CS/EE 146 Control and optimization of networks (2024 Spring)

Units	9 (3-3-3; class-project-prep)
Lectures	Tue, Thur 10:30-11:55am, Rm 314 ANB
Prerequisites	Ma 2, Ma 3; optimization theory (or instructor permission)
URL	http://courses.cms.caltech.edu/cs146
Instructor	Steven Low <slow@caltech.edu>
Assistant	Christine Ortega <cortega@caltech.edu>
TA	Nicolas Christianson <nchristianson@caltech.edu>
Office Hours	On demand (send me email any time)

Course Description

This year, we will focus on optimization problems in power networks. In the US, about 84% of greenhouse gases are emitted from energy use. Optimal power flow is a class of constrained optimization problems. They are important because they underly numerous power system applications. They are computationally challenging because they are large-scale, nonconvex, and uncertain. In this course, we will study how OPF arises in power systems, how to deal with nonconvexity, scalability, and uncertainty of OPF.

Lecture Notes:

• Power Systems Analysis: a Mathematical Approach (draft)

Homework

During the first 5-6 weeks of class, there will be weekly problem sets. Problems will be assigned from the lecture notes associated with each week's lectures and will be due the Friday of the following week. Homework solutions are preferrably written up in LaTeX, but handwritten solutions are acceptable so long as they are legible.

You should try to solve the problems yourself first. You should consult the instructor (Steven Low) or the TA (Nico Christianson) any time, in person or over email, whenever you have questions. You must however write up your own solution independently. Do not look at previous years' solutions; this includes completed assignments from past students.

Homework grading policy

Homework will be graded with a combination of self-grading and spot-checking by the TA. After the submission deadline each Friday, homework solutions will be released on Canvas along with a self-grading quiz, which will be due on the following Tuesday. To complete the self-grading quiz, you should read through the provided solutions and grade each of your answers on the following 1-5 scale:

• 1: no solution.
• 2: made an attempt at solving, but was not on the right track to getting the correct answer.
• 3: made an attempt at solving and got halfway to the correct answer.
• 4: mostly correct, with 1-2 minor errors.
• 5: 100% correct.

If you assign yourself a grade between 2 and 4 on a problem, you should provide a brief (1-2 sentence) justification of your score, including details on where you made errors in your solution.

The purpose of the self-grading process is to encourage students to continue engaging with the material after homework submission, as well as to highlight areas of difficulty for the instructors to focus more attention on. To that end, the TA will grade a (possible non-strict) subset of homework problems each week to (a) ensure that students' self-grades accurately reflect their performance on problems (and are not inflated), and (b) check whether there are common errors that should be addressed by the course instructors. Your self-grades will count as your homework grades unless there are any concerns regarding (a).

Grading

This is tentative and subject to change:

• Homework: 50%
• Project: 50%
• Project proposal (due wk 5), weekly project updates/class participation (wks 7 - 10).
• Project presentation I (wk 7), final project presentation (TBD).
• Project report

Course Schedule (tentative)

Week	Topic	Notes (continually updated)
4/2	Ch 2 Basic concepts	Slides: HW 1: 1.1, 1.3, 1.6, 1.9 (bonus), 1.10 (Homeworks are due Thurs the following weeks in class)
4/9	Ch 4 Bus injection models	Slides: HW 2: 4.2, 4.3, 4.4, 4.7, 4.10, 4.11, 4.13, 4.14 (choose at least any 7 of 8 problems)
4/16	Ch 12 Power system operations	Slides: HW3: Project proposal
4/23	Ch 11 Smooth convex optimization	Slides: pptx PDF HW4:
4/30	Ch 13 Optimal power flow	Slides: HW 5:
5/7	Ch 14 Semidefinite relaxation: BIM	Slides: SDP relaxation, partial matrices and completion, feasible sets, tightness of relaxations, exactness conditions HW 6:
5/14	Project presentation, I
5/21	Robust optimization	Tractability of robust LP, convex quadratic program, semidefinite program Ref: Ben-Tal, El Ghaoui and Nemirovski (2009), Robust Optimization: Ch 1, 6, 8
5/28	Chance-constrained optimization	Convexity, differentiability, KKT condition, duality, safe approximation by robust optimization Scenario-based solution, sample complexity, optimality Ref: Shapiro,Dentcheva and Ruszczynski (2014), Lectures on Stochastic Programming: Modelling and Theory, 2nd Ed: Ch 4
6/6	Stochastic optimization	Two-stage stochastic LP with recourse; multi-stage and nonlinear stochastic programs Ref: Birge and Louveaux (2011), Introduction to Stochastic Programming, 2nd Ed: Ch 3