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The Optimal Power Flow (OPF) problem is pivotal for power system operations, guiding generator output and power distribution to meet demand at minimized costs, while adhering to physical and engineering constraints. The integration of renewable energy sources, like wind and solar, however, poses challenges due to their inherent variability. This variability, driven largely by changing weather conditions, demands frequent recalibrations of power settings, thus necessitating recurrent OPF resolutions. This task is daunting using traditional numerical methods, particularly for extensive power systems. In this work, we present a cutting-edge, physics-informed machine learning methodology, trained using imitation learning and historical European weather datasets. Our approach directly correlates electricity demand and weather patterns with power dispatch and generation, circumventing the iterative requirements of traditional OPF solvers. This offers a more expedient solution apt for real-time applications. Rigorous evaluations on aggregated European power systems validate our method's superiority over existing data-driven techniques in OPF solving. By presenting a quick, robust, and efficient solution, this research sets a new standard in real-time OPF resolution, paving the way for more resilient power systems in the era of renewable energy., Comment: Submitted to Elsevier

Networked control systems are feedback control systems with system components distributed at different locations connected through a communication network. Since the communication network is carried out through the internet and there are bandwidth and packet size limitations, network constraints appear. Some of these constraints are time delay and packet loss. These network limitations can degrade the performance and even destabilize the system. To overcome the adverse effect of these communication constraints, various approaches have been developed, among which a representative one is networked predictive control. This approach proposes a controller, which compensates for the network time delay and packet loss actively. This paper aims at implementing a networked predictive control system for controlling a robot arm through a computer network. The network delay is accounted for by a predictor, while the potential of packet loss is mitigated using redundant control packets. The results will show the stability of the system despite a high delay and a considerable packet loss. Additionally, improvements to previous networked predictive control systems will be suggested and an increase in performance can be shown. Lastly, the effects of different system and environment parameters on the control loop will be investigated.

Energy system models underpin decisions by energy system planners and operators. Energy system modelling faces a transformation: accounting for changing meteorological conditions imposed by climate change. To enable that transformation, a community of practice in energy-climate modelling has started to form that aims to better integrate energy system models with weather and climate models. Here, we evaluate the disconnects between the energy system and climate modelling communities, then lay out a research agenda to bridge those disconnects. In the near-term, we propose interdisciplinary activities for expediting uptake of future climate data in energy system modelling. In the long-term, we propose a transdisciplinary approach to enable development of (1) energy-system-tailored climate datasets for historical and future meteorological conditions and (2) energy system models that can effectively leverage those datasets. This agenda increases the odds of meeting ambitious climate mitigation goals by systematically capturing and mitigating climate risk in energy sector decision making., Comment: MTC, JW and LPS contributed equally to this manuscript. 25 pages, 2 figures. Fixed typos in manuscript title. This perspective is based on the discussion held at the 2021 Next Generations Challenges in Energy-Climate Modelling (NextGenEC'21) workshop

Spatial and temporal data for earthquakes with magnitude M greater than or equal to 6.5 can provide crucial information about the seismic history and potential for large earthquakes in a region. We analyzed approximately 313,500 events that occurred in the Sunda-arc region during the last 56 years, from 1964 to 2020, reported by the International Seismological Center. We report a persistent increase in the annual number of the events with mb greater than or equal to 6.5. We tested this increase against the null hypothesis and discarded the possibility of the increase being due to random groupings. The trend given by Auto-Regressive Integrated Moving Average suggests continuing increase of such large-magnitude events in the region during the next decade. At the same time, the computed Gutenberg Richter b value shows anomalies that can be related to the occurrence of the mega 2004 Sumatra earthquake, and to possible state of high tectonic stress in the eastern parts of the region.

Global warming is one of the main threats to the future of humanity and extensive emissions of greenhouse gases are found to be the main cause of global temperature rise as well as climate change. During the last decades international attention has focused on this issue, as well as on searching for viable solutions to mitigate global warming. In this context, the pricing of greenhouse gas emissions turned out to be the most prominent mechanism: First, to lower the emissions, and second, to capture their external costs. By now, various carbon dioxide taxes have been adopted by several countries in Europe and around the world; moreover, the list of these countries is growing. However, there is no standardized approach and the price for carbon varies significantly from one country to another. Regionally diversified carbon prices in turn lead to carbon leakage, which will offset the climate protection goals. In this paper, a simplified European power system with flexible carbon prices regarding the Gross Domestic Product (GDP) is investigated. A distribution parameter that quantifies carbon leakage is defined and varied together with the base carbon price, where the combination of both parameters describes the spatially resolved price distribution, i.e. the effective carbon pricing among the European regions. It is shown that inhomogeneous carbon prices will indeed lead to significant carbon leakage across the continent, and that coal-fired electricity generation will remain a cheap and therefore major source of power in Eastern and South-Eastern Europe - representing a potential risk for the long term decarbonization targets within the European Union., Comment: 19 pages, 10 figures

In the process of decarbonization, the global energy mix is shifting from fossil fuels to renewables. To study decarbonization pathways, large-scale energy system models are utilized. These models require accurate data on renewable generation to develop their full potential. Using different data can lead to conflicting results and policy advice. In this work, we compare several datasets that are commonly used to study the transition towards highly renewable European power system. We find significant differences between these datasets and cost-difference of about 10% result in the different energy mix. We conclude that much more attention must be paid to the large uncertainties of the input data., Comment: 36 pages, 10 figures

We apply well-established concepts of Langevin sampling to derive a new class of algorithms for the efficient computation of free energy differences of fluctuating particles embedded in a 'fast' membrane, i.e., a membrane that instantaneously adapts to varying particle positions. A geometric potential accounting for membrane-mediated particle interaction is derived in the framework of variational hybrid models for particles in membranes. Recent explicit representations of the gradient of the geometric interaction potential allows to apply well-known gradient based Markov Chain Monte-Carlo (MCDC) methods such as Langevin-based sampling.

Power system expansion models are a widely used tool for planning powersystems, especially considering the integration of large shares of renewableresources. The backbone of these models is an optimization problem, whichdepends on a number of economic and technical parameters. Although theseparameters contain significant uncertainties, the sensitivity of power systemmodels to these uncertainties is barely investigated. In this work, we introduce a novel method to quantify the sensitivity ofpower system models to different model parameters based on measuring theadditional cost arising from misallocating generation capacities. The value ofthis method is proven by three prominent test cases: the definition of capitalcost, different weather periods and different spatial and temporal resolutions.We find that the model is most sensitive to the temporal resolution. Fur-thermore, we explain why the spatial resolution is of minor importance andwhy the underlying weather data should be chosen carefully.

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., Comment: 6 pages, 11 figures

Renewable energies are deployed worldwide to mitigate climate change and push power systems towards sustainability. However, the weather-dependent nature of renewable energy sources often hinders their integration to national grids. Combining different sources to profit from beneficial complementarity has often been proposed as a partial solution to overcome these issues. This paper introduces a novel method for quantifying total temporal energetic complementarity between three different variable renewable sources, based on well-known mathematical techniques: correlation coefficients and compromise programming. It has the major advantage of allowing the simultaneous assessment of partial and total complementarity. The method is employed to study the complementarity of wind, solar and hydro resources on different temporal scales in a region of Poland. Results show that timescale selection has a determinant impact on the total temporal complementarity., Comment: Submitted for peer review

It is expected, and regionally observed, that energy demand will soon be covered by a widespread deployment of renewable energy sources. However, the weather and climate driven energy sources are characterized by a significant spatial and temporal variability. One of the commonly mentioned solutions to overcome the mismatch between demand and supply provided by renewable generation is a hybridization of two or more energy sources in a single power station (like wind-solar, solar-hydro or solar-wind-hydro). The operation of hybrid energy sources is based on the complementary nature of renewable sources. Considering the growing importance of such systems and increasing number of research activities in this area this paper presents a comprehensive review of studies which investigated, analyzed, quantified and utilized the effect of temporal, spatial and spatio-temporal complementarity between renewable energy sources. The review starts with a brief overview of available research papers, formulates detailed definition of major concepts, summarizes current research directions and ends with prospective future research activities. The review provides a chronological and spatial information with regard to the studies on the complementarity concept., Comment: 34 pages 7 figures 3 tables

In order to reduce greenhouse gas emissions of the power sector, high shares of renewable power sources need to be integrated into existing systems. This will require vast amounts of investments. Cost of the capital needed for these investments are unevenly distributed among European regions. They show a clear North-South and West-East divide, which has not exhibited significant signs of narrowing in recent years. Power system studies investigating a continent-wide European power system, however, usually assume homogeneous cost of capital. The objective of this paper is to investigate how regional differences in cost of capital affect the result of these studies with respect to the optimal power system design. Our analysis is based on power system optimization with inhomogeneous cost of capital in Europe. We find that assuming homogeneous cost of capital leads to estimates on the levelized costs of electricity in a highly renewable European power system, which are too conservative. The optimal system design is significantly affected compared to an inhomogeneous scenario. In particular, we show that inhomogeneous cost of capital favors overall wind power deployment in the case of Europe, while the investment in solar power decreases.

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.

There are two competing concepts in the literature for the integration of high shares of renewable energy: the coupling of electricity to other energy sectors, such as transport and heating, and the reinforcement of continent-wide transmission networks. In this paper both cross-sector and cross-border integration are considered in the model PyPSA-Eur-Sec-30, the first open, spatially-resolved, temporally-resolved and sector-coupled energy model of Europe. Using a simplified network with one node per country, the cost-optimal system is calculated for a 95% reduction in carbon dioxide emissions compared to 1990, incorporating electricity, transport and heat demand. Flexibility from battery electric vehicles (BEV), power-to-gas units (P2G) and long-term thermal energy storage (LTES) make a significant contribution to the smoothing of variability from wind and solar and to the reduction of total system costs. The cost-minimising integration of BEV pairs well with the daily variations of solar power, while P2G and LTES balance the synoptic and seasonal variations of demand and renewables. In all scenarios, an expansion of cross-border transmission reduces system costs, but the more tightly the energy sectors are coupled, the weaker the benefit of transmission reinforcement becomes., Comment: 24 pages, 13 figures; accepted to Energy

The Vietnamese Power system is expected to expand considerably in upcoming decades. However, pathways towards higher shares of renewables ought to be investigated. In this work, we investigate a highly renewable Vietnamese power system by jointly optimising the expansion of renewable generation facilities and the transmission grid. We show that in the cost-optimal case, highest amounts of wind capacities are installed in southern Vietnam and solar photovoltaics (PV) in central Vietnam. In addition, we show that transmission has the potential to reduce levelised cost of electricity by approximately 10%., Comment: 5 pages, 4 figures

A fully renewable European power system comes with a variety of problems. Most of them are linked to the intermittent nature of renewable generation from the sources of wind and photovoltaics. A possible solution to balance European generation and consumption are European hydro power with its seasonal and North African Concentrated Solar Power with its daily storage characteristics. In this paper, we investigate the interplay of hydro and CSP imports in a highly renewable European power system. We use a large weather database and historical load data to model the interplay of renewable generation, consumption and imports for Europe. We introduce and compare different hydro usage strategies and show that hydro and CSP imports must serve different purposes to maximise benefits for the total system. CSP imports should be used to cover daily deficits, whereas hydro power can cover seasonal imbalances. If hydro is used in a "Hydro First" strategy, only around one quarter of North African Solar Power could be exported to Europe, whereas this number increases to around 60\%, if a cooperative hydro strategy is used., Comment: 7 pages, 5 figures

We consider a discrete-continuum model of a biomembrane with embedded particles. While the membrane is represented by a continuous surface, embedded particles are described by rigid discrete objects which are free to move and rotate in lateral direction. For the membrane we consider a linearized Canham-Helfrich energy functional and height and slope boundary conditions imposed on the particle boundaries resulting in a coupled minimization problem for the membrane shape and particle positions. When considering the energetically optimal membrane shape for each particle position we obtain a reduced energy functional that models the implicitly given interaction potential for the membrane-mediated mechanical particle-particle interactions. We show that this interaction potential is differentiable with respect to the particle positions and orientations. Furthermore we derive a fully practical representation of the derivative only in terms of well defined derivatives of the membrane. This opens the door for the application of minimization algorithms for the computation of minimizers of the coupled system and for further investigation of the interaction potential of membrane-mediated mechanical particle--particle interaction. The results are illustrated with numerical examples comparing the explicit derivative formula with difference quotient approximations. We furthermore demonstrate the application of the derived formula to implement a gradient flow for the approximation of optimal particle configurations.

This paper is concerned with minimization of a fourth-order linearized Canham-Helfrich energy subject to Dirichlet boundary conditions on curves inside the domain. Such problems arise in the modeling of the mechanical interaction of biomembranes with embedded particles. There, the curve conditions result from the imposed particle--membrane coupling. We prove almost-$H^{\frac{5}{2}}$ regularity of the solution and then consider two possible penalty formulations. For the combination of these penalty formulations with a Bogner-Fox-Schmit finite element discretization we prove discretization error estimates which are optimal in view of the solution's reduced regularity. The error estimates are based on a general estimate for linear penalty problems in Hilbert spaces. Finally, we illustrate the theoretical results by numerical computations. An important feature of the presented discretization is that it does not require to resolve the particle boundary. This is crucial in order to avoid re-meshing if the presented problem arises as subproblem in a model where particles are allowed to move or rotate.