Source: https://guthlabs.ai/docs/instruments/three-phase-power-calculator/
instrument / verified-with-binding-errata
# Three-Phase Power Calculator
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Electrical & Electronics Engineering — Circuits, Power Systems, Electronics Lab
**Tranche**: tranche-4
**Evidence ID**: t4-042
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The current specification is incomplete for its claimed outputs and leaves the PF sign convention, RMS convention, and balanced-system scope unstated. The honest label should explicitly state that results apply to balanced three-phase RMS systems and that reactive-power sign requires a leading/lagging input.
### Formula and scope findings
- P=√3·VL·IL·cosθ is correct for a balanced three-phase system using RMS line-to-line voltage, RMS line current, and power factor, but the spec does not state the balanced, sinusoidal, RMS assumptions.
- VL=√3·VPh is correct for a balanced wye connection only. For delta, VL=VPh; this required relationship is missing.
- The claimed Q output has no formula. For balanced operation, Q=√3·VL·IL·sinθ, but PF magnitude alone does not determine the sign of Q; leading versus lagging must be supplied.
- The claimed S output has no formula. For balanced operation, apparent power magnitude is S=√3·VL·IL.
- The claimed IL/IPh conversions are not specified. For wye, IL=IPh; for delta, IL=√3·IPh.
- The PF input is ambiguous: it must be identified as a magnitude with a separate leading/lagging indicator, or as a signed quantity. PF=cosθ alone is insufficient to determine reactive-power sign.
### Unit assumptions
- VL and VPh are RMS volts; VL is line-to-line voltage and VPh is per-phase voltage.
- IL and IPh are RMS amperes; IL is line current and IPh is per-phase current.
- P and Q are watts and vars; S is volt-amperes.
- PF is dimensionless and represents the magnitude of displacement or true power factor, normally between 0 and 1; leading or lagging must be separately specified for Q sign.
- The formulas assume a balanced three-phase system. The listed voltage and current relationships assume standard wye or delta connections.
- Angles and trigonometric functions use degrees or radians consistently; the examples use PF directly and derive |sinθ|=√(1−PF²).
## Boundary hardening
### Recorded hazards
- Division by √3 is safe, but any inverse calculation such as current=power/(voltage·PF) requires explicit zero-voltage and zero-PF handling.
- PF values outside [0,1] are invalid if PF is an unsigned magnitude; the implementation must reject them or define signed-PF semantics.
- PF=0 makes calculations that divide by PF undefined, even though direct P, Q, and S calculations remain valid.
- Q sign is indeterminate unless leading or lagging behavior is provided; silently assuming lagging would produce misleading results.
- Unbalanced loads, non-sinusoidal waveforms, phase-to-neutral versus line-to-line voltage confusion, and peak-versus-RMS inputs can produce incorrect results.
- Connection type must be validated before applying wye/delta voltage and current conversions.
## Errata and corrections
### Tranche errata
**S_VA, Q_var** · vector 3
4782.860228
4780.4602
used √3≈1.7329 in S (her own Vph used the correct 1.73205)
**S_VA, Q_var** · vector 4
S 3600, Q 2160
S 1800, Q 1080
S doubled; contradicts her own correct P=1440 at PF 0.8
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"connection": "wye",
"VL_V": 400,
"IL_A": 10,
"PF": 0.8,
"reactive_behavior": "lagging"
},
"expected_outputs": {
"VPh_V": 230.940108,
"IPh_A": 10,
"P_W": 5542.562585,
"Q_var": 4156.921939,
"S_VA": 6928.20323
},
"working": "VPh=VL/√3=400/1.732050807=230.940108 V. For wye, IPh=IL=10 A. P=√3·VL·IL·PF=1.732050807·400·10·0.8=5542.562585 W. S=√3·VL·IL=1.732050807·400·10=6928.20323 VA. |sinθ|=√(1−0.8²)=√0.36=0.6; lagging gives positive Q, so Q=S·0.6=6928.20323·0.6=4156.921939 var."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche4/tranche4-results.json`