Class #30 Review for Exam 3 5-6-04
Transcript of Class #30 Review for Exam 3 5-6-04
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Class 30
Review for Exam 3
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Class 17
Start Voltage Regulation Definitions
Review two winding transformers
Autotransformer
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Class #18
Step-Voltage Regulators
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Step-Voltage Regulator
+
-
V
SL
+
-
V
R
L
Source
Load
-
PreventiveAutotransformer
ReversingSwitch
Series
Winding
ShuntWinding
PTControl
ControlCT
S
L
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Control Circuit
Line Dr op
Co mpensato r Relay
Voltage Time
Delay
Motor
Operating
Circuit
Control Current TransformerLine C urrent
Control Po tential Transformer
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Control Settings
Voltage level - voltage to hold at the load
center
Bandwidth - allowed variance from voltage
hold
Time delay - time before tap change takes
place
Line drop compensator - equivalent R and
X from regulator to the load center
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Type A Step-Up Regulator
SL
SL
E2
N2
-
VL
+
+
+
- -
N1
E1
L
S +
-
VS
IS
LIL
R I2
I1
S
IS
SV
+
-
L
LI
+
-
VL
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Type B Step-Up Regulator
+
-
V
S
SL
+
-
V
R
S
L
+
-
I1
E1
+
-
E
I2
2
IS
IS
IL
S
+
SV
-
SL
LV
L
LI
IS
+
-
L
N2
N1
L
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Regulator Ratio as Function of
Tap Position1 0.00625_ _
1 0.00625_ _
0.00625 120 0.75 _ /
a TapR Type A
a TapR Type B
volts step
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Generalized Matrices
Type A: Type B:
1
0
0
R
R
aa
b
cd a
0
0
1
R
R
a ab
c
da
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Line Drop Compensator
Circuit
Voltage
Relay
R line + jX line
LoadCenter
MVA ratingkV hi - kV lo
R' X'
+ -V drop
I line
I comp
Npt:1
CTp:CTs
+
-
V reg
+
-
V R
1:1
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Compensator Equations
Zcomp Zlinepu pu
VLN
Zcomp Rline jXlineohms ohms ohm N CTPT S
VLNZcomp Rline jXlinevolts ohms ohmNPT
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Class 19
Three-Phase Voltage Regulators
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Three-Phase Regulators
Single-phase
Three regulators connected in grounded
wye
Two regulators connected in open wye
Two regulators connected in open delta
Three regulators connected in closed delta
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Grounded Wye Type A
Equations
10 0
10 0
1
0 0
0 0
0 0
0 0
1 0.00625
VLN a VLN b I ABC abc abc
I c VLN d IABC abc abc
aR
aaR
aR
aR
d aR
aR
a TapR
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Grounded Wye Type B
Equations
0 0
0 0
0 0
10 0
10 0
10 0
1 0.00625
VLN a VLN b I ABC abc abc
I c VLN d IABC abc abc
aR
a aR
aR
aR
daR
aR
a TapR
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Class #20
IEEE 13 Node Test Feeder
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Class 21
Design Project
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Class 22
Single-Phase Transformer Model
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Center Tapped Transformer
+
-
V1
+
-
V2
+
-
E1
+
E2
-
Z0
+ I0 +
E0
- -
V
Z1
Z1
I1
I2
n :1t
n :1t
V
+
-
LS
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Center Tapped Transformer
Equations_ 1 2 _
_ _1 2
0.5
0 1
0 2
0 1 2
0.5 0.80
0.41 2
V Rated H H voltageS
V Rated X X voltageL
VSntVL
E n Et
E n Etn I I I t
Z R j XT T
Z Z R j XT T
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Class #23
Secondary Systems
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Triplex Secondary Included
I1
I2
In
+
-
E1
+
E2
-
Z0
+ I0 +
E0
- -
Z1
Z1
H1
H2
VSZL2
ZL1
X1
X0
X2
VL
+
-
v1
v0
v2
+
-
V2
+
-
V1
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Triplex Cable
212
12
1 212
Dia TD
Dia TD DN N
1 2
N
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Triplex Cable Impedance
Plug into Carson for a 3x3 matrix
No Kron reduction
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Class #24
Three-Phase Transformer
ConnectionsPart 1
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Transformer ConnectionsA
B
C
N
a
bc
n
VAN
VABVCNVCA
VBN
VBC
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Delta-Grounded Wye Standard
30 Degree Connection
Ztb Ztc
+ + +_ _ _
Zta
VCA VAB VBC
Vta
Vtb
Vtc
VabVbc+
_+
_
tn
g
+ _Vag
X3-cX2-b
X1-a
H3-CH2-BH1-A
_+ _+ _+
Ia
Ib
Ic
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General Three-Phase
Transformer BanksI
I
I
I
V
V
V
V
V
AN
BN
CN
AB
BC
A
B
C
N
+
+
+
- - -
+
+
+
-
-
-
VCA
V
V
V
V
V
V
an
bn
cn
ab
bcca
I
I
I
a
b
c
In
+
---
+
+
+
+
+
-
-
-
Source Side Load Side
H0
H1 X1
H2
H3
X2
X3
X0
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Generalized Matrix Equations
for All Connections
ABC t abc t abc
ABC t abc t abc
abc t ABC t abc
VLN a VLN b I
I c VLN d I
VLN A VLN B I
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Class #25
Transformer Models - 2
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Constant Z Loads
*2
1
2
3
1
1
1
*1000
0 0
0 0
0 0
ABC t abc t abc
ii
i
abc
abc abc abc
ABC t t abc abc abc
abc ABC
VLN a VLG b I
VLGZL
SL
ZL
ZL ZL
ZL
I ZL VLG
VLN a b ZL VLG X VLG
VLG X VLN
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Serving Single-Phase and Three-Phase
Loads Wye-Delta
Ungrounded wye
Grounded wye
Open Wye-Delta
Leading connection
Lagging connection
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Wye-Delta Connection
A
B
C
N
ab
cMotor
S-3
VBN
VAN
VCN
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Leading Open Wye - Open Delta
A
B
C
N
a
b
cMotor
S-3
VBN
VAN
VCN
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Lagging Open Wye-Open Delta
A
B
C
N
ab
cMotor
S-3
VBN
VAN
VCN
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DeltaGrounded Wye
Common substation transformer connection
Provides 4-wire grounded wye feeder
Isolates LG faults
Distribution transformer
Used for providing balanced single-phase
loadingNot good for three-phase motor loads
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Ungrounded Wye - Delta
Primary use
Supply combination single-phase and three-
phase loads Ungrounded wye so that upstream LG fault
currents do not flow thru transformers
Loss of one transformer will cause single-phasing on three-phase load
Really bad if the three-phase load is aninduction motor
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Grounded Wye - Delta
Seldom used
Upstream ground faults can flow thru
transformersLoss of one transformer and the connection
becomes an open wye-open delta and will
continue to provide three-phase voltages to the
three-phase load
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Open WyeOpen Delta
Can supply combination single-phase and
three-phase loads
Leading connection lightingtransformer on leading phase voltage
Lagging connection lighting
transformer on lagging phase voltage Reduced ratings (chalk board)
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Class #26
Catch Up
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Class 27
Induction Motor
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Three-Phase Induction Motor
Balanced Three-Phase Voltages
1 ii ii
sRL Rr
s
Rs jXs jXr Rr
Ir RL
Is
Vs
-
+
jXm Im
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Three-Phase Induction Motor
Unbalanced Voltages
abc abc abcIM YM VLL
InductionMotor
IMb
IMa
IMc
+
_
+_
+
_
Vab
Vbc
Vca
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Class #28
Ladder Network Iterative Method
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This is what it is all about
Transformer
Substation
Regulator
Voltage
Primary Feeder
Transformer
DistributionInductionMotor
Static
Load
A B
a b
c d
A B
a b
c d
A B
a b
c d
A B
a b
c d abcYM
Sabc
ABC abc abc
ABC abc abc
abc ABC abc
VLN a VLN b I
I c VLN d I
VLN A VLN B I
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Class #29
Short Circuit Analysis
Distribution Feeder Protection
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Three-Phase Equivalent Circuit
c
b
a+
+
+
x-
-
-
Vax
Vbx
Vcx+
-
VxgFaultedNode
Ea Eb Ec
+++
---
[ZTOT]
Zf
Zf
Zf
Ifa
Ifb
Ifc
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Basic Equations
1
ZEQ ZTOT ZF
IP ZEQ Eabc
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Common Equations
0 0
0 0
0 0
Simplify:
Z VE Z Z Z If If Vf xga aa ab ac a a ax
E Z Z Z If Z If V Vb ba bb bc b f b bx xg
E Z Z Z If If VZ Vc ca cb cc c c cxf xg
IP Ifa a
IP Ifb b
IP Ifc c
0 0
0 0
0 0
VY Y Y V Ys xgaa ab ac ax a
Y Y Y V Ys V ba bb bc bx b xg
Y Y Y V Ys Vca cb cc cx c xg
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Matrix Equation to Solve
1 0 0
0 1 0
0 0 1
0
0
0
0
IfIP Y Y Y Ys aa aa ab ac aIfIP Y Y Y Ys bb ba bb bc b
IfIP Y Y Y Ys cc ca cb cc cVax
Vbx
Vcx
Vxg
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Exam 3
(Given) Open Book
You will be given a floppy disk with a system that needs
to be fixed
You will be given an exam booklet
General questions
Transformer connection
Numerical problems
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Exam 3
(Turn in) Turn in
Floppy
Fixed System Mathcad problems
Exam booklet