{
  "node": {
    "id": "term:equivalent-circuit-model",
    "type": "Term",
    "label": "Equivalent circuit model",
    "properties": {
      "id": "equivalent-circuit-model",
      "name": "Equivalent circuit model",
      "abbr": "ECM",
      "aka": [
        "Thevenin model"
      ],
      "section": "topic-transport",
      "definition": "A cell model built from a voltage source for OCV, a series resistor and one or more RC pairs for the slower dynamics. Its few parameters are fitted from pulse tests, and it is what most battery management systems run in real time.",
      "related": [
        "rc-pair",
        "open-circuit-voltage",
        "hppc",
        "kalman-filter",
        "single-particle-model"
      ],
      "url": "https://lemonergy.com/learn/glossary/equivalent-circuit-model/",
      "mentions": []
    }
  },
  "edges": [
    {
      "id": "edge:167",
      "source": "term:equivalent-circuit-model",
      "target": "workflow:rc-response",
      "type": "usedIn",
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        "sourceFile": "wiki-blocks.json"
      }
    },
    {
      "id": "edge:2143",
      "source": "term:equivalent-circuit-model",
      "target": "topic:topic-transport",
      "type": "belongsTo",
      "properties": {
        "sourceFile": "terms.json"
      }
    },
    {
      "id": "edge:2144",
      "source": "term:equivalent-circuit-model",
      "target": "term:rc-pair",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2145",
      "source": "term:equivalent-circuit-model",
      "target": "term:open-circuit-voltage",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2146",
      "source": "term:equivalent-circuit-model",
      "target": "term:hppc",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2147",
      "source": "term:equivalent-circuit-model",
      "target": "term:kalman-filter",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
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      "id": "edge:2148",
      "source": "term:equivalent-circuit-model",
      "target": "term:single-particle-model",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2149",
      "source": "term:equivalent-circuit-model",
      "target": "visual:rc",
      "type": "illustratedBy",
      "properties": {
        "sourceFile": "visual-pages.json"
      }
    },
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      "source": "term:equivalent-circuit-model",
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      "type": "cites",
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    {
      "id": "workflow:rc-response",
      "type": "Workflow",
      "label": "Observe an RC time constant",
      "properties": {
        "id": "rc-response",
        "title": "Observe an RC time constant",
        "kind": "studio",
        "summary": "An RC circuit uses source, resistor, capacitor and reference blocks.",
        "steps": [
          "Keep R = 1 Ω and C = 1 F.",
          "Inspect capacitor voltage after one and two time constants."
        ],
        "example": "From zero initial voltage with a 1 V step, ideal capacitor voltage is about 0.632 V at 1 s and 0.865 V at 2 s.",
        "observe": "Doubling resistance or capacitance doubles the time constant.",
        "limits": "This generic circuit does not identify cell parameters from measurements.",
        "url": "https://design.lemonergy.com/cosim.html?example=physical-rc",
        "label": "Open the RC example",
        "evidence": [
          "js/physical-network.js",
          "js/studio-examples.js"
        ]
      }
    },
    {
      "id": "topic:topic-transport",
      "type": "Topic",
      "label": "Transport and modelling",
      "properties": {
        "id": "topic-transport",
        "name": "Transport and modelling",
        "lede": "How ions move, and the equations and models that describe a cell.",
        "context": "Specify phase, direction and boundaries.",
        "example": "The same concentration difference across 10 μm gives ten times the gradient across 100 μm; at equal D, first-law flux magnitude is ten times greater.",
        "lesson_url": "https://lemonergy.com/learn/transport/ficks-first-law/",
        "lesson_label": "Open diffusion"
      }
    },
    {
      "id": "term:rc-pair",
      "type": "Term",
      "label": "RC pair",
      "properties": {
        "id": "rc-pair",
        "name": "RC pair",
        "aka": [
          "RC element",
          "RC branch"
        ],
        "section": "topic-transport",
        "definition": "A resistor and capacitor in parallel, the building block of an equivalent circuit model. Each pair reproduces one time constant of the cell’s voltage response, from the seconds of charge transfer to the minutes of diffusion.",
        "formula": "τ = R × C",
        "related": [
          "equivalent-circuit-model",
          "relaxation",
          "charge-transfer"
        ],
        "example": {
          "title": "Calculate a response time",
          "text": "An illustrative 0.02 Ω resistance and 500 F capacitance have τ = RC = 10 s. A first-order step response reaches about 63% of its final change after one time constant."
