TRANSIENT STABILITY STUDIES(POWERTRS)

Indonesia Clean Energy Development (ICED) project

Indonesia Wind Sector Impact AssessmentPresented by:

Dr. Balaraman, Ph.D.

Makassar, February 17 to 21, 2014

Voltage stability

Rotor angle stabilityStudy period: 0-10

sec

Mid-term/long-term stabilityStudy period: seconds to

several minutes(slow dynamics)

Small signal stability

Non-oscillatory Insufficient synchronizing torque

OscillatoryUnstable control

action

Transient stabilityLarge disturbance(First swing)

Stability

f, v, loading acceptable, load met,n-1 or n-2 contingency acceptable

f, v, loading acceptable

load met n-1 or n-2 contingency

not satisfied

f, v, loading not acceptable,

load not met

Normal

Alert Restorative

Cascaded system

syste

m In Extremis Emergency

Power System Operating States

Pool control centre

System control centre

To other systemTo other system To other system

Transmission system Power plant

DS DS DS G G G

DS: Distribution SystemG : Generator

Control Hierarchy

f Ptie Pgtotal

Schedule System generation controlLoad frequency control with

economic allocation

Other generating unitsand associated controls

Generating units control

Prime mover & control

Excitation system &control

Generator f/N or

Pg Vt

If

Pm f/N

Transmission ControlsReactive power, Voltage control,HVDC transmission and others

Pg

f Ptie Pg.total

Power System Subsystem & Controls

Power System Stability

• Ability of a power system to remain in synchronism

• Classification of transients : Electromagnetic and Electromechanical

Stability classification • Transient stability : Transmission line faults, sudden load

change, loss of generation, line switching etc.• Dynamic stability : Slow or gradual variations. Machine,

governor - Turbine, Exciter modelling in detail.• Steady state stability : Changes in operating condition. Simple

model of generator.

Transient Stability: First swing and Multiple Swings

Stable Unstable

Stable Unstable

t Sec. t Sec.

t sec.t Sec.

m2

m2

m1 m1

0 0

00

Assumptions :• Synchronous speed current and voltage are

considered.• DC off set currents, harmonics are neglected.• Symmetrical components approach.• Generated voltage is independent of machine speed.• Circuit parameters are constant at nominal system

frequency. (Frequency variation of parameter neglected).

Stable Unstable

Stable

Unstable

Steady State Stability

J dd t

T T T N mma m e*

2

2

• J : Moment of inertia of rotor masses (kg-mt2 )• m : Angular displacement of rotor w.r.t. a stationary axis

(mechanical radians)• t : Time (seconds)• Tm : Mechanical or Shaft Torque ( N-m )• Te : Net electrical torque (N-m )• Ta : Net accelerating torque (N-m)•  • For generator, Tm and Te are +ve.

Mechanical Equation

Reference Axis Stationary

m

Reference axis at sm

sm

sm

Rotor axis at rotor speed

m sm mt m : Angular displacement of the rotor in mechanical radians.

ddt

ddt

ddt

ddt

Jddt

T T N m

ddt

Angular velocity in radians per

Jddt

P P watts

Mddt

P P Approx

msm

m

m m

mm e

mm

mm

m e

mm e

2

2

2

2

2

2

2

2

2

2

sec.

( )

Where M : Inertia constant = at synchronous speed in Joules-sec per mechanical radian.

Constant is defined as the ratio of stored Kinetic Energy in Mega Joules at synchronous speed and machine rating in MVA

 

emm

sm

emm

sm

smsm

PPdt

dHS

wattsPPdt

dM

radianmechanicalperMJSHM

MVAMJS

M

S

JH

2

2

2

2

2

2

2

/21

21

ems

emm

sm

emm

sm

PPdtdH

puPPdt

dH

SPP

dtdH

2

2

2

2

2

2

2

2

2

2

2

2

2

deg

180

2

12 1 ,

22 ,

m e

m e

m e ss

m e

s

s

s

H d P P pu SwingEquationf dt

If inelectrical d rees

H d P P puf dt

H d dP Pdt dt

Let P P puH d pu t

dt HIf t H

Pm

Pe = 1 pu

• At t = 0, breaker is opened.• Initially Pe = 1 pu on machine rating Pm = 1pu and

kept unchanged.• In 2H seconds, the speed doubles.

