Influence of damping winding, controller settings and exciter on the damping of rotor angle ...

101 Pages·2011·5.56 MB·English

UPTEC E 11 002
Examensarbete 30 hp
Februari 2011

Influence of damping winding, controller
settings and exciter on the damping of rotor
angle oscillations in a hydroelectric generator
The testing of a mathematical model
Jonathan Hanning
Abstract
Influence of damping winding, controller settings and
electrical feeders on the damping of rotor angle
oscillations in a hydroelectric generator
Jonathan Hanning

Teknisk- naturvetenskaplig fakultet
UTH-enheten This thesis has been performed in the university context for Master thesis 30 credits,
which is a compulsory exercise in order to gain a degree in electrical engineering.
Besöksadress:
Ångströmlaboratoriet
The thesis main objectives were to investigate how the damping and the stiffness of a
Lägerhyddsvägen 1
Hus 4, Plan 0 hydroelectric generator changed depending on different parameter values, and to test
a new mathematical model to calculate the damping and stiffness constants Kd and Ks.
Postadress: The work has been performed at the request of VG Power, but has been performed
Box 536
at the division for electricity at Uppsala University. The reason for undertaking this
751 21 Uppsala
thesis was to ensure that generators are robust. But also when building future models

Telefon: for generators, to have a system that can be used to compute robustness.
018 – 471 30 03
During this thesis a power cabinet has also been constructed to be able to test the
Telefax:
simulated model on a real generator. Under the first five weeks a power cabinet was
018 – 471 30 00
constructed in the laboratory at the division for electricity. The tests were then
Hemsida: performed at a generator with a rated power of 75 kVA.

http://www.teknat.uu.se/student
Handledare: Martin Ranlöf
Ämnesgranskare: Urban Lundin
Examinator: Nora Masszi
ISSN: 1654-7616, UPTEC E 11 002
Sammanfattning

Detta examensarbete har utförts vid avdelningen för elektricitetslära vid Uppsala universitet.
Uppgiften var att undersöka hur dämpning och styvhet påverkas av olika faktorer i en
generator. En del av arbetet bestod i att jämföra skillnaden mellan kontrollerad dämpning med
hjälp av en automatisk spänningsregulator tillsammans med en PSS, mot ett system som
använder kopparskenor för dämpning.

Den viktigaste slutsatsen som kan dras av detta examensarbete är att om man vill ange
riktlinjer för tillverkare av generatorer, när systemet endast består av en generator och en
regulator, bör riktlinjerna bestämmas utifrån massan. Eftersom denna faktor är den viktigaste
för robustheten i systemet. Tanken med systemet skulle vara att för varje viktig variabel, så
skulle ett värde erhållas och skulle sedan kunna kontrolleras mot en tabell för att säkerställa
att inga farliga värden erhålls. Att konstruera denna tabell är ett annat examensarbete, som
skulle kräva fler simuleringar på många fler maskiner, och därför bör utföras av någon med en
bakgrund inom beräkningsvetenskap.

Den matematiska modellen som testats i detta arbeta behöver lite mer justering på grund av att
den inte verkade matcha helt den nuvarande accepterade modellen. Det måste dock sägas, till
den nyares försvar, att med vissa inställningar, så korrelerade den mycket bra med den äldre
modellen. Men det kommer att behöva ändras och anpassas lite mer, särskilt i beaktande vid
beräkningen av den synkrona vridmomentskoefficienten, som nästan alltid verkade vara 10
till 30 procent för låg.
Abbreviations
AVR Automatic Voltage Regulator
D-Q-axis Direct and Quadrature axis
DAE Differential-Algebraic Equation
Et Terminal Voltage
H An inertia constant
Ka/Kp Gain constant in the feedback system
Kd (1) Damping constant in electric torque equation
Kd (2) Derivative constant in the feedback system
Ki Integrating constant in the feedback system
Ks Synchronous constant in electric torque equation
ODE Ordinary Differential Equation
Pf Power Factor
PhD “Philosophiæ Doctor” or Doctor of Philosophy
PSS Power System Stabilizer
P.U. Per Unit
Re Resistance in the tie-line
SMIB Single Machine, infinite bus
St Power output
Td Foresight of the time step
Te Electrical torque
Xe Reactance in the tie-line
UU Uppsala University
Conclusion
This master thesis has been conducted at the division of electricity at Uppsala University. The
task was to conduct research about the damping and stiffness of a generator. One part was to
compare the difference with controlled damping with the help of an automatic voltage
regulator, together with a power system stabilizer. And also a system which used copper bars
for damping.