        },
        "url": "https://lemonergy.com/learn/glossary/rc-pair/",
        "mentions": [
          "diffusion",
          "capacitor"
        ]
      }
    },
    {
      "id": "term:open-circuit-voltage",
      "type": "Term",
      "label": "Open-circuit voltage",
      "properties": {
        "id": "open-circuit-voltage",
        "name": "Open-circuit voltage",
        "abbr": "OCV",
        "section": "topic-state",
        "definition": "The voltage across a cell’s terminals when no current flows and the cell has rested long enough for the voltage to settle. It depends on state of charge and temperature, and a cell whose open-circuit voltage falls unusually fast in storage may have an internal short.",
        "unit": "V",
        "related": [
          "ocv-soc-curve",
          "relaxation",
          "voltage-hysteresis",
          "k-value",
          "internal-short-circuit"
        ],
        "lesson": "fundamentals/cell-production/#finishing",
        "url": "https://lemonergy.com/learn/glossary/open-circuit-voltage/",
        "mentions": [
          "state-of-charge"
        ]
      }
    },
    {
      "id": "term:hppc",
      "type": "Term",
      "label": "Hybrid pulse power characterisation",
      "properties": {
        "id": "hppc",
        "name": "Hybrid pulse power characterisation",
        "abbr": "HPPC",
        "section": "topic-testing",
        "definition": "A test that applies a short discharge pulse and a short charge pulse at each state of charge, from which resistance and power capability are read as a function of SOC. It is the standard source of equivalent-circuit parameters.",
        "related": [
          "equivalent-circuit-model",
          "state-of-power",
          "internal-resistance",
          "dcir",
          "pulse-test"
        ],
        "url": "https://lemonergy.com/learn/glossary/hppc/",
        "mentions": [
          "state-of-charge"
        ]
      }
    },
    {
      "id": "term:kalman-filter",
      "type": "Term",
      "label": "Kalman filter",
      "properties": {
        "id": "kalman-filter",
        "name": "Kalman filter",
        "section": "topic-state",
        "definition": "A recursive estimator that blends a model prediction with noisy measurements according to how much each is trusted. In a BMS an extended Kalman filter combines coulomb counting with a voltage model to track SOC and sometimes resistance.",
        "related": [
          "coulomb-counting",
          "equivalent-circuit-model",
          "state-of-charge",
          "bms",
          "fuzzy-logic",
          "data-driven-soc-estimation"
        ],
        "url": "https://lemonergy.com/learn/glossary/kalman-filter/",
        "mentions": [
          "coulomb"
        ]
      }
    },
    {
      "id": "term:single-particle-model",
      "type": "Term",
      "label": "Single-particle model",
      "properties": {
        "id": "single-particle-model",
        "name": "Single-particle model",
        "abbr": "SPM",
        "section": "topic-transport",
        "definition": "A simplified physics model that represents each electrode as one spherical particle and neglects electrolyte gradients. It runs fast enough for a BMS and is accurate at low to moderate currents.",
        "related": [
          "newman-model",
          "equivalent-circuit-model",
          "solid-state-diffusion",
          "bms"
        ],
        "url": "https://lemonergy.com/learn/glossary/single-particle-model/",
        "mentions": [
          "electrode",
          "electrolyte"
        ]
      }
    },
    {
      "id": "visual:rc",
      "type": "Visual",
      "label": "Voltage response and relaxation",
      "properties": {
        "title": "Voltage response and relaxation",
        "summary": "One time constant completes about 63% of a first-order voltage change.",
        "readout": "At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.",
        "formula": "τ = RC; step response = 1 − e^(−t/τ)",
        "note": "Two separate analytical experiments; normalized voltage, not measured data.",
        "software": {
          "status": "reference",
          "label": "Reference concept",
          "body": "An analytical RC response explains polarization and relaxation. It is not an identified RC network or a native Studio battery capability.",
          "href": "../chapter-1/"
        },
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relaxation experiment (dashed)</span></div></figure>"
      }
    },
    {
      "id": "reference:plett-modeling",
      "type": "Reference",
      "label": "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification",
      "properties": {
        "title": "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification",
        "publisher": "Journal of Power Sources",
        "url": "https://doi.org/10.1016/j.jpowsour.2004.02.032",
        "type": "Research article",
        "scope": "Battery charge balance, open-circuit voltage, ohmic loss, polarization dynamics and model identification; parameters require cell-specific data.",
        "year": 2004,
        "authors": [
          "Gregory L. Plett"
        ],
        "accessed": "2026-10-27"
      }
    }
  ]
}
