EngiMetric Arena / Spot the Error
Review this voltage-drop check: the phase factor is wrong
Competency Quantitative reasoning primary Evidence interpretation supporting
What you should take away: Use the correct voltage-drop factor for a balanced three-phase circuit and distinguish a failed check from a failed design.
The situation
What is happening
A 400 V, 100 A balanced three-phase feeder runs 150 m to a packaged plant. The conductor resistance is 0.727 ohm/km and the project allows 5 % voltage drop. The reviewer used a round-trip factor of 2 and rejected the design at 5.45 %. Review the calculation.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| System voltage | 400 | V | Line-to-line, balanced three-phase. |
| Design current | 100 | A | Full-load current. |
| One-way run | 150 | m | Cable route length. |
| Conductor resistance | 0.727 | ohm/km | 25 mm2 copper at the calculator reference temperature. |
| Allowable drop | 5 | % | Project limit. |
Assumptions this challenge makes
- The load is balanced across the three phases.
- Reactance is neglected, as in the voltage-drop engine used here.
- The conductor resistance is taken at the calculator reference temperature.
Your call
Your answer
Hints
- Write down the voltage-drop relationship before looking at the numbers. What changes between a single-phase and a balanced three-phase circuit?
- The current goes out in three phases, not out and back in one conductor pair. The factor is not 2.
- Compute the drop with sqrt(3) and compare it with the 5 % limit. Then ask whether the rejection was a calculation error or a real failure.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- For a balanced three-phase feeder the voltage drop is sqrt(3) x I x R x L. The factor 2 applies to a single-phase or DC round trip.
- Here R x L = 0.727 x 0.150 = 0.10905 ohm. The drop is sqrt(3) x 100 x 0.10905 = 18.89 V, or 4.72 % of 400 V.
- The reviewer used 2 instead of sqrt(3), obtaining 21.81 V and 5.45 %. That is the single-phase result applied to a balanced three-phase circuit.
- The feeder therefore passes the stated 5 % limit. The design was rejected because of the factor, not because the cable is inadequate.
- The same distinction matters in reverse: a passing calculation does not prove the cable is acceptable for ampacity, fault level, termination or derating. Those are separate checks.
What this challenge does not establish
- Reactance is neglected. On large conductors or high-current feeders, reactance can be a significant part of the drop.
- The conductor resistance is a table value at a reference temperature, not the operating temperature of this installation.
- Ampacity, short-circuit withstand, protective-device coordination and derating are not assessed here.
- The load is assumed balanced; an unbalanced three-phase load needs a different calculation.