arXiv subjects

Tom Brown

Publications and source records attributed to Tom Brown.

At least 73 records · Page 4Linked to original sources

arXiv2020

Modeling Curtailment in Germany: How Spatial Resolution Impacts Line Congestion

This paper investigates the effects of network constraints in energy system models at transmission level on renewable energy generation and curtailment as the network is being spatially aggregated. We seek to reproduce historically measured curtailment in Germany for the years 2013-2018 using an open model of the transmission system, PyPSA-Eur. Our simulations include spatial and temporal considerations, including congestion per line as well as curtailment per control zone and quarter. Results indicate that curtailment at high network resolution is significantly overestimated due to inaccurate allocation of electricity demand and renewable capacities to overloaded sites. However, high congestion rates of the transmission network decrease as the network is clustered to a smaller number of nodes, thus reducing curtailment. A measure to capture errors in the assignment of electricity demand and power plants is defined and hints towards a preferable spatial resolution. Thus, we are able to balance the effects of accurate node assignment and network congestion revealing that a reduced model can capture curtailment from recent historical data. This shows that it is possible to reduce the network to improve computation times and capture the most important effects of network constraints on variable renewable energy feed-in at the same time.

physics.soc-ph↗

arXiv2020

Approximating Power Flow and Transmission Losses in Coordinated Capacity Expansion Problems

With rising shares of renewables and the need to properly assess trade-offs between transmission, storage and sectoral integration as balancing options, building a bridge between energy system models and detailed power flow studies becomes increasingly important, but is computationally challenging. W compare approximations for two nonlinear phenomena, power flow and transmission losses, in linear capacity expansion problems that co-optimise investments in generation, storage and transmission infrastructure. We evaluate different flow representations discussing differences in investment decisions, nodal prices, the deviation of optimised flows and losses from simulated AC power flows, and the computational performance. By using the open European power system model PyPSA-Eur we obtain detailed and reproducible results aiming at facilitating the selection of a suitable power flow model. Given the differences in complexity, the optimal choice depends on the application, the user's available computational resources, and the level of spatial detail considered. Although the commonly used transport model can already identify key features of a cost-efficient system while being computationally performant, deficiencies under high loading conditions arise due to the lack of a physical grid representation. Moreover, disregarding transmission losses overestimates optimal grid expansion by 20%. Adding a convex relaxation of quadratic losses with two or three tangents to the linearised power flow equations and accounting for changing line impedances as the network is reinforced suffices to represent power flows and losses adequately in design studies. We show that the obtained investment and dispatch decisions are then sufficiently physical to be used in more detailed nonlinear simulations of AC power flow in order to better assess their technical feasibility.

physics.soc-ph↗

arXiv2020

Transmission Expansion Planning Using Cycle Flows

The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as introducing a large number of auxiliary variables, the angle-based formulation has the disadvantage that it is not well-suited to considering the connection of multiple disconnected networks, It is, however, possible to circumvent these auxiliary variables and reduce the required number of constraints by expressing Kirchhoff's voltage law directly in terms of the power flows, based on a cycle decomposition of the network graph. In computationally challenging benchmarks such as generation capacity expansion with multi-period LOPF, this equivalent reformulation was shown in previous work to reduce solving times for LOPF problems by an order of magnitude. Allowing line capacity to be co-optimized in a discrete TEP problem makes it a non-convex mixed-integer problem. This paper develops a novel cycle-based reformulation for the TEP problem with LOPF and compares it to the standard angle-based formulation. The combinatorics of the connection of multiple disconnected networks is formalized for both formulations, a topic which has not received attention in the literature. The cycle-based formulation is shown to conveniently accommodate synchronization options. Since both formulations use the big-$M$ disjunctive relaxation, useful derivations for suitable big-$M$ values are provided. The competing formulations are benchmarked on a realistic generation and transmission expansion model of the European transmission system at varying spatial and temporal resolutions. The cycle-based formulation solves up to 31 times faster for particular cases, while averaging at a speed-up of factor 4.

