This article implements the Ion-Motion Optimization (IMO) optimizer to solve non-convex economic load dispatch (EcLD) problem in power system. The concept of Ion motion optimization is modeled from the attraction and repulsion forces among anions and cations in the real world. The mathematical model of IMO is quiet simple and very easy to implement. The liquid phase of IMO performs exploration and crystal phase simulates the exploitation. To handle the power balance equality constraint, exterior penalty method is used. Finally, EcLD problem having 13-generators is solved using ion motion optimization.

1. An Experimental Study of Ion Motion
Optimization for Constraint Economic Load
Dispatch Problem
• Presented By: Mohit Kumar
• Department of Electrical and Instrumentation engineering,
Sant Longowal Institute of Engineering and Technology
• Longowal, Sangrur, India

2. Table of Content
1. Introduction
3. Motivation for the Proposed Work
4. Modeling of the problem
5. Ion Motion Optimization
6. Result Analysis
7. Conclusion
8. References

3. 1. Introduction
Economic Load dispatch in power systems is an
important, real world optimization problem that
has minimization of generation cost as its
objective.
Solving the Economic Load dispatch Problem has
been attempted from the early 1970's [1].
These early attempts employed classical, gradient
based techniques such as lambda-iteration
method, gradient method and dynamic
programming [2].

4. Cont’d
However, gradient based methods require that
the function to be optimized be differentiable,
continuous and convex to successfully locate the
global optimum.
The Economic Load Dispatch problem has to
satisfy a number of constraints including the
presence of prohibited operating zones, valve
point loading effect, and ramp rate constraints,
which make the problem a non-convex and
discontinuous one.

5. Cont’d

6. Cont’d

7. Cont’d
These complicating factors also led to a huge
interest in gradient free, evolutionary
computation or metaheuristic methods of
optimization being employed to solve the
Economic Load Dispatch problem.
Some meta-heuristic methods employed to solve
EcLD problems are Evolutionary programming
(EP) [2], Shuffled differential evolution (SDE) [3],
effective Lightning Flash Algorithm (LFA) [4] and
enhanced particle swarm optimization
(Enhanced-PSO) [5].

8. 2.Motivation for the Proposed Work
Problem Solving Tools applied to solve selected power system
problems
Classical/Traditional Techniques Metaheuristic/Soft-computing
Techniques
Lambda-iteration method
 Gradient method
Dynamic programming
Branch and bound method
 Linear Programming
Improved Lambda-iteration
method, etc.
 Genetic Algorithm and its
variants
Particle swarm optimization
and its variants
Differential evolution and its
variants
Harmony search algorithm
and its variants, etc.

9. Cont’d
But none of above can claim to be the best
problem solving tool because each technique
has its own limitations, advantages and
disadvantages.
For example:
 Traditional methods are only applicable for
the problems which have continuous
differentiable objective function.

10. Cont’d
 The tuning of genetic algorithm parameters in
complex search spaces is difficult.
 Premature convergence of genetic algorithm
reduces its performance and search capability.
 An evolutionary computation technique,
known as particle swarm optimization, has
become a candidate for many optimization
applications due to its high performance and
flexibility but is not self adaptive.

11. 4.Modeling of the problem
• 𝐹𝑖 𝑥𝑖 = 𝑎𝑖 𝑥𝑖
2
+ 𝑏𝑖 𝑥𝑖 + 𝑐𝑖 + 𝑒𝑖 × sin 𝑓𝑖(𝑥𝑖
𝑚𝑖𝑛
− 𝑥𝑖)
• 𝐹 𝑇 = 𝑖=1
𝑁𝑣
𝐹𝑖(𝑥𝑖)
• 𝑖=1
𝑁𝑣
𝑥𝑖 − 𝑃𝐿 − 𝑃 𝐷 = 0
• 𝑥𝑖
𝑚𝑖𝑛
≤ 𝑥𝑖 ≤ 𝑥𝑖
𝑚𝑎𝑥
𝑖 = 1,2, … , 𝑁𝑣
• 𝑃𝐿 = 𝐵00 + 𝑖=1
𝑁 𝑉
𝐵0𝑖 𝑥𝑖 + 𝑖=1
𝑁 𝑉
𝑗=1
𝑁 𝑉
𝑥𝑖 𝐵𝑖𝑗 𝑥𝑗
• 𝐹𝑇 =
𝐹𝑇 ; 𝑥𝑖 ∈ 𝐹𝑅
𝐹𝑇 + 𝑟 𝑖=1
𝑁
𝑥𝑖 − 𝑥 𝐿 − 𝑥 𝐷
2
; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

12. ION MOTION OPTIMIZATION
Cation
Anion
Best Cation
Best Anion

13. Cont’d
• 𝑥𝑗𝑖 = 𝑥𝑖
𝑚𝑖𝑛
+ 𝑟𝑎𝑛𝑑 𝑗, 𝑖 𝑥𝑖
𝑚𝑎𝑥
− 𝑥𝑖
𝑚𝑖𝑛
• 𝐴𝑗𝑖 = 𝑥𝑗𝑖 ; 𝑖 = 1,2, … , 𝑁𝑣; 𝑗 = 1,2, … , 0.5𝑁𝑝
• 𝐶𝑗𝑖 = 𝑥𝑗𝑖 ; 𝑖 = 1,2, … , 𝑁𝑣; 𝑗 = 0.5𝑁𝑝 + 1, 0.5𝑁𝑝 + 2, … , 𝑁𝑝
• 𝐴𝑗𝑖
𝐹
=
1
1+𝑒𝑥𝑝
(−
0.1
𝐴 𝑗𝑖
𝐷)
• 𝐴𝑗𝑖
𝐷
= 𝐴𝑗𝑖 − 𝐶𝑖
𝑏𝑒𝑠𝑡
• 𝐶𝑗𝑖
𝐹
=
1
1+𝑒𝑥𝑝
−
0.1
𝐶 𝑗𝑖
𝐷
• 𝐶𝑗𝑖
𝐷
= 𝐶𝑗𝑖 − 𝐴𝑖
𝑏𝑒𝑠𝑡
Cation
Anion
Best Cation
Best Anion

