ECE 476 – Power System Analysis Fall 2009
Homework 1
Due Date: Thursday September 3, 2009
Problems 2.7, 2.12, 2.21 and 2.26 of GS&0
2.7) Let a 100-V sinusoidal source be connected to a series combination of a 3-Ω resistor, an 8-Ω
inductor, and a 4–Ω capacitor.
(a) Draw the circuit diagram.
(b) Compute the series impedance.
(c) Determine the current I delivered by the source. Is the current lagging or leading the source volt-
age? What is the power factor of this circuit?
2.12) The voltage v(t) = 678.8 cos(ωt +π/4) volts is applied to a load consisting of a 10-Ω resistor
in parallel with a capacitive reactance XC= 25Ω. Calculate:
(a) The instantaneous power absorbed by the resistor.
(b) The instantaneous power absorbed by the capacitor.
(c) The real power absorbed by the resistor.
(d) The reactive power delivered by the capacitor.
(e) The load power factor.
2.21) An industrial plant consisting primarily of induction motor loads absorbs 1000kW at 0.7
power factor lagging.
(a) Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging.
(b) Calculate the resulting power factor if a synchronous motor rated 1000 hp with 90% efficiency op-
erating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume
constant voltage. (1 hp = 0.746 kW)
2.26) A small manufacturing plant is located 2km down a transmission line, which has a series
reactance of 0.5 Ω/km. The line resistance is negligible. The line voltage plant is 48060 V (rms), and
the plant consumes 120 kW at 0.85 power factor lagging. Determine the voltage and power factor at
the sending end of the transmission line by using:
(a) A complex power approach.
(b) A circuit analysis approach.