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By

Saurabh BhardwajTeaching Cum Research fellow

Instrumentation and Control Engineering DepartmentNSIT, New Delhi

Intelligent Tools for Various Engineering Applications

Genetic Algorithm

The general idea behind GAs is that wecan build a better solution if wesomehow combine the "good" parts ofother solutions (schemata theory), justlike nature does by combining theDNA of living beings.

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Genetic Algorithm

HOW ARE GENETIC ALGORITHM DIFFERENT

FROM TRADITIONAL METHODS?

Classical Algorithm

Generates a single point at each iteration. The sequence of points approaches an optimal solution.

Selects the next point in the sequence by a deterministic computation

Genetic Algorithm

Generates a population of points at each iteration. The best point in the population approaches an optimal solution.

GA work with a coding of the parameter set not the parameter themselves.

GA use payoff ( objective function ) information, not derivatives or other auxiliary knowledge.

GA use probabilistic transition rules not deterministic rules.

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Genetic Algorithm

ADVANTAGES OF GA

It approaches towards the global optimum

It can be applied to solve a variety of optimization problems that

are not well suited for standard optimization algorithms,

including problems in which the objective function is

discontinuous, non-differentiable, stochastic, or highly nonlinear

Genetic Algorithm manipulate decision or control variable

representation at the string level to exploit similarities among

high performance strings. Other methods usually deal with

functions and their control variables directly.

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Genetic Algorithm

The general idea behind GAs is that wecan build a better solution if wesomehow combine the "good" parts ofother solutions (schemata theory), justlike nature does by combining theDNA of living beings.

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LIMITATIONS OF GAEven though GA is capable of obtaining global optimum withmultiple peaks. For MFD ( Multiple fault diagnosis ) problem theGA exhibits lower reliability than our local search algorithm. Toachieve higher reliability we simply combine the two algorithmsto form a hybrid. This is a straight forward to do with geneticalgorithms via the introduction of local improvement operators.

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

plotobjective();

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Genetic Algorithm

Genetic Algorithm

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Number of Design Solutions 4n = 4

Number of Bits = 8 [25.5 = 255= 8 bits]

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String

Number

Initial

Pop

InitialPop

(Binary)

Yi Yi/Yi Count Mating Pool

1 4.2 00101010 110.67 0.286 1 01100101

2 10.1 01100101 64.95 0.168 2 01100101

3 16.4 10100100 81.23 0.210 1 00101010

4 23.5 11101011 129.59 0.335 0 10100100

Mating Pool Mate Cross

over

Site

New Pop New Pop Yi Yi/Yi Count Mating pol

01100101 4 4 01100100 10.0 65 0.20 2 01100100

01100101 3 5 01100010 96 65.12 0.206 1 01100100

00101010 2 5 00101101 4.5 104.05 0.329 0 01100010

10100100 1 4 10100101 16.5 81.72 0.259 1 10100101

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Stri

ng

Num

ber

Ini

tial

Po

p

InitialPop

(Binary)

Yi Yi/

Yi

C

o

u

nt

Mating

Pool

Mat

e

Cros

sover

Site

New Pop Ne

w

Pop

Yi Yi/

Yi

C

ou

nt

Mating

pol

1 4.2 00101010 110.6

7

0.28

6

1 01100101 4 4 01100100 10.0 65 0.20 2 01100100

2 10.

1

01100101 64.95 0.16

8

2 01100101 3 5 01100010 96 65.1

2

0.20

6

1 01100100

3 16.

4

10100100 81.23 0.21

0

1 00101010 2 5 00101101 4.5 104.

05

0.32

9

0 01100010

4 23.

5

11101011 129.5

9

0.33

5

0 10100100 1 4 10100101 16.5 81.7

2

0.25

9

1 10100101

Genetic Algorithm

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Genetic Algorithm

BOILER TDL

Y(K)CONCENTRATION OF CO2

U(k)

Flow rate

Box and Jenkins Furnace

Input, u(t), is gas flow rate & output,y(t), is carbon dioxide concentration.

