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STABn:iTi . .\
STEADY STATE ,. ANALls,rS OF AC-DC POWER SYSTEKS
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FAROOQ AHMAD QURESHY
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A Thesis
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Submitted to the School of Graduate Studies
·in Partial FulfiJ,ment of the Requireme'ntst
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Doctor of Philosophy ..
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McMas'ter University
May 1985
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STEADY STAn; STUILITl ANALYSIS OF AC-DC POWER SYSTEMS
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In the name oE 1\11ah, th., l3eneEicent,
the Mer~iEuL
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Glory be ~o God, and
praise be fo God! There is no
deity save God. God is Supreme.
There is no strength nor power
. save in God.
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DOCTOR OF PIIILOSOPHY (I985) McMaster University,
(Electrical &Computer Engine~ing) Hamilton, Ontario
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TITLE: 'STEADY STATE STABILITY ANALYSIS OF AC-DC POWER
SYSTEMS ...
AUTHOR: Farooq Ahmad Qureshy
B.Sc. (Elect. Eng., West Pakistan University of
Engineering &Technology, Lahore)
M.S. (Elect. Eng., Polytechnic Institute of New
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York, New York)
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SUPERVISOR: R.T• Alden, Ph.D., P..Eng.
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NUMBER OF PAGES: 'xvi,
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I would like to expre;s1i my sincere apprecl,at,ion and gratitude
to 'Professor R.T.H. Alden foi' his guidance and encouragement and for
having 'made this work a pleasurable" exchang~: of information.
are due to Professors N.K. Sinha, R.D. Findlay and Dr. P~ Kundur for
their continuing support and helpful ~dvice.
Thanks an; rightly, due to my associates Dr. I. EI-Nahas and
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Dr. M. EI-Sobki for their useful discussions both on msthematical
~ tech,!ique and physical interpretatiot!.
The financial support of McMaster University, the Natural
Sciences and Engineering Research Council of Canada and the Government
of Ontario (Ontario Graduate Scholarship Program) is gratefully
acknowledged.
I would like to thank Mrs. Dianne Crabtree of Dianne's Word
Processing Service, Burlington, Ontario, for her typing and cheerful
co~eration in the 'preparation of this msnuscript.
Finally, I would like ·to express special thsrtks to m~ wife
Shahnaz and parents Asrar and Mutahhirs ~reshy for their love,
encouragement and support. It is to them that I dedicate this thesis.
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ABSTRACT
This thesis presents a comprehensive approach for the steady
state stability analysis of AC-llC power systems. A new method is
presentod for the evaluation of the system state· matrix which is then
used to determine system stability and develop new algorithms for the
stability analysis and" control of large powe~ systems.
The method exploits the powerful features of the Component
Connection .Method for power system modelling and overcomes "the
disadvantages of the eariier \TIerhods. The sta.te matrix is formulated
from two separate sets of equations. One set models the component
subsystems whereas the other defines the interconnection between the
subsystems. The main advantage of this is the great flexibility
provided in the modelling of· the power. system compon,mts. As .long as
the input-output quantities are fixed the modelling complexity of the
subsystems may be changed without affecting the interconnection equa-
tion. A compact interconnection equation has been derived relating
machine voltages and currents in the presence of a multiterminal HVDC
network. The subsystems retain their physical identity in this formu-
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lation and allow the derivatives of the system state !"atrix to be
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easily obtained. system operating .point is determined by a
new sequential AC-llC loadflow scheme. Any AC loadflow method can be
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used•. The IX: -network is solved using the Gauss-Siedel method and any
HVDe network configuration and terminals control scheme can he accommo-'
dated. The IX: network solution need not be repeated and the method
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ens,ures that a feasible HVDe system operating point is selefted.
A new eigenvalue tracking algorithm ha,s been developed based on
the evaluation of the sensitivity of a matrix determinant. .It itera
tively updates the eigenvalues following anf,.:ha'nge in the system state
matrix at one-third the cost of eigenval~ computation using the QR
algorithm. Used togeAr with the proposed state m'l.trix formulation
method, it is particularly useful for identifying the modes due to any
.particular subsystem.
pOle~ement
Two new methods for decentralized have been
developed. The first method assigns the given poles among the various
subsystems,and the elements of the feedback gain matrix are varied to
cancel the effects of the Sfstem interconnection. The second method is
based on the sensitivity of a matrix determinant and aolves the decen-
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tralized pole placement problem as an inverse eigenvalue problem. Both
methods are easy to implement and computationally efficient.
The methods presented in this thesis have all been verified by
app]ying them to realftic power system models. These have included a
single machine infinite bus system, a three-machine AC system with sIx
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buses and nine lines and a three-machine three-terminal AC-IX: system•
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These applications i~clude simulation, analysis and decentralized
controller design.
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LIST OF PRINCIPAL' SYMbOLS
Gener~ting Unit Hodel
- stator voltages in direct- and quadrature-axis cir~
cu!ts, respectively.
- stator voltages in, DO synchronous reference frame.
- stator voltage.
- stator currents in direct- and quadrsture-axis cir-
cuits, respectively.
- stator currents in DO sYnchronous reference frame.
- stato~ flux linkages in direct- and quadrature-axis
ci~cuits, respectively.
- synchronous reactances in direct- and quadrature
axis circuits, respectively.
- self, reactances of field and direct-axis damper
winding'a.
Xkq - self 'reactances of quadr,ature-axis damper windings.
xaf - stator field mutual reactance.
xad,xaq - stator-rotor mutual reactances with damper wind-
'" ings.
rs - stator resistance.
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rf,rkd,rkq - fiei~damper windiDK resistances.
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if ,ikd ,.ikq - currenLs in f1pld and dHmpcr windings.
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Efd - field voltage. .
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" '- total reactance between generato,r terminal and bus-
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total resistance between generator terminal and
busbar.
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\ - sngular frequency of infinite bus.
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H - inertia constant. ,""
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Tm input torque to generator shaft.
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T - generator output electrical torque.
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W - angular speed of rotdr.
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p.O active 'and reactiVe power. "
E - voltage 'behind synchronous impedance.'
Ed - voltage proportional to quadrature-axis flux link-
age.
- voltage proportional to direct-axis flux linkage.
x' - stator transient reactance.
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- quadrature-axis transient open-circuit time con-
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direct-axis ,transient ope!'-circuit tl,me con,stant.
- damping coefficient.
Excitation Syate.
- voltage sensor output.
- amplifier output voltage.
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V stabilizer output vPltage.
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vo~ge Be~Bor
TR • tim.e constant.
fA amplifier time constant.
TF - stabildzing loop 'time constant.
'E - exciter time constant. I
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KA - amplifier gain.
KF - stablizing loop gain
KE - exciter gain.
Vref - exciter reference voltage.
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DC Terainal Controller
IOC terminal OC current.
VOC - terminal DC voltage.
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IREF - reference current.
VREF , ~ reference voltage
VST - stabilizing input.
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- firing angle.
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KAC - constant current controller amplifier gain. .'
KAV - constant voltage controller amplifier gain.
KS - atabilizing input gain.
Tc - current controller time constant.
TV - voltage controller time constant.
DC Converter Stabilizer
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- atabilizer gain.
- voltage feedback gain.
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Description:STEADY STATE STABn:iTi ANALls,rS OF AC-DC POWER SYSTEKS. , .,. , . I. -\. , by .. (C) Glory be ~o God, and praise be fo God! There is no.
