ECE 5500 WINTER 2015

POWER SYSTEM ANALYSIS

Homework Assignment # 1 Due Date: January 22, 2015submit by midnight EST

1) Express each of the following complex numbers in polar form

(a) 12 − j

√32

(b) 1 + j

(c) (1− j)2

(d) j(1− j)

(e) 1+j1−j

(f)√2+j

√2

1+j√3

(g) (√3 + j3)(1− j)

Note: I expect full detailed solution not just output from calculator or MATLAB

2) Express each of the following complex numbers in rectangular form

(a) 12e

jπ

(b) 12e

−jπ

(c) ejπ2

(d) e−j π2

(e)√2ej

π4

(f)√2ej

−9π4

(g) ejπ3 −1

1+j√3

Note: I expect full detailed solution not just output from calculator or MATLAB

3) A small industrial plant is located 2.5 km down a transmission line, which has a series reactanceof 0.4 Ω/km. The line resistance is neglected. The line voltage at the plant is 480∠0 V (rms), andthe plant consumes 110 kW at 0.87 power factor lagging. Determine the voltage, complex powerand power factor delivered by the source (sending end of the transmission line). Also, draw thesource power triangle.

4) A single-phase voltage source of 480 V rms supplies three loads connected in parallel:Load 1 absorbs 14 kW and 7 kVAR;Load 2 absorbs 10 kW at unity power factor;Load 3 absorbs 6 kVA, 0.92 power factor leading.Calculate:

1

(a) current of each individual load and impedance of each load;

(b) complex power supplied by the source and power factor;

(c) equivalent impedance seen by the voltage source.

5) A three-phase 12 hp electrical motor with 92% efficiency and 87% power factor lagging is oper-ating at full load. Voltage at its terminals is 440 V (rms, line-to-line).

(a) Determine the current, and the values of P and Q drawn by the motor

(b) If the impedance of each of the three lines connecting the motor to a source bus is 0.2 + j0.8Ω per phase, find the line-to-line voltage at the source bus which supplies the motor.

Note: 1hp≈746 W

6) A balanced ∆-connected three-phase load consisting of pure resistance of 18 Ω per phase isconnected in parallel with a balanced Y-connected three-phase load having per phase impedance of15 + j10 Ω. The loads are supplied from 110 V three-phase supply through three identical feederswith per phase impedance of 0.5 + j2 Ω. Taking the phase to neutral supply voltage Van as areference, calculate:

(a) the current drawn from the supply and the line-to-line voltage at the combined loads;

(b) the phasor currents in each load;

(c) the complex power of each load; the total active and reactive power supplied from the source,and the power factor at the source end.

2