Nishant Final_1.pptx

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Guided By:

-

Prof. A.

S. Walkey(DEEE)

NITTTR, Bhopal

Head of Department:

-

Dr. (Mrs.)

C.S. RAJESHWARI

(DEEE)NITTTR, Bhopal

Presented By:

-

Nishant

ChaturvediM.E. (P.S.)

0012EE11ME08





In power generation our main aim is to generate the requiredamount of power with minimum cost.

Economic load dispatch means that the generators real and

reactive power are allowed to vary within certain limits, so asto meet a particular load demand with minimum fuel cost.

This allocation of load are based on some constraints

Equality Constrain Inequality Constrain



Literature Survey

Pluhacek michal et al (2013) a new approach for chaos drive particle swarm optimization (PSO) algorithm is suggested. Two

different chaotic maps are alternatively used as pseudorandom

number generator and switch over during the run of chaos driven

PSO algorithm.

Rani C. et al (2013) A chotic local search operator is introduced

in the proposed algorithm to avoid premature convergence.

Park Jong-Bae et al (2010) An improved PSO framework

employing chaotic sequence combined with conventional

linearly decreasing inertia weights and adopting a cross overoperation scheme to increase both exploration and exploitation

capability of the PSO.





Literature Survey

Chaturvedi K. T. Et al (2008) A novel self organizinghierarchical particle swarm optimization ( SOH_PSO) for the

nonconvex economic dispatch to handle the problem of

premature convergence.

Araujo Ernesto et al (2008) Particle swarm optimization

approach intertwined with lozi map chaotic sequence to obtain

Takagi- Sugeno (TS) fuzzy model for representing dynaic

behavior are proposed.

Leandro dos Santos Coelho et al (2008) The use of combining

of particle swarm optimization, Gaussian probability distributionfunction and chaotic sequence.



Park Jong- Bae et al (2006) A novel and efficient method forsolving the economic dispatch problem with valve point effect

by integrating the particle swarm optimization with the chaotic

sequences.

Chuanwen J. et al (2005) Suggested a self – adaptive chaotic particle swarm optimization is used to solve the ELD problem in

deregulated environment. Logistic map chaotic sequence to

generate the random number R 1, R 2 and self- adaptive inertia

weight scale in original PSO to improve the performance.

Literature Survey



OBJECTIVE The main objective of study is to minimize generation cost using partical

swarn optimization (PSO) algorithm for the economic load dispatch (ELD) problem.

The purpose of the economic load dispatch (ELD) problem is to control the

committed generator’s output such that the total fuel cost is minimized,

while satisfying the power demand and other physical and operational

constraints.

To integrate PSO method with Chaotic map for solving ELD problem

having generated unit with non smooth cost function and multi-fuel.To maximize the power generation by proposing a PSO algorithm to

obtain the optimum scheduling of generator



METHODOLOGY

Particle swarm optimization

• Proposed by james kennedy & russell

eberhart in 1995

• Inspired by social behavior of birds

and fishes

• Combines self-experience with social

experience

• Population-based optimization



Concept of PSO

Uses a number of particles that constitute a swarm moving

around in the search space looking for the best solution.Each particle in search space adjusts its “flying” according to its

own flying experience as well as the flying experience of other

particles.

PSO ALGORITHM

Basic algorithm of PSO

1. Initialize the swarm form the solution space

2.Evaluate the fitness of each particle

3. Update individual and global bests

4. Update velocity and position of each particle

5. Go to step 2, and repeat until termination condition





FLOW CHART OF BASIC PSO

Start

Define the parameter of PSO Constants

C1, C2 Particle (P), and Dimension (D)

Initialize particles with random

Position (P) and Velocity vector (V)

Calculate fitness for each Population

Update the Population local best

Update best of local bests as gbest

Upadate Particle velocity using

eq. (1) and Postion using eq. (2)

If iteration

Completed

Stop

No

Yes



CHOTIC THEORY

Chaos : a state of disorder and irregularity.

