EE533 POWER OPERATIONS Component Models and CharacteristicsContd.

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EE533 POWER OPERATIONSComponent Models and
Characteristics(Contd.) Satish J. Ranade Fall
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Transformers

• Two- and Three-winding transformer models
• Three winding ( Auto with delta tertiary most
  common in transmission)
• Parameters
• Regulating Transformers
• Models and Performance

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Transformers

• Two- and Three-winding transformer models (per
  unit nominal tap)

S
Zs
P
S
Zt
Zp
P
Zt
T
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Transformer Parameters

• Three winding example ( Glover Sarma Chapter 3)
• Short circuit (Heat Run) test

Energize P, Short S -- Measures Zps Zp Zs in
perunit -- Similary Zpt ZpZt
ZstZsZt
Then Zp (ZpsZpt-Zst)/2 Zs
(ZstZps-Zpt)/2 Zt (ZstZpt-Zps)/2
Gives impedances in model
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Transformer Parameters

• Three winding example ( Glover Sarma Chapter 3)

P 300 MVA 13.8 kV S 300 MVA
199.2 kV T 50 MVA 19.92kV
Zps j0.1 on 300 MVA, 13.8 kV base Zpt j0.16
on 50 MVA, 13.8 kV base Zst j 0.14 on 50 MVA,
199.2
Zpt j0.16 j0.96 pu Zst j 0.14 j0.84 pu
On 300 MVA base
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Transformer Parameters

• Three winding example ( Glover Sarma Chapter 3)

On 300 MVA base Zp j0.11 pu Zs-j0.01 pu Ztj
0.85 pu
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Regulating Transformer

• Taps
• Transformers are equipped with load and no load
  tap changers
• On large units the tap changer is a separate unit
• Phase shifting
• On three phase transformers tap changers can be
  wired to effect phase shift
• In per phase models of balanced three-phase
  transformers we can think of the transformer as
  having a complex per unit turns ration a

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Regulating Transformer
P
S
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Regulating Transformer
P
S
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Transformer Model
I1
I2
Zt
V1
V2
V2
a
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Off- Nominal Tap Example

• Three phase 500 MVA 13.8-345 kV Ztj0.05 pu
• 32x5/8 taps for 10 on H side
• - at -10 a1/0.9 steps down secondary voltage
• -j20 j22.22
• Y
• j22.22 -j24.69

Drops voltage
J0.045
-J0.45
J0.405
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Off- Nominal Tap Example

• Three phase 500 MVA 13.8-345 kV Ztj0.05 pu
• 32x5/8 taps for 10 on H side
• - at -10 a1/0.9 steps down secondary voltage
• -j20 j22.22
• Y
• j22.22 -j24.69

Drops voltage
J0.045
-J0.45
J0.405
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Phase Shift Example

• Three phase 500 MVA 345-345 kV Ztj0.1 pu
• 30 deg shift
• Assume V1 1/d V21/0
• I1 ( V1-V2)/j0.1 I2(V1-V2/?)/j0.1
• I1I2 1

J0.2
I1
1j0
J0.1
S2
correction
V1
V2
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Phase Shift Example

• I1-I2(V2/? V2)/j0.1 I1I21
• I2 (1- (1/ ? 1)/j0.1)/2
• S2V2I2(1- (1/ ? 1)/j0.1)/2

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Transmission Lines
Carsons Equations
R from tables XL0.1213 ln (DEQ/DSL)
ohm/mi B3.37510-5 / ln(DEQ/DSC) mho/mi
Symmetrical Component Transformation
Positive sequence model
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Transmission Lines
Long-line PI model used in analysis programs
ZZc sinh(?l) Y/2(cosh(?l)-1)/Zcsinh(?l) z
RjXl ohm/mi yjB ohm/mi Zc(z/y)1/2 ? (zy)1/2
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Transmission Lines
Surge Impedance Loading and Voltage
Profiles Ignoring resistance Zc is real SIL
Vrated2 /Zc
Open ltSIL SIL gtSIL Short
Shunt Comp.
V
Vs
Series Comp.
Length
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Transmission Lines
Power Transfer and loadability Pr (VrVs/Z)
cos(?z-d) A Vr2 cos (?z- ?A)/Z Prmax occurs
at d90 practically d lt 40deg Prmax Vrated 2
/X
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Transmission Lines
Power Transfer Thermal Loadability -- Raw
ampacity is usually very large -- Actual
controlled by Sag -- Sag design based on NESC --
Actual sag needs to be be considered based on
vegetation, etc.
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Transmission Lines
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Transmission Lines
765 kV 300 Km line z.016j0.33 ohm/km y j 4.7
uS/km
Z 97 ohm/mi Y/2 .037709 uS
SIL 2200 MW Pmax 5974 MW ideal
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FACTS Devices
FACTS Flexible ac transmission systems --
Family of devices based on power electronics --
Power Transmission -- Reactive Power
Support -- Power flow enhancement/control --
Most valuable during transients/disturbances --
Also useful in Normal Operation
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HVDC Line and and Back-Back dc terminals
HVDC Line Competitive with ac in long distance
high power gt 500 Mi gt 2000 MW Back-back tie -
Interconnection between large systems Basic
Technology Line Commutated Converter/Inverter Mor
e Recent Voltage source converter
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HVDC Line and and Back-Back dc terminals
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Thyristor Switched Capacitor
Shunt-
Series
Both SCRs fully on or off Synchronized switching.
Turnon at zero voltage crossing Turn off at zero
current
Cascade Q, 2Q, 4Q to get control in increments
of Q
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Thyristor Switched Capacitor
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Thyristor Controlled Reactor
Static Var Compensator
The SCR firing angle is controlled to vary the
lagging reactive current in the reactor Thus the
reactive power can be varied from capacitive to
inductive Significant filtering is necessary.
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Voltage Source Converter