Source: https://guthlabs.ai/docs/instruments/ac-power-triangle-calculator/mechanism/

instrument mechanism / verified-clean

# AC Power Triangle Calculator mechanism

The inspectable method record for AC Power Triangle Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

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

- `BOUNDARY_HAZARD_CATALOG.json`