Ask Question
1 October, 17:26

Calculate the resulting power factor if a synchronous motor rated at 500 hp with 90% efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor.

Assume constant voltage (1 hp = 0.746 kW).

+2
Answers (1)
  1. 1 October, 17:29
    0
    The question is incomplete. Below is the complete question

    "An industrial plant consisting primarily of induction motor loads absorbs 500 kW at 0.6 power factor lagging. (a) Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging. (b) Calculate the resulting power factor if a synchronous motor rated 500 hp with 90% efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume constant voltage. (1 hp = 0.746 kW) "

    Answer:

    a. 424.5KVA

    b. 0.808 lagging.

    Explanation:

    Let's first determine the real power, reactive and the apparent power delivered.

    Ql = Ptan (the real power angle)

    Ql=500*tan53.13°

    Ql=666.7 Kvar

    The reactive angle is

    Arccos (0.9) = 25.84°

    Now we calculate the reactive power

    Qs=Ptan25. 84°

    Qs=242.4KVAR

    Hence the apparent power is

    Qc=Ql-Qs

    Qc=666.7-242.2

    Qc=424.5KVAR

    The required KVA rating of the shunt capacitor is 424.5KVA

    b. To calculate the resulting power factor we first determine the power absorbs by the synchronous motor.

    Pm = (500*0.746) / 0.9

    Pm=414.4KW

    The total reactive power is

    Ps=P+Pm

    Ps=414.4+500=914.4KW

    Hence we compute the source power factor as

    PF=cos[arctan (Qs/Ps) ]

    PF=cos[arctan (666.7/914.4)

    From careful calculation, we arrive at

    PF=0.808.

    Note this power factor will be lagging.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Calculate the resulting power factor if a synchronous motor rated at 500 hp with 90% efficiency operating at rated load and at unity power ...” in 📗 Engineering if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers