Download A Study of De-Excitation after Abrupt 3

A Study of De-Excitation after Abrupt 3-phase Short Circuit
of a Hydraulic Generator
CHEN, Xianming
ZHU, Xiaodong
WANG,,Wei
Nanjing Automation Research Institute
P.O.Box 323, Nanjing ,210003, PRC
Email: [email protected]
ASTRACT
The paper describes simulation results of de-excitation of a hydraulic generator after abrupt 3-phase short circuit. The
mathematical model of the generator is built on “Park equations of synchronous machine”. In order to avoid undue
complexity the effect of damping winding on rotor is ignored. In addition, the non-linear no-load characteristics of the
generator is expressed approximately by an analysis expression, that facilitates the simulation and raises confidence
level of it. Finally, an example of de-excitation simulation with non-linear resistors ZnO for a 700 Mw hydraulic
generator of Three-gorge power plant with help of MATLAB/Simulink is given .
Keywords: de-excitation, hydraulic generator, 3-phase short circuit, simulation
1
INTRODUCTION
De-excitation of a large hydraulic generator is an
important matter, which influences safety of
generators.
Specially, there are 26 hydraulic
generators of 700Mw have been or will be installed in
Three-gorge hydro-power plant in China. According
latest estimating, there will be about one hundred
such hydraulic generators which will be installed in
southwest area of China in next decade.
De-excitation of no-load hydraulic generator while
mal-forced excitation happened has been studied [1].
However, another very important de-excitation
situation, namely de-excitation after abrupt 3-phase
short-circuit of hydraulic generators is still unsolved.
That is why the paper will deal with it.
The paper describes the comparison results of amount
of magnetic energy absorbed for de-excitation of the
generator after abrupt 3-phase short circuit sustaining
different time.
There are two cases considered here, t.e. de-excitation
after abrupt 3-phase short circuit of no-load and
loading generator.
2.
PARK EQUATIONS
GENERATOR
OF
SYNCHRONOUS
In order to simplify discussion, the effect of damping
winding on rotor of generator is neglected.
Park differential equations of voltage in d ,q axis are
as follows:
U d  pd  q p  ri d (1)
U q  pq  d p  ri q
(2)
U f  i f r f  p f
(3)
The equations of magnetic flux linkage in real
physical values:
(4)
d  Ld id  L'ad i f /K
q   Lq iq
(5)
 f   Lad id K  L f i f
(6)
It should be noted that parameters of synchronous
machine usually represent in per unit. Besides, there
are some different ways for conversion between
quantities of stator and rotor.
In order to have real image for simulation both
quantities of stator and rotor should be represented in
real physical values. In that case, it is necessary to
introduce conversion coefficient concerned to above
Park equations.
Relationship between quantities of stator and rotor of
generator may only be represented via magnetic flux
linkage. So when all quantities of stator and rotor
adopted are represented by their real physical values,
the conversion can be simply implemented by
conversion factor K for magnetic flux linkage from
rotor to stator.
Substitute equations (4),(5),(6) to (1)，(2)，(3) and use
the accustom of Simulink, it can obtain following
equations： (S=d/dt –--differential operator)
U d  S (Ld id  L'ad i f / K )  X q iq  rid
(7)
U q  S (Lq iq )  X d id  2fL'ad i f / K  riq
U f  r f i f  S ( Lad Kid  L f i f )
(8)
(9)
In equations (7),.(8),(9) all parameters and quantities
of stator are in real physical values, and the same as
for all parameters and quantities of rotor. Only a
conversion factor K is introduced between magnetic
flux linkage of stator and rotor. It should be noted
that in order to distinguish d axis mutual inductance
for stator from that for rotor. Lad is used for d axis
mutual inductance of stator, and Lad’ for that of rotor.
3. SIMULATION FOR SOLVING DIFFERENTIAL
EQUATIONS
A method utilized here for simulation is solving
differential equation directly so as to avoid complex
calculation burden. As an example, Fig.1 shows the
Simulink structure scheme for solving differential
equation (7) with integral operator 1/S, proposed by
authors.
In order to facilitate calculation of magnetic field
energy of the generator.
An approximate
expression of N-LC of generator is adopted here [2].
That is: Uo=L i f ,
if i f <= Ib
(10)
Uo=(M* i f )/(N+ i f ) ,
Fig.1 Scheme for solving differential equation
Practice proved that the method for solving
differential equations is very convenient.
