Chapter 12 ThreePhase Circuits Power Factor Correction Medium
- Slides: 42
Chapter 12 Three-Phase Circuits
Power Factor Correction Medium Voltage Metal Enclosed Capacitor Banks A balanced three-phase circuit
Three-Phase Voltages (a) The three windings on a cylindrical drum used to obtain three-phase voltages (b) Balanced three-phase voltages
Three-Phase Voltages Generator with six terminals
Three-Phase Balanced Voltages Phase sequence or phase rotation is abc Positive Phase Sequence neutral terminal Phase sequence or phase rotation is acb Negative Phase Sequence
Two Common Methods of Connection phase voltage (a) Y-connected sources (b) -connected sources
Phase and Line Voltages The line-to-line voltage Vab of the Y-connected source Similarly
The Y-to-Y Circuit A four-wire Y-to-Y circuit
The Y-to-Y Circuit (cont. ) Four - wire The average power delivered by the three-phase source to the three-phase load When ZA = ZB = ZC the load is said to be balanced
The Y-to-Y Circuit(cont. ) There is no current in the wire connecting the neutral node of the source to the neutral node of the load. The average power delivered to the load is
The Y-to-Y Circuit (cont. ) A three-wire Y-to-Y circuit
The Y-to-Y Circuit (cont. ) Three - wire Solve for VNn We need to solve for VNn
The Y-to-Y Circuit (cont. ) When the circuit is balanced i. e. ZA = ZB = ZC The average power delivered to the load is
The Y-to-Y Circuit (cont. ) Transmission lines A three-wire Y-to-Y circuit with line impedances
The Y-to-Y Circuit (cont. ) The analysis of balanced Y-Y circuits is simpler than the analysis of unbalanced Y-Y circuits. VNn = 0. It is not necessary to solve for VNn. The line currents have equal magnitudes and differ in phase by 120 degree. Equal power is absorbed by each impedance. Per-phase equivalent circuit
Example 12. 4 -1 S = ? Unbalanced 4 -wire
Example 12. 4 -1 (cont. ) The total complex power delivered to the three-phase load is
Example 12. 4 -2 S = ? Balanced 4 -wire The total complex power delivered to the three-phase load is Also
Example 12. 4 -3 S = ? Unbalanced 3 -wire Determine VNn
Example 12. 4 -3 (cont. ) The total complex power delivered to the three-phase load is
Example 12. 4 -4 S = ? Balanced 3 -wire The total complex power delivered to the three-phase load is
Example 12. 4 -5 PLoad = ? PLine = ? PSource = ? Balanced 3 -wire The phase voltage at the load is per-phase equivalent circuit
Example 12. 4 -5 (cont. ) The power delivered by the source is The power delivered to the load is The power lost in the line is
The -Connected Source and Load Circulating current Unacceptable Total resistance around the loop Therefore the sources connection is seldom used in practice.
The -Y and Y- Transformation
Example
The Y- Circuits where
The Y- Circuits (cont. ) or
Example 12. 6 -1 IP = ? IL = ? The -connected load is balanced with The line currents are
The Balanced Three-Phase Circuits Y-to- circuit equivalent Y-to-Y circuit per-phase equivalent circuit
Example 12. 7 -1 IP = ?
Example 12. 7 -1 (cont. ) The voltages in the per-phase equivalent circuit are The line-to-line voltages are
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
Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced Y-connected load is Phase A
Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced -connected load is
Example 12. 8 -1 P = ?
Two-Wattmeter Power Measurement cc = current coil vc = voltage coil W 1 read W 2 read For balanced load with abc phase sequence
Two-Wattmeter Power Measurement(cont. ) To determine the power factor angle
Example 12. 9 -1 P = ? line-to-line voltage = 220 Vrms The phase voltage The line current and
Electrodynamic Wattmeter
Digital Power Meter pf Meter VAR Meter
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 -f Load Two-Wattmeter Power Measurement
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