Describe the equations that relate the resistances in a Wye (Y) and Delta () resistor network

Describe the equations that relate the resistances in a Wye (Y) and Delta () resistor network.

• Describe 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 Circuits

• Describe a bridge circuit in terms of wye and delta subcircuits.

3 terminal arrangements – commonly used in power systems

• 3 terminal arrangements – commonly used in power systems

Drawn as a 4 terminal arrangement of components.

• Drawn as a 4 terminal arrangement of components.

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

• 2 of the terminals are connects at one node. The node is a distributed node in the case of the  network.

To transform a Delta into a Wye

• To transform a Delta into a Wye

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

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

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

Distribution of 3 phase power

• 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.

Measurement of the voltage VCD is used in sensing and full-wave rectifier 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.

Back-to-back Wye networks

• Back-to-back Wye networks

Or two Delta networks where Rc1 = Rc2 = ∞.

• Or two Delta networks where Rc1 = Rc2 = ∞.

Alternatively, the bridge circuit can be constructed from one Delta and one Wye network where Rc = ∞

• Alternatively, the bridge circuit can be constructed from one Delta and one Wye network where Rc = ∞

Original circuit redrawn.

• Original circuit redrawn.

• VCD = VC – VD
• If RA = RB = RC = R and RD = R - R

There is a conversion between the resistances used in wye and delta resistor networks.

• 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.