EECS 598 - Computational Power Systems

Overview: The growing digitization of power systems, the rapid penetration of distributed energy resources, and the decentralization of decision-making call for new computational algorithms to support power system operations and electricity markets. This course provides an overview of computational problems in power systems and introduces a range of computational algorithms to solve them, while recognizing the trade-offs between performance, speed, and data requirements. The course is arranged in three parts. The first part overviews optimization problems in power systems, ranging from economic dispatch and market clearing in high-voltage grids to distributed algorithms for voltage control and peer-to-peer markets in distribution grids. This part also overviews how machine learning (ML) aids these optimization problems. The second part focuses on decentralized/distributed decision-making in high-voltage and distribution grids, and how agents can solve dispatch, control, and learning problems autonomously using decentralized/distributed algorithms, such as dual decomposition, ADMM, and their variants. The third part is devoted to prescriptive analytics for power systems and introduces the algorithms for decision-focused learning in the context of renewable power forecasting and other relevant analytic tasks. The course participants will work on final projects to be presented before, and evaluated by, their peers.

Lectures and course materials:

  1. Intro (slides, tutorial, lecture notes)
  2. Duality, optimality, and pricing (slides, tutorial, lecture notes)
  3. Optimal power flow (OPF) & Locational pricing (slides, tutorial, lecture notes)
  4. Alternating Direction Method of Multipliers (ADMM) (slides, tutorial, lecture notes)
  5. ADMM applications to OPF (slides, tutorial, lecture notes)
  6. Online optimization (slides, tutorial, lecture notes)
  7. Online optimization for Volt/VAr Control (slides, tutorial, lecture notes)
  8. Online optimization for economic dispatch (slides, tutorial, lecture notes)
  9. Renewable power forecasting (slides, tutorial-1,tutorial-2, lecture notes)
  10. Decision-focused analytics (slides, tutorial, lecture notes)
  11. Inverse optimization for market analytics (slides, tutorial, lecture notes)

List of topics

  1. Introduction to Modern Power System Optimization
    • Intro to (non-)convex optimization and duality theory
    • Power flow models, optimal power flow, convexification and relaxation
    • Electricity pricing, desirable market properties, integrality constraints
  2. Decentralized/Distributed Optimization of Power Systems
    • Introduction to decentralized/distributed optimization algorithms
    • From Dual ascent to alternating direction method of multipliers (ADMM)
    • Consensus- and exchange-ADMM. Applications to optimal power flow
  3. Decentralized/Distributed Control of Power Systems
    • Online optimization, gradient flow algorithms
    • Online feedback optimization for Volt/VAr control
    • Online feedback optimization for real-time economic dispatch
  4. Prescriptive Analytics for Power Systems
    • Intro to renewable power forecasting
    • Prediction- versus decision-focused learning
    • Bilevel optimization, implicit differentiation, multiparametric programming
    • Inverse optimization for market analytics

Prerequisite: Students will follow the course more seamlessly having experience with power systems modeling, convex optimization (linear programming, duality theory), basic concepts of data science (for example, probability, sampling, regression), and have a good command of programming languages (e.g., Julia or Python). Formally, for this graduate-level course, the students are expected to take (EECS 463) and (IOE 310 or EECS 536 or IOE 510 or Math 561 or OMS 518) and (Math 425 or IOE 265 or EECS 301) before registering for this course, or get permission of the instructor.

Assessment: The final grade is made of: (i) five homework assignments (biweekly, 40%), (ii) paper review (15%), (iii) final project (25%), (iv) participation (quizzes, notes, piazza, course evaluation, 20%).

Literature:

  • M. Cain et al. “History of optimal power flow and formulations.” Federal Energy Regulatory Commission
  • R. O’Neill et al. “Efficient market-clearing prices in markets with nonconvexities.” European journal of operational research
  • J. Lavaei and S. Low. “Zero duality gap in optimal power flow problem.” IEEE Transactions on Power systems
  • D. Molzahn et al. “A survey of distributed optimization and control algorithms for electric power systems.” IEEE Transactions on Smart Grid
  • A. Hauswirth et al. “Optimization algorithms as robust feedback controllers.” Annual Reviews in Control
  • S. Boyd and L. Vandenberghe. Convex optimization. Cambridge university press
  • S. Boyd et al. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine learning
  • J. Mandi et al. Decision-focused learning: Foundations, state of the art, benchmark and future opportunities. Journal of Artificial Intelligence Research
  • T. Chan et al. Inverse optimization: Theory and applications. Operations Research

Ackowledgement: Some of the course materials are adapted from the following publicly available resources. I am grateful to the instructors for sharing their excellent content:

Final project information: Before starting the project, your proposal must be approved by the instructor. The group work is encouraged with up to 3 students in each group; we ask to report individual contributions in the separate section of the report. The deliverables include a 6-page report and presentation before the class.

Course Policies

  • Homework will be released on Friday, due two weeks after (i.e., the next, next Friday). Students can discuss homework assignments with other students, but their answers must be their own. Students should list people they have talked to about each problem at the top of each report.

  • All assignments are encouraged to be typed using LaTeX; submit the .pdf file electronically by 11:59 PM Eastern Standard Time on the assigned due date. Hand-written and scanned .pdf versions are allowed, which will not result in grading differences.

  • Requests for assignment due date extensions must be made in advance. Failure to do so will result in 50% off of the assignment points; Each person can make up to 2 extensions at most, and up to 5 days in total.

  • The regrading request needs to be submitted within 2 weeks after the grade is released.

  • Your lecture notes will count towards the final grade. To earn the maximum score, student should sign up to scribe at least 5 lectures. The notes are encouraged to be typed using LaTeX in the template provided at the beginning of the course; students using LaTeX are allowed to work in groups of up to 3 people. The lecture recording will be posted on canvas to help this effort.

  • Piazza will be used for discussions among students. Participation in Piazza conversations will be a significant part of the final score. Please feel free to post technical and conceptional questions, but after screening already posted questions.

  • Please help us to improve the course by submitting mid-term and final course evaluations; each evaluation is worth 0.5% points.

  • Any honor code violation will result in an additional loss of 50% points (beyond the findings/recommendations of the honor council).