091207 Tutorial Generator

TUTORIAL ON GENERATOR: CAPABILITY

Z1=Z2=0.098, Z0=0.36

Z1=Z2=0.19, Z0=0.608

Z1=Z2=0.082, Z0=0.26

Z1=Z2=0.505, Z0=1.893

GEN: X"d=0.17, Xd=2.1, X2=0.21

GT:21/765KV Z=0.147

ICT: Z=0.082

Seoni

Raipur

Z1bu=0.0212

Korba

Z1bu=0.0212

Ranchi, Z1bu=0.0212

Z=0.055

IBT

132 / 400 KV

ST

11 / 132 KV

UT: 21/11KV

Z=1.503

SIPAT SAMPLE SYSTEM: p.u. on Gen Base

Z1bu=0.0111

System Impedance at gen terminal= GSU+Grid {Seoni lines ׀׀ [ICTs+400 kV lines]} Zsys (normal)= 0.182

Zsys (Both Seoni line out)= 0.231

THE SAMPLE SYSTEM

Tutorial Objectives:

• Develop understanding of the parameters that define normal operation of the generator

• Analyze the various malfunctions that can befall a generator

Operation Scenario:

• The variation in system configuration and voltage have a significant effect on the operation of the generator and associated auxiliary equipment

Variation in system configuration:

• Impact of change in system configuration is shown in sample system diagram

Variation in system voltage:

• Impact of change in system voltage is discussed in next slide

THE SAMPLE SYSTEM

Variation in system voltage:

Light Load Periods:

• Voltage drop through system components such as lines and transformers is minimal

• Generators may be required to operate with reduced field current, consuming excess Vars from the system

High load Periods:

• The increased voltage drop caused by flow of Watts and Vars through highly inductive components, causes system voltage to fall

• The voltage drop caused by an amp of reactive current is greater than that caused by an amp of real current

• The system voltage regulation is amplified by the reactive characteristic of the long high voltage (HV) transmission lines

• At peak system load, generators operate near full field current, supplying Vars to support system voltage

• When the system is in normal configuration, a portion of the generators’ reactive capability should be held in reserve to boost voltage in the event of a forced outage of a major tie line or generator

GENERATOR CAPABILITY

Nameplate rating of sample generator:

• 500 MW at 0.85 power factor, 21 kV

Generator capability curve:

• Nameplate rating defines only one limiting point of operation for the machine

• A reduction in MVAR output would allow some increase in MW output and a reduction in MW would allow higher MVAR output

• These allowable variations are defined by the generator capability curve which defines the Watt/Var (P/Q) operating limit as a function of coolant pressure. The actual coolant pressure for an operating unit is often less than the design maximum pressure

• Capability curve is normally plotted at the rated terminal voltage for the generator

• Capability curve is a composite of three distinct limits as shown in the next slide


0 0.2 0.4 0.6 0.8 1-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Sample Generator Capability Curve

MW (PU)Lea

din

g(U

nd

erex

cite

d)

M

VA

R(P

U)

L

agg

ing

(Ove

rexc

ited

)

Terminal Voltage= 1.0PU

0.9PF

A

C

B

D

0.85PF


Three distinct sections of the capability curve:• Right hand section (B-C):

It represents the limit imposed by the ampere rating of the stator winding

• Top section (A-B): The ampere rating of the field winding limits the output of Vars into the

power system termed as lagging Vars

• Bottom section (C-D): It defines the maximum Vars the generator can consume from the power

system termed as leading Vars. This limit is the result of heating in the end laminations of the stator core

which is caused by the flux that flares from the end of the stator when the generator is operating at low field current

Capability curve for a hydro unit:• Hydro units are of salient pole construction and do not have end core

regions• The leading Var limit is determined by the current rating of the stator

winding


0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Generator Capability Curve: Steam, Gas and Hydro Units

MW (PU)

Un

der

exci

ted

MV

AR

(PU

)

Ove

rexc

ited

Terminal Voltage= 1.0PU

0.9PF

A

C

B

D

0.85PF

GasTurbine

Steam

Hydro

VOLTAGE LIMITATIONS

GSU limits:

• No load requirement:

Voltage limit at no load= 110% rated voltage for any tap position

• Rated load requirement:

GSU is operating on 784.125 kV tap with impedance of 14.7%

I= kVA/Esec= 1.0/1.05= 0.952 0.76= 36.90-ے -j0.57

Ep=1.05+j0.147(0.76-j0.57)= 1.13 + j 0.11 = 1.135 <5.1°

• Therefore max allowable continuous voltage on GSU primary (LV) winding is 13.5% as defined by requirement of 0.8 pf, rated load with 105% rated voltage at secondary terminals

Generator limit:

• ANSI/ IEEE C50.12 and C50.13 define permissible operating range of cylindrical rotor or salient pole machines to be ±5% rated voltage

SYSTEM LIMITATIONS

-Q

+Q

P(P,Q)

Center = Et2/Zs

Radius=Et*Esys/Zsys

Et

ZsysEsys

• The MW output of generator is limited by driving torque available from turbine.

