Optimization in modern power systems

• Describe the fundamental principles and properties of convex optimization and linear programming.
• Explain and compare different methods for optimization under uncertainty, by examining their problem structure (input data, decision variables, objective function, constraints), underlying assumptions, and computational complexity.
• Critically evaluate the solutions of optimization models by analyzing how input data and modeling choices affect feasibility, accuracy, optimality, and computational complexity.
• Formulate the dual problem and optimality conditions of linear and convex optimization problems, and explain their mathematical properties and implications.
• Interpret and characterize the structure and properties of real-life decision-making problems in power systems described in natural language, by identifying key components (objectives, constraints, decision variables, and input data) and explaining their interactions.
• Translate real-life decision-making problems into a well-defined mathematical optimization models, formulating efficiently the constraints, objective and decision variables.
• Collaboratively develop and implement scientific code to efficiently solve real-life decision-making problems in power systems using suitable solution algorithms, effectively integrating contributions and documenting workflows.
• Interpret the solutions of optimization models for complex decision-making problems in power systems, by identifying key insights and supporting data to explain their implications for operational or planning decisions.
• Interpret the meaning, from a techno-economic perspective, of the optimality conditions, dual formulation and dual variables of power system optimization problems, by linking them to marginal costs, resource valuations, and operational constraints, and using them to provide valuable insights into the solutions of these optimization problems.
• Effectively communicate the solutions of complex decision-making problems in power systems to a broad audience through clear and compelling narratives and visualization aids.
• Identify relevant real-life decision-making problems in power systems, design and implement tailored optimization models to provide realistic and practical solutions, and motivate these modelling choices.
• Provide clear, constructive, and actionable peer feedback on the identification and formulation of relevant decision-making problems in power systems, suitability of various modelling choices to tackle these problems, as well as the interpretation and effective communication of key insights.

Students will gain a deep understanding of linear programming and convex optimization, duality theory, complementarity modelling, and optimization techniques under uncertainty, and learn how to apply these tools to a range of real-world challenges in power systems. Key applications include capacity expansion planning, economic dispatch, unit commitment, optimal power flow, value-oriented forecasting, market clearing, dynamic pricing, strategic investment, self-scheduling and bidding in electricity markets.

• 36 – 49 (Wed 8-12)

46700/46705/02402/42112/42101, or equivalent. Solid programming skills (Python, Julia or similar) are expected, since programming is an essential part of the course assignments. It is highly recommended that students are familiar with the fundamentals of electric power systems modelling and operation, including balanced three-phase circuits, power system components modelling, and power flow equations, and electricity markets organization.

i) Flipped classrooms and asynchronous content, such as short videos, readings, and self-assessment quizzes;
ii) Hybrid (in-person and online) sessions traditional lectures, individual and group exercises, board games, poster presentations, industry talks, Q&A, and peer discussions;
iii) Weekly exercises focused on mathematical modeling, scientific coding, and critical result analysis.

This course has been redesigned as part of the DigiWind project to foster advanced digital skills in wind and energy systems engineering. The learning objectives, activities, and evaluation methods have been restructured to emphasize computational thinking, model-based reasoning, and mathematical programming skills. A variety of digital tools are integrated to support active and differentiated learning.