Single-Course 5 ECTS

# Optimization in modern power systems

## Overall Course Objectives

Operating a complex system such as power systems requires taking decisions under uncertainty and risk, be it defining the optimal market clearing for electricity market operators, to identifying optimal bidding strategies for generators, and determining optimal control actions or investments for grid operators. Decision makers must ask: What is the best possible outcome? What actions would lead to this outcome? What are the constraints restricting these actions? Optimization theory answers these questions by providing mathematical formulations and solution methods for a variety of decision-making problems. This course introduces the students to fundamental principles and algorithms of optimization theory, and shows them how to apply them to relevant decision-making problems in power systems. The knowledge acquired through this course can be applied to any real-life decision making process, e.g. devise the optimal stock portfolio for a bank, find the fastest transportation route, etc.

See course description in Danish

Learning Objectives

• Recognize and formulate optimization problems for power systems operation
• Describe the fundamental principles of convex optimization and linear programming
• Formulate and explain the dual problem and KKT optimality conditions of a convex optimization problem
• Formulate, solve, analyze and interpret the solutions of operational problems in power systems, such as the Economic Dispatch, Unit Commitment, and Optimal Power Flow problems (DC-OPF)
• Describe and compare the different methods of stochastic, and data-driven optimization in terms of input data, problem structure (objective, constraints, decision variables), and computational complexity
• Explain and apply solution methods for mutli-stage decision-making problems under uncertainty
• Apply and motivate the suitability of the various methods for specific operational problems in the electricity system
• Organize, plan, and carry out work in a group project
• Analyze, structure and present results to a broad audience

Course Content

This course focuses on how to take optimal decisions that deal with both the economic and the technical aspects of power systems operation. We learn how to formulate and solve optimization problems, with different objectives, decision variables, constraints, uncertainty levels. The applications studied in this course cover the Economic Dispatch, Unit Commitment, and Optimal Power Flow problems, which aim at finding optimal device settings and energy flows in the power system. On the theoretical side, this course focuses on convex and linear optimization problems, single- and multi-stage stochastic optimization problems with uncertain objectives and probabilistic constraints, and data-driven optimization problems. The students will learn to discuss and implement solution methods to reduce the curse of dimentionality.

Introduction

Decision-making problems in power systems operation
– Economic dispatch
– Unit commitment
– Optimal power flow (DC-OPF)

Convex optimization
– Linear optimization and duality
– Convex optimization and lagrangian duality

Stochastic optimization
– Scenario-based optimization
– Chance-constrained optimization
– Robust optimization

Data-driven optimization
– Distributionally robust optimization
– Feature-driven optimization and decision-making with contextual information

Multi-stage optimization
– one-stage, two-stage and multi-stage optimization problems
– Solutions methods for large-scale problems

Recommended prerequisites

46705/02402/42112, or equivalent. Knowledge of a programming language such as Matlab, Python or Julia is recommended

Teaching Method

Lectures, exercises, computer exercises, project work

Faculty

Limited number of seats

Minimum: 10.

Please be aware that this course will only be held if the required minimum number of participants is met. You will be informed 8 days before the start of the course, whether the course will be held.

See course in the course database.

## Registration

Duration 13 weeks Wind DTU Lyngby Campus 46750 Candidate Week 35 Week 48 Tues 8-12
Price 7.500,00 DKK