Transcript PSERC - Power Systems Engineering Research Center

Voltage Security Margin Assessment
Liang Zhao
Nirmal-Kumar C Nair
Professor Dr. Garng Huang
Industrial Advisory Board Meeting
December 6-7, 2001
PSERC
Voltage Security Margin
Assessment
PSERC
Tasks
• Modeling of control devices, loads and transactions for stability
evaluations
• Use of stability margin and stability index calculations
• Transaction based stability margin and utilization factors
calculation
Implementation
•
•
•
•
Voltage stability studies and modeling issues
Stability index for static voltage security analysis
Dynamic stability index issues
A new OPF based algorithm to evaluate load curtailment incorporating
voltage stability margin
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Voltage Stability Constrained OPF
algorithm using L index
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n
min  load _ curtaili
Objective:
i 1
S.T.:
n
Pgi  Pli  |Vi ||Vj | ( Gij cosij  Bij sinij )  0
(1)
j 1
n
Qgi  Qli  |Vi ||Vj | ( Gij sinij  Bij cosij )  0
(2)
j1
Pli / Plireq  Qli / Qlireq
(3)
0  Pli  Plireq
(4)
0  Qli  Qlireq
(5)
| Vi |min | Vi || Vi |max
(6)
Pgi min  Pgi  Pgi max
(7)
Qgimin  Qgi  Qgimax
(8)
Pij2  Qij2  S ij2 max
Li  Lcrit
(9)
(10)
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Effect of FACT Components on
Voltage Stability Margin PSERC
4
BPA Test system for Dynamic
Voltage Collapse Studies
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Dynamic Voltage Collapse
(ULTC Operation Scenario)
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Publications
PSERC
• An OPF based Algorithm to Evaluate Load Curtailment
Incorporating Voltage Stability Margin Criterion
( North Atlantic Power System Conference 2001)
• Voltage Stability Constrained Load Curtailment Procedure to
Evaluate Power System Reliability Measures
(To be presented at IEEE-PES Winter Meeting 2002)
• An XML based CIM compliant Real-time Load flow data
exchange approach amongst proprietary Energy Management
Systems
(To be Communicated : Journal of Computer Applications to Power Systems)
• Incorporating TCSC into Voltage Stability Constrained OPF
(To be Communicated :IEEE-PES Summer Meeting 2002)
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Present Focus
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• Investigating the effect of FACT components on the steady state
voltage stability margin
• Incorporating the FACT component parameters into the voltage
stability constrained OPF algorithm formulated by the authors
•
Investigating the dynamic voltage collapse phenomenon
following a major disturbance like fault with associated control
components like TCSC, Tap changers etc.
•
To identify the locally measurable quantities to predict the
voltage collapse of the system
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Voltage Security Margin Assessment
Liang Zhao
Nirmal-Kumar C Nair
Professor Dr. Garng Huang
March 22, 2002
PSERC
Voltage Security Margin
Assessment
PSERC
Recent Implementation
•
Incorporating TCSC into the voltage stability constrained OPF
(VSCOPF) formulation.
•
Investigate into dynamic voltage collapse issues.
•
Applicability of index L to detect dynamic voltage collapse during:
•
•
•
•
Slowly increasing loading
Sudden large load increase
Loss of line
Data Communication Issues amongst EMS
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TCSC Incorporated VSCOPF
algorithm
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n
Objective: min  load _ curtail i
i 1
S.T.:
n
Rij+jXij
Pgi  Pli  |Vi ||Vj | ( Gij cosij  Bij sinij )  0
XTCSC
j 1
i
j
n
Qg i  Qli  | Vi || V j | ( Gij sin ij  Bij cos ij )  0
Bshunt
(2)
j 1
Pli / Plireq  Qli / Qlireq
0  Pli  Plireq
Bshunt
(1)
(3)
(4)
0  Qli  Qlireq
(5)
| Vi |min | Vi || Vi |ma x
(6)
Pgimin  Pgi  Pgimax
(7)
Q gi min  Q gi  Q gi max
(8)
Steady State Model of TCSC
P  Q  S
2
Lij
i
2
L ij
crit
2
ij max
(9)
(10)
0.5 X mn  X TCSC  0.5 X mn
(11)
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Observations
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• TCSC improves line flow distribution, hence effectively reducing
load curtailment
• A steady state TCSC description could be effectively integrated
into the VSCOPF algorithm
• By effectively redistributing reactive flows, TCSC is observed to
relieve a voltage stability constrained system operation
• The simulation shows the TCSC could be used as a congestion
management and voltage stability margin enhancement tool
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Dynamic Voltage Collapse Detection
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Slow increase in Bus 5 load
Large Sudden increase in Bus 5 load
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Observations
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Modeling and Simulation
•
•
Modeling of all the components of the test system were created in EUROSTAG (To run timedomain simulations)
Generator voltage regulator and governor dynamics were incorporated in the simulations
Results of Simulation
•
•
•
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Slow changing loading, sudden large loading and loss of line situations were investigated.
