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  "assumptions": [
    "AC steady-state with RMS voltage and current magnitudes.",
    "Three-phase mode is balanced sinusoidal AC using line-to-line RMS voltage, where V_LL = √3 V_LN and line currents are equal. IEEE 1459 covers a wider set of conditions; this calculator does not.",
    "Total power factor λ is not applied to VA/kVA results."
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  "limitations": [
    "Not for DC systems",
    "Not for unbalanced or nonsinusoidal three-phase; √3 formula assumes balanced sinusoidal V_LL = √3 V_LN and equal line currents",
    "Not for line-to-neutral three-phase mode",
    "Not for equipment protection or conductor sizing",
    "When power_factor is supplied, REST/MCP include derived.estimated_real_power; omitted when λ is absent"
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    "Power factor outside [0, 1] is rejected when provided; not silently ignored. λ=0 is accepted (P_est=0 when S>0).",
    "Negative primary (current or VA) is rejected",
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    {
      "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)",
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      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-46",
      "supports": "λ = |P| / S, so λ = 0 when P = 0 and S > 0; optional page/API estimate P_est = S × λ_entered uses this definition",
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      "url": "https://standards.ieee.org/ieee/1459/7578/",
      "supports": "IEEE 1459 covers sinusoidal, nonsinusoidal, balanced, and unbalanced conditions. This calculator implements only the balanced sinusoidal three-phase model S = √3 × V_L-L × I_L (V_LL = √3 V_LN, equal line currents).",
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      "accessed": "2026-09-04",
      "publisher": "IEEE",
      "published": "2025-05-16",
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      "title": "BIPM SI Brochure (9th edition, version 4.01)",
      "section": "SI base and derived units for ampere, volt, and power",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "V, A, W, and VA unit relationships",
      "kind": "reference",
      "accessed": "2026-09-04",
      "published": "2026-06",
      "doi": "https://doi.org/10.59161/AUEZ1291"
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