secure operation of sustainable power systemsmishra/systmod_presentations/2013_apr… · center for...

Center for Electric Power and EnergyDepartment of Electrical Engineering

Secure Operation of Sustainable Power SystemsSystmod Seminar at the University of Liege

Hjörtur JóhannssonAssistant Professor

Center for Electric Power and Energy

26-04-2013

Hjörtur Jóhannsson (DTU) SOSPO 26-04-2013 1 / 39


Introduction to DTU and CEE

Outline

1 Introduction to DTU and CEE

2 Background for the SOSPO Project

3 Overview of the SOSPO Poject

4 Methods for Real-Time Assessment and Visualisation

5 Example: Early Warning for the 2003 Blackout in E-DK and S-SW


Technical University of Denmark

Key Figures

Total Students ~8.900

- Including PhDs

- And Int. M.Sc.

1.300

700

Total DTU staff ~5.000

- Professors

- Assoc. Prof. & senior researchers

- Assist. Prof, researchers & postdocs

150

722

592



DTU main Campus - Lyngby



DTU Organization


CEE established 15 August 2012 as a merger of existing units:

– Center for Electric Technology, DTU Electrical Engineering

– Intelligent Energy Systems, Risø National Laboratory for Sustainable Energy

Main competences

– Electric Power Engineering

– Automation and control

– Information and Communication Technology

A strong university center within its field

– Staff: 85 persons incl. PhD-students

– Covers discipline oriented research as well as national lab type application-driven research and proof-of-concept

Strategic partnerships g p p

Center for Electric Power and Energy (CEE) Department of Electrical Engineering



Research Challenges




Research Challenges

The Main Research Challenge of CEE

Development of a reliable, cost effective and environmentally friendlyelectric power and energy system based on renewable energy sources.


Center for Electric Power and Energy Organisation

Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

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Research groups

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Bogi B

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Administrative support (ADM)

SLBO

Technical support (TEK)

PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard

Deputy Head of Center

Joachim Holbøll

ADM Solveig Lind Bouquin

TEK Per Munch Jakobsen

ELCO Bogi Bech Jensen

ELSY Arne Hejde Nielsen

ELMA Pierre Pinson

ERES Chresten Træholt

ESOM Henrik Bindner


Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

Ele

ctr

ic p

ow

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syste

ms (

EL

SY

)

AH

N

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Research groups

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Bogi B

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SLBO


PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard


Joachim Holbøll





ELMA Pierre Pinson


ESOM Henrik Bindner

Electric Power Components (ELCO)

Examples of research activities:

- Superconducting generators and superconducting drive train

- Lightning protection of wind turbine blades

- Transient conditions and protection in HVDC offshore grids


Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

Ele

ctr

ic p

ow

er

syste

ms (

EL

SY

)

AH

N

Ele

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PP

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Research groups

Ele

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co

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EL

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Bogi B

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Jense

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SLBO


PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard


Joachim Holbøll





ELMA Pierre Pinson


ESOM Henrik Bindner

Electric Power Systems (ELSY)


- Secure operation of sustainable power systems

- Operation of distribution networks after electrification oftransport and heating

- Application of smart grid in photovoltaic power systems


Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

Ele

ctr

ic p

ow

er

syste

ms (

EL

SY

)

AH

N

Ele

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Research groups

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Bogi B

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SLBO


PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard


Joachim Holbøll





ELMA Pierre Pinson


ESOM Henrik Bindner

Electricity Markets (ELMA)


- Electricity market design for distributed energy resources andflexible demand

- Impact of Stochastic Generation on Electricity MarketDynamics

- Electric vehicle integration in a real-time market


Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

Ele

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ic p

ow

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syste

ms (

EL

SY

)

AH

N

Ele

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SLBO


PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard


Joachim Holbøll





ELMA Pierre Pinson


ESOM Henrik Bindner

Energy Resources, Services and Control (ERES)


- Energy storage and energy system integration

- Intelligent electric vehicle integration

- Local area coordination, fleet management, home automationand individual RES controllers

- Energy conversion, storages and flexible demand technologiesand their efficiency


Infrastructure

Education

Projects

Center management

(MAN)

JOE, JH

Ele

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syste

ms (

EL

SY

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AH

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Research groups

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SLBO


PMJA

Center

committee

Support

gro

ups

Head of Center

Jacob Østergaard


Joachim Holbøll





ELMA Pierre Pinson


ESOM Henrik Bindner

Energy Systems, Operation and Management (ESOM)


