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).Comment: 10 pages, 5 figures; version 2 includes table comparison with other software; version 3 is the final accepted journal versio

For a given carbon budget over several decades, different transformation rates for the energy system yield starkly different results. Here we consider a budget of 33 GtCO₂ for the cumulative carbon dioxide emissions from the European electricity, heating, and transport sectors between 2020 and 2050, which represents Europe’s contribution to the Paris Agreement. We have found that following an early and steady path in which emissions are strongly reduced in the first decade is more cost-effective than following a late and rapid path in which low initial reduction targets quickly deplete the carbon budget and require a sharp reduction later. We show that solar photovoltaic, onshore and offshore wind can become the cornerstone of a fully decarbonised energy system and that installation rates similar to historical maxima are required to achieve timely decarbonisation. Key to those results is a proper representation of existing balancing strategies through an open, hourly-resolved, networked model of the sector-coupled European energy system.