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Page 1: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 1

Modeling, Simulation, and Analysis

of Variable Frequency

Transformers

Brian C. RaczkowskiPeter W. Sauer

Page 2: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 2

Overview

Power Flow Control Langlois Converter Project Derivation of Model Small Power System Case Experimental Case Future Work

Page 3: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 3

Ways to control power flow

Prime mover and excitation control of generators

Open and Close Breakers Reactive Power Compensation

Page 4: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 4

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

Page 5: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 5

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

Page 6: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 6

Drawbacks of These Methods

Set minimum and maximum constraints

Fixed change Power transfer frequency

requirement Harmonics

Page 7: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 7

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

Page 8: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 8

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)

Page 9: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 9

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

Page 10: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 10

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

Page 11: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 11

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

Page 12: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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

Page 13: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 13

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

Page 14: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 14

VFT Ideal Use

Drive Motor

ControlSystem

PowerSystem

Area#2

PowerSystem

Area#1

Variable Frequency Transformer

Page 15: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 15

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

Page 16: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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

Page 17: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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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

Page 18: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 18

VFT Model (per phase)

Page 19: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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Small Power System Case

Glover and Sarma example

Page 20: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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Small Power System with 3 VFTs

Line 1

Line 2 Line 3

Just by inserting VFTs, the flows have changed

Page 21: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 21

Power Flows in Small Power System from -21.9° to +30°

Pin

Pload

Pline2

Ploss

Pline3

Pline1

Page 22: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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

Page 23: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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

Page 24: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 24

Test System Results - No Caps

Page 25: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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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

Page 26: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 26

Test System Results – with Caps

Page 27: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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Interesting Cases Results verified in Power World Simulator

Page 28: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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Circulating Real Power

Page 29: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

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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

Page 30: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 30

Future Work

Larger Test Systems Higher Voltage Torque Analysis Multiple Frequencies Stability of the System Economical Impact

Page 31: 5/12/061 Modeling, Simulation, and Analysis of Variable Frequency Transformers Brian C. Raczkowski Peter W. Sauer.

5/12/06 31

Questions

Questions??


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