- Communication architecture for service based control ofdistributed power systems

- Smart modelling of optimal integration of large amount of PV

- Integrated communication and electric power distributionsystem design



Center for Electric Power and Energy

For further information:

http://www.cee.dtu.dk



Background for the SOSPO Project

Outline


2 Background for the SOSPO ProjectFuture ChallengesThe added value of PMUs





Danish Government Energy

Target towards 2050

50% wind in the

electricity system No coal

100% RE in

electricity and

heating systems

100% RE

(incl. transport and

industry)

Background for the SOSPO Project Future Challenges

Future Challenges:Secure Operation of Sustainable Electric Power Systems

Future visions: a society with minimal dependency of fossil fuels

Requires power production to be mainly based on renewable energy sources (RES)Production becomes subject to prevailing weather conditions






The challenge of maintaining balance between production andconsumption has received significant research focus

Demand as a frequency controlled reserveUtilize controllable loads (EVs, heat pumps, etc.)






The challenge of maintaining balance between production andconsumption has received significant research focus

Demand as a frequency controlled reserveUtilize controllable loads (EVs, heat pumps, etc.)

The effect that large amount of RES has on the overall systemstability or security has not received same attention

Highly loaded grid during high wind situationsConditions for other types of stability problems



Need for Real-Time Stability/Security Assessment

Region of system operation





StableUnstable

Border of stableoperation





Secure

StableUnstable

Border of secureoperation






Secure

StableUnstable



Operating point





Secure

StableUnstable



Operating point

Historically, security assessment is based on off-line analysis⇒ Time consuming





Secure

StableUnstable



Operating point

Historically, security assessment is based on off-line analysis⇒ Time consuming

System with high share of production based on non-controllable energy sources⇒ Fluctuating operating point

⇒ Need for real-time security/stability assessment

⇒ PMUs as enabling technology


Background for the SOSPO Project The added value of PMUs

Phasor Measurment Unit (PMU)Introduction




+

GPS Antenna PMU




+

Synchronized Sampling

GPS Antenna PMU




V1

V2

θ

Im

Re

+

Synchronized Sampling

GPS Antenna PMU

Synchronizedphasors



Advancing Power System Protection and Control

Traditionally, power system protection and control has been based on local measurements

Electric Power System






Transmission line protectionuses local measurementsof voltages and currents






Transmission line protectionuses local measurementsof voltages and currentsGenerator control and protection

is based on local measurementsof f, V, P and Q








Under load tap changing trans-formers use low-voltage sidemeasurements for voltage control









During critical operatingconditions, the control andprotection equipment can havenegative effect on the systemstability and directly contribute tothe process leading to a systemblackout.








During critical operatingconditions, the control andprotection equipment can havenegative effect on the systemstability and directly contribute tothe process leading to a systemblackout.

Wide area measurement can be used to identify critical operating conditions and use thatinformation to change control and protection parameters to avoid large scale blackout



Overview of the SOSPO Poject

Outline



3 Overview of the SOSPO PojectProject ObjectiveProject Partners and ParticipantsOverview of Major R&D TasksProject Structure


5 Example: Early Warning for the 2003 Blackout in E-DK and S-SWHjörtur Jóhannsson (DTU) SOSPO 26-04-2013 17 / 39

Overview of the SOSPO Poject Project Objective

The SOSPO Project - ObjectiveSecure Operation of Sustainable Power Systems

The SOSPO project aims to solve critical, difficult and not yettreated problems in relation to the operation of future powersystems:

How to ensure a secure operation of the future power

system where the operating point heavily is fluctuating?



The SOSPO ProjectSecure Operation of Sustainable Power Systems

Households withmicro generation

Electricvehicles

Windpower

Solar power Synchronizedmeasurements

Validation ofwide-area PMUmeasurements

Stability andsecurity assess-

ment in real time

Wide-areaProsumption∗

Control

Control actionunder emerg-

ency conditions

Supervisionand

operator interface

Operator

Control centerFuture power system

Valid data

SA info

Situ

atio

nalawara

ness

info

rmatio

n

Wide-area PMUmeasurements

Wide-areacontrol actions

*Prosumption involves both distributed production and consumption



The SOSPO ProjectSecure Operation of Sustainable Power Systems

Households withmicro generation

Electricvehicles

Windpower

Solar power Synchronizedmeasurements

Validation ofwide-area PMUmeasurements

Stability andsecurity assess-

ment in real time

Wide-areaProsumption∗

Control

Control actionunder emerg-

ency conditions

Supervisionand

operator interface

Operator

Control centerFuture power system

Valid data

SA info

Situ

atio

nalawara

ness

info

rmatio

n

Wide-area PMUmeasurements

Wide-areacontrol actions

*Prosumption involves both distributed production and consumption

Resources Persons Man Months

Senior Researches 14 105Research Training 8 240TAP 3 63TOTAL 25 408

Total budget: DDK 32.2 mio. (EUR 4.3 mio.)DSF grant: DDK 20.2 mio. (EUR 2.7 mio.)

Funded by:


Overview of the SOSPO Poject Project Partners and Participants

The SOSPO Project - Partners

Partners from academia:

Center for Electric Power and Energy (CEE)

Automation & Control (AUT) Att. Olof Samuelsson

Att. Göran Anderson Att. Bo Egardt


Overview of the SOSPO Poject Project Partners and Participants

The SOSPO Project - Partners

Partners from academia:

Center for Electric Power and Energy (CEE)

Automation & Control (AUT) Att. Olof Samuelsson

Att. Göran Anderson Att. Bo Egardt

Partners from industry and consultants:

KenM Consulting

Att. Ken MartinThe Danish TSO Siemens AG, Germany


Overview of the SOSPO Poject Overview of Major R&D Tasks

Major R&D Tasks in SOSPO

The SOSPO

Project

PMU-Validation

Real-TimeStability

& SecurityAssessment

AperiodicRotor Angle

Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers

Supervision &Visualization

Implementation

FastAlgorithms

SW-development




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PhD Project:Fast Dynamic Evaluation of N-1 criteria

PhD Student: Tilman Weckesser

Objective: Develop methods forreal-time assessment of dynamicsecurity.

Supervisors: Prof. Jacob Østergaardand Assist. Prof. Hjörtur Jóhannsson

PhD Project




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PhD Project:Real-Time Assessment of Voltage Stability

PhD Student: Angel Perez

Objective: Develop methods for elementwise assessment of voltage stability inreal-time

Supervisors: Prof. Jacob Østergaard,Assist. Prof. Hjörtur Jóhannsson

PhD Project

PhD Project




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PhD Project:Wide-Area Emergency Control of Power Syst.

PhD Student: Andreas SøndergaardPedersen

Objective: Develop methods for fastwide area emergency control

Supervisors: Prof. Mogens Blanke,Assist. Prof. Hjörtur Jóhannsson

PhD ProjectPhD Project

PhD Project




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PostDoc Candidate: Pieter Vancraeyveld

Education: PhD in Physics, Universityof Gent (2011)

Expertise: Numerical Algorithms andimplementation

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%

PostDoc




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PostDoc Candidate: Hugo Morais

Education: PhD in Electrical andComputer Engineering, University ofTrás-os-Montes and Alto Douro (2012),M.Sc. Electrical Engineering - PowerSystems, Polytechnic Institute of Porto,Portugal, (2010)

Expertise: Virtual Power Players (VPP),energy resource management, powersystems

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%

PostDoc

PostDoc




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

PostDoc Candidate: S. Mojtaba Tabatabaeipour

Education: PhD in Automation andControl, Aalborg University (2010),M.Sc. in Automation andInstrumentation, Petroleum Universityof Technology, Tehran, Iran, (2006)

Expertise: Fault Diagnosis andFault-Tolerant Control of HybridSystems

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%

PostDoc

PostDoc

PostDoc




The SOSPO

Project

PMU-Validation

Real-TimeStability



Stability

VoltageStability

Assessment

DynamicSecurity

Assessment

StaticSecurity

Assessment

Wide-AreaControl

ProsumptionControl

EmergencyControl

AdaptiveStabilizers


Implementation

FastAlgorithms

SW-development

SW-developer: Allan Pedersen

Education: PhD in Electric PowerEngineering, DTU (1992), M.Sc. inElectric Power Engineering, DTU (1989)

Expertise: SW-development ofmonitoring and control systems forcommunication networks

PhD Project

PhD Project

PhD Project

PhD Project

PhD Project

50%

50%

PostDoc

PostDoc

PostDoc

SW-developer


Overview of the SOSPO Poject Project Structure

The SOSPO Project - Project Structure

Steering Group

Project

Management Team

WP1

Specifications

Guang-Ya Yang

WP3

Stability and Security

Assessment

Hjörtur Jóhannsson

WP5

WA Emergency Control

Mogens Blanke

WP7

Implementation and Test

Pieter Vancraeyveld

WP4

WA Prosumption Control

Arne Hejde Nielsen

WP2

PMU Validation

Hjörtur Jóhannsson(temp.)