The main conclusion that can be drawn from this thesis is that if you want to provide
guidelines for manufacturers of generators, when the system contains only of the generator
and a regulator, the guidelines should be determined by the mass. Since this factor is the most
important one for the robustness of the system. The idea of the system would be that for each
important variable, a number is acquired and could then be checked against a table to ensure
that no dangerous values are obtained. To construct a table like this is another thesis, which
would need a lot more machines to be simulated on, and therefore should be performed by
someone with a background in scientific computing.

The mathematical model tested in this thesis need some more adjusting, due to the fact that it
did not seem to match entirely to the current accepted model. It must be said, though the
latter’s defense, that with some settings, the altered mathematical model matched very well.
But it will need to be modified and tuned some more, especially in regard to the calculation of
the synchronous torque coefficient, which almost always seemed to be 10 to 30 percent to
low.
2010-12-31
Influence of damping winding, controller settings and exciter on the damping of
rotor angle oscillations in a hydroelectric generator
Foreword
This thesis has been performed in the university context for Master thesis 30 credits, which is
a compulsory exercise in order to gain a degree in electrical engineering.

The thesis was to investigate how the damping and the stiffness of a hydroelectric generator
changed depending on different parameter values. And also to test an altered mathematical
model to calculate the damping and stiffness constants Kd and Ks. The work has been
performed at the division for electricity at Uppsala University, as a joint operation together
with VG Power. The reason for undertaking this thesis was to ensure that generators are
robust. But also when building future models for generators, to have a system that can be used
to compute robustness.

I would like to especially thank my supervisor Martin Ranlöf for the time he has spent helping
me over the threshold incurred during my work. My thanks are also directed to the people in
the same working group, Johan Lidenholm, whose thesis has been very helpful, but who has
also helped with understanding some problems in Matlab. Thanks also to Mattias Wallin for
much practical instruction during the construction of the power cabinet. Also big thanks to
Urban Lundin for the hydropower course and for making this thesis possible and I would also
like to thank Kjartan Halvorsen for the help with the automatic control. Also thanks to Stefan
Pålsson for this knowledge with Matlab. Last but absolutely not least, all the teachers who has
put in much effort in my education so that the courses I have read has become much more
interesting, thanks also to my examiner, Nora Masszi.

Jonathan Hanning
January 2011
Uppsala
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2010-12-31
Influence of damping winding, controller settings and exciter on the damping of
rotor angle oscillations in a hydroelectric generator