For the last two cases, it was observed that the dynamic voltage collapse loadability was
less than the steady state loadability for the system.
For slowly increasing load the index L was able to track the voltage collapse situation
effectively
For a step increase, the index evaluated at the first largest dip of voltage is able to track the
dynamic collapse of the system
For a loss of line scenario, the index evaluated at the first dip of voltage approximately
approaches unity at dynamic collapse loading.
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Related Publications
PSERC
• Incorporating TCSC into Voltage Stability Constrained OPF
formulation
(Communicated :IEEE-PES Summer Meeting 2002)
• Detection of Dynamic Voltage Collapse
(Communicated :IEEE-PES Summer Meeting 2002)
• An XML based CIM compliant load flow/state estimation data
exchange approach amongst proprietary Energy Management
Systems
(To be Communicated : Journal of Computer Applications to Power Systems)
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Contribution Allocation for Voltage Stability
In Deregulated Power Systems
----A new application of Bifurcation Analysis
Dr.Huang
Kun Men
Texas A&M University
PSerc Review Meeting
College Station, March 22, 2002
PSERC
Two model of the power system
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Traditional Operation Model of Power System
Generation
Power
Companies
Distribution

System Control
New Operation Model of Power System based on the transaction
(The voltage collapse could be due to different parts of the system)
Generation
Companies
Generation

Transactions of
the system
Transmission
Companies
Load
(Utilities)
Integrated
Companies
Responsibility
Distribution

System Control
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steady-state margin VS dynamic
stability margin
PSERC
• Steady-state margin is easier to find by power flow analysis, and is
usually bigger than the dynamic stability margin.
• Steady-state margin does not take the dynamic response of the system
into account, and it is possible to have a voltage collapse inside the
steady-state margin. For many cases, the dynamic stability margin is
the real margin for the voltage stability.
• Analyzing the dynamic stability margin and its relationship with system
components, we can effectively predict and avoid voltage collapses.
We can also allocate the contribution of devices to the stability margin.
• The dynamic stability margin is usually obtained by dynamic analysis
(Here we use bifurcation analysis), which is more time consuming than
the power flow analysis.
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steady-state margin VS dynamic
stability margin
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• Dynamic stability margin is determined by Hopf bifurcation point
(denoted as A), or by a saddle-node bifurcation point(denoted as B).
The size of the exciter and the the generator limits will have.
• Steady-state stability margin is determined by singularity induced
bifurcation point (C), which can be computed from power-flow function.
But when a P-regulator (Efd0 is constant, shown as below figure, C is in
the lower part of the PV curve, B equals to Pmax) is used, the steadystate margin could be the B point, which can be obtained by solving the
equations of exciter, regulator and the power-flow. It is a steady-state
method that involves more than power flow analysis.
1.2
Voltage
1.1
1
0.9
0.8
A
0.7
B
0.6
C
0.5
0.4
0.3
0.2
0.5
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0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
Real Power
Power flow steady-state Analysis VS
dynamic analysis
1. When the steady state analysis is good enough?
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(Here we assume that regulator is well tuned.)
1) The transmission line is not too long, x is not very large
and the regulator is not P-regulator (Efd0 is constant)
2) The xd is not too large and the regulator is not a Pregulator (Efd0 is constant)
3) The exciter is reasonably large in terms reactive power
capacity.
For these cases, we found that steady-state stability margin
equals to dynamic stability margin, it determines the stability
margin, so steady state analysis is good enough.
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2. When steady state analysis is not good
enough? How would it happen?
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1) The transmission line is too long, x is very big .
2) The xd is too big.
