Problem 84-3    Source:   Problem elaborated by the author of the site.

Using the data from the previous problems, calculate:

a) The total real power at each phase.

b) The total reactive power and in each phase.

c) The total apparent power at each phase.

Solution of the Problem 84-3

The previous problems (84-1 and 84-2) there are the following data to solve this problem:

V_AB = 180.3 ∠86.3°,   V_BC = 234.3 ∠-33.7°,     V_CA = 212.6 ∠-166.4°,

I_AB = 18.03 ∠56.3°  ,   I_BC = 19.53 ∠-3.7°,     I_CA = 11.81 ∠-226.4°,

Z_AB = 10 ∠30°  ,   Z_BC = 12 ∠-30°   and   Z_CA = 18 ∠60°.

Given these data, we can calculate the values requested in the problem. So:

Note that the angles of complex apparent power are exactly the angles of the impedances of each phase. In order to calculate the active and reactive power of each phase it is enough to transform the complex apparent power from the phasor to the Cartesian form. Soon:

Thus, the real part of the apparent power in the Cartesian form is active power and the imaginary part is the reactive power. The above results are the values for each phase.

To calculate the total values just add the three phases, real part with real and imaginary part with imaginary. Thus:

To calculate the total apparent power, we use a eq. 82-08, shown below.

Substituting the numerical values and performing the calculation: