electric motor based projects

8/8/2019 Electric Motor based Projects

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EXPERT SYSTEMS AND SOLUTIONS

Email: [email protected]

[email protected]

Cell: 9952749533www.researchprojects.info

PAIYANOOR, OMR, CHENNAI

Call For Research Projects Final

year students of B.E in EEE, ECE, EI,

M.E (Power Systems), M.E (Applied

Electronics), M.E (Power Electronics)

Ph.D Electrical and Electronics.

Students can assemble their hardware in our

Research labs. Experts will be guiding theprojects.


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PRESENTATION ON

SYNCHRONOUS MACHINEMODEL

TANDIN JAMTSHO

STUDENT #3226091


3/31

This presentation shall cover thefollowing topics Introduction

Mathematical model

Circuit based model used for both steady state and transientanalysis

Differential equation model

Conclusion

Discussion at the end of presentation


4/31

The main component of powersystem are

GeneratorStep up

Transformer

Transmission

Line

Step down

TransformerLoad


5/31

Principle of synchronous machine Based on the principle of Faradays

law of electromagnetic induction

Generally the armature winding arelocated on the stator and fieldwinding on the rotor

The field winding is excited by adirect current


6/31

What is mean by synchronous

machine ? A machine that operates at constant

speed and frequency with respect to

time is called the synchronousmachine.

N=120f/P

N=speed of the machine in rev/min

F=frequency in Hz

P=number of poles


7/31

Assumptions made are: The stator windings are sinusoidally

distributed electrically

The effect of the stator slots on thevariation of any rotor inductanceswith rotor angle is neglected

Saturation effect neglected.


8/31

Mathematical model Source of the diagram:

Mohamed E. El-Hawary,Electric Power Systems

Design and Analysis


9/31

By Faradays, the voltage induced in the stator coil

cricpeb

ribpeariape

c

b

a

!

!!

P

PP


10/31

Where

ea = terminal voltage of phase a

P = total flux linkage of phase aia = current in phase a

a,b and c are phases

r = the resistance of each armature winding,

assumed to be same for all three phasesp = the derivative operator d/dt, t is the time

ef = p Pf +rfif


11/31

Inductance

The self inductance of any stator winding phases are given by

U2cos20 aaaaaa LLl !

)120(2cos20 ! Uaaaabb LLl)120(2cos20 ! Uaaaacc LLl

The mutual inductance between any two stator phases are given by

)]30(2cos[ 20 !! Uaaababab LLll

)]90(2cos[ 20 !! Uaaabcbbc LLll)]150(2cos[ 20 !! Uaaabac LLllca


12/31

Elimination of old variable ia ,ib, ic,by introducing

a new variable io

Now I o=1/3(ia+ib+ic )

-

!

3/13/13/1

)120sin(3/2)120sin(3/2sin3/2

)120cos(3/2)120cos(3/2cos3/2

UUU

UUU

-

o

q

q

i

i

i

-

c

b

a

i

i

i


13/31

The new variable for flux linkage

,qP 0P,dPThe equivalent d-axis moving armature coil self

inductance is

The equivalent quadrature-axis moving armature

self inductance is

Zero sequence self inductance is

23/20 aaaboaa LLLL !

23/20 aaaboaaq LLLL !

abaa LLL 200 !


14/31

The armature voltage equation in terms of d,q

and 0 becomes

000 ripe

rippe

rippe

qdqq

dqdd

!

!

!

P

UPP

UPP


15/31

Under steady state operation, flux linkage in per unit along d

and q axis and the voltage relation can be written as

qqq

fdadddd

iL

iLiL

!

!

P

P

dddfdaddq

dqqqd

riixixie

riixrie

q

d

r !

!

!

!

P

P


16/31

On open circuit condition id=iq=0

ed=0 and eq=xadifd Voltage in the q-axis is due to excitation in the

d-axis, lets denote it by E

E= xadifd

ed=xqiq-rid eq=E-xdid-riq

e=ed+jeq

i=id+jiq

Eq=E-(xd-xq)id eq=Eq-xdid-riq

eq=jEq-(r+jxq)I

J Eq=e+(r+jxq)i


17/31

Steady state Vector diagram

H

JO

A

C

D

E

F

B

q-axis

d-axis


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OA=e OD=current, i AC=ir drop CD=jxq OD=e+(r+jxq)i DE=j(xd-xq)id

OE=jE=jEq+j(xd-xq)id If xd=xq, the triangle DEF will vanish

for round rotor machine.


19/31

Determination of xd, xq and xo From slip test

Xd=Max. voltage/Min. current

Xq=Min.voltage/Max current

Xd=open ckt. Voltage/Isc By applying positive sequence current to the armature

and measure the voltage for obtaining Xd and xq.

Xo is measured by connecting the three phasewinding in series and passing single phase current

Xd will be within the range of 0.6 to 2.2

Xq will be within the range of 0.4 to 1.4

X0 will be within the range of 0.01 to 0.25 per unit forall the cases.


20/31

Circuit based models for round rotor and salient

pole synchronous machine are

Reactance of air gap flux is represented xo and the leakage fluxreactance is represented by xl

Xs= xo+xl

Xs

I

E +++

-

V 0

-

+


21/31

D-axis equivalent circuit

dP

fdPd1P

id ifd

i1d


22/31

Q-axis equivalent circuit

dP

qPq1P

iq i1q

q1P


23/31

Transient circuit based model D-axis equivalent circuit for the sub-transient

perioddi(

dP(di(

fdi( di1(


24/31

Q-axis equivalent circuit for the sub-transient period

qi(

dP

qP(qi( qi1(


25/31

Sub-transient and transient reactance The idea of transient for a very short period is called Sub-

transient, the sub-transient direct and quadrature axis aredefined as

Xd= d/id Xq= q/iq

Xd=Ll+ (1/(1/Lad+1/Lfd+1/L1d+---)) Xq=Ll+ (1/(1/Laq+1/L1q+---)) The transient which last for some time around 30 cycles is

termed as transient, the transient reactance of direct andquadrature axis are given by

Xd=Ll+ (1/(1/Lad+1/Lfd))

Xq=Ll+ (1/(1/Laq)) X2=( Xd+ Xq)/2

P

PP

P


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Time constants

Tdo=Xffd/rfd ( direct axis transient open circuit timeconstant, 2 to 11 seconds)

Td=Xd*Tdo/Xd (direct axis transient short circuit

time constant Td=Xd*Tdo/Xd (direct axis sub-transient time

constant Tdo =(x11d-x2f1d/xffd)/r1d (direct axis sub-

transient open circuit time constant) Tqo=x11q/r1q

Tq=xq*Tqo/xq Ta=x2/r (armature short circuit time constant)


27/31

Swing equation of synchronous

machine We know that per unit mechanical acceleration

equation

p2=(Tm

-T

e

)/H

P=d/dt, angle in electrical radians between d-axis and the centre of phase a axis.

H=inertia constant of machine in per unit(KW-rad/kVA)

Tm=mechanical torque input in per unit

Te =electromagnetic torque developed in per


28/31

=t+

the reference axis and the quadrature axis

The equation can be written as =angle between

p2 =(Tm-T

e)/H

By expressing angle in degrees and time in seconds it becomes

p2 =180fb(Tm-T

e)/H

Since p.u electrical torque =p.u air gap power developed

p2 =180fb(Pm-P

e)/H


machine


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In literature the quantities involved are expressed in their

natural units without the use of per unit notation

p2 =(Pm-Pe)/M

M=GH/180fb,G is the rating of the machine in kVA,

H in kW-sec/kVA ,Pm and Pe in kW


machine


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Conclusion One can get the idea of basic machine parameters

associated with synchronous machine for building models.

After understanding the machine parameters the models

used in MATLAB are built.

This can help in choosing the right model for analysing theperformance of the synchronous machine.

It will be very useful for those working in power stations.


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Reference Mulukutla S.Sarma, Synchronous Machine (Their

Theory, Stability and Excitation Systems).

Charles Concordia, Shycnronous Machines Theory and

Performance.

Mohamed E. El-Hawary, Electric Power SystemsDesign and Analysis

Yao-Nan Yu, Electric Power System Dynamics.

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