Optimal Power Flow (OPF) problems are of crucial importance for the operation of electrical energy grids. A prime indicator are the steadily increasing costs for generator redsipatch and curative grid actions in Germany –cf. the monitoring report by the German grid authority (Bundesnetzagentur BNA)– as these operational decisions are based on the solution of OPF problems. In this context, we investigate novel numerical methods including stochastic OPF formulations and distributed solution algorithms. The former is driven by the increasing share of volatile renwables in the energy mix, which have to be modelled by non-Gaussian distributions. We use Polynomial Chaos Expansions to achieve a tractable reformulation. The modelling of such uncertainties is one of our research topics in the Collaborative Research Center/Transregio CRC/TRR 391 Spatio-temporal Statistics for the Transition of Energy and Transport.

We also investigate distributed optimization algorithms to solve optimal power flow problems in stationary and time coupled multi-stage formulations as well as the application of design of experiments to enable in-operation estimation of parameters. 

[1] Mühlpfordt, T., Roald, L., Hagenmeyer, V., Faulwasser, T., & Misra, S. (2019). Chance-constrained AC optimal power flow: A polynomial chaos approach. IEEE Transactions on Power Systems, 34(6), 4806-4816.

[2] Faulwasser, T., Engelmann, A., Mühlpfordt, T., & Hagenmeyer, V. (2018). Optimal power flow: an introduction to predictive, distributed and stochastic control challenges. at-Automatisierungstechnik, 66(7), 573-589.

[3] Mühlpfordt, T., Zahn, F., Hagenmeyer, V., & Faulwasser, T. (2020). PolyChaos. jl—A Julia package for polynomial chaos in systems and control. IFAC-PapersOnLine, 53(2), 7210-7216.

[4] Mühlpfordt, T., Faulwasser, T., & Hagenmeyer, V. (2018). A generalized framework for chance-constrained optimal power flow. Sustainable Energy, Grids and Networks, 16, 231-242.

[5] Engelmann, A., Jiang, Y., Mühlpfordt, T., Houska, B., & Faulwasser, T. (2018). Toward distributed OPF using ALADIN. IEEE Transactions on Power Systems, 34(1), 584-594.

[6] Engelmann, A., Jiang, Y., Houska, B., & Faulwasser, T. (2020). Decomposition of nonconvex optimization via bi-level distributed ALADIN. IEEE Transactions on Control of Network Systems, 7(4), 1848-1858.

[7] Engelmann, A., Jiang, Y., Benner, H., Ou, R., Houska, B., & Faulwasser, T. (2022). ALADIN‐a—An open‐source MATLAB toolbox for distributed non‐convex optimization. Optimal Control Applications and Methods, 43(1), 4-22.

[8] Murray, A., Engelmann, A., Hagenmeyer, V., & Faulwasser, T. (2018). Hierarchical distributed mixed-integer optimization for reactive power dispatch. IFAC-PapersOnLine, 51(28), 368-373.

[9] Du, X., Engelmann, A., Jiang, Y., Faulwasser, T., & Houska, B. (2020). Optimal experiment design for ac power systems admittance estimation. IFAC-PapersOnLine, 53(2), 13311-13316.

[10] Stomberg, G., Raetsch, M., Engelmann, A., & Faulwasser, T. (2024). Large problems are not necessarily hard: A case study on distributed NMPC paying off. arXiv preprint arXiv:2411.05627.