TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
D10
Sll
Si l St bilit
D
ay
10
-
S
ma
ll
-
Si
gna
l

St
a
bilit
y
July17,2013
Prepared by: Peter Anderson
eBook for You
SMALL
SIGNAL STABILITY
2
SMALL
-

A
na
l
ys
i
s
 Eigen Value/Vector Analysis using Linearized
Differential Equations
Differential

Equations
eBook for You
APPLICATIONS
3
APPLICATIONS
Power System Size

I i th h G th i I t ti

I
ncreas
i
ng
th
roug
h

G
row
th

 Inter-Area Oscillations
 System Disintegration/Widespread Blackouts
eBook for You
EIGEN
-
VALUE ANALYSIS
4
EIGEN
VALUE

ANALYSIS
Applied to a Linearized Model of the Power
System
System

 Importance of the Initial Conditions

Small Disturbances

Small

Disturbances
 Inter-Area Oscillations

Sub
synchronous
Torsional
Interactions

Sub

–
WideRangeof
Domain Disturbances
Non‐linearities representedin
detail
WeaklyDampedModesmaynot
beExcitedorObserved
Results areFamiliar ModesofDifferent
Frequencies/DampingareMixed
EvaluationofResults‐Difficult
Frequency
Domain
RevealsRulesbehindSystem
Dynamics
Non‐linearities notwell
repr esented
NoneedtoApplyDisturbances LinearizationofCertainElements
canbeDifficult
IndividualModes areAnalyzed ResultsnotFamiliar
Sitin
g
andTunin
g
ofDam
p
in
g

g
g pg

FACTSControllers
MonotonouswithStrongDamping
Many modesneartheOrigin(Low
Damping)areduetoElementswithlong
timeconstants‐notanindicationof
instability
eBook for You
SWING MODES
7
SWING

MODES
Inter-Area Modes
FrequencyRange(0.1to0.8Hz)
LargeNumberofGenerators
GeneratorsinoneAreaswing againstOtherAreas

k

Wea
k
Inter‐AreaTieLines
LowFrequency/WeakDamping
Local Modes
FrequencyRange(0.8to3Hz)
SmallNumberofGeneratorsinaSmallArea
HighFrequency/StrongDamping
eBook for You
SWING MODES
8


Load/Maximum

Generation
•MinimumLoad/MinimumGeneration
•Maximum/MinimumIntertieTransfers
It dit Ld
Mi Hd
•
I
n
t
erme
di
a
t
e
L
oa
d
‐
M
ax
i
mum
H
y
d
ro
•In termedia teLoad‐MaximumThermal

a
bilit
y
July 17, 2013Prepared by: Mohamed El Chehaly
eBook for You
OUTLINE
2
OUTLINE
• Small-Signal Stability
• NEVA – PSS NETOMAC
eBook for You
3
SMALL
-
SIGNAL STABILITY
SMALL
-
SIGNAL

STABILITY
eBook for You
Modal Analysis
4
SMALL-SIGNAL STABILITY
Modal

Analysis

Exclusively suitable for small signal


Linearization

of

non
linear

systems

at

a

specified operating point (steady-state
load flow condition
)
)
 Typical applications include inter area
oscillations, sub synchronous torsional
interactions, voltage stability…
eBook for You
Modal Analysis
5
SMALL-SIGNAL STABILITY
Modal

Analysis
eBook for You
Modal Analysis
6

eBook for You
Modal Analysis
7
SMALL-SIGNAL STABILITY
Modal

Analysis

Modal analysis provides the following

Modal

analysis

provides

the

following

information

Frequencies and damping

Frequencies

and

damping
 Mode observability and controllability


Method
-
Advantages

Wide application fields

Wide

application

fields
 Nonlinearities represented in detail

No modeling limitations

No

modeling

limitations
 Time domain results in curves show a
representation of the real system
representation

of

the

real


Trial
-
and
-
Error approach by applying

Trial
and
Error

approach

by

applying

disturbances and observing responses

Different disturbances have to be applied

Different

disturbances

have

to

be

damping are mixed
 No s
y
stematic information re
g
ardin
g
most
ygg
effective damping controllers
eBook for You
Modal Analysis
Advantages
11
SMALL-SIGNAL STABILITY
Modal

Analysis
-
Advantages

Systematic approach which reveals rules

Systematic

approach

which

reveals

Modal

Analysis
-
Disadvantages

Only suitable for small
-
signal stability

Only

suitable

for

small
signal

stability
 Nonlinearities are not well reflected

Linearization of some elements is difficult

Linearization

of

some


State space representation of a linear

State

space

representation

of

a

linear

dynamic system

Transfer function

Transfer

function

Eigenvalues
(Modes) are the solution of

Eigenvalues
(Modes)

are



eigenvalue
Real eigenvalue
With


j
s




s
With

is called damping (in 1/s)
illd lf (i1/)


i
s ca
ll
e
d
angu
l
ar
f
requency
(i