Source: https://guthlabs.ai/docs/instruments/three-phase-power-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# Three-Phase Power Calculator mechanism

The inspectable method record for Three-Phase Power Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

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.

- 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.

## Units and conventions

- 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).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "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."
}
````

## Failure boundary

- 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.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/three-phase-power-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/three-phase-power-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/three-phase-power-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`