EE 456: Power System Analysis

 

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 j2.4

 

as shown in Fig. 1. V1 50016.26V and V2 585 0V. Plot   V1,V2 and I12 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 12per 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 j3per 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