ee 369 power system analysis lecture 9 transformers, per unit calculations tom overbye and ross...
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EE 369POWER SYSTEM ANALYSIS
Lecture 9Transformers, Per Unit Calculations
Tom Overbye and Ross Baldick
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Announcements• For lectures 8 to 10 read Chapter 3• Homework 7 is 5.9, 5.14, 5.24, 5.26, 5.27, 5.28,
5.29, 5.32, 5.33, 5.37, 5.38, 5.43; due October 23. • Homework 8 is 5.19, 5.23, 3.1, 3.3, 3.4, 3.7, 3.8,
3.10, 3.12, 3.13, 3.14, 3.16; due October 30.• Homework 9 is 3.17, 3.18, 3.20, 3.23, 3.25, 3.26,
3.28, 3.29, 3.34, 3.37, 3.41, 3.45; due November 6. Turn in to grader at beginning of UT power plant tour.
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Per Unit Change of MVA BaseParameters for equipment are often given using
power rating of equipment as the MVA baseTo analyze a system all per unit data must be on
a common power base
2 2
Hence Z
Z
/base base
OriginalBase NewBasepu actual pu
OriginalBase NewBasepu puOriginalBase NewBase
BaseBase
NewBaseOriginalBase NewBaseBasepu puOriginalBase
Base
Z Z Z
V VZ
S S
SZ
S
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Per Unit Change of Base Example
•A 54 MVA transformer has a leakage reactance of 3.69% (on its own MVA base). •What is the reactance on a 100 MVA base?
1000.0369 0.0683 p.u.
54eX
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Transformer ReactanceTransformer reactance is often specified as a
percentage, say 10%. This is a per unit value expressed as a percentage on the power base of the transformer.
Example: A 350 MVA, 230/20 kV transformer has leakage reactance of 10%. What is p.u. value on 100 MVA base? What is value in ohms (230 kV)?
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1000.10 0.0286 p.u.
350
2300.0286 15.1
100
eX
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Three Phase Transformers•There are 4 different ways to connect 3 transformers
Y-Y -
Usually 3 transformers are constructed so all windingsshare a common core 6
3 Transformer Interconnections
-Y Y-
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Y-Y Connection
Magnetic coupling with An/an, Bn/bn & Cn/cn
1, ,An AB A
an ab a
V V Ia a
V V I a
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Y-Y Connection: 3 Detailed Model
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Y-Y Connection: Per Phase Model
Per phase analysis of Y-Y connections is exactly the same as analysis of a single phase transformer.
Y-Y connections are common in transmission systems.
Key advantages are the ability to ground each side and there is no phase shift is introduced.
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- Connection
Magnetic coupling with AB/ab, BC/bb & CA/ca
1 1, ,AB AB A
ab ab a
V I Ia
V I a I a
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- Connection: 3 Detailed Model
To use the per phase equivalent we need to usethe delta-wye load transformation
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- Connection: Per Phase Model
Per phase analysis similar to Y-Y except impedances are decreased by a factor of 3.
Key disadvantage is - connections can not be grounded; not commonly used.
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-Y Connection
Magnetic coupling with AB/an, BC/bn & CA/cn
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-Y Connection V/I Relationships
, also 3 30
3030Hence 3 and 3
For current we get
1
13 30 30
31
303
AB ABan ab an
an
AnABab an
ABa AB
a
A AB AB A
a A
V Va V V V
V a
VVV V
a a
II a I
I a
I I I I
I a I
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-Y Connection: Per Phase Model
Note: Connection introduces a 30 degree phase shift!
Common for transmission/distribution step-down sincethere is a neutral on the low voltage side.
Even if a = 1 there is a sqrt(3) step-up ratio
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Y- Connection: Per Phase Model
Exact opposite of the -Y connection, now with a phase shift of -30 degrees.
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