Problem: Single phase AC Circuit
The supply voltage in Figure 1 is given by v(t) 150 cos wt and the load is inductive with impedance Determine the expression for instantaneous current i (t) and the instantaneous power p(t). Use MATLAB to plot i(t), v(t), p(t), pR (t), and pX (t) over the interval of 0 to 2π.

Problem: 3-phase AC Circuit
For the previous problem, determine the expression for instantaneous current i (t) and the instantaneous power p(t) for the three-phase balanced load. Use MATLAB to plot i(t), v(t), p(t), pR (t), and pX (t) over the interval of 0 to 2π.

Problem: Write a MATLAB program for the system shown in Figure 1 such that the phase angle of source 1 is changed from its initial value by ±30o in steps of 10o. Voltage magnitudes of the two sources and the voltage phase angle of source 2 are to be kept constant. Compute the complex power for each source and the line loss. Tabulate the real power and plot P1, and P2, and PL versus voltage phase angle δ

Problem: A 24,000-kVA, 17.32-kV, 60-Hz, three-phase synchronous generator has a synchronous reactance of 5 ?/phase and negligible armature resistance.

a) At a certain excitation, the generator delivers rated load, 0.8 power factor lagging to an infinite bus bar at line-to-line voltage of 17.32 kV. Determine the excitation voltage/phase.

b) The excitation voltage is maintained at 13.4 kV/phase and terminal voltage at 10-kV/phase. What is the maximum three-phase real power that the generator can develop before pulling out of synchronism?

c) Determine the armature current for the condition of part (b).

Problem: A 150-kVA, 2400/240-V, single-phase transformer has the parameters as shown in Figures.

a) Determine the equivalent circuit referred to the high-voltage side.

b) Find the primary voltage and voltage regulation when the transformer is operating at full load 0.8 power factor lagging and 240 V.

c) Find the primary voltage and voltage regulation when the transformer is operating at full load 0.8 power factor leading.

d) Verify your answers by running the trans program in MATLAB and obtain transformer efficiency curve.

Problem: The three-phase power and line-line ratings of the electric power system shown in Figure 1 are given below

One-line diagram for Figure 1:

G1 : 60 MVA 20 kV X = 9%

T1 : 50 MVA 20/200 kV X = 10%

T2 : 50 MVA 200/20 kV X = 10%

M : 43.2 MVA 18 kV X = 8%

Line : 200 kV X = 120+j200?

Load : 18 kV S = 24 MW + j32 Mvar

a- Draw an impedance diagram showing all impedances in per-unit on a 100-MVA base. Choose 20 kV as the voltage base for the generator using the following equations:

b- Determine the voltage at the generator bus bar (Vg ).

c- Determine the generator and the motor internal emfs.

Problem: Short Transmission Line

A 220 KV, three-phase transmission line is 40 km long. The line has a per phase series impedance of 0.15 + j 0.5 ? per Km. Write a MATLAB program to find the voltage and power at the sending end, the voltage regulation and efficiency when the line is supplying a three-phase load of

a) 381 MVA at 0.8 power factor lagging at 220 kV.

b) 381 MVA at 0.8 power factor leading at 220 kV.

Problem: Medium & long Transmission line models

A 230 KV, three-phase transmission line is 200 km long. The line has a per phase series impedance of 0.05 + j 0.45 ? per Km and a shunt admittance of y = j3.4 * 10-6 Siemens per km. Write a MATLAB program to determine the following as short, medium, and long TL

a) The transmission line ABCD constants.
Find the sending end voltage and current, the voltage regulation and the sending end power& efficiency when delivers:

b) 200 MVA at 0.8 power factor lagging at 220 kV.

c) 306 MW, unity power factor at 220 kV.