Optimisation under uncertainty

Course "Optimisation of energy systems"

• Fundamentals of probability theory and statistics: distributions, key figures
• Estimating distributions from data, generating scenarios from distributions (Monte Carlo simulation)
• Model predictive control: optimisation with forecasts incl. updating
• Stochastic optimisation using linear optimisation, value of perfect and (un)complete information
• Application examples: Price, demand and resource uncertainties, uncertain electrical consumption, uncertain arrival times of an electric car, prices, PV yields, uncertain weather variables, control of stochastic energy systems such as charging load management in electromobility, optimal management of energy generation plants and energy storage systems with uncertain data using forecasts, etc

At the end of the course, students will be able to identify, model and simulate uncertainties in energy systems and integrate them into optimisations. Students will be able to

• understand and apply the necessary basics of probability theory and statistics,
• estimate probability distributions from data,
• generate scenarios from distributions and simple forecasts,
• carry out Monte Carlo simulations of a stochastic system and evaluate them using key figures,
• understand and apply Model Predictive Control,
• perform simple linear stochastic optimisations and quantify their value in comparison to deterministic optimisations,
• implement the methods learnt on the computer.

Students acquire the following future skills:

• Digital Literacy: Implementing on the computer with Python
• Academic Creativity: Modelling of stochastic energy systems
• Communication Skills: Presentation and explanation of mathematical concepts
• Environmental and Sustainability Awareness: Application to energy problems

Integrated course with lectures and exercises.

• Exercises (20%)
• Written exam (80%)

For a positive grade, a minimum of 50% of the possible points must be achieved in each part of the examination.

None

• Schiller, John J.; Srinivasan, R. Alu; Spiegel, Murray R. (2013): Schaum’s Outline of Probability and Statistics: 897 Solved Problems + 20 Videos. 4 edition, McGraw-Hill Education Ltd.
• Camacho, Eduardo F.; Alba, Carlos Bordons (2007): Model Predictive Control. 2nd edition, Springer.
• Kall, Peter; Mayer, János (2012): Stochastic Linear Programming: Models, Theory, and Computation. 2nd eEdition, Springer.
• Birge, John R.; Louveaux, François (2011): Introduction to Stochastic Programming. 2nd ed. 2011. New York: Springer.
• Jordaan, Ian (2011): Decisions under Uncertainty: Probabilistic Analysis for Engineering Decisions. 1st edition, Cambridge University Press.
• Kovacevic, Raimund M.; Pflug, Georg Ch; Vespucci, Maria Teresa (2013): Handbook of Risk Management in Energy Production and Trading. Springer.

Presence Course and blended learning (guided learning with a website). Students are informed of the lecturer's attendance requirements before the start of the course.