3) The regulator is a P-regulator with Efd0 is constant
4) The regulator is not well tuned; for example, the Kp is too small, even the
x and xd are not very big.
5) when the exciter hits the limit.
In these cases, we found that the dynamic stability margin is usually
smaller than the steady-state margin, and the dynamic stability
margin determines the stability margin.
We will explain the phenomenon by the bifurcation analysis.
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Our research focus on two fields:
PSERC
1.How to allocate the contribution/responsibility by
bifurcation analysis.
Three typical bifurcations are used here:
1) Hopf bifurcation point, we denote it as A
2) Saddle node, we denote it as B
3) Singularity induced bifurcation point, we denote is as C
2. How the capacity limits and parameters of the system
influence the bifurcation points?
1) The parameters of the generator
2) The parameters of the transmission line
3) The influence of the reserve limits on the voltage stability
a. The influence of the size of the exciter
b. The influence of other limits of the system
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A simple one generator and one load bus system is
studied to demonstrate our analysis.
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(It include three basic part: Exciter & Regulator, Generator
and Transmission part.)
Load
Exciter
In the above system, we assume that the power
factor of the load is constant as the load changes.
We also assume that the voltage dynamic is
decoupled from the angle dynamic, which is well
behaved, and the angle dynamic can be
approximated out.
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Reduced Jacobian matrix is used here to find
the bifurcations.
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
x  f (x, y, p), f :nmq n
0  g(x, y, p), g :nmq m
x X n , y Y m, p P q




Reduced Jacobian matrix: Fx   f x  f y g y 1gx 
Differential equation denote the dynamic model of dynamic control
devices, such as exciter, generator,…, and so on. Algebraic equation denote
the power flow.
x: State variable of control devices;
y: Power flow variable;
p: load and system topography parameter….
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Topic 1: How to identify the responsibility by
bifurcation analysis?
PSERC
First, we will show that if there is no voltage regulator control, the PV
curve of the system will be changed drastically:
The PV curve with and without controller
Above figure shows that the Pmax will increase with a controller to keep the
Eg≡Er, which implies that the regulator will increase the stability margin. (Note:
the regulating range of a voltage regulator is decided by its exciter size )
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Then we focused on three widely used controller:
PSERC
1) P-controller (
Td' 0  5,T  1.5, x  0.1, xd'  0.2, Q  0.5P, Er  1.0
,
Efd0 is rescheduled as load change to keep Eg as Er)
The above figure shows that how the three bifurcations
vary with the change of KP
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When KP=2.5, 5, 10, the below figures shows that how the
eigenvalue vary with the change of KP
PSERC
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).
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Through the analysis and Figures showed above,
we can see that there are three basic patterns :
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1) A<B<C. When P∈(A,B), both the eigenvalue EigT and
EigC are positive; when P∈(B,C), only the eigenvalue EigT is
positive.
2) A<C<B. When P∈(A,C), both the eigenvalue EigT and
EigC are positive; when P∈(C,B), only the eigenvalue EigC is
positive.
3) A disappear and B<C. Only the eigenvalue EigT is
positive when P∈(B,C)
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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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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 with the P controller when Kp→
∞ , it is included in the basic pattern 2.
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Conclusion for topic 1: An easy way to identify
responsibility between the controller and
transmission
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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 real 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 real
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 real
stability margin of the system.
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Conclusion for topic 1:
continued
PSERC
4) The tuning of the control parameters will
influence point A and thus the dynamic
stability margin of the system. The
contribution with and without the controller /
regulator can be easily assessed.
5)
The analysis also explains why a
dynamic stability margin is smaller than the
static analysis.
