V SEPOPE Conference, Recife, Brazil, May 1996

Oscillations Damping Analysis and Control Studies of the Future Interconnection Between

the North-Northeast and South-Southeast Systems

Nelson Martins (CEPEL)Hermínio J. C. P. Pinto (CEPEL)

Carlos A. Gama (ELETRONORTE)Jurandir A. Cavalcanti (CHESF)

Roberto L Leoni (ELETROBRÁS)Ronaldo V. Souto (ELETROBRÁS)

Nilo J. P. Macedo (FURNAS)Maria José X. Eiras (FURNAS)

Procedures for Stabilization of Electromechanical Oscillations in Interconnected Power Systems

n Application of Damping ControllersProblem IdentificationSitingInput Signal Selection and FilteringClosed Loop Control DesignPerformance EvaluationAdverse Side Effects

Software PacDynSmall Signal Stability Analysis and Control

n 8 Generator Models (Salient and Round Rotors, with saturation)n Excitation Control Systems (any kind)n Stabilizing Signals (any kind)n Governors (any kind)n 2 Induction Motor Modelsn HVDC Links and HVDC/CCC Schemesn FACTS Devices

Static Var CompensatorsThyristor Controlled Series CompensatorsSTATCOM

n User Defined Controllers (UDC)n Dynamic Loads

Software PacDynSmall Signal Stability Analysis and Control

n Eigenvalue Computation AlgorithmsFull eigensolution (QR and QZ)Partial eigensolution (Simult. Iteration; Dominant Pole Alg.)

n Transfer Function Zerosn Modal Sensitivities

Transfer Function ResiduesControlability FactorsObservability Factors (Mode Shapes)Participation Factors

n Frequency and Linear Time Response Plotsn Coordinated Controller Design

Geographic Map of the Proposed North-South Interconnection

RI O

XINGU

RI O

DAS

A LMA

S

RI O

AR

AGU

AIA

RI O

TO

CA

NT

I NS

R IOPA

RANAO ANT I NZI NH

RI O

S. F

R

ANC

I SCO

R IO

F ORM

OSO

R I OCOR R E N T E

R I O P AR AGU A C U

O JE Q

U I T I N H ONH

A

RI O

ARA

A I

R I OP R E T O

RIO

TO

CANT

IN

S

AGUA

S.SIMAOITUMBIARA

S.GOTARDO 2

JAGUARAPORTOMARIMBONDO

IRAPE

PIRAPORA

FSA

MOCAMBINHO

JEQUITINHONHA

ALMEN

S. ANTONIO DE JESUS

ITABAIANINHA

JARDIM

PENEDO

SOBRADINHO

P.BR

BOA ESPERANCA

EUNAPOLIS

ELISEU

PICOS

BOM NOME

COREMAS

ACU

TAP/XIN1

F.3

M.A.GRANDE

MIRADOR

BELEM

S.DIVISA

SALVADOR

SME/TMA

GOV

MASCARENHAS

ALTAMIRA

BELO MONTE

TUCURUI

REP

V. CONDE

IPI/MAR

ESTREITO

MARABA

SERRA QUEBRADA

IMPERATRIZ

FRAGOSO

LAJ/SOB

LAJ/IRE

BARREIRAS

IRECE SOB/SLV

IRE/SLV

MUSSURE

S. LUIS

FORTALEZA

PIRIPIRI

CRATEUSTERESINA

QUIXADA

MILAGRES

RUSSAS

MOSSORO

SOBRAL PENTECOSTES

B. ESP/MIL

SJP/MIL

MIRANDA

PRES. DUTRA

SEC.T/P

SERRA da

S. ROMAO

SME/BJLBOM JESUS

GOV

FUNIL

TRES MARIAS

XAVANTES

BANDEIRANTES

CORUMBA

NOVA PONTE

CAPIM BRANCO

CAMACARI

NIQUELANDIA

LAJ/SJP

SAM/BJL

IR

V.GRANDE

VALADARES

MANGABEIRA

VERMELHA

COLOMBIA

MARTINS

MESA

S.G.PARA TAQUARIL

VARZEADA PALMA

IPATINGA

T.OESTES.LUZIA

MACEIOJAGUARI

NATAL

NATAL II

DA LAPA

S. JOAO DO PIAUI

ICO

BJL/GMB

PERISES

C. PENA

BANABUIU

QUI/REC

RECIFE

MIL/REC

XINGO

ANGELIM

AFONSO

ITABAIANACICERODANTAS

OLINDINA

SENHOR DOBONFIM

JUAZEIRO

ANHANGUERA

EMBORCACAO

M.CLAROS

NEVES MESQUITA

DOURADACACHOEIRA

ITAPEBI

SAMAMBAIA

POMPEU

GU

PERITORO

ITAPARICA

PAULOMOXOTO MESSIAS

RIBEIRAO

BRASILIA GERAL

BARRO ALTO

CATU

DERIVACAO

S. ISABEL

RT.

