Two Wattmeter Method — Power Measurement in Three-Phase Circuits
The Two Wattmeter Method is the most widely used technique for measuring total power in a three-phase system. It works for both balanced and unbalanced loads, star or delta connected, making it indispensable in electrical power measurement. This article covers the complete theory, derivation, power factor determination, effect of load type on wattmeter readings, and practical applications.
Wattmeter Basics
A wattmeter consists of two coils:
- Current Coil (CC) — A low-resistance coil connected in series with the line carrying current.
- Pressure Coil (PC) — A high-resistance coil connected across the two points whose potential difference is to be measured.
The wattmeter reading equals the product of current through CC, voltage across PC, and the cosine of the angle between them.
Circuit Arrangement
In the Two Wattmeter Method, current coils of two wattmeters are inserted in any two of the three lines. The pressure coil of each wattmeter is connected between its respective line and the third line (the line without a current coil).
This arrangement works for both star-connected and delta-connected loads:
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| Two Wattmeter Connection for Star-Connected Load |
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| Two Wattmeter Connection for Delta-Connected Load |
Proof: W1 + W2 = Total Power
Consider a balanced three-phase star-connected load with phase voltages VR, VY, VB and line currents IR, IY, IB. Wattmeter current coils are in lines R and Y; pressure coils are connected to line B.
W2 = IY × (VY − VB)
Adding both readings:
= VRIR + VYIY − VB(IR + IY)
By Kirchhoff's Current Law: IR + IY + IB = 0, therefore IR + IY = −IB
Hence, the sum of two wattmeter readings gives the total power consumed in a three-phase circuit — regardless of whether the load is balanced or unbalanced, star or delta connected.
Power Factor from Wattmeter Readings
For a balanced load with power factor angle φ, the individual wattmeter readings are:
W2 = VL × IL × cos(30° + φ)
From these expressions, the power factor can be determined:
Power Factor = cos φ = cos[arctan(√3 × (W1 − W2) / (W1 + W2))]
This formula allows determination of power factor without needing separate voltage and current measurements — a significant practical advantage.
Effect of Power Factor on Wattmeter Readings
Key insight: When power factor is less than 0.5, one wattmeter gives a negative reading. In practice, the pressure coil connections of that wattmeter are reversed, and the reading is subtracted from the other wattmeter's reading to get total power.
Advantages & Limitations
Advantages:
- Measures total power in any three-phase, three-wire system (balanced or unbalanced)
- Works for both star and delta connections
- Power factor can be determined from the two readings alone
- Reactive power can also be calculated: Q = √3 × (W1 − W2)
- Only two instruments needed instead of three
Limitations:
- Not applicable to three-phase, four-wire systems (use three wattmeter method instead)
- For unbalanced loads, individual phase powers cannot be separated
- When PF < 0.5, one reading becomes negative — requires reversing connections
Solved Numerical Example
Problem: Two wattmeters connected to a balanced three-phase load read W1 = 5000 W and W2 = 1500 W. Find the total power, power factor, and reactive power.
tan φ = √3 × (W1 − W2) / (W1 + W2)
tan φ = 1.732 × (5000 − 1500) / (5000 + 1500)
tan φ = 1.732 × 3500 / 6500 = 0.932
φ = arctan(0.932) = 43°
Power Factor = cos 43° = 0.731 (lagging)
Reactive Power Q = √3 × (W1 − W2) = 1.732 × 3500 = 6062 VAR
Frequently Asked Questions
1. Why is the Two Wattmeter Method the most popular for three-phase power measurement?
It requires only two instruments to measure total power in any three-wire system, works for both balanced and unbalanced loads, and additionally provides power factor information — making it the most economical and versatile method.
2. Can the Two Wattmeter Method be used for a four-wire system?
No. In a four-wire (three-phase + neutral) system, the neutral carries current, and KCL at the load point gives IR + IY + IB + IN = 0. The derivation relies on IR + IY + IB = 0, which doesn't hold. Use the three wattmeter method instead.
3. What does a negative wattmeter reading indicate?
A negative reading on one wattmeter indicates that the power factor of the load is less than 0.5 (φ > 60°). The pressure coil connections are reversed, and the reading is treated as negative in the total power calculation: P = W1 − |W2|.
4. How do you find reactive power using the Two Wattmeter Method?
For a balanced load, reactive power Q = √3 × (W1 − W2). This is derived from the individual wattmeter expressions involving cos(30° ± φ) and using trigonometric identities.
5. Does the Two Wattmeter Method work for delta-connected loads?
Yes. The proof uses only KCL at the load terminals and makes no assumption about whether the load is star or delta connected. The method is valid for any three-phase, three-wire load configuration.