Transcript Document

PSERC Project
Contribution Allocation for Voltage Stability Assessment In Deregulated Power Systems
Our research focus:
Topic 2
----A new application of Bifurcation Analysis
1.How to allocate the contribution/responsibility by
bifurcation analysis.
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2. How the capacity limits and parameters of the system
components influence the bifurcation points?
•Considered capacity limits and parameters
3) b) The impacts of limits of the Generator
Dr. Huang (PI), Kun. Men, N.Nair (Students)
Texas A&M University
A simple one generator and one load
bus system is used to demonstrate
our analysis.
PSERC
PSerc Review Meeting Albany, NY, May 28, 2002
(It include three basic part: Exciter &
Regulator, Generator and Transmission
part.)
1) The parameters of the generator, the controller

X ,X
2) The parameters of the transmission line
E, 
X
E ,  
3) The impact of the reserve limits on the voltage stability
E
E
Load
E
a. The impact of the size of the exciter
Exciter
b. The impact of other limits of the system
•Three typical bifurcation points are found and
In the above system, we assume
considered:
that the power factor of the load is
constant as the load changes. We also
1) Hopf bifurcation point, we denote it as A
assume that the voltage dynamic is
2) Saddle node, we denote it as B
decoupled from the angle dynamic,
3) Singularity induced bifurcation point, we denote is as C which is well behaved, and the angle
d
d
fd
G
r
dynamic can be approximated away.
1) P-controller
(
Td' 0  5,T  1.5, x  0.1, xd'  0.2, Q  0.5P, Er  1.0
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When K =2.5, 5, 10, the below figures shows that how the eigenvalue vary with the
, Efd0 is rescheduled as
In these figures, note that Kp has little
influence on one of the eigenvalues (denoted by
EigT), while Kp has a substantial impact on the
other eigenvalue (denoted by EigC).
We should also note that B will vary with
the change of KP; BPmax with K
; and
P
B>C when KP>5.25; B  A when KP=1.895;
when KP<1.895, A will disappear; and B 
0.735 with KP 0 .
2) PI-controller (Kp=2.5, TI=5.0 ) and PID-controller
(Kp=2.5, TI=5.0, KD=1,TD=0.01 )
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continued
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P
load change
to keep Eg as Er)
change of KP
Topic 2-
We can observe three basic patterns by the
ordering of A, B, C :
1)
A<B<C. When P∈(A,B), both EigC and EigT are positive; when P∈(B,C),
only the EigT is positive. From the parameter analysis, we can conclude that the
voltage collapse is due to both controller and transmission when P∈(A,B). The
voltage collapse is only caused by transmission part when P∈(B,C). In this case,
[A, C] is the unstable area, and A defines the dynamic stability margin boundary—
the valid stability margin of the system.
2)
A<C<B. When P∈(A,C), both EigC and EigT are positive; when
P∈(C,B), only the EigC is positive. From the parameter analysis we can conclude
that the voltage collapse is due to both controller and transmission when P∈(A,C).
The voltage collapse is caused by controller when P∈(C,B). In this case, [A, B] is
the unstable area, and A defines the dynamic stability margin boundary —the valid
stability margin of the system.
3)
A disappears and B<C, only the EigT is positive when P∈(B,C). Thus,
the voltage collapse is only due to transmission when P∈(B,C). In this case, [B, C]
is the unstable area, and B is the dynamic stability margin boundary —the valid
stability margin of the system.
Topic 2: Influence Of Capacity
Limits and Other System
Parameters On Stability :
xd
1.2
0.3
a) P-controller:
xd
1.2
0.3
b) PI-controller:
c) PID-controller:
When P∈(A,C), both the eigenvalue EigT and EigC are positive;
when P∈(C,B), only the eigenvalue EigC is positive.
We can see that the bifurcation locations of PI and PID
controller are very similar to the P controller as Kp→ ∞ ,
which is included in the basic pattern 2 we mentioned later.
xd
1.2
0.3
Pmax
3.09
3.09
Pmax
3.09
3.09
Pmax
3.09
3.09
A
1.416
2.016
B
1.584
2.719
A
1.297
2.005
A
1.415
2.0158
B
3.09
3.09
C
2.116
2.116
C
2.116
2.116
B
3.09
3.09
C
2.116
2.116
Pmax
3.09
2.58
1.55
A
1.416
1.360
1.148
B
1.584
1.509
1.242
C
2.116
1.966
1.465
P-regulator(Efd0 is rescheduled)
When Efd hit the limit Efd max, the input Efd of the exciter will keep as Efd max
patterns by upper or lower intersections:
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, there are two basic
(Note:To our experience, pattern 1
usually appears with big ratio of xd/x,
and pattern2 usually appears with small
ratio of xd/x. Also note that when a
regulator is not functioning, C1 is
always at the lower curve
and there is no A1)
Lower intersection pattern 1:
.
