation
Method description
ALO
0.1222
Ant Lion Optimizer FA
0.1474
Firefly Algorithm
PSO
0.1506
Particle Swarm Optimizer
BHBO [2]
0.1262
Black-Hole-Based Optimization

11. RESULTS Method Lmax Method description ALO 0.1140 Ant Lion Optimizer
Case 3: Voltage stability enhancement
Thus, the objective function may be given as [1]:
(6)
Where, (7)
(8)
Table 4 : Optimal Values for Case 3.
Method
Lmax
Method description
ALO
0.1140
Ant Lion Optimizer FA
0.1184
Firefly Algorithm
PSO
0.1180
Particle Swarm Optimizer
BHBO [2]
0.1167
Black-Hole-Based Optimization

12. Voltage Deviation (P.U)
RESULTS
Table 5: Optimal settings of control variables obtained by ALO.
 Variables
Min
Max
Initial
Case 1
Case 2
Case 3
𝐏 𝐆𝟏 50
200
𝐏 𝐆𝟐 20 80
49.012
48.347
𝐏 𝐆𝟓 15
21.829
21.160
𝐏 𝐆𝟖 10 35
19.974
25.810
𝐏 𝐆𝟏𝟏 30
14.073
22.839
𝐏 𝐆𝟏𝟑 12 40
12.001
13.040
𝐕 𝐆𝟏
0.95
1.1
1.05
1.1000
1.038
1.100
𝐕 𝐆𝟐
1.04
1.0882
1.022
1.088
𝐕 𝐆𝟓
1.01
1.0622
1.014
1.068
𝐕 𝐆𝟖
1.0703
1.006
1.098
𝐕 𝐆𝟏𝟏
1.0825
1.004
𝐕 𝐆𝟏𝟑
1.0958
T11
1.078
1.0140
0.983
1.035
T12
1.069
0.9866
0.939
0.996
T15
1.032
1.0458
0.971
1.002
T36
0.9972
0.966
0.969
QC10 5
2.8048
3.051
1.856
QC12
2.0604
3.552
4.979
QC15
2.2544
3.925
5.000
QC17
4.7050
4.221
QC20
4.7442
3.230
QC21
2.6848
4.999
2.334
QC23
3.8919
4.485
4.161
QC24
2.9886
4.597
1.669
QC29
4.1214
2.479
Fuel cost ($/h) -
Voltage Deviation (P.U)
1.1496
0.1222
Lmax
0.1723
0.1140

13. Conclusion
The Antlion Optimizer, Firefly Algorithm and Particle Swarm Optimization Algorithm are successfully applied to standard IEEE 30-bus systems to solve the optimal power flow problem for the various types of cases.
ALO proves its effectiveness in terms of maximum efficiency extraction from unknown search space and in minimum computational time. The results gives the optimal settings of control variables with different methods which demonstrate the effectiveness of the particular technique.
The results shows that the solutions obtained from the ALO approach have fast convergence characteristics and it gives the competitive results compared with FA and PSO methods which confirms the effectiveness of proposed algorithm.

14. References
H.R.E.H. Bouchekara, Optimal power flow using black-hole-based optimization approach, Appl. Soft Comput. (2013).
Bouchekara, M.A. Abido, M. Boucherma, Optimal power flow using Teaching-Learning-Based Optimization technique, Electr. Power Syst. Res. 114(2014) 49–59.
H.R.E.H. Bouchekara, M.A. Abido, A.E. Chaib, R. Mehasni, Optimal power flow using the league championship algorithm: a case study of the Algerian power system, Energy Convers. Manag. 87 (2014) 58–70.
Lee K, Park Y, Ortiz J. A united approach to optimal real and reactive power dispatch. IEEE Trans Power Appar Syst 1985;104(5): 1147–53.
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98.

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