eess.SY↗

arXiv2020

The Near-Optimal Feasible Space of a Renewable Power System Model

Models for long-term investment planning of the power system typically return a single optimal solution per set of cost assumptions. However, typically there are many near-optimal alternatives that stand out due to other attractive properties like social acceptance. Understanding features that persist across many cost-efficient alternatives enhances policy advice and acknowledges structural model uncertainties. We apply the modeling-to-generate-alternatives (MGA) methodology to systematically explore the near-optimal feasible space of a completely renewable European electricity system model. While accounting for complex spatio-temporal patterns, we allow simultaneous capacity expansion of generation, storage and transmission infrastructure subject to linearized multi-period optimal power flow. Many similarly costly, but technologically diverse solutions exist. Already a cost deviation of 0.5% offers a large range of possible investments. However, either offshore or onshore wind energy along with some hydrogen storage and transmission network reinforcement are essential to keep costs within 10% of the optimum.

physics.soc-ph↗

arXiv2019

The role of photovoltaics in a sustainable European energy system under variable CO2 emissions targets, transmission capacities, and costs assumptions

PyPSA-Eur-Sec-30 is an open-source, hourly-resolved, networked model of the European energy system which includes one node per country as well as electricity, heating, and transport sectors. The capacity and dispatch of generation and storage technologies in every country can be cost-optimised under different CO2 emissions constraints. This paper presents an overview of the most relevant results previously obtained with the model, highlighting the influence of solar photovoltaic (PV) generation on them. For 95% CO2 emissions reduction, relative to 1990 level, PV generation supplies in average 33% of the electricity demand. Southern European countries install large PV capacities together with electric batteries, while northern countries install onshore and offshore wind capacities and use hydrogen storage and reinforced interconnections to deal with wind fluctuations. The strong daily generation profile of solar PV heavily impacts the dispatch time series of backup generation and storage technologies. The optimal PV and wind capacities are investigated for variable CO2 emissions, transmission interconnection among neighbouring countries, and cost assumptions.

physics.soc-ph↗

arXiv2019

The role of storage technologies throughout the decarbonisation of the sector-coupled European energy system

We use an open, hourly-resolved, networked model of the European energy system to investigate the storage requirements under decreasing CO$_2$ emissions targets and several sector-coupling scenarios. For the power system, significant storage capacities only emerge for CO$_2$ reductions higher than 80% of 1990 level in that sector. For 95% CO$_2$ reductions, the optimal system includes electric batteries and hydrogen storage energy capacities equivalent to 1.4 and 19.4 times the average hourly electricity demand. Coupling heating and transport sectors enables deeper global CO$_2$ reductions before the required storage capacities become significant, which highlights the importance of sector coupling strategies in the transition to low carbon energy systems. A binary selection of storage technologies is consistently found, i.e., electric batteries act as short-term storage to counterbalance solar photovoltaic generation while hydrogen storage smooths wind fluctuations. Flexibility from the electric vehicle batteries provided by coupling the transport sector avoid the need for additional stationary batteries and reduce the usage of pumped hydro storage. Coupling the heating sector brings to the system large capacities of thermal energy storage to compensate for the significant seasonal variation in heating demand.

physics.soc-ph↗

arXiv2019

Heuristics for Transmission Expansion Planning in Low-Carbon Energy System Models

Governments across the world are planning to increase the share of renewables in their energy systems. The siting of new wind and solar power plants requires close coordination with grid planning, and hence co-optimization of investment in generation and transmission expansion in spatially and temporally resolved models is an indispensable but complex problem. Particularly considerations of transmission expansion planning (TEP) add to the problem's complexity. Even if the power flow equations are linearized, the optimization problem is still bilinear and mixed-integer due to the dependence of line expansion on line impedance and a discrete set of line expansion options. While it is possible to linearize this mixed-integer nonlinear program (MINLP) by applying a big-M disjunctive relaxation, the resulting MILP is still hard to solve using state-of-the-art solvers for large-scale energy system models. In this paper we therefore develop heuristics to incorporate integer transmission expansion and responsive line impedances in energy system models, while retaining the lower computational effort of continuous linear programming (LP) by applying sequential linear programming (SLP) techniques, relaxation and discretization approaches. We benchmark their performance against the results of the exact formulation for a policy-relevant case study of the German transmission system in terms of their speed-up in computation time, deviation from optimal total system cost, and similarity of line expansion. Using heuristics we reduce computation times of joint generation and transmission optimisation by 82% with a maximal total system cost deviation of only 1.5%. The heuristics closely mirror optimal integer line investment of the exact MINLP with considerable time savings for policy-relevant low-carbon energy system optimization models.