C

C. GRANDE

TACAIMBOGOIANINHA

PAU FERRO

PAPAGAIO

S.3BLAJEADO

IPUEIRAS

PEIXE

CANA BRAVA

TUPIRATINS

500 kV AC TRANSMISSION REINFORCEMENT ALTERNATIVENORTH-SOUTH INTERCONNECTION

ALTERNATIVES

DCIMPERATRIZ

ACIMPERATRIZ

S. DA MESA S. DA MESA

PEIXE

TUPIRATINS

LEGEND

HYDROELECTRIC PLANT

SUBSTATION

LT 230 kV

LT 500 kV

EletrobrásGRUPO COORDENADOR DE PLANEJAMENTO

DO S S ISTEM AS ELÉ TR ICO S - GCPSLT 345 kV

SOUTHEAST

NORTHEAST

NORTH

CENTRAL WEST

Courtesy of Eletrobrás/GTOT

Small-Signal Time Responses of Major System Generators

-0,02

-0,01

0,01

0,02

0 5 10 15 20 25

Time (s)

Term

inal M

W D

eviat

ion (p

u)

-0,02

-0,01

0,00

0,01

0,02

0 5 10 15 20 25

Time (s)

Term

inal

MW

Dev

iatio

n (p

u)

South Exporting 1,000 MW to Northλ = −0.172+j0.98

North Exporting 1,000 MW to Southλ = −0.011+j 0.802

Small-Signal Power Oscillations in the North-South Intertie

South Exporting 1,000 MW to North

North Exporting 1,000 MW to South-0 ,1 2

-0 ,1 0

-0 ,0 8

-0 ,0 6

-0 ,0 4

-0 ,0 2

0 ,0 0

0 ,0 2

0 5 1 0 1 5 2 0 2 5

T im e (s )

Po

we

r F

low

De

via

tio

Brazilian North-South Interconnection

North-South Tie-Line Power

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Activ

e Po

wer

Flo

w D

evia

tion

-pu

ANATEM PacDyn

North-South Tie-Line Power

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Activ

e Po

wer

Flo

w D

evia

tion

-pu

ANATEM PacDyn

Comparing Simulations from Small Signal Stability and Transient Stability Programs

Brazilian North-South Interconnection

Active power flow in the North-South tie-line

Comparing step responses from the full-order linear model and a 4th order modal equivalent

Brazilian North-South Interconnection

Step response equation and constants for the 4th order modal equivalent

∑=

⋅ −≅4

1)1()(

i

t

i

i ieRty λ

λ

0044.0275.0802.0011.0

34

12

jj

±−=±−=

λλ

007.0039.0251.0006.0

34

12

jRjR

±−=±−=

Rotor Speed Mode Shape for North-South Mode)802.0011.0( 12 j±−=λ

South and Southeast Generators

North and Northeast Generators

Phasor Diagram Representation of Transfer Function Residues (Pij

k/Bijk, k = 1,nl)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-0.6 -0.4 -0.2 0 0.2 0.4

Imperatriz - Tupiratins

Tupiratins - Peixe

B. Esperança - S.J. Piaui

Determining the Most Effective System Branches for InstallingTCSCs with PODs for Damping the N-S mode

Single TCSC with POD Controller

CompleteCompleteSystemSystem

Linear ModelLinear Model

∆Bij ∆Pij

TCSC DampingTCSC DampingController TransferController Transfer

FunctionFunction

Frequency Response of ∆|Pij|(s) / ∆Bij(s)

North Exporting 1,000 MW to South

0.8 rad/s

4.5 rad/s

Frequency Response of ∆|Pij|(s) / ∆Bij(s) . TCSC(s)

North Exporting 1,000 MW to South

0.8 rad/s

Block Diagram for POD Controller of Single TCSC

∆Pij 428 42s s+ +.

1 0 61 25

2++

ss

.

.

Quadratic Filter

16ss5

1 5+

Washout Double -Lag Gain∆Bij

Linear Time Response of Tie-Line MW Flow as a Function of the TCSC POD Controller Gain

North Exporting 1,000 MW to South

-0 ,12

-0 ,10

-0 ,08

-0 ,06

-0 ,04

-0 ,02

0 ,00

0 ,02

0 5 1 0 15 20 25

T im e (s )

Po

wer

Flo

w D

evia

tio

n

K = 4 0

K = 1 6

K = 0

K = 8

Linear Time Response of Tie-Line MW Flow as a Function of the TCSC POD Controller Gain

South Exporting 1,000 MW to North

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.000 5 10 15 20 25

Time (s)

Pow

er F

low

Dev

iatio

n (p

u)

K = 40

K = 8

K = 16

K = 0

Linear Time Responses of Major System Generators in the Presence of a Single TCSC with POD Controller

