Homework

The next problem(s) addresses the following course learning objective(s):
- Understand balanced three phase circuits.
- Analyze various three phase circuits such as Y-Y, Y-Δ, Δ-Y, and Δ-Δ

1. Problem 1
a) Find I_o in the circuit in Fig. P11.6.
b) Find V_AN.
c) Find V_AB.
d) Is the circuit a balanced or unbalanced three-phase system?

Figure P11.6

2. Problem 2

The time-domain expressions for three line-to-neutral voltages at the terminals of a Y-connected load are
v_AN = 7967 cos ωt V,
v_BN = 7967 cos (ωt + 120°) V,
v_CN = 7967 cos (ωt - 120°) V.

What are the time-domain expressions for the three line-to-line voltages v_AB, v_BC, and v_CA?

3. Problem 3

A balanced three-phase circuit has the followily characteristics:
- Y-Y connected;
- The line voltage at the source, V 120√3∠0° V;
- The phase sequence is positive;
- The line impedance is 2 + j3 Ω/Φ;
- The load impedance is 28 + j37 Ω/Φ.

a) Draw the single phase equivalent circuit for the a-phase.

b) Calculated the line current in the a-phase.

c) Calculated the line voltage at the load in ilia a-phase.

4. Problem 4

A balanced Y-connected load having an impedance of 96 - j28 Ω/Φ is connected in parallel with a balanced A-connected load having an impedance of 144 + j42 Ω/Φ. The paralleled loads are fed from a line having an impedance of j.5 Ω/Φ. The magnitude of the line-to-neutral voltage of the Y-load is 7500 V.

a) Calculate the magnitude of the current in the line feeding the loads.
b) Calculate the magnitude of the phase current in the A-connected load.
c) Calculate the magnitude of the phase current in the Y-connected load.
d) Calculate the magnitude of the line voltage at the sending end of the line.

5. Problem 5

A three-phase Δ-connected generator has an inter¬nal impedance of 0.6 + j4.8 Ω/Φ. When the load is removed from the generator, the magnitude of the terminal voltage is 34,500 V. The generator feeds a A-connected load through a transmission line with an impedance of 0.8 + j6.4 Ω/Φ. The per-phase impedance of the load is 2877 - j864 Ω

a) Construct a single-phase equivalent circuit.
b) Calculate the magnitude of the line current.
c) Calculate the magnitude of the line voltage at the terminals of the load.
d) Calculate the magnitude of the line voltage at the terminals of the source.
e) Calculate the magnitude of the phase current in the load.
f) Calculate the magnitude of the phase current in the source.

5. Problem 6

a) Find the rms magnitude and the phase angle of ICA in the circuit shown in Fig. P11.28.

b) What percent of the average power delivered by the three-phase source is dissipated in the three-phase load?

Figure P11.28

Problem 7

A balanced three-phase distribution line has an impedance of 1 + j5 Ω/Φ. This line is used to supply three balanced three-phase loads that are connected in parallel. The three loads are L₁ = 75 kVA at 0.96 pf lead, L₂ = 150 kVA at 0.80 pf lag, and L₃ = 168 kW and 36 kVAR (mag-netizing). The magnitude of the line voltage at the terminals of the loads is 2500VA V.

a) What is the magnitude of the line voltage at the sending end of the line?

b) What is the percent efficiency of the distribution line with respect to average power?