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Hydrogen and carbon dioxide transport can both play an essential role in climate-neutral energy systems. Hydrogen networks help serve regions with high energy demand, while excess emissions are transported away in carbon dioxide networks. For the synthesis of carbonaceous fuels, it is less clear which input should be transported: hydrogen to carbon point sources or carbon to low-cost hydrogen. We explore both networks' potential synergies and competition in a cost-optimal carbon-neutral European energy system. In a direct comparison, a hydrogen network is more cost-effective than a carbon network, as it serves to transport hydrogen to demand and to point source of carbon for utilization. However, in a hybrid scenario where both networks are present, the carbon network effectively complements the hydrogen network, promoting carbon capture from distributed biomass and reducing reliance on direct air capture. The layouts of the hydrogen and carbon dioxide networks are robust if the climate target is tightened to be net-negative.

In wind- and solar-dominated energy systems it has been assumed that there are synergies between producing electricity and electrolytic hydrogen since electrolysis can use excess electricity that would otherwise be curtailed. However, it remains unclear whether these synergies hold true at higher levels of hydrogen demand and how they compare with benefits of off-grid, islanded hydrogen production, such as better renewable resources and cost savings on electronics due to relaxed power quality standards. Using a mathematical model across two geographical locations for Germany, Spain, Australia, and Great Britain, we explore trade-offs and synergies between integrated and islanded electrolysers. Below a certain threshold, between 5% and 40% hydrogen share depending on the country, integrated electrolysers offer synergies in flexibility and reduced curtailment. Above these thresholds, islanded electrolysers become more favourable. Without cost advantages, systems including islanded electrolysers in Germany achieve up to 21% lower hydrogen costs than systems with only integrated electrolysers. With 25% island cost advantage, this benefit rises to 40% lower hydrogen costs. Our study identifies three investment regimes with country-specific transition points that vary based on island cost advantages and each country's renewable resources. Based on our results we provide guidelines for countries considering how to deploy electrolysers.

The integration of large shares of wind and solar power into the power system benefits from transmission network expansion. However, the construction of new power lines requires long planning phases and is often delayed by citizen protests. As a non-invasive alternative, Dynamic Line Rating (DLR) offers the potential to leverage the existing grid by dynamically adjusting the transmission line capacities to the prevailing weather conditions. In this study, we present the first investment model that includes DLR in a large-scale power system with real-world network data and a high temporal resolution. Using Germany as an example, we show that a system-wide integration of DLR improves the integration of existing and additional renewables while reducing grid congestion. The evolving synergies between DLR and increased wind generation result in total cost savings of about 3% of all system costs for a scenario with 80% renewable power production, mainly due to reduced storage and solar capacity needs. If considering a fully decarbonized electricity system, the cost savings from DLR amount to up to 5.5% of the system costs, i.e. 4 billion Euro per year. Our results underscore the importance of a rapid implementation of DLR in power systems to support the energy transition and relieve grid congestion., Comment: arXiv admin note: text overlap with arXiv:2208.04716

The German government recently announced that 80\% of the power supply should come from renewable energy by 2030. One key task lies in reorganizing the transmission system such that power can be transported from sites with good renewable potentials to the load centers. Dynamic Line Rating (DLR), which allows the dynamic calculation of transmission line capacities based on prevailing weather conditions rather than conservative invariant ratings, offers the potential to exploit existing grid capacities better. In this paper, we analyze the effect of DLR on behalf of a detailed power system model of Germany including all of today's extra high voltage transmission lines and substations. The evolving synergies between DLR and an increased wind power generation lead to savings of around 400 million euro per year in the short term and 900 million per year in a scenario for 2030., Comment: 6 pages, 6 figures