-0.02

-0.01

0

0.01

0.02

0 5 10 15 20 25

Time (s)

Term

inal

MW

Dev

iatio

n (p

u)

North Exporting 1,000 MW to Southλ = −0.251+j0.823

-0.02

-0.01

0.00

0.01

0.02

0 5 10 15 20 25

Time (s)Te

rmin

al M

W D

evia

tion

(pu)

South Exporting 1,000 MW to Northλ = −0.286+j1.022

Inter-Area Eigenvalue Locus as a Function of the Gain of a Single TCSC POD Controller

(0)(5) (8) (16)

(16) (8) (5) (0)

Notation: Symbol ‘a’ relates to South to North, 1,000 MW FlowSymbol ‘r’ relates to North to South, 1,000 MW Flow

Brazilian North-South Interconnection

Comparing Simulations from Small Signal Stability and Transient Stability Programs

-0.9Activ

e Po

wer

Flo

w D

evia

tion

-

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 2 4 6 8 10 12 14 16 18 20

Time (s)puNorth-South Tie-Line Power

ANATEMPacDyn

-0.9Activ

e Po

wer

Flo

w D

evia

tion

-

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 2 4 6 8 10 12 14 16 18 20

Time (s)puNorth-South Tie-Line Power

ANATEMPacDyn

Activ

e Po

wer

Flo

w D

evia

tion

-

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 2 4 6 8 10 12 14 16 18 20

Time (s)puNorth-South Tie-Line Power

ANATEMPacDyn

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 2 4 6 8 10 12 14 16 18 20

Time (s)puNorth-South Tie-Line Power

ANATEMPacDyn

Eigenvalue Spectrum of the 50,000 MW, Brazilian North-South Interconnection

(with just one TCSC POD Controller)

North Exporting 1,000 to South

Root-Loci Varying the TCSC POD Controller Gain

North Exporting 1,000 MW to South

K = 0K = 20

Phasor Diagram Representation of Transfer Function Residues (ωi/Vref

i, i = 1, ng)

0

-1 -0.5 0

Paulo Afonso 4

Xingó

Paulo Afonso 3

ItaipuSobradinho

Itaparica

Determining the Most Effective Generators forInstalling Enhanced Stabilizers

Dominant Pole Spectrum for ∆ω(s) / ∆Vref(s)

Xingó Power Plant

0,0

2,0

4,0

6,0

8,0

10,0

-4,00 -3,00 -2,00 -1,00 0,00 1,00

Real

Imag.(rad/s)

Pole Residues are also depicted

Initial Displacements of Dominant Poles Due to Incremental Gain Stabilizer

Xingó Power Plant

0,0

2,0

4,0

6,0

8,0

10,0

-4,00 -3,00 -2,00 -1,00 0,00 1,00Real

Imag.(rad/s)

PSS s ss

ss

ss

( ) ..

..

=+

++

++

ε 31 3

1 0 41 0 04

1 0 271 2 7

2

Tie-Line Small-Signal Power Oscillations for Original and Enhanced PSSs in Xingó and P. Afonso IV

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0 5 10 15 20 25

Time (s)

Pow

er F

low

Dev

iatio

n (p

u)

Original

Modified

North Exporting 1,000 MW to SouthOriginal PSS

Enhanced PSSs

Small-Signal Power Oscillations at North-South Intertie

North Exporting 1,000 MW to South

Original System

Enhanced PSSs

Enhanced PSSs in Xingó, P. Afonso IV, Itaparica and Sobradinho

Brazilian North-South InterconnectionTransient Stability Simulation of a Fault with Line Clearance

and Subsequent Reclosure

600

700

800

900

1000

1100

1200

1300

0 5 10 15 20 25Time (s)

Pow

er F

low

(MW

)

Existing PSS's

Proposed PSS's in Xingó,Paulo Afonso IV & Itaparica

Small-Signal Power Oscillations at North-South Intertie

North Exporting 1,000 MW to South

Enhanced PSS’s + TCSC (K=8)

Enhanced PSS’s

Small-Signal Power Oscillations at North-South IntertieNorth Exporting 1,000 MW to South

Enhanced PSS’s + TCSC (K=8)TCSC (K=16)

Original System

Conclusionsn Power Oscillation Damping (POD) controller on a TCSC

located along the North-South Inter-Tie was shown to effectively damp the Brazilian 0.17 Hz North-South mode

n Enhanced PSSs in four Northeastern power plants can also effectively damp this oscillation

n Small signal analysis software is very effective for coordinatedstabilizer design

n Good graphics and program interactivity makes the engineer’s task much easier in complex engineering studies

n Step responses of linearized system model, as demonstrated in this paper, when used for preliminary comparison of alternative damping solutions, may speed-up oscillation damping control studies (50 times faster than transient stability solutions)