1 Introduction ............................................................................................................................. 4
1.1 Background .................................................................................................................. 4
1.2 Method ............................................................................................................................. 5
1.3 Demarcation ..................................................................................................................... 5
1.4 Objectives ......................................................................................................................... 5
2 Theory ..................................................................................................................................... 7
2.1 Synchronous generator ..................................................................................................... 7
2.2 The damping and synchronous coefficient ....................................................................... 7
2.3 System analysis ................................................................................................................ 8
2.4 The mathematical model .................................................................................................. 9
2.4.1 Direct and Quadrature axis ........................................................................................ 9
2.4.2 Per unit representation ............................................................................................. 10
2.4.3 State-space representation ....................................................................................... 10
2.4.4 Automatic control .................................................................................................... 10
2.4.5 The nine basic equations ......................................................................................... 11
2.4.6 Ordinary differential equations solver ..................................................................... 12
2.4.7 Standard parameters ................................................................................................ 12
2.5 Rotor angle oscillation ................................................................................................... 12
3 Method and construction ....................................................................................................... 14
3.1 Mathematical model in matlab for simulation ............................................................... 14
3.1.1 The introducing of state space representation ......................................................... 14
3.2 The construction of the power cabinet ........................................................................... 16
3.2.1 Modifying the generator with damper bars ............................................................. 16
3.3 Operating the generator ...................................................................................................... 17
4 Results ................................................................................................................................... 18
4.1 Simulation results ........................................................................................................... 18
4.1.1 Single machine without regulators .......................................................................... 18
4.1.2 Single machine with an automatic voltage P-regulator ........................................... 19
4.1.3 Single machine with an automatic voltage PD-regulator ........................................ 20
4.1.4 Single machine with an automatic voltage PID-regulator ...................................... 21
4.1.5 Single machine with both PID-regulator and PSS .................................................. 22
4.1.6 The mathematical model ......................................................................................... 22
4.1.7 Unstable systems ..................................................................................................... 23
4.2 Laboratory tests .............................................................................................................. 23
4.2.1 Connecting the generator to the grid ....................................................................... 23
5 Discussion ............................................................................................................................. 25
5.1 The simulation model ..................................................................................................... 25
5.2 The constructed power cabinet ....................................................................................... 25
5.3 The results ...................................................................................................................... 25
5.4 Future work .................................................................................................................... 26
5.5 Confounding ................................................................................................................... 26
6 References ............................................................................................................................. 27
6.1 Literature ........................................................................................................................ 27
7 Appendix ............................................................................................................................... 28
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2010-12-31
Influence of damping winding, controller settings and exciter on the damping of
rotor angle oscillations in a hydroelectric generator

1 Introduction

A different model, [1] compared with the accepted model, has been expanded and tested to
calculate the synchronizing and damping components of electrical torque developed in a
synchronous machine. The method is based on the numerical analysis of system response
time, using least squares adjustment.

1.1 Background
Since the introduction of synchronous generators in the late 19th century, the way of operating
a system with several generators has significantly improved. In the early years, it was not
unusual to have power black-outs over a huge area of the grid. But when the regulation was
modernized, it has become more and more unusual with power failure. Nowadays it is almost
required a storm which destroys a cable to receive a power failure.

The stability of a power grid is depending both on the total grid, but also on its individual
components. Usually in a grid there are power consumers, power producers, power
transmission and power control. And since the producers are depending on the consumers,
there has always been an interest of how the producing unit reacts to changes in consuming.
For example how the electrical torque changes when a huge load is connected to the grid. The
electrical torque is built up by the synchronous and damping constants of the generator.
Therefore these constants have been of interest for some time.

The ability to calculate the damping and synchronizing constants has been an important
problem since the expansion of power system interconnections. And since the improvement
of digital computers and modern control theory, a better control of power systems has been
gained. However, the method how to calculate these torque components has not improved at
the same rate. This new approach is thus based on the time-domain analysis of system
response. Precision depends on how good the accuracy was of the time response.

Due to imperfection in the system, a couple of oscillations will occur. The most interesting
and important one is the rotor angle oscillation. This oscillation occurs when the power is
raised or lowered, and the generator is trying to find its new equilibrium, the equilibrium
between the torque from the turbine and the electrical torque. This oscillation gives a few
other oscillations, which will be studied in this thesis. For example the oscillation in the
power produced. The power produced is connected to the swing equation, equation 1b, which
is connecting the rotor angle acceleration, the mechanical torque, and the electrical torque.
This is further described in chapter 2.2.

