Problem + Hard 84-2    Source:  Problem prepared by the author of the site.

Regarding the previous problem calculate:

a) the line voltages over the load.

b) the apparent, average and reactive power in the load.

c) determine the power factor of the load.

d) make a phasor diagram of the currents and voltages involved in solving the problem.

Solutiom of the Problem + Hard 84-2

Item a

Calculating the line voltages across the load is to determine the values ​​of V_AB,  V_BC  and  V_CA. Like this:

Carrying out the calculation we find:

In a similar way we do for the other two voltages and we find:

Item b

As we are working on a circuit with unbalanced loads, we must calculate the apparent power for each phase and then sum them algebraically. Let's start with phase A.

Where the current I^*_A is the complex conjugate of the current in phase A. Carrying out the calculation we find:

Repeating the calculations for the powers of the phases   B and C,   where S_B = V_BN I^*_B   and   S_C = V_CN I^*_C, we find:

To find the total apparent power of the circuit, we algebraically add the powers calculated above, or:

The problem asks to calculate the average and reactive power. However, we know that the average power is the real value of the power apparent and the reactive power is the imaginary part of that power. Soon:

Item c

Evidently, the power factor is given by the cosine of the apparent power angle, that is:

Item d

In Figure 84-2.2 we have the phasor diagram requested by the problem where we show the voltages and currents involved in solving the problem.