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)
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-1 | 1.0600 | 0.000 | 2.3239 | -0.1655 |
| bus-2 | 1.0450 | -4.983 | 0.1830 | 0.3086 |
| bus-3 | 1.0100 | -12.725 | -0.9420 | 0.0608 |
| bus-4 | 1.0177 | -10.313 | -0.4780 | 0.0390 |
| bus-5 | 1.0195 | -8.774 | -0.0760 | -0.0160 |
| bus-6 | 1.0700 | -14.221 | -0.1120 | 0.0523 |
| bus-7 | 1.0615 | -13.360 | 0.0000 | 0.0000 |
| bus-8 | 1.0900 | -13.360 | 0.0000 | 0.1762 |
| bus-9 | 1.0559 | -14.939 | -0.2950 | -0.1660 |
| bus-10 | 1.0510 | -15.097 | -0.0900 | -0.0580 |
| bus-11 | 1.0569 | -14.791 | -0.0350 | -0.0180 |
| bus-12 | 1.0552 | -15.076 | -0.0610 | -0.0160 |
| bus-13 | 1.0504 | -15.156 | -0.1350 | -0.0580 |
| bus-14 | 1.0355 | -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"
}
]
}