# MAE M.S. in Power & Energy Systems

# Introduction

Students in the Energy Systems track are exposed to a rigorous curriculum on fundamentals and applications in the optimization of electric power systems. As the penetration of variable renewables (solar and wind) on the electric power grid has increased, economic and reliable integration into the power system has become the principal engineering challenge. Power systems are also increasingly shifting away from an overly conservative, insufficiently metered, and inflexible operation. Modern power systems instead reduce operating costs and greenhouse gas emissions through flexible distributed energy resources (energy storage, electric vehicles, and flexible loads), abundant metering, and easier market access. The field of optimization lies at the intersection of these thrusts. To learn more about the M.S. program and its requirements, visit the MAE M.S. Program page.

# Required Courses

All students will take the core courses.

## Fundamentals of Energy Systems (MAE 206)

This course is designed to introduce students to the fundamentals of the energy system and outline its possible futures given the need to radically reduce global carbon emissions. UC San Diego has several courses that investigate different aspects of the energy system, including the fundamental science and engineering behind promising new technologies (mainly in JSOE) and the political economy of energy (in GPS and Economics).

None of these offers an explanation of how the system is structured, the imperatives and constraints under which it operates, and how it is likely to evolve given the competing demands it serves and the range of challenges facing its constituent technologies. The goal of this course is to impart a knowledge of these realities, and to help students develop the skills to critically evaluate the technology, economic, and policy choices that will have to be made when modernizing it, with a key focus on innovation in creating new opportunities. It is designed to help students build a foundation for future coursework on energy systems.

## Electric Power Systems Modeling (MAE 243)

This course will teach students constrained optimization problems and associated solution methods, how to implement and apply linear and mixed integer linear programs to solve such problems using Julia/JuMP, and the practical application of such techniques in energy systems engineering. The course will first introduce students to the theory and mathematics of constrained optimization problems and provide a brief introduction to linear programming, including problem formation and solution algorithms. Next, to build hands-on experience with optimization methods for energy systems engineering, the course will introduce students to several canonical problems in electric power systems planning and operations, including: economic dispatch, unit commitment, optimal network power flow, and capacity planning. Finally, several datasets of realistic power systems are provided which students will use in conjunction with building a model for a course project that answers a specific power systems question. Course Repo.

## Convex Optimization for Engineers (MAE 227)

This course focuses on convex optimization theory, convexification of non-convex problems, engineering applications, modeling and implementation in a programming language (MATLAB or choice). This course covers: convex sets and functions, convex optimization problems (LP, QP, SOCP, SDP, robust and stochastic optimization), weak and strong duality, optimality conditions (complementary slackness, Karush-Kuhn-Tucker), and solution and shadow price interpretation. Some applications include: design in mechanical engineering, optimal control problems, machine learning, energy, transportation, etc. Prerequisites: nongraduate students may enroll with consent of instructor.

## Mathematics for Engineers (MAE 208)

This course will reintroduce the mathematics fundamentals necessary for success in the engineering graduate program in MAE. Topics will include calculus, ODE’s, vector calculus, linear algebra, probability and PDE’s.

## Linear Systems Theory (MAE 280A)

Linear algebra: inner products, outer products, vector norms, matrix norms, least squares problems, Jordan forms, coordinate transformations, positive definite matrices, etc. Properties of linear dynamic systems described by ODEs: observability, controllability, detectability, stabilizability, trackability, optimality. Control systems design: state estimation, pole assignment, linear quadratic control.

# Electives

Students should expect to take 4 additional elective courses. Please review the MAE M.S. Program page (MC 92) for the approved list.