Final answer:
To raise the power factor from 0.8 to 0.95 lagging for a 150 kW load, we calculate the initial and target reactive power, then determine the reactive power to be provided by the capacitor, which is 103.603 kVAR. A power triangle can be drawn to visually represent the relationship between real power, reactive power, and apparent power before and after compensation.
Step-by-step explanation:
To calculate the reactive power (Q) delivered by the capacitor to improve the power factor, we can use the following approach. First, we need to calculate the initial reactive power (Qinitial) using the apparent power (S) and actual power (P) relationship, S = P / power factor, and then find Qinitial = √(S2 - P2). For a single-phase source delivering 150 kW (P) at a power factor of 0.8 lagging, we find Qinitial = 112.5 kVAR.
We then recalculate the apparent power with the target power factor of 0.95 lagging to find the new apparent power (Snew) with Snew = P / 0.95, followed by calculating the target reactive power (Qtarget) using the same relation. The capacitance reactive power (Qc) necessary is the difference, Qc = Qinitial - Qtarget. After calculations, we find Qc = 103.603 kVAR.
The power triangle for the source and load indicates the relation between real power (P), reactive power (Q), and apparent power (S). Before compensation, the triangle is wider due to the higher reactive power component. After compensation, the triangle becomes narrower, corresponding to a higher power factor and reduced Q.