math.OC↗

arXiv2019

Transfer of Adversarial Robustness Between Perturbation Types

We study the transfer of adversarial robustness of deep neural networks between different perturbation types. While most work on adversarial examples has focused on $L_\infty$ and $L_2$-bounded perturbations, these do not capture all types of perturbations available to an adversary. The present work evaluates 32 attacks of 5 different types against models adversarially trained on a 100-class subset of ImageNet. Our empirical results suggest that evaluating on a wide range of perturbation sizes is necessary to understand whether adversarial robustness transfers between perturbation types. We further demonstrate that robustness against one perturbation type may not always imply and may sometimes hurt robustness against other perturbation types. In light of these results, we recommend evaluation of adversarial defenses take place on a diverse range of perturbation types and sizes.

cs.LG↗

arXiv2019

The role of hydro power, storage and transmission in the decarbonization of the Chinese power system

Deep decarbonization of the electricity sector can be provided by a high penetration of renewable sources such as wind, solar PV and hydro power. Flexibility from hydro and storage complements the high temporal variability of wind and solar, and transmission infrastructure helps the power balancing by moving electricity in the spatial dimension. We study cost-optimal highly-renewable Chinese power systems under ambitious CO$ _2 $ emission reduction targets, by deploying a 31-node hourly-resolved techno-economic optimization model supported by a validated weather-converted 38-year-long renewable power generation and electricity demand dataset. With a new realistic reservoir hydro model, we find that if CO$_2$ emission reduction goes beyond 70\%, storage facilities such as hydro, battery and hydrogen become necessary for a moderate system cost. Numerical results show that these flexibility components can lower renewable curtailment by two thirds, allow higher solar PV share by a factor of two and contribute to covering summer cooling demand. We show that expanding unidirectional high-voltage DC lines on top of the regional inter-connections is technically sufficient and more economical than ultra-high-voltage-AC-connected "One-Net" grid. Finally, constraining transmission volume from the optimum by up to 25\% does not push total costs much higher, while the significant need for battery storage remains even with abundant interconnectivity.

physics.soc-ph↗

arXiv2019

A validated high-resolution hydro power time-series model for energy systems analysis

We expand the renewable technology model palette and present a validated high resolution hydro power time series model for energy systems analysis. Among the popular renewables, hydroelectricity shows unique storage-like flexibility, which is particularly important given the high variability of wind and solar power. Often limited by data availability or computational performance, a high resolution, globally applicable and validated hydro power time series model has not been available. For a demonstration, we focus on 41 Chinese reservoir-based hydro stations as a demo, determine their upstream basin areas, estimate their inflow based on gridded surface runoff data and validate their daily inflow time series in terms of both flow volume and potential power generation. Furthermore, we showcase an application of these time series with hydro cascades in energy system long term investment planning. Our method's novelty lies in:it is based on highly resolved spatial-temporal datasets; both data and algorithms used here are globally applicable; it includes a hydro cascade model that can be integrated into energy system simulations.

physics.soc-ph↗

arXiv2018

The Impact of Climate Change on a Cost-Optimal Highly Renewable European Electricity Network

We use three ensemble members of the EURO-CORDEX project and their data on surface wind speeds, solar irradiation as well as water runoff with a spatial resolution of 12 km and a temporal resolution of 3 hours under representative concentration pathway 8.5 (associated with a temperature increase of 2.6 to 4.8 degrees C until the end of the century) until 2100 to investigate the impact of climate change on wind, solar and hydro resources and consequently on a highly renewable and cost-optimal European power system. The weather data is transformed into power, different aspects such as capacity factors and correlation lengths are investigated and the resulting implications for the European power system are discussed. In addition, we compare a 30-node model of Europe with historical and climate change-affected data, where investments in generation, transmission and storage facilities are optimised for deep carbon dioxide reductions. Differences in capacity factors among European countries are more strongly emphasized at the end of the century compared to historic data. This results in a significantly increased photovoltaic share in the cost-optimal power system. System costs increase by 5% until the end of the century and the impact of climate change on these costs is of similar magnitude as differences between the ensemble members.

physics.soc-ph↗

arXiv2018

Principal Flow Patterns across renewable electricity networks

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.

eess.SP↗

arXiv2018

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.