It describes many physical phenomena with complex behavior by simple laws.

Dynamical systems : systems that develop in time in a non-trivial manner.

Determini stic chaos : irregular motion generated by nonlinear

dynamical systems whose laws determine the time evolution of astate of the system from a knowledge of its previous history.

i) Logistic Map

11 1..

k k k f f f





ii) Lozi map

Lozi introduced in a short note, a two-dimensional map the

equations and attractors of which resemble those of the

celebrated h´enon map. Simply, a quadratic term in the

latter is replaced with a piecewise linear contribution in the

former. This allows one to rigorously prove the chaotic

character of some attractors. The lozi map is depicted in fig.The map equations are given below. The parameters used in

this work are: a=1.7 and b=0.5.

nnn

bY X a X

||11

nn X Y 1



Where a and b are the real non-vanishing parameters. Inside

the region where the orbits remain bounded, the lozi map

may present both regular and chaotic behaviours.The new proposed algorithm utilizes lozi map for the first

part of the optimization process. When pre-defined number

of iterations is achieved, the lozi map is switched over to

logistic map.



Problem formulation An objective function expresses the main aim of the model

which is either to be minimized or maximized. It is expressed interm of design variable and other problem parameter. In presentwork the goal is to minimize the generation cost of committedgenerating unit i.e three, forty, and ten which are given below

Where,

FT: Total Generating Cost

: Cost Function of ℎ Generating Unit , , : Cost Function of Generator i

Pi: Output Power of Generator i

N: Number of Generator

N

iiiT P F F

1

iiiii c P b P a 2



Equality and inequality constraints

Active power balance equation: for power balance, an

equality constraint should be satisfied. The total generated power should be the same as the total load demand plus

the total line loss.

Where is the total system load. The total

transmission network loss, is a function of the unit

power outputs that can be represented using B coefficients

as follows:

n

i

lossload i P P P 1

n

i

n

j

n

i

ii jijiloss B P B P B P P 1 1 1

000









IMPLEMENTATION Pseudo Code for ELD

Input required power (Pd)Initialize the coefficients a, b, c, e and f of all generators.

Select the optimization technique

Initialize the value of a_lozi = 1.7, and b_lozi = 0.5;

Provide the upper bound (UB) and lower bound (LB) constrains on generators

Initialize the PSO coefficients c1 = 2, c2 = 1, = 0.9, =0.1,

Configure the PSO running parameters population size ()

= 100 and total iterations (

) = 50Initialize the values of =0.63 and mu ( ) = 4 for logistic map

Initialize the initial position and velocity matrix to zero

For iter = 1:iter_max



For i = 1:pop_size

For j=1:nvars

If iter = = 1

Generate random number for initial positions (Pij) and velocities (Vij)

Check for upper and lower bond and modified accordingly

else

assign lastly calculated Pij and Vij

endif

Endfor

Endfor

Endfor



Now update the variables to satisfy the Pd constrain

while (sum(init_positions (i,:)~=Pd))

temp_Pij = Pd – (sum(init_positions(i,:)) – init_positions(i,j));

temp_vij = init_velocity (i,j);

end

w = w_max– ((w_max

– w_min)/iter_max) * iter;

update the value of w

If (the technique is standard)

calculate w normally

elseif (the technique is previous)calculate the next value from logistic map and use it to modify the w

= * * (1-fkpre);



= w* ;

else (the technique is proposed)

if (iter is odd the)

calculate the next value from logistic map and use it to modify the w

= * * (1-fkpre);

= w * ;

else

calculate the next value from lozi map and use it to modify the w

lozi_X = 1–

a_lozi * abs (lozi_X_pre) + b_lozi * lozi _Y_pre; = w * lozi _ X;

end





init_velocity = w_new * init_velocity + c1 * rand * ( – init_positions)+c2

* rand * ( – init_positions);

calculate the new velocity and positions for all the population and repeat

FLOW CHART



Start

If mod (Iter,2) ==1

End

Take Initialization

Parameters

Define Objective Function

Define Objective Constrains

Set Iter = 1

Generate Initial Population

Evaluate Objective Function

Use Lozi Map Use Logistic Map

Update Velocity and Positions

Select Best Solution

If iter == ter_max

FLOW CHART

RESULTS & DISCUSSION



RESULTS & DISCUSSION

Test System 1: This system comprises of 3 generating unit and the

input data of 3-generating system are given in Here, the total

demand for the system is set to 850MW.

