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Homework 3 Material Type: Notes; Professor: Johnson; Class: Power System Protection and Relaying; Subject: Electrical & Computer Engr; University: University of Idaho; Term: Fall 2012;
Typology: Study notes
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Session 16; Page 1/
Solution
138 kV10 0M VAZS
= j0.1 pu ZS
= Z
S
ZS
=Z
S Vs
= 1.0pu
Bus
Bus
ZL
= j0.1 pu
B
ZL
=Z
L
Bus
138:12 .47kV 50 MV AX = 10%R = 0D-Y
g
ZL
= j0.3 pu
B
on 100MVAand 1 38kV
B
Load3 MWunity
R1 pf
Load3 MWunity
R2 pf
Load3 MWunity
pf
Each
of the 3 feeder
sections has:
Zfeeder
=Z
feeder
= j0.1pu
Zfeeder
= j0.3pu
Bus
Bus
Bus
Assume the following:
Set the coordinating time interval at 6 cycles for each device (relay/recloser control)
The worst case zero sequence imbalance for each load current on the distribution feeder is 20%
The transformer follows the ANSI/IEEE standard phase shift
The fault currents by location and fault type are as follows (note that you will need refer currents
across the transformer for some coordination cases. See spreadsheet on web pageDefine constants:
1000kW
pu
a^
j 120e ^
deg
Summary settings on page 25
012
(^12) a a
1 a^2 a
Session 16; Page 2/
Set base quantities:
B_HV
138kV
B_LV
B_HV
12.47kV 138kV
B_LV
12.47 kV
B_HV
B_LV
Load Currents:
IloadLV
B_LV
IloadLV
pf
LV
Iload_HV
B_HV
Iload_HV
pf
HV
Fault Currents:
At Bus 1:
Three phase fault:
SLG fault:
LL fault:
IA3phB
2091.85A e
j (^) (^90)
deg
1568.9A e
j (^) (^90)
deg
0A e
j 0^
deg
IB3phB
2091.85A e
j (^) (^210)
deg
0A e
j (^) (^0) deg
1811.6A e
j (^) (^180)
deg
IC3phB
2091.85A e
j 30^
deg
0A e
j 0^
deg
1811.6A e
j 0^
deg
Session 16; Page 4/
1. Determine relay settings for feeder relay (B3) and reclosers (R1 and R2). Coordinate settings between theprotective devices for phase faults (phase to phase and 3 phase) and with the transformer damage curve. Include aninstantaneous element for B3 to improve response time.
Determine CTR for B3, R1 and R2:
IloadR
IloadLV
IloadR
R
IloadR
loadLV
IloadR
R
IloadB
loadLV
IloadB
B
Phase element settings for recloser R2:
IloadR2_sec
IloadR2CTR
R
IloadR2_sec
Imin_f_R2_sec
R
Imin_f_R2_sec
Note that I'm using the phase to phase fault. The phase
element will be a backup to the ground element forSLG faults
^ min_f_R2_sec
^ loadR2_sec
Note that there is a big difference between these.
Set pick up for the phase element at 2X load current.
Session 16; Page 5/
IpuP_R
loadR2_sec
IpuP_R
Another option that is acceptable is to split the difference between the load current and the
minimum fault current. This does give better margin for inrush currents, but less resistive faultcoverage.
IpuP_R2_Alt
^ loadR2_sec
min_f_R2_sec
IpuP_R2_Alt
Since this recloser does not coordinate with anything else, set TD for the phase element at the minimum
R2_P
Phase element settings for recloser R1:
IloadR1_sec
IloadR1CTR
R
IloadR1_sec
Imin_f_R1_sec
R
I'm using the Bus5 fault since I want to ensure detection
Also note that I'm using the phase to phase fault. The
phase element will be a backup to the ground elementfor SLG faults
Imin_f_R1_sec
^ min_f_R1_sec
^ loadR1_sec
Again, there is a big difference, just use 2X the load current for the pickup
IpuP_R
loadR1_sec
IpuP_R
Session 16; Page 7/
Now find M for recloser 1 for this fault:
R1P_If_max
IA3phB4CTR
R
IpuP_R
R1P_If_max
Now express TD as a function of time:
VI
t req
t^ reqsec 3.88^2 M
Now for the case at hand:
R1P_calc
VI
t pu_R1P_desired
R1P_If_max
R1P_calc
Set TD for the phase element at:
R1_P
Session 16; Page 8/
Phase element settings for relay controlling breaker B3:
IloadB3_sec
IloadB3CTR
B
IloadB3_sec
Imin_f_B3_sec
B
I'm using the Bus5 fault since I want to ensure detection
Also note that I'm using the phase to phase fault. The
phase element will be a backup to the ground elementfor SLG faults
Imin_f_B3_sec
^ min_f_B3_sec
^ loadB3_sec
Again, there is a big difference, just use 2X the load current for the pickup
IpuP_B
loadB3_sec
IpuP_B
Another option that is acceptable is to split the difference between the load current and the
minimum fault current. This does give better margin for inrush currents, but less resistive faultcoverage.
