Improve Power Factor Calculation in Industrial Plant
How can we improve the power factor in an industrial plant?
An industrial plant consisting primarily of induction motor loads absorbs 500 kW at 0.6 power factor lagging. Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging.
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. 424.5 KVA
b. 0.808 lagging.
Let's first determine the real power, reactive, and apparent power delivered. Given that the industrial plant absorbs 500 kW at 0.6 power factor lagging, we can calculate the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging.
The reactive power is calculated by Ql = Ptan(the real power angle), which equals 666.7 Kvar. The reactive angle is found to be Arccos(0.9) = 25.84°. By calculating the reactive power Qs = Ptan(25.84°), we get 242.4 KVAR. Hence, the apparent power is determined as Qc = Ql - Qs, resulting in 424.5 KVA, the required KVA rating of the shunt capacitor.
To calculate the resulting power factor when 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, we first determine the power absorbed by the synchronous motor. Pm = (500 * 0.746) / 0.9, leading to 414.4 KW. The total reactive power Ps = P + Pm, which equals 914.4 KW. The source power factor is then computed as PF = cos(arctan(Qs/Ps)), resulting in PF = 0.808. This power factor is lagging.