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Bálint Hartmann

Publications and source records attributed to Bálint Hartmann.

13 recordsLinked to original sources
arXiv2025

Topology and Fragility of European High-Voltage Networks: A Cross-Country Comparative Analysis

Reliable electricity supply depends on the seamless operation of high-voltage grid infrastructure spanning both transmission and sub-transmission levels. Beneath this apparent uniformity lies a striking structural diversity, which leaves a clear imprint on system vulnerability. In this paper, we present harmonized topological models of the high-voltage grids of 15 European countries, integrating all elements at voltage levels above 110 kV. Topological analysis of these networks reveals a simple yet robust pattern: node degree distributions consistently follow an exponential decay, but the rate of decay varies significantly across countries. Through a detailed and systematic evaluation of network tolerance to node and edge removals, we show that the decay rate delineates the boundary between systems that are more resilient to failures and those that are prone to large-scale disruptions. Furthermore, we demonstrate that this numerical boundary is highly sensitive to which layers of the infrastructure are included in the models. To our knowledge, this study provides the first quantitative cross-country comparison of 15 European high-voltage networks, linking topological properties with vulnerability characteristics.

eess.SY↗
arXiv2025

Investigating the emergent invariant properties of Hungarian electric distribution networks

Electric power distribution networks serve as the final and essential stage in power delivery, bridging transmission infrastructure and end users. The structural configuration of these networks plays a critical role in determining system reliability, fault tolerance, and operational efficiency. Although the design of distribution systems is influenced by various regional factors, such as geography, customer density, and planning standards, the extent to which consistent structural characteristics emerge across different networks remains an open question. In this study, we perform a detailed spatial and topological analysis of five MV distribution networks in Hungary. Despite notable differences in geographic layout and consumer distribution, we identify statistically consistent patterns across several key metrics, including degree, BC, and powerline length. These findings suggest the influence of common underlying design principles or optimization constraints, potentially indicating universal structural tendencies in MV network design. The results provide insight into the organization of real-world distribution systems and offer a basis for improved planning, risk mitigation, and system optimization in future grid developments.

physics.soc-ph↗
arXiv2025

Quantitative comparison of power grid reinforcements

This paper presents a quantitative comparison of power grid reinforcement strategies. We evaluate three approaches: (1) doubling transmission links (bridges) between different communities, (2) adding bypasses around weakly synchronized nodes, and (3) reinforcing edges that trigger the largest cascade failures. We use two different models of the Hungarian high-voltage network. These models are built from the official data provided by the transmission system operator, thus eliminating the assumptions typically used in other studies. The coupling strength distribution of the Hungarian models shows good agreement with our previous works using the European and North American grids. Additionally, we examine the occurrence of Braess' paradox, where added transmission capacity unexpectedly reduces overall stability. Our results show that reinforcement through community-based bridge duplication yields the most significant improvements across all parameters. A visual comparison highlights differences between this method and traditional reinforcement approaches. To the authors' knowledge, this is the first attempt to quantitatively compare results of oscillator-based studies with those relying on power system analysis software. Characteristic results of line-cut simulations reveal cascade size distributions with fat-tailed decays for medium coupling strengths, while exponential behavior emerges for small and large couplings. The observed exponents are reminiscent of the continuously changing exponents due to Griffiths effects near a hybrid type of phase transition.

cond-mat.dis-nn↗
arXiv2024

Studying power-grid synchronization with incremental refinement of model heterogeneity

Modeling power-grid systems has got a major importance in present days as transformation to renewable energy sources requires the complete re-design of energy transmission. Renewable energy sources can be located quite far from their consumption points because urban and industrial structures do not follow physical constraints and capabilities. Important examples are the sea coast vs inland divisions in the case of wind power. Ill-constructed high-voltage (HV) power grids can cause catastrophic damages to economies as it was demonstrated in recent history via the emergence of large blackout events. The probability distributions of such events was found to be fat-tailed, exhibiting power-law (PL) tails very often. To understand them, self-organized critical direct current (DC) models have been constructed~\cite{car2} and have been shown to describe well the PL exponents of empirical values. However, many details could not be understood as power-grids work with alternating currents (AC) in which phase differences are the primary causes of the power-flows.

nlin.AO↗
arXiv2024

Uncovering the inherited vulnerability of electric distribution networks

Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between certain structural properties of networks and their vulnerabilities, leading to an inherent weakness. The purpose of present work was twofold: to test the hypotheses already examined on evolving transmission networks and to gain a deeper understanding on the nature of these inherent weaknesses. For this, historical models of a medium-voltage distribution network supply area were reconstructed and analysed. Topological efficiency of the networks was calculated against node and edge removals of different proportions. We found that the tolerance of the evolving grid remained practically unchanged during the examined period, implying that the increase in size is dominantly caused by the connection of geographically and spatially constrained supply areas and not by an evolutionary process. We also show that probability density functions of centrality metrics, typically connected to vulnerability, show only minor variation during the early evolution of the examined distribution network, and in many cases resemble the properties of the modern days.

physics.soc-ph↗
arXiv2023

Improving power-grid systems via topological changes, or how self-organized criticality can help stability

