Balanced Three-Phase Circuits and Ideal Transformers ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall.

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Balanced Three-Phase Circuits and Ideal Transformers ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall

Three-Phase Sources  Most common multiple-phase AC voltage source configuration Wye connected (Y connected) ELEC 3082

Three-Phase Sources ELEC 3083

Wye-Wye Connection ELEC 3084

Wye-Wye Connection  Lines Wires a-A, b-B, c-C  Neutral Wire n-N  Balanced Load Three load impedances are equal  Phase Voltage or Line-to-Neutral Voltage Peak magnitude of one source, V Y  Line Currents Values I aA, I bB, and I cC ELEC 3085

Wye-Wye Connection  Neutral current is ZERO in a BALANCED three- phase system Can eliminate the neutral wire ELEC 3086

Cost Advantage  Three (or four) wires needed to connect a three-phase source with three loads  Six wires needed to connect three single- phase sources with three loads ELEC 3087

Three-Phase Power  Total power is CONSTANT with respect to time ELEC 3088

Three-Phase Reactive Power  The reactive power delivered to a balanced three-phase load is given by ELEC 3089

Line-to-Line Voltages ELEC 30810

Analysis of a Wye-Wye System  Balanced wye-connected 60-Hz three-phase source has line- to-neutral voltages of V Y = 1000 V.  Balanced wye-connected load consisting of a 0.1H inductance in series with a 50-Ω resistance.  Find the line currents, the line-to-line voltages, the power, and the reactive power delivered to the load.  Draw a phasor diagram showing the line-to-neutral voltages, the line-to-line voltages, and the line currents. ELEC 30811

Analysis of a Wye-Wye System ELEC 30812

Delta-Connected Sources ELEC 30813

Delta-Connected Loads ELEC 30814

Delta-Delta Connection ELEC 30815

Power Transmission Losses  Power Line Losses Large Voltages and Small Currents Smaller Line Loss ELEC 30816

Ideal Transformers ELEC 30817

Ideal Transformers ELEC 30818

Example  Determine the rms values of the currents and voltages. ELEC 30819

Power Transmission  Step-Up and Step-Down Transformers 99% Efficiency (vs. 50% with no transformers) ELEC 30820

U.S. Power Grid ELEC 30821

Summary  Three-Phase Circuits Wye-Wye Connection Three-Phase Power  Ideal Transformers  U.S. Power Grid ELEC 30822