Question

1 A single phase AC system

Consider a single phase AC distribution system in which there a single home connected to a 10kVA service transformer. Let’s assume that the primary of the distribution transformer can be modeled as an ideal 240V (rms) AC source and that the effective impedance of the transformer is 2% resistance and 3% reactance. (See lecture notes for converting % to Ohms). Connected to the secondary of the transformer is 200 ft of #6 AWG aluminum cable. Let’s assume that #6 AWG aluminum cable has 0.659Ω per 1000 ft resistance and 0.1194Ω per 1000 ft reactance. Connected to the end of the triplex cable is the home, which is serving the following loads (in parallel):

• An air conditioning system with a 2kW of load, and a 0.8 power factor (lagging)

• An electric resistance hot water heater with a load of 4.5kW (purely resistive)

• An electric vehicle with a 6kW charging load (unity power factor)

• An additional 500 W of miscellaneous “plug” loads (assume 0.9 pf lagging)

Given this information, perform the following calculations :

• Find the active and reactive power of the combined house load

• Find the apparent power of the load • Find the combined power factor of the load

• Find the power factor angle of the load

• Find the current traveling through the cable (magnitude only in Amps)

• Find the voltage magnitude drop in Volts and percent between the (implied) 240V source and the load.

• Find the active power losses in the line

• Do you have any concerns about this distribution system design? What distribution system design changes would you suggest?

Answer 1

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