WP6

Supervision and

Operator Interface

Morten Lind

WP8

Administration and

Management

Jacob Østergaard

Advisory Board

Jacob ØstergaardHjörtur JóhannssonMogens BlankeArne Hejde NielsenMorten Lind



Methods for Real-Time Assessment and Visualisation

Outline









Early Warning Against Emerging BlackoutsElement-wise assessment of stability

Element-wise assessment of a particularmechanism of instability

Individual assessment of each relevantsystem element (a generator or a node)Focussing on an assessment of oneparticular stability mechanismThe system model is reduced such that onlyfactors that have a significant influence onthe stability mechanism are includedPossibility for assessment times suitable forreal-time operation

G1

G2

G3

G4

G5

G6

G7

G8

G9

G10

G11

G12Unstable Region

Stable Region

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Margin




Early Warning Against Emerging BlackoutsElement-wise assessment of stability

Element-wise assessment of a particularmechanism of instability

Individual assessment of each relevantsystem element (a generator or a node)Focussing on an assessment of oneparticular stability mechanismThe system model is reduced such that onlyfactors that have a significant influence onthe stability mechanism are includedPossibility for assessment times suitable forreal-time operation

G1

G2

G3

G4

G5

G6

G7

G8

G9

G10

G11

G12Unstable Region

Stable Region

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Margin

Provides both a proximity-to-instability information and themechanism of instability (where and what)



Early Warning Against Emerging BlackoutsOverall assessment in real-time

Real-Time

Wide-Area

Measurements

System observability obtainedby synchronized measurements

The N’th

Assessment

Method

. . .The 2nd

The 1st

Paralell execution of Ndifferent assessment methods

Overall

Stability

Assessment

Assambles the output fromthe N assessment methods



Early Warning Against Emerging BlackoutsElement-Wise Assessment of Stability

V 1

2

3

4

5 6 7

8

9G1

G2 G4

G3

IG1

Category: Aperiodic small-signal rotor angle stability

Mechanism: Steady state torque balance in each generator Gi

Boundaries: Maximum steady-state injectable power from Gi

The stability can be assessed if Zinj and Zth are known




Early Warning Against Emerging BlackoutsAssessment of Aperiodic Small Signal Stability - Stability Boundary

ℑm(Z inj)

ℜe(Z inj)

ZTH

Z∗

TH

−Z∗

TH

−ZTH

Boundary of maximuminjectable power

Boundary:

Zinj = −Zth sin θ

sinφth



Early Warning MethodAssessment of Aperiodic Small Signal Stability: Generator Representation

The synchronous machines have to be appropriately represented whenthe assessment is carried out

This includes that excitation control and protection (AVR and OXL)have to be considered

jXdZext

Power System

Eq Et V ext

Point of constant volt-age when the machineis manually excited orwhen an OXL is acti-vated

Point of constant volt-age when AVR is main-taining constant termi-nal voltage

Point of constant voltagewhen AVR is maintainingconstant voltage at an ex-ternal point located Zext

away from the terminal

MachineterminalInternal

nodeExternal

node



Visualizing System Operating ConditionsNormalizing Multiple Operating Points

The method performs an element-wise assessment of the generatorsstability by utilizing their operating points

{

Zinj,i, Zth,i

}





{

Zinj,i, Zth,i

}

In a system with k generators, k Thevenin impedances Zth,i aredetermined resulting in k different stability boundaries

The boundaries are circular - can be normalized as a unit circleAll of the k operating points can be visualized in the same normalized injectionimpedance and held against the same stability boundary





{

Zinj,i, Zth,i

}



Deriving characteristic lines in a normalized injection impedance planeprovides useful visualization of operating conditions for all generators





