CHAPTER 11CHAPTER 11

Balanced Three - Phase Balanced Three - Phase CircuitsCircuits

CHAPTER CONTENTSCHAPTER CONTENTS 11.1 Balanced Three-Phase Voltages11.1 Balanced Three-Phase Voltages 11.2 Three-Phase Voltage Sources11.2 Three-Phase Voltage Sources 11.3 Analysis of the Wye-Wye Circuit11.3 Analysis of the Wye-Wye Circuit 11.4 Analysis of the Wye-Delta Circuit11.4 Analysis of the Wye-Delta Circuit 11.5 Power Calculations in Balanced T11.5 Power Calculations in Balanced T

hree-hree- Phase CircuitsPhase Circuits 11.6 Measuring Average Power in Thr11.6 Measuring Average Power in Thr

ee-ee- Phase CircuitsPhase Circuits

11.1 Balanced Three-Phase 11.1 Balanced Three-Phase VoltagesVoltages

Phasor diagrams of a balanced set of three-phase voltages. (a) The abc (positive) sequence. (b) The acb (negative) sequence.

(a)

(b)

11.2 Three-Phase 11.2 Three-Phase Voltage SourcesVoltage Sources

The two basic The two basic connections of connections of an ideal three-an ideal three-phase source. phase source.

(a) A Y-(a) A Y-connected connected source.source.

(b) A ∆- (b) A ∆-connected connected sourcesource

A model of a three-phase source A model of a three-phase source with winding impedance: with winding impedance: (a) A Y-connected source.(a) A Y-connected source.(b) A ∆-connected source(b) A ∆-connected source

11.3 Analysis of the Wye-Wye C11.3 Analysis of the Wye-Wye Circuitircuit

A three-phase Y-Y system

Phasor diagrams showing the relationship between line-to-line and line-to-neutral voltages in a balanced system.

(a)The abc sequence.

(b)The acb sequence.

11.4 Analysis of the Wye-Delta 11.4 Analysis of the Wye-Delta CircuitCircuit

A circuit used to establish the relationship between line currents and phase currents in a balanced ∆ load.

Phasor diagrams showing the relationship between line currents and phase currents in a ∆-connected load.

(a)The positive sequence.

(b)The negative sequence.

11.5 Power Calculations in 11.5 Power Calculations in Balanced Three-Phase Balanced Three-Phase

CircuitsCircuitsTOTAL REAL POWER IN A BALANCED THREE-PHASE LOAD

TOTAL REACTIVE POWER IN A BALANCED THREE-PHASE LOAD

TOTAL COMPLEX POWER IN A BALANCED THREE-PHASE LOAD

11.6 Measuring Average 11.6 Measuring Average Power in Three-Phase Power in Three-Phase

CircuitsCircuits A wattmeter A wattmeter

measures the measures the average power average power delivered to a load delivered to a load by using a current by using a current coil connected in coil connected in series with the series with the load and a load and a potential coil potential coil connected in connected in parallel with the parallel with the load.load.

A circuit used to analyze the two-wattmeter method of measuring average power delivered to a balanced load.

THE ENDTHE END