EEE3233

Tutorial 2: Three-phase system and power concept

Problem 1

If ν = 141.4 sin (ωt+30°) V and i = 11.31cos (ωt-30°) A, find for each;

a) The maximum value,b) The rms value,c) The phasor expression in polar and rectangular form if voltage is the reference. Is the

circuit inductive or capacitive?

Problem 2

If the circuit of Problem 1 consist of a purely resistive and a purely reactive element, find R and X;

a) if the elements are in series

b) if the elements are in parallel

Problem 3

Three identical impedances of 10∠-15° Ωare Y-connected to balanced three-phase line voltages of 208 V. Specify all the line and phase voltages and the currents as phasors in polar form with Vca as reference for a phase sequence of abc.

Problem 4

A balanced-∆ load consisting of pure resistances of 15 Ω per phase is in parallel with a balanced-Y load having phase impedances of 8 + j6 Ω. Identical impedances of 2 + j5 Ω are in each of the three lines connecting the combined loads to a 110-V three phase supply. Find the current drawn from the supply and line voltage at the combined loads.

Problem 5

A three-phase load draws 250 kW at a power factor of 0.707 lagging from a 440-V line. In parallel with this load is a three-phase capacitor bank which draws 60 kVA. Find the total current and resultant power factor.

Problem 6

A three-phase motor draws 20 kVA at 0.707 power factor lagging from a 220-V source. Determine the kilovolt ampere rating of capacitors to make the combined power factor 0.90 lagging, and determine the line current before and after the capacitor are added.

Noorlina Mohd Zainuddin

EEE3233

Problem 7

Three loads are connected in parallel across a 1400-Vrms, 60-Hz single-phase supply as shown in Figure 1.

Load 1: Inductive load, 125kVa at 0.28 power factor

Load 2: Capacitive load, 10kW and 40kvar

Load 3: Resistive load of 15kW

Problem 8

A three-phase line has an impedance of 0.4+j2.7Ω per phase. The line feeds two balanced three-phase loads that are connected parallel. The first load is absorbing 560.1kVA at 0.707 power factor lagging. The second load absorbs 132kW at unity power factor. The line-to-line voltage at the load end of the line is 3810.5V.

Determine:

a) The magnitude of the line voltage at the source end of the line.b) Total real and reactive power loss in the line.c) Real power and reactive power supplied at the sending end of the line.

Noorlina Mohd Zainuddin