Library / Circuits, electronics and noise / ELN-43
Circuits, electronics and noise
Total real power by the two-wattmeter method
Total real power of a three-phase, three-wire circuit as the algebraic sum of the two wattmeter readings in the standard connection.
- Ref
- ELN-43
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Ptotal [W]
In a three-wire three-phase system with two wattmeters connected in the standard way, each with its current coil in one line and its voltage coil between that line and the third line, the sum of the two readings equals the total real power. This holds for any load, balanced or not. A reading can be negative: for a power factor below 0.5 one meter reads backwards, and the sign must be kept in the sum.
Total real power of a three-phase, three-wire circuit as the algebraic sum of the two wattmeter readings in the standard connection. A reading can be negative, and the circuit does not have to be balanced.
Calculator
- Difference of the readings, W₁ − W₂2,800 W
- Share of the total carried by meter 1120 %
- Balanced power factor from the readings0.3812
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The two meters read 2,400 W and −400 W, so the load takes 2,000 W in total.
- If the load is balanced the readings also give the power factor: here 0.381.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W) | Local step | Change in result |
|---|---|---|---|---|---|---|
| W1 Wattmeter 1 reading (signed) | −5,000 to 5,000 W | −5,400 | 4,600 | 10,000 | +200 W | +10 % |
| W2 Wattmeter 2 reading (signed) | −5,000 to 5,000 W | −2,600 | 7,400 | 10,000 | +200 W | +10 % |
Sweep of Wattmeter 2 reading (signed)
| Wattmeter 2 reading (signed) (W) | Total real power (W) |
|---|---|
| −5,000 | −2,600 |
| −3,750 | −1,350 |
| −2,500 | −100 |
| −1,250 | 1,150 |
| 0 | 2,400 |
| 1,250 | 3,650 |
| 2,500 | 4,900 |
| 3,750 | 6,150 |
| 5,000 | 7,400 |
Sweep one variable
Variables and how each one contributes
Total real power
What the equation gives you. Everything else feeds it.
Wattmeter 1 reading (signed)
The reading of wattmeter 1, in W, with its sign. Adds one for one to the total. Raising it by 10 % (to 2,640) moves the result by +12 %, from 2,000 to 2,240 W.
Wattmeter 2 reading (signed)
The reading of wattmeter 2, in W, with its sign. Adds one for one to the total. Raising it by 10 % (to −440) moves the result by −2 %, from 2,000 to 1,960 W.
Worked example with the values above
- Meter 1 reads 2,400 W.
- Meter 2 reads −400 W, a negative value that must be subtracted.
- P = 2,400 + (−400) = 2,000 W.
Assumptions and limits
- Sinusoidal steady state with RMS values, and a balanced three-phase load where stated.
- Accurately connected meters in the standard two-wattmeter arrangement.
Common mistakes
- Using peak voltage where RMS is needed.
- Ignoring the sign of one wattmeter reading, which can be negative for power factors below 0.5.
- Using line-to-line voltage where the phase voltage is needed, or the reverse, a factor of √3.
Statistics and uncertainty
Meter errors, supply voltage fluctuation and unbalance all move these results. Wattmeter readings carry the meter’s accuracy class, and for the balanced-load formulas any unbalance gives an error, so check the readings against the total power.
Where it is used
- Power-factor correction in plants and workshops.
- Measuring power in three-phase motors and checking delta loads and cables.
Maths you need
- RMS values: the equivalent steady value of an AC quantity
- Real, reactive and apparent power: P, Q and S
- Three-phase systems: line and phase quantities differ by √3