© 2019 SEL
Capability Curve-Based Generator Protection Minimizes Generator Stressand Maintains Power System Stability
Matchyaraju Alla, Armando Guzmán,Dale Finney, and Normann Fischer
Schweitzer Engineering Laboratories, Inc.
Generator Capability Curve
0
50
100
150
200
Q (M
VA
R)
-150
-100
-50
P(MW)
15010050
Lagging PF
Leading PF
0.95
0.90
1
2
3
1. I2R rotor heating
2. I2R stator heating
3. End-iron heating for a round rotor or stability for a salient-pole generator
Fringe Flux Increases During LOF Conditions
End-Core Heating Limit VariesWith the Terminal Voltage
0 0.2 0.4 0.6 0.8 1P (pu)
-0.6
-0.4
-0.2
0
VT = 1.05 pu
VT = 1.0 pu
Q (p
u)
( ) =
21 T
d
k • VCenter P,Q 0,X
= 2 T
d
k • VRadiusX
Steady-State Stability Limit (SSSL)
SSSL is
• valid when the automatic voltage regulator (AVR) is in manualmode
• not valid during transients dueto changes in Xd
Loss of SSSL rarely occurswith modern AVRs
( )I SE
EQ
E VP sinX
= δ
Rotor Position (deg)
PM
P
δ δ 0
Rea
l Pow
er (W
)
SSSL Varies With Terminal Voltage and System Impedance
Q
0P
Weak System
Strong System
Reduced VT
= −
2T
S d
V 1 1Center 0,2 X X
= +
2T
d S
V 1 1Radius2 X X
=2
RATED T
d
MVA • VIntersectionX
Underexcitation Limiter
0
50
100
150
200
Q (M
VA
R)
-150
-100
-50
P(MW)
15010050
H2 Pressure (kPA) Lagging PF
Leading PF
0.95
20610335 0.90
UEL
• The UEL acts to increase the VT setpoint to prevent generator underexcitation
• The UEL should coordinate with SSSL and end-core heating
• The UEL can change based on VT
K, where K = 0, 1, or 2
Coolant pressure/temperature
LOF Element – Impedance PlaneX
Xd
Scheme 1
RXʹd / 2
Z11 pu
Xd
Z2
X
Scheme 1
HeavyLoad
RXʹd / 2
XʹqZ11 pu
Xd
Xʹd
Z2
X
Xd
Scheme 1
Xq
HeavyLoad
RXʹd / 2
LightLoad
Z11 pu
Xd
Z2
LOF Protection – Impedance Scheme 1
0 0.2 0.4 0.6 0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
MW
Capability Curve
MV
AR
UEL
Zone 2 Zone 1
LOF Element – Impedance PlaneX
Xd
Xʹq
Xq
Xʹd / 2XS
DirectionalElement
HeavyLoad
R
LightLoad
Scheme 2
Z1Xʹd
Z2
1.1Xd + XS
1.1Xd – X'd/2
LOF Protection – Impedance Scheme 2
0 0.2 0.4 0.6 0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
MW
Capability Curve
MV
AR
UEL
Zone 1
Zone 2
LOF Protection in the Admittance Plane
• The admittance plane preserves the shape of GCC
• GCC varies with voltage
• SSSL is fixed
B (pu)
0.8
0.6
0.4
0.2
0
SSSLUEL
GCC
G (p
u)
0.4 0 -0.4 -0.81.2 0.8
Z2Z1
• Zone 1 operates quickly for severe events
• Zone 2 coordinates with the UEL
• Zone 3 provides an alarm for operating point encroachment on SSSL
• Zone 4 provides an alarm for generator operation near GCC limits
GCC-Based LOF Protection and MonitoringQ
P
Lagg
ing
Pow
er F
acto
rLe
adin
g P
ower
Fac
tor
Zone 2
Zone 4
Zone 1
Zone 3
Zone 1 Operates for Severe LOF Conditions
• Operates for LOF at heavy loading conditions
• Is set in the power plane but operates in the admittance plane
• Can be set similarly to traditional approaches
Lagg
ing
Pow
er F
acto
rLe
adin
gP
ower
Fac
tor
Heavy Load
Zone 1
P
GCC
Q
Zone 2 Coordinates With UEL
• UEL can have a curved ormulti-segmented characteristic
• Zone 2 element matches the shape of the UEL and varies with VT
