The Optimization and Control (OC) group at the Institute for Automation and Applied Informatics (IAI) works on optimization and control methods tailored to applications in future energy systems. A strong focus is on interdisciplinary research between optimization, control, and forecasting. More specifically, we are focussing on three research fields. The first research field is the development of solution methods for optimal power flow. Here we consider uncertainty as well as distributed algorithms. Second, we aim to combine flat systems and hybrid automata theory to enable new control algorithms for the energy system. Finally, we examine the interplay between forecasting and optimization problems.
The Interplay of Forecasting and Optimization
With the energy transition, the number of volatile and decentral generators increases, for example, residential PV systems. These volatile and decentral generators challenge the electrical grid. Thus, the electrical grid must become more flexible and react more autonomously. Typical methods for increasing flexibility are demand-side management and PV-storage systems. However, these methods introduce optimization problems that rely on accurate forecasts. For example, a residential PV-storage system needs forecasts for consumption and generated solar power.
Thus, in our research, we aim to examine the interplay of forecasts and optimization problems considering the realistic constraints of the smart grid. Additionally, we aim to develop forecasting methods considering the specific properties of energy time series.
Optimal Power Flow under Uncertainty
The ever growing relevance of renewable energy sources faces power grid operators with an increasing number of uncertain parameters. The growing amount of uncertainty makes the goal of guaranteeing a robust, reliable and cost efficient power distribution a major challenge in the transition towards a cleaner energy production.
In order to be able to cope with this, Stochastic Optimal Power Flow is a well-studied optimization problem which is used to solve just these challenges in a probabilistic setting. Hence, one has to deal with an optimization problem incorporating random variables and vectors, which is an infinite-dimensional optimization problem.
One solution methodology for this comes from the field of uncertainty quantification. Polynomial Chaos Expansion (PCE) provides a Hilbert-space decomposition of random variables and yields a finite representation with deterministic coefficients. While this approach has recently led to promising results it has the drawback that it is computationally infeasible for larger problem instances.
The aim of ongoing research is to explore, implement and analyze methods that promise to address this curse of dimensionality. Our main focus lies on sparse PCE methods which can yield a more compact system representation while maintaining a sufficiently good model approximation. Further methods from uncertainty quantification such as sensitivity analysis and copula theory are to be explored and incorporated as well.
Hybrid Systems and Control
The combination of digital and mechanical components in cyberphysical systems, together with an ever increasing interconnection, leads to unprecedented complexity of modern technical systems. Classic approaches from computer science and from nonlinear or linear control are not always able to model and to savely automate these systems.
Discrete models like finite or infinite automata are a powerful model class with a rich theory. An equally important class of dynamic models are nonlinear differential equations. Although both these model classes are quite mature, their combination to hybrid systems remains an active field of research.
From an engineering perspective, cyberphysical systems and network systems like e.g. electrical power grids, automated production systems and robots are some of the most important technical systems that show hybrid behavior. We believe that hybrid system theory can play an important role in the future development of these systems. Therefore, we research new methods and approaches by combining concepts from control theory like differential flatness and controllability, and theory and algorithms from computer science with known hybrid systems theory.
DC OPF & Shapley Value
With the rise of renewable energy sources (RES) its control gets more complex. Optimal Power Flow (OPF) plays a significant role in calculating both generation and the network flows.
On the one hand, I work with DC OPF in transmission networks and ask how we can balance the arising uncertainties (from RES) with the help of storages (grid boosters). Using storages we can keep the uncertainty away from generators, which smoothes the generation curve and hence eases control.
A second topic coming along with more RES, but also through a higher complexity of our energy grids, is a fair distribution of costs. For example, if there is a line outage, at the moment the transmission system operator (TSO) carries the costs, or the users through network charges (“Netzentgelte”), respectively. A fairer way to distribute the costs is for example the Shapley value from game theory, which I will work on. This project is in collaboration with TransnetBW, the TSO of the state Baden-Württemberg.
|Martha Maria Frysztacki, M.Sc.||+49 721 608-25707||martha frysztacki∂ kit edu|
|Prof. Dr. Veit Hagenmeyer||+49 721 608-29200||veit hagenmeyer∂ kit edu|
|Benedikt Heidrich, M. Sc.||benedikt heidrich∂ kit edu|
|Dr. phil. Taouba Jouini||+49 721 608-23400||taouba jouini∂ kit edu|
|Dorina Werling||+49 721 608-29201|
|Frederik Zahn, M.Sc.||+49 721 608-24920|
|2 additional persons visible within KIT only.|