Phần 1 KHÓA ĐÀO TẠO TÍNH TOÁN ỔN ĐỊNH VÀ ỨNG DỤNG TRÊN PHẦN MỀM PSSE CHO KỸ SƯ HỆ THỐNG ĐIỆN (Lý thuyết về Ổn định hệ thống điện)

TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
D1
BiPiil
Day
1
- Bas
i
c Pr
i
ncip
l
es
•
July4,2013
Prepared by: Peter Anderson
eBook for You
OUTLINE
2
OUTLINE
• Definitions of Stability
T f St bilit
•
T
ypes o
f

St
a

bilit
y
•
Angular Stability Analysis
•
Angular

Stability

Analysis
•
Operational Limits of Synchronous
Operational

Limits

of

Synchronous

Machines
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BASIC PRINCIPLES
3
BASIC

PRINCIPLES
Power System Stability:
What does it mean?
A power system at a given operating state is stable if

following a given disturbance or a set of disturbances
following

a

given

disturbance
,
or

a

set

of

disturbances
,
the system state stays within specified bounds and the
system reaches a new stable equilibrium state within a
ifid id fti
spec
ifi
e
d
per
i
o
d

o
f

ti
me
Multi-faceted problem depending on:
Time S
p
an of Interest
p
Nature & Size of the Disturbance
Physical Nature of any resulting Instability
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BASIC PRINCIPLES
4
BASIC

PRINCIPLES
Power System Stability:
IEEE/CIGRE Working Group
IEEE/CIGRE

Working

Group
Power system stability is the ability of an electric power
system, for a given initial operating condition, to regain a
state of o
p
eratin

g
e
q
uilibrium after bein
g
sub
j
ected to a
pgq gj
p
hysical disturbance, with most system variables bounded so
that practically the entire system remains intact
It is not necessary that the system regains the same steady state
ti ilib i i t th di t b Thi ld b th
opera
ti
ng equ
ilib
r
i
um as pr
i
or
t
o
th
e
di
s
t

ur
b
ance.
Thi
s wou
ld

b
e
th
e
case when e.g. the disturbance has caused any power system
component (line, generator, etc.) to trip. Voltages and power flows will
not be the same after the disturbance in such a case. Most
disturbances that are considered in stability analyses incur a change
disturbances

that

are

considered

in

stability

analyses

incur

a

change

in system topology or structure.
It is important that the final steady state operating equilibrium after the
fault is steady state acceptable. Otherwise protections or control
actions could introduce new disturbances that might influence the
actions

could

introduce

new

disturbances

that

might

influence

the

stability of the system. Acceptable operating conditions must be
clearly defined for the power system under study.
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TYPES OF STABILITY
5
TYPES

OF

STABILITY
PowerSystemStability
Fre q uencyStability
AngularStability
VoltageStability
Small
Disturbance s
Large
Disturbance s
ShortTerm LongTerm
Small
Disturbances
Large
Disturbances
ShortTerm LongTermShortTerm
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TYPICAL TIME SPANS
6
TYPICAL

TIME

SPANS
Harmonics

Pow er Flow
FaultCurrents
Long ‐TermStability
Short‐TermStability
Stato rTransi ents
Resonance/Saturation
Resonance/Saturation
Switching
Lightning
Time (s)
Time

(s)
1.E‐06 1.E‐03 1.E+00 1 .E+03
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ANGULAR STABILITY
7
ANGULAR

STABILITY
The ability of the Synchronous Machines
within a Power System to remain In
Synchronism following a disturbance
 Large Disturbances (Transient Stability)

Small Disturbances (Small
signal or Dynamic

Small

Disturbances

(Small
-
signal

or

Dynamic

Stability)
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FREQUENCY STABILITY
8
FREQUENCY

STABILITY
The ability of the Synchronous Machines
ithi P S t t t th S t
w
ithi
n a
P
ower
S
ys
t
em
t
o res

t
ore
th
e
S
ys
t
em
Frequency to within an acceptable range
following a disturbance
following

a

disturbance

Short
-
Term (Governor action)

Short
-
Term

(Governor

action)
 Long-Term (Turbines, Boilers, Nuclear Reactors)
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VOLTAGE STABILITY

9
VOLTAGE

STABILITY
At every node in the system, the “Actual
Injected Reactive Power” is equal to the
Injected

Reactive

Power”

is

equal

to

the

“Desired Injected Reactive Power” required
to maintain the node voltage within
tbl li it
accep
t
a
bl
e
li
m

it
s

Local in nature since it is difficult to transport

Local

in

nature

since

it

is

difficult

to

transport

reactive power through the network (X>>R)
 Short-Term (1-5 s Induction motors, Electronically
controlled loads, HVDC converters)
controlled

loads,

HVDC

converters)
 Long-Term (10s-5 m Tap changers,
Thermostatically controlled loads, Generation
current limiters
)
)
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APPLICATION OF ANGULAR STABILITY
10
ANALYSIS
Disturbance
Corrective
Actions
STATE‐A
STATE‐A'
STATE‐B
State-A: Power Flow
St t
BP Fl
St
a
t
e-
B
:
P
ower
Fl

ow
Transit from State
-
A to State
-
A
’
: Stability Analysis
Transit

from

State
-
A

to

State
-
A:

Stability

Analysis
Transit from State-A’ to State-B: Stability Analysis
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SYNCHRONOUS MACHINES
11
SYNCHRONOUS