The standard PSO

0 5 10 15 20 25 30 35 40 45 508200

8250

8300

8350

8400

8450

8500

8550

8600

8650

8700

Iterations

C o s t

Figure 1: Operating Cost of 3 generating unit using standard PSO





400



1 2 30

50

100

150

200

250

300

350

400

Generator Number

O p e r a t i n g P o w e r

Figure 5: Operating Power of 3 generating unit using PSO 1

Technique Minimum Cost

PSO 1 8.2416e3

Figure 6: Result window of 3 generating unit using PSO 1

Table 2: Minimum cost of 3 generating unit using PSO 1



400



1 2 30

50

100

150

200

250

300

350

400

Generator Number


Figure 8: Operating Power of 3 generating unit using PSO 2


PSO 2 8.2341e3

Figure 9: Result window of 3 generating unit using s PSO 2




Minimum Operational Cost by all Three Techniques

0 5 10 15 20 25 30 35 40 45 508200

8250

8300

8350

8400

8450

8500

8550

8600

8650

8700

Iterations

C o s t

PSO

PSO 1

PSO 2

Figure 10 : Comparison of cost minimization vs. iterations for PSO, PSO with chaotic map (PSO 1) and

Proposed PSO (PSO 2) with 2 chaotic maps.





Test System 2: In this case the test system consists of 40



Test System 2: In this case the test system consists of 40-generating units and the input data are given. The totaldemand is set to 10500 MW.

•The standard PSO

0 5 10 15 20 25 30 35 40 45 501.315

1.32

1.325

1.33

1.335

1.34

1.345

1.35

1.355 x 10

5

Iterations

C o s t


600



0 5 10 15 20 25 30 35 40 450

100

200

300

400

500

Generator Number


Figure 14: Operating Power of 40 generating

unit using standard PSO

Figure 15: Result window of 40 generating unit using

standard PSO

Table 5: Minimum cost of 40 generating unit using standard PSO


PSO 1.3195e5



600



0 5 10 15 20 25 30 35 40 450

100

200

300

400

500

600

Generator Number


Figure 17: Operating Power of 40 generating unit using PSO 1 Figure 18: Result window of 40 generating unit using PSO 1

Table 6: Minimum cost of 40 generating unit using PSO

1


PSO 1 1.3093e5



•The PSO with double (alternative) chaotic operation

0 5 10 15 20 25 30 35 40 45 501.27

1.28

1.29

1.3

1.31

1.32

1.33

1.34

1.35

1.36x 10

5

Iterations

C o s t

Figure 19: Operating Cost of 40 generating unit using PSO 2

600



0 5 10 15 20 25 30 35 40 450

100

200

300

400

500

Generator Number




PSO 2 1.2717e5




0 5 10 15 20 25 30 35 40 45 501.28

1.29

1.3

1.31

1.32

1.33

1.34

1.35

1.36x 10

5

Iterations

C

o s t

PSO

PSO 1

PSO 2

Figure 22 : Comparison of cost minimization vs. iterations for PSO, PSO with chaotic map

(PSO 1) and Proposed PSO (PSO 2) with 2 chaotic maps

600



0 5 10 15 20 25 30 35 40 450

100

200

300

400

500

Generator Number

O p

e r a t i n g P o w e r

PSO

PSO 1

PSO 2

Figure 23: Comparison of optimum operational condition for 40 generator units for

PSO, PSO with chaotic map (PSO 1) and Proposed PSO (PSO 2) with 2 chaotic maps.