H Stored KEMachine Rating

H Machine Rrating H systemMVA

H H Machine ratingSystem MVA

mech system

system mech

Inertia constant (H) is in the range 2 - 9 for various types of machines. Hence H-constant is usually defined for machine.

machineS

NWR

H

Wattslbft

lbftNWRKE

feetingyrationofRadiusRpoundsinpartrotationalofWeightW

ftlbWRInertiaofMoment

622

22

22

10550746

602

2.3221

746sec/55060

22.322

1

::

2.32

Relation between H constant and Moment of Inertia is given by:

Example :Smach = 1333 MVA, WR2 = 5820000 lb – ft2, N= 1800

RPM

= 3.2677575 pu (MJ/ MVA)On 100 MVA base : H = 1333 / 100 = 43.56 (MJ /

MVA)

13336018002

2.325820000

2110

550746 2

6

H

G1 ,H1

Pe1Pm1

G2 ,H2

Pm2Pe2

Hf

ddt

P Pm e1

21

2 1 1

2222

22

em PPdt

dfH

H Hf

d

dtP P P Pm m e e

1 22

2 1 2 1 2

PePtd

df

Hm2

2

HStored energy at rated speed in MWs

MVA rating

H = H1 + H2

Pm = Pm1 + Pm2

Pe = Pe1 + Pe2

G1 and G2 are called coherent machines.

Inertia Constant

ratingMVARPMJ

ratingMVA

JH

RPMradianmechanicalinspeedRated

mkgininertiaofMomentJ

MWsJ

wattsJ

energyKineticenergyStored

om

om

om

om

29

62

2

62

2

1048.5

1021

602sec/:

:

1021

21

MKS system

22

22

356.12.32

)(

mkgWRJ

ftlbgyrationofradiusofsquarepartrotatingofWeightWR

British units

Given

JWR

kg mt

HJ RPM

MVA ratingMWs MVA

Stored energyH MVA rating MWs

Mechanical starting timeH onds

22

62

32 21356 27547 77168

548 10

2

.. .

.( )

/

sec

MVA rating : 555WR2 : 654158 lb-ft2

Example

Non coherent machines

Hf

ddt

Pm Pe12

12 1 1

ddt

fH

P Pm e

21

21

1 1

Hf

ddt

P Pm e2

22

2 2 2

ddt

fH

P Pm e

22

22

2 2

Unit Type H ConstantHydro Unit 2 to 4

Thermal unit

2 pole – 3600 RPM 2.5 to 6

4 pole – 1800 RPM 4 to 10

Typical Values

ddt

f

HP P

fH

P P

f

d

dt

H P P P P H

H H

H HH H f

d

dtH

H HP P

HH H

P P

H HH H f

d

dtH P H P

H H

H P H P

H H

H

m e m e

m e m e

m e m e

m m e e

2

2 1 21

1 12

2 2

21 2

22 1 1 2 2 1

1 2

1 2

1 2

21 2

22

1 21 1

1

1 22 2

1 2

1 2

21 2

22 1 1 2

1 2

2 1 1 2

1 2

1

1

1

fddt

P P

Where

HH H

H HP

H P H P

H H

PH P H P

H H

m e

mm m

ee e

2122 12 12

1 2

1 212

2 1 1 2

1 2

122 1 1 2

1 2

,

Relative swing (with reference to one machine) is more important, rather than absolute swing.

Relative Plot (i-)Absolute Plot

1

o

2

3

4

3

20

1

T in sec. T in sec.

Swing curves

Relative swing (with reference to one machine) is more important, rather than absolute swing.

I

E’ = Vt + (0 + jxd’) I

E’

Vt

jxd’ I

Ref.Vt

I

E’

jxd’+

-

Classical model : (Type 1) Constant voltage behind transient reactance

E1 : Magnitude of voltage at bus1E2 : Magnitude of voltage at bus2 : 1 - 2Xs : Reactance

PE EXs

1 2 sin

jXs

E2 2E1 1

Power angle equation

Machine Parameters Synchronous : Steady state, sustained.Transient : Slowly decaying Sub-transient : Rapidly decayingE=?

X=?

X X X X X

T T

T T

d q q q d

d do

qo qo

' " "

' "

' "

0

Typical values Parameter Hydro (pu) Thermal (pu)

xd 0.6 - 1.5 1.0 - 2.3

xq 0.4 - 1.0 1.0 - 2.3

xd’ 0.2 - 0.5 0.15 - 0.4

xq’ ------- 0.3 - 1.0

xd” 0.15 - 0.35 0.12 -0.25

xq” 0.2 - 0.45 0.12 -0.25

Td0’ 1.5 - 9.0 s 3.0 -10.0 s

Tq0’ ------- 0.5 - 2.0 s

Td0” 0.01 - 0.05 s 0.02 - 0.05 s

Tq0” 0.01 - 0.09 s 0.02 - 0.05 s

Ra 0.002 - 0.02 0.0015 - 0.005

Stability

Stable At s ; Pm = Pe ; net accelerating torque = 0.Let Pe decrease slightly.      

increase (acceleration) comes back to original position.Stable region . Hence s is stable operating point.

