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. EL � �3�Ef � (1.73)(120 V) � 208 V. Therefore,<br />

EAB � EBC � ECA � 208 V<br />

c. Vf � Ef. Therefore,<br />

Van � EAN Vbn � EBN Vcn � ECN Van 120 V �0° 120 V �0°<br />

IfL � Ian ����� ���<br />

Zan 3 ��j 4 � 5 � �53.13°<br />

� 24 A ��53.13°<br />

Vbn 120 V ��120°<br />

Ibn ��� �� �24 A ��173.13°<br />

Zbn 5 � �53.13°<br />

Vcn 120 V ��120°<br />

Icn ����� �24 A �66.87°<br />

Zcn 5 � �53.13°<br />

and, since IL � IfL, IAa � Ian � 24 A ��53.13°<br />

IBb � Ibn � 24 A ��173.13°<br />

ICc � Icn � 24 A �66.87°<br />

d. Applying Kirchhoff’s current law, we have<br />

In rectangular form,<br />

E AN<br />

I N � I Aa � I Bb � I Cc<br />

IAa � 24 A ��53.13° � 14.40 A � j 19.20 A<br />

IBb � 24 A ��173.13° � �22.83 A � j 2.87 A<br />

ICc � 24 A �66.87° � �09.43 A � j 22.07 A<br />

Σ(IAa � IBb � ICc) � 0 � j 0<br />

and IN is in fact equal to zero, as required for a balanced load.<br />

22.6 THE Y-D SYSTEM<br />

A<br />

+<br />

120 V 0°<br />

120 V θ θ3<br />

+<br />

C<br />

–<br />

ECN –<br />

N<br />

–<br />

EBN 120 V θ θ2<br />

+<br />

B<br />

There is no neutral connection for the Y-D system of Fig. 22.14. Any<br />

variation in the impedance of a phase that produces an unbalanced system<br />

will simply vary the line and phase currents of the system.<br />

E CA<br />

E BC<br />

E AB<br />

I Aa<br />

I N<br />

I Bb<br />

I Cc<br />

FIG. 22.13<br />

Example 22.1.<br />

I an<br />

a<br />

THE Y-D SYSTEM ⏐⏐⏐ 985<br />

+<br />

3 Ω<br />

V an<br />

–<br />

–<br />

–<br />

+<br />

+<br />

n<br />

Vcn 4 Ω Balanced<br />

load<br />

4 Ω Vbn<br />

3 Ω<br />

c<br />

Icn 4 Ω<br />

3 Ω<br />

b<br />

Ibn

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