Page 417 - Power Electronic Control in Electrical Systems

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396 Examples, problems and exercises

Fig. 9.17
p
(b) I a ˆ 415/ 3/9:184 ˆ 26:088 A (unchanged)
p p
I b ˆ 415/ 3e j120 /(3 ‡ j17 150/50) ˆ 415/ 3e j120 /51:088e j86:634
ˆ 4:690e j206:634 ˆ 4:192 ‡ j2:102 A
p p
I c ˆ 415/ 3e j120 /(3 j17 50/150) ˆ 415/ 3e j120 /6:412e j62:103
ˆ 37:369e j182:103 ˆ 37:344 j1:371 A
I n ˆ I a ‡ I b ‡ I c ˆ 15:448 ‡ j0:731 ˆ 15:465e j177:29 A.
23. (i) Draw a circuit diagram and a phasor diagram showing the two-wattmeter
method of measuring power in a three-phase system.
(ii) Prove from first principles that the two-wattmeter method is valid for
instantaneous power and not just for average power.
(iii) Figure 9.17 shows a single-phase load of 3 ‡ j14
supplied from a sinusoidal
voltage source of rms value 115 V and frequency 50 Hz. A single-phase
wattmeter is connected with its current coil in series with the load. The
voltage coil is connected via a voltage divider circuit comprising resistors of
10 k
and 30 k
as shown.
Calculate
(a) the current
(b) the real and reactive power P ‡ jQ at the terminals
(c) the reading W on the wattmeter
(d) the wattmeter reading if the 10 k
resistor is replaced by a capacitor
whose impedance at 50 Hz is j6:429 k
.

(i)

Fig. 9.18

(ii) Total instantaneous power p ˆ v a i a ‡ v b i b ‡ v c i c