{
  "language": "en",
  "interfaceLanguage": "en",
  "url": "https://voltformer.com/articles/transformer-differential-protection-87t-inrush-restraint-and-ct-sizing",
  "id": "art-23",
  "slug": "transformer-differential-protection-87t-inrush-restraint-and-ct-sizing",
  "title": "Transformer Differential Protection (ANSI 87T): Biased Slope, Inrush Restraint, and CT Saturation",
  "summary": "Dual-slope percentage restraint differential protection, 2nd harmonic magnetizing inrush restraint (I_2nd > 15%), 5th harmonic overexcitation blocking, and CT knee-point voltage (Vk) calculation per IEC 61869-2 / IEEE C57.13.",
  "readTime": "9 min read",
  "date": "2026-08-25",
  "author": "Voltformer Relay Protection & Automation Engineering",
  "category": "Protection Relays & ANSI 87T",
  "tags": [
    "Differential Protection",
    "ANSI 87T",
    "Inrush Restraint",
    "CT Sizing",
    "IEC 60255-187-1"
  ],
  "contentMarkdown": "### 1. Transformer Differential Protection (ANSI 87T) Principles\n\nPer **IEC 60255-187-1**, percentage biased differential protection (ANSI 87T) serves as the primary unit protection for power transformers against internal short circuits.\n\n### 2. Dual-Slope Operating Characteristic Equations\n\n$$ I_{diff} = |\\vec{I}_{HV} + \\vec{I}_{LV\\_referred}| $$\n$$ I_{bias} = \\frac{|\\vec{I}_{HV}| + |\\vec{I}_{LV\\_referred}|}{2} $$\n\n#### Trip Regions:\n- **Slope 1 ($K_1 = 20\\% - 30\\%$):** Sensitive tripping for internal turn-to-turn and low-current ground faults during normal load.\n- **Slope 2 ($K_2 = 60\\% - 80\\%$):** High restraint preventing false tripping during severe through-faults with CT saturation.\n\n### 3. Harmonic Inrush & Overexcitation Restraint\n\n| Harmonic Component | Threshold Ratio | Relay Action | Physical Root Cause |\n|---|---|---|---|\n| **2nd Harmonic ($100\\text{ Hz}$)** | **$I_{2nd} / I_{fundamental} > 15\\%$** | **Block Differential Trip** | Magnetizing inrush current during energization |\n| **5th Harmonic ($250\\text{ Hz}$)** | **$I_{5th} / I_{fundamental} > 35\\%$** | **Block / Alarm** | Core overexcitation from system overvoltage |\n\n### 4. Current Transformer (CT) Knee-Point Voltage ($V_k$) Sizing\n\nTo prevent CT saturation during maximum external through-fault current ($I_{f\\_max}$):\n\n$$ V_k \\ge 2 \\cdot I_{sec\\_max} \\cdot (R_{ct} + 2 \\cdot R_{lead} + R_{relay}) $$\n\nWhere $R_{ct}$ is CT secondary winding resistance and $R_{lead}$ is one-way lead wire resistance.\n\n*Reference: IEC 60255-187-1:2021; IEC 61869-2:2012; IEEE Std C37.91-2021.*",
  "contentLanguage": "en",
  "sources": []
}