Load Flow

This workspace now includes a Newton-Raphson AC load flow engine with reference scenarios, bus-voltage results, and branch-flow outputs. You can start from a standard benchmark case or build and tune a custom one-line model directly in the browser.

Workspace

Build a one-line model, run an AC load flow solve, and inspect voltage and branch flow outputs.

Reference scenarios

Solve against standard benchmark cases, or switch back to the current editor graph model.

Active solve case: IEEE 14-Bus IEEE 14-bus transmission benchmark adapted from MATPOWER case14.

Single-line diagram

Interactive topology view of buses and branches.

100% (Ctrl + wheel)
line-1-2-1 156.88 MWline-1-5-2 75.51 MWline-2-3-3 73.24 MWline-2-4-4 56.13 MWline-2-5-5 41.52 MWline-3-4-6 23.29 MWline-4-5-7 61.16 MWline-4-7-8 28.07 MWline-4-9-9 16.08 MWline-5-6-10 44.09 MWline-6-11-11 7.35 MWline-6-12-12 7.79 MWline-6-13-13 17.75 MWline-7-8-14 0.00 MWline-7-9-15 28.07 MWline-9-10-16 5.23 MWline-9-14-17 9.43 MWline-10-11-18 3.79 MWline-12-13-19 1.61 MWline-13-14-20 5.64 MWBus 1SLACKV: 1.060 puθ: 0.00°Bus 2PVV: 1.045 puθ: -4.98°Bus 3PVV: 1.010 puθ: -12.73°Bus 4PQV: 1.018 puθ: -10.31°Bus 5PQV: 1.020 puθ: -8.77°Bus 6PVV: 1.070 puθ: -14.22°Bus 7PQV: 1.062 puθ: -13.36°Bus 8PVV: 1.090 puθ: -13.36°Bus 9PQV: 1.056 puθ: -14.94°Bus 10PQV: 1.051 puθ: -15.10°Bus 11PQV: 1.057 puθ: -14.79°Bus 12PQV: 1.055 puθ: -15.08°Bus 13PQV: 1.050 puθ: -15.16°Bus 14PQV: 1.036 puθ: -16.03°

Palette

Add buses, then connect them with line elements.

Topology selection

Properties

Solve results

Converged in 3 iterations.

Bus|V| (pu)θ (deg)P inj (pu)Q inj (pu)
bus-11.06000.0002.3239-0.1655
bus-21.0450-4.9830.18300.3086
bus-31.0100-12.725-0.94200.0608
bus-41.0177-10.313-0.47800.0390
bus-51.0195-8.774-0.0760-0.0160
bus-61.0700-14.221-0.11200.0523
bus-71.0615-13.3600.00000.0000
bus-81.0900-13.3600.00000.1762
bus-91.0559-14.939-0.2950-0.1660
bus-101.0510-15.097-0.0900-0.0580
bus-111.0569-14.791-0.0350-0.0180
bus-121.0552-15.076-0.0610-0.0160
bus-131.0504-15.156-0.1350-0.0580
bus-141.0355-16.034-0.1490-0.0500