• The Var output is function of Et, Esys and Zsys. It is common to encounter voltage limitation before generator Var limit is reached.

• The relationship between P and Q, Esys and Zsys is often represented by power circle diagram

Power circle diagram• Centre= Et2/Zsys• Radius= Et*Esys/Zsys• If resistance is neglected, the center is

located on Var out axis as shown in figure

SYSTEM LIMITATIONS

Practical operating limits: System normal

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

Power (pu)

U/E

R

ea

cti

ve

(p

u)

O/E

0.85

0.9

Turbine LimitField Limit

Et= 1.05

Et= 0.95

Stator Limit

End core Limit

Esys= 1.0Zsys= 18.2% (Gen Base)

• The MW output of generator is limited by driving torque available from turbine.

• The Var output is function of Et, Esys and Zsys. It is common to encounter voltage limitation before generator Var limit is reached.

• The relationship between P and Q, Esys and Zsys is often represented by power circle diagram

• Centre= Et2/Zsys• Radius= t*Esys/Zsys

SYSTEM LIMITATIONS

Practical operating limits: Seoni Bus outaged

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

Power (pu)

U/E

R

ea

cti

ve

(p

u)

O/E

0.85

0.9

Normal System

Seoni Lines Out

SYSTEM LIMITATIONSPractical operating limits: All lines in, vary grid voltage

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

Power (pu)

U/E

R

ea

cti

ve

(p

u)

O/E

0.85

0.9

Esys = 1.0

Esys = 0.96

Esys = 1.055

Esys = 0.96

Esys = 1.0

Esys = 1.055

GENERATOR CAPABILITY VARIATIONS WITH VOLTAGE

• Generator Terminal voltage is provided operating range of 95-105 % but capability curves are only available for rated voltage (100%).

• It is possible to estimate portions of the capability curve for voltages other than rated voltage.

STATOR CAPABILITY VARIATIONS WITH VOLTAGE

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0MW (pu)

Lea

d(U

/E)

MV

AR

(pu

)

Lag

(O/E

)

0.85 PF

0.9 PF

Ra0.95 Ra

1.05 Ra

The Length of Ra in MVA = Rated KA x Rated KV x √3

- Et = 0.95

- Et = 1.0

- Et = 1.05

FIELD LIMIT VARIATIONS WITH VOLTAGE

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0MW (pu)

Lea

d(U

/E)

MV

AR

(pu

)

Lag

(O/E

)

0.85 PF

0.9 PF

1.05 Rf1.052 C

1.0 RfC0.95 Rf

0.952 C

C = -Et2 / Xd

R = Et x EI / Xd

LEADING VAR LIMIT VARIATIONS WITH VOLTAGE

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0MW (pu)

Lea

d(U

/E)

MV

AR

(pu

)

Lag

(O/E

)

0.85 PF

0.9 PF

Et= 1.05

Et= 1.0

Et= 0.95

Centre (P,Q) =

(0 , K1 x Et2 / Xd)

Radius =

K2 x Et / Xd

• K1 and K2 are derived from published curves.

• Leading Var capability is markedly reduced as Et increases.

TUTORIAL ON GENERATOR: STABILITY LIMITS

CLASSICAL VIEW OF STEADY STATE STABILITY

Classical View:

SinXsXd

EsEP

XqXdFor

XsXqXsXd

XqXdESin

XsXd

EsEP

IE

SIE

*

2sin))((2

)(* 2

Es

I(Xd+Xs)

EI

δ

• Generator is operating at fixed excitation on manual regulator

• Stability limit is found by changing system parameters very slowly to eliminate oscillatory parameters and need for damping.

• Stability limit occurs when δ=90 for salient machines and δ<90 for non-salient machines.

CLASSICAL VIEW OF STEADY STATE STABILITY

Power Angle Curve

00.2

0.40.6

0.81

1.21.4

1.61.8

0 20 40 60 80 100 120 140 160 180

Degrees

Po

wer

(P

U)

E=100%

Reduced E

Pe=Electrical Power

Pm=Mechanical Power

Operating point

MANUAL REGULATOR STEADY STATE STABILITY LIMITS

Ir Et

Ir * Xs

Ix * Xq

IIx

Ix * Xs

Ir * Xq

Eq

β

α

Es

Generator current Voltage Vector Diagram defines Es and Eq in terms of Et, Ir and Ix.

MANUAL REGULATOR STEADY STATE STABILITY LIMITS

XsXdtE

RXdXs

tEC

PQXdXs

tE

XsXdtE

PXdXs

tQEXsXdQtE

XdXstE

IxXqEt

IrXq

IxXsEt

IrXs

IxXsEt

IrXs

IxXqEt

IrXq

whenoccursLimitStabilitytheXqXdWith

Et

QIx

Et

PIr

11

2

211

2

2,0

22

11

2

2211

2

2

22)(22

2

10

tan,tan

0tantan1,tantan1

tantan)tan(

090,

,

MANUAL REGULATOR STEADY STATE STABILITY LIMITSCircle Diagram of Manual Regulator Steady State Limit

XdXe

EtR

XdXe

EtjC

11

2

11

22

2

Weak System

Strong System

Above circle defines stability criterion against which MEL limit is usually evaluated

• AVR rapidly varies field voltage in response to system condition.

• The change in field voltage for a given change in terminal voltage defines the gain of regulator (ke)

• The regulator time constant (Te) and generator field time constant defined the speed of field current response which ultimately determines the response at generator output terminal.

• AVR sharply increases synchronizing power.

• But, the gain and speed of AVR reduce system damping torque.

• In the absence of adequate damping torque, minor system oscillations may grow in magnitude until connected generators and tie lines trip.

AUTOMATIC REGULATOR STABILITY LIMITS

AUTOMATIC REGULATOR STABILITY LIMITS(Simplified Block diagram)

*1

)(314)(

1*)()(

)()()()(

90

)(*)(

)(1

0

DKTmTa

ss

s

MssTas

sTdsTssTmsTa

withquadratureinisTd

byleads

sDsTd

withphaseinisTsyn

sKTs

• The Synchronizing and damping torque produced as a result of the interaction of the generator and system determine the stability of the power system.

• The boundary of steady state stability occurs when Tsync=0

• The boundary of dynamic stability occurs when Td=0

ΔTm

Δ

Δ

Δ

ΔδΡδ=ω


1628,

1314,

21sin211

22

1

113141314

1

)()(

)(

314/)()(

)()(

*1

2

1

2

k

nDFactorDamping

M

knFrequencyNatural

tnnten

nn

sL

sk

Dsk

Mk

sTms

sforsolvingAnd

sssAnd

ssMsTangSubstituti

DKTmTa


• The Rotor Angle Δδ varies as an exponentially decreasing sinusoidal function.

• Damping factor, ξ, controls rate of decay and frequency of oscillation.

• If ξ = 0, oscillation is sustained at a fixed magnitude at natural frequency.

• If ξ = -ve, oscillation grows without bound and instability occurs

AUTOMATIC REGULATOR STABILITY LIMITS(Including generator flux linkages but no AVR)

)'1(

))](4)((32)'31)((1)['31('31

)](4)([32)'31)((1

)()()(

)(314

)(

)()()()(

)(4)()(

)('31

32)(

)(1)(

223

2

2

doTks

skSEfdkkdoTskskdoTskTe

doTsk

skSEfdkkdoTskskTe

sTbsTasTeTorqueElectrical

sTcMs

s

sTbsTasTmsTc

skSEfdsEe

sEedoTsk

kksTb

sksTa

ΔTm

Δ

Δ

ΔΔδ

Δ

ΔEfd

*

* ρδ=ωden(s)=1 +sK3T’do


MkdokTM

kkkdokjMT

dampsT

M

knstabilitydynamicofLimittheFor

PQXdXs

E

XsXd

EsyncsTe

stabilitystaticofLimittheFor

skkkksyncsTe

statesteadyFor

kT

skkkdoTjdampsT

kT

skkTkkkksyncsT

kT

skkTkkkkskkkdoTjsTe

jsngsubstitutiandEfdregulatorManualWith

tt

dodo

do

do

do

231

232

2

2222

23

22

232

23

22

23

22

23

22

23

22232

'314

13144'

0)(

1314,

11

2

11

2,0)(

,

)()4321()(

0

1'

)()4'()(,

1'

)()1'4321()(

1'

