In a three-phase system, power is measured by two wattmeter method. If the reading of the wattmeters are +1000 W and -1000 W, then which of the following is correct?

Explanation:

Two Wattmeter Method in a Three-Phase System

Definition: The two wattmeter method is a technique used to measure power in a three-phase system. It involves connecting two wattmeters to the system in such a way that they measure the power consumed in the three-phase load. This method is particularly useful for both balanced and unbalanced loads.

Working Principle: In the two wattmeter method, the wattmeters are connected in such a way that each wattmeter measures the power in one phase of the three-phase system. The total power consumed by the load is the algebraic sum of the readings of the two wattmeters. The readings of the wattmeters depend on the power factor of the load and the phase angle between the line voltages and the currents.

Measurement and Analysis:

• Power Measured by Wattmeters: Let the readings of the two wattmeters be W1 and W2.
• In a balanced three-phase system, the total power (P) consumed by the load is given by:
  P = W1 + W2
• The power factor (pf) of the load can be determined using the readings of the two wattmeters:
  pf = cos(θ) = (W1 - W2) / (W1 + W2)
• Given: The readings of the wattmeters are +1000 W and -1000 W.

Calculations:

• Total Power:
  P = W1 + W2 = 1000 W + (-1000 W) = 0 W
• Power Factor:
  pf = cos(θ) = (W1 - W2) / (W1 + W2) = (1000 W - (-1000 W)) / (1000 W + (-1000 W)) = 2000 W / 0 W
  Since the denominator is zero, the power factor is undefined in a real-world sense, but it indicates that the phase angle is 90 degrees, leading to a power factor of zero.

Conclusion:

Option 1: Power factor of load is zero and total power is zero.

This option is correct because the total power calculated is zero, and the power factor is zero, which corresponds to a purely reactive load where the voltage and current are 90 degrees out of phase.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Power factor of load is one and total power is zero.

This is incorrect because a power factor of one (unity) implies that the load is purely resistive, and in such a case, the wattmeter readings would not be equal and opposite. Instead, both wattmeters would show positive readings, and their sum would not be zero.

Option 3: Power factor of load is zero and total power is 2000.

This is incorrect because while the power factor is indeed zero, the total power calculated from the given wattmeter readings is zero, not 2000 W.

Option 4: Power factor of load is one and total power is 2000.

This is incorrect because a power factor of one implies a purely resistive load, which would result in both wattmeters showing positive readings. Additionally, the total power calculated from the given readings is zero, not 2000 W.

Conclusion:

The two wattmeter method provides valuable insights into the power consumption and power factor of a three-phase system. By analyzing the readings of the wattmeters, one can determine the total power and the nature of the load. In this case, the readings indicate a purely reactive load with a power factor of zero and a total power of zero, making option 1 the correct choice.