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Topic 2: Influence Of Capacity Limits and
Other System Parameters On Stability :
PSERC
1) The parameter of the generator (xd)
a) P-controller: (KP=2.5)
xd
1.2
0.3
Pmax
3.09
3.09
A
1.416
2.016
B
1.584
2.719
C
2.116
2.116
b) PI-controller: (KP=2.5,TI=5.0)
xd
1.2
0.3
Pmax
3.09
3.09
A
1.297
2.005
B
3.09
3.09
C
2.116
2.116
c) PID-controller: (KP=2.5, TI=5.0, KD=1.0, TD=0.01)
xd
1.2
0.3
Pmax
3.09
3.09
A
1.415
2.0158
B
3.09
3.09
C
2.116
2.116
Note:For case a),b) and c), A point (determine the
dynamic stability margin) is the real stability margin
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Topic 2:
2) The parameter of the transmission (x)
PSERC
a) P-controller: (KP=2.5 , xd=1.2)
x
0.1
0.12
0.2
0.25
0.28
Pmax
3.09
2.58
1.55
1.24
1.11
A
1.416
1.360
1.148
1.03
0.965
B
1.584
1.509
1.242
1.098
1.02
C
2.116
1.966
1.465
1.227
1.05
b) PI-controller: (KP=2.5,TI=5.0 , xd=1.2)
x
0.1
0.12
Pmax
3.09
2.58
A
1.297
1.2506
B
3.09
2.58
C
2.116
1.966
c) PID-controller: (KP=2.5, TI=5.0, KD=1.0, TD=0.01, xd=1.2)
x
0.1
0.12
Pmax
3.09
2.58
A
1.415
1.3589
B
3.09
2.58
C
2.116
1.966
Note:For case a),b) and c), A point (determine the
dynamic stability margin) is the real stability margin
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Topic 2:
3) The influence of the capacity limits
a) The influence of the size of the exciter
PSERC
When Efd hit the limit Efd max, the input Efd of the exciter will keep as Efd max, there are two basic
patterns:
Pattern 1:
The cross point of the two PV
curve is in the lower part of the PV
curve which have no regulator.
Right figure show that how the
voltage change with P when there is
a limit Efd max=2.0, we can see that
when exciter hit the limit at point D,
the voltage will increase with the
bigger P.
In this basic patter, there are several
 A<D, then the dynamic stability margin is A
possibilities for the dynamic
 A>D and C1<D, then the dynamic stability margin is D
stability margin:
 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 B1
C>D and C1>=D, then the steady-state margin is C1.
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Pattern 2:
The cross point of the two PV curve is in
the upper part of the PV curve which have
no regulator
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Fig1 The steady-state PV curve,Efd input=1.2 ,xd=0.3
1.4
Upper part of PV curve
Lower part of PV curve
1.2
without regulator
A
1
0.8
D--Cross point
C
B
B1
V
In this basic patter, there are also several
possibilities for the dynamic stability
margin:
 A<D, then the dynamic stability margin
is A
 A>D ,then the dynamic 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
0.6
0.4
with regulator
C1
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
P
When the dynamic stability margin is A, the regulator determines the dynamic stability margin,
and thus the regulator is responsible for the voltage collapse; Otherwise the size of the exciter
determines the dynamic stability margin and the exciter (or a regulator such as SVC) is responsible.
When the stability margin is C, the regulator determines the steady-state stability margin, and the
regulator is responsible; Otherwise (B determines the margin) the the size of the exciter determines
the stability margin, and the exciter is responsible.
It is clearly that D and B1 will increase with bigger Efd max, thus, bigger size of exciter contributes
to both the increase of the dynamic and steady-state stability margins.
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Topic 2:
3) b) The influence of limits of the Generator
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· Section E–F–G of the curve shows limits 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 limits 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 short-circuit
ratio (SCR).
· Section H–G of the curve shows limits 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
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Three Basic Pattern:
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i) Three bifurcation points A,B and C are all located outside the boundary D-E-FG-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 appears 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 actualstability margin here.
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.
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PSERC
Basic pattern i) usually appear 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.
It is very similar with the analysis of when the steady-state analysis method is good
enough or not (In page 5 and 6)
In basic pattern i), the limit of field current determine that how much reactive power the
generator can apply--Qmax; The limit of stator current determine that how much real power
the generator can apply--Pmax; The Over-heating limitation of the stator core determine that
how much reactive power the generator can absorb—Qs-max. But for pattern ii) and iii),
things will be more complex, these maximum value may no longer be determined by the
limitations of generator, they may be influenced by the regulator, exciter or the length of the
transmission line.
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Summary
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1. We clarify the limitation of the steady-state analysis,
point out the importance of the dynamic stability
margin and how to get it.
2. We can unbundle the contribution of voltage stability
to generator owners, transmission owners and
voltage control owners based on our analysis.
3. We demonstrate that how the limits of the system and
parameters of the system (generator and transmission)
affect the bifurcation patterns and the stability
margin. The knowledge will enable us to design the
controller and optimize the system performance.
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