Optimizing the total cost of power systems is a common tool for network operation and planning. Besides valuable information about how to run and possibly expand a power system, the optimization provides an optimal Locational Marginal Price per node and time step. This price can be seen as the price of electricity paid by consumers and purchased by suppliers, while maximizing social welfare. Naturally, it is a direct result of the optimization problem, and therefore does not give any information about its internal composition. This paper shows that by applying Flow Tracing, an algorithm for tracking flows in complex networks, it is possible to interlink Locational Marginal Prices in a coherent mathematical way. This does not only lead to important insights into the price structure, but also provides an intuitive decomposition and allocation of all system costs. Then individual consumers see how much they have to pay to individual generators and transmission lines in the power system. This method, introduced as Price Tracing, outperforms similar approaches provided by the literature, since the resulting cost allocations are transparent, plausible, and consistent with the Locational Marginal Prices from the optimization. The Price Tracing method is applied and discussed on behalf of a power system model of Germany with a high share of renewable power. The presented analysis and its implications can help in finding a more efficient market design to promote renewable power supply., Comment: This paper is refactored, more comprehensive and extended version of arXiv:2010.13607

Global warming is one of the main threats to the future of humanity and extensive emissions of greenhouse gases are found to be the main cause of global temperature rise as well as climate change. During the last decades international attention has focused on this issue, as well as on searching for viable solutions to mitigate global warming. In this context, the pricing of greenhouse gas emissions turned out to be the most prominent mechanism: First, to lower the emissions, and second, to capture their external costs. By now, various carbon dioxide taxes have been adopted by several countries in Europe and around the world; moreover, the list of these countries is growing. However, there is no standardized approach and the price for carbon varies significantly from one country to another. Regionally diversified carbon prices in turn lead to carbon leakage, which will offset the climate protection goals. In this paper, a simplified European power system with flexible carbon prices regarding the Gross Domestic Product (GDP) is investigated. A distribution parameter that quantifies carbon leakage is defined and varied together with the base carbon price, where the combination of both parameters describes the spatially resolved price distribution, i.e. the effective carbon pricing among the European regions. It is shown that inhomogeneous carbon prices will indeed lead to significant carbon leakage across the continent, and that coal-fired electricity generation will remain a cheap and therefore major source of power in Eastern and South-Eastern Europe - representing a potential risk for the long term decarbonization targets within the European Union., Comment: 19 pages, 10 figures

Power system models are a valuable and widely used tool to determine cost-minimal future operation and investment under political or ecological boundary conditions. Yet they are silent about the allocation of costs of single assets, as generators or transmission lines, to consumers in the network. Existing cost-allocation methods hardly suit large networks and do not take all relevant costs into account. This paper bridges this gap. Based on flow tracing, it introduces a peer-to-peer or more precisely an asset-to-consumer allocation of all costs in an optimized power system. The resulting cost allocation is both locally constrained and aligned with locational marginal prices in the optimum. The approach is applied and discussed using a future German scenario., Comment: 12 pages (+8 pages appendix), 18 figures

We develop novel quantitative techno-economic evaluation criteria for power flow allocation schemes. Such schemes assign which nodes are responsible for which proportion of power flows on a line in a meshed electricity transmission network. As this allocation is, as such, indeterminate, the literature has proposed a number of dedicated schemes. To better understand the implications of applying different schemes, our criteria comprise their (i) fairness, (ii) plausibility, (iii) uniqueness, and (iv) stability. We apply, illustrate, and discuss these criteria for four prominent schemes based on results of a detailed electricity sector model with linear power flow for a German mid-term future case., Comment: 22 pages, 9 figures

Carbon prices are one of the most prominent methods to reduce global greenhouse gas emissions and have been adopted by several countries around the world. However, regionally different carbon prices can lead to carbon leakage. We investigate a simplified European power system where carbon prices are varied with respect to GDP per capita and find that inhomogeneous carbon prices lead to significant carbon leakage due to coal-fired generation remaining a major source of power in Eastern Europe., Comment: 6 pages, 11 figures

The interconnected European Electricity Markets see considerable cross-border trade between different countries. In conjunction with the structure and technical characteristics of the power grid and its operating rules, the corresponding commercial flows translate into actual physical flows on the interconnection lines. From the interplay of different physical, technical, and economic factors thus emerge complex spatiotemporal power flow patterns. Using Principal Component Analysis, in this contribution hourly time-series of cross-border physical flows between European countries in 2017 and 2018 are analyzed. The most important patterns in the time series of imports/exports and cross-border physical flows are identified. Their spatial and temporal structure, as well as their contribution to the overall variance is described. Additionally, we apply a tracing technique to the overall flow patterns, which allows identifying the physical power transfers between European countries through the common grid infrastructure., Comment: Accepted conference proceedings paper for the EEM 2019

