wye – delta transformations - virginia techliab/lectures/ch_2/slides/wye_delta... · objective of...
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Also known as T-P transformations
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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.
Chapter 2.7 Fundamentals of Electric Circuits
Describe a bridge circuit in terms of wye and delta subcircuits.
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Wye and Delta Networks 3 terminal arrangements – commonly used in power
systems
Wye (Y) Delta (D)
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T and P
Drawn as a 4 terminal arrangement of components.
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T and P
2 of the terminals are connects at one node. The node is a distributed node in the case of the P network.
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To transform a Delta into a Wye
To transform a Wye into a Delta
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Simplification If R1 = R2 = R3 = R, then Ra = Rb =Rc = 3R
If Ra = Rb = Rc = R’, then R1 = R2 = R3 = R’/3
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Uses Distribution of 3 phase power
Distribution 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.
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Bridge Circuits Measurement of the voltage
VCD is used in sensing and full-wave rectifier circuits.
If RA = RB = RC = RD, VCD = 0V
In 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.
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Bridge Circuits (con’t) Back-to-back Wye networks
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Bridge Circuit (con’t) Or two Delta networks
where Rc1 = Rc2 = ∞W.
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Bridge Circuits (con’t) Alternatively, the
bridge circuit can be constructed from one Delta and one Wye network where Rc = ∞W.
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Bridge Circuits (con’t) Original circuit redrawn.
VCD = VC – VD
If RA = RB = RC = R and RD = R - dR
VC VD
+
VT
_
TCD
TDDCD
DCCD
TDDD
TDC
VRRV
VRRRRV
VVV
VRRRV
VRRRV
1/1
)(
d
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Summary There 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.