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MIT International Journal of Electrical and Instrumentation Engineering Vol. 1, No. 2, Aug 2011, pp 108-115 108

ABSTRACTTransformers are a critical part of an electrical

utilitys asset base. Loss of a transformer in a utility,

generation plant or process can cost many millions of

dollars, depending on how long it is out-of-service. On-

line monitoring and diagnostics is a useful tool to help

operators to manage their assets and make decisions on

continuing operation, maintenance or replacement. To

condition monitoring of larger power transformers, a

practical method is to use the available bushing tap

connection, which is called SFRA. Sweep Frequency

Response Analysis (SFRA) is an established tool for

determining the core deformations, bulk winding

movement relative to each other, open circuits and short

circuit turns, residual magnetism, deformation within the

main transformer winding, axial shift of winding etc. Inthis paper, we will discuss a custom high-power signal

generator that injects high-frequency signals on the

bushing tap of the transformer under investigation, as well

as a circuit to replace the bushing tap short and allow

online operation of the system.

I. INTRODUCTION

Induction motors are being widely used for almost allpractical purposes in industrial and domestic world, givingrise to the consumption of maximum share of the totalelectrical power generated. So, their efficiency, torque

produced and cost becomes a major concern to be optimized.But the optimal design of I.M. is a problem due to thefollowing reasons:

1. Induction motor involves so many variables, which non-linearly affects the performance of machine.

2. Due to involvement of various conflicting parameters,objectives and their non-linear behavior during designand operation of the machine, it becomes quitenecessary to balance between many variables,sacrificing one for the other to obtain the best possible

Design Optimization of 7.5 Kw, 4pole, 3-Phase,

50 Hz Induction Motor Employing Genetic

Algorithm/Improved Genetic Algorithm using

Sweep Frequency Response Analysis

Shivendra Prakash Verma

Asstt. Prof. S.G.I.T.,

Ghaziabad

performance and optimized design depending on enduser specifications.

The effect of motor performance on surroundings andenvironment is of great concern also, e.g., the level of noiseand acoustic comfort of train passengers and nearby residentshas to be ensured. The motor starts making noise due toMaxwells air gap forces, which causes in creating statorvibrations in audible range.

The problem of induction motor optimal design has receivedmuch attention since the beginning of computer sciences[4,13,16]. Many solutions and algorithms were designed basedon following points.

Actually many conventions are made on the basis of practicalexperiences with manipulations of Induction motor design,e.g., a small air gap improves the efficiency, but increases themagnetic sound level and decreases the overload capacity ofthe motor; increasing the stator length of yoke to diameterratio generally lowers magnetic vibrations [14]; but itincreases the material cost; and with a fixed motor size, itdecreases the available out-put torque with increased rotortemperature.

In literature so many single as well as multiple objectiveapproaches for the electrical machine design has been proposed[13, 17]; using various methods and techniques. These multipleobjective approaches may be dealt with several NLP methods[8, 9, 10, 11], as well as genetic algorithm [5, 6, 7, 12, 18] and

improved genetic algorithm [15].

II. PROBLEM DEFINITIONAND DESIGNAPPROACHES

The generally used single phase equivalent circuit model ofthe motor is shown in Fig.1. The model offers reasonably goodprediction accuracy with modest computational efforts, despiteits shortcomings. This model is basically a per phaserepresentation of a balanced poly-phase induction motor inthe frequency domain, comprising six model parameters. Thesix parameters have their usual meaning [5].

ISSN 2230-7656 MIT Publications

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Fig. 1. Equivalent circuit Model of induction motor

III. AN OVERVIEWOF OPTIMIZATIONBY GENETIC

ALGORITHM

In the most general sense, GA-based optimization is astochastic search method that involves the random generationof potential design solutions and then systematically evaluatesand refines the solutions until a stopping criterion is met. There

are three fundamental operators involved in the search processof a genetic algorithm: selection, crossover, and mutation.The genetic algorithm implementation steps are shown asfollows:

1. Define parameters and objective functions (Initializing).

2. Generate first population in a random manner fromsearch space.

3. Evaluate population by using objective functions andarrange in order of merit.

4. Test convergence. If satisfied then stop else continue.

5. Start reproduction process (Selection, Crossover,

Mutation & elitism).

6. Form new generation of offspring and treat as

new population. To continue the optimization, return

to step 3.