{

Zinj,i, Zth,i

}



Deriving characteristic lines in a normalized injection impedance planeprovides useful visualization of operating conditions for all generators

The mapping of{

Zinj,i, Zth,i

}

into a normalized injection impedanceplane was derived such that the voltage phase angle margin ∆δ to thecritical stability boundary and the lines of constant V/Eth,i ratio werepreserved


Visualizing System Operating ConditionsMultiple Operating Points in Normalized Injection Impedance Plane

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Lines of Constant ∆δ and Constant V/E


Example: Early Warning for the 2003 Blackout in E-DK and S-SW

Outline





5 Example: Early Warning for the 2003 Blackout in E-DK and S-SWLarge Scale Test of the Assessment Method


Example: Early Warning for the 2003 Blackout in E-DK and S-SWLarge Scale Test of the Assessment Method

Test I: 2003 Blackout in E-DK and S-SWIntroduction

Simulation of the 2003 blackout in E-DK and S-SW was carriedout for the purpose of testing the method on a realistic case

Output used to generate synthetic PMU measurementsUsed to test the performance of the method






Simulation Model

Detailed model of E-Denmark combined with a simplified modelfor the of the nordic systemSize of the extended system 488 nodes and 672 edges






Simulation Model

Detailed model of E-Denmark combined with a simplified modelfor the of the nordic systemSize of the extended system 488 nodes and 672 edges

Assessment of 144 generator states in 7.86ms




Test I: 2003 Blackout in E-DK and S-SWThe Development of the Blackout

Initial Conditions

⇒ Stable and Secure





Initial Conditions


Fault in Oskarshamn

⇒ Loss of 1200MW unit⇒ Actions initiated to raise the frequency





Initial Conditions


Fault in Oskarshamn


Fault in Horred

⇒ Double busbar fault five minutes afterOskarshamn⇒ 4× 400kV lines and 2× 900MW units lost⇒ Slowly decaying voltage over a period of ≈ 80 s





Initial Conditions


Fault in Oskarshamn


Fault in Horred

⇒ Double busbar fault five minutes afterOskarshamn⇒ 4× 400kV lines and 2× 900MW units lost⇒ Slowly decaying voltage over a period of ≈ 80 s

⇒ Distance relays activated → system separation



Actual Measurements from the Blackout

Odensala (Uppland) 2003-09-23 kl. 12:35

t/s0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

B400/kV

325

350

375

400

t/s0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

FL4 S4 P/MW

-1000

-900

-800

-700

-600

t/s0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

FL4 S4 Q/Var

-6,000e+008

-4,000e+008

-2,000e+008

t/s0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

FREKVENS B400/mHz

-750

-500

-250

0

250

FrekvensstegringFrekvensfall


Test I: 2003 Blackout in E-DK and S-SWTest - Simulated vs Measured Frequency

Fre

quen

cy[H

z]

Time in secods after 12:30:29 (CET)

Simulated Frequency at Bus 3100 (Central Sweden)

Measured FrequencySimulated Frequency

300 310 320 330 340 350 360 370 380 39049.2

49.4

49.6

49.8

50

50.2


Demonstration of a Large-Scale Test


Test I: ResultsVoltage at Bus 30300 (S-Sweden)

Vol

tage

[pu]

Time in seconds after 12:30:20 (CET)

I

II III IV

V

300 310 320 330 340 350 360 370 380 390

0.7

0.8

0.9

1

1.1

Detected boundary crossover

∆t = 53.9 s

Test Results

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Snapshot I at t=298.65 s

2.5% margin

4.9% margin

5.7% margin

Test Results

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Snapshot II at t=324.78 s

0.3% margin

1.3% margin

2.3% margin

Test Results

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Snapshot III at t=342.54 s

Boundary crossover of a74MVA machine

0.6% margin

1.8% margin

Test Results

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Snapshot IV at t=369.85 s

Boundary crossover ofa 310MVA machine

Test Results

0.20.40.4

0.60.6

0.80.8

1.4 1.4

2.02.0

3.03.0

1.01.0

80°

80°

70°

70°

60°

60°

50°50°

40° 30° 20° 10°

90°

90° 100°

100°

110°

110°

120°

120°

130°130°

140°150°

160°

1.01.0

Snapshot V at t=396.44 s

Remaining generators inthe area are rapidly ap-proaching the boundaries


thank you


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