Optimal Power Flow: Relaxation, Online Algorithm, Fast Dynamics
summary
Shows that SDP and much cheaper SOCP relaxations turn AC optimal power flow into convex problems and that SOCP exact on radial grids under a half‑plane phase condition; gives a concrete SDP→partial‑matrix reduction and cycle condition to check exactness. Proposes an online gradient control using network as implicit solver where controllable device settings get a gradient step, the grid settles and is measured, and updates track changing loads. Tests on real distribution feeders give big speedups versus CVX with nearly identical cost, and cites 2–10 billion/year potential savings from switching DC to AC economic dispatch.
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chapters (13)
- 0:00Introduction to OPF
- 0:24Power network basics
- 2:51OPF challenges and relaxation
- 5:02Semidefinite relaxation
- 8:57Optimal solutions
- 15:28SOCP relaxation
- 20:56Practical implementation
- 26:25Online OPF overview
- 30:31Online algorithm design
- 36:50Optimality and tracking
- 40:32Performance analysis
- 44:55Simulation results
- 50:16Future applications and Q&A
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