wye – delta transformations

14
Also known as T- transformations

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Wye – Delta Transformations. Also known as T- P transformations. Objective of Lecture. Describe the equations that relate the resistances in a Wye (Y) and Delta ( D ) resistor network. Wye networks are some times called T networks and Delta networks are occasionally called P networks. - PowerPoint PPT Presentation

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Page 1: Wye  – Delta Transformations

Also known as T- transformations

Page 2: Wye  – Delta Transformations

Objective of LectureDescribe the equations that relate the

resistances in a Wye (Y) and Delta () resistor network.Wye networks are some times called T

networks and Delta networks are occasionally called networks.

Chapter 2.7 Fundamentals of Electric CircuitsDescribe a bridge circuit in terms of wye and

delta subcircuits.

Page 3: Wye  – Delta Transformations

Wye and Delta Networks3 terminal arrangements – commonly used in

power systems

Wye (Y) Delta ()

Page 4: Wye  – Delta Transformations

T and Drawn as a 4 terminal

arrangement of components.

Page 5: Wye  – Delta Transformations

T and 2 of the terminals

are connects at one node. The node is a distributed node in the case of the network.

Page 6: Wye  – Delta Transformations

To transform a Delta into a Wye

To transform a Wye into a Delta

Page 7: Wye  – Delta Transformations

SimplificationIf R1 = R2 = R3 = R, then Ra = Rb =Rc = 3R If Ra = Rb = Rc = R’, then R1 = R2 = R3 =

R’/3

Page 8: Wye  – Delta Transformations

UsesDistribution of 3 phase powerDistribution of power in stators and windings

in motors/generators.Wye windings provide better torque at low rpm

and delta windings generates better torque at high rpm.

Page 9: Wye  – Delta Transformations

Bridge CircuitsMeasurement of the voltage

VCD is used in sensing and full-wave rectifier circuits. If RA = RB = RC = RD, VCD = 0VIn sensing circuits, the

resistance of one resistor (usually RD) is proportional to some parameter – temperature, pressure, light, etc. , then VCD becomes a function of that same parameter.

Page 10: Wye  – Delta Transformations

Bridge Circuits (con’t)Back-to-back Wye

networks

Page 11: Wye  – Delta Transformations

Bridge Circuit (con’t)Or two Delta

networks where Rc1 = Rc2 = ∞.

Page 12: Wye  – Delta Transformations

Bridge Circuits (con’t)Alternatively, the

bridge circuit can be constructed from one Delta and one Wye network where Rc = ∞

Page 13: Wye  – Delta Transformations

Bridge Circuits (con’t)Original circuit redrawn.

VCD = VC – VD

If RA = RB = RC = R and RD = R - R

VC VD

+

VT

_

TCD

TDDCD

DCCD

TDDD

TDC

VRRV

VRRRRV

VVV

VRRRV

VRRRV

1/1

)(

Page 14: Wye  – Delta Transformations

SummaryThere is a conversion between the

resistances used in wye and delta resistor networks.

Bridge circuits can be considered to be a combination of wye-wye, delta-delta, or delta-wye circuits.Voltage across a bridge can be related to the

change in the resistance of one resistor if the resistance of the other three resistors is constant.