代写EEE 471/591: Power System Analysis [Face-to-Face] Homework #1代做留学生SQL语言

EEE 471/591: Power System Analysis [Face-to-Face]

Homework #1

Problem 1 (16 Points)

The instantaneous voltage across a circuit element is v(t) = 400 × cos(wt + 30°) volts, and the instantaneous current entering the positive terminal of the circuit element is i(t) = 100 × sin(wt + 10°) A. For both the current and voltage, determine (a) the maximum value, (b) the rms value, (c) the phasor expression, (d) calculate the instantaneous power absorbed by this circuit element, (e) calculate the real power for this circuit element, state whether it is delivered or absorbed, (f) calculate the reactive power for this circuit element, state whether it is delivered or absorbed.

Problem 2 (16 Points)

The voltage v(t) = 359.3 × cos (wt) volts is applied to a load consisting of a 10Ω resistor in series with a capacitive reactance XC = 25Ω. Calculate (a) the instantaneous power absorbed by the resistor, (b) the instantaneous power absorbed by the capacitor, (c) the real power absorbed by the resistor, (d) the reactive power delivered by the capacitor, and (e) the load power factor.

Problem 3 (17 Points)

Consider a single-phase load with an applied voltage v(t) = 150 × cos(wt + 10°) volts and load current i(t) = 5 × cos (wt − 50°) A. (a) Find the power factor and specify whether it is lagging or leading. (b) Calculate the reactive power supplied by capacitors in parallel with the load that correct the power factor to 0.9 lagging.

Problem 4 (17 Points)

An industrial plant consisting primarily of induction motor loads absorbs 500 kW at 0.6 power factor lagging. (a) Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging. (b) Calculate the resulting power factor if a synchronous motor rated at 500 hp with 90% efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume constant voltage (1 hp = 0.746 kW).

Problem 5 (17 Points)

The real power delivered by a source to two impedances, Z1 = 4 + j5 Ω and Z2 = 10 Ω connected in parallel, is 1000 W. Determine (a) the real power absorbed by each of the impedances and (b) the source current.

Problem 6 (17 Points)

A source supplies power to the following three loads connected in parallel: (1) a lighting load drawing 10 kW, (b) an induction motor drawing 10 kVA at 0.90 power factor lagging, and (3) a synchronous motor operating at 10 hp, 85% efficiency and 0.95 power factor leading (1hp = 0.746 kW). Determine the real, reactive, and apparent power delivered by the source.