arXiv subjects

Frederik Geth

Publications and source records attributed to Frederik Geth.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Network Prices for Prosumer-aware Hosting Capacity Management

The fast uptake of distributed energy resources (DERs) presents increasing challenges for managing hosting capacity in distribution networks. Existing solutions include direct load control, operating envelopes, and price-based control through dynamic energy prices. Despite their effectiveness, these methods often rely on assumed prosumer behavioural patterns and overlook prosumers' desire to retain control over their devices. Additionally, current fixed or Time-of-Use (ToU) prices are based on spatial and temporal averages, having limited impact on network conditions and DER operation. To address these limitations, this paper proposes a bilevel optimisation framework that explicitly models prosumer decision-making in the design of dynamic network prices. The upper level represents the distribution system operator (DSO), setting network prices under cost-recovery and network constraints, while the lower level models prosumers optimising DER operation in response. The proposed framework preserves customer prerogative, enhances DER flexibility, and offers actionable insights for network hosting capacity management and the evolution of network tariff structures under high DER penetration.

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arXiv2025

Stochastic Security Constrained AC Optimal Power Flow Using General Polynomial Chaos Expansion

Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper presents a stochastic security constrained optimal power flow model with chance constraints supporting nonlinear AC power flow equations and non Gaussian uncertainties. We use general polynomial chaos expansion to model arbitrary uncertainties of finite variance, enabling accurate moment computations and robust prediction of system states across diverse operating scenarios. The chance constraints probabilistically limit inequality violations, providing a more flexible representation of controllable variables and the consequent power system operation. Case studies validate the proposed models effectiveness in satisfying operational constraints and capturing uncertainty with high fidelity. Compared to the deterministic formulation, it also uncovers a wider set of unsecure contingencies, highlighting improved uncertainty capture and operational insight.

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arXiv2025

Distribution System State and Impedance Estimation Augmented with Carson's Equations

The impedances of cables and lines used in (multi-conductor) distribution networks are usually unknown or approximated, and may lead to problematic results for any physics-based power system calculation, e.g., (optimal) power flow. Learning parameters from time series data is one of the few available options to obtain improved impedance models. This paper presents an approach that combines statistical learning concepts with the exploitation of domain knowledge, in the form of Carson's equations, through nonlinear mathematical optimization. The proposed approach derives impedance matrices for up-to-four-wire systems, using measurement data like those obtained from smart meters. Despite the lack of phasor measurements, the low signal-to-noise ratio of smart meter measurements, and the inherent existence of multiple equivalent solutions, our method produces good quality impedance models that are fit for power system calculations, significantly improving on our previous work both in terms of accuracy and computational time.

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arXiv2024

AC-DC Power Systems Optimization with Droop Control Smooth Approximation

This paper addresses the challenges of embedding common droop control characteristics in ac-dc power system steady-state simulation and optimization problems. We propose a smooth approximation methodology to construct differentiable functions that encode the attributes of piecewise linear droop control with saturation. We transform the nonsmooth droop curves into smooth nonlinear equality constraints, solvable with Newton methods and interior point solvers. These constraints are then added to power flow, optimal power flow, and security-constrained optimal power flow problems in ac-dc power systems. The results demonstrate significant improvements in accuracy in terms of power sharing response, voltage regulation, and system efficiency, while outperforming existing mixed-integer formulations in computational efficiency.

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arXiv2024

The Inverse Carson's Equations Problem: Definition, Implementation and Numerical Experiments

In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components due to the lack of datasets with fully parameterized impedance matrices. This assumes that the network impedance is balanced, which is typically not the case in the low-voltage network and therefore risks the accuracy of the study. This paper proposes a methodology for the recovery of more detailed impedance data from sequence components as an inverse problem, i.e. the inverse Carson's equations problem, for both overhead lines and cables. We consider discrete properties like material and configuration of conductors common in the distribution network and investigate what data can be reliably recovered from only sequence components using nonlinear optimisation models. Presented results include uniqueness of recovered variables and the likelihood of mismatch.