To apply the GA approach, objective functions andconstraints have to be defined to evaluate how good eachmotor design is.

IV. IMPLEMENTATIONOFTHE OPTIMAL

DESIGN PROCEDURE

The formulation of the objective function [5] is as per thefollowing process:

j j

j

F(x ) P[g ( x), r If F( x) P[g ( x), r ] 0F(x)

0 , If F(x) P[g (x), r] 0

!

(1)

Where, F (x) is the objective function, motor material cost/efficiency/torque, r is the penalty coefficient related to the

value of objective function and x is design variable set.The penalty functions, P [g

j(x), r], are expressed with respect

to the type of inequality used.

By means of exterior penalty function, constrained problemsare converted to unconstrained problems by removingconstraints. According to constraints, penalty function isdefined as following [5]:

2j

j 2j

r [max (0, g )] , j 1, 2, mP(g (x), r)

r [min (0, g )] , j m,....m

(2)

When the constraint inequality is satisfied, the penaltyfunction becomes inactive. The objective function emphasizesthe larger constraint violations and the optimization searchtries to reduce these violations to zero, in the feasible region.This would result in pushing the search into the feasible designregion. All the constraints are satisfied within this region andthe optimization approach attempts to move the design intoits best optimum solution [5].

However, order of magnitudes of various constraints is muchdifferent from one another in case of electric motors.Therefore, constraint functions need to be normalized withrespect to the specified objective function to have meaningfulconvergence criteria. It is to be ensured that constraints withhigher values do not dominate over others. The normalizedconstraint functions in the penalty function are developed asshown in the following [5].

gj norm

(x) = (bj ref

- bj) / b

j, j = 1, 2,n (3)

where bjref

is the calculated value from the current generation/evaluation whereas b

jis the expert defined constant as shown

in Table 1. The main purpose for defining the constraint bj isto have the final design for practically be feasible andacceptable. In general, the constraints are decided upon withgreat care taking into consideration the availability ofmaterials, customers requirements and manufacturingstandards. Table 1 is also referred to as the motorspecifications and their constraint values. Constraint valuesof variables can be expressed by following inequality [5] givenbelow.

g1(x) = s - b

1 0, g

6(x) = I

start/ I

- b

6 0

g2(x) = B

sy b

2 0, g

7(x) = CosF - b

7 0

g3(x) = B

ry b

3 0, g8(x) = Tp / T- b8 0 (4)

g4(x) = B

st- b

4 0, g

9(x) = T

st/ T

- b

9 0

g5(x) = F

f- b

5 0, g

10(x) = h

- b

10 0

In Eqn. 4, there are two different conditions ofinequality constraint which are explained in followingsections.


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Table 1: Inequality Table For Motor Parameters

Sr. no. Name Of Parameter Inequality (Bj)

1 Slip, s (b1

= 0.05)

2 Stator yoke flux density, Bsy

(b2= 0.6)

3 Rotor yoke flux density, Bry

(b3

= 0.6)

4 Stator teeth flux density, Bst

(b4

= 1.7)

5 Stator slot filling factor, Ff

(b5

= 0.90)

6 Starting current to rated currentratio, I

start/ I (b

6= 7)

7 Power factor, cosF (b7

= 0.8)

8 Pull-out torque to rated torque,T

p/ T (b

8= 1.5)

9 Starting torque to rated torqueratio T

st/ T (b

9= 0.6)

10 Efficiency (h) (b10

= 0.85)

4.1 F IRSTCONDITION

It is not permitted that some constraints (as gj(x), j=7,10)

are below the expert defined level. For example, high valueof power factor is desired for good performance in inductionmotor. If the expert-defined constraint for power factor asshown in Table 1 was 0.8, then anything less than that wouldbe a violation.

4.2 S ECOND CONDITION

It is not permitted that some constraints (as gj(x), j=1,..6)

are above the expert defined level. For example, stator yokeflux density may not exceed certain values on account of ironlosses. If the expert-defined constraints for stator yoke fluxdensity as shown in Table 1 was 0.6, then anything more thanthat would be a violation.

The software developed for the design optimization of theinduction motor was prepared using JAVA, which cananalyze, optimize & evaluate design parameters andperformance of motor. Parameters of the motor or materials

used can be easily modified to investigate their effect onperformance. Selection and optimization type (efficiency,torque, cost etc.) can be made depending on user. The

Fig. 2: Flow Chart For 3-phase Inductionmotor Design using nlp

GA optimization algorithm was based on a roulettewheel selection, single point crossover, bit mutation andelitism.


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The flow chart for design optimization process using NLP isgiven in Fig. 2 and the flow chart for design optimizationprocess using GA is given in Figs. 3 & 4. Each block consistsof a number of subroutines.

Fig. 3: Flow Chart For Optimization using GA/IGA

Fig. 4: Flow Chart For 3-Phase Induction Motor DesignUSING GA/IGA

V. MODEL FOR3-PHASE INDUCTION MOTORDESIGN

OPTIMIZATION

The highly nonlinear constrained multivariable optimizationproblem is very difficult to be solved by the conventionalmethods. The optimization problem for 3-phase inductionmotor design can be formulated as [15]:

j

j

Min f(x)

g (x) 0, i 1, 2, 3, . ... ., n

h (x) 0, i 1, 2, 3, ... .., n

(5)

Where f(x) is the objective function of optimization, gi(x)

and hi(x) are constraining functions, and x is the design

variable set.

5.1 OBJECTIVE FUNCTIONS

In order to reduce the active (main) material cost andimprove the efficiency of 3-phase induction motors, threedifferent objective functions of optimization are definedseparately as: [15]

1 Fe.pu fe Cu.pu cu.s Al.pu Al.r,

2 3

f (x) C W C W C W

f (x) , f (x) T

K

(6)

Where CFe.pu

, CCu.pu

, CAl.pu

are the unit prices of magneticmaterial, copper wire and aluminum conductive bars

respectively, WFe, WCu, and WAl are the masses of thecorresponding materials, h is the motor efficiency and T isfull load torque produced.

= Pout-put

/ (Pout-put

+ Losses) (7)

Where, Losses = Stator iron loss + Stator copper loss + Rotor

copper loss + mechanical loss,

& Pout-put

= Pin-put

Losses = 3 VL

IL

cos Losses (8)

5.2 DESIGNOPTIMIZATIONVARIABLES

There is a lot of design variables involved in design of

3-phase induction motor and it is required to choose criticallythe suitable parameters as the optimization design variablesas per the following carefully [15]:

X = [x1, x

2, x

3, x

4, x

5, x

6, x

7, x

8, x

9, x

10, x

11, x

12]

[L, D, lg, Z, H

s, W

s, l

b, b

b, ATm, B

av,

Cu,

Al] (9)

Where L stator core length, D stator core inner diameter, lg

length of air gap, Z number of stator conductors, Hsheight of

stator slot, Ws

width of stator slot, lb

height of rotor slot, bb

width of rotor slot, ATm ampere conductors per meter, Bav

average flux density, dCu

current density in stator windingconductor, d

Alcurrent density in rotor bars.

5.3 C ONSTRAINING FUNCTIONS

The Genetic Algorithm usually adopts the sequentialunconstrained minimization technique (SUMT) to solve theproblems defined by Article [6.2]. Experiences and simulationshave shown that if the penalty factor is selected too large, theCGA may cause premature convergence. On the other hand, ifthe penalty factor is selected too small, the CGA may yield ahighly computational burden. To overcome it, a new annealingpenalty function, which adopts self-adaptive annealing penalty


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factors, is developed for Improved genetic algorithm (IGA)[15]:

f(x, s) = f(x) + p(x, s) (10)

where, p(x, s) = s [Si|min(0, g

i(x)| + S(x)|]

where s is the penalty factor (s = 1 / T, Ti+1

= Tia, T is the

value of the parameter under control, a is the proportionality

constant within the range of (0-1), p(x, s) the penalty function,and f(x, s) the generalized objective function defined by theIGA.

To reflect the changing feature of the nature and imitate theparameter under control becoming more rigorous with thedevelopment of the generations, the fitness value of a stringis defined as

fit = fm

- f(x, s) (11)

Where, fm

is a maximum objective function in a generation.To avoid prematurity, another technique known as the multi-turn evolution strategy was used.

5.4 A PPLICATIONOF IGA TO 3-PHASE I.M. DESIGN

OPTIMIZATION

The IGA is applied for design optimization of the 3-phaseinduction motor. In the process of optimization, the objectiveas well as constraining functions in Article (5,6.3) areimplemented as the following [15]:

g1(x) = L - L 0, g

2(x) = D - D 0

g3(x) = l

g- l

g 0, g

4(x) = Z - Z 0

g5(x) = H

s- H

s 0, g

6(x) = W

s W

s 0

g7(x) = l

b l

b

0, g

8(x) = b

b b

b 0

g9(x)=ATmATm 0, g10(x)=BavBav 0g

11(x)=d

Cu d

Cu 0, g

12(x)=d

Al d

Al 0 (12)

Symbols have their meanings as given in Eqn 9.

VI. OBJECTIVE FORMATIONS

The major performance parameters, which majorly affectthe machine performance, can be collected as: (1) Cost ofmachine, (2) Efficiency & Torque (FL) produced, (3) Breakdown torque, (4) Starting torque, (5) Power factor of themachine, (6) Full load slip of machine, (7) Starting to ratedcurrent ratio, (8) Pullout to rated torque ratio, (9) Magnetic

vibrations & noise.

6.1 C OSTOFMACHINE

It involves following parameters:

COST OF IRON:

Cfe

= L * OD2 * ks* P

fe* C

Fe-pu(13)

COST OF COPPER:

Ccu.s

= 3 * Lswdg

* As* P

cu.d* C

Cu-pu(14)

COST OF ALUMINUM:

CAl.r

= Le* A

b* S

2* P

Al* C

Al-pu(15)

COST OF INSULATION:For a given voltage, Cost of Insulation material is

proportional to Temperature rise of Machine and hence is

proportional to total losses of the machine, and will beconsidered in efficiency maximization.

Total cost of the machine can be given by:

CT

= Cfe

+ Ccu.s

+ CAl.r

+ CInsulation

+ Cp

(16)

6.2 E FFICIENCYAND TORQUEPRODUCEDATFULL LOAD

The function for minimizing the losses can be used asfunction for maximizing the efficiency.

We know that,

Efficiency(h) a [Pout-put

/ (Pout-put

+ Losses)] (17)

And Losses in the motor can be given by:Total Losses = W

i+ W

cu+ Friction and windage loss (18)

For maximum efficiency of the motor at full load, iron lossescan be taken as equal to P

cu.stator.And friction and windage

loss can be taken as 10% of full load rotor copper loss (Pcu.rotor

).

So, now total losses can be given by:

Total Losses = 2 Pcu.stator

+ 1.1 Pcu.rotor

(19)

Total Losses = 2 * 3 Iph

2 Rswdg

+ 1.1 * Ib

2 (Rb

S2

+ Rring

) (20)

6.3 BREAKDOWN (PULL-OUT) TORQUE

TBD

a {1 / rotor reactance(Xr)} (21)

6.4 S TARTINGTORQUE

We can obtain better starting torque with R / X ratio near to1 at standstill, i.e.

Tsta R

r; If R

r/ X

r= 1; T

st= T

BD

Better starting torque can also be obtained by deep bar ordouble cage rotor, as there is a limitation on rotor resistancedue to increased losses with greater rotor resistance.

6.5 POWER FACTOR

We know very well that power factor of the motor is betterwith smaller air gap length (l

g).

Pfa (1 / lg) (22)

6.6 F ULL LOAD SLIP

We know that slip, s = Pcu

/ Pg

(23)

Or, s a Copper Losses (24)


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6.7 S TARTINGTO RATED CURRENTRATIO

Starting Current is low with high rotor resistance, so it canbe understood that if R/X ratio is near to one for better startingtorque, the starting current will be low and ratio of startingcurrent to rated current will be better for such a motor, but atthe cost of efficiency.

6.8 PULLOUTTO RATED TORQUERATIO

Pull out to rated torque ratio

= (TPull-out

/ TRated

) (1 / X

r* efficiency) (25)

6.9 M AGNETIC VIBRATIONS AND NOISE

We know that noise caused due to magnetic vibrations is abig problem, which is due to the zig-zag leakage reactance,which is inversely proportional to the air-gap length of themotor, i.e.

Noise a Zig-Zag leakage reactance a [1/air-gap length(lg)]

(26)

But on the contrary larger air gap give rise to the magnetizingreactance which causes lower power factor and hence inferiorperformance of the motor. So, one has to make balancebetween the noise and power factor of the motor.

VII. PERFORMANCE INDEX

Now we can write performance index as:

J = k1

CT

+ k2

(1 (1/h))

+ k3

[(Rr/X

r)1]

+ k4 [1 (1 / lg)]+ k

5[1 (1 / X

r* efficiency)]

+ k6

(1 / lg) (27)

Where, k1, k

2....k

6are weight constants given to different

functions, given in Table 2.