Fig.2
shows the full structure scheme for resolving the topic
of the paper ,which includes differential equations (7),
(8),(9) ,etc
.In Fig.2 modules “Eq.1”,”Eq.2”,”Eq.3” represent
expressions (7),(8),(9) respectively.
if
i f >Ib
(11)
Where Ib is excitation current of intersect point of
both above functions. If a real N-LC is known, then
suitable coefficients L, M, N can be determined by try
and error method. For the conventional N-LC they
can be adopted as follows:
L=1.1, M=1.95,
N=0.95. After substituting them to above expressions,
Then can be found Ib=0.823. The last two rows of
Table 1 shows U0’ the substituted N-LC.
The error between the substituted N-LC U0’ and
conventional N-LC U0 is so small that the former
used for engineering calculation is fully permitted.
The direct-axis inductance corresponding to main
magnetic flux Lad’ equals:
If if, <=Ib=0.823 then：
Lad’=λL
(12)
If if >Ib=0.823 then Lad’=λUo / i f ,namely,
Lad’=λM/(N+ i f )=1.95λ/(0.95+ i f )
(13)
Coefficient λ is used for getting real value of Lad’ in
henry. Expressions (12),(13) is implemented by
module “inductance” in Fig.2
N-LC of a no-load generator is represented as
follows:
Uo=f(if)
For a loading generator it becomes:
U=f(if±id)
Where U represents E.M.C behind leakage reactance
Xp. id represents armature reaction of d axis
stator current. When load of generator is
inductive, negative sign should be used.
Positive sign is for capacitive.
Fig.2 Simulation structure for voltage build up, short
circuit & de-excitation of generator
It is well known that no-load characteristic(N-LC) of
hydraulic generator is non-linear. It should be noted
that for a reasonably designed hydraulic generators in
economic and technical aspects, N-LC may not differ
from the following conventional characteristic Uo=f(if)
(in per unit) too much.
Table 1 Conventional N-LC ( in first 2 rows)
Uo
0 0.55 1.0
1.21
1.33
1.4
0
0.5
1.0
1.5
2.0
2.5
i
Fig.3 De-excitation circuit of generator
Module “d,q->a,b,c” in Fig.2 is used for stator
current conversion from d, q axis component to a, b, c
phase current.
Module “de-ex” is used for implementation of
de-excitation with non-linear resistor ZnO and for
magnetic energy (W,Wr) calculation.
Fig.3 shows de-excitation circuit of the generator.
Here the field equation for de-excitation becomes:
(14)
0  r f i f  kiaf  S (Lad Kid  L f i f )
Uo'
where ki f =Ux is voltage drop on non-linear resistor
f
0 0.55
1.0
1.194
1.322
1.412
Here 1 per unit excitation current corresponds no-load rated
terminal voltage (1 per unit) of the generator.
a
R.
Assuming α=1, R becomes linear resistor. For
non-linear resistor ZnO a=0.046，SiC a=0.28-0.36,
Selection of k depends on allow reverse voltage
adopted.
When 3-phase short circuit happens to a no-load
generator, that means electric circuit structure is
changed.
In order to deal with this change in
simulation, it may be considered that an external
3-phase voltage with same amplitude but opposite
direction of E.M.F of no-load generator , applies to its
stator terminals so, that no current output from stator.
Abrupt 3-phase short circuit happens when the
external voltage becomes zero. Fig.4 shows
equivalence scheme of no-load generator. In order
Fig.4 Equivalence scheme of no-load generator
to produce external 3-phase voltage above mentioned
module “no-load” in Fig.2 is used.
For no-load generator id=iq=0, then Eq..(7),(8),(9)
become:
(15)
U d  S ( L'ad i f / K )
U q  2fL'ad i f / K
(16)
U f  r f i f  SL f i f
(17)
And module ”no-load” is formed on them. Its output
voltages Ud, Uq are just the same as E.M.F produced
by modules “Eq.1”,”Eq.2”,”Eq.3” for no-load
generator.
The voltage building up process of
generator may also be observed.
Clock1 in Fig.2 is for control instant of 3-phase short
circuit. Clock is for control instant of de-excitation.
Usually before start simulation values of some
parameters concerned must be given in “ command
window ” of Simulink.
4. A SIMULATION EXAMPLE
An example of de-excitation of a hydraulic generator
of 700 Mw for Three-gorge power plant on left-shore
after abrupt 3-phase short circuit is given here.
(data provided from ABB Corp.)
Its main data as follows:
Rated power: 700Mw Rated voltage: 20Kv
Rated speed: 75 r.p.m Rated power factor: 0.9
Rated field voltage, current: 475.9 V , 4158 A Field
voltage, current at rated terminal voltage of no-load
generator: 191.8V, 2352 A.