)()1'4321()()4'()(

0,


2222

2

2

)'3(]1)6'(3[

}0'3)54(

])3465('34[{23

0)(

0)(

,

)163(

23]}36)54(5[4{

)(

0)(

0

doTkTekekdoTeTk

dTkkekk

kekkkkdoTeTkkTekjk

dampsT

dampsT

n

stabilitydynamicofLimittheFor

kekk

kkkkkekkkkek

syncsT

syncsTand

statesteadyFor

The torque equations for the system under AVR control are derived from the expanded Block Diagram

Δ

Δ

Δ

ΔTm

ΔE’q

ΔEfd

Ee Δet

Δδ

Δet ref

*

* ρδ=ω


))('(2

)('16

sin)(cos'

cos)'(sin5

]cossin)[()'(

4

1))('(13

))('(12

]cos)'(sin))('[(

cos)'(sin[1 ]

XeXqdXXeerA

AerXq

eto

edo

A

XqXedX

eto

eqok

A

oEoXqXeoEoerdXeto

eqo

A

oEodXXeoEoerXqeto

edok

oeroXqXeA

dXXdEok

A

XqXedXXdk

A

XqXedXXqAEoerk

odXXqeroXqXedXXqAiqoEo

odXXeoerA

EqoEok

All k factors except k3 vary with load


• Besides specialized computer based study programs, electronic spread sheets and iterative solvers can be used to determine stability limits.

• One such spreadsheet downloaded from CRC Publishers is provided in the program content.

• The parameters including system voltage Eo, generator terminal voltage Eto and real and reactive current components are used to calculate K factors. These parameters are calculated from standard generator vector diagram and applicable equations are given in next slide

• Steady state and dynamic stability limits are found using Excel’s “Goal Seek” tool to find the value of Q&P necessary to produce Zero Tsync or Tdamp.


iqoXqedo

EqoIqoXqetoetoeqo

Eqo

IqoXqetoIqoXqpoIido

Eqo

IqoIpoXqIqoXqetoIpoiqo

EqoEoqoIpoIXeXqeIporXeXqIqoeto

etoo

EqoEo

eetoIqorqoIpoIXqerXeXqetoIpoo

erIqoIpoXeIqoXeerIpoetoEo

IpoXqIqoXqetoEqo

eto

QIgo

eto

pIpo

]/)[(

)]([

])([

)([cos

)(sin

)()(

)()(

,

2

22]

22

22

22

STABILITY LIMIT PLOTS

Manual-SS

AVR-Dyn

AVR Gain Ke = 10

AVR-SS

STABILITY LIMIT PLOTS

Manual-SS

AVR-Dyn Ke =30

AVR-Dyn Ke = 10

AVR-SS

Ke = 10 or 30

TRANSIENT STABILITY

Ability of system to remain synchronized following an abrupt change such as a fault or switch of a key line

Power Angle Equation:

X’d value is typically used in power angle equation to construct swing loci because lower impedances produce a smaller swing diameter

ZsXdXZ

SinZ

EsEgPe

TRT

T

'

*

Slip (S, %) Generator Impedance (Xg) Remark

0 Xd

0.33 2X’d Range of slip for a typical event of loss of synchronism50 X’d

100 X’’d

TRANSIENT STABILITY

Power Angle Plot

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160 180

Degrees

Po

we

r (P

U)

Pe – Both Lines In

Pe – One Line Out

Pm

δ1 δ2

TRANSIENT STABILITY

Power Angle with line switching

Pe – Both Lines In

Pe – One Line Out

A

A1

A2

B

C D Pm

TRANSIENT STABILITY: Power Angle Plot for Fault Condition

Initial Operating point

Open CB1

Open CB2

Both Lines In

Bkr 1 tripped

Line B Out

Fault Both Lines InA B

CD

EFJOPm Pm

A1A2

A3

Line AEg EsLine B

1 2

Stability exists whenA3 > (A1+A2)

TRANSIENT STABILITY

Classical Swing Impedance Characteristic:

• Graphical representation for the system impedance trajectory as seen at generator terminal

XgCotjZsXXg

Z

nEsEgFor

XgSinn

SinjnnZsXXg

I

VZ

SinjandEsEgnLetting

XgZsXXg

EsEgEgV

IXgEgV

ZsXXg

EsEgI

TRR

TRR

R

TRR

R

TR

21

2

)1(

)cos(

)cos()(

cos1/

22

TRANSIENT STABILITY

Eg EsX’d XsysXtr

X

- R R

B

A Eg

Swing Impedance Path

PX’d

Xtr

ZsysEs

δ=120° δ=90°

δ=60°

TRANSIENT STABILITY

• At δ =180°, pole slip occurs. There exists a critical swing angle for any system from which the system cannot recover. As a thumb rule, critical swing angle δc is considered to be 120°.

