Three-Phase Power Calculator mechanism

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

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