14. Cont’d
• 𝐶𝑗𝑖
𝑛𝑒𝑤
= 𝐶𝑗𝑖 + 𝐶𝑗𝑖
𝐹
𝐴𝑖
𝑏𝑒𝑠𝑡
− 𝐶𝑗𝑖
• 𝐴𝑗𝑖
𝑛𝑒𝑤
= 𝐴𝑗𝑖 + 𝐴𝑗𝑖
𝐹
𝐶𝑖
𝑏𝑒𝑠𝑡
− 𝐴𝑗𝑖
Cation
Anion
Best Cation
Best Anion

15. Cont’d
• 𝐶𝑗𝑖
𝑛𝑒𝑤
=
𝐶𝑗𝑖 + 𝜑1 𝐴𝑖
𝑏𝑒𝑠𝑡
− 1 ; z𝑗𝑖 > 0.5
𝐶𝑗𝑖 + 𝜑1 𝐴𝑖
𝑏𝑒𝑠𝑡
; z𝑗𝑖 < 0.5 𝑎𝑛𝑑 z𝑗𝑖 > 0.05
𝑥𝑖
𝑚𝑖𝑛
+ z𝑗𝑖 (𝑥𝑖
𝑚𝑎𝑥
−𝑥𝑖
𝑚𝑖𝑛
) ; z𝑗𝑖 < 0.05
• 𝐴𝑗𝑖
𝑛𝑒𝑤
=
𝐴𝑗𝑖 + 𝜑2 𝐶𝑖
𝑏𝑒𝑠𝑡
− 1 ; z𝑗𝑖 > 0.5
𝐴𝑗𝑖 + 𝜑2 𝐶𝑖
𝑏𝑒𝑠𝑡
; z𝑗𝑖 < 0.5 𝑎𝑛𝑑 z𝑗𝑖 > 0.05
𝑥𝑖
𝑚𝑖𝑛
+ z𝑗𝑖 (𝑥𝑖
𝑚𝑎𝑥
−𝑥𝑖
𝑚𝑖𝑛
) ; z𝑗𝑖 < 0.05

16. Result Analysis
Generator Number Power output (MW)
𝒙 𝟏
∗
(𝐌𝐖) 629.0191
𝒙 𝟐
∗
(𝐌𝐖) 299.4592
𝒙 𝟑
∗
(𝐌𝐖) 297.7103
𝒙 𝟒
∗
(𝐌𝐖) 60.0
𝒙 𝟓
∗
(𝐌𝐖) 60.0
𝒙 𝟔
∗
(𝐌𝐖) 60.0
𝒙 𝟕
∗
(𝐌𝐖) 60.0
𝒙 𝟖
∗
(𝐌𝐖) 60.00001
𝒙 𝟗
∗
(𝐌𝐖) 109.9108
𝒙 𝟏𝟎
∗
(𝐌𝐖) 40.0
𝒙 𝟏𝟏
∗
(𝐌𝐖) 40.00003
𝒙 𝟏𝟐
∗
(𝐌𝐖) 55.0
𝒙 𝟏𝟑
∗
(𝐌𝐖) 55.0
Loss (𝑷 𝑳) (𝐌𝐖) 26.09937
Minimum cost (𝑭 𝑻) ₹ /𝒉 18205.670
Average cost ₹/𝒉 18371.92733
Maximum cost ₹/ 18485.020
Standard deviation (SD) 76.844125

17. Cont’d
1.832358E+04
1.842358E+04
1.852358E+04
1.862358E+04
1.872358E+04
1.882358E+04
1.892358E+04
0 100 200 300 400 500 600 700
Fuelcost(₹/hr)
Iteration
13 Generator problem with loss
(@ PD=1800MW)

18. Conclusion
 In this paper IMO algorithm is
presented and applied on real world
economic load dispatch.
 The algorithm performance is very good
and it may be the good optimization
technique for many other engineering
optimization problems.
 A future study may be directed towards
inclusion of chaotic maps in IMO
algorithm.

19. References
1. Dhillon JS, Kothari DP. Power system optimization. Prentice Hall of India
Private Limited. 2010.
2. Sinha N, Chakrabarti R and Chattopadhyay PK, “Evolutionary
programming techniques for economic load dispatch”, IEEE Transactions
on evolutionary computation, vol. 7(1), pp.83-94, 2013
3. A. S. Reddy and K. Vaisakh, “Shuffled differential evolution for large scale
economic dispatch,” Electr. Power Syst. Res., vol. 96, pp. 237–245, 2013.
4. M. Kheshti, X. Kang, Z. Bie, Z. Jiao, and X. Wang, “An effective Lightning
Flash Algorithm solution to large scale non-convex economic dispatch
with valve-point and multiple fuel options on generation units,” Energy,
vol. 129, pp. 1–15, 2017.
5. Q. Qin, S. Cheng, X. Chu, X. Lei, and Y. Shi, “Solving non-convex / non-
smooth economic load dispatch problems via an enhanced particle swarm
optimization,” Appl. Soft Comput. J., vol. 59, pp. 229–242, 2017.
6. B. Javidy, A. Hatamlou, and S. Mirjalili, “Ions motion algorithm for solving
optimization problems,” Appl. Soft Comput. J., vol. 32, pp. 72–79, 2015