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Chap. 11 Balanced Three-Phase Circuits
Contents11.1 Balanced Three-Phase Voltages11.2 Three-Phase Voltage Sources11.3 Analysis of the Wye-Wye Circuit11.4 Analysis of the Wye-Delta Circuit11.5 Power Calculations in Balanced Three-Phase Ckts11.6 Measuring Average Power in Three-Phase Circuits
以表示單相的量,如: V, I, Z, P 及 Q 分別代表每相之電壓、 電流、阻抗、實功率及無效功率。
在 Y 型接法 線電流與相電流相同 線電壓 = line-to-line voltage 相電壓 = line-to-neutral voltage在型接法 線電壓與相電壓相同 相電壓 line-to-neutral voltage
EX 11.1 Analyzing a Y-Y Circuit
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A balanced three-phase Y-connected generator with positive sequence has an impedance of 0.2 + j 0.5 / and an internal voltage of 120 V/ .The generator feeds a balanced three-phase Y-connected load having an impedance of 39 + j 28 / . The impedance of the line connecting the generator to the load is 0.8 + j 1.5 / . The a-phase internal voltage of the generator is specified as the reference phasor.
The Y-connected source feeds a -connected load through a distribution having an impedance of 0.3 + j 0.9 / . The load impedance is 118.5 + j 85.8 / . Use the a-phase internal voltage as the reference.
a) The a-phase equivalent
b) The line currents IaA , IbB & IcC
c) The phase voltages at the load terminals
Y
EX 11.2 Analyzing a Y- Circuit (Contd.)
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d) The phase currents of the load
e) The line voltages at the source terminals
Check!
11.5 Power Calculations in Balanced Three-Phase Circuits
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Average Power in a Balanced Wye Load
Complex Power in a Balanced Wye Load
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Power Calculations in a Balanced Delta Load
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Instantaneous Power in a Three-Phase Circuit
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若以線至中性點瞬時電壓 vAN 為參考,且為正相序, 為相位角差,各單相的瞬時功率可表示為 pA, pB, pC ,總瞬時功率 pT 為三者之和。
EX 11.3 Calculating Power in a Three-Phase Y-Y Circuit
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Consider the circuit described in EX 11.1 .
a) The average power per phase delivered to the load
b) The total average power delivered to the load
c) The total power lost in the line
或
或
d) The total internal power lost in the generator
e) The total number of magnetizing vars absorbed by the load
f) The total complex power delivered by the source
Check!
EX 11.4 Calculating Power in a Three-Phase Y- Circuit
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Consider the circuit described in EX 11.2 .
a) The total complex power delivered to the -connected load
b) The percentage of the average power reaching the load
From EX 11.2
99.25%687.74682.56
EX 11.5 Three-Phase Power with an Unspecified Load
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a) The a-phase equivalent
A balanced three-phase load requires 480 kW at a lagging power factor of 0.8. The load is fed from a line having an impedance of 0.005 + j 0.025 /. The line voltage at the terminals of the load is 600 V.
b) The magnitude of the line currents
或
EX 11.5 Three-Phase Power with an Unspecified Load (Contd.)
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c) The magnitude of the line voltage at the sending end of the line
或
d) The power factor at the sending end of the line
11.6 Measuring Average Power in Three-Phase Circuits
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右圖由 n 條導線供應功率的一般網 路,以 n 為參考電壓點,其總功率 p = v1i1 +v2i2 + … + vn-1in-1 。對三相平衡電路而言,因為中性線沒有電流通過,故只需兩個瓦特計,即可量測總功率。
EX 11.6 Computing Wattmeter Readings in Three-Phase Circuits
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a)
Calculate the reading of each wattmeter in the previous circuit if the phase voltage at the load is 120 V and (a) Z = 8 + j 6 ; (b) Z = 8 j 6 ;(c) Z = 5+j5√3 ; and (d) Z = 10∠−75◦ .