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arXiv2024

Improved Algebraic Inverter Modelling for Four-Wire Power Flow Optimization

This paper discusses the modeling of inverters used in distributed energy resources in steady state. Modeling the interaction between distribution grids and inverter-based resources is crucial to understand the consequences for the network's operational and planning processes. This work highlights the limitations of existing models and emphasizes the need for better representations of inverters and their control laws in decision-making contexts. Improved steady-state grid-following and grid-forming inverter models are presented, including both three-leg and four-leg converter variants. The advantages of these improved models in mathematical optimization contexts are showcased by investigating the power quality improvement capabilities of the inverters. Numerical studies integrating the proposed inverter models in a four-wire unbalanced optimal power flow engine are presented, and trade-offs between modeling detail and computational intensity are illustrated.

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arXiv2023

Making Distribution State Estimation Practical: Challenges and Opportunities

In increasingly digitalized and metered distribution networks, state estimation is generally recognized as a key enabler of advanced network management functionalities. However, despite decades of research, the real-life adoption of state estimation in distribution systems remains sporadic. This systematization of knowledge paper discusses the cause for this while comparing industrial and academic experiences and reviewing well- and less-established research directions. We argue that to make distribution system state estimation more practical and applicable in the field, new perspectives are needed. In particular, research should move away from conventional approaches and embrace generalized problem specifications and more comprehensive workflows. These, in turn, require algorithm advancements and more general mathematical formulations. We discuss lines of work to enable the delivery of tangible research.

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arXiv2023

Real-Value Power-Voltage Formulations of, and Bounds for, Three-Wire Unbalanced Optimal Power Flow

Unbalanced optimal power flow refers to a class of optimization problems subject to the steady state physics of three-phase power grids with nonnegligible phase unbalance. Significant progress on this problem has been made on the mathematical modelling side of unbalanced OPF, however there is a lack of information on implementation aspects as well as data sets for benchmarking. One of the key problems is the lack of definitions of current and voltage bounds across different classes of representations of the power flow equations. Therefore, this tutorial-style paper summarizes the structural features of the unbalanced (optimal) power problem for three-phase systems. The resulting nonlinear complex-value matrix formulations are presented for both the bus injection and branch flow formulation frameworks, which typically cannot be implemented as-is in optimization toolboxes. Therefore, this paper also derives the equivalent real-value formulations, and discusses challenges related to the implementation in optimization modeling toolboxes. The derived formulations can be re-used easily for continuous and discrete optimization problems in distribution networks for a variety of operational and planning problems. Finally, bounds are derived for all variables involved, to further the development of benchmarks for unbalanced optimal power flow, where consensus on bound semantics is a pressing need. We believe benchmarks remain a cornerstone for the development and validation of scalable and reproducible optimization models and tools. The soundness of the derivations is confirmed through numerical experiments, validated w.r.t. OpenDSS for IEEE test feeders with 3x3 impedance matrices.

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arXiv2023

Data quality challenges in existing distribution network datasets

Existing digital distribution network models, like those in the databases of network utilities, are known to contain erroneous or untrustworthy information. This can compromise the effectiveness of physics-based engineering simulations and technologies, in particular those that are needed to deliver the energy transition. The large-scale rollout of smart meters presents new opportunities for data-driven system identification in distribution networks, enabling the improvement of existing data sets. Despite the increasing academic attention to system identification for distribution networks, researchers often make troublesome assumptions on what data is available and/or trustworthy. In this paper, we highlight some differences between academic efforts and first-hand industrial experiences, in order to steer the former towards more applicable research solutions.