Self-shunt static
  10.1s Td  3.2s
excitation system adopted. Tdo
Ta  0.28s
(unsaturated/saturated)
xd  0.3 1 5/ 0.2 9 5
xd  0.939 / 0.835
x  0.24 / 0.2 and r fd  0.1144(130o C)
''
d
Obviously, the parameters provided above is not
enough for simulation. Appendix shows calculation or
selection of all parameters concerned in detail.
Fig.6A,6B show whole processes of field current if
and d,q axis stator current id ,iq during rated voltage
building up, 3-phase short circuit at t1=46” and
de-excitation at t2=48” of 700Mw generator. Fig.3C
shows variation of d axis mutual inductance Lad’
during that period. It is a constant 0.803H in first
section, then decreases in saturation section of N-LC,
and returns to 0.803H after 3-phase short circuit.
The time for voltage building up is long owing to
Tdo’=10.1” of 700Mw generator.
In order to be more clearly, other pictures in Fig.6
only show in part interval from t=45” to 50”.
Fig.6D,6F show if, id and iq, Fig6E : if—id(f) in
interval of short circuit and de-excitation. Where
if—id(f) is effective field current, equals real field
current if minus equivalent d axis armature reaction
id(f). That causes Lad’ located in non-saturation
section. It can be seen that there are large ac
component superimposing on dc current of if ,id ,iq.
Fig.6G,6H,6I show short circuit phase current ia,
ib ,ic , Fig.6J,6K: q axis stator voltage Uq, magnetic
energy in same interval. De-excitation time here is
0.69”
Table 1 shows the magnetic energy W, Wr absorbed
by varistor ZnO and field winding of 700 Mw
generator at different short circuit sustaining interval.
In Fig.6 the latter is t2－t1=48”--46”=2”.
Tabel 1
Interval sec. 2”
1”
0.5”
0.1”
W
MJ
2.81
3.845
4.554
5.32
Wr
MJ
0.375 0.588
0.765
1.0258
In order to obtained abrupt 3-phase short circuit and
de-excitation of loading generator, field current if
and voltage Uf, stator voltage in d, q axis Ud, Uq
must be determined in accordance to load of generator
with simplified vector diagram (Fig.5) of synchronous
generator in steady state .
Fig.5
Simplified steady state vector diagram of
synchronous generator
Assuming that terminal voltage U, load current I, and
power factor cosΦ are given, then power angleδ
can be calculated as follows（18）:
(A)
(B)
(C)
(D)
(E)
(G)
(H)
(J)
(F)
(I)
(K)
Fig.6
Simulation results of
no-load ,3-phase short circuit &
de-excitation
of
700Mw
generator
U
IXq

.
sin( 90     ) sin 
（18）
o
Where Xq is q axis synchronous reactance. And
Ud=Usinδ
Uq=Ucosδ
In addition, field current and voltage for such load
must be given so as to obtain steady state operation
condition of the generator.
Fig.7 shows the simulation results of an abrupt
3-phase short circuit and de-excitation of the loading
700Mw generator . The steady state of the generator
is assumed : Ud=0, Uq=(20/√3)Kv=11547v (rated
phase voltage) and field current if =4158A (rated
field current). Uf=if×rf. For implementing simulation
here module “no-load ” is replaced by a transfer
switch controlled by Clock1 in Fig.2, which changes
Ud ,Uq from value mentioned just above to both zero.
Besides, values of Uf ,if are put into proper
places of module “ Eq.3” in Fig.2.
Fig.7A,7B,7C show if, if －id(f) ,and id,iq of
700Mw generator in interval of abrupt 3-phase short
circuit at t1=46”and de-excitation at t2=48”.
Fig.7D,7E,7F show stator phase current ia ,ib ,ic of
700 Mw generator in same interval.
Fig.7G shows the magnetic energy concerned ,and
Table 2 gives the detail for different short circuit
sustaining intervals. Table 2
Interval sec. 2”
1”
0.5”
0.1”
W
MJ
4.835
5.822
6.471
7.135
Wr
MJ
0.876
1.14
1.33
1.585
Fig.7H shows the variation of d axis mutual
inductance Lad’. Lad’ for loading 700Mw generator
is a saturation value about 0.6H, it becomes
unsaturation value 0.803H after short circuit.
De-excitation time here is about 0.93 Sec.
5. CONCLUSION
A). The paper shows the successful simulation of
de-excitation after abrupt 3-phase short circuit of
generators. In the mean time the saturation of N-LC is
considered fully by using approximate analysis
expressions.
