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

5/12/06 3

Ways to control power flow

Prime mover and excitation control of generators

Open and Close Breakers Reactive Power Compensation

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

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

5/12/06 6

Drawbacks of These Methods

Set minimum and maximum constraints

Fixed change Power transfer frequency

requirement Harmonics

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

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)

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

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

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

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

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

5/12/06 14

VFT Ideal Use

Drive Motor

ControlSystem

PowerSystem

Area#2

PowerSystem

Area#1

Variable Frequency Transformer

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

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)

5/12/06 19

Small Power System Case

Glover and Sarma example

5/12/06 20

Small Power System with 3 VFTs

Line 1

Line 2 Line 3

Just by inserting VFTs, the flows have changed

5/12/06 21

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

5/12/06 24

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

5/12/06 26

Test System Results – with Caps

5/12/06 27

Interesting Cases Results verified in Power World Simulator

5/12/06 28

Circulating Real Power

5/12/06 29

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??