Small Signal Stability Introduction

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


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)


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


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


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.)


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


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


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)




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.


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

Documents

Small Signal Stability Introduction