IpuP_B3_Alt
^ loadB3_sec
min_f_B3_sec
IpuP_B3_Alt
Determine M for R1 and breaker B3 for the largest fault right at the downstream side of R1:
R1P_If_max
IA3phB3CTR
R
IpuP_R
R1P_If_max
Session 16; Page 10/
B3LL_B
B
IpuP_B
R1LL_B
R
IpuP_R
R2LL_B
R
IpuP_R
tpu_R2P_LLBus
tVI
R2_P
R2LL_B
tpu_R2P_LLBus
51.508 ms
tpu_R1P_LLBus
tVI
R1_P
R1LL_B
tpu_R1P_LLBus
160.297 ms
tpu_B3P_LLBus
tVI
B3_P
B3LL_B
tpu_B3P_LLBus
315.19 ms
tpu_R1P_LLBus
tpu_R2P_LLBus ^
0.11 s ^
ok coordination
tpu_B3P_LLBus
tpu_R1P_LLBus ^
0.15 s ^
ok coordination
tpu_R2P_LLBus
tVI
R2_P
R2LL_B
tpu_R2P_LLBus
52.724 ms
tpu_R1P_LLBus
tVI
R1_P
R1LL_B
tpu_R1P_LLBus
173.1 ms
tpu_B3P_LLBus
tVI
B3_P
B3LL_B
tpu_B3P_LLBus
360.42 ms
tpu_R1P_LLBus
tpu_R2P_LLBus ^
0.12 s ^
ok coordination
tpu_B3P_LLBus
tpu_R1P_LLBus ^
0.19 s ^
ok coordination
Session 16; Page 11/
Instantaneous Element for B3: ^
Current for a three phase at 60% from Bus 2 to Bus 3
If3phase_0.6FBus2_3pu
j 0.1^
j 0.1 ^
j 0.2 ^
0.6 j
If3phase_0.6FBus2_3pu
2.174i
pu
If3phase_0.6FBus2_
I f3phase_0.6FBus2_3pu
If3phase_0.6FBus2_
10.07i
kA
IB3_sec
If3phase_0.6FBus2_
B
IB3_sec
IB3_inst_set
As a comparison, here is the time the 51P element at Bus 3 would take to respond to this fault
tVI
B3_P
IB3_sec IpuP_B
0.25 s ^
So big difference in response time.
2. Determine relay settings for feeder relay (B3) and reclosers (R1 and R2). Coordinatesettings between the protective devices for ground faults (SLG) and with the transformer.
Zero sequence load currents
IloadB3_
loadB
IloadB3_
IloadR1_
loadR
IloadR1_
IloadR2_
loadR
IloadR2_
Assume that the ground element currents in the relays are calcuated using measurements from the phase CTs rather than
having separate neutral CTs.Therefore the CTRs do not change from the previous part of the problem
Session 16; Page 13/
Ground element settings for recloser R1:
IloadR10_sec
IloadR1_0CTR
R
IloadR10_sec
Imin_f_R1_3I0_sec
R
Imin_f_R2_3I0_sec
I'm using the Bus5 fault since I want to
ensure detection
^ min_f_R2_3I0_sec
^ loadR10_sec
Again, there is a big difference, just use 2X the load current for the pickup
IpuG_R
loadR10_sec
IpuG_R
Another option that is acceptable is to split the difference between the load current and the
minimum fault current. This does give better margin for inrush currents, but less resistive faultcoverage.
IpuG_R1_Alt
^ loadR10_sec
min_f_R1_3I0_sec
IpuG_R1_Alt
Now the time dial setting will need to account for the coordinating time interval.
