arXiv subjects

Frederik Zahn

Publications and source records attributed to Frederik Zahn.

7 recordsLinked to original sources

arXiv2026

Distributed coordination for transmission-distribution systems with nonlinear flexibility aggregation

High shares of distributed energy resources (DERs) transform distribution systems into active participants in integrated transmission and distribution (ITD) operations. Linear models enable scalable distribution-level flexibility aggregation but can misclassify AC feasible operating points, whereas direct nonlinear aggregation becomes costly, especially in multiperiod ITD coordination. This paper reformulates transmission-distribution coordination within a hierarchical optimization framework and introduces a non-iterative predictor-corrector aggregation method. By leveraging path-following techniques from real-time optimal control, the approach achieves tractable computation with guaranteed error bounds. Across 24 radial distribution-network cases and seven meshed variants, including the real KIT Campus North grid, the proposed method yields substantially lower sampled false- and lost-flexibility rates than linear surrogates and a convex relaxation. On two 24-period ITD testcases, the formulation reduces end-to-end wall-clock time by factors of 6 relative to the corresponding centralized formulation, primarily through dimensionality reduction.

eess.SY↗

arXiv2026

Stochastic Model Predictive Control based on Mixed Random Variables for Economic Energy Management

Optimal scheduling of batteries has significant potential to reduce electricity costs and to enhance grid resilience. However, effective battery scheduling must account for both physical constraints as well as uncertainties in consumption and generation of renewable energy sources. Instead of optimizing fixed battery power setpoints, we propose an approach that optimizes battery power intervals, allowing the optimization to explicitly account for uncertain consumption and generation as well as how the battery system should respond to them within its physical limits. Our method is based on mixed random variables, represented as mixtures of discrete and continuous probability distributions. Building on this representation, we develop an analytical stochastic formulation for minimizing electricity costs in a residential setting with load, photovoltaics, and battery storage. We demonstrate its effectiveness across real-world data from 15 residential buildings over five consecutive months. Compared with deterministic and probabilistic benchmark controllers, the proposed interval-based optimization achieves the lowest costs. These results show that mixed random variables are a practical and promising tool for decision-making under uncertainty.

math.OC↗

arXiv2025

Averaging favors MPC: How typical evaluation setups overstate MPC performance for residential battery scheduling

Residential prosumers with PV-battery systems increasingly manage their electricity exchange with the power grid to minimize costs. This study investigates the performance of Model Predictive Control (MPC) and Rule-Based Control (RBC) under 15/30/60 minute averaging commonly used in research, when Net Billing and battery degradation are considered. We simulate five consecutive months for 15 buildings in northern Germany, generating costs at up to 1-minute resolution while scheduling at 15/30/60 minutes. We find that time-averaged evaluations make MPC look consistently better than RBC, yet when costs are recomputed at minute-level ground-truth, the reported advantage shrinks by 69\% on average for hourly schedulers. For individual buildings, the finer evaluation can reverse conclusions, and simple RBC can achieve lower total costs than an MPC with perfect foresight. These findings caution against drawing conclusions from coarse averages and show how a fair assessment of battery scheduling approaches can be obtained.

math.OC↗

arXiv2025

Error Accumulation using Linearized Models for Aggregating Flexibility in Distribution Systems

This paper investigates flexibility aggregation approaches based on linear models. We begin by examining the theoretical foundations of linear AC power flow, two variants of so-called DC power flow, and the LinDistFlow model, along with their underlying assumptions. The discussion covers key system details, including network topology, voltage constraints, and line losses. Simulations are conducted on the KIT Campus Nord network with real demand and solar data. Results show that, in the absence of negative losses, line losses are generally underestimated by linear models. Furthermore, line losses errors tend to accumulate both at the point of common coupling (PCC) and over extended time horizons.

eess.SY↗

arXiv2025

Enhanced Flexibility Aggregation Using LinDistFlow Model with Loss Compensation

With the increasing integration of renewable energy resources and the growing need for data privacy between system operators, flexibility aggregation methods have emerged as a promising solution to coordinate integrated transmissiondistribution (ITD) systems with limited information exchange. However, existing methods face significant challenges due to the nonlinearity of AC power flow models, and therefore mostly rely on linearized models. This paper examines the inherent errors in the LinDistFlow model, a linearized approximation, and demonstrates their impact on flexibility aggregation. To address these issues, we propose an intuitive compensation approach to refine the LinDistFlow-based flexibility set. Simulation results demonstrate the effectiveness of the proposed method in efficiently coordinating ITD systems.

eess.SY↗

arXiv2024

Probabilistic Day-Ahead Battery Scheduling based on Mixed Random Variables for Enhanced Grid Operation

The increasing penetration of renewable energy sources introduces significant challenges to power grid stability, primarily due to their inherent variability. A new opportunity for grid operation is the smart integration of electricity production combined with battery storages in residential buildings. This study explores how residential battery systems can aid in stabilizing the power grid by flexibly managing deviations from forecasted residential power consumption and PV generation. The key contribution of this work is the development of an analytical approach that enables the asymmetric allocation of quantified power uncertainties between a residential battery system and the power grid, introducing a new degree of freedom into the scheduling problem. This is accomplished by employing mixed random variables - characterized by both continuous and discrete events - to model battery and grid power uncertainties. These variables are embedded into a continuous stochastic optimization framework, which computes probabilistic schedules for battery operation and power exchange with the grid. Test cases demonstrate that the proposed framework can be used effectively to reduce and quantify grid uncertainties while minimizing electricity costs. It is also shown that residential battery systems can be actively used to provide flexibility during critical periods of grid operation. Overall, this framework empowers prosumers to take an active role in grid stabilization, contributing to a more resilient and adaptive energy system.

math.OC↗

arXiv2020

PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying mathematical framework to study systems under arbitrary uncertainties of finite variance; we introduce this problem as a so-called mapping under uncertainty. For practical PCE-based applications we require orthogonal polynomials relative to given probability densities, and their quadrature rules. With PolyChaos we provide a Julia software package that delivers the desired functionality: given a probability density function, PolyChaos offers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products. PolyChaos is the first PCE-related software written in Julia, a scientific programming language that combines the readability of scripted languages with the speed of compiled languages. We provide illustrating numerical examples that show both PCE and PolyChaos in action.

eess.SY↗