Power Systems Lab · 18 modules · all computed in your browser
Newton-Raphson power flow
Editable 3-bus network, iteration stepping, line outages.
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Power Systems Lab · 18 modules · all computed in your browser
Editable 3-bus network, iteration stepping, line outages.
Loading module…
Newton-Raphson power flow · 3-bus, 100 MVA base (Saadat Ex. 6.10)
| Bus | Type | |V| pu | P gen | P load | Q load |
|---|---|---|---|---|---|
| 1 · Slack | slack | ||||
| 2 · Load | PQ | ||||
| 3 · Gen | PV |
| Line | R pu | X pu | In service |
|---|---|---|---|
| 1–2 | |||
| 1–3 | |||
| 2–3 |
Converged
yes · 3 it.
Slack P / Q
218.4 MW / 140.9 Mvar
Losses
18.42 MW
| Bus | |V| pu | θ ° | P inj MW | Q inj Mvar |
|---|---|---|---|---|
| 1 · Slack | 1.0500 | 0.000 | 218.4 | 140.9 |
| 2 · Load | 0.9717 | -2.696 | -400.0 | -250.0 |
| 3 · Gen | 1.0400 | -0.499 | 200.0 | 146.2 |
| Flow | P MW | Q Mvar | Loss MW |
|---|---|---|---|
| 1→2 | 179.4 | 118.7 | 8.39 |
| 1→3 | 39.1 | 22.1 | 0.18 |
| 2→3 | -229.0 | -148.1 | 9.85 |
Max mismatch per iteration (pu)
Learn it
Power flow finds the voltage magnitude and angle at every bus that make generation, load and line flows balance. Real power follows angle differences across reactances. Reactive power follows voltage-magnitude differences. Newton’s method linearizes these equations around a guess, solves for corrections, and repeats. Near the solution it converges quadratically, so the mismatch roughly squares each iteration (watch the table).
Take a line out of service and see how flow redistributes and the load bus voltage sags. That is an N-1 contingency in miniature.
Quiz · 0/3
1. At a PV bus the solver finds…
2. Why is a slack bus needed?
3. Real-power flow on a lossless line is roughly…