The document presents a bacterial foraging optimization algorithm to solve the economic load dispatch problem. It describes the economic load dispatch problem and formulations. It then provides details on bacterial foraging techniques, including chemotaxis, reproduction, swarming, and elimination-dispersal processes that mimic bacterial foraging behavior. The algorithm applies these bacterial foraging techniques to optimize the load dispatch among generators. Results show the proposed approach finds a solution with lower costs compared to other evolutionary algorithms like genetic algorithms and particle swarm optimization.

1. BACTERIAL FORAGING OPTIMIZATION APPLIED TO
ECONOMIC LOAD DISPATCH
PRESENTED BY: SAMBIT PRADHAN
ROLLNO:25225 GUIDED BY: Sr Lect Mrs. Asima Rout
ELECTRICAL ENGINEERING DEPARTMENT
INDIRA GANDHI INSTITUTE OF TECHNOLOGY
SARANG – 759146, DHENKANAL, ORISSA
3 september 2009 ELECTRICAL ENGINEERING DEPARTMENT 1

2. OUTLINES
• INTRODUCTION
• ELD
• ELD PROBLEM FORMULATION
• BACTERIAL FORAGING
• FORAGING BEHAVIOUR
• ALGORITHM FOR THE PROPOSED SCHEME
• RESULTS AND COMPARISION
• CONCLUSION
• REFERENCE
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3. INTRODUCTION
• Economic load dispatch problem is a constrained optimization problem
• It has the objective of dividing the total power demand among the online
participating generators economically while satisfying the various constraints.
• Bacterial foraging optimization to solve ELD problem is a newly emerged
technique.
• The social foraging behaviour of bacteria E.coli has been studied to solve the
Optimization problem.
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4. ECONOMIC LOAD DISPATCH
• In a practical power system under normal operating condition the generation
capacity is more than total demand and losses.
• In an Interconnected power system the objective is to find power scheduling of
each power plant in such a way so that total operating cost is minimum.
• This means power output of generator is allowed to vary within Certain limits so
as to meet a particular load demand with minimum fuel cost. This is called
“ELD”.
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5. ELD PROBLEM DESCRIPTION
• Minimize ( ) = ∑ + + (1)
• Subjected to equality constraints = + (2)
• Inequality constraints (3)
Where i= 1,2…......... n, n= no of generators, = power output
, , are the cost coefficients,
= Total load demand,
= total losses, and are the minimum and maximum
output of generators.
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6. BACTERIAL FORAGING
• The survival of species in any natural evolutionary process depends upon their
fitness criteria(i.e,their food searching ability and motile behaviour).
• The law of evolution supports species with better food searching ability and
either eliminates or reshapes those with poor search ability.
• So a clear understanding and modelling of foraging behaviour in any of the
evolutionary species leads to its suitable application in any non linear system.
• The E.coli bacterium present in our intestine have foraging strategy governed by
four process namely chemotaxis, reproduction, swarming and elimination-
dispersal.
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7. CHEMOTAXIS
• The characteristics of movement of bacteria in search of food can be defined in
two ways, i.e. swimming and tumbling together known as chemotaxis.
• A bacterium is said to be ‘swimming’ if it moves in a predefined direction
and ‘tumbling' if moving in an altogether different direction.
• Depending upon the rotation of flagella in each bacterium, it decides whether it
should go for swimming or for tumbling, in its entire life time.
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8. REPRODUCTION
• The original set of bacteria, after getting evolved through several chemotactic
stages reach the reproduction stage.
• The best set of bacteria (chosen out of all the chemo tactic stages) gets divided
into two groups. The healthier half replaces the other half, which gets eliminated,
owing to their poorer foraging abilities.
• This makes the population of bacteria constant in the evolution process.
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9. SWARMING
• It is cell to cell attraction or repulsion behaviour of bacteria.
• For bacteria to reach at the food location more rapidly it is desired that optimum
bacteria should attract other bacteria.
• To achieve this, a penalty function based on the relative distances of each
bacterium from the fittest bacteria is added to original cost function.
• Finally, when all bacteria have merged into the solution point this penalty
function becomes zero.
• Penalty function is given by equation (4)
( 4)
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1
2
1 1
2
1 1
( , ( , , )) ( , ( , , ))
exp ( )
exp ( )
S
i i
cc cc
i
S P
i
attract attract m m
i m
S P
i
repellant repellant m m
i m
J P j k l J j k l
d
h
  
  
  

 
 

 
 
 
   
 
 
 
 
 
 
 
 
  
 
 
 
 
 

 
 