Right figure show that how the
voltage changes with P when there is a
limit Efd max=2.0. In this basic pattern,
the valid stability margin depends on
the ordering.
 A<D, then the dynamic stability margin is A
 A>D and C1<D, then the dynamic stability margin is D
 A>D and C1>=D, then the dynamic stability margin is C1.
For the steady stability margin, there are also several possibilities:
C<D, then the steady-state margin is C
C>D and C1<D, then the steady-state margin is D
C>D and C1>=D, then the steady-state margin is C1.
Note that the stability margin of Pregulator and PID-regulator are nearly
the same, both bigger than the margin
of the PI-controller. But for the dynamic
response, PID and PI have no steadystate error after a small disturbance; the
response speed of PI and PID are faster
than P-regulator; and PID have less
oscillation than PI-regulator, so PID is
the best regulator.
We can see that the shorter
transmission line will increase the
stability margin for all regulators.
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i) Three bifurcation points A, B and C are all located outside the boundary D-E-F-G-H, so
F is the stability margin (Here we neglect the limit of the prime motor—Pm, it is clear that if
Pm is less then F, then Pm will be stability margin).
ii) A or B appear within the boundary D-E-F-G-H, C is out of this boundary, so F replace
C to be the steady-state stability margin, the point A or B (when A disappear) will be the
dynamic stability margin—the valid stability margin.
iii) A,B and C are all within the boundary D-E-F-G-H, the point A or B (when A
disappear) will be the dynamic stability margin, and bifurcation point C or B(When C is in
the lower part of the PV curve) may be the steady-state stability margin.
Basic pattern i) usually appears with three commonly used regulator when they are well
tuned and the x and xd are not very big. When the regulator is not well tuned, the size of
exciter is too small or the transmission line is too long, basic pattern ii) and iii) may
appear).Basic pattern iii) usually appear with P- regulator (Efd0 is constant), even the
transmission line is not very long and the exciter size is not too small.
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Fig1 The steady-state PV curve,Efd input=1.2 ,xd=0.3
1.4
In this basic pattern, there are also
several possibilities for the dynamic
stability margin:
 A<D, then the valid (dynamic) stability
margin is A
 A>D ,then the valid stability margin is
B1
For the steady stability margin:
C<D, then the steady-state margin is C
C>D, then the steady-state margin is B1
Three Basic Patterns characterized by
points A B C inside or outside of
DEFGH:
Conclusion:
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2) The parameter of the transmission (x)
x
0.1
0.12
0.2
3) The impacts of the capacity limits
a) The impact of the size of the exciter
Upper intersection pattern 2:
1) The parameter of the generator (xd) (KP=2.5, TI=5.0, KD=1.0, TD=0.01)
· Section E–F–G of the curve shows limit
due to stator (armature) current. This section
is a portion (arc) of a circle that has its
center in the origin of – (MW-Mvar)
coordinates of the generator.
· Section D–E of the curve shows limit due
to field current limitations. This is a portion
(arc) of a circle that has its center on the Y
axis (Mvar) and shifted from the origin by a
value proportional with the machine shortcircuit ratio (SCR).
· Section H–G of the curve shows limit due
to over-heating of the stator core end when
the generator is under-excited in conditions
of leading PF, when the generator is
absorbing Mvars
:
Upper part of PV curve
Lower part of PV curve
1.2
without regulator
A
1
0.8
D--Cross point
C
B
From topic 1, we know that A or B(When A disappears) will
be the valid stability margin when the system dose not hit the
limits, and dynamic analysis must be applied. From topic 2, we
know that D, B1 or F may be the valid stability margin instead of
A or B when the system hits the limits; in this case, steady state
analysis is good enough.
When all of below three conditions are satisfied, the steady-state analysis is
good enough. Otherwise the dynamic analysis should be applied.
0.6
0.4
with regulator
C1
0.2
0
0
0.5
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B1
V
Topic 1: Three widely used controllers:
-continued:
1
1.5
2
2.5
3
3.5
P
When A determines the valid stability margin, the regulator controller is responsible for the voltage
collapse; Otherwise the size of the exciter determines the valid stability margin and the exciter (or a
device such as SVC size) is responsible.
When the valid stability margin is C, the regulator controller determines the steady-state stability
margin, and the regulator is responsible; Otherwise (B1 determines the margin) the the size of the
exciter determines the stability margin, and the exciter is responsible.
It is clear that D and B1 will increase with bigger Efd max, thus, bigger size of exciter contributes to
both the increased dynamic and steady-state stability margins.To keep the same stability margin, bigger
xd need bigger exciter size.
1) The value of x+xd is not very big .
2) The regulator is not P-regulator with a constant Efd0.
3) The regulator is well tuned.
The detailed algorithm is under development.