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Wye – Delta Transformations

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.

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Wye – Delta Transformations

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  1. Wye – Delta Transformations Also known as T-P transformations

  2. 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.

  3. Wye and Delta Networks • 3 terminal arrangements – commonly used in power systems Wye (Y) Delta (D)

  4. T and P • Drawn as a 4 terminal arrangement of components.

  5. 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.

  6. To transform a Delta into a Wye To transform a Wye into a Delta

  7. Simplification • If R1 = R2 = R3 = R, then Ra = Rb =Rc = 3R • If Ra = Rb = Rc = R’, then R1 = R2 = R3 = R’/3

  8. 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.

  9. 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.

  10. Bridge Circuits (con’t) • Back-to-back Wye networks

  11. Bridge Circuit (con’t) • Or two Delta networks where Rc1 = Rc2 = ∞W.

  12. Bridge Circuits (con’t) • Alternatively, the bridge circuit can be constructed from one Delta and one Wye network where Rc = ∞W.

  13. Bridge Circuits (con’t) • Original circuit redrawn. • VCD = VC – VD • If RA = RB = RC = R and RD = R - dR + VT _ VC VD

  14. 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.

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