Phần 21 KHÓA ĐÀO TẠO TÍNH TOÁN ỔN ĐỊNH VÀ ỨNG DỤNG TRÊN PHẦN MỀM PSSE CHO KỸ SƯ HỆ THỐNG ĐIỆN (Ổn định kích thích nhỏ và ứng dụng trên Phần mềm PSSE)

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
-

SIGNAL

STABILITY
Transient Stability:

Ti D i A l i

Ti
me
D
oma
i
n
A
na
l
ys
i
s
 Stepwise Integration of Differential Equations
Small-Signal Stability

FDiAli

F
requency
D
oma
i
n

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

i
n
I
n
t
erconnec
ti
ons
 Driven by Potential Cost Savings (Economies of
Scale, Use of Lowest
-
cost Generating Units)
Scale,

Use

of

Lowest
cost

Generating

Units)
 Focus on Generation-Not on Transmission
Disadvantages
 Increased Vulnerabilit
y
y

 Inter-Area Oscillations
 System Disintegration/Widespread Blackouts
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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

-
synchronous

Torsional
Interactions
 Electro-mechanical Performance in the
Low Frequency Range (0 1 to 3Hz)
Low

Frequency

Range

(0
.
1

to

3Hz)
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COMPARISON OF APPROACHES
5
COMPARISON

OF

APPROACHES
Approach Advantages Disadvantages
Time WideApplicationFields Trial&Error

–
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

Controllers
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NATURE OF MODES
6
NATURE

OF

MODES
Swing Modes
AreaofPrimeInterest
NeartheImaginaryAxis(0.1to3Hz)
DampingFactor>=5%Satisfactory

f

DampingFactor<3%Unsatis
f
actory
Co
n
t
r
o
ll
e
r M
odes
Co t o e odes
Voltage/SpeedRegulators

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
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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
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SWING MODES
8

SWING

MODES
12 3
eBook for You
CONTROLLER MODES
9
CONTROLLER

MODES
Controller Impact
DampingFactor
ParticipationFactor
Siting Indices(Transfe rFunctionResidues)
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APPLICATION OF THE APPROACH
10
APPLICATION

OF

THE

APPROACH
Initial Conditions
Steady‐stateLoadFlow
OperatingScenarios
•
Peak Load/Maximum Generation
Peak


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

•OutageConditions
eBook for You
TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
D10
Aliti fS ll
Si l St bilit
D
ay
10
-
A
pp
li
ca
ti
on o
f

S
ma
ll
-
Si
gna
l

St

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


Exclusively

suitable

for

small

signal

stability studies

Also know as
Eigenvalue
analysis

Also

know

as

Eigenvalue
analysis
 Analysis of linear systems

Linearization of non
-
linear systems at a


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

SMALL-SIGNAL STABILITY
Modal

Analysis

Simulation method in the time domain:

Simulation

method

in

the

time

domain:
 Disturbances are applied
 S
y
stem res
p
onses are calculated
yp
 Dynamics are observed through plotted curves
 Model analysis
 Not necessary to apply any disturbances
 Inherent properties of a studied dynamic system
are revealed by Eigenvalues and Eigenvectors

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

 Controller location and tuning
eBook for You
Modal Analysis
8
SMALL-SIGNAL STABILITY
Modal

Analysis

Example of a multi
–
machine system

Example

of

a

multi

machine

system
eBook for You
Simulation Method
Advantages
9
SMALL-SIGNAL STABILITY
Simulation

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

system

behaviour

Programs for time domain simulation are

Programs

for

time

domain

simulation

are

well established and available worldwide
eBook for You
Simulation Method
Disadvantages
10
SMALL-SIGNAL STABILITY
Simulation

Method
-
Disadvantages


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

applied
 For each load flow, new cases are required

Certain weakly damped and unstable

Certain

weakly

damped

and

unstable

modes may not be observed

Modes of different frequencies and

Modes

of

different

frequencies

and

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

rules

behind complicated phenomena

No need to apply disturbances

No

need

to

apply

disturbances
 For each load flow one modal calculation
is sufficient
 Weakly damped and unstable modes are
p
icked out and anal
y
zed in detail
py
 Individual modes are analyzed
eBook for You
Modal Analysis
Disadvantages
12
SMALL-SIGNAL STABILITY

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

elements

is

difficult
 Frequency domain modal results are not
familiar to many people
familiar

to

many

people
 Requires a lot of memory for large
systems
systems
 System modeling and Eigenvalue
al
g
orithms are so
p
histicated
gp
eBook for You
Eigenvalue
13
SMALL-SIGNAL STABILITY
Eigenvalue


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

the

solution

of

the characteristic equation
eBook for You
Eigenvalue
14
SMALL-SIGNAL STABILITY
Eigenvalue
Eigenvalue
: mathematical term
Eigenvalue
:

mathematical

term
Mode: engineering term
Complex
eigenvalue


j
s


Complex

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

n
1/
s
)

eBook for You
Eigenvalue
15
SMALL-SIGNAL STABILITY
Eigenvalue
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