 

veisPPdtd

fH

em 2

2

P

Pmmmm

O

Pe=Pmax sin

u

900 s 1800

Unstable

At u; Pm = Pe ; Net accelerating torque = 0 ,

Let Pe decrease slightly.

increases, (acceleration)Pe further decreases.Chain reaction never comes back to normal valueHence u is unstable operating point.

veisPPdtd

fH

em 2

2

System

Infinite bus • Generator connected to infinite bus.• High inertia. H compared to other machines in the

system. • Frequency is constant.• Low impedance. Xd

’ is very small.• E’ is constant and Vt is fixed.• Infinite fault level symbol.

200 MW1.05 pu V

250 MVA250 MVA Slack bus

1 pu - V

Example :

H = 3.2 , Z = 10% on own rating , Xd1 = 25% , tap = 1, Ra

= 0.0 and neglect R.• Establish the initial condition.• Perform the transient stability without disturbance.• Open the transformer as outage & do the study.• How long the breaker can be kept open before closing,

without losing synchronism.

Load Load11 kVSwitchedCapacitor

132/110 kV

Load Modeling

fo

Po

frequency

Power

·       Vary the tap.·       Switch on the capacitor.·       Determine the response (charge) in load.·       Compute the parameters.•   P = P0 (CP + CI . V + CZ . V2) ( 1+Kf . f) ·       P varies with time, voltage andfrequency.·       P0 varies with time - can be constant at agiven time of a day.·       CP, CI, CZ & Kf are constants.·       V & f are known at any time instant.·       P is known from measurements.·       Solve the non linear problem over a set ofmeasurements.

• Let the load be 10,000 MW. i.e. P0 = 10,000• Let for 1 Hz change in frequency, let the load change be 700 MW.

• What it implies :– Initial load 10,000 MW.– Loss of generation 700 MW– Increase in load 700 MW – Frequency 49 Hz.

5.350

1100

7

:100,;

%7000,10

700

7001

700)(

)(700

pf

pf

pfoo

pfo

C

baseMVAonthenfrequencyinchangeunitpertheisfpuinisPIf

C

numberpowerCffP

loadindecreaseCfP

Load model parameters

Measurement based approach Input: Connected load Measurement: P,V, f over a period Out put: Parameters

Component based approach Industrial Commercial residential Agricultural

Load model Parameters

Loads

Transducer

Regulator Exciter Generator

Limiter + relay

PSS

Excitation System Components

Ref.

ControllerRegulator

Poweramplifier(Exciter) Plant

Feedback elements

Block Schematic

EtEfdVtrVer

Vref

Reactive Power Control

•Synchronous generators•Overhead lines / Under ground cables•Transformers•Loads•Compensating devices

Control devices

• Sources /Sinks --- Shunt capacitor, Shunt inductor (Reactor), Synchronous condenser, and SVC.

• Line reactance compensation --- Series capacitor• Transformer -----OLTC, boosters

AGC

Speedchanger

SpeedGovernor

Valve/gate

ElectricalSystem

Energy Supplysteam or water

TurbineGenerator

Speed

Tie line Power

Frequencies

Speed governor systems:

1/R 11TTws

ws

1T Kms D

speed

TurbineDroop(Goveror) Generator+

-

SpeedRef.

Types of Control:• Primary Control : Governor action• Secondary Control : AGC, load frequency control (For

selected generators)

Under Frequency operation :· Vibratory stress on the long low pressure turbine blades· Degradation in the performance of plant auxiliaries say,

induction motor

Limitations

• Only maximum spinning reserve can be achieved• Turbine pickup delay• Boiler slow dynamics• Speed governor delay

Trip signal 49.50.4 Hz/s

48

10% load rejection

15% load rejection

50% load rejection

30% load rejection

1 Hz/s

4 Hz/s

2 Hz/s

Other measures :* Fast valving* Steam by-passing

Load shedding

Modules in a program• Data reading• Initialization

– Steady state load flow– Control block parameter AVR, Gov., Machine, Motor, PSS, HVDC, SVC.

