page 73
6.2.1.6 - Power Factor
• The power factor (p.f.) is a good measure of how well a power source is being used.
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P2 + Q2 |
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As this value approaches 1 the power consumption becomes entirely real, and the load becomes purely resistive.
• It is common to try to correct power factor values when in industrial settings. For example, if a large motor were connected to a power grid, it would introduce an inductive effect. Capacitors can be added to compensate.
6.2.1.7 - Average Power Calculation
• If we want to find the average power, consider the following,
Pavg
Likewise,
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Pavg = |
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6.2.1.8 - Maximum Power Transfer
• Consider the thevenin circuit below. We want to find the maximum power transfered from this circuit to the external resistance.
page 74
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Zs |
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Vs 0° |
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Zs = Rs + jXs |
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ZL = RL + jXL |
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Vs 0° |
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I = Z---- |
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+-----Z---- |
L- |
s--- |
+-----R------)----+-----j--(---X--- |
s---- |
+-----X------)- |
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The average power delivered to the load is,
PL
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+ jX ) |
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+ R ) 2 |
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To find the maximum we can then take a partial derivative for the resistance,
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Vs2( ( Rs + RL) 2 + ( Xs |
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( Rs |
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= 0 |
∂ RL |
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+ ( Xs + XL) ) |
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0 = ( Rs + RL) 2 + ( Xs + XL) 2 – 2RL( Rs + RL)
0 = R2L + R2s + 2RLRs + X2L + X2s + 2XLXs – 2R2L – 2RLRs
R2L( –1) + RL( 0) + ( R2s + X2L + X2s + 2XLXs) = 0
RL = 
R2s + ( XL + Xs) 2