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

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

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


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.
eBook for You

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
eBook for You
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


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)
eBook for You
VOLTAGE STABILITY

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,


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
eBook for You
SYNCHRONOUS MACHINES
11
SYNCHRONOUS

=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)
eBook for You
STEADY
STATE OPERATIONAL LIMITS
13
STEADY
-
STATE

OPERATIONAL

LIMITS
Limiting Factors:
Stator Current Thermal Limit
•

it
•Dependent on Exciter Speed of Response
eBook for You
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%
eBook for You
OPERATIONAL LIMITS FOR SYNCHRONOUS
15
GENERATORS
Stator Current Limit
1.25
Stator

Current

Limit
I
rated
=1.0pu
Centre = 00

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

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

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

/ /
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

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
5
50
5
REACTIVE POWER (MVAR)
eBook for You