MA3 - Optimization and Applications in Energy Systems 1

In future energy systems, long-term hydropower scheduling should consider short-term variability and detailed system constraints. This can be achieved by decomposing the problem and representing aggregated hydropower systems by linear inequalities derived from detailed system descriptions that define the feasible operating space.

This presentation offers a new approach for solving the short-term deterministic Hydro Unit Commitment problem using a layered directed acyclic graph and a Resourced Constrained Shortest Path algorithm. The problem aims at maximizing the energy production of cascaded dams by taking deciding how much water to discharge every hour and by choosing which turbines to use for both dams. This work is done in a regulated market context, where the price of energy is not considered. The graph solver is compared on a real case with optimal results from a Mixed Integer Linear Program and historical decisions. The models are compared on ten instances, where each instance covers 96 hourly decisions. The preliminary results of the graph model are close to optimal, while being faster to compute than the MILP it is compared to.

Lithium-ion batteries (LIBs) are currently the core energy storage component of electric vehicles (EVs). Real-time, accurate, and robust state-of-charge (SOC) estimation is critical for reliable range prediction and for preventing cell degradation due to overcharging or deep discharge. Current model-based estimation methods, based on equivalent circuit models and filters, such as the extended Kalman filter (EKF) and unscented Kalman filter (UKF), provide effective real-time SOC estimation. However, they typically assume a Gaussian process and measurement noise with known mean and covariance, which may not hold in practice. Distributionally robust Kalman filtering (DRKF) utilizes the Wasserstein distance to construct an ambiguity set around a nominal process and measurement noise, thereby accounting for errors in the nominal assumptions. In this paper, we propose a new distributionally robust extended Kalman filter (DREKF), which broadens this methodology to nonlinear problems and applies it to the battery state estimation problem. We benchmark the DREKF against the EKF and UKF using simulations based on an open-source urban dynamometer driving schedule dataset. Results across multiple temperatures demonstrate that the DREKF achieves accuracy and computation time comparable to conventional EKF and UKF approaches under nominal conditions, while offering improved resilience to measurement outliers.

The modified and augmented analysis-based optimal power flow (MANA-OPF) is a complex current-voltage formulation of the OPF. MANA-OPF provides a systematic current–voltage representation that enables the explicit and straightforward modelling of a wide range of network components, including generators, loads, transmission lines, transformers, breakers, and voltage-defined devices, within a sparse matrix structure. As for conventional AC-OPF formulations, MANA-OPF is a nonconvex quadratic program due to bilinear power flow equations and nonlinear voltage magnitude constraints. We employ McCormick envelopes to obtain a convex relaxation of the MANA-OPF and couple it with optimization-based bound tightening (OBBT) to obtain a global solution. The OBBT procedure iteratively reduces variable domains by solving auxiliary optimization problems. We show that the combined McCormick–OBBT approach asymptotically tightens the relaxation and converges to a global optimum of the original MANA-OPF. The resulting solution is compared to load flow solutions for electrical feasibility using the EMTP’s MANA load flow. Experiments on standard IEEE and the 1354Pegase test systems demonstrate accurate modelling of network components. Tests also show that our approach are consistent with convex relaxation and improves the quality of the solution with respect to nonlinear solvers.