Objective is to maintain concentration of carbon dioxide

y(k)=f{y(k-1), y(k-2), y(k-3), y(k-4), u(k) u(k-1 ), u(k- 2),u(k-3), u(k-5), u(k-4) }

THE SYSTEM UNDER STUDY

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Genetic

Algorithm

fp(k)

fpn(k)

Desired non-linear

function

Neural network

u(k)

-

+

BLOCK DIAGRAM FOR SYSTEM

IDENTIFICATION

E(k)

SIMULATION RESULTS FOR

IDENTIFICATION

1 2 3 4 5 6 7 8 9 104.034

4.0345

4.035

4.0355

4.036

4.0365

4.037

4.0375

4.038plot of performance index for identification

No. of generations

am

plit

ude

Plot of Performance Index for Identification using BP

& gradient descent

Plot of Performance Index for Identification using GA

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COMPARATIVE STUDY OF GA, BP & GRADIENT

DESCENT AS LEARNING ALGORITHM FOR

IDENTIFICATION

Learning algorithm used Minimum value of

performance index

Genetic Algorithm 4.0345 at 10 th generation

BP & Gradient descent 36 at 100th iteration

BLOCK DIAGRAM (CONTROLLER)

NN/GA

ControllerPLANT

SET POINT ACTUAL O/P

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SIMULATION RESULTS FOR

CONTROL

1 2 3 4 5 6 7 8 9 103.68

3.685

3.69

3.695

3.7

3.705

3.71x 10

-6 plot of fittness function for direct control

no. of generations

square

of

err

or

Plot for Square of error for off-line control using BP &

gradient descent

Plot for Square of error for off-line control using GA

COMPARATIVE STUDY OF GA, BP & GRADIENT

DESCENT AS LEARNING ALGORITHM FOR OFF

LINE CONTROL

Learning algorithm used Minimum value of

square of error

Genetic Algorithm 3.697*10-6 at 7th iteration

BP & Gradient descent 50 at 7th generation

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PARTICLE SWARM

OPTIMIZATION

PARTICLE SWARM

OPTIMIZATION

Evolutionary computational technique based on the movement

and intelligence of swarms looking for the most fertile feeding

location

It was developed in 1995 by James Kennedy and Russell

Eberhart

Simple algorithm, easy to implement and few parameters to

adjust mainly the velocity

A swarm is an apparently disorganized collection

(population) of moving individuals that tend to cluster together

while each individual seems to be moving in a random direction

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CONTINUED It uses a number of agents (particles) that constitute a

swarm moving around in the search space looking for the best solution.

Each particle is treated as a point in a D-dimensional space which adjusts its flying according to its own flying experience as well as the flying experience of other particles

Each particle keeps track of its coordinates in the problem space which are associated with the best solution (fitness) that has achieved so far. This value is called pbest.

CONTINUED Another best value that is tracked by the PSO is the

best value obtained so far by any particle in the neighbors of the particle. This value is called gbest.

The PSO concept consists of changing the velocity(or accelerating) of each particle toward its pbest and the gbest position at each time step.

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PSO ALGORITHMFor each particle

Initialize particle with feasible random numberENDDo

For each particle Calculate the fitness valueIf the fitness value is better than the best fitness value (pbest) in history

Set current value as the new pbestEnd

Choose the particle with the best fitness value of all the particles as the gbestFor each particle

Calculate particle velocity according to velocity update equation Update particle position according to position update equation

End While maximum iterations or minimum error criteria is not attained

gbest & lbest global version:

vx[ ][ ] = vx[ ][ ] + 2*rand( )*(pbest[ ][ ] presentx[ ][ ]) +2*rand( )*(pbestx[ ][gbest] presentx[ ][ ])

local version:

vx[ ][ ] = vx[ ][ ] + 2*rand( )*(pbest[ ][ ] presebtx[ ][ ]) + 2*rand( )*(pbestx[ ][lbest] presentx[ ][ ])

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PSO VS GA In PSO unlike GA each iteration is not a process of replacing the

previous population with a new one, but rather a process of adaptation.

PSO does not have genetic operators like crossover and mutation. Particles update themselves with the internal velocity and have memory.

In GAs, chromosomes share information with each other. So the whole population moves like one group towards an optimal area. In PSO, only gBest gives out the information to others. It is a one way information sharing mechanism. The evolution only looks for the best solution. Compared with GA, all the particles tend to converge to the best solution quickly [18].

.

ADVANTAGES OF PSO & GD

One of the well known disadvantage of GD is that itmay get stuck at local minima and the programmermay end in a solution far away from global minima.PSO does not use any gradient on objective function.If only PSO algorithm is used then it is seen thatsquare of error fluctuates randomly and it may takemany iterations to converge.

Thus in a way PSO takes care of the disadvantages ofGD

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POWER QUALITY ISSUSES

Voltage

Sag / Swell

Voltage

Transients

Voltage

unbalanceHarmonics

Load Frequency

Deviation

Voltage

Flicker

PROBLEMS DISCUSSED

A comparative study of different algorithms to train the weights of neural network i.e. Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Gradient Descent (GD) and a hybrid of PSO& GD is made for the above problems.

Three problems of power quality are discussed in this study.1. voltage flicker estimation, 2. load frequency estimation,

In the first problem the proposed algorithm is tested on given equations, then in second and third problem the algorithm is applied on real data.