Figure 24: Result window for comparison of 40 generating unit for PSO, PSO with chaotic map

(PSO 1) and Proposed PSO (PSO 2) with 2 chaotic maps.

Technique Minimum cost

PSO 1.3017e5

PSO 1 1.2932e5

PSO 2 1.2839e5

Table 8: Minimum Operational Cost for 40 generating unit by all Three Techniques

T S M l i F l i h V l P i Eff Th



Test System 3: Multi-Fuels with Valve-Point Effect The testsystem consists of 10-generating units considering multi-fuels

with valve-point effects. The total system demand is set to 2700

MW.•The standard PSO

0 5 10 15 20 25 30 35 40 45 50300

400

500

600

700

800

900

1000

Iterations

C o s t


450

500



1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

Generator Number


Figure 26: Operating Power of 10 generating unit using

standard PSOFigure 27: Result window of 10 generating unit using standard PSO

Table 9: Minimum cost of 10 generating unit using standard PSO


PSO 318.4248



•The PSO with single chaotic operation

0 5 10 15 20 25 30 35 40 45 50200

300

400

500

600

700

800

900

1000

Iterations

C o s t


450

500



1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

450

Generator Number

O p e r a t i n g P o w e

r




PSO 1 294.1963





0 5 10 15 20 25 30 35 40 45 50200

300

400

500

600

700

800

900

1000

Iterations

C o s t


300

350



1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

Generator Number

O p e r a t i n g P o w

e r




PSO 2 239.8838




p y q

0 5 10 15 20 25 30 35 40 45 50200

300

400

500

600

700

800

900

1000

Iterations

C o s t

PSO

PSO 1

PSO 2

Figure 34: Comparison of cost minimization vs. iterations for PSO, PSO with chaotic map

(PSO 1) and Proposed PSO (PSO 2) with 2 chaotic maps



1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

450

500

Generator Number

O p

e r a t i n g P o w e r

PSO

PSO 1

PSO 2

Figure 35: Comparison of optimum operational condition for 10 generator units for




Figure 36: Result window for comparison of 10 generating unit for


Table 12: Minimum Operational Cost for 10 generating

unit by all Three Techniques


PSO 317.5348

PSO 1 302.1667

PSO 2 247.6402

CONCLUSION AND FUTURE SCOPE




This work presents an efficient approach for enhancing the

performance of standard PSO algorithm by alternative use of twodifferent chaotic maps for velocity updation and applied to the ELD

problem and tested for three different systems and objectives. The

simulation results shows the superiority of the proposed algorithm

over the previously proposed single chaotic map based PSO algorithm

and support the idea that switching over of chaotic pseudorandom

number generators in the PSO algorithm improves its performance

and the optimization process.




The results for three different experiments are collected with different

settings and results compared with other methods which show that the

proposed algorithm improves the results by at least 10% for all three

cases. Although the result has improved we can further develop the

algorithm by utilizing multiple maps and optimizing the chaotic maps parameters however these considerations are leaved for future

enhancements.


REFERENCES



[1] J. Kennedy, “The Particle Swarm Optimization: Society Adaptation of Knowledge”,

in Proc. 4th IEEE Cong. Evolutionary Computation, pp. 303-308, 1997.

[2] Michal Pluhacek, Roman Senkerik and Ivan Zelinka,Donald Davendra, “Chaos PSO

Algorithm Driven Alternately by two Different Chaotic Map – an Initial Study”,

Congress on Evolutionary Computation Cancun Mexico, IEEE 2013, June 20-23, pp.

2444-2449.

[3]C. Rani, D. P. Kothari, and K. Busawon, “Chaotic Self Adaptive Particle Swarm

Approach for Solving Economic Dispatch Problem with Valve-Point Effect.”

International Conference on Power Energy and Control, ICPEC IEEE 2013, pp. 405-

410.