B).From the simulation, it can be seen :
---the less time short circuit sustained, the larger
magnetic energy absorbed.
---value of d-axis mutual inductance Lad’ of loading
generator is in saturation area ,and can be determined
by simulation. The saturation can be ignored when
3-phase short circuit happens. Obviously armature
reaction in this case is quite big to cancel some effect
of field current.
C). There is lack to discuss the quantitative matter of
electric quantities such as if ,id, iq and ia ,ib ,ic,etc.
because not enough parameters for simulation are
given.. Some parameters were assumed by
authors. .
However, we hope that simulation method proposed
by authors may be useful for electrical engineers to
refer.
Appendix
Determination of parameters for 700Mw generator.
ON STATOR SIDE:
Rated stator current
In=700×103/(20×0.9×√3)=22453a
Base impendence Zb=20/(√3×22.453)=0.5143 ohms
Phase voltage Ufφ=20/(√3)=11547V
Xd=0.939×0.5143=0.483 ohms
Ld=0.483/(2*pi*50)=0.00154 H
Suppose Xp=0.17
Then: Xad=Xd-Xp=0.939-0.17=0.769
Xad=0.769×0.5143=0.3955 ohms
Lad=0.3955/(2*pi*50)=0.00126 H
Xf=Xad2/(Xd－Xd’)=0.948
Xfs=Xf-Xad=0.948-0.769=0.179
Suppose Xq=0.7Xd
Xq=0.7×0.939×0.5143=0.338 ohms
Lq=0.338/(2*pi*50)=0.001076 H
Ta=X2/(2*pi*50*r)
Resistancer of stator r= X2/(2*pi*50*Ta)
Usually X2=0.5(Xd”+Xq”) or =√(Xd”×Xq”)
General speaking: For hydraulic generator
Xd”= 0.14----0.26 Xq”=0.15-----0.35
Suppose Xq”=0.34
Then: X2=0.5(0.24+0.34)=0.29
Or X2=√(0.24×0.34)==0.2856
Suppose X2=0.285
X2=0.285×0.5143=0.1466 ohms
Stator resistance
r=0.1466/(2*pi*50*0.28)=0.00167 ohms
ON ROTOR SIDE:
rf=0.5[(191.8/2352 )+0.1144]=0.098 ohms
Lf=rf×Tdo’=10.1×0.098=0.99 H
Lfs=(0.179/0.948)×0.99=0.187 H
Lad’=(0.769/0.948)
×
0.99=0.803 H
For N-LC of 700Mw
generator Lets L=1.1
ifo’=1/L=1/1.1=0.91
×
2352=2138a
Base value of field current
in “Xad” system ifb=0.769×2138=1644a
Ufo=2352×0.098=230V
id(f)) d axis stator current convert to rotor (field
Winding; id(f)=id×1644/22453=id/13.66
Ratio K of magnetic flux linkage from stator side to
rotor (field winding) side:
K
L'ad i fb
Lad I n

0.803  1644
 46.7
0.00126  22453
(A)
Fig.7
(B)
(D)
(E)
(G)
(
H)
(C)
(F)
Simulation results of abrupt 3-phase short circuit, de-excitation of loading 700 Mw generator
Reference
1). CHEN Xianming et al “A simulation study of
de-excitation of no-load water-wheel generators “
Paper Abstracts IP1-01 ICEE--C0178
ICEE-2005 July 10-14,2005 Kunming, China
Full paper on CD :
Industrial Process and
Automation IP1-01
2). B.A.Torvenski “Universal no-load characteristic of
synchronous generator and their analysis expressions”
Journal of former USSR “Electric Force” factory
pp45-54 No.2-3 1945 Leningrad
(in Russian)
Biographs
CHEN, Xianming was born in Nanjing, China. He
graduated from Dept.of EE Harbin polytechnic
Institute, Heilongjiang province in1958 and has
worked in several research Institutes in China. Now he
is with NARI as a senior engineer. His interest is in
power electronics and excitation of alternators.
ZHU, Xiaodong He graduated from Dept.of EE
Hehai University, Nanjing in 1992 and received M.S
degree in 1995, since then he work in NARI. Now he
is a senior engineer and his interest in power
electronics and power plant control.
WANG, Wei
He graduated from Dept.of EE
Wuhan Sciense&Technical Institute ,Wuhan, in 2001
And received M.S degree of NARI in 2004, Since
then he is with NARI as an engineer. His interest is in
application of power electronics, excitation of ac
generators and digital simulation.