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Fabian Hofmann
Frankfurt Institute for Advanced Studies (FIAS), Goethe University, 60438 Frankfurt, Germany

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Journal article
Published: 24 June 2021 in Journal of Open Source Software
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ACS Style

Fabian Hofmann; Johannes Hampp; Fabian Neumann; Tom Brown; Jonas Hörsch. atlite: A Lightweight Python Package for Calculating Renewable Power Potentials and Time Series. Journal of Open Source Software 2021, 6, 3294 .

AMA Style

Fabian Hofmann, Johannes Hampp, Fabian Neumann, Tom Brown, Jonas Hörsch. atlite: A Lightweight Python Package for Calculating Renewable Power Potentials and Time Series. Journal of Open Source Software. 2021; 6 (62):3294.

Chicago/Turabian Style

Fabian Hofmann; Johannes Hampp; Fabian Neumann; Tom Brown; Jonas Hörsch. 2021. "atlite: A Lightweight Python Package for Calculating Renewable Power Potentials and Time Series." Journal of Open Source Software 6, no. 62: 3294.

Journal article
Published: 06 March 2020 in Energies
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In power systems, flow allocation (FA) methods enable to allocate the usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator-specific or producer-specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBEs), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDFs). Despite their intuitive and computationally efficient concepts, they are restricted to networks with passive transmission elements only. As soon as a significant number of controllable transmission elements, such as high-voltage direct current (HVDC) lines, operate in the system, they lose their applicability. This work reformulates the two methods in terms of Virtual Injection Patterns (VIPs), which allows one to efficiently introduce a shift parameter q to tune contributions of net sources and net sinks in the network. In this work, major properties and differences in the methods are pointed out, and it is shown how the MP and EBE algorithms can be applied to generic meshed AC-DC electricity grids: by introducing a pseudo-impedance ω¯, which reflects the operational state of controllable elements and allows one to extend the PTDF matrix under the assumption of knowing the current flow in the system. Basic properties from graph theory are used to solve for the pseudo-impedance in dependence of the position within the network. This directly enables, e.g., HVDC lines to be considered in the MP and EBE algorithms. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of 181 nodes and an 18% transmission expansion compared to today’s total transmission capacity volume. The allocations of MP and EBE show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion, a method of distributing operational and capital expenditures is proposed. In addition, it is shown how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.

ACS Style

Fabian Hofmann; Markus Schlott; Alexander Kies; Horst Stöcker. Flow Allocation in Meshed AC-DC Electricity Grids. Energies 2020, 13, 1233 .

AMA Style

Fabian Hofmann, Markus Schlott, Alexander Kies, Horst Stöcker. Flow Allocation in Meshed AC-DC Electricity Grids. Energies. 2020; 13 (5):1233.

Chicago/Turabian Style

Fabian Hofmann; Markus Schlott; Alexander Kies; Horst Stöcker. 2020. "Flow Allocation in Meshed AC-DC Electricity Grids." Energies 13, no. 5: 1233.

Preprint
Published: 29 January 2020
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In power systems, flow allocation (FA) methods allow to allocate usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator specific or producer specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBE), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDF). Despite their intuitive and computationally efficient concept, they are restricted to networks with \emph{passive} transmission elements only. As soon as a significant number of \emph{controllable} transmission elements, such as High-voltage direct current (HVDC) lines, operate in the system, they loose their applicability. This work reformulates the two methods in terms of Virtual Injection Patters (VIP) which allows to efficiently introduce a shift parameter $q$, tuning contributions of net sources and net sinks in the network. Major properties and differences of the methods are pointed out. Finally, it is shown how the MA and EBE algorithm can be applied to generic meshed AC-DC electricity grids: Introducing a \emph{pseudo-impedance} which reflects the operational state of controllable elements, allows to extend the PTDF matrix under the assumption of knowing the current system's flow. Basic properties from graph theory are used for solving the pseudo-impedance dependent on the position in the network. This directly enables \emph{e.g.} HVDC lines to be considered in the MP and EBE algorithm. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of N=181 and an 18\% transmission expansion. The allocations of VIP and MP, show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion a method of distributing operational and capital expenditures is proposed. Further it is shown, how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.

ACS Style

Fabian Hofmann; Markus Schlott; Alexander Kies; Horst Stöcker. Flow Allocation in Meshed AC-DC Electricity Grids. 2020, 1 .

AMA Style

Fabian Hofmann, Markus Schlott, Alexander Kies, Horst Stöcker. Flow Allocation in Meshed AC-DC Electricity Grids. . 2020; ():1.

Chicago/Turabian Style

Fabian Hofmann; Markus Schlott; Alexander Kies; Horst Stöcker. 2020. "Flow Allocation in Meshed AC-DC Electricity Grids." , no. : 1.

Preprint
Published: 05 December 2019
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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.

ACS Style

Markus Schlott; Fabian Hofmann; Changlong Wang; R. O. Gomes; Alexander Kies. The effect of inhomogeneous carbon prices on the cost-optimal design of a simplified European power system. 2019, 1 .

AMA Style

Markus Schlott, Fabian Hofmann, Changlong Wang, R. O. Gomes, Alexander Kies. The effect of inhomogeneous carbon prices on the cost-optimal design of a simplified European power system. . 2019; ():1.

Chicago/Turabian Style

Markus Schlott; Fabian Hofmann; Changlong Wang; R. O. Gomes; Alexander Kies. 2019. "The effect of inhomogeneous carbon prices on the cost-optimal design of a simplified European power system." , no. : 1.

Journal article
Published: 01 July 2016 in The Astrophysical Journal
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We revisit the problem of predicting the spin magnitude and direction of the black hole (BH) resulting from the merger of two BHs with arbitrary masses and spins inspiraling 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 an rms error σ ≈ 0.002 for aligned/anti-aligned binaries and σ ≈ 0.006 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.

ACS Style

Fabian Hofmann; Enrico Barausse; Luciano Rezzolla. THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS. The Astrophysical Journal 2016, 825, L19 .

AMA Style

Fabian Hofmann, Enrico Barausse, Luciano Rezzolla. THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS. The Astrophysical Journal. 2016; 825 (2):L19.

Chicago/Turabian Style

Fabian Hofmann; Enrico Barausse; Luciano Rezzolla. 2016. "THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS." The Astrophysical Journal 825, no. 2: L19.