Optimization in modern power systems

• Describe the fundamental principles of convex optimization and linear programming, including problem structure, feasibility, optimality, and computational complexity.
• Explain and compare methods for optimization under uncertainty, examining their problem structure, underlying assumptions, and computational trade-offs.
• Formulate and analyze the dual and optimality conditions of convex optimization problems.
• Interpret the geometric and techno-economic implications of the dual and optimality conditions of optimization problems in power systems, by linking them to marginal costs, resource valuations, and operational constraints.
• Translate real-life decision-making problems in power systems from natural language into well-defined mathematical optimization models, identifying objectives, decision variables, constraints, and input data.
• Critically evaluate the solutions of optimization models by analyzing how modeling choices affect feasibility, optimality, and computational complexity, and extract actionable insights for operational or planning decisions.
• Collaboratively design and implement scientific code to solve real-life power systems optimization problems, integrating contributions across group members and documenting workflows clearly.
• Effectively communicate the solutions of complex decision-making problems in power systems to a broad audience through clear and compelling narratives and visualization aids.
• Communicate the formulation, solution process, and insights of complex optimization problems to a broad audience through clear written analysis, compelling narratives, and visualization aids.

Students will learn to formulate, solve, and critically analyze optimization models for real-world decision-making problems in modern power systems. The course covers convex optimization, duality theory, complementarity modelling, and optimization under uncertainty, applied to a broad range of problems, including: power system operation and planning, value-oriented forecasting, electricity markets, and demand response.

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 classroom preparation for selected topics, including short videos, reading materials, and self-assessment quizzes;
ii) Interactive lectures, including traditional instruction, individual and group exercises, board games, and group discussions;
iii) Weekly (optional) exercises in 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.