Overordnede kursusmål
The increasing integration of renewable energy sources exposes the
energy systems to more variability and uncertainty in supply, which
challenges the way the current energy markets work. The modern
energy systems need coordination of different sectors, e.g., power,
natural gas and heat systems, and different entities, e.g.,
transmission and distribution system operators, for revealing the
maximum potential operational flexibility in energy systems with
high penetration of renewables. This requires developing advanced
decision-making as well as analysis tools using optimization,
equilibrium, and game-theoretic models. These tools are expected to
properly capture the physics of energy systems, potential
uncertainties, and interactions of different sectors and market
players, while being able to solve problems in a computationally
tractable manner. In practice, most of those problems are
significantly simplified and then solved through conventional
techniques. This course first presents advanced optimization,
equilibrium, and game-theoretic techniques to efficiently develop
the required tools. Then, it presents several decomposition and
distributed optimization techniques to efficiently solve the
large-scale optimization and equilibrium problems in energy
markets, which are compatible with their practical requirements.
The main focus of this course is on electricity systems and
markets, while taking into account the other sectors, e.g., natural
gas and district heating systems.
Læringsmål
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
- Explain the reasons why one would need mathematical
optimization, equilibrium and game-theoretical techniques in energy
systems
- Formulate an energy market clearing problem in both
optimization and equilibrium forms
- Investigate the satisfaction of desirable economic properties
in energy markets
- Apply the methods for modeling uncertainty to a number of
representative problems in energy markets, and compare their
performance
- Develop complementarity models for a few problems in energy
markets
- Solve large-scale optimization problems in energy systems using
decomposition and distributed optimization techniques
- Implement the mathematical techniques in programming languages
such as GAMS, Python, and Julia
- Analyze the numerical outcomes obtained and appraise their
quality
- Organize, plan, and carry out work in group projects
Kursusindhold
1) Energy market clearing
1.1) As an optimization problem
1.2) As an equilibrium problem
1.3) Desirable economic properties
2) Uncertainty modeling in energy markets
2.1) Stochastic programming
2.2) Robust optimization
2.3) Distributionally robust chance-constrained optimization
3) Hierarchical (e.g., bi-level) optimization: Complementarity
programming
3.1) Concept and mathematical background
3.2) Different applications to energy markets: from operational to
planning problems
4) Potential large-scale problems in energy markets for
decomposition
4.1) Problems with complicating variables
4.2) Problems with complicating constraints
5) Benders’ decomposition
5.1) Concept and mathematical background
5.2) Different applications to energy markets: from operational to
planning problems
6) Lagrangian relaxation
6.1) Concept and mathematical background
6.2) Different decomposition techniques based on Lagrangian
relaxation, including dual decomposition, augmented Lagrangian
relaxation, alternating direction method of multipliers (ADMM),
consensus- and exchange-ADMM
6.3) Different applications to energy markets: from operational to
planning problems
Sidst opdateret
17. december, 2020