K , where K = 0, 1, or 2• Zone 2 element includes
an accelerated path for undervoltage conditions
UEL
Lagg
ing
Pow
er F
acto
rLe
adin
gP
ower
Fac
tor
P
GCC
Q
Light Load
Zone 2
Zone 3 Is Dedicated to Coordinate With SSSL
• Implements the SSSL equation by using only Xd and XS
• Varies with VT2
• Alarms when thePQ locus crosses the SSSL
• Trips when the PQ locus crosses the SSSL AND the AVR is in manual mode OR VT collapses
− = − −
*2 2T T
puS d
j3• V j3• VZ3 Re S • SX X
Zone 4 Monitors GCC Limits
• Is set based on GCC• Adapts to changes in
cooling capabilities• Alarms for any segment
violation
Q
Lead
ing
Po
wer
Fac
tor
Minimum CoolingMaximum Cooling
Lagg
ing
Po
wer
Fac
tor
3
2
1
P
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 1.00 pu
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
UEL
GCC
-5
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 1.00 pu
Zone 1 Per Impedance Scheme 2
Zone 1 Settings
Value (pu)
40P1P 0.6 pu
Tilt –5 deg
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
UEL
Zone 1 (VT = 1.0 pu)
GCC
-5
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 1.00 pu
Coordination of UEL and Zone 2 Characteristics
UEL Settings in AVR [P, Q] (Primary)
Zone 2 Settings Value (Primary)
[40, –12.6] [UELP1, UELQ1] [40, –12.6][20, –18] [UELP2, UELQ2] [20, –18][0, –19.8] [UELP3, UELQ3] [0, –19.8]
Margin 10%Characteristic LinearVoltage Dependency (k) 0
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 2
UEL
Zone 1 (VT = 1.0 pu)
GCC
-5
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 1.00 pu
SSSL Characteristic
Zone 3 Settings
Value (pu)
Xd 1.8
XS 0.2
Voltage Acceleration
0.8
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 2
UEL
Zone 3 (VT = 1.0 pu)
Zone 1 (VT = 1.0 pu)
GCC
-5
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 1.00 pu
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 2Zone 4
Zone 3 (VT = 1.0 pu)
Zone 1 (VT = 1.0 pu)
GCC
-5
UEL
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 0.95 pu
• UEL, Zone 2, and Zone 4 are static
• Zone 1 and Zone 3 change in direct proportion to VT
2
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 2Zone 3
UEL
GCC
-5
Zone 1
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 0.90 pu
Zone 3 moves closerto UEL
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 2Zone 3
UEL
GCC
-5
Zone 1
UEL With Static Characteristic in the Power PlaneK = 0 at VT = 0.80 pu
• LOF conditions for weak systems can lead to pole slipping
• Stable power swings can enter Zone 3 and Zone 1
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
0
P (MW)
Q (M
VA
R)
Zone 3
Zone 1
GCC
-5
Zone 2UEL
UEL With Dynamic CharacteristicK = 1 at VT = 1.00 pu
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
UEL
Zone 1
UEL With Dynamic CharacteristicK = 1 at VT = 1.00 pu
Coordination of UEL and Zone 2 Characteristics
UEL Settings in AVR [P, Q] (Primary)
Zone 2 Settings Value (Primary)
[40, –12.6] [UELP1, UELQ1] [40, –12.6][20, –18] [UELP2, UELQ2] [20, –18][0, –19.8] [UELP3, UELQ3] [0, –19.8]
Margin 10%Characteristic QuadraticVoltage Dependency (k)
1
