In polyphase AC circuits, particularly three-phase systems, it is possible to measure reactive power using only one wattmeter, provided the circuit configuration and conditions are appropriate. To achieve this, the circuit must be balanced (equal line voltages and equal load impedances) and the power factor angle (φ) should be known or measured.
Here's how you can calculate reactive power (Q) using a single wattmeter in a balanced three-phase circuit:
Measure Active Power (P): The wattmeter measures the total power (P) in the circuit. This power includes both active (real) power and reactive power. In a balanced circuit, the wattmeter reading will give you the sum of active and reactive power.
Calculate Apparent Power (S): Since the circuit is balanced, you can calculate the apparent power (S) using the formula: S = √3 * VL * IL, where VL is the line voltage and IL is the line current.
Calculate Active Power (P_actual): Using the power factor angle (φ) or cos(φ), you can calculate the actual active power (P_actual) as: P_actual = P / cos(φ).
Calculate Reactive Power (Q): Once you have the apparent power (S) and actual active power (P_actual), you can calculate the reactive power (Q) using the relationship: Q = √(S^2 - P_actual^2).
Keep in mind that this method assumes a balanced circuit and known power factor angle (φ). If the circuit is unbalanced or the power factor angle is not known, this method won't provide accurate results. Also, the direction of reactive power (leading or lagging) cannot be determined using this approach.
It's important to note that in practical situations, two-wattmeter methods or other techniques are often preferred for accurate power measurements and power factor calculations, especially in unbalanced or complex systems.