When measuring is performed on a generator, different variables are calculated in order to be
able to compare the results. It is usual to use either damping time constant T , which is the
d
time required for the amplitude to decrease to a new value from its original value. Another
value that is often use is the damping torque coefficient, K , which is used to identify the rotor
d
angle stability of the system. Yet another constant that is interesting is the damping capacity
b, which is the ability to absorb vibration by internal friction. In the current situation, there is
some confusion about what requirements that should be set on the generator supplier,
concerning the damping qualities.
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2010-12-31
Influence of damping winding, controller settings and exciter on the damping of
rotor angle oscillations in a hydroelectric generator

The purpose of this thesis is to show how the damping and synchronous constant is affected
by the electrical design, selection of exciters, adding damping parameters and inertia. The
equation relationship between attenuation and these factors are certainly well known, but are
found in various places in the literature. The study of damping has been performed on a two-
axle model of a generator.

1.2 Method
This thesis will analyze this problem in two different ways; first the expanded mathematic
model which will be tested in Matlab. In this thesis are also included some testing on a real
generator. To make this possible, a synchronization unit will be built to link up one of the
division of electricity´s generator to the electrical grid. Since Uppsala does not have any great
waterfall, the generator is driven by a motor which is connected to the rotor, instead of a
turbine. Therefore there will be the possibility to perform quick torque changes. The idea is
then that the natural damping of the generator, which occurs due to the copper in the rotor
windings, together with the quick torque change, will give rise to oscillating revolutions per
minute. This oscillation should continue until the generator has found its new steady-state
level of operation. This should also provide an oscillating power curve. Another test will be to
connect a network of copper bars to get a stronger damping, due to the current that will be
induced in these which will counteract the change in torque.

1.3 Demarcation
The idea of this thesis is to develop a functional program for the mathematic model in Matlab,
which can simulate different machines, with different parameter values. This program will
then be modified so that you can connect an automatic voltage regulator in front of the
generator, and the final version should also include a power system stabilizer. This is done to
be able to compare the stability and robustness of a system, due to variation in settings on the
control systems and various types of generators. A proposal will also be included of how the
value of the included parameters in the regulator should be, to ensure stable systems. If the
results of the simulations in Matlab give a distinct and unambiguous picture, a proposal for
recommendation of generator design in terms of robustness and torque stability will be made.
Primary focus will be to investigate the influence of the automatic voltage regulator’s
parameters on stability of the system, while the power system stabilizer will more or less, if
not time permits, just be implemented. The simulations will only be on a single machine
infinite bus. No simulation will be tested on island grids (weak bus). Primary focus will be on
the synchronous coefficient and the damping coefficient, described more closely in chapter
2.2. Secondary focus will be on the changes in rotor angle velocity, and torque change and
also how the electric angle between rotor and stator magnetic axes difference. Most units in
this program will be measured in per unit, and the reason is that it gives more comparable
data.

1.4 Objectives
The primary objective is to construct a program for analysis of the damping and synchronous
coefficient. Secondary is to build a functional synchronizing unit to be able to connect a
generator to the grid. This to make it possible to try the theory in reality, but also for further
experiments being performed by other students and PhD under the division of electricity.
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2010-12-31
Influence of damping winding, controller settings and exciter on the damping of
rotor angle oscillations in a hydroelectric generator
After completing the main objective, a series of add-ons is desirable. For example, the
possibility to use an automatic voltage regulator and a power system stabilizer to increase the
robustness and stability of the system. Another sub objectives there would be to investigate
how the different parameters change the system. Another sub objective is to analyze how the
new mathematical model works, compared to the old accepted model, with other words, if
they correlate. Another objective is to try to make up a system so companies who design
generators can have some kind of model for robustness and stability when designing the
generators. It would also be desirable to look into the stability from an automatic control
perspective, due to the fact that both the automatic voltage regulators as well as the power
system stabilizers are feedback systems. A desirable and maybe final objective would be if
the simulated results would correlate with those which can be measured in the laboratory,
primary the change in rotor speed when a disturbance in torque is being done. This thesis is
being done because there is a gap in the literature concerning how the stability is inflicted by
an automatic voltage regulator and its parameters.
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