• The plots consider variation of δ but, all other system parameters are held constant.

• In reality, swing locus shows the effect of rotor oscillation and changes in Eg.

• Eg is controlled by generator constants and type of excitation (manual or automatic), governor action, mechanical damping of nearby units, shunt loads, shunt capacitance effect and generator saliency.

• Computer simulations are required to obtain accurate impedance (swing) plots.

• If a system has one or two generators isolated from other machines, impedance plot can be derived using Excel Workbook provided in the program.

LOSS OF SYNCHRONISM(Stable Swing With Manual Regulator)

LOSS OF SYNCHRONISM (Stable Swing With Auto Regulator)

LOSS OF SYNCHRONISM (Unstable Swing With Manual Regulator)

LOSS OF SYNCHRONISM (Unstable Swing With Auto Regulator)

TUTORIAL ON GENERATOR: LOSS OF SYNCHRONISM

LOSS OF SYNCHRONISM

Event:

• Normally, all generators within an interconnected power system operate at like frequency with their magnetic poles coupled through interaction with the network

• Interconnecting force is elastic allowing some angular play between generators in response to system disturbances

• A loss of synchronism occurs when the bonding force is insufficient to hold a generator or group of generators in step with rest of the power system

Causes:

Loss of synchronism can occur when

• Equipment outages or low voltage weaken the system or

• The force is inadequate to restrain extreme rotor excursions following a system fault or switching

LOSS OF SYNCHRONISM

Mechanism:• A loss of synchronism results from some form of system instability• When the manual regulator is in service, the systems can be vulnerable to the

loss of steady state or dynamic stability. When AVR is in service, minimum excitation limiter (MEL) is provided to prevent these types of instability

• However, a generator is most likely to loose transient stability. This is the ability of the system to remain synchronized following an abrupt change such as a fault or switch of a key line

• Out of step generator or generators operate at slightly different frequencies. A generator that pulls out of step ahead of the system with a slip frequency of 4 Hz, will be operating at a speed of 1+slip/50= 1.08 pu or 8% over speed.

• The system and generator voltage vectors sweep past one another at slip frequency, producing a pulsating current with peak magnitude potentially greater than a 3 phase fault at the generator terminal

I= (Eg ے δ– Es)/ (Xg+Xtr+Zs) • If Eg=Es, no current will flow when δ =0. System will appear as an open circuit

with infinite impedance. As δ increases, so will the current untill the system reaches a separation of 1800. At this point, the driving voltage will be twice normal, the sum of Eg and Es, and the current will be at a maximum.

LOSS OF SYNCHRONISM

• Electrically, this condition is identical to that produced by a 3 phase fault located one half the electrical distance to the remote terminal or at Z= 0.5(Xg+Xtr+Zs). This imaginary fault location is called the electrical center of the system

• The location of electrical center denotes the severity of the event with respect to the generator. When it is located in the GSU transformer or generator itself, it represents an event equivalent to a GSU fault or generator fault with severe stress to local equipment

• The location of the system electrical center is not fixed. The center will move away from the generator as the system impedance increases due to equipment outages.

• The center is also slip dependent because Xg varies slip frequency.

• Electrical center also varies with system and generator voltages.

LOSS OF SYNCHRONISM

Turbine Generator Damage:

• As the electrical center moves from the system into generator, the current magnitude increases and with it thermal and mechanical stress on the generator and GSU transformer.

• On a strong system, Xtr+Xs can be less than Xg: the electrical centre will lie within generator and current at 1800 exceeds that of a 3 phase fault at the generator terminals.

• During out of step event, Xg=X’d but with low Xtr and Xs, the out of step current can exceed the designed machine withstand limit (sub transient fault current at the generator terminal). The absence of DC offset current does lessen the stress from that of the fault case

• The point is that as the location of electrical center moves towards the neutral end of generator, current induced thermal and mechanical stress can approach design limit. The generator is exposed to these conditions each slip cycle. After a severe event, restacking of the stator core may be required. Local hot spots may also damage stator windings

LOSS OF SYNCHRONISM

Generator rotor:

• Slip frequency will induce currents in the rotor. Prolonged exposure to these currents will cause thermal damage to damper windings, rotor teeth, wedges and rotor body.

Torque pulsations:

• The current pulsations associated with each slip cycle causes severe torque transients in the turbine generator shaft. The stress is at a maximum during initial period of each torque pulsation. This is the period when shaft damage normally occurs.

• The fatigue life of the shaft can be used up after a few pole slip events.