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
Zone 2
UEL
Zone 1
UEL With Dynamic CharacteristicK = 1 at VT = 1.00 pu
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
Zone 3
UEL
Zone 1
Zone 2
UEL With Dynamic CharacteristicK = 1 at VT = 1.00 pu
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
Zone 4 Zone 2
UEL
Zone 1
Zone 3
UEL With Dynamic CharacteristicK = 1 at VT = 0.95 pu
• UEL, Zone 2, and Zone 4 vary in direct proportion to VT
• Zone 1 and Zone 3 vary in direct proportion to VT
2
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
UEL
Zone 2
Zone 3 Zone 1
UEL With Dynamic CharacteristicK = 1 at VT = 0.90 pu
• Zone 3 encroachesinto GCC
• UEL can protect generator operationfrom reaching SSSL
0 5 10 15 20 25 30 35 40 45
-30
-25
-20
-15
-10
-5
0
P (MW)
Q (M
VA
R)
UEL Zone 2
Zone 3 Zone 1
Case 1: Lack of CoordinationBetween Zone 2 and UEL
Imag
inar
y (s
econ
dary
ohm
s)–20 –10 0 10 20 30
–40
–30
–20
–10
0
10
20
30
Real (secondary ohms)
Capability Curve
Zone 2
UEL
0 20 40 60 80 100
–60
–40
–20
0
20
40
60
80
MW
Capability Curve
Zone 2
MVA
R
UEL
Apparent Impedance Entered Zone 2, Causing Undesired Operation
–60
–40
–20
0
20
40
60
80
MW
MVA
R Operating Point
0 20 40 60 80 100
–40
–30
–20
–10
0
10
20
30
Real (secondary ohms)
Imag
inar
y (s
econ
dary
ohm
s)
Operating Point
–20 –10 0 10 20 30
After Improving Coordination,Apparent Impedance Is Outside Zone 2
–60
–40
–20
0
20
40
60
80
MW
MVA
R Operating Point
0 20 40 60 80 100
–40
–30
–20
–10
0
10
20
30
Real (secondary ohms)
Imag
inar
y (s
econ
dary
ohm
s)–20 –10 0 10 20 30
Operating Point
Seconds
-1
0-0.5
Q (p
u)0.5 1 1.5 2 2.5 3 3.5 4 4.5
20
0.51.5
1
0P (p
u)
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0.5
1.51
I T (p
u)
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0.5
1
0.5
VT
(pu)
1 1.5 2 2.5 3 3.5 4 4.5
(a)
(b)
(c)
(d)
Case 2: Loss of Stability When AVRWas in Manual Mode During Black Start
P (M
W)
Steady State PE
PM
δ (degrees)
Generator Lost Stability When Mechanical Power Was Increased Beyond SSSL
q-axis
d-axis
NRotor
S Rotor
SStator
The Relay Operated Whenthe Apparent Impedance Entered Zone 2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2R (pu)
-2
-1.5
-1
-0.5
0
0.5
1
X (p
u)
Zone 1
Zone 2
Directional Element
SSSL
Xd
X'd2
0 10 20 30 40 50 60P (MW)
-30
-25
-20
-15
-10
-5
0
Q (M
VA
R)
Zone 3 Would Have Operated Faster ThanTraditional Protection
Conclusions• LOF scheme is tailored to GCC and improves
generator protection and monitoring• LOF scheme includes four zones, each with a
specific purpose• Scheme is easy to set Enter UEL and GCC characteristics directly to configure
the scheme
Enter XS and Xd to replicate SSSL
Conclusions• A graphical view of the elements in the PQ and
impedance planes minimizes setting errors• Achieve improved coordination with UEL The K setting allows the relay to exactly match the
dynamics of the UEL
The characteristic can expand and contract accordingto a measurement of cooling capability
Improved coordination can maximize utilization of the generator
Questions?
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