Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.09060

Efficient Quantile-Resolved Hosting Capacity Assessment on Nodal Level for Low-Voltage Grids

Maximilian Köhler·Edwin Mora·Mathias Duckheim·Stefan Niessen
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hosting capacity - the maximum additional capacity a network can accommodate without violating operational limits - is a key metric in distribution system planning and operation. Decisions on grid reinforcements and the deployment of flexibility management require not only the worst-case HC but also an understanding of the distribution of HC under different likelihoods in load and generation patterns. Quantile-resolved HC distributions provide this view by expressing HC as a function of an acceptable operational limit exceedance likelihood. Monte Carlo sampling is the established approach for computing such distributions but demands large computational resources. Approximations sacrifice either accuracy, the ability to capture uncertainty correlations, or scalability when assessing real-world networks. This paper introduces a computationally efficient method for calculating distributions for quantile-resolved HC. It uses a representation of load samples as multivariate normal distribution, propagated through a linearized power flow model. This allows for leveraging a re-parametrized AC-OPF problem for each hosting capacity quantile. Benchmarking against Monte Carlo-based methods on realistic LV networks demonstrates that the proposed method achieves comparable accuracy with a mean deviation of approx. 3%, while reducing computational time by orders of magnitude. For the exemplary networks the computational time decreases from 11 min to 2 s, and 38 h to 50 s, respectively. The method's scalability is also suitable for recalculation in 15-minute cycles encountered in DSO practice for e.g., real-time grid management.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Maximilian Köhler, Edwin Mora, Mathias Duckheim, Stefan Niessen. 2026-09-08. Efficient Quantile-Resolved Hosting Capacity Assessment on Nodal Level for Low-Voltage Grids. https://arxiv.org/abs/2609.09060

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.SY subjecteess.SY subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

arXiv2026

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY↗
arXiv2026

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY↗
arXiv2026

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY↗