Lý thuyết về quá trình Ổn định quá độ (Transient Stability) bao gồm các nội dung cơ bản sau: • The Swing Equation. • Application to Synchronous Machines. • StepbyStep Solution Method.
Trang 1A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
Day 2 - Transient Stability
July 5, 2013 Prepared by: Peter Anderson
Trang 22
OUTLINE
Trang 3THE SWING EQUATION
THE SWING EQUATION
10 kVA
) RPM (
× ) GD (
× 48163
5
= H
Imperial: WR 2 in lb.ft 2
6
2 2
10 kVA
) RPM (
× ) WR (
× 231 0
= H
Trang 4ANALYSIS OF THE SWING EQUATION
In terms of short-term transient stability studies
In terms of short-term transient stability studies,
Trang 5APPLICATION TO SYNCHRONOUS
MACHINES
Increase in Mechanical Power Input
Pm increased
Rotor accelerates from 25
deg to new operating point
1.4
g Rotor overshoots to 60 deg,
where area above Pm equals
the area below Pm
Now Pe >Pm and rotor
0.8 1
Now Pe Pm and rotor
θ 40 deg.
If the overshoot reaches
θ=140 deg The rotor will not
be able to return to the new
operating point and will slip
0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
operating point and will slip
to the next pole position
Trang 6STEP BY STEP SOLUTION METHOD
0.2 0.4 0.6 0.8
0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Trang 7STEP BY STEP SOLUTION METHOD
STEP-BY-STEP SOLUTION METHOD
Pm Increased from 0.42 to 0.8 pu
1.00 1.20
0.60 0.80
0.20 0.40
0.00
Trang 8STEP BY STEP SOLUTION METHOD
Trang 9STEP BY STEP SOLUTION METHOD
STEP-BY-STEP SOLUTION METHOD
Pm Increased from 0.42 to 0.8 pu
80 0 90.0 100.0
50.0 60.0 70.0 80.0
Time (s)
Trang 10TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
Day 3 - Transient Stability
July 8, 2013 Prepared by: Peter Anderson
Trang 11CASE STUDY: ANALYSIS OF A FAULT CASE
CASE STUDY: ANALYSIS OF A FAULT CASE
Pre-fault Power Angle Curve = sinθ/0.8
Post-fault Power Angle Curve = sinθ/1.1
Fault duration = 0.1 s
Time Step = 0.02 s
Trang 12CASE STUDY: ANALYSIS OF A FAULT CASE
3
CASE STUDY: ANALYSIS OF A FAULT CASE
1.40
1.00 1.20
0 40 0.60 0.80
0.00 0.20 0.40
Trang 13CASE STUDY: ANALYSIS OF A FAULT CASE
CASE STUDY: ANALYSIS OF A FAULT CASE
Step 1: Construct Step-by-Step Table
Trang 14CASE STUDY: ANALYSIS OF A FAULT CASE
5
CASE STUDY: ANALYSIS OF A FAULT CASE
Step 1: Plot Results
100.0 120.0
60.0 80.0
Trang 15THREE PHASE SHORT CIRCUIT
THREE PHASE SHORT-CIRCUIT
Steady-state:
Leakage Reactance of the machine (X )
Leakage Reactance of the machine (X l )
Armature Reaction to the Fault Current (X a )
Trang 16THREE PHASE SHORT CIRCUIT
7
THREE PHASE SHORT-CIRCUIT
At the instant of the Fault:
Trang 17THREE PHASE SHORT CIRCUIT
THREE PHASE SHORT-CIRCUIT
Shortly after the instant of the Fault:
Trang 18THREE PHASE SHORT CIRCUIT
Trang 19SYNCHRONOUS MACHINE MODELS
SYNCHRONOUS MACHINE MODELS
Single Phase Equivalent of a 3-phase Generator
Trang 20SYNCHRONOUS MACHINE MODELS
11
SYNCHRONOUS MACHINE MODELS
Three Possible Generator Models:
behind Xd”))
•Sub-transient model allows exciter effects to be explicitly
represented
For each model, the prime mover can be
represented as a fixed power model or a variable
power model under the control of governor
action
Trang 21MODEL APPLICATION
MODEL APPLICATION
Use of Mixed Generator Models:
Complex models used for machines of interest
Simpler models used for remote machines
•Requires less data
•Significantly reduces the computing burden
With the removal of computer limitations, it
is recommended to use the sub-transient
model for all generators
Trang 22TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
Day 4 - Transient Stability
July 9, 2013 Prepared by: Peter Anderson
Trang 23• Machine Differential Equations
• Exciter Differential Equations
• Governor Differential Equations
• Solution of Differential Equations
• Network Solution
• Sample Cases
Trang 24BASIC MODELS IN STABILITY STUDIES
' q q
' d
"
d q
"
q q
' d d
fd '
' q
"
q d
"
d
' d
' q
"
"
q
d q q q '
0 q
d d
q q q
"
0 q
d
E
‐ I X
‐ X
‐ E
1
= pE E
‐ I X
‐ X
‐ E
1
=
pE
E I X
X T
pE E
I X
X T
pE
0 d
q q
d d d q
"
0 d
q
T
p T
p
Trang 25BASIC MODELS IN STABILITY STUDIES
BASIC MODELS IN STABILITY STUDIES
Synchronous Machines
Algebraic Model:
V
‐ E Y
= I
I
X
‐ R
Re System to
Frame ference
Re Machine from
tion Transforma
V E Y
I I
R X
Trang 26BASIC MODELS IN STABILITY STUDIES
V V K T
pE
fb fd f
f
fb
fd fb
t s E E
fd
max D pE
; max E
≤
V min E
; V + K
Trang 27BASIC MODELS IN STABILITY STUDIES
BASIC MODELS IN STABILITY STUDIES
0 s
c
on
P
‐ C T
‐ ω
‐ P T
Trang 28SOLUTION OF DIFFERENTIAL EQUATIONS
Implicit Trapezoidal Rule
( ) ( ( ) ( ) )
Variable Integrable
=
Y
pY + pY 2
h + Y
=
20 30 40 50 60
Y
Length Step
n Integratio
=
h
Variable
t
h + t )
h + Y
= t tan Cons
=
YC
X YX + YC
.
YX
Trang 29SOLUTION OF DIFFERENTIAL EQUATIONS
SOLUTION OF DIFFERENTIAL EQUATIONS
Solution Algorithm:
Rule
Numerically Stable
In Step 2 in practice, an extrapolated value of X (t) is used
except immediately after a discontinuity using
X (t+h) = 2X (t) – X (t-h)
Trang 303 Calculate Norton equivalent Nodal Injected Current
4 Solve for V using I = Y.V where Y = Nodal Admittance
4 Solve for V using I Y.V where Y Nodal Admittance
Matrix
5 Use New values for V to move to next time step
6 Network Solution carried out simultaneously with
Integration Process eBook for You
Trang 31400km
100km 50km
GBUS‐3 HVBUS‐3
1x590MVA,21/400kV 600MVA, 0.975pf
1200MVA, 0.975pf
500MW‐ST
Trang 33HVBus1 HVBus3 GBus1 GBus2 GBus3
Trang 35GENERATOR EXCITATION CONTROL
GENERATOR EXCITATION CONTROL
Line Fault close to Generator HV Bus (GBUS-3_
Trang 37GENERATOR MODEL TYPE
GENERATOR MODEL TYPE
Line Fault close to Generator HV Bus (GBUS-3_
Trang 38FAULT CLEARING TIME
17
FAULT CLEARING TIME
Line Fault close to Generator HV Bus (GBUS-3)
Trang 40Fault Clearing Time & Voltage Dependency of Load have
the most significant impacts on stability