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Chapter 12 Three-Phase Circuits

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Power Factor Correction A balanced three-phase circuit Medium Voltage Metal Enclosed Capacitor Banks

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Three-Phase Voltages (b) Balanced three-phase voltages (a)The three windings on a cylindrical drum used to obtain three-phase voltages

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Three-Phase Voltages Generator with six terminals

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Three-Phase Balanced Voltages Phase sequence or phase rotation is abc Positive Phase Sequence Phase sequence or phase rotation is acb Negative Phase Sequence neutral terminal

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(a) Y-connected sources (b) -connected sources Two Common Methods of Connection phase voltage

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Phase and Line Voltages The line-to-line voltage V ab of the Y-connected source Similarly

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The Y-to-Y Circuit A four-wire Y-to-Y circuit

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The Y-to-Y Circuit (cont.) The average power delivered by the three-phase source to the three-phase load When Z A = Z B = Z C the load is said to be balanced Four - wire

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The Y-to-Y Circuit(cont.) The average power delivered to the load is There is no current in the wire connecting the neutral node of the source to the neutral node of the load.

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The Y-to-Y Circuit (cont.) A three-wire Y-to-Y circuit

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Three - wire We need to solve for V Nn The Y-to-Y Circuit (cont.) Solve for V Nn

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When the circuit is balanced i.e. Z A = Z B = Z C The Y-to-Y Circuit (cont.) The average power delivered to the load is

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A three-wire Y-to-Y circuit with line impedances The Y-to-Y Circuit (cont.) Transmission lines

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The Y-to-Y Circuit (cont.) The analysis of balanced Y-Y circuits is simpler than the analysis of unbalanced Y-Y circuits. V Nn = 0. It is not necessary to solve for V Nn. The line currents have equal magnitudes and differ in phase by 120 degree. Equal power is absorbed by each impedance. Per-phase equivalent circuit

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Example S = ? Unbalanced 4-wire

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Example (cont.) The total complex power delivered to the three-phase load is

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Example S = ?Balanced 4-wire The total complex power delivered to the three-phase load is Also

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Example S = ? Unbalanced 3-wire Determine V Nn

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Example (cont.) The total complex power delivered to the three-phase load is

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Example S = ?Balanced 3-wire The total complex power delivered to the three-phase load is

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Example P Load = ? P Line = ? P Source = ? Balanced 3-wire per-phase equivalent circuit The phase voltage at the load is

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Example (cont.) The power delivered by the source is The power delivered to the load is The power lost in the line is

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The -Connected Source and Load Total resistance around the loop Circulating current Unacceptable Therefore the sources connection is seldom used in practice.

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The -Y and Y- T ransformation

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Example

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The Y- Circuits where

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The Y- Circuits (cont.) or

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Example I P = ? I L = ? The -connected load is balanced with The line currents are

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The Balanced Three-Phase Circuits per-phase equivalent circuit Y-to- circuit equivalent Y-to-Y circuit

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Example I P = ?

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Example (cont.) The voltages in the per-phase equivalent circuit are The line-to-line voltages are

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Instantaneous and Average Power in BTP Circuits One advantage of three-phase power is the smooth flow of energy to the load. The instantaneous power

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Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced Y-connected load is Phase A

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Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced -connected load is

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Example P = ?

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Two-Wattmeter Power Measurement cc = current coil vc = voltage coil W1 read W2 read For balanced load with abc phase sequence

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Two-Wattmeter Power Measurement(cont.) To determine the power factor angle

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Example P = ? line-to-line voltage = 220Vrms The phase voltage The line current and

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Electrodynamic Wattmeter

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Digital Power Meter VAR Meter pf Meter

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Summary Three-Phase voltages The Y-to-Y Circuits The -Connected Source and Load The Y-to- Circuits Balanced Three-Phase Circuits Instantaneous and Average Power in Bal. 3 Load Two-Wattmeter Power Measurement

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