10. ELIMINATION AND DISPERSAL
• In an evolution process a sudden unforeseen event can occur, which may alter
the process of evolution and cause the elimination of the set of bacteria and or
disperse them to a new environment.
• Instead of disturbing the usual chemotactic growth of the set of bacteria, this
unknown event may place a newer set of bacteria nearer to the food location.
• In its application to optimization it helps in avoiding being trapped in a
premature solution point .
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11. ALGORITHM FOR THE PROPOSED SCHEME
Initialization
• Number of bacterias(GENERATORS) ‘S’ to be used for searching the total
region
• Swimming length Ns(MAXIMUM GENERATIONS BY A SINGLE
GENERATOR).
• Nc is the number of iterations(GENERATIONS) to be undertaken in a
chemotactic loop.
• Nre is the maximum number of reproduction to be under taken.
• Ned is the maximum number of elimination and dispersal events.
• Ped is the probability of elimination and dispersal.
• The location of each bacterium which is specified by random numbers on [-
1,1].
• The value of C(i) ( step size) is. assumed constant for simplification of
calculation. .
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12. Iterative Algorithm for optimization
This section models the bacterial population
Elimination-dispersal loop: l= l+1
Reproduction loop: k=k+1
Chemo taxis loop: j=j+1
For i=1, 2,….S,
a) calculate cost function value(with penalty function added) for each bacteria,
i.E
J(i,j,k,l).
Let J(last)= J(i,j,k,l) to save this value since we may find a better cost via a run.
b) Take the tumbling /swimming decision.
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13. CHEMOTACTIC PART OF ALGORITHM
Generate a random vector ∆(i) ε R With each element (i), m=1…..p , a
random no on [-1, 1].
(c) Move :let
θ(i,j,+1,k,l)= θ(i,j,k,l)+C(i) ∆(i)
Compute J(i,j+1,k,l) , this is for tumble part
(d) Swim
m= 0 ( initial swim length) and let m= m+1
While m<Ns
Let if J(i,j+1,l) < J(LAST) (if doing better)
Let J(LAST)= J(i,j+1,l) and let
θ(i,j,+1,k,l)= θ(i,j,k,l)+C(i) ∆(i)
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14. SWIM PART
• And compute J(i,j+1,k,l)
else let m=Ns .
• If j<Nc then continue chemotaxis as life of bacteria is not over.
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15. REPRODUCTION AND ELIMINATION PART OF
ALGORITHM
• For the given k and l, and for each i= 1,2,…S let J(health) =
be the health of the bacterium i. Sort bacteria in order of ascending cost
J(health) i.e higher cost means lower health.
• Then Sr = (S/2), bacteria with highest J(health) values die and other Sr bacteria
with best value split.
• If k<Nre, then, we have not reached the number of specified reproduction
steps, so we start the next generation in the chemo tactic loop.
• For i=1, 2…S, with probability Ped, eliminate and disperse each bacteria with
probability Ped. To do this if you eliminate a bacteria, simply disperse one to
the optimization domain.
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16. RESULT FOR A SIX-UNIT SYSTEM FOR DEMAND OF 1263 MW
Generator Power
Output (MW)
BF GA PSO
PG1 446.7146 447.4970 474.8066
PG2 173.1485 73.3221 178.6363
PG3 262.7945 263.4745 62.2089
PG4 143.4884 139.0594 134.2826
PG5 163.9163 165.4761 151.9039
PG6 85.3553 87.1280 74.1812
Total Power
Generation (MW)
1275.4 1276.01 1276.03
Minimum Cost
($/hr)
15444.1564 15450 15459
Ploss (MW) 12.4220 12.9584 13.0217
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17. CONCLUSION
• The proposed approach has produced results comparable and better than those
generated by other evolutionary algorithm.
• The solutions obtained have good convergence characteristics.
• Minimum cost using the proposed approach is less as compared to other
methods.
• From comparative study it can be concluded that applied algorithm can be used
to solve both smooth and non smooth constrained ELD problem.
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18. REFERENCE
1) D.H Kim, Ajit Abraham, Jae Hoon Choo, “A Hybrid genetic algorithm and
bacterial foraging approach for global optimization”, Information sciences
177(2007) 3918-3917.
2) Tai- Chen Chen, Pei-Wei Tsai, Shuan-Chuan chu, and Jeng-Shyang Pan, “A
Novel Optimization Approach” : Bacterial-GA Foraging,0-7695-2882-1/07 ©
2007 IEEE.
3) Arijit Biswas, Sambarta Dasgupta, Swagatam Das, “Synergy Of PSO and
Bacterial Foraging Optimization – A Comparative Study on Numerical Bench
Marks”, ASC 44,pp 255-263, 2007©Springer-Veriag Berlin Heidelberg 2007.
4) B.H Choudhary, and S. Rahman, “A Review of recent advances in economic
dispatch,” IEEE Trans. On Power System, Vol.5,No.4,pp.1248-1259,Nov.1990.
5) Hadi Saadat.“ Power System Analysis” .Tata McGraw-Hill, New Dehli, 2009.
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