Each problem must be documented separately!
1. (a) Determine the conditions for delivering maximum torque at starting of a three-phase induction motor.
(b) A 500-V, 3-phase, 8-pole, 50Hz, Y-connected induction motor has the following equivalent circuit parameters; RI = 0.135, R2 = 0.1352, x, = 0.652, .x2 = 0-652 .The magnetizing branch admittance Y. = 0.004 - j0.0511 referred to the stator (primary) side. The full-load slip is
5% and the rotational losses (mechanical losses) is 890 W. Using the approximate equivalent circuit; determine the full-load electromagnetic torque, the shaft torque, the stator input current, the total input power and input power factor, the gross mechanical output, the rotor copper losses and efficiency.
(c) Describe the no-load (light running) and locked rotor tests of a 3-phase induction motor.
The following problem must be solved in MATLAB (attach all codes, results and methods)
2. A single-phase load is supplied by a 277V source and drawing 14 kW at 0.55 power factor lagging. It's decided to connect a capacitor bank in parallel with the load to reduce the total line current provided by the utility source.
(a) Calculate the capacitance (uF) required to improve the power factor to 0.95 lagging
(b) Calculate and plot the capacitance against the power factor for the range 0.55pf lagging to unity power factor.
(c) Calculate and plot the magnitude of the current provided by the source against the power factor for the range 0.55p1 lagging to unity power factor.
(d) Calculate and plot the magnitude of the current against the capacitance for the range 0.55pf lagging to unity power factor.
3) A 50KVA, 440V,60HZ distribution transformer has a maximum efficiency at full load and unity power factor of 92%. The transformer is loaded over a 24 hours period as follows: no load for 11 hours:1/4 full load for 4 hours; 1/2 full load for 6 hours and full load for 3 hours. Calculate the all-day efficiency of this transformer.
A two-bus power system is shown below. The line impedance is j 0.5 p.u., and the load demand at bus 2 is PD +jQD = 0.4 +j 0 p.u.
(a). Write the equations you need to perform the Newton Raphson power flow algorithm. Show only the equations needed to find the voltage phasors at all buses.
(b). Perform one iteration of the Newton Raphson algorithm to find the voltage phasor at bus 2. Use the flat start initial conditions.
VI= 1.0 /0° V2
