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
GENERATOR CAPABILITY
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
GENERATOR CAPABILITY
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
GENERATOR CAPABILITY
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
AUTOMATIC REGULATOR STABILITY LIMITS
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
AUTOMATIC REGULATOR STABILITY LIMITS
• 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
AUTOMATIC REGULATOR STABILITY LIMITS
MkdokTM
kkkdokjMT
dampsT
M
knstabilitydynamicofLimittheFor
PQXdXs
E
XsXd
EsyncsTe
stabilitystaticofLimittheFor
skkkksyncsTe
statesteadyFor
kT
skkkdoTjdampsT
kT
skkTkkkksyncsT
kT
skkTkkkkskkkdoTjsTe
jsngsubstitutiandEfdregulatorManualWith
tt
dodo
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231
232
2
2222
23
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22
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23
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11
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11
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)()4321()(
0
1'
)()4'()(,
1'
)()1'4321()(
1'
)()1'4321()()4'()(
0,
AUTOMATIC REGULATOR STABILITY LIMITS
2222
2
2
)'3(]1)6'(3[
}0'3)54(
])3465('34[{23
0)(
0)(
,
)163(
23]}36)54(5[4{
)(
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doTkTekekdoTeTk
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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
AUTOMATIC REGULATOR STABILITY LIMITS
))('(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
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XqXedXXqAEoerk
odXXqeroXqXedXXqAiqoEo
odXXeoerA
EqoEok
All k factors except k3 vary with load
AUTOMATIC REGULATOR STABILITY LIMITS
• 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.
AUTOMATIC REGULATOR STABILITY LIMITS
iqoXqedo
EqoIqoXqetoetoeqo
Eqo
IqoXqetoIqoXqpoIido
Eqo
IqoIpoXqIqoXqetoIpoiqo
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etoo
EqoEo
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eto
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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
T tan,
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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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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