{
  "$schema": "https://ps-wiki.github.io/schema/v1/term.schema.json",
  "id": "equal-area-criterion",
  "title": "Equal Area Criterion",
  "description": "To determine the maximum permissible increase in mechanical power input for system stability.",
  "language": "en",
  "tags": [
    "stability",
    "book"
  ],
  "related": [
    "extended-equal-area-criterion"
  ],
  "breaking": false,
  "dates": {
    "created": "2025-03-15",
    "last_modified": "2025-11-01"
  },
  "authors": [
    {
      "name": "Jinning Wang",
      "url": "https://jinningwang.github.io"
    }
  ],
  "content": {
    "sections": [
      {
        "order": 1,
        "id": "definition-in-a-textbook",
        "title": "Definition in a Textbook",
        "type": "definition",
        "source_keys": [
          "kundur1994Power"
        ],
        "page": "p831, first edition",
        "body_md": "> The equal-area criterion is useful in determining the maximum permissible increase in $P_{m}$ for the system illustrated in Figure 13.14. Stability is maintained only if an area $A_{2}$ at least equal to $A_{1}$ can be located above $P_{m}$. If $A_{1} > A_{2}$, then the rotor angle $\\delta$ will exceed its critical value, and stability will be lost. For $\\delta > \\delta_{\\max}$, $P_{m}$ exceeds $P_{e}$, leading to net acceleration rather than deceleration.\n\n<!-- prettier-ignore-start -->\n> Another earlier reference to the Equal Area Criterion can be found in <d-cite key=\"dahl1935stability\"></d-cite>.\n{: .block-tip }\n<!-- prettier-ignore-end -->\n",
        "figures": [
          {
            "path": "/assets/img/pswiki/response-to-a-step-change-in-mechanical-power-input.png",
            "caption_md": "Fig. 13.14 Response to a step change in mechanical power input (from <d-cite key=\"kundur1994Power\"></d-cite>)",
            "alt": "Fig. 13.14 Response to a step change in mechanical power input",
            "zoomable": true,
            "source_keys": [
              "kundur1994Power"
            ]
          }
        ]
      }
    ]
  }
}