• Disturbance model• Control block modeling• Machine modeling• Load flow solution• Protective relay modeling• Special functions

– Cyclic load– Arc furnace– Re-closure

• Results Output– Report– Graph

Time in seconds

AVR & PSS

Constant Efd

AVR with no PSS

65432

90

60

30

1

Typical swing curve :

0.01

0.090

0.025

5 4 3 2 1

180

120

60

Time in Sec.

Rotor angle degrees

Integration step size : Typical value : 0.01 seconds, Range : 0.005 to 0.02 seconds

Typical swing curve :

11 1sT

ksT1

21

s=f(Efd)

sksT3

41

1

2 3k sT

PSS

+-

+

Vref

+

- EfdVT

AVR : Type 1

Efd11 1sT

ksT1

21

sk

sT sT3

4 51 1

Vs

+-

+

Vref

SE

1

2 3k sT+

-VT

VRmax

VRmin-

AVR : Type 2

VT 11001. s

k sT sTsT sT

1 2 3

4 5

1 11 1

( )

+

- +

Vref VRmax

VRmin

Efdmax

Efdmin

11 1sT

AVR TYPE – 5

ref

+

1/T31/S

+PrefP5

Pmax

C min

P-up

P-dn

1+sT2

0 k1(1+sT1)

-

+

- Pmin

C max

Steam Turbine Governing System

K1: 0.05 Pmax: 1.0T1: 0.1 Pmin: 0.0

T2: 0.03 Pup: 0.1

T3: 0.4 Pdn: -1.0

P

1/(1+sT1 ) 1/(1+sT2)

k1+k2 k3+k4

(1/1+sT3) (1/1+sT4)

k5+k6 k7+k8

Ps

  

Turbine Model

+

111sT-

+

-

1

2T Pmin

Pmax

Ps

ksTsT13

31.

k2

Transient Droop Compensator

Permanent Droop Compensator

ref

+

+

CminP-dn

Cmax

1s

P-up

 

Hydro Governor

Hydro Turbine

Ps1-sT1

1+0.5sT1

DM

T1 (T) : 1.0

Transient Stability Enhancement

Philosophy• Minimize the disturbance influence by

minimizing the fault severity and duration.• Increase the restoring synchronizing forces.• Reduce accelerating torque.

Transient Stability EnhancementMethods :

1. High speed fault clearing.2. Reduction of transmission system reactance.3. Regulated shunt compensation.4. Dynamic Braking.5. Reactor switching.6. Independent pole operation of circuit breaker.7. Single pole switching8. Fast valving.9. Generator tripping.10. Controlled system separation and load shedding.11. High speed excitation systems.12. HVDC transmission link control.

Major references used in the development of Transient Stability Studies Module

1. Dommel, N. Sato “Fast Transient Stability Solutions”, IEEE Transactions on Power Apparatus and Systems, 1972, PP 1643 - 1650.

2. W. Dommel, “Digital computer solution of electromagnetic transients in single and multiphase networks”, IEEE Transactions on Power Apparatus and Systems, April 1969, Vol. PAS-88, PP 388 - 399.

3. IEEE Committee Report, “Dynamic Models for Steam and Hydro Turbines in Power System Studies”, IEEE PES Winter Meeting, New York, Jan./Feb. 1973. (Paper T 73 089-0).

4. IEEE Committee Report, “Proposed Excitation System Definitions for Synchronous Machines”, IEEE Transactions on Power Apparatus and

Systems, Vol. PAS-88, No. 8, August 1969.5. IEEE Committee Report, “Computer representation of excitation

systems”, IEEE Transactions Power on Apparatus and Systems, June 1968, Vol. PAS-87, PP 1460 - 1464.

For further information please contact:

Office Address of ICED-USAID (Indonesia Clean Energy Development – United States Agency for International Development)

•ICED-USAID Jakarta Office: Tifa Building, 5th Floor, Jl. Kuningan Barat No. 26 Jakarta 12710; Phone/Facsimile: +62 21 52964445/ 52964446

•ICED-USAID Medan Office: Jl. Tengku Daud No. 7A Medan 20152; Phone/Facsimile: +62 61 4519675/ 4519058

Contact Person:Pramod Jain, Ph.D.

President, Innovative Wind Energy, Inc.pramod@i-windenergy.com

+1-904-923-6489, http://i-windenergy.com Dr.K.Balaraman Ph.D

CGM, PRDCbalaraman@prdcinfotech.com

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