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Find the voltages, currents, powers and power factors of the first circuit as it is. Then do the same for the second one and compare them.

 

Find the voltages, currents, powers and power factors of the first circuit as it is. Then do the same for the second one and compare them.

I don't know how to treat the panels in the circuit.

 

Find the real power dissipated by each panel and then add these real powers to get the total real power dissipated by the circuit. Then find the total power factor of the circuit. Set a reference voltage to have a zero angle and find each panel's current angle with respect to this reference voltage angle, then add the currents to get the total current supplied to all panels. Find the angle between the voltage and current of phase A to find the total power factor of the circuit. Then calculate the cost by using the total real power plus the penalty due to the low power factor. To the same process for the second circuit and compare them.

 

Your motor load is the only one of the three that exhibits a power factor less than 1.
Motors contain coils and iron which create inductors. The inductive property of the motors cause the current in the circuit to lag the voltage to some degree.
To correct the lagging current, you must introduce something into the circuit which will cancel the effects of the motor inductance. What type of device exhibits tendencies which are opposite of inductance?

 

Find the real power dissipated by each panel and then add these real powers to get the total real power dissipated by the circuit. Then find the total power factor of the circuit. Set a reference voltage to have a zero angle and find each panel's current angle with respect to this reference voltage angle, then add the currents to get the total current supplied to all panels. Find the angle between the voltage and current of phase A to find the total power factor of the circuit. Then calculate the cost by using the total real power plus the penalty due to the low power factor. To the same process for the second circuit and compare them.

Ok, so maybe I'm not understanding this as well as I though.
As I'm going through trying to calculate the real power, I'm getting imaginary numbers... and also, I'm not familiar with the concept of setting a voltage to have a zero angle- could you explain what that means? We just moved to covering this in my class, and my textbook is not very helpful.

 

Well, you have to assume that a voltage has an angle of zero as to calculate all the other angles (current and impedance angles) referred to it. You can assume anything to have an angle of zero and make calculations referred to it but voltages are the usual thing.

For example, if you calculate a current to have an angle of 40 degrees, this value of 40 degrees has to be referred to another quantity,e.g voltage. This other quantity is your reference point where all the other angles are measured to.