Cascade failures in power grids occur when the failure of one component or subsystem causes a chain reaction of failures in other components or subsystems, ultimately leading to a widespread blackout or outage. Controlling cascade failures on power grids is important for many reasons like economic impact, national security, public safety and even rippled effects like troubling transportation systems. Monitoring the networks on node level has been suggested by many, either controlling all nodes of a network or by subsets. This study identifies sensitive graph elements of the weighted European power-grids (from 2016, 2022) by two different methods. Bridges are determined between communities and "weak" nodes are selected by the lowest local synchronization of the swing equation. In the latter case we add bypasses of the same number as the bridges at weak nodes, and we compare the synchronization, cascade failure behavior by the dynamical improvement with the purely topological changes. The results are also compared if bridges are removed from networks, which results in a case similar to islanding, and with the addition of links at randomly selected places. Bypassing was found to improve synchronization the best, while the average cascade sizes are the lowest with bridge additions. However, for very large or small global couplings these network changes do not help, they seem to be useful near the synchronization transition region, where self-organization drives the power-grid. Thus, we provide a demonstration for the Braess' Paradox on continent-sized power grid simulations and uncover the limitations of this phenomenon. We also determine the cascade size distributions and justify the power-law tails near the transition point on these grids.

physics.soc-ph↗
arXiv2023

Dynamical heterogeneity and universality of power-grids

While weak, tuned asymmetry can improve, strong heterogeneity destroys synchronization in the electric power system. We study the level of heterogeneity, by comparing large high voltage (HV) power-grids of Europe and North America. We provide an analysis of power capacities and loads of various energy sources from the databases and found heavy tailed distributions with similar characteristics. Graph topological measures, community structures also exhibit strong similarities, while the cable admittance distributions can be well fitted with the same power-laws (PL), related to the length distributions. The community detection analysis shows the level of synchronization in different domains of the European HV power grids, by solving a set of swing equations. We provide numerical evidence for frustrated synchronization and Chimera states and point out the relation of topology and level of synchronization in the subsystems. We also provide empirical data analysis of the frequency heterogeneities within the Hungarian HV network and find q-Gaussian distributions related to super-statistics of time-lagged fluctuations, which agree well with former results on the Nordic Grid.

physics.soc-ph↗
arXiv2023

Revisiting and modeling power-law distributions in empirical outage data of power systems

The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has been done by various threshold models, which are self-tuned at their critical points, but as many papers pointed out, explanations are intuitive, and more empirical data is needed to support hypotheses. In this paper, the authors analyze outage data collected from various public sources to calculate the outage energy and outage duration exponents of possible power-law fits. Temporal thresholds are applied to identify crossovers from initial short-time behavior to power-law tails. We revisit and add to the possible explanations of the uniformness of these exponents. By performing power spectral analyses on the outage event time series and the outage duration time series, it is found that, on the one hand, while being overwhelmed by white noise, outage events show traits of self-organized criticality (SOC), which may be modeled by a crossover from random percolation to directed percolation branching process with dissipation, coupled to a conserved density. On the other hand, in responses to outages, the heavy tails in outage duration distributions could be a consequence of the highly optimized tolerance (HOT) mechanism, based on the optimized allocation of maintenance resources.

cond-mat.stat-mech↗
arXiv2022

Synchronization dynamics on the EU and US power grids

Dynamical simulation of the cascade failures on the EU and USA high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter $K$ with metasatble states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large $K$ approximation and by comparing it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values $T$. The PDFs $p(N_f)$ of the cascade failures exhibit PL tails near the synchronization transition point $K_c$. Near $K_c$ the exponents of the PL-s for the US power grid vary with $T$ as $1.4 \le τ\le 2.1$, in agreement with the empirical blackout statistics, while on the EU power grid we find somewhat steeper PL-s characterized by $1.4 \le τ\le 2.4$. Below $K_c$ we find signatures of $T$-dependent PL-s, caused by frustrated synchronization, reminiscent of Griffiths effects. Here we also observe stability growth following the blackout cascades, similar to intentional islanding, but for $K > K_c$ this does not happen. For $T < T_c$, bumps appear in the PDFs with large mean values, known as "dragon king" blackout events. We also analyze the delaying/stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps.

cond-mat.stat-mech↗
arXiv2020

Power-law distributions of dynamic cascade failures in power-grid models

Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous 2D lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D lattice) is not sufficient to find power-law distributed cascades. On the other hand too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution both for the US and Hungarian systems remained insensitive and have kept the universal tails, characterized by the exponent $τ\simeq 1.8$. We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid.

nlin.AO↗
arXiv2018

Heterogeneity effects in power-grid network models

We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to the inertia the synchronization transitions are of first order type, characterized by fast relaxation and hysteresis by varying the global coupling parameter K. Finite size scaling analysis shows that there is no real phase transition in the thermodynamic limit, unlike in the mean-field model. The order parameter and its fluctuations depend on the network size without any real singular behavior. In case of power grids the phase synchronization breaks down at lower global couplings, than in case of 2D lattices of the same sizes, but the hysteresis is much narrower or negligible due to the low connectivity of the graphs. The temporal behavior of de-synchronization avalanches after a sudden quench to low K values, has been followed and duration distributions with power-law tails have been detected. This suggests rare region effects, caused by frozen disorder, resulting in heavy tailed distributions, even without a self organization mechanism as a consequence of a catastrophic drop event in the couplings.

physics.soc-ph↗