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992 ⏐⏐⏐ POLYPHASE SYSTEMS<br />

Average Power The average power delivered to each phase can be<br />

determined by any one of Eqs. (22.14) through (22.16).<br />

(watts, W) (22.14)<br />

where v Vf<br />

If indicates that v is the phase angle between V f and I f. The<br />

total power to the balanced load is<br />

or, since Vf � � and If � IL �3�<br />

then PT � 3 IL cos v Vf � If<br />

�3�<br />

But � � (1) � � � �<br />

�3� ��3� ���3� �<br />

Therefore,<br />

(W) (22.15)<br />

3�3�<br />

����3� 3<br />

(W) (22.16)<br />

Reactive Power The reactive power of each phase (in volt-amperes<br />

reactive) is<br />

The total reactive power of the load is<br />

or, proceeding in the same manner as above, we have<br />

(VAR) (22.17)<br />

(VAR) (22.18)<br />

Apparent Power The apparent power of each phase is<br />

The total apparent power of the load is<br />

or, as before,<br />

Pf � VfIf cos v Vf<br />

If � I 2 fRf � � V R<br />

�<br />

Rf 3<br />

P T � 3P f<br />

E L<br />

P T � �3�E LI L cos v Vf<br />

If � 3I 2 LR f<br />

Qf � VfIf sin v Vf<br />

If � I 2 fXf � � VX<br />

�<br />

Xf 3<br />

E L<br />

Q T � 3Q f<br />

Q T � �3�E LI L sin v Vf<br />

If � 3I 2 LX f<br />

S f � V fI f<br />

S T � 3S f<br />

�3�<br />

S T � �3�E LI L<br />

2<br />

2<br />

(VAR) (22.19)<br />

(VA) (22.20)<br />

(VA) (22.21)<br />

(VA) (22.22)

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