Book
Power System Analysis - Analytical Tools and Structural Properties
Steven H. Low, Caltech
This rough draft is based on lecture notes for the Power System Analysis courses that I have been teaching at Caltech for the last decade or so. Any corrections, questions, comments, or pointers will be greatly appreciated!
Current draft (May 21, 2025)
- Part I: Power network: models, operations, analysis (Ch 1 - 7)
- Part II: Power flow optimization (Ch 8 - 13)
- Part III: Unbalanced three-phase networks (Ch 14 - 18)
- Appendix: Linear algebra preliminaries (Ch 19)
Solution manual
Solutions to most of the exercises are available to instructors for teaching or researchers for self study. Request solution.
Slides
The slides below that are dated on or after Dec 13, 2024 match the chapters in the textbook. (Slides dated before Dec 13, 2024 are for the dated versions of the draft and undated slides are for the Feb 16, 2023 version of the draft.)
- Part I: Power network: models, operation, analysis
- Ch 1 Basic concepts: Keynote PDF
- Ch 2 Transmission line models: Keynote PDF
- Ch 3 Transformer models: Keynote PDF (last update: July 5, 2023)
- Ch 4 Bus injection models: Keynote PDF (last update: Dec 13, 2024)
- Ch 5 Branch flow models: radial networks: Keynote PDF (last update: Dec 13, 2024)
- Ch 6 System operation: power balance: Keynote PDF (last update: April 15, 2025)
- Ch 7 System operation: estimation and control: Keynote PDF (last update: April 15, 2025)
- Part II: Power flow optimization
- Ch 8 Smooth convex optimization:
- Ch 9 Optimal power flow: Keynote PDF (last update: Dec 13, 2024)
- Ch 10 Semidefinite relaxations: BIM: Keynote PDF (last update: Dec 13, 2024)
- Ch 11 Semidefinite relaxations: BFM: Keynote PDF (last update: Dec 13, 2024)
- Ch 12 Nonsmooth convex optimization: Keynote PDF (last update: Feb 7, 2025)
- Ch 13 Stochastic OPF: Keynote PDF (last update: April 15, 2025)
- Part III: Unbalanced three-phase networks