AC power analysis

Question

A transformer rated at a maximum of 25 kVA supplies a 12-kW load at power factor 0.60 lagging. What percent of the transformer rating does this load represent? How many kW in additional load may be added at unity power factor before the transformer exceeds its rated kVA?

This is a question in one of my textbooks. I have solved the first part, comes 80%. For the second part I saw the solution in which they assumed that "reactive power " will remain same. I don't understand why?

The active power across the additional load is 7.2 kW, so this means total active power would be 12 + 7.2 = 19.2 and this is when power factor is unity, so S (complex power) = active power (19.2). But this is not the case, why?

Answer 1

The question assumes the added power will be unity power factor which implies zero reactive power. So unity power factor implies zero change to the reactive power.

My advice to you with this problem is to figure out the real, reactive and complex power for the first part of the question (which I assume you've already done since you've solved that part of the problem already). Then change the complex power to the rated power of the transformer and (as already stated) keep the reactive power the same. From this, calculate the new real power and figure out how much it has changed by. Use a vector diagram, if necessary, because a drawing can help make things more clear in your head.