Post on 14-Apr-2015
Small Signal Stability IntroductionFor the Learning Project No.2
Presented By:Debra Dai
05 Jan 2013Restricted
Power System Stability
Angle Stability Frequency Stability Voltage Stability
Transient StabilityLarge Disturbance
Voltage Stability
Small Disturbance
Voltage Stability
Short Term Short TermLong Term Long Term
Small SignalStability
Power System StabilityPower System Stability
Angle StabilityAngle Stability Frequency StabilityFrequency Stability Voltage StabilityVoltage Stability
Transient StabilityTransient StabilityLarge Disturbance
Voltage Stability
Large Disturbance
Voltage Stability
Small Disturbance
Voltage Stability
Small Disturbance
Voltage Stability
Short TermShort Term Short TermShort TermLong TermLong Term Long TermLong Term
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
Angle Stability It is defined as the capability of the synchronous
generators in the system to maintain its synchronism after being subjected to a disturbance.
Small-disturbance Angle Stability Small-disturbance (or small signal) angle stability is concerned with the ability of the power system to maintain synchronism under small disturbance.
Concept
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
Short-term angle stability Short-term angle stability is characterized by dynamic
components such as excitation of synchronous generators, controllers, such as AVR and PSS, electronically controlled devices such as HVDC and induction motors . The time scale of short-term is ~20 second following a disturbance. The time frame of interest in small-signal stability studies is on the order of 10- 20 seconds following a disturbance.
Concept (con’t)
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
System operators need to know the exact situation after the system suffers a disturbance. Post-contingency operating point usually has smaller security margin compared to the initial operation point.
Why need Small Signal Stability Analysis
V
P
maximum power flow boundary
small–signal stability boundary
Contingency
V
VSM
P
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
Why need Small Signal Stability Analysis (con’t)
1 2
PL+jQL
3
|V1|=1.0 puP1= 1.0 pu
V2=0.995+j0 pu
=1.0+j0.3 pu
Z=1.0 p.u.
3-bus test system dynamic data:Bus H xd xd1 xq xq1 Td1 Tq1 Damp1 3.2 2.5 0.39 2.1 2.1 9.6 0 0
Excitation system of typeDC1A
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
Why need Small Signal Stability Analysis
0.0 .5 1.0 1.5 2.0
0.0
.2
.4
.6
.8
1.0
Hopf Bifurcation BoundaryLoad Flow BoundaryInitial Operating Point
Qp.u.
P ( p.u.)
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
The disturbance is so small that the power system can be linearized around an operating point and the analysis is typically based on eigenvalue and eigenvector techniques.
The Analysis Method
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
System DAE Model and State Matrix
stabilizer
Vrefexcitationsystem
potentialtransformer
powersystem
turbine
governorsystem
O
UT
PU
T
voltage Vt
reactive power Qactive power Pe
frequency frotor speed
Epss
fspec
Efd
Pm
+
+
mmmmm
G
m
Reference : Plant Scheduling and Load Allocation Rules CLP-HEC Interconnection Operating Practices
System DAE Model and State Matrix (con’t)
Models of system: synchronous generators; excitation systems, controllers and/or induction motors
State variables: rotor angle; rotor speed; d-axis transient voltage; q-axis transient voltage; the scaled field voltage and so on
Algebraic variables: voltage’s amplitude and phase
Eigenvalue and Stability
Interarea oscillation: 0.2~ 0.8 Hz
Iocal oscillation: 0.8~ 1.2 Hz
Eigenvalue and Stability (con’t)
-7 -6 -5 -4 -3 -2 -1 0 10
0. 32
0. 64
0. 95
1. 3
1. 6
1. 9
real (1/s)
Fre
quen
cy
(Hz)
Control modes
local mode
Control modesIocal mode
Mode 1
Mode 4
Mode 2
Damping ratio 0.05
Interarea mode
Modal Analysis
Modal Analysis (con’t)
Modal Analysis (con’t)
Modal Analysis (con’t)
Modal Analysis (con’t)
West-east
East-West North-south
South-North
South-Rio Grande valley
Rio Grande valley-south
From-Houston
Modal Analysis (con’t)SSAT Monday, April 08, 2002, 10:11:43
SSAT 1.2critctgscan.binPowertech Labs Inc.
Copyright 2002 All rights reservedPage 1 of 1
Mode ShapeReal = 0.0073 1/s Imaginary = 3.6442 rad/s Frequency = 0.5800 Hz Damping = -0.20 %Case: critctgscan.ssa Scenario: 2004 pk southnorth Contingency: No faultDominant State: 8161 : CLO #1 24.0 : 0 : : 1 : GENROU : : Psi_fdMode Shape Reference: 6677 : VALTNTP269.0 : 0 : : 1 : GENROU : : Speed
1.00 6677 : VALTNTP269.0 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.96 60000 : ENR_NRP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.93 6020 : ENR_SP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.91 6637 : KM_NWP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.91 60007 : KM_SWP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.90 6634 : WDWRDU1 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.90 60005 : KM_SEP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.89 60003 : KM_NEP 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.87 38332 : WDWRDU2 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.78 6017 : ORNNWP1 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.69 6016 : SWMESA 34.5 : 0 : : 1 : GENROU : : Speed : 8 [ ]0.57 1045 : CALENG1G13.8 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.57 1046 : CALENG2G13.8 : 0 : : 2 : GENROU : : Speed : 1 [ ]0.56 11022 : TIECT12G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.56 11023 : TIECT21G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.56 11024 : TIECT22G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.56 11021 : TIECT11G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.54 1008 : PB6 G18.0 : 0 : : 6 : GENROU : : Speed : 1 [ ]0.50 11020 : TIE ST1G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]0.50 11025 : TIE ST2G18.0 : 0 : : 1 : GENROU : : Speed : 1 [ ]
-0.69 8306 : LAP #5 13.8 : 0 : : 5 : GENROU : : Speed : 8 [ ]-0.69 8442 : NBY #7 22.0 : 0 : : 7 : GENROU : : Speed : 8 [ ]-0.69 8459 : DAV #1 24.0 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.69 8981 : HIDGN1 18.0 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.69 8982 : HIDGN2 18.0 : 0 : : 2 : GENROU : : Speed : 8 [ ]-0.70 8048 : FAL #1 13.8 : 0 : : 1 : GENSAL : : Speed : 13 [ ]-0.70 8511 : STARCO#113.8 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.70 8928 : LGEGN#3 13.8 : 0 : : 3 : GENROU : : Speed : 8 [ ]-0.71 8936 : CALGN#1 16.0 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.71 8937 : CALGN#2 16.0 : 0 : : 2 : GENROU : : Speed : 8 [ ]-0.71 8933 : FGNTS00118.0 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.71 8934 : FGNTS10118.0 : 0 : : 2 : GENROU : : Speed : 8 [ ]-0.71 8983 : HIDGN3 18.0 : 0 : : 3 : GENROU : : Speed : 8 [ ]-0.73 8517 : CEL-B #113.8 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.77 8307 : LAP #7 13.8 : 0 : : 7 : GENROU : : Speed : 8 [ ]-0.77 5935 : SI RAY8 13.8 : 0 : : 8 : GENROU : : Speed : 15 [ ]-0.79 8506 : VAL #1 13.8 : 0 : : 1 : GENROU : : Speed : 8 [ ]-0.79 8507 : VAL #2 13.8 : 0 : : 2 : GENROU : : Speed : 8 [ ]-0.81 8457 : COSW#2 13.8 : 0 : : 2 : GENROU : : Speed : 8 [ ]-0.81 8456 : COSW#1 13.8 : 0 : : 1 : GENROU : : Speed : 8 [ ]
Modal Analysis (con’t)SSAT Monday, April 08, 2002, 10:09:38
SSAT 1.2critctgscan.binPowertech Labs Inc.
Copyright 2002 All rights reserved
Mapped Mode ShapesReal = 0.0073 1/s Imaginary = 3.6442 rad/s Frequency = 0.5800 Hz Damping = -0.20 %Case: critctgscan.ssa Scenario: 2004 pk southnorth Contingency: No faultDominant State: 8161 : CLO #1 24.0 : 0 : : 1 : GENROU : : Psi_fdMode Shape Reference: 6677 : VALTNTP269.0 : 0 : : 1 : GENROU : : Speed
Unit With Positive Mode ShapeUnit With Negative Mode Shape
Note: Shading Indicates Magnitude.
Modal Analysis (con’t)
PSS – Enhance the Damping of the Systems (1)
PSS – Enhance the Damping of the Systems (2)
• In modern power systems, in order to make generators operate at the nominal voltage, AVR is implemented. As a consequence, the synchronizing torque is increased. But in the case of heavy load, AVR may introduce negative damping torque to the system.
•PSS is the most effective corrective measure to add damping to the system
Frequency Deviation and Tie-line SwingMore than one modes are in the connected systemOscillation is between HEC and GPG
Frequency Deviation and Tie-line Swing (con’t) CLP and HEC are in the same group
CLP is not the dominant party in this event