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Comprehensive Problems

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Comprehensive Problems

  • 12.77 A three-phase generator supplied 10 kVA at a power factor of 0.85 lagging. If 7,500 W are delivered to the load and line losses are 160 W per phase, what are the losses in the generator?
  • 12.78 A three-phase 440-V, 51-kW, 60-kVA inductive load operates at 60 Hz and is wye-connected. It is desired to correct the power factor to 0.95 lagging. What value of capacitor should be placed in parallel with each load impedance?
  • 12.79 A balanced three-phase generator has an abc phase sequence with phase voltage Van = 554.3⧸ 0° V. The generator feeds an induction motor which may be represented by a balanced Y-connected load with an impedance of 12 + j5 Ω per phase. Find the line currents and the load voltages. Assume a line impedance of 2 Ω per phase.
  • 12.80 A balanced three-phase source furnishes power to the following three loads:

Load 1: 6 kVA at 0.83 pf lagging Load 2: unknown Load 3: 8 kW at 0.7071 pf leading

If the line current is 84.6 A rms, the line voltage at the load is 208 V rms, and the combined load has a 0.8 pf lagging, determine the unknown load.

12.81 A professional center is supplied by a balanced three-phase source. The center has four balanced three-phase loads as follows:

Load 1: 150 kVA at 0.8 pf leading Load 2: 100 kW at unity pf Load 3: 200 kVA at 0.6 pf lagging Load 4: 80 kW and 95 kVAR (inductive)

If the line impedance is 0.02 + j0.05 Ω per phase and the line voltage at the loads is 480 V, find the magnitude of the line voltage at the source.

  • 12.82 A balanced three-phase system has a distribution wire with impedance 2 + j6 Ω per phase. The system supplies two three-phase loads that are connected in parallel. The first is a balanced wye-connected load that absorbs 400 kVA at a power factor of 0.8 lagging. The second load is a balanced delta-connected load with impedance of 10 + j8 Ω per phase. If the magnitude of the line voltage at the loads is 2400 V rms, calculate the magnitude of the line voltage at the source and the total complex power supplied to the two loads.
  • 12.83 A commercially available three-phase inductive motor operates at a full load of 120 hp (1 hp = 746 W) at 95 percent efficiency at a lagging power

factor of 0.707. The motor is connected in parallel to a 80-kW balanced three-phase heater at unity power factor. If the magnitude of the line voltage is 480 V rms, calculate the line current.

12.84 Figure 12.76 displays a three-phase delta-connected motor load which is connected to a line voltage of 440 V and draws 4 kVA at a power factor of 72 per cent lagging. In addition, a single 1.8 kVAR capacitor is connected between lines a and b, while a 800-W lighting load is connected between line c and neutral. Assuming the abc sequence and taking Van = Vp⧸0°, find the magnitude and phase angle of currents Ia, Ib, Ic, and In.

Figure 12.76

For Prob. 12.84.

12.85 Design a three-phase heater with suitable symmetric loads using wye-connected pure resistance. Assume that the heater is supplied by a 240-V line voltage and is to give 27 kW of heat.

12.86 For the single-phase three-wire system in Fig. 12.77, find currents IaA, IbB, and InN.

Figure 12.77

For Prob. 12.86.

12.87 Consider the single-phase three-wire system shown in Fig. 12.78. Find the current in the neutral wire and the complex power supplied by each source. Take Vs as a 220⧸ 0°-V, 60-Hz source.

Figure 12.78 For Prob. 12.87.