• If slip cycle frequency coincides with a normal frequency of one of the shaft sections, shaft failure can result

LOSS OF SYNCHRONISM

Excitation System:

• Prolonged asynchronous operation can also cause diode failures within the excitation system. During each pole slip, these diodes will experience high voltage as they block reversed rotor current. The over voltage stresses insulation and can result in breakdown

Power System:

• A loss of synchronism by one or more units will result in cyclic voltage fluctuations as generators slip poles

• These voltage dips can cause disruption to customers served from the grid. Induction motors may stall and synchronous motors may loose synchronism. Other processes would be disrupted when the voltage dips cause the motor contactors to drop out

TUTORIAL ON GENERATOR: LOSS OF FIELD

LOSS OF FIELD

Event:

Excitation to the generator field winding fails

Causes:

Equipment failure, inadvertent opening of the field breaker, an open or short circuit in the excitation system, or slip ring flashover

Mechanism:

• If and Eg decay at a rate determined by the field circuit time constant

• Var output decreases and becomes negative as generator draws increasing reactive from power system to replace excitation formerly provided by the field circuit. Var consumption can exceed the generator MVA rating

• The reduction in Eg also weakens the magnetic coupling between rotor and stator. At some point during the decay, the coupling will become too weak to transmit prime mover output power to the electrical system i.e. loss of steady state stability occurs

LOSS OF FIELD

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160 180

Degrees

Po

we

r (P

U)

Field Current = 100% FL

80% FL

40% FL

60% FLPm

δ at FL

LOSS OF FIELD

• The effect of decaying Eg is to reduce amplitude of power angle curve with time• The intersection of Pe and Pm define the operating angle (δ) of the generator

rotor with respect to the system voltage• δ increases to maintain power equilibrium

• When δ reaches 900 electrical, power output is at maximum. If decay beyond this point renders the generator incapable of transmitting all the mechanical power to the electrical system

• The excess mechanical power is dissipated by acceleration of the generator rotor. As speed increases beyond synchronous speed, synchronism is lost

• As speed increases, turbine output decreases as dictated by droop setting of the governor and electrical power increases as dictated by the slip torque characteristic of the power system.

• Eventually, Pm and Pe will reach a new equilibrium, with generator operating above synchronous speed as an induction generator drawing excitation from the power system in the form of Vars

cereacgeneratoreffectiveXgXsystXtrXgimpedancetransferXXT

EgEsPeEquationSwingPower

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sin:

LOSS OF FIELD

• A loss of synchronism following a field failure is not a high speed phenomenon

• Typically, it will take a fully loaded steam turbine generator several seconds to loose synchronism

• Final slip is affected by the droop setting of the governor, system impedance and initial loading. For a machine initially operating at full load, final slip is typically in the 2 to 5% range.

• The power output of the induction generator is less than the pre failure power output

Impact of LOF operation:

• The final or steady state slip of the induction generator is important because it determines Xg which in turn defines the impact of post LOF operation

• A LOF event can be represented by XT, a series circuit including Xg, Xtr and

Xsyst. Xg decreases with increasing slip and slip increases with initial generator load.

• Thus, the higher the initial load, the greater the asynchronous current and more severe the consequences to both the generator and the connected system

LOSS OF FIELD

Other factors affecting LOF severity:

• The initial load is the major factor in determining the potential damage from a LOF event.

• At first glance, a strong power system would appear to offer high post fault currents. This is not necessarily true. A reduction in Zs will reduce the final slip frequency and increase the power output from the induction generator. Because of lower final slip, Xg will increase thereby reducing the stator current. Thus, a failure on a strong system may actually be less damaging than a failure on a weak system

• A LOF event is more likely to be initiated by a shorted field circuit than an open field circuit. The former will produce higher stator current, larger reactive intake and generally more severe consequences than would be experienced with an open field circuit.

LOSS OF FIELD

• When machines are connected directly to a common bus, the potential for damage increases. As If decays on the unit with failed excitation, AVR on healthy machines will initiate full field forcing to support the falling bus voltage. This increases the Var supply to the faulted machine. The situation is aggravated when the units are connected to a strong system. An IEEE study documents a study of 2 generators connected to a common bus and a moderate strength power system. The unit with failed excitation saw a peak MVA loading in excess of 2 pu and peak stator current in excess of 2.5 pu. The healthy unit was also severely stressed with a peak MVA of 1.5 pu and peak current of 2 pu

• A LOF on a hydro unit at light load may not result in a loss of synchronism since salient pole machines can carry up to 25% rated load following a loss of field without loss of synchronism. However, once a salient pole machine looses synchronism, it accelerates rapidly to a high slip. The slower acting hydro governor and the fact that a salient pole machine makes an inefficient induction generator causes this response. If the hydro generators field is lost near full load, the effects are the same as for steam turbine units.