60Hz
0.1 s ^
Rather short, but was specified in the problem
Again choose the Very Inverse Curve:
Session 16; Page 14/
tVI
sec
Determine M for R2 and R1 for the largest fault right at the downstream side of R2:
R2G_If_max
R
IpuG_R
R2G_If_max
tpu_R2G_If_max
tVI
R2_G
R2G_If_max
tpu_R2G_If_max
0.05 s
Minimum pickup time for R1 for the same fault: ^ t
pu_R1G_desired
tpu_R2G_If_max
tpu_R1G_desired
0.15 s
Now find M for recloser 1 for this fault:
R1G_If_max
R
IpuG_R
R1G_If_max
Now express TD as a function of time (repeated from above):
VI
t req
t^ reqsec 3.88^2 M
Session 16; Page 16/
Determine M for R1 and breaker B3 for the largest fault right at the downstream side of R1:
R1G_If_max
R
IpuG_R
R1G_If_max
tpu_R1G_If_max
tVI
R1_G
R1G_If_max
tpu_R1G_If_max
0.15 s
Minimum pickup time for R1 for the same fault: ^ t
pu_B3G_desired
tpu_R1G_If_max
tpu_B3G_desired
0.25 s
Now find M for recloser 1 for this fault:
B3G_If_max
B
IpuG_B
B3G_If_max
Now determine time dial for B3 phase
B3G_calc
VI
t pu_B3G_desired
B3G_If_max
B3G_calc
Set TD for the phase element at:
B3_G
Session 16; Page 17/
Now verify coordination for all phase elements at B3, R1 and R2 (look at faults at Bus 4 and Bus 5):
B3SLG_B
B
IpuG_B
R1SLG_B
R
IpuG_R
R2SLG_B
R
IpuG_R
B3SLG_B
B
IpuG_B
R1SLG_B
R
IpuG_R
R2SLG_B
R
IpuG_R
tpu_R2G_SLGBus
tVI
R2_G
R2SLG_B
tpu_R2G_SLGBus
48.274 ms
tpu_R1G_SLGBus
tVI
R1_G
R1SLG_B
tpu_R1G_SLGBus
155.67 ms
tpu_B3G_SLGBus
tVI
B3_G
B3SLG_B
tpu_B3G_SLGBus
266.048 ms
tpu_R1G_SLGBus
tpu_R2G_SLGBus ^
0.01 s ^
OK coordination
tpu_B3G_SLGBus
tpu_R1G_SLGBus ^
0.01 s ^
OK coordination
tpu_R2G_SLGBus
tVI
R2_G
R2SLG_B
tpu_R2G_SLGBus
48.344 ms
tpu_R1G_SLGBus
tVI
R1_G
R1SLG_B
tpu_R1G_SLGBus
156.56 ms
tpu_B3G_SLGBus
tVI
B3_G
B3SLG_B
tpu_B3G_SLGBus
269.45 ms
tpu_R1G_SLGBus
tpu_R2G_SLGBus ^
0.01 s ^
OK coordination
tpu_B3G_SLGBus
tpu_R1G_SLGBus ^
0.01 s ^
OK coordination
Session 16; Page 19/
Fall 2012
I012LL_bus
012
(^1)
I012LL_bus
arg I
012LL_bus
deg
I0LL_bus2_HV
I1LL_bus2_HV
I012LL_bus
1
j 30e ^
deg
I1LL_bus2_HV
arg I
1LL_bus2_HV
deg
I2LL_bus2_HV
I012LL_bus
2
e^
j 30 ^
deg
I2LL_bus2_HV
arg I
2LL_bus2_HV
60 deg
IABC_LL_Bus2_HV
012
IABC_LL_Bus2_HV
arg I
ABC_LL_Bus2_HV
deg
In this case the largest phase has about the same current as the 3 phase fault at Bus 2 when referred to the primary.
Determine CTR for B1 and B2, assuming 40MVA loading on transformer is worst case.:
IloadB
Iload_HV
IloadB
B
Session 16; Page 20/
IloadB
IloadB
IloadB
B
IloadB2_sec
IloadB2CTR
B
IloadB2_sec
I'm using the Bus3 fault since I want to ensure detection
Also note that I'm using the SLG fault since that has the
lowest phase currents on the HV side.
Use fault current referred to HV side
Imin_f_B2_sec
IABC_SLG_Bus2_HV
0
B
Imin_f_B2_sec
^ min_f_B2_sec
^ loadB2_sec
Sufficient difference, use 2X the load current for the pickup
IpuP_B
loadB2_sec
IpuP_B
Another option that is acceptable is to split the difference between the load current and the
minimum fault current. This does give better margin for inrush currents, but less resistive faultcoverage.
IpuP_B2_Alt
^ loadB2_sec
min_f_B2_sec
IpuP_B2_Alt