REFERENCES



[4] A. Jaini, I. Musirin, N. Aminudin, M. M. Othman and T. K. A Raman, “Particle

Swarm Optimization (PSO) Technique in Economic Power Dispatch Problems “The 4th

International Power Engineering and Optimization Conf., Shah Alam, Selangor, IEEE,

Malaysia: 23-24 June 2010.pp. 308-312

[5] Tao Zhang and Cai Jin-Ding, “ A new Chaotic PSO with Dynamic Inertia Weight for

Economic Dispatch Problem”, IEEE, 2009. April 6-7, pp.1-6.

[6] K.T.Chaturvedi, Manjaree Pandit “Self -Organizing Hierarchical Particle Swarm

Optimization for Nonconvex Economic Dispatch” IEEE transactions on power

system,vol.23,august 2008.

[7] Ernesto Araujo and Leandro dos S. Coelho, “ Particle Swarm Approaches usingLozi map Chaotic Sequences to Fuzzy Modelling of an Experimental Thermal-Vacuum

System”, Applied Soft Computing, Vol.8 (2008), pp.1354-1364.

REFERENCES

[8] L d d S C lh d Ch Sh L “S l i E i L d Di h



[8] Leandro dos Santos Coelho and Chu-Sheng Lee, “Solving Economic Load Dispatch

Problems in Power Systems using Chaotic and Gaussian Particle Swarm Optimization

Approaches”, Electrical Power and Energy Systems, Vol. 30 (2008), pp. 297-307.

[9] Jong-Bae Park, Yun-Won Jeong, Hyun-Houng Kim and Joong-Rin Shin “An

Improved Particle Swarm Optimization for Economic Dispatch with Valve-Point

Effect” International Journal of Innovations in Energy Systems and Power, Vol. 1, no. 1

(November 2006).

[10] Jiang Chuanwen and Etorre Bompard, “ A Self-Adaptive Chaotic Particle Swarm

Algorithm for short time Hydroelectric System Scheduling in Deregulated

Environment”, Energy Conservation and Management,

Vol.46,Issue.17,Oct.2005,pp.2689-2696.

REFERENCES

[11] K M H G W Zh Y D d Kit P W “Q t



[11] Ke Meng, Hong Gang Wang, Zhao Yang Dong and Kit Po Wong, “Quantum-

Inspire Particle Swarm Optimization for Valve-Point Economic Load Dispatch”,

Transactions on Power systems, IEEE, vol. 25, no. 1, February 2010.

[12] Jong-Bae Park, Yun-Won Jeong, Woo-Nam Lee, Joong-Rin Shin power

engineering society general meeting, 2006 IEEE.

[13] N.Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary programming

techniques for economic load dispatch,” IEEE Trans. On Evolutionary Computations,

Vol. 7, No. 1, pp. 83-94, Feb. 2003.

[14] C.L. Chiang, “Improved genetic algorithm for power economic dispatch of units

with valve-point effects and multiple fuels.” IEEE Trans. Power Syst., vol. 20. no.4, pp.1690-1699, Nov. 2005.

List of Publications Nishant Chaturvedi, A. S. Walkey and N. P. Patidar, “ A Modified PSO Based



, y ,

Solution Approach for Economic Load Dispatch Problem in Power System.

International Journal of scientific and engineering Research. ISSN : 2229-5518,

Vol. 5, Issue 4,pp. 292-300, April 2014.

Nishant Chaturvedi and A. S. Walkey, “ A Survey on Economic Load Dispatch

Problem using Particle Swarm Optimization technique” International Journal of

emerging Technology and Advanced Engineering. ISSN: 2250-2459, ISO 9001:

2008, Vol. 4, Issue 3, pp. 188-193, March 2014.

Nishant Chaturvedi and A. S. Walkey, “ A Noval Approach for Economic Load

Dispatch Problem Based on GA and PSO” , International Journal of Engineering

Research and Application. ISSN: 2248-9622, Vol. 4, Issue 3 (Version 2), March

2014, pp. 24-31.



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Nishant Final_1.pptx