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arXiv2023

An Open Optimal Power Flow Model for the Australian National Electricity Market

The Australian National Electricity Market (NEM) is a complex energy market that faces challenges due to the increasing number of distributed energy resources (DERs) and the transition to a net-zero emissions target. Power system modelling plays a crucial role in addressing these challenges by providing insights into different scenarios and informing decision-making. However, accessing power system data containing sensitive information can be a concern. Synthetic data offer a solution by allowing researchers to analyze and develop new methods while protecting confidential information. This paper utilizes an existing synthetic network model based on the NEM (`S-NEM2300'-bus system) to develop a benchmark for power system optimization studies. The model is derived and enhanced using PowerModels.jl and MATPOWER data models, and feasibility is ensured through power flow and optimal power flow studies. The resulting benchmark model, called `S-NEM2000'-bus system, is validated and enriched with additional parameters such a thermal limits, generation fuel categories and cost models. The `S-NEM2000'-bus system is an \emph{open} dataset which provides a valuable resource for optimization studies in the power system domain.

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arXiv2023

On the Implementation of the Fixed Point Iteration Current Injection Method to Solve Four-Wire Unbalanced Power Flow in PowerModelsDistribution.jl

This report serves as a technology description of a Julia-based re-implementation of the fixed-point current injection algorithm, available in PowerModelsDistribution.jl [1]. This report does not describe a novel method for solving unbalanced power flow problems. It merely provides a description of the fixed point iteration variant of the current injection method, inspired by the existing open-source implementation in OpenDSS1 [2]. The current injection method is commonly conceived as a system of nonlinear equalities solved by Newton s method [3, 4]. However, as Roger Dugan points out in the OpenDSS documentation, the fixed point iteration variant commonly outperforms most methods, while supporting meshed topologies from the ground up. We note that the unbalanced power flow algorithm in turn relies on matrix solvers for sparse systems of equations. In the context of circuits and factorizing nodal admittance matrices, the sparsity-exploiting KLU solver [5] has proven to be both reliable and scalable. OpenDSS uses KLU. This report documents work-in-progress, and the authors aim to update it when learnings are obtained or more features are added to the implementation in PowerModelsDistribution.jl. The authors invite collaborators to contribute through pull requests on the repository.

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arXiv2023

The Importance of Technical Distribution Network Limits in Dynamic Operating Envelopes

End-users more often decide to invest in distributed generation (DG) units that help them in decreasing electricity bills and allow them to become a market player by selling the excess produced electricity. However, the installation of DG is often limited by technical constraints of the network, standards, and national grid codes. As a method for removing the mentioned obstacles, the potential of dynamic operating envelopes (DOEs) is recently becoming recognized as a way for maximizing the benefits of installing DG. In this paper, we present an improvement of the already developed models that often neglect voltage unbalance constraints or are not based on an optimization approach. To test the model, two realistic case studies are defined. The results show that not all technical constraints are equally important, that the voltage unbalance constraint impacts the calculated DOEs for single-phase installed DG units, and that neglecting the temporal and spatial component in determining the limitation power is inadequate.

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arXiv2023

Combined Unbalanced Distribution System State and Line Impedance Matrix Estimation

To address the challenges that the decarbonization of the energy sector is bringing about, advanced distribution network management and operation strategies are being developed. Many of these strategies require accurate network models to work effectively. However, distribution network data are known to contain errors, and attention has been given to techniques that allow to derive improved network information. This paper presents a novel method to derive line impedance values from smart meter measurement time series, with realistic assumptions in terms of meter accuracy, resolution and penetration. The method is based on unbalanced state estimation and is cast as a non-convex quadratically constrained optimization problem. Both line lengths and impedance matrix models can be estimated based on an exact nonlinear formulation of the steady-state three-phase network physics. The method is evaluated on the IEEE European Low Voltage feeder (906 buses) and shows promising results.

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arXiv2023

Pitfalls of Zero Voltage Values in Optimal Power Flow Problems

The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it is not possible to rely on such bounds for a variety of real-world network optimization problems. This paper discusses a few issues related to 0 V assumptions made during the process of deriving optimization formulations in the current-voltage, power-voltage and power-lifted-voltage variable spaces. The differences between the assumptions are illustrated for a 2-bus 2-wire test case, where the feasible sets are visualized. A nonzero relaxation gap is observed for the canonical multiconductor nonlinear power-voltage formulation. A zero gap can be obtained for the branch flow model semi-definite relaxation, using newly proposed valid equalities.