LOSS OF FIELD

System Impact:

• A generator operating asynchronously without excitation can consume Vars in the range of 0.4 to 1.9 times the unit name plate rating as slip increases from near zero to 4%

• The impact of LOF on the system is determined by it’s ability to withstand not only the loss of real and reactive output, but to supply the large Var demand imposed by the faulted generator after LOF.

• Inability of system to meet VAR demand of failed unit can result in a widespread system outage

• Initially, excitation on nearby generators will go to full boost to supply reactive to the generator with failed excitation and support the grid voltage, The large Var influx can overload and trip the area transmission lines.

• If the failed generator is not disconnected, field current limiters on the adjacent units will time out, initiating an immediate reduction in field current to continuous rated value? The resulting reduction in area Var support is likely to produce severe voltage degradation. System voltage collapse or multi machine instability can result causing a regional system outage

LOSS OF FIELD

System Impact:

• Dynamic studies similar to those used in transient stability analysis are required to determine accurately system response to a LOF event. These studies are time consuming and expansive.

• A screening technique using a standard load flow can determine where full dynamic studies are required.

• At the generator of interest, a worst case LOF event is simulated in load flow by setting the reactive flow into the machine at (-)1.5 times the name plate MW rating.

• If a Load flow solves with reasonable system voltages, the system is considered capable of withstanding the LOF event

• However, if the solution fails to converge or severely depressed voltage results, the event must then be modeled dynamically to determine if the system can survive the field failure.

LOSS OF FIELD

Generator damage:

• The potential for generator damage following a LOF is dependent on generator design and final slip during asynchronous operation.

• Although the asynchronous capabilities are not addressed in the standards, modern expectations, particularly for conductor cooled machines are much lower, with damage in as little as 10 second for some instances.

• The improved cooling techniques result in larger MVA ratings from a given physical size. These machines have higher per unit impedance and lower inertia than indirect cooled machines and therefore tend to operate at a higher slip. This reduces Xg during asynchronous operation, increasing the stator and induced rotor current

• Conductor cooled machine will also have lower thermal time constants, hence faster temperature rise for a given current than indirect cooled machines

Load before LOF Final slip Effect on generator

<=30% rated load 0.1-0.2% Damage unlikely

100% rated load 2-5% Exposed to damage

LOSS OF FIELD

Stator winding overload:

• The large –Q and depressed Et following a LOF load can give rise to Is well above rated. Peak currents of 2.5 pu have been reported

• ANSI C50.12,13,14 defines a required short time O/L capability for stator windings which is the limiting value to prevent stator winding damages

LOSS OF FIELD

Rotor damage:• Can occur as a result of rapid heating caused by currents induced in

rotor• LOF by shorted field circuit: the induced current is divided between

rotor structure and the field winding. This reduces heating in rotor structures

• The induced field current is generally below rated in salient pole machines and only slightly above rated in a few cases with cylindrical rotor machines

• LOF by open field circuit: maximum rotor heating occurs. Also, damaging over voltage will be induced in the field circuit for all but very low slip events.

• In a cylindrical rotor machine, induced currents flow along the length of rotor body, creating heat in teeth, slot wedges, and, if present, the amortisseur winding. Thermal damage is most likely to occur near the ends of the rotor where currents converge to enter the retaining rings

• In a salient pole machine, induced currents are found in the amortisseur bars located in each pole face

LOSS OF FIELD

Stator end core damage:

• Thermal damage at the ends of the stator core of a cylindrical rotor machine when operated at reduced field current.

• This limitation forms the leading Var boundary of the generator capability curve

• A LOF represents the extreme in field current reduction.

• A LOF from full load can result in leading Var loading in excess of the generator’s MVA rating. Typically, the generator manufacturer’s capability curve limits leading Var intake to about 40 to 60% of the generator rating

• The reduction in terminal voltage that accompanies a LOF markedly increases the Var capability, but this increase is insufficient to accommodate a potential 2.0pu leading Var inflow.

• The voltage dependent Var limitation is circular on the P-Q plane with the following characteristics:

Centre (Q,P) = 0, K1*et2/Xd Radius = K2*et/Xd

• Excessive end core heating would result in bluing of metallic end core structure, charring of stator winding insulation and failure of the insulation medium between laminations.

LOSS OF FIELD

Torque pulsations:

• Originate from the electrical and magnetic difference between the d- and q-axes.