Serialized case preview

{
  "baseMVA": 100,
  "buses": [
    {
      "id": "bus-1",
      "name": "Bus 1",
      "baseKV": 0,
      "type": "SLACK",
      "voltageMagnitudeSetpoint": 1.06,
      "voltageAngleSetpointDeg": 0,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-2",
      "name": "Bus 2",
      "baseKV": 0,
      "type": "PV",
      "voltageMagnitudeSetpoint": 1.045,
      "voltageAngleSetpointDeg": -4.98,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-3",
      "name": "Bus 3",
      "baseKV": 0,
      "type": "PV",
      "voltageMagnitudeSetpoint": 1.01,
      "voltageAngleSetpointDeg": -12.72,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-4",
      "name": "Bus 4",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.019,
      "voltageAngleSetpointDeg": -10.33,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-5",
      "name": "Bus 5",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.02,
      "voltageAngleSetpointDeg": -8.78,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-6",
      "name": "Bus 6",
      "baseKV": 0,
      "type": "PV",
      "voltageMagnitudeSetpoint": 1.07,
      "voltageAngleSetpointDeg": -14.22,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-7",
      "name": "Bus 7",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.062,
      "voltageAngleSetpointDeg": -13.37,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-8",
      "name": "Bus 8",
      "baseKV": 0,
      "type": "PV",
      "voltageMagnitudeSetpoint": 1.09,
      "voltageAngleSetpointDeg": -13.36,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-9",
      "name": "Bus 9",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.056,
      "voltageAngleSetpointDeg": -14.94,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-10",
      "name": "Bus 10",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.051,
      "voltageAngleSetpointDeg": -15.1,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-11",
      "name": "Bus 11",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.057,
      "voltageAngleSetpointDeg": -14.79,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-12",
      "name": "Bus 12",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.055,
      "voltageAngleSetpointDeg": -15.07,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-13",
      "name": "Bus 13",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.05,
      "voltageAngleSetpointDeg": -15.16,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    },
    {
      "id": "bus-14",
      "name": "Bus 14",
      "baseKV": 0,
      "type": "PQ",
      "voltageMagnitudeSetpoint": 1.036,
      "voltageAngleSetpointDeg": -16.04,
      "voltageMagnitudeMin": 0.94,
      "voltageMagnitudeMax": 1.06
    }
  ],
  "branches": [
    {
      "id": "line-1-2-1",
      "fromBusId": "bus-1",
      "toBusId": "bus-2",
      "r": 0.01938,
      "x": 0.05917,
      "bHalf": 0.0264,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-1-5-2",
      "fromBusId": "bus-1",
      "toBusId": "bus-5",
      "r": 0.05403,
      "x": 0.22304,
      "bHalf": 0.0246,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-2-3-3",
      "fromBusId": "bus-2",
      "toBusId": "bus-3",
      "r": 0.04699,
      "x": 0.19797,
      "bHalf": 0.0219,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-2-4-4",
      "fromBusId": "bus-2",
      "toBusId": "bus-4",
      "r": 0.05811,
      "x": 0.17632,
      "bHalf": 0.017,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-2-5-5",
      "fromBusId": "bus-2",
      "toBusId": "bus-5",
      "r": 0.05695,
      "x": 0.17388,
      "bHalf": 0.0173,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-3-4-6",
      "fromBusId": "bus-3",
      "toBusId": "bus-4",
      "r": 0.06701,
      "x": 0.17103,
      "bHalf": 0.0064,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-4-5-7",
      "fromBusId": "bus-4",
      "toBusId": "bus-5",
      "r": 0.01335,
      "x": 0.04211,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-4-7-8",
      "fromBusId": "bus-4",
      "toBusId": "bus-7",
      "r": 0,
      "x": 0.20912,
      "bHalf": 0,
      "tapRatio": 0.978,
      "phaseShiftDeg": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-4-9-9",
      "fromBusId": "bus-4",
      "toBusId": "bus-9",
      "r": 0,
      "x": 0.55618,
      "bHalf": 0,
      "tapRatio": 0.969,
      "phaseShiftDeg": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-5-6-10",
      "fromBusId": "bus-5",
      "toBusId": "bus-6",
      "r": 0,
      "x": 0.25202,
      "bHalf": 0,
      "tapRatio": 0.932,
      "phaseShiftDeg": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-6-11-11",
      "fromBusId": "bus-6",
      "toBusId": "bus-11",
      "r": 0.09498,
      "x": 0.1989,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-6-12-12",
      "fromBusId": "bus-6",
      "toBusId": "bus-12",
      "r": 0.12291,
      "x": 0.25581,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-6-13-13",
      "fromBusId": "bus-6",
      "toBusId": "bus-13",
      "r": 0.06615,
      "x": 0.13027,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-7-8-14",
      "fromBusId": "bus-7",
      "toBusId": "bus-8",
      "r": 0,
      "x": 0.17615,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-7-9-15",
      "fromBusId": "bus-7",
      "toBusId": "bus-9",
      "r": 0,
      "x": 0.11001,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-9-10-16",
      "fromBusId": "bus-9",
      "toBusId": "bus-10",
      "r": 0.03181,
      "x": 0.0845,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-9-14-17",
      "fromBusId": "bus-9",
      "toBusId": "bus-14",
      "r": 0.12711,
      "x": 0.27038,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-10-11-18",
      "fromBusId": "bus-10",
      "toBusId": "bus-11",
      "r": 0.08205,
      "x": 0.19207,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-12-13-19",
      "fromBusId": "bus-12",
      "toBusId": "bus-13",
      "r": 0.22092,
      "x": 0.19988,
      "bHalf": 0,
      "status": "IN_SERVICE"
    },
    {
      "id": "line-13-14-20",
      "fromBusId": "bus-13",
      "toBusId": "bus-14",
      "r": 0.17093,
      "x": 0.34802,
      "bHalf": 0,
      "status": "IN_SERVICE"
    }
  ],
  "generators": [
    {
      "id": "gen-1",
      "busId": "bus-1",
      "pSet": 232.4,
      "vSet": 1.06,
      "qMin": 0,
      "qMax": 10,
      "status": "ON"
    },
    {
      "id": "gen-2",
      "busId": "bus-2",
      "pSet": 40,
      "vSet": 1.045,
      "qMin": -40,
      "qMax": 50,
      "status": "ON"
    },
    {
      "id": "gen-3",
      "busId": "bus-3",
      "pSet": 0,
      "vSet": 1.01,
      "qMin": 0,
      "qMax": 40,
      "status": "ON"
    },
    {
      "id": "gen-4",
      "busId": "bus-6",
      "pSet": 0,
      "vSet": 1.07,
      "qMin": -6,
      "qMax": 24,
      "status": "ON"
    },
    {
      "id": "gen-5",
      "busId": "bus-8",
      "pSet": 0,
      "vSet": 1.09,
      "qMin": -6,
      "qMax": 24,
      "status": "ON"
    }
  ],
  "loads": [
    {
      "id": "load-2",
      "busId": "bus-2",
      "p": 21.7,
      "q": 12.7,
      "status": "ON"
    },
    {
      "id": "load-3",
      "busId": "bus-3",
      "p": 94.2,
      "q": 19,
      "status": "ON"
    },
    {
      "id": "load-4",
      "busId": "bus-4",
      "p": 47.8,
      "q": -3.9,
      "status": "ON"
    },
    {
      "id": "load-5",
      "busId": "bus-5",
      "p": 7.6,
      "q": 1.6,
      "status": "ON"
    },
    {
      "id": "load-6",
      "busId": "bus-6",
      "p": 11.2,
      "q": 7.5,
      "status": "ON"
    },
    {
      "id": "load-9",
      "busId": "bus-9",
      "p": 29.5,
      "q": 16.6,
      "status": "ON"
    },
    {
      "id": "load-10",
      "busId": "bus-10",
      "p": 9,
      "q": 5.8,
      "status": "ON"
    },
    {
      "id": "load-11",
      "busId": "bus-11",
      "p": 3.5,
      "q": 1.8,
      "status": "ON"
    },
    {
      "id": "load-12",
      "busId": "bus-12",
      "p": 6.1,
      "q": 1.6,
      "status": "ON"
    },
    {
      "id": "load-13",
      "busId": "bus-13",
      "p": 13.5,
      "q": 5.8,
      "status": "ON"
    },
    {
      "id": "load-14",
      "busId": "bus-14",
      "p": 14.9,
      "q": 5,
      "status": "ON"
    }
  ],
  "shunts": [
    {
      "id": "shunt-9",
      "busId": "bus-9",
      "kind": "CAPACITOR",
      "bPu": 0.19,
      "status": "ON"
    }
  ]
}

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