Table 2: Weights For Performance Index

Sr.no. Name of Function Weight Given to

The Function

1 Cost of the motor 0.1

2 Total losses 0.53 Starting torque 0.1

4 PF (Length of air gap, lg) 0.15

5 Pull out to rated torque ratio 0.1

6 Magnetic Vibration and Noise 0.05Function

Total Weight of Performance 1Index

Table 3: Methods Used In Ga / Iga

Sr.no. Parameter Value / Criteria

1 Population Size 4002 Cross over rate 0.83 Mutation rate 0.014 Elite count 2

5 Stopping criteria IPerformance IndexI 0.15&&[1/{I Performance Index_1 -

Performance Index_0 I}]= null

6 Number of 10,00,000 (Max)generations

7 Cross over Single point crossovermethod with fixed cross over

rate (0.8)8 Mutation method Bit string mutation with

fixed mutation rate(0.01)

9 Selection Fitnesscoefficient

10 Fitness method Genetic load

These weights are decided for a motor running for an

Atta-Chakkiunder following conditions:

1. Continuous running for more than 20 hrs per day.

2. The motor should be economic but due to its continuousrunning energy efficiency is more important.

3. The motor is to be used in a silent environment (sayresidential area). So, we have to consider weight fornoise function also, but it is very less due to the fact

that it conflicts with the power factor and hence theefficiency of the motor.

VIII. RESULTS

Results are summarized and analyzed in Tables 4, and Figs. 5,6 & 7 given at the end.

IX. CONCLUSION

Result analysis of design, optimization and validation (byMATLAB/SIMULINK MODEL) gives the following conclusion:

1. The output of the GA program and its validation using

SIMULINK / MATLAB shows that: The cost of motor decreases with increase in efficiency.

Starting current of motor increases considerably butwith better starting torque, which is required in theassumed case, as on load starting is required.Breakdown torque is also improved considerably andhence overload capacity also.

The optimized motor design using GA/IGA reachesfull speed faster having lesser transient time, lowerslip & higher efficiency at full load and lower cost.


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IX. TABLES

Table 4: Comparision of Performance By Output Of Simulink / Matlab

Sr.no. Parameter / Machine No. Manual Nlp Ga

Amount % Improv. Amount % Improv.

1 Stator Voltage(Volt) 399.94 399.94 399.94 2 Stator starting current(Amp) (DOL) 89.87 118.23 31.54 (incr.) 148.99 26.01 (incr.)

3 Stator starting current(Amp) (Y-D) 29.95 39.41 31.54 (incr.) 49.66 26.01 (incr.)

4 Stator steady state current(Amp) 9.61 9.39 2.28 (decr.) 9.33 0.60 (decr.)

5 Rotor starting current(Amp) 80.47 117.99 46.63 (incr.) 148.14 25.54 (incr.)

6 Rotor steady state current(Amp) 9.44 9.23 2.24 (decr.) 9.19 0.38 (decr.)

7 Starting Torque(N-m) (DOL) 188.15 327.70 74.17 (incr.) 474.36 44.75 (incr.)

8 Starting Torque(N-m) (Y-D) 62.72 109.23 74.17 (incr.) 158.12 44.75 (incr.)

9 Break Down Torque(N-m) 164.47 242.50 47.4 (incr.) 355.50 46.59 (incr.)

10 Load Torque(N-m) 54.10 56.90 5.17 (incr.) 57.20 0.52 (incr.)

11 Time to reach full speed(Sec) 0.70 0.24 65.71 (decr.) 0.15 60 (decr.)

12 Rotor Speed(rpm) 1472.00 1475.00 0.20 (incr.) 1476.00 0.067 (incr.)

13 Slip(%) 1.86 1.67 10.2 (decr.) 1.60 4.19 (decr.)

14 Cost Function (a Cost in Rupees) 1187.278 1110.611 6.457 (decr.)

X. FIGURES

Fig. 5: Manual Design Fig. 6: NLP Design Fig. 7: GA/IGA Design

Charateristics Of 7.5 Kw Induction Motor (Transient Response Showing Variation Of Stator Voltage, Stator Current, RotorCurrent, Torque, Speed, Speed Torque Curve Is Also Shown

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