The course covers various aspects of optimization theory with applications to large-scale energy networks. Following a general introduction into optimization theory, i.e. how to set up an optimization problem, how to solve it, etc., several techniques are discussed that make it possible to decompose a large optimization problem into smaller subproblems for which the optimal solution is the same as for the overall problem. Such decompositions are necessary for large systems such as power systems where it is often not possible to formulate and solve a single optimization problem for the entire system. Model Predictive Control (MPC) is then introduced as a dynamic control technique based on optimization. A model of the system is used to predict the evolution of the system state over a given future time horizon to determine the optimal input values to achieve a certain objective. Applications of these techniques to energy systems are presented. As the main focus lies on power systems, a short introduction into power systems will be provided.
Pre-requisites for the course are mathematical basics such as linear algebra, calculus, complex values; basics in system theory such as the concept of system variables, inputs and outputs, state space representation; basics in electric circuits, i.e. voltage, current, impedance and their complex representation, ohms laws.