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L36 / Power-flow analysis

Power Flow V

Use Newton's Jacobian and corrections, then validate convergence, branch flows, and operating limits.

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This lecture's concept outline

L36

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Original slide headings41
  1. 1Lecture outline
  2. 2From sequential to coupled updates
  3. 3A scalar Newton step
  4. 4Linearizing the power equations
  5. 5Jacobian blocks
  6. 6Use radians for angle corrections
  7. 7Two-bus example
  8. 8Two-bus equations
  9. 9Two-state Jacobian
  10. 10Flat start
  11. 11First Newton correction
  12. 12State update
  13. 13Recalculate the original powers
  14. 14First residual check
  15. 15Second Jacobian
  16. 16Optional: second Newton correction
  17. 17Optional: second residual check
  18. 18Two-bus convergence history
  19. 19Two-bus solved voltage
  20. 20Two-bus power balance
  21. 21Two-bus operating checks
  22. 22Common case: data and initial state
  23. 23Common case: Jacobian order
  24. 24Reference: off-diagonal derivatives
  25. 25Reference: diagonal derivatives
  26. 26Common case: Newton system
  27. 27Common case: first correction
  28. 28Common case: convergence history
  29. 29Common case: solved bus records
  30. 30If the PV reactive limit binds
  31. 31Branch-flow sign convention
  32. 32Example: power on branch 2–3
  33. 33Common case: real-power paths
  34. 34Common case: flows and ratings
  35. 35Common case: independent power balance
  36. 36Common case: operating checks
  37. 37Stored precision and displayed precision
  38. 38Practice: change one branch rating
  39. 39Practice: rating-change answer
  40. 40Optional: comparing the methods
  41. 41Complete power-flow workflow
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L36_power_flow_v/L36_power_flow_v.pdf

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EXPLORE

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Inspect Newton corrections and distinguish a converged solution from an acceptable operating point.

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COMPUTE

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