Final answer:
To find the complex power per phase of the Δ-connected load, subtract the complex power of the Y-connected load from the total supplied power. first, calculate the complex power of the Y-connected load using its apparent power and power factor then find the remaining power for the Δ-connected load.
Step-by-step explanation:
To calculate the complex power per phase of the Δ-connected load, we must first understand that the total complex power supplied is the vector sum of the complex powers consumed by the Y-connected and the Δ-connected loads in parallel. Given that a three-phase positive sequence Y-connected source supplies 14 kVA with a power factor of 0.75 lagging, and the Y-connected load uses 9 kVA at a power factor of 0.6 lagging, we can find the complex power for the Y-connected load and subsequently for the Δ-connected load.
For the Y-connected load, the complex power S is given by S = P + jQ, where P is the real power and Q is the reactive power. Using the apparent power (9 kVA) and the power factor (cos φ = 0.6), we have:
- P (Y-load) = Apparent Power × Power Factor = 9 kVA × 0.6 = 5.4 kW
- Q (Y-load) can be found using the Pythagorean theorem: Q = √(S² - P²)
After calculating the reactive power Q for the Y-connected load, we subtract the Y-connected load's complex power from the total supplied complex power to find the Δ-connected load's complex power per phase.