Dr Chloi Syranidou
email: c.syranidou@fz-juelich.de

Matthias Koch

Björn Matthes

Christian Winger

Jochen Linssen

Christian Rehtanz

Detlef Stolten

Jochen Linßen

Prof. Detlef Stolten

Oriol Raventós

Chinonso Unaichi

Julian Bartels

Jan Buschmann

Wided Medjroubi

Andreas Bruckmeier

Timo Kern

Felix Böing

Tobias Schmid

Christoph Pellinger

Thomas Dengiz

Rafael Finck

Armin Ardone

Katrin Seddig

Manuel Ruppert

Franziska Flachsbarth

Sebastian Palacios

Susanne Krieger

Jonas Mehlem

Lukas Weber

Annika Klette

Levin Skiba

Alexander Fehler

Jan Peper

Hannes Hobbie

Christina Wolff

David Schönheit

Dominik Möst

Development of an Open Framework for a Qualitative and Quantitative Comparison of Power System and Electricity Grid Models for Europe

published or not. The documents may come

Introduction

A significant increase in the desire for analyzing the European power system has been observed over the past decade, resulting in a variety of modeling approaches that have been developed by scientists in order to accurately represent its properties and behavior. One of the most important drivers for this trend includes the commitment of the European Union to decarbonize its economy, and the power sector constitutes one of the highest emitters, which will require the use of a variety of novel generation, transmission and storage technologies. Such technologies may substantially alter and pose challenges to the traditional way of power system operation, control and security, while also questions regarding costefficient transition can become difficult to ask. Another significant driver consists of the economic transformation of the European power market, where the goal is to accelerate the integration of a single market and facilitate a variety of system flexibilities within a liberalized environment.

Power systems constitute a field with a long history of analysis, however the new challenges introduced by the system transition typically require a variety of novel methods, increased computational resources as well as a greater scope. For instance, the increasingly decentralized and inflexible power supply needs to be accurately described in both spatial and temporal dimensions in order to capture the most important dynamics. Therefore, this paper focuses on power system models which concentrate on this new technology landscape as well as the economic and operational effects. Moreover, such models should incorporate the complete and realistic depiction of both the system conditions and operation, for example the consideration of the existing grid infrastructure or load curves at each bus, and not merely an aspect of those or synthetic conditions. As with energy system modeling in general, power system models describe complex problems with different approaches and many different models may produce contrasting results while trying to represent the same real world system. Therefore, it has always been interesting to compare such models with each other and explore the inner workings, which among others can provide crucial understanding of the system itself as well as benefit the understanding and improvement of each individual model and the modeling process in general. A more comprehensive review of the existing model comparison techniques is presented in section 2, where it is observed that such a comparison is rarely conducted for power systems. Especially transmission expansion planning's main steps, namely: regionalization of generation and demand, power market simulation, transmission grid and congestion management simulation have not been analyzed in a structured model comparison yet. Considering a model comparison frameworks that enables structured comparisons of various power system models dealing with the aforementioned steps in the field of transmission expansion planning, a research gap can be identified.

The goal of this paper is to describe the various challenges and aspects of model comparisons for power systems as well as to provide a framework on how to approach such a task. The framework includes comparison methods and tools for all aspects of power system modeling within the specific context such as formulating the system conditions, congestion management methods or market output. Although a more detailed description of some aspects may lie outside the scope of this paper, all comparison approaches are discussed individually as well as a whole. Moreover, specific models are used to better illustrate these approaches and provide further insight; however, a complete comparison of models is beyond the scope of this paper, which focuses primarily on developing and discussing the comparison framework itself.

Model comparisons aim to compare existing approaches in terms of methodology including model structures and data. The aim is to gain a better understanding of the respective approaches and to identify opportunities for further development. Furthermore, a model comparison offers an ideal platform for indepth discussion for model developers. Model comparisons have been an effective means of achieving these goals for many years. At the international level, the Energy Modeling Forum (EMF) should be mentioned here, which was introduced in the 1970s and has been continued ever since. On the EU level, the Energy Modelling Platform for Europe (EMP-E), the project ACROPOLIS (Assessing Climate Response Options: POLIcy Simulations -Insights from using national and international models) and CASCADE-MINTS (CAse Study Comparisons And Development of Energy Models for Integrated Technology Systems) should be mentioned [START_REF]CASCADE-MINTS: Case Study Comparisons and Development of Energy Models for Integrated Technology Systems, The contribution of renewable energy to a sustainable energy system[END_REF]. Between 1997 and 2007, a total of five model experiments were carried out by the German Federal Ministry of Education and Research (BMBF) and the German Federal Ministry for Economic Affairs and Energy (BMWi) within the framework of the FORUM for Models [START_REF] Fahl | Energiemodelle zum Klimaschutz in Deutschland[END_REF]. Model comparisons were carried out on the example of selected problems, which included models of different categories as well as the coupling of models. Recently running research projects in Germany are RegMex [START_REF]RegMex -Modellexperimente und -vergleiche zur Simulation vonWegen zu einer vollständigregenerativen Energieversorgung[END_REF] [4], 4NEMO -Research Network for the Development of New Methods in Energysystem Modeling [START_REF] Savvidis | The gap between energy policy challenges and model capabilities[END_REF] and BEAM-ME [START_REF] Cao | Classification and Evaluation of Concepts for Improving the Performance of Applied Energy System Optimization Models[END_REF] [START_REF] Scholz | Speeding up Energy System Models -a Best Practice Guide[END_REF]. These model comparisons performed on power generation models with a specific focus on flexibility (RegMex), economic and social dynamics (4NEMO) or calculation algorithm and acceleration strategies (BEAM-ME).

Transmission grid models are often used to analyze the impact of integrating high shares of renewables into the power system. In this case, the analysis is usually coupled with power plant dispatch and the regionalization of generation and demand to grid node level [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF]. Depending on the focus set, the underlying models can differ, among other things, in the type of load flow modeling and control, in the level of detail modelling individual grid components, in the geographic scope that is covered in detail, and in the consideration of network expansion and congestion management in general.

Regarding the power-flow calculation in transmission grid models, a distinction can be made mainly between Power Transfer Distribution Factor (PTDF)-based, Direct Current (DC) and Alternating Current (AC) approaches as well as Net Transmission Capