EXPERT SYSTEMS AND SOLUTIONS Project Center For Research in Power Electronics and Power Systems IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E Email: expertsyssol@gmail.com, Cell: +919952749533, +918608603634 www.researchprojects.info OMR, CHENNAI IEEE based Projects For Final year students of B.E in EEE, ECE, EIE,CSE M.E (Power Systems) M.E (Applied Electronics) M.E (Power Electronics) Ph.D Electrical and Electronics. Training Students can assemble their hardware in our Research labs. Experts will be guiding the projects. EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS We provide guidance and codes for the for the following power systems areas. 1. Deregulated Systems, 2. Wind power Generation and Grid connection 3. Unit commitment 4. Economic Dispatch using AI methods 5. Voltage stability 6. FLC Control 7. Transformer Fault Identifications 8. SCADA - Power system Automation we provide guidance and codes for the for the following power Electronics areas. 1. Three phase inverter and converters 2. Buck Boost Converter 3. Matrix Converter 4. Inverter and converter topologies 5. Fuzzy based control of Electric Drives. 6. Optimal design of Electrical Machines 7. BLDC and SR motor Drives

1. EXPERT SYSTEMS AND SOLUTIONS
Email: expertsyssol@gmail.com
expertsyssol@yahoo.com
Cell: 9952749533
www.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 the
projects.

2. PRESENTATION ON
SYNCHRONOUS MACHINE
MODEL
TANDIN JAMTSHO
STUDENT #3226091

3. This presentation shall cover the
following topics
 Introduction
 Mathematical model
 Circuit based model used for both steady state and transient
analysis
 Differential equation model
 Conclusion
 Discussion at the end of presentation

4. The main component of power
system are
Step up Transmission
Generator
Transformer Line
Step down
Load
Transformer

5. Principle of synchronous machine
 Based on the principle of Faraday’s
law of electromagnetic induction
 Generally the armature winding are
located on the stator and field
winding on the rotor
 The field winding is excited by a
direct current

6. What is mean by synchronous
machine ?
 A machine that operates at constant
speed and frequency with respect to
time is called the synchronous
machine.
 N=120f/P
 N=speed of the machine in rev/min
 F=frequency in Hz
 P=number of poles

7. Assumptions made are:
 The stator windings are sinusoidally
distributed electrically
 The effect of the stator slots on the
variation of any rotor inductances
with rotor angle is neglected
 Saturation effect neglected.

8. Mathematical model
 Source of the diagram:
 Mohamed E. El-Hawary,
Electric Power Systems
Design and Analysis

9. By Faraday’s, the voltage induced in the stator coil
ea p a ria
eb p b ri
b
ec p c ric

10. Where
ea = terminal voltage of phase a
= total flux linkage of phase a
ia = current in phase a
a,b and c are phases
r = the resistance of each armature winding,
assumed to be same for all three phases
p = the derivative operator d/dt, t is the time
ef = p f +rfif

11. Inductance
The self inductance of any stator winding phases are given by
laa Laa0 Laa 2 cos2
lbb Laa 0 Laa 2 cos 2( 120)
lcc Laa 0 Laa 2 cos 2( 120)
The mutual inductance between any two stator phases are given by
lab lab [ Lab0 Laa 2 cos2( 30)]
lbc lcb [ Lab0 Laa 2 cos2( 90)]
lca lac [ Lab0 Laa 2 cos 2( 150)]

12. Elimination of old variable ia ,ib, ic,by introducing
a new variable io
 Now I o=1/3(ia+ib+ic )
iq 2 / 3 cos 2 / 3 cos( 120 ) 2 / 3 cos( 120 ) ia
iq 2 / 3 sin 2 / 3 sin( 120 ) 2 / 3 sin( 120 ) ib
io 1/ 3 1/ 3 1/ 3 ic

13. The new variable for flux linkage
d, q, 0
The equivalent d-axis moving armature coil self
inductance is
Ld Laa 0 Labo 2 / 3 Laa 2
The equivalent quadrature-axis moving armature
self inductance is
Lq Laa 0 Labo 2 / 3 Laa 2
Zero sequence self inductance is
L0 Laa 0 2 Lab

14. The armature voltage equation in terms of d,q
and 0 becomes
ed p d p
q rid
eq p q dp riq
e0 p 0 ri0

15. Under steady state operation, flux linkage in per unit along d
and q axis and the voltage relation can be written as
d Li d d L i ad fd
q Li q q
ed q rid xqiq rid
eq d riq xadifd xdid rid

16.  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. Steady state Vector diagram
F
q-axis
E
D
O
A
B C
d-axis

18.  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. 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 phase
winding 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 for
all the cases.

20. Circuit based models for round rotor and salient
pole synchronous machine are
 Reactance of air gap flux is represented xo and the leakage flux
reactance is represented by xl
 Xs= xo+xl
I ө
Xs +
V 0
E δ +++
- -

21. D-axis equivalent circuit
d i1d
id ifd
fd
1d

22. Q-axis equivalent circuit
d
q iq
i1q
1q
1q

23. Transient circuit based model
 D-axis equivalent circuit for the sub-transient
period
id
d
id
ifd i1d

24.  Q-axis equivalent circuit for the sub-
transient period
d
q
i
q
ii
q1q

25. 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 are
defined 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 and
quadrature axis are given by
 Xd’=Ll+ (1/(1/Lad+1/Lfd))
 Xq’=Ll+ (1/(1/Laq))
 X2=( Xd’’+ Xq’’)/2

26. Time constants

 T’do=Xffd/rfd ( direct axis transient open circuit time
constant, 2 to 11 seconds)
 T’d=X’d*T’’do/Xd (direct axis transient short circuit
time constant
 T’’d=X’’d*T’’do/X’d (direct axis sub-transient time
constant
 T’’do =(x11d-x2f1d/xffd)/r1d (direct axis sub-
transient open circuit time constant)
 T’’qo=x11q/r1q
 T’’q=x’’q*T’’qo/xq
 Ta=x2/r (armature short circuit time constant)


27. Swing equation of synchronous
machine
 We know that per unit mechanical acceleration
equation
 p2Θ=(Tm-Te)/H’
 Θ angle in electrical radians between d-
P=d/dt,
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. Swing equation of synchronous
machine
 Θ=t+δ
 the reference axis and the quadrature axis
 The equation can be written as δ =angle between
 p2 δ =(Tm-Te)/H’
 By expressing angle in degrees and time in seconds it becomes
 p2 δ =180fb(Tm-Te)/H’
 Since p.u electrical torque =p.u air gap power developed
 p2 δ =180fb(Pm-Pe)/H’

29. Swing equation of synchronous
machine
 In literature the quantities involved are expressed in their
natural units without the use of per unit notation
 p2 δ =(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

30. 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 the
performance of the synchronous machine.
 It will be very useful for those working in power stations.

31. 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 Systems
Design and Analysis
 Yao-Nan Yu, Electric Power System Dynamics.