• More severe for shorted field circuit than an open circuit condition

• The torque magnitude associated with a LOF is less severe than that accompanying an out of step condition with full excitation, but mechanical damage remains a significant concern following a LOF event

• Asynchronous operation exposes the generator and the prime mover to two stress cycles each slip cycle.

• Fatigue is cumulative, and extended asynchronous operation can consume a considerable portion of the fatigue life of the shaft and associated structures, including the machine foundations

• These pulsations are also potentially resonant with shafts, turbine blades and other components.

Thank you

MINIMUM EXCITATION LIMITER

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TRANSIENT STABILITY

Criterion for determination of non-recoverable Swings:• Improved cooling techniques have increased generator impedance whereas

system impedance declined due to reinforcement• Electrical Centers moved from transmission system into the GSU and the

generator itself• Following a system disturbance, generator rotors experience angular

perturbations as they attempt to adjust a new steady state operating condition• In a stable system rotor oscillations are damped ; initial angular displacement is

largest and proportional to the severity of disturbance• There exists a maximum swing angle known as critical swing angle (δC) from

which the system can not recover• System modeling on a transient stability program is best way to determine δC.

Tools and time to use them are generally not available to all and a less accurate method is often adopted.

• A general assumption is made that δ>1200 is not recoverable and thereafter instability is imminent

• The minimum system impedance and X’d values are typically used to construct swing loci because lower impedances produce a smaller swing diameter

TRANSIENT STABILITY

Swing Velocity:

• A fault changes system impedance instantaneously while impedance change during a system transient is constrained by inertia and generator time constants

• GE publication GER-3179 (J Brady) lists the following average velocities for the first half of the first slip cycle

• Maximum acceleration occurs after each pole slip at the midpoint of the slip cycle

• Plot indicates slip < 5Hz at the beginning of second slip cycle. This value is good estimation of upper limit of slip being calculated for a light machine (H=3)

Unit Type ωs, deg/sec ωs, slip cycles/sec

Steam units 1296-1728 3.6-4.8

Tandem units 250-400 0.694-1.11

Compound units 400-800 1.11-2.22

LOSS OF FIELD

• The full load LOF event depicted in figure in earlier slide is typical

• It produces cyclic Is with variation between 1.14 and 2.13pu each slip cycle

• In theory, the stator heating is related to the RMS current over a slip cycle.

• The incremental form for RMS current is

tITRMSI

T

021

• In the case of the full load LOF event depicted in figure, the RMS current at final slip was calculated as 1.74pu

• ANSI standards require that this current is limited to 22 sec to prevent winding damage

• The stator waveform is not sinusoidal, because slip is not constant through the slip cycle. Figure in next slide shows the stator current waveform for the same LOF condition but with Xs reduced from 0.2 to 0.1.

• The incrementally calculated RMS current for this condition is 1.34pu. The corresponding stator overload limit for this current is 50 sec from ANSI standards.

• This demonstrates that generator stress can increase with increased system impedance

IRMS can be calculated from incremental currents and slip cycle duration determine from the spreadsheet

LOSS OF FIELD

• NPS current induces rotor currents at 2fs whereas frequency of asynchronously induced rotor current is equal to slip frequency and is usually less than 5 Hz

• As frequency increases, skin effect increases the effective resistance of a conductor . Thus, higher I2R and more heating per ampere are produced by NPS operation than those by asynchronous operation

• The 2fs current produced by NPS current does not have sufficient penetration into the rotor lots to induce current into the field winding. Therefore, the NPS limit is, is, in effect, based on an open field circuit

• The NPS limits are based on the limiting temperature for pole face amortisseur winding in salient pole machines and teeth or wedges in round rotor machine with induced currents at 2fs. A realistic estimate of asynchronous limits requires an adjustment of conductor resistance for lower frequency asynchronous case

• An AIEEE paper gives expression Tmax = CI2t/d2

Where Tmax= the limiting temperature for a component, C= constant for a particular machine, I= stator current, and d= depth of penetration

• The physical differences between conducting structure in salient and round rotor machines, result in different treatments for the resistance variation

LOSS OF FIELD

• The NPS short time limit is defined in terms of K, a constant representing the maximum (I2eq)2*t value the machine can withstand

• The I2eq term refers to equivalent RMS pu NPS current in the event the current is time variant

• IEEE standard C37.102:

K= 40 for salient pole machine

K= 10 for large conductor cooled machine

• For pole face amortisseurs on a salient pole machine and other small conductors, ‘d’ varies proportional to 1/√f

• Assume IRMS = 1.74pu at final slip under asynchronous operation

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LOSS OF FIELD

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