physics.soc-ph↗

arXiv2018

Counter-intuitive behaviour of energy system models under CO2 caps and prices

The mitigation of climate change requires a fundamental transition of the energy system. Affordability, reliability and the reduction of greenhouse gas emissions constitute central but often conflicting targets for this energy transition. Against this context, we reveal limitations and counter-intuitive results in the model-based optimization of energy systems, which are often applied for policy advice. When system costs are minimized in the presence of a CO2 cap, efficiency gains free a part of the CO2 cap, allowing cheap technologies to replace expensive low-emission technologies. Even more striking results are observed in a setup where emissions are minimized in the presence of a budget constraint. Increasing CO2 prices can oust clean, but expensive technologies out of the system, and eventually lead to higher emissions. These effects robustly occur in models of different scope and complexity. Hence, extreme care is necessary in the application of energy system optimization models to avoid misleading policy advice.

physics.soc-ph↗

arXiv2018

Cost optimal scenarios of a future highly renewable European electricity system: Exploring the influence of weather data, cost parameters and policy constraints

Cost optimal scenarios derived from models of a highly renewable electricity system depend on the specific input data, cost assumptions and system constraints. Here this influence is studied using a techno-economic optimisation model for a networked system of 30 European countries, taking into account the capacity investment and operation of wind, solar, hydroelectricity, natural gas power generation, transmission, and different storage options. A considerable robustness of total system costs to the input weather data and to moderate changes in the cost assumptions is observed. Flat directions in the optimisation landscape around cost-optimal configurations often allow system planners to choose between different technology options without a significant increase in total costs, for instance by replacing onshore with offshore wind power capacity in case of public acceptance issues. Exploring a range of carbon dioxide emission limits shows that for scenarios with moderate transmission expansion, a reduction of around 57% compared to 1990 levels is already cost optimal. For stricter carbon dioxide limits, power generated from gas turbines is at first replaced by generation from increasing renewable capacities. Non-hydro storage capacities are only built for low-emission scenarios, in order to provide the necessary flexibility to meet peaks in the residual load.

physics.soc-ph↗

arXiv2018

Skill Rating for Generative Models

We explore a new way to evaluate generative models using insights from evaluation of competitive games between human players. We show experimentally that tournaments between generators and discriminators provide an effective way to evaluate generative models. We introduce two methods for summarizing tournament outcomes: tournament win rate and skill rating. Evaluations are useful in different contexts, including monitoring the progress of a single model as it learns during the training process, and comparing the capabilities of two different fully trained models. We show that a tournament consisting of a single model playing against past and future versions of itself produces a useful measure of training progress. A tournament containing multiple separate models (using different seeds, hyperparameters, and architectures) provides a useful relative comparison between different trained GANs. Tournament-based rating methods are conceptually distinct from numerous previous categories of approaches to evaluation of generative models, and have complementary advantages and disadvantages.

stat.ML↗

arXiv2018

Technical Report on the CleverHans v2.1.0 Adversarial Examples Library

CleverHans is a software library that provides standardized reference implementations of adversarial example construction techniques and adversarial training. The library may be used to develop more robust machine learning models and to provide standardized benchmarks of models' performance in the adversarial setting. Benchmarks constructed without a standardized implementation of adversarial example construction are not comparable to each other, because a good result may indicate a robust model or it may merely indicate a weak implementation of the adversarial example construction procedure. This technical report is structured as follows. Section 1 provides an overview of adversarial examples in machine learning and of the CleverHans software. Section 2 presents the core functionalities of the library: namely the attacks based on adversarial examples and defenses to improve the robustness of machine learning models to these attacks. Section 3 describes how to report benchmark results using the library. Section 4 describes the versioning system.

cs.LG↗

arXiv2018

Flow-based analysis of storage usage in a low-carbon European electricity scenario

The application of the flow tracing method to power flows in and out of storage units allows to analyse the usage of this technology option in large-scale interconnected electricity systems. We apply this method to a data-driven model of the European electricity network, which uses a techno-economic optimisation to determine generation and storage capacities and dispatch, assuming a 95% reduction of CO2 emission compared to 1990 levels. A flow-based analysis of the power inflow into the different storage technologies confirms the intuition that longer-term hydrogen storage is mainly utilised for wind, whereas short-term battery storage mostly receives inflow from solar power generation. The usage of storage technologies in general shows a local-but-global behaviour: Whereas on average the power outflow from these capacities is predominantly consumed locally inside the same node, when exported it is also transmitted over long distances as a global flexibility option for the entire system.

physics.soc-ph↗