ECE 4300/5300 ELECTRIC POWER SYSTEMS SPRING 2016 HW #1 DUE: 02/01/2016

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ECE 4300/5300 ELECTRIC POWER SYSTEMS SPRING 2016 HW #1 DUE: 02/01/2016

NOTE**: There are answers to some of the problems at the ends of the some of the course textbooks. To get full credit, you must show how you got your answers or you will receive

ZERO

score. 1. In general the voltage across an inductor and the current through a capacitor are

v L

L di L dt

and

i C

C dv C dt

respectively. (a) Consider the simple RLC circuit shown in Fig. P1.1. Choosing the inductor (b) current and the capacitor voltage as the states or variables, obtain the two integral equations for

i

L and

v

C in terms of the states or variables and the input voltage Obtain the SIMULINK simulation block diagram for the equations of (a).

i

S

R

1

i

C

R

2

v

L

L i V

S1 Fig. P1.1

2. Consider the network of Fig. P2.1. (a) Label all node voltages and branch currents (b) Compute the voltages

V

1 and

V

2 . (c) Determine the currents

I

1 ,

I

2 ,

I

3 ,

I

4 , and

I

5 . (d) Determine the total complex power of the sources. (e) Determine the total complex power from the components. (f) Draw one closed phasor/vector diagram of the currents.

v

C

V

1

C

2

Ω j

2

R

3

V

2 L

R

4

i

R

V

S2 10

Ω I

1

I

2

j

5

I

3

I

4 3

Ω I

5 5/0 o V 10/45 o V -

j

4 Fig. P2.1

3. Power System: Analysis & Design by Glover, etc. - Problem #2.50 pp. 84. 5

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