5/12/06 1
Modeling, Simulation, and Analysis
of Variable Frequency
Transformers
Brian C. RaczkowskiPeter W. Sauer
5/12/06 2
Overview
Power Flow Control Langlois Converter Project Derivation of Model Small Power System Case Experimental Case Future Work
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Ways to control power flow
Prime mover and excitation control of generators
Open and Close Breakers Reactive Power Compensation
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Ways to control power flow (cont.)
High Voltage DC (HVDC) Rectifies AC to DC then inverts DC to
AC Economical for long distances Harmonics Isolation
Frequency
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Ways to control power flow (cont.)
Transformers Tap-Changing-Under-Load (TCUL)
Transformers Ability to change the ratio of transformation while
energized Requires additional circuitry
Phase shifting transformer Addition of “90° out of phase” voltage Useful for controlling real power Most cases there is a fixed range
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Drawbacks of These Methods
Set minimum and maximum constraints
Fixed change Power transfer frequency
requirement Harmonics
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Another Kind of Transformer Induction machine
Squirrel cage rotor Conducting bars laid in slots and shorting rings
Wound rotor 3Φ windings with mirror images of windings on
stator
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Another Kind of Transformer (cont.)
Doubly-Fed Induction Machine (DFIM) Rotor end not shorted Wound rotor machine with access to rotor
windings Slip rings provide connection to rotor Typically used to alter torque-speed curve Same as Variable Frequency Transformer
(VFT)
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VFT Advantages Continuous and no fixed set change
points Response for stability purposes Simple model for power system use HVDC alternative Can transfer power at different
frequencies More control of the real power flow
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VFT Disadvantages
Limits on maximum power flow capability
More lossy especially in reactive power losses
Works at low kV range so it needs step up/down transformers
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Langlois Converter Project
GE investigated a new power transmission technology (2002)
Variable Frequency Transformer (VFT)
Controllable, bidirectional transmission device with ability to transfer power between asynchronous networks
5/12/06 12
World’s First VFT
Hydro-Quebec’s Langlois substation
Exchange +100MW to -100MW between power grids of Quebec (Canada) and New York (USA)
Closed Loop Control System to increase or decrease power delivery to maintain stability
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General VFT Core technology is rotary transformer with
three phase windings on both rotor and stator Continuously variable phase shifting
transformer Uses 2 transformers, a switched capacitor
bank and a DC motor Change rotor angle to change the power flow
through the machine Limits of the phase angle can be set as large
as needed
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VFT Ideal Use
Drive Motor
ControlSystem
PowerSystem
Area#2
PowerSystem
Area#1
Variable Frequency Transformer
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Model Derivation
The machine is assumed to be a two-pole three phase machine with an a:1 turns ratio
X
X
X
X
X
X
as
bs
cs
ar
brcr
as
bs
cs
ar
br cr
tm
mrs
5/12/06 16
Starting Equations
mslsss LLL
mrlrrr LLL
mrsrms LaaLL 2
)cos( tIi ssas
)3
2cos(
tIi ssbs
)3
2cos(
tIi sscs
)cos( tIi rrar
)3
2cos(
tIi rrbr
)3
2cos(
tIi rrcr
)3
2cos()
3
2cos(cos
22
srcrsrbrsrarcsms
bsms
asssas LiLiLiiL
iL
iL
)3
2cos()
3
2cos(cos
22
srcssrbssrascrmr
brmr
arrrar LiLiLiiL
iL
iL
dt
diRV asassas
dt
diRV ararrar
rr Ia
I 1rr VaV
rr RaR 2
lrlr LaL 2
5/12/06 17
Final Equations
)(2
3)
2
3(
rmsssmslsssss ILjILLjRV
)(2
3)
2
3(
smsrrmslrrrrr ILjILLjRV
r
s
mslrrms
msmslss
rr
ss
I
I
LLjRLj
LjLLjR
V
V
)2
3(
2
32
3)
2
3(
)(
lsls LX lrlr LX msms LX 2
3
5/12/06 18
VFT Model (per phase)
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Small Power System Case
Glover and Sarma example
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Small Power System with 3 VFTs
Line 1
Line 2 Line 3
Just by inserting VFTs, the flows have changed
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Power Flows in Small Power System from -21.9° to +30°
Pin
Pload
Pline2
Ploss
Pline3
Pline1
5/12/06 22
Experimental System Setup GE I689, 7.5 hp, 3Φ, 6-pole induction
machine 2.93:1 turns ratio
SLACK
1
52 3 VFT
1:93.2 je
6WALL S R
1:2.93
Line 2
Line 1
Pin
Pline2
Pline1
Pstator Pload
5/12/06 23
Experimental System Notes
Variac used to match odd turns ratio Slack Bus was the standard wall outlet Load is purely resistive 12.8Ω Source had 10A fuses 1° mechanical was 3° electrical Verification in PowerWorld Simulator
Voltage - 1000x Power – 1e6x
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Test System Results - No Caps
5/12/06 25
Make Things Better System is already inherently lossy Add a capacitor bank to cut reactive
losses 121.5µF to each phase at Bus 3 Current reduced from 7.03Arms to
2.45Arms
Needed 61.32V to achieve 7.05Arms
For comparative purposes Vin=20.4Vrms
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Test System Results – with Caps
5/12/06 27
Interesting Cases Results verified in Power World Simulator
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Circulating Real Power
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VFT Conclusions
Alternative method to control power flow
Easy model Use in small power system case Use in experimental power system
case
5/12/06 30
Future Work
Larger Test Systems Higher Voltage Torque Analysis Multiple Frequencies Stability of the System Economical Impact
5/12/06 31
Questions
Questions??