Problem 83-6    Source:   Problem 11.17 - page 273 - Book: Circuitos Elétricos - NILSSON, James W. & RIEDEL, Susan A. - 5ª edição - Editora LTC - 1999.

In a circuit we have three balanced loads associated in parallel and connected to a source that has an effective voltage of 220 ∠0°. Load 1 is known to absorb 90 KVAr with power factor FP = 0.8 delayed. Load 2 absorbs 100 kW and 40 KVAr with advanced power factor, while load 3 absorbs 140 kW with unit power factor. Consider loads 1 and 2 formed by two elements connected in series.

a) Calculate the module of the apparent power provided by the source..

b) Calculate the line current modulus provided by the source..

c) What is the power factor of the system.

Solution of the Problem 83-6

Item a

To calculate the total apparent power we must know the average power and the reactive power of each load. Thus, for load 1 we must calculate the average or real power. Knowing the power factor, we can calculate the angle because FP = cos θ = 0.80. Then:

On the other hand, we know that Q₁ = S₁ sin θ. So, we have:

Therefore, the average power will be:

For load 2 we know that P₂ = 100 kW and - j Q₂ = - j40 kVAr, because it’s early. Therefore, we can calculate the total average power and the total reactive power of the system. So:

With these data it is possible to calculate the total apparent power of the system, or:

Carrying out the calculation:

Item b

To calculate the system line current we know that S_T = I_T V_linha. So:

Item c

Starting from the result of item a we have: