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  "assumptions": [
    "Sinusoidal RMS voltage and current magnitudes.",
    "Balanced three-phase when 3φ L-L or L-N modes are selected.",
    "Correction capacitor estimate (UI) fully offsets computed Q toward unity PF (idealized)."
  ],
  "limitations": [
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    "Not for harmonic-rich or engineered bank design",
    "When P > S, PF is capped at 1 and Q = 0 (soft clamp)",
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    "Missing V/I/P_kW → MISSING_REQUIRED_INPUT",
    "Negative I or P_kW → VALUE_MUST_BE_NON_NEGATIVE",
    "Unknown mode → INVALID_MODE",
    "When P > S, PF capped at 1 and Q = 0 (soft clamp)",
    "I = 0 and P = 0 → S = 0, pf = 0 (valid)"
  ],
  "sources": [
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Apparent power (IEV 131-11-41)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-41",
      "supports": "S = U × I definition of apparent power; unit volt-ampere (VA / kVA)",
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      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Reactive power (IEV 131-11-44)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-44",
      "supports": "Q = S sin φ under sinusoidal conditions; unit var / kVAR",
      "kind": "standard",
      "accessed": "2026-09-05",
      "clause": "IEV 131-11-44"
    },
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Power factor (IEV 131-11-46)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-46",
      "supports": "λ = |P| / S; PF displayed as P/S (sinusoidal displacement factor cos φ when applicable)",
      "kind": "standard",
      "accessed": "2026-09-05",
      "clause": "IEV 131-11-46"
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    {
      "title": "IEEE Std 1459-2025",
      "section": "Power factor as P/S; apparent, active, and reactive power (S² = P² + Q²)",
      "url": "https://standards.ieee.org/ieee/1459/7578/",
      "supports": "PF = P/S; Q = √(S² − P²); capacitor sizing from Q and f",
      "kind": "standard",
      "accessed": "2026-09-05",
      "publisher": "IEEE",
      "published": "2025-05-16",
      "errata_checked": true
    },
    {
      "title": "BIPM SI Brochure (9th edition, version 4.01)",
      "section": "SI units related to electrical power",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "V, A, W relationships underlying kVA/kVAR scaling",
      "kind": "reference",
      "accessed": "2026-09-05",
      "published": "2026-06",
      "doi": "https://doi.org/10.59161/AUEZ1291"
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