MACHINES
Single Phase Equivalent of a 3-phase Generator
jXd I
EU
~
Im
E
jXd I
jXd
.
I
δ Re
θ U
I
I
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SYNCHRONOUS MACHINES
12
SYNCHRONOUS

MACHINES
Power-An
g
le Relationshi
p
gp
∂sin
X
U.E

=P
d
1.2
1.4
04
0.6
0.8
1
Powe r(pu)
0
0.2
0
.
4
0 30 60 90 120 150 180
LoadAngle(deg)
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STEADY
STATE OPERATIONAL LIMITS
13
STEADY
-
STATE

OPERATIONAL

LIMITS
Limiting Factors:
Stator Current Thermal Limit
•

Rated Current (1 0 pu)
•
Rated

Current

(1
.
0

pu)
Field Current Thermal Limit
•Short Circuit Ratio (SCR≈1/Xd)

R t A l St bilit Li it

R
o
t
or
A
ng
l
e
St
a
bilit
y
Li
m

it
•Dependent on Exciter Speed of Response
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OPERATIONAL LIMITS FOR SYNCHRONOUS
14
GENERATORS
Xd=2.0pu
SCR=0.5
Powerfactor=0.8
Exciter No‐loadMargin Full‐loadMargin
Slow‐Actin
g
35% 20%
g
Fast‐Acting 20% 10%
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OPERATIONAL LIMITS FOR SYNCHRONOUS
15
GENERATORS
Stator Current Limit
1.25
Stator

Current

Limit
I
rated
=1.0pu
Centre = 00

0.75
1
Q
Centre

=

0
,
0
Radius=1.0
0
0.25
0.5
P
‐0.5
‐0.25
00.250.50.7511.25
P
‐
1.25
‐1
‐0.75
1.25
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OPERATIONAL LIMITS FOR SYNCHRONOUS
16
GENERATORS
Field Current Limit
1.25

Q
Field

Current

Limit
I
Frated
=√{(SCR+sinθ)
2
+cosθ
2
}
Centre = 0
‐
SCR
05
0.75
1
Q
Centre

=

0
,
‐
SCR
Radius=I
Frated

0
0.25
0
.
5
P
I
Frated
=√{(0.5+0.6)
2
+0.8
2
}
=
1.36
‐0.5
‐0.25
0 0.25 0.5 0.75 1 1.25

1.36
Centre=0,‐0.5
‐1.25
‐1
‐0.75
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OPERATIONAL LIMITS FOR SYNCHRONOUS
17
GENERATORS
Rotor Angle Stability Limit
1

Q
Rotor

Angle

Stability

Limit
LowerFieldVoltage=LessStability
Fast‐actingExciter:
0.25
0.5
0.75
NLMargin(NLM)=0.2
FLMargin(FLM)=0.1
‐0.25
0
0 0.25 0.5 0.75 1 1.25
P
Q=tanα *Pg ‐ (SCR‐NLM*cosθ)
•tanα =tanβ‐NLM[0.258]
•
cos
β
= 1/(1+FLM) [0 909
β
= 24 6⁰]
‐
1
‐0.75

‐0.5
•
cos
β
=

1/(1+FLM)

[0
.
909
,
β
=

24
.
6⁰]
Q=‐0.34forPg=0
Q=0.258*0.8‐(0.5‐0.2*0.8)=‐0.134forPg=0.8
‐1.25
1
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OPERATIONAL LIMITS FOR SYNCHRONOUS
18
GENERATORS
Composite Operating Limits
1.25
Composite

Operating

Limits
Limits are reduced by:
0.75
1
Q
Limits

are

reduced

by:
•HighXd/LowSCR
•
Slow Exciter
0
0.25
0.5
P
Slow

Exciter
‐0.5
‐0.25
0
0 0.25 0.5 0.75 1 1.25
P
‐1

‐0.75
‐1.25
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OPERATIONAL LIMITS FOR SYNCHRONOUS
19
GENERATORS
Case Study
Case

Study
UsingMS‐Excel,constructthemachinecapabilitycurvefor
thefollowinggenerator:
RatedMVA=200MVA
Xd = 15
Xd

=

1
.
5
Ratedpowerfactor=0.9
Using
a. SlowExciter
b. FastExciter
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OPERATIONAL LIMITS FOR SYNCHRONOUS
20
GENERATORS
Case Study

/ /
RatedMVA=200MVA
/
Xd=1.5
/
Ratedpowerfactor=0.9
220
180MW Generator/Slow-Acting Exciter
RATED MW
140
160
180
200
220
(
MW)
60
80
100
120
140
R
EAL POWER
(
0
20
40
60
-
100

-
75
-
50
-
25
0
25
50
75
100
125
150
175
R
100
75
50
25
0
25
50
75
100
125
150
175
REACTIVE POWER (MVAR)
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OPERATIONAL LIMITS FOR SYNCHRONOUS

21
GENERATORS
Case Study
/
/
RatedMVA=200MVA
/
Xd=1.5
/
Ratedpowerfactor=0.9
220
180MW Generator/Fast-Acting Exciter
RATED MW
140
160
180
200
220
(MW)
60
80
100
120
140
R
EAL POWER
0
20
40
-1

00
-7
5
-
50
-2
5
0
2
5
50
7
5
1
00
12
5
1
50
17
5
R
00
5
50
5
0
5
50
5

00
5
50
5
REACTIVE POWER (MVAR)
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