arXiv subjects

Andrew Keane

Publications and source records attributed to Andrew Keane.

At least 19 recordsLinked to original sources

arXiv2026

A distributed-delay model for the El Ni\~no Southern Oscillation with a minimum delay: a case study of the shifted linear chain trick

When modelling a system of interest with a delay differential equation, a distributed delay may be the appropriate modelling choice when the delayed response occurs over a significant range of times rather than with a single constant delay. In systems with a minimum physical transit or processing time, however, the delay kernel should respect a fixed and positive minimum delay. A shifted Erlang kernel is a convenient choice, because the shifted linear chain trick allows one to replace the convolution associated with this type of kernel by a finite auxiliary-variable representation with one constant delay. As we demonstrate with a case study of the Ghil-Zaliapin-Thompson (GZT) model of the El Ni\~no Southern Oscillation with seasonal forcing and distributed delayed oceanic feedback, this reduction makes it possible to perform a bifurcation analysis with numerical continuation techniques for any width of the Erlang distribution. Specifically, we present the bifurcation and resonance structure of the distributed-delay GZT model in the plane of forcing strength and delay for different widths of the distribution. To ensure a like-for-like comparison and determine the influence of delay distribution, we present these results in terms of the effective delay and, moreover, rescale the feedback strength to account for its attenuation with increasing width of the distribution.

math.DS↗

arXiv2025

Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors

Artificial Intelligence has advanced significantly in recent years thanks to innovations in the design and training of artificial neural networks (ANNs). Despite these advancements, we still understand relatively little about how elementary forms of ANNs learn, fail to learn, and generate false information without the intent to deceive, a phenomenon known as `confabulation'. To provide some foundational insight, in this paper we analyse how confabulation occurs in reservoir computers (RCs): a dynamical system in the form of an ANN. RCs are particularly useful to study as they are known to confabulate in a well-defined way: when RCs are trained to reconstruct the dynamics of a given attractor, they sometimes construct an attractor that they were not trained to construct, a so-called `untrained attractor' (UA). This paper sheds light on the role played by UAs when reconstruction fails and their influence when modelling transitions between reconstructed attractors. Based on our results, we conclude that UAs are an intrinsic feature of learning systems whose state spaces are bounded, and that this means of confabulation may be present in systems beyond RCs.

math.DS↗

arXiv2025

Modelling hydrogen integration in energy system models: Best practices for policy insights

The rapid emergence of hydrogen in long-term energy strategies requires a broad understanding on how hydrogen is currently modelled in national energy system models. This study provides a review on hydrogen representation within selected energy system models that are tailored towards providing policy insights. The paper adopts a multi-layered review approach and selects eleven notable models for the review. The review covers hydrogen production, storage, transportation, trade, demand, modeling strategies, and hydrogen policies. The review suggests existing models would often opt for a simplified representation that can capture each stage of the hydrogen supply chain. This approach allows models to strike a balance between accuracy and preserving computational resources. The paper provides several suggestions for modeling hydrogen in national energy system models.

physics.soc-ph↗

arXiv2024

Linear energy storage and flexibility model with ramp rate, ramping, deadline and capacity constraints

The power networks are evolving with increased active components such as energy storage and flexibility derived from loads such as electric vehicles, heat pumps, industrial processes, etc. Better models are needed to accurately represent these assets; otherwise, their true capabilities might be over or under-estimated. In this work, we propose a new energy storage and flexibility arbitrage model that accounts for both ramp (power) and capacity (energy) limits, while accurately modelling the ramp rate constraint. The proposed models are linear in structure and efficiently solved using off-the-shelf solvers as a linear programming problem. We also provide an online repository for wider application and benchmarking. Finally, numerical case studies are performed to quantify the sensitivity of ramp rate constraint on the operational goal of profit maximization for energy storage and flexibility. The results are encouraging for assets with a slow ramp rate limit. We observe that for resources with a ramp rate limit of 10% of the maximum ramp limit, the marginal value of performing energy arbitrage using such resources exceeds 65% and up to 90% of the maximum profit compared to the case with no ramp rate limitations.

eess.SY↗

arXiv2024

Mean-field approximation for networks with synchrony-driven adaptive coupling

Synaptic plasticity is a key component of neuronal dynamics, describing the process by which the connections between neurons change in response to experiences. In this study, we extend a network model of $\theta$-neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of $\theta$-neuron oscillators. We investigate two approaches for implementing this plasticity: pairwise coupling strength updates and global coupling strength updates. A mean-field approximation of the system is derived and we investigate its validity through comparison with the $\theta$-neuron simulations across various stability states. The synchrony of the system is examined using the Kuramoto order parameter. A bifurcation analysis, by means of numerical continuation and the calculation of maximal Lyapunov exponents, reveals interesting phenomena, including bistability and evidence of period-doubling and boundary crisis routes to chaos, that would otherwise not exist in the absence of adaptive coupling.

q-bio.NC↗

arXiv2024

Impact of Phase Selection on Accuracy and Scalability in Calculating Distributed Energy Resources Hosting Capacity

Hosting capacity (HC) and dynamic operating envelopes (DOEs), defined as dynamic, time-varying HC, are calculated using three-phase optimal power flow (OPF) formulations. Due to the computational complexity of such optimisation problems, HC and DOE are often calculated by introducing certain assumptions and approximations, including the linearised OPF formulation, which we implement in the Python-based tool ppOPF. Furthermore, we investigate how assumptions of the distributed energy resource (DER) connection phase impact the objective function value and computational time in calculating HC and DOE in distribution networks of different sizes. The results are not unambiguous and show that it is not possible to determine the optimal connection phase without introducing binary variables since, no matter the case study, the highest objective function values are calculated with mixed integer OPF formulations. The difference is especially visible in a real-world low-voltage network in which the difference between different scenarios is up to 14 MW in a single day. However, binary variables make the problem computationally complex and increase computational time to several hours in the DOE calculation, even when the optimality gap different from zero is set.

eess.SY↗

arXiv2023

Solving scalability issues in calculating PV hosting capacity in low voltage distribution networks

The share of end-users with installed rooftop photovoltaic (PV) systems is continuously growing. Since most end-users are located at the low voltage (LV) level and due to technical limitations of LV networks, it is necessary to calculate PV hosting capacity. Most approaches in calculating a network's hosting capacity are based on three-phase optimal power flow (OPF) formulations. Linearized and relaxed three-phase OPF formulations respectively lose their accuracy and exactness when applied to solve the hosting capacity problem, and only non-linear programming (NLP) models guarantee the exact solution. Compared to linearized or relaxed models, NLP models require a higher computational time for finding an optimal solution. The binary variables uplift the problem to mixed-integer (MI)NLP and increase the computational burden. To resolve the scalability issues in calculating the hosting capacity of single-phase connected PVs, we propose a method that does not entail binary variables but still ensures that PVs are not connected to more than one phase at a time. Due to a risk of a sub-optimal solution, the proposed approach is compared to the results obtained by the MINLP formulation. The comparison includes values of the solution time and technical quantities such as network losses, voltage deviations, and voltage unbalance factor.

eess.SY↗

arXiv2023

Bifurcation analysis of a North Atlantic Ocean box model with two deep-water formation sites

The tipping of the Atlantic Meridional Overturning Circulation (AMOC) to a 'shutdown' state due to changes in the freshwater forcing of the ocean is of particular interest and concern due to its widespread ramifications, including a dramatic climatic shift for much of Europe. A clear understanding of how such a shutdown would unfold requires analyses of models from across the complexity spectrum. For example, detailed simulations of sophisticated Earth System Models have identified scenarios in which deep-water formation first ceases in the Labrador Sea before ceasing in the Nordic Seas, en route to a complete circulation shutdown. Here, we study a simple ocean box model with two polar boxes designed to represent deep-water formation at these two distinct sites. A bifurcation analysis reveals how, depending on the differences of freshwater and thermal forcing between the two polar boxes, transitions to 'partial shutdown' states are possible. Our results shed light on the nature of the tipping of AMOC and clarify dynamical features observed in more sophisticated models.

physics.ao-ph↗

arXiv2023

Transitional cluster dynamics in a model for delay-coupled chemical oscillators

Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental set-up controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, additional secondary states, where phase differences differ, are detected. Previous work on this system saw the development of a mathematical model that explains how the existence, stability, and common frequency of the experimentally observed cluster states can be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals a complex interconnectedness between branches of different cluster types; in particular, we find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. Otherwise, for a smaller voltage, all the branches of secondary states are completely unstable and therefore hidden to experimentalists.

math.DS↗

arXiv2022

Pp OPF -- Pandapower Implementation of Three-phase Optimal Power Flow Model

Challenges in the planning and operation of distribution networks caused by the integration of distributed energy resources (DERs) create the need for the development of tools that can be easily used by system operators, industry, and the research society but are also easily upgraded with new functionalities. The full implementation of one such open source tool, named pp OPF (pandapower Optimal Power Flow), is presented in this paper. Pp OPF is the tool used for three-phase optimal power flow (OPF) calculations and it is based on already existing functionalities of pandapower, a Python library for power system calculations. The developed tool enables the possibility to use both power-voltage and current-voltage formulation in different OPF problems, such as determining the photovoltaics (PVs) hosting capacity in three-phase distribution networks, the problem on which the functionality of the developed tool is tested. Additionally, the accuracy of pp OPF is verified by comparing the results with ones obtained by pandapower power flow calculation for the same set of input values. The open-source implementation allows further upgrades, the addition of new functionalities, and the creation of new case studies relevant to the planning and operation of distribution networks.

math.OC↗

arXiv2022

Stabilising millennial oscillations in large-scale ocean circulation with a delayed feedback due to a circumpolar current

The global ocean circulation plays a pivotal role in the regulation of the Earth's climate. The specific pattern and strength of circulation also determines how carbon and nutrients are cycled and via the resulting distribution of dissolved oxygen, where habitats suitable for marine animals occur. However, evidence from both geological data and models suggests that state transitions in circulation patterns have occurred in the past. Understanding the controls on marine environmental conditions and biodiversity requires a full appreciation of the nature and drivers of such transitions. Here we present stable millennial oscillations of meridional overturning circulation in an Earth system model of intermediate complexity, cGENIE, that appear to only occur in the presence of a circumpolar current. To demonstrate that a circumpolar current can act as a driver of stable oscillations, we adapt a simple ocean box model to include a delayed feedback to represent the effect of a circumpolar current on meridional overturning circulation. We investigate the millennial oscillatory solutions that arise in the box model by bifurcation analysis and show that the model can reproduce the same bifurcation structure observed in the Earth system model. Our results provide new insights into the nature of oscillations that could have occurred under certain continental configurations in the geological past, and also highlight the potential influence of the changing Antarctic circumpolar current speed on the stability of the Atlantic meridional overturning circulation.

math.DS↗

arXiv2021

Enhanced Transmission and Distribution NetworkCoordination to Host More Electric Vehicles and PV

Distributed energy resources (DERs) installed at electric distribution networks create different opportunities and challenges for the distribution system operator (DSO). By increasing the penetration level of DERs, the impacts of these technologies are also sensed by the transmission system operator (TSO). The focus of this paper is on investigating and managing the impacts of the Electric Vehicle (EV) charging and solar Photo-Voltaic (PV) generation considering TSO-DSO interaction constraints. These constraints include the driving point impedance that reflects the impact of the DER-rich distribution system on the upstream HV network and voltage profile control through the on-load tap changing (OLTC) transformer's operation. The aim is to optimally utilize the existing assets and flexibilities to have more EVs and PVs at the distribution level without violating constraints at both transmission and distribution levels. The proposed model could readily be used by policymakers to design and implement the proper time-of-use tariffs for improved handling of the increasing EVs and PVs penetrations in emerging distribution networks. The proposed method is implemented on the IEEE 69-bus standard MV distribution network to demonstrate the applicability.

eess.SY↗

arXiv2021

Signatures consistent with multi-frequency tipping in the Atlantic meridional overturning circulation

The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly associated with the disappearance of steady-state or periodic solutions at fold bifurcations. We discuss here multi-frequency tipping (M-tipping), which is tipping due to the disappearance of an attracting torus. M-tipping is a generic phenomenon in systems with at least two intrinsic or external frequencies that can interact and, hence, is relevant to a wide variety of systems of interest. We show that the more complicated sequence of bifurcations involved in M-tipping provides a possible consistent explanation for as yet unexplained behavior observed near tipping in climate models for the Atlantic meridional overturning circulation. More generally, this work provides a path towards identifying possible early-warning signs of tipping in multiple-frequency systems.

