EE 456: Power System Analysis I

Homework 1:

1. The electric current and voltage at one terminal of a single phase transmission line are:

141cos( 10 ),

390cos( 5 ),

I t A

V t V

Compute the rms values of the electric current and voltage, the complex power, and the real and

reactive power flowing into the line.

2. Two single-phase ideal voltage sources are connected by a line of impedance of 0.7 *j*2.4

as shown in Fig. 1. *V*1 50016.26 V and *V*2 585 0 V. Plot *V*1,*V*2 and *I*12 in a phasor

diagram. Also, find the real and reactive power loss in the line.

Fig. 1

3. A single-phase inductive load consisting of R and X in series feeding from a 2400-V rms

single-phase supply absorbs 288 kW at a lagging power factor of 0.8. Determine R and X.

4. The system shown in Fig. 2 is balanced. Assume that:

10 15

*ca *208 120

Z

V V

Find *Vab *,*Vbc *,*Van *,*Vbn *,*Vcn *, *Ia *, *Ib *and *Ic*

Fig. 2

5. A balanced delta-connected load consisting of a pure resistances of 18 per phase is in

parallel with a purely resistive balanced Y-connected load of 12 per phase as shown in Fig. 3.

The combination is connected to a three-phase balanced supply of 346.41-V rms (line-to-line) via

a three-phase line having an inductive reactance of *j*3 per phase. Taking the phase voltage *Van*

as reference, determine

(a) The magnitudes of current, real power, and reactive power drawn from the supply.

(b) The line-to-neutral and the line-to-line voltage magnitudes of phase *a *at the combined load

terminals.

Fig. 3