Source: https://guthlabs.ai/docs/instruments/power-factor-correction-capacitor-sizer/mechanism/

instrument mechanism / verified-clean

# Power Factor Correction Capacitor Sizer mechanism

The inspectable method record for Power Factor Correction Capacitor Sizer, kept separate from implementation and qualification.

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

## Model scope

The core reactive-power correction relationship is standard, but the specification is not sufficiently explicit to produce unambiguous three-phase capacitance. Add explicit definitions for θ, lagging/leading behavior, capacitor connection, voltage reference, and whether Qc and capacitance are total or per phase/branch. Preserve the honest label: industrial sizing estimate—verify against equipment nameplate and code before installation.

- Qc=P(tanθ1−tanθ2) is standard only when θ1=acos(existing PF), θ2=acos(target PF), P is real load power, and the load is lagging. These definitions are not stated.

- C=Qc/(2πfV²) is valid for a single capacitor phase/branch when Qc is the reactive power handled by that individual capacitor and V is its RMS voltage. For a three-phase bank, total Qc must first be divided by three; the required division and capacitor connection are unspecified.

- The specification does not define whether V means line-to-line voltage, line-to-neutral voltage, or voltage across each capacitor. Delta and wye banks require different voltage interpretations.

- The phases input does not identify the capacitor connection. Three-phase capacitance cannot be determined unambiguously from phase count and voltage alone.

- The new-PF calculation is not given. With ideal compensation and an exactly sized bank, new PF equals target PF, but rounded capacitor values produce a different PF.

## Units and conventions

- P is real power in kW; Qc is reported in kVAR, so Qc=P×(tanθ1−tanθ2) numerically gives kVAR.

- For capacitance, Qc must be converted from kVAR to VAR by multiplying by 1000.

- f is frequency in Hz and V is RMS voltage across one capacitor element.

- Capacitance is reported per phase/branch in farads, with microfarads shown in the test vectors.

- For three-phase examples, total reactive power is divided by three before applying C=Q/(2πfV²).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "load_kW": 10,
    "existing_PF": 0.8,
    "target_PF": 0.95,
    "V_V": 230,
    "f_Hz": 50,
    "phases": 1,
    "connection": "single-phase"
  },
  "expected_outputs": {
    "required_kVAR": 4.213159,
    "capacitance_per_phase_F": 0.000253514,
    "capacitance_per_phase_uF": 253.514,
    "new_PF": 0.95
  },
  "working": "θ1=acos(0.8), so tanθ1=sqrt(1−0.8²)/0.8=sqrt(0.36)/0.8=0.6/0.8=0.75. θ2=acos(0.95), so tanθ2=sqrt(1−0.95²)/0.95=sqrt(0.0975)/0.95=0.328684. Qc=10×(0.75−0.328684)=4.213159 kVAR. Convert to VAR: 4.213159×1000=4213.159 VAR. C=4213.159/(2π×50×230²)=4213.159/(2π×50×52900)=4213.159/16619025.119=0.000253514 F=253.514 µF. With ideal exact correction, new PF=0.95."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The instrument has an undefined-result failure at target_PF=0 because tan(acos(target_PF)) diverges. It also has a potentially threefold sizing error unless three-phase power, line-to-line voltage, and per-phase versus total-bank capacitance conventions are made explicit.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/power-factor-correction-capacitor-sizer/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/power-factor-correction-capacitor-sizer/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/power-factor-correction-capacitor-sizer/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`