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arXiv2022

Computational Analysis of Impedance Transformations for Four-Wire Power Networks with Sparse Neutral Grounding

In low-voltage distribution networks, the integration of novel energy technologies can be accelerated through advanced optimization-based analytics such as network state estimation and network-constrained dispatch engines for distributed energy resources. The scalability of distribution network optimization models is challenging due to phase unbalance and neutral voltage rise effects necessitating the use of 4 times as many voltage variables per bus than in transmission systems. This paper proposes a novel technique to limit this to a factor 3, exploiting common physical features of low-voltage networks specifically, where neutral grounding is sparse, as it is in many parts of the world. We validate the proposed approach in OpenDSS, by translating a number of published test cases to the reduced form, and observe that the proposed "phase-to-neutral" transformation is highly accurate for the common single-grounded low-voltage network configuration, and provides a high-quality approximation for other configurations. We finally provide numerical results for unbalanced power flow optimization problems using PowerModelsDistribution.jl, to illustrate the computational speed benefits of a factor of about 1.42.

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arXiv2022

Optimal Power Flow in Four-Wire Distribution Networks: Formulation and Benchmarking

In recent years, several applications have been proposed in the context of distribution networks. Many of these can be formulated as an optimal power flow problem, a mathematical optimization program which includes a model of the steady-state physics of the electricity network. If the network loading is balanced and the lines are transposed, the network model can be simplified to a single-phase equivalent model. However, these assumptions do not apply to low-voltage distribution networks, so the network model should model the effects of phase unbalance correctly. In many parts of the world, the low-voltage distribution network has four conductors, i.e. three phases and a neutral. This paper develops OPF formulations for such networks, including transformers, shunts and voltage-dependent loads, in two variable spaces, i.e. current-voltage and power-voltage, and compares them for robustness and scalability. A case study across 128 low-voltage networks also quantifies the modelling error introduced by Kron reductions and its impact on the solve time. This work highlights the advantages of formulations in current-voltage variables over power-voltage, for four-wire networks.

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arXiv2022

Notes on BIM and BFM Optimal Power Flow With Parallel Lines and Total Current Limits

The second-order cone relaxation of the branch flow model (BFM) and bus injection model (BIM) variants of optimal power flow are well-known to be equivalent for radial networks. In this work we show that in meshed networks with parallel lines, BIM dominates BFM, and propose novel constraints to make them equivalent in general. Furthermore, we develop an improvement to the second-order cone relaxations of optimal power flow, adding novel and valid linear constraints on the lifted current expressions. We develop two simple test cases to highlight the advantages of the proposed constraints. These novel constraints tighten the second-order cone relaxation gap on test cases in the `PG Lib' optimal power flow benchmark library, albeit generally in limited fashion.

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arXiv2022

Load Balancing in Low-Voltage Distribution Networks via Optimizing Residential Phase Connections

Unbalance issues in low-voltage distribution networks (LVDN) can be worsened by increasing penetration of residential PV generation if unevenly distributed among three phases. To address this issue, the phase-switching device (PSD) provides a viable and efficient method by dynamically switching customers to other phases. This paper further investigates how to optimize residential phase connections by controlling PSDs efficiently. The optimization problem is formulated as a mixed-integer non-convex programming (MINCP) problem considering relevant operational requirements of an LVDN based on the exact formulation of unbalanced three-phase optimal power flow (UTOPF). Unlike most heuristic algorithms and the linearization techniques in our previous work, this paper proposes to solve the MINCP problem via an iteration-based algorithm after exact reformulations and reasonable approximations of some constraints. The proposed method is tested in a real LVDN and compared with the approach of Zhao et al. based on the well-known linear UTOPF formulation. Case studies based on the European low-voltage test feeder demonstrate the proposed method's efficiency in mitigating the network unbalance while ensuring network security and flexibility to deal with more controllable resources.

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