Jonas Hörsch

PyPSA: Python for Power System Analysis

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).

The role of spatial scale in joint optimisations of generation and transmission for European highly renewable scenarios

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 todays capacities are only around 20% more expensive than with cost-optimal grid expansion.

Dual Theory of Transmission Line Outages

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 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.

Power Flow Tracing in Complex Networks

The increasing share of decentralized renewable power generation represents a challenge to the current and future energy system. Providing a geographical smoothing effect, long-range power transmission plays a key role for the system integration of these fluctuating resources. However, the build-up and operation of the necessary network infrastructure incur costs which have to be allocated to the users of the system. Flow tracing techniques, which attribute the power flow on a transmission line to the geographical location of its generation and consumption, represent a valuable tool set to design fair usage and thus cost allocation schemes for transmission investments. In this article, we introduce a general formulation of the flow tracing method and apply it to a simplified model of a highly renewable European electricity system. We review a statistical usage measure which allows to integrate network usage information for longer time series, and illustrate this measure using an analytical test case.

Linear optimal power flow using cycle flows

Abstract 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-base 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.

Flow tracing as a tool set for the analysis of networked large-scale renewable electricity systems

Abstract 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.

Flow-based nodal cost allocation in a heterogeneous highly renewable European electricity network

Abstract For a cost efficient design of a future renewable European electricity system, the placement of renewable generation capacity will seek to exploit locations with good resource quality, that is for instance onshore wind in countries bordering the North Sea and solar PV in South European countries. Regions with less favorable renewable generation conditions benefit from this remote capacity by importing the respective electricity as power flows through the transmission grid. The resulting intricate pattern of imports and exports represents a challenge for the analysis of system costs on the level of individual countries. Using a tracing technique, we introduce flow-based nodal levelized costs of electricity (LCOE) which allow to incorporate capital and operational costs associated with the usage of generation capacity located outside the respective country under consideration. This concept and a complementary allocation of transmission infrastructure costs is applied to a simplified model of an interconnected highly renewable European electricity system. We observe that cooperation between the European countries in a heterogeneous system layout does not only reduce the system-wide LCOE, but also the flow-based nodal LCOEs for every country individually.

PyPSA-Eur: An open optimisation model 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.

Integrating balancing reserves and congestion management to re-balance the German system

The current electricity market is facing new challenges as the sector moves towards a low-carbon energy system. Germanys power system is currently moving to a regional concentration of electricity supply and demand, which increases network congestion. In order to solve possible contingencies, reserve requirements are used to ensure that enough energy is available to re-balance the system. However, this measure might not be reliable in congested systems. To that extent, zones are used to address inter-zonal congestion, but intra-zonal congestion is still a problem that lacks efficient ways to solve it. We focus on quantifying the benefit of managing intra-zonal congestion using tertiary reserve capacities and of additionally splitting the reserve market into zones. The results show that the combination of balancing and congestion market is the most efficient solution since it decreases the total reserve demand quantities needed to solve possible contingencies.