CHAP. 11]

POLYPHASE CIRCUITS

259

In summary, power, reactive power, apparent power, and power factor in a three-phase system are pﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃ pﬃﬃﬃ P P ¼ 3V L IL cos  Q ¼ 3VL IL sin  S ¼ 3VL IL pf ¼ S Of course, all voltage and currents are eﬀective values.

11.13

POWER MEASUREMENT AND THE TWO-WATTMETER METHOD

An ac wattmeter has a potential coil and a current coil and responds to the product of the eﬀective voltage, the eﬀective current, and the cosine of the phase angle between them. Thus, in Fig. 11-19, the wattmeter will indicate the average power supplied to the passive network, P ¼ Veff Ieff cos  ¼ Re ðVeff Ieff Þ (see Section 10.7).

Fig. 11-19

Two wattmeters connected in any two lines of a three-phase, three-wire system will correctly indicate the total three-phase power by the sum of the two meter readings. A meter will attempt to go downscale if the phase angle between the voltage and current exceeds 908. In this event, the current-coil connections can be reversed and the upscale meter reading treated as negative in the sum. In Fig. 11-20 the meters are inserted in lines A and C, with the potential-coil reference connections in line B. Their readings will be WA ¼ Re ðVAB eff IA eff Þ ¼ Re ðVAB eff IAB eff Þ þ Re ðVAB eff IAC eff Þ WC ¼ Re ðVCB eff IC eff Þ ¼ Re ðVCB eff ICA eff Þ þ Re ðVCB eff ICB eff Þ in which the KCL expressions IA ¼ IAB þ IAC and IC ¼ ICA þ ICB have been used to replace line currents by phase currents. The ﬁrst term in WA is recognized as PAB , the average power in phase AB of the delta

Fig. 11-20

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An