math.DS↗

arXiv2020

Resilient Identification of Distribution Network Topology

Network topology identification (TI) is an essential function for distributed energy resources management systems (DERMS) to organize and operate widespread distributed energy resources (DERs). In this paper, discriminant analysis (DA) is deployed to develop a network TI function that relies only on the measurements available to DERMS. The propounded method is able to identify the network switching configuration, as well as the status of protective devices. Following, to improve the TI resiliency against the interruption of communication channels, a quadratic programming optimization approach is proposed to recover the missing signals. By deploying the propounded data recovery approach and Bayes' theorem together, a benchmark is developed afterward to identify anomalous measurements. This benchmark can make the TI function resilient against cyber-attacks. Having a low computational burden, this approach is fast-track and can be applied in real-time applications. Sensitivity analysis is performed to assess the contribution of different measurements and the impact of the system load type and loading level on the performance of the proposed approach.

eess.SY↗

arXiv2020

Technical Barriers for Harnessing the Green Hydrogen: A Power System Perspective

Extracting green hydrogen from renewable energy sources is a new concept in the energy industry. As an energy carrier, hydrogen is well capable of facilitating a strong coupling between various energy sectors, as well as integration of renewable energy sources. This paper investigates the system-wide technical factors that might limit the amount of producible hydrogen in a given power system. A non-linear programming formulation is proposed to quantify the impact of voltage security constraints, the location and size of power to hydrogen facilities, and finally the wind penetration levels on the harvest-able green hydrogen. The applicability of the proposed framework is demonstrated on the IEEE 39 bus system.

eess.SY↗

arXiv2020

Use of fitted polynomials for the decentralized estimation of network variables in unbalanced radial LV feeders

The lack of comprehensive monitoring equipment in low voltage (LV) residential feeders, impedes a near-term deployment of centralized schemes for the integration of domestic-scale distributed generation (DG). In this context, this paper introduces a technique that generates a set of fitted polynomials, derived from offline simulations and regression analysis, that characterise the magnitude of representative network variables (i.e. key for network operation) as a direct analytical expression of the controllable local conditions of any DG unit (i.e. active and reactive power injections). Crucially, the coefficients of these polynomials can be estimated, autonomously at the location of each DG unit, without the need for remote monitoring (i.e. using only locally available measurements). During online implementation, the method consists only of direct calculations (i.e. non-iterative), facilitating real-time operation. The accuracy of the polynomials to estimate the magnitude of the network variables is assessed under multiple scenarios on a representative radial LV feeder. Furthermore, the robustness of the method is demonstrated under the presence of new generation and electric vehicles.

eess.SP↗

arXiv2020

Border-collision bifurcations in a driven time-delay system

We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.

nlin.CD↗

arXiv2020

Strategic Scheduling of Discrete Control Devices in Active Distribution Systems

The frequent actuation of discrete control devices dcds, e.g., on-load tap changers, drastically reduces their lifetime. This, in turn, imposes a huge replacement cost. Simultaneous scheduling of these \textsc{dcd}s and continuous control devices, e.g., distributed energy resources, is imperative for reducing the operating cost. This also increases the lifetime of \textsc{dcd}s and helps to avoid the sub-optimal/infeasible solutions. Considering the high cost of discrete control actions (dcas), they may never be justified against the other options in a short scheduling horizon (sh). With a longer sh, their benefits over a long period justify dcas. However, a shorter \textsc{sh} helps to hedge against the risk impelled by uncertainties. Here, the system's future is modeled as a set of multi-period scenarios. The operator exploits a long sh, but solely applies the decisions made for the first period and waits for updated data to make the next decisions. This enables cost reduction by strategically applying dcas prior to the time that they are inevitable while avoiding them when unneeded. The proposed branch-and-cut-based solution methodology accurately deals with dcas while applying some expediting heuristics. During the branching process, a globally convergent trust-region algorithm solves the integer relaxed problems.

eess.SY↗