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VOLTAGE FLICKER ESTIMATION

VOLTAGE FLICKER

Changes in the envelope of 60Hz supply voltage is called

instantaneous flicker level.

When there are large fluctuating loads such as arc furnace, arc

welder, spot welder, shredder motors flicker becomes a problem of

concern, as it can propagate to neighboring customer connection

points in power system.

The periodic fluctuation can be modeled as an amplitude modulated

signal; where the fundamental power frequency represents the carrier

signal and the voltage flicker represents the modulating signal .

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CONTINUED

)sin()()( fffo twtAAtv

oAfA

fw

f

1

1

11sin)(

cos)(]cossin[)(

tA

tAtwtwtv

2

11

1 tanw

w

The shape can be a sinusoidal function with a frequency lower than the supply

frequency as in the ac arc furnaces as follows:

is the magnitude of the fundamental voltage ,is the magnitude of the voltage flicker,

is the angular frequency of the voltage flicker, and

is the phase angle.To allow the proposed estimation technique to track the envelope of the measured voltage waveform, it is written as:

and is the phase angle.

)()( tWtX

BLOCK DIAGRAM FOR ESTIMATION OF VOLTAGE

FLICKER ENVELOPE AND PHASE ANGLE

2

2

2

1)( wwtAVen

2

11

1 tanw

w

Finally, the envelope is given by:

and the phase angle can be

calculated from:

sum

Weight Adaptation algorithm

Rectangular to polar

w1

v(k)

+

Error

v^(k) -

X1

X2

w2

Ven

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PLOT OF ACTUAL AND ESTIMATED VOLTAGE FLICKER, VOLTAGE FLICKER

ENVELOPE, FUNDAMENTAL PHASE ANGLE WHEN NN IS TRAINED WITH

PSO&GD.

0 0.05 0.1 0.15 0.2 0.25 0.3

-5

0

5

time in seconds

volta

ge a

mpl

itude

0 0.05 0.1 0.15 0.2 0.25 0.3

0

2

4

6

volta

ge e

nvel

ope

time in seconds

0 0.05 0.1 0.15 0.2 0.25 0.3-2

0

2

4

time in seconds

phas

e an

gle

actual voltage envelope

tracked voltage envelope

actual phase angle

tracked phase angle

actual voltage

tracked voltage

COMPARISON OF SQUARE OF

ERROR IN FLICKER PROBLEM

LMS GD PSO GA PSO & GD

0.02 in 12 iterations 0.01 in 450 iterations 0.008 in 450 iterations 0.1 in 480 iterations 0.0057 in 2 iterations

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 35.5

6

6.5

7

7.5

8

8.5

9

9.5x 10

-3 Error Plot with PSO& GD

Number of iterations

Am

plitu

de

Plot of square of error with PSO & GD

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POWER SYSTEM LOAD FREQUENCY ESTIMATION ON REAL DATA

IMPORTANCE OF

FREQUENCY ESTIMATON

With increasing levels of distortions, there is large variations in

frequency.

Control and Protection require accurate estimate of frequency.

Frequency estimation is a highly non linear problem.

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PROBLEM FORMULATION

A constant frequency is estimated. Effect like sudden change in frequency is also

considered.

Energy in MWH drawn in Northern grid of NTPC for different states is recorded after

every 15 minutes.

Frequency codes from "00" to "99" are for frequency range of 49.00 to 51.00 Hz ("00" for frequency = 51.00 Hz).

Data for the state of Punjab recorded on 17-11-2003 is used for off-line training of the

neural network. For the next 24 hours load frequency is estimated.

Estimated frequency is then compared with actual recorded frequency on 18-11-2003.

Practical conditions like sudden change in load and random noise are also considered.

Genetic

Algorithm

fp(k)

fpn(k)

Desired non-linear

function

Neural network

u(k)

-

+

BLOCK DIAGRAM OF FREQUENCY

ESTIMATOR

E(k)

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ESTIMATION OF FREQUENCY FROM THE

REAL DATA

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300plot for target frequency& estimated frequency

No. of samples

am

plit

ude

target frequency

estimated frequency

energy input

COMPARISON OF SQUARE OF ERROR IN LOAD FREQUENCY PROBLEM

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

20

25

30

35

40

45Square of Error with PSO & GD

Number of iterations

Am

plit

ude

GD GA PSO PSO&GD

2 in 480 iterations 4 in 160 iterations 3 in 180 iterations 2.8 in 180 iterations

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NN & PSO BASED FREQUENCY ESTIMATION

NN & PSO BASED VOLTAGE FLICKER

Thank You