Python for Power System Analysis (PyPSA) is a free software toolbox for simulating and optimising modern electrical power systems over multiple periods. PyPSA includes models for conventional generators with unit commitment, variable renewable generation, storage units, coupling to other energy sectors, and mixed alternating and direct current networks. It is designed to be easily extensible and to scale well with large networks and long time series. In this paper the basic functionality of PyPSA is described, including the formulation of the full power flow equations and the multi-period optimisation of operation and investment with linear power flow equations. PyPSA is positioned in the existing free software landscape as a bridge between traditional power flow analysis tools for steady-state analysis and full multi-period energy system models. The functionality is demonstrated on two open datasets of the transmission system in Germany (based on SciGRID) and Europe (based on GridKit).

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 timeseries 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. challenges for the efficient design and regulation of electricity markets; the need to decarbonise heating and transport is driving electrification of these sectors; and finally energy markets are being integrated across the continent [1].To study this transformation, accurate modelling of the transmission grid is required. The need to take account of international electricity trading and the possibility of smoothing variable renewable feed-in over large distances (wind generation has a typical correlation length of around 600 km [2]) mean that models should have a continental scope. At the same time, high spatial detail is required, since national grid bottlenecks are already hindering the uptake of renewable energy today [3], and given persistent public acceptance problems facing new transmission projects [4], severe grid bottlenecks will remain a feature of the energy system for decades to come.Currently there is no openly-available model of the full European transmission network with which researchers can investigate and compare different approaches to the energy transformation. The transmission grid dataset provided by the European Network of Transmission System Operators for Electricity (ENTSO-E) for the 2016 Ten Year Network Development Plan (TYNDP) [5] is rendered unusable by restrictive licensing, the exclusion of Finland, Norway and Sweden, and a lack of geographic...

Abstract-The effects of the spatial scale on the results of the optimisation of transmission and generation capacity in Europe are quantified under a 95% CO2 reduction compared to 1990 levels, interpolating between one-node-per-country solutions and many-nodes-per-country. The trade-offs that come with higher spatial detail between better exposure of transmission bottlenecks, exploitation of sites with good renewable resources (particularly wind power) and computational limitations are discussed. It is shown that solutions with no grid expansion beyond today's capacities are only around 20% more expensive than with cost-optimal grid expansion.

In the last decades, energy modelling has supported energy planning by offering insights into the dynamics between energy access, resource use, and sustainable development. Especially in recent years, there has been an attempt to strengthen the science-policy interface and increase the involvement of society in energy planning processes. This has, both in the EU and worldwide, led to the development of open-source and transparent energy modelling practices. This paper describes the role of an open-source energy modelling tool in the energy planning process and highlights its importance for society. Specifically, it describes the existence and characteristics of the relationship between developing an open-source, freely available tool and its application, dissemination and use for policy making. Using the example of the Open Source energy Modelling System (OSeMOSYS), this work focuses on practices that were established within the community and that made the framework's development and application both relevant and scientifically grounded.

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe a new formulation that expresses the loading constraints directly in terms of the flows themselves, using a decomposition of the network graph into a spanning tree and closed cycles. We provide a comprehensive study of the computational performance of the various formulations, in settings that include computationally challenging applications such as multi-period LOPF with storage dispatch and generation capacity expansion. We show that the new formulation of the LOPF solves up to 7 times faster than the angle formulation using a commercial linear programming solver, while another existing cycle-based formulation solves up to 20 times faster, with an average speed-up of factor 3 for the standard networks considered here. If generation capacities are also optimized, the average speed-up rises to a factor of 12, reaching up to factor 213 in a particular instance. The speed-up is largest for networks with many buses and decentral generators throughout the network, which is highly relevant given the rise of distributed renewable generation and the computational challenge of operation and planning in such networks.

A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is presented, a new formula for the computation of Line Outage Distribution Factors (LODFs) is derived, which is not only computationally faster than existing methods, but also generalizes easily for multiple line outages and arbitrary changes to line series reactance. In addition, the dual formalism provides new physical insight for how the effects of line outages propagate through the network. For example, in a planar network a single line outage can be shown to induce monotonically decreasing flow changes, which are mathematically equivalent to an electrostatic dipole field.

Renewable energy sources are likely to build the backbone of the future global energy system. One important key to a successful energy transition is to analyse the weather-dependent energy outputs of existing and eligible renewable resources. atlite is an open Python software package for retrieving global historical weather data and converting it to power generation potentials and time series for renewable energy technologies like wind turbines or solar photovoltaic panels based on detailed mathematical models. It further provides weather-dependent output on the demand side like building heating demand and heat pump performance. The software is optimized to aggregate data over multiple large regions with user-defined weightings based on land use or energy yield. Statement of needDeriving weather-based time series and maximum capacity potentials for renewables over large regions is a common problem in energy system modelling. Websites with exposed open APIs such as renewables.ninja ) exist for such purpose but are difficult to use for local execution, e.g. in cluster environments, and restricted to non-commercial use. Further, by design, they neither expose the underlying datasets nor methods for deriving time series, here referred to as conversion functions/methods. This makes them unsuited for utilizing different weather datasets or exploring alternative conversion functions. The pvlib (Holmgren et al., 2018) is suited for local execution and allows interchangeable input data but is specialized to PV systems only and intended for single location modelling. Other packages like the Danish REatlas (Andresen et al., 2015) face obstacles with accessibility, are based on proprietary code, miss documentation and are restricted in flexibility regarding their inputs.

The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This article presents a reformulation that is applicable to arbitrary compositions of inflow appearing naturally in models of large-scale electricity systems with a high share of renewable power generation. We propose an application which allows to associate power flows on the grid to specific regions or generation technologies, and emphasizes the capability of this technique to disentangle the spatio-temporal patterns of physical imports and exports occurring in such systems. The analytical potential of this method is showcased for a scenario based on the IEEE 118 bus network.