Question

A three-phase balanced, 500 V, 50 Hz AC voltage source is delivering power to a three-phase balanced lagging load. Two-wattmeter method is used to measure the power consumed by the balanced three-phase load. The reading of the two wattmeters are 12.6 kW and 7.3 kW, respectively. Determine the power factor of the load (PF load).

Answer 1

The power factor of the balanced three-phase load, calculated from the given two wattmeter readings and the equation PF = (W1 - W2) / (W1 + W2), is approximately 0.266, indicating a lagging power factor.

Step-by-step explanation:

To determine the power factor of the load (PF load), we can use the readings from the two wattmeters and the line voltage of the three-phase system. The total power consumed by the load is the sum of the readings of the two wattmeters: P = W1 + W2 = 12.6 kW + 7.3 kW = 19.9 kW. In a balanced three-phase system, the power factor can be calculated using the formula PF = P / (√3 * VL * IL), where P is the total power, VL is the line voltage, and IL is the line current.

Since the load is balanced, we can also obtain the power factor using the expression involving the two wattmeters' readings: PF = (W1 - W2) / (W1 + W2), where W1 and W2 are the readings of the wattmeters. Using the values given, PF = (12.6 kW - 7.3 kW) / (12.6 kW + 7.3 kW). Calculating this gives us the power factor of the load:

PF load = (12.6 - 7.3) kW / (12.6 + 7.3) kW
PF load = 5.3 kW / 19.9 kW
PF load ≈ 0.266

This value of the power factor indicates that the load has a lagging power factor, which is common in circuits that have inductive elements.