EE 456: Power System Analysis I Homework 1: 1. The electric current and voltage at one terminal of a

 

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  50016.26 V and V2  585 0 V. 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 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 j3 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

 

 

 

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