• Engineering

## Homework Statement

An induction motor load of 2000 kVA has power factor 0.80 lagging. Synchronous motors totaling 500 kVA are added an operated at a leading power factor. If the overall power factor is then 0.90 lagging, what is the power factor of the synchronous motors?

## Homework Equations

i use power triangle to solve the values of powers in induction motor..

## The Attempt at a Solution

i have solve the reactive power = 1200 kvar ; p=1600 kw..
i am confuse how to use the total power factor... in need to find the real power in the synchronous motors... in order to find the power factor of the synchronous motors...

It's vectors and algebraic problem. Write down all all real and reactive powers and solve for unknowns.

We add real powers together and reactive power together.

Say, induction motor has pf of 'x'.

Your total system real power will be 1200+500*x
Your total system reactive power will be1600 + .....
Relation between total real and reactive power is given by pf of 0.9

hello sir i am the one who ask the question about ac circuit analysis power....i am confuse on what other equations i will make since there reactive power are different other one is lagging and other one is leading. i am really confused sir and i am afraid if the same procedure of problem will come out on our exam .... thank you sir and sorry for the disturbance

Yes the reactive powers are different: one is positive other is negative. Let's say reactive power of synchronous is Reactive_sync

Then the total system reactive power will be be 1600 - Reactive_sync

Now, we have x and y components of the total system.

y/x = tan (acos pf_total_system)...

Yes the reactive powers are different: one is positive other is negative. Let's say reactive power of synchronous is Reactive_sync

Then the total system reactive power will be be 1600 - Reactive_sync

Now, we have x and y components of the total system.

y/x = tan (acos pf_total_system)...

how can i find the reactive power of the synchronous motors when there is no given phase angle.....will i use arccosine of x to find x?....

how can i find the reactive power of the synchronous motors when there is no given phase angle.....will i use arccosine of x to find x?....

Yes that's right. Or you can use Pythagoras theorem .

Yes that's right. Or you can use Pythagoras theorem .

is this equation correct (1600-arcos x...)/(P1+P2) = tan (arcos 0.90)