Load Flow Analysis

Change the load. See where power flows and how voltages respond.

NetworkLoad · 100%

Grid supply and a local generator feeding two loads. The load slider scales P and Q together; generator P setpoints stay fixed.

Total demand

110.0 MW / 40.0 MVAr

Voltage range

0.966–1.040 pu

Active power loss

3.43 MW

Solution

Converged · 3 iterations

Single-line diagram

Hover or focus for power details; tap to inspect. Drag buses to move, background to pan. Pinch or ⌘/Ctrl-scroll to zoom.

━━ P · MW┄┄ Q · MVAr● V < 0.95 pu● 0.95–1.05 pu● V > 1.05 puGeneratorLoadGrid supply

Arrows show flow at each end. Thicker lines mean larger magnitudes. Voltage bands are visual guides, not equipment limits. Phasors show angle relative to the slack bus, at true scale. Crossings are not connections. Device values show total generation or demand at each bus.

Motion speed is proportional to power magnitude on a fixed scale—not AC wave speed or transient behavior. Reduced-motion settings keep it still.

Inspect

1.0400 pu ∠ 0.000° · Net injection 63.43 MW / 35.53 MVAr

Edit selected element

Numeric edits apply on Enter or when you leave the field. Load values below are before the global load multiplier.

NameBus typeBase kVVoltage setpoint (pu)Reference angle (°)Load P (MW)Load Q (MVAr)

Bus voltages & branch flows

Positive terminal power enters the line; negative power leaves it. The two ends need not agree because of losses and line charging. Net Q can be negative.

Bus voltages and injections
Bus	V (pu)	θ (°)	P injection (MW)	Q injection (MVAr)
bus-1	1.0400	0.000	63.43	35.53
bus-2	1.0250	-0.447	30.00	-2.95
bus-3	0.9662	-5.032	-90.00	-30.00

Branch flows and losses
Branch · from → to	From end		To end		Net absorbed
Branch · from → to	MW	MVAr	MW	MVAr	MW	MVAr
line-1-2 bus-1 → bus-2	20.30	17.67	-20.15	-20.43	0.14	-2.76
line-1-3 bus-1 → bus-3	43.13	17.87	-41.48	-15.44	1.65	2.43
line-2-3 bus-2 → bus-3	50.15	17.48	-48.52	-14.56	1.63	2.91

Network editor & model

From busTo bus

Balanced, steady-state AC power flow using Newton–Raphson on a 100 MVA base. Loads are constant P/Q. Lines use a π model with charging at both ends; transformers support taps and phase shifts. Slack fixes voltage and angle; PV fixes active generation and voltage. Generator reactive-power limits and thermal limits are not enforced. Convergence is not a claim of safe operation.

Case JSON

{
  "baseMVA": 100,
  "buses": [
    {
      "id": "bus-1",
      "name": "Slack",
      "baseKV": 230,
      "type": "SLACK",
      "voltageMagnitudeSetpoint": 1.04,
      "voltageAngleSetpointDeg": 0
    },
    {
      "id": "bus-2",
      "name": "Gen Bus",
      "baseKV": 230,
      "type": "PV",
      "voltageMagnitudeSetpoint": 1.025
    },
    {
      "id": "bus-3",
      "name": "Load Bus",
      "baseKV": 230,
      "type": "PQ"
    }
  ],
  "branches": [
    {
      "id": "line-1-2",
      "fromBusId": "bus-1",
      "toBusId": "bus-2",
      "r": 0.02,
      "x": 0.06,
      "bHalf": 0.015
    },
    {
      "id": "line-1-3",
      "fromBusId": "bus-1",
      "toBusId": "bus-3",
      "r": 0.08,
      "x": 0.24,
      "bHalf": 0.0125
    },
    {
      "id": "line-2-3",
      "fromBusId": "bus-2",
      "toBusId": "bus-3",
      "r": 0.06,
      "x": 0.18,
      "bHalf": 0.01
    }
  ],
  "generators": [
    {
      "id": "gen-2",
      "busId": "bus-2",
      "pSet": 50,
      "vSet": 1.025,
      "qMin": -40,
      "qMax": 80,
      "status": "ON"
    }
  ],
  "loads": [
    {
      "id": "load-2",
      "busId": "bus-2",
      "p": 20,
      "q": 10,
      "status": "ON"
    },
    {
      "id": "load-3",
      "busId": "bus-3",
      "p": 90,
      "q": 30,
      "status": "ON"
    }
  ],
  "shunts": []
}