CHAP. 11]

253

POLYPHASE CIRCUITS

By KCL, line current IA is given by IA ¼ IAB þ IAC ¼ 33:9 758  33:9 1958 ¼ 58:7 458 A Similarly, IB ¼ 58:7 758 A and IC ¼ 58:7 1658 A. The line-to-line voltages and all currents are shown on the phasor diagram, Fig. 11-9. Note particularly the balanced currents. After one phase current has been computed, all other currents pﬃﬃﬃ pﬃﬃﬃmay be obtained through the symmetry of the phasor diagram. Note also that 33:9  3 ¼ 58:7; that is, IL ¼ 3IPh for a balanced delta load.

Fig. 11-9

11.7

Three identical impedances connected as shown in Fig. 11-10 make up a balanced Y-connected load. the currents in the impedances are also the line currents; so the directions are chosen from the source to the load, as before. EXAMPLE 11.3 A three-phase, four-wire, CBA system, with an eﬀective line voltage of 120 V, has three impedances of 20 308  in a Y-connection (Fig. 11-10). Determine the line currents and draw the voltage-current phasor diagram.

Fig. 11-10 pﬃﬃﬃ The maximum line voltage is 169.7 V, and the line-to-neutral magnitude, 169:7= 3 ¼ 98:0 V. 11-7(b), VAN ¼ 98:0 908 V Then

IA ¼

VBN ¼ 98:0 308 V

VCN ¼ 98:0 1508 V

VAN 98:01 908 ¼ ¼ 4:90 608 A Z 20 308

and, similarly, IB ¼ 4:90 608 A, IC ¼ 4:90 1808 A.

From Fig.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An