School of Engineering and Computer Science | Baylor University
Smart Grid, Fall 2020HW#2. Sending Power Down a WireConnect a Vs = 480Vrms, single-phase voltage source to one end of a long wire approx.. 30 feet above the Earth to supply power to serve an oil pump some distance away. The wire-over-the-Earth model has parameters R, L, and shunt C per meter or km. R = 0.1 ohms/km, L = 1.0 μH per meter, C = 10 pF per meter. Since the line is less than 5% of the wavelength of 60 Hz, it can modeled as lumped values of series R and L, plus one-half of C on each end to ground.Do not use input numbers yet! Develop the phasor ratio of customer Vload divided by Vs. Compare your results to those in class.Now, enter the numbers and compute polar form values for the voltage across every element and the current through the element.Use the equations and values to compute the currents in all branches. Confirm your solution using KCL at both major nodes (i.e., Vs and Vload)So that you’ll have voltages across all branches, determine the voltage across the wire R and across the wire L Now, compute the average p(t) power absorbed by every element. The sum must be zero because of conservation of power..Write the voltage currents in time-domain form.HW#3. Sending Power Down a Wire, cont. All spreadsheet.Now, you will use the power down a wire spreadsheet. Each of you has a variation from the original problem. Place your inputs into the spreadsheet, and determine the value of motor load resistance that will result in Mag(Vload/Vs) = 0.80. The value of 0.80 is important because it is at the point of voltage collapse, as seen in the spreadsheet graph.A motor draws 5 times normal current during start-up. If the voltage falls below 0.8 pu, it will not start. Insert an inductance Lmot in series with the motor resistance that has 1/5th the ohms of the motor load resistance. Check part (a) again, there should not be much change.Now remove the motor load resistance so that the start-up motor model is only Lmot.Repeat (a), raising the Lmot until the voltage drop is 0.80pu. Now, Lmot_new = LmotA motor with load resistance = 5 times the Lmot_new impedance represents the largest motor that your wire can realistically supply. Use 480V^2 / new motor load resistance to approximate the max motor kW that the customer can use. ................
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