Library / Circuits, electronics and noise / ELN-45
Circuits, electronics and noise
Balanced delta line current
RMS line current of a balanced delta load whose identical branch impedances have magnitude |Z|, from the line-to-line voltage.
- Ref
- ELN-45
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Iline [A]
In a balanced delta load each branch is connected between two lines, so it carries the full line-to-line voltage, giving a branch current Vline/|Z|. The line current is the phasor difference of two branch currents 120° apart, which is √3 times the branch current. So Iline = √3 Vline/|Z|, or three times the line current of the same impedances in a star at the same line voltage.
RMS line current of a balanced delta load whose identical branch impedances have magnitude |Z|, from the line-to-line voltage. The line current is the phasor difference of two branch currents 120° apart.
Calculator
- Branch (phase) current, Vline/|Z|20 A
- Line current if the same impedances were in star11.55 A
- Ratio of delta to star line current3
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.
- A 400 V supply and 20 Ω branches give 20 A in each branch and 34.64 A in each line.
- The cable must be sized for the line current of 34.64 A, which is 1.73 times the branch current.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (A) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vline RMS line-to-line voltage | 100 to 10,000 V | 8.66 | 866 | 857.4 | +10% | +10 % |
| |Z_Δ| Magnitude of each delta branch impedance | 1 to 1,000 Ω | 0.6928 | 692.8 | 692.1 | +10% | −9.09 % |
Sweep of Magnitude of each delta branch impedance
| Magnitude of each delta branch impedance (Ω) | Line current (A) |
|---|---|
| 1 | 692.8 |
| 2.371 | 292.2 |
| 5.623 | 123.2 |
| 13.34 | 51.95 |
| 31.62 | 21.91 |
| 74.99 | 9.239 |
| 177.8 | 3.896 |
| 421.7 | 1.643 |
| 1,000 | 0.6928 |
Sweep one variable
Variables and how each one contributes
Line current
What the equation gives you. Everything else feeds it.
RMS line-to-line voltage
The RMS line-to-line voltage, in V. Raises both branch and line currents in direct proportion. Raising it by 10 % (to 440) moves the result by +10 %, from 34.64 to 38.11 A.
Magnitude of each delta branch impedance
The magnitude of each delta branch impedance, in Ω. A larger impedance reduces the current in inverse proportion. Raising it by 10 % (to 22) moves the result by −9.09 %, from 34.64 to 31.49 A.
Worked example with the values above
- Branch current: Vline/|Z| = 400 / 20 = 20 A.
- Multiply by √3 = 1.7321.
- Iline = 34.641 A.
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