AC Power Triangle Calculator mechanism

Model scope

The instrument cannot honestly claim a complete AC power-triangle calculator until it replaces or clarifies S=VI*, defines RMS phasor assumptions, supports the stated P-and-Q input mode, specifies angle units and reactive-power sign convention, and handles S=0 without division.

• S=VI* is not the scalar apparent-power formula as written. For RMS scalar voltage and current inputs, apparent power is |S|=V_rms I_rms in VA. For complex RMS phasors, complex power is S_complex=V I*, while apparent power is |S_complex|.
• P=VI cos(theta) and Q=VI sin(theta) are valid for balanced sinusoidal steady-state AC when V and I are RMS magnitudes and theta is the voltage-current phase angle. They are not generally valid for arbitrary nonsinusoidal waveforms.
• PF=P/S is valid only when S means the nonnegative apparent-power magnitude |S|. With the complex-power interpretation of S=VI*, this division is ambiguous or invalid.
• The input option 'or P & Q' is not supported by the listed formulas. If P and Q are inputs, the calculator needs S=sqrt(P^2+Q^2) and PF=P/S, with an explicit convention for the sign of Q.
• The specification does not state whether theta is in degrees or radians, and it does not define the sign convention for positive or negative reactive power.

Units and conventions

• V and I are RMS magnitudes, not peak values.
• V and I must use compatible units; the worked vectors convert 0.120 kV to 120 V before calculation.
• P and Q are in watts and vars, S is in volt-amperes, and PF is dimensionless.
• theta is the voltage phase angle minus the current phase angle and is expressed in degrees in these test vectors.
• Positive Q denotes inductive (lagging-current) reactive power; negative Q denotes capacitive (leading-current) reactive power.
• The formulas assume single-phase sinusoidal steady-state conditions unless an explicit three-phase configuration and line/phase convention are added.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "V": 120,
    "V_unit": "V",
    "I": 10,
    "I_unit": "A",
    "phase_angle": 30,
    "phase_angle_unit": "degrees"
  },
  "expected_outputs": {
    "P_W": 1039.2305,
    "Q_var": 600,
    "S_VA": 1200,
    "PF": 0.8660254
  },
  "working": "S = V I = 120 x 10 = 1200 VA. P = V I cos(theta) = 120 x 10 x cos(30 degrees) = 1200 x 0.8660254 = 1039.2305 W. Q = V I sin(theta) = 1200 x 0.5 = 600 var. PF = P/S = 1039.2305/1200 = 0.8660254."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-voltage input produces S=0 and makes PF=P/S equal to 0/0, so the calculator must reject the input or report power factor as undefined rather than returning a numeric value.

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
• BOUNDARY_HAZARD_CATALOG.json