In energy modelling, open data and open source code can help enhance traceability and reproducibility of model exercises which contribute to facilitate controversial debates and improve policy advice. While the availability of open power plant databases increased in recent years, they often differ considerably from each other and their data quality has not been systematically compared to proprietary sources yet. Here, we introduce the python-based "powerplantmatching" (PPM), an open source toolset for cleaning, standardizing and combining multiple power plant databases. We apply it once only with open databases and once with an additional proprietary database in order to discuss and elaborate the issue of data quality, by analysing capacities, countries, fuel types, geographic coordinates and commissioning years for conventional power plants. We find that a derived dataset purely based on open data is not yet on a par with one in which a proprietary database has been added to the matching, even though the statistical values for capacity matched to a large degree with both datasets. When commissioning years are needed for modelling purposes in the final dataset, the proprietary database helps crucially to increase the quality of the derived dataset.

Using Principal Component Analysis (PCA), the nodal injection and line flow patterns in a network model of a future highly renewable European electricity system are investigated. It is shown that the number of principal components needed to describe 95$\%$ of the nodal power injection variance first increases with the spatial resolution of the system representation. The number of relevant components then saturates at around 76 components for network sizes larger than 512 nodes, which can be related to the correlation length of wind patterns over Europe. Remarkably, the application of PCA to the transmission line power flow statistics shows that irrespective of the spatial scale of the system representation a very low number of only 8 principal flow patterns is sufficient to capture 95$\%$ of the corresponding spatio-temporal variance. This result can be theoretically explained by a particular alignment of some principal injection patterns with topological patterns inherent to the network structure of the European transmission system.

PyPSA-Eur, the first open model dataset of the European power system at the transmission network level to cover the full ENTSO-E area, is presented. It contains 6001 lines (alternating current lines at and above 220 kV voltage level and all high voltage direct current lines), 3657 substations, a new open database of conventional power plants, time series for electrical demand and variable renewable generator availability, and geographic potentials for the expansion of wind and solar power. The model is suitable both for operational studies and generation and transmission expansion planning studies. The continental scope and highly resolved spatial scale enables a proper description of the long-range smoothing effects for renewable power generation and their varying resource availability. The restriction to freely available and open data encourages the open exchange of model data developments and eases the comparison of model results. A further novelty of the dataset is the publication of the full, automated software pipeline to assemble the load-flow-ready model from the original datasets, which enables easy replacement and improvement of the individual parts. This paper focuses on the description of the network topology, the compilation of a European power plant database and a top-down load time-series regionalisation. It summarises the derivation of renewable wind and solar availability time-series from re-analysis weather datasets and the estimation of renewable capacity potentials restricted by land-use. Finally, validations of the dataset are presented, including a new methodology to compare geo-referenced network datasets to one another., Comment: 20 pages, 6 figures, 5 tables

We revisit the problem of predicting the spin magnitude and direction of the black hole resulting from the merger of two black holes with arbitrary masses and spins inspiralling in quasi-circular orbits. We do this by analyzing a catalog of 619 recent numerical-relativity simulations collected from the literature and spanning a large variety of initial conditions. By combining information from the post-Newtonian approximation, the extreme mass-ratio limit and perturbative calculations, we improve our previously proposed phenomenological formulae for the final remnant spin. In contrast with alternative suggestions in the literature, and in analogy with our previous expressions, the new formula is a simple algebraic function of the initial system parameters and is not restricted to binaries with spins aligned/anti-aligned with the orbital angular momentum, but can be employed for fully generic binaries. The accuracy of the new expression is significantly improved, especially for almost extremal progenitor spins and for small mass ratios, yielding a root-mean-square error $\sigma\approx0.002$ for aligned/anti-aligned binaries and $\sigma\approx0.006$ for generic binaries. Our new formula is suitable for cosmological applications and can be employed robustly in the analysis of the gravitational waveforms from advanced interferometric detectors., Comment: 6 pages, 3 figures. Matches ApJL accepted version. Coefficients $\epsilon_\alpha$, $\epsilon_\beta$ and $\epsilon_\gamma$ slightly changed to reflect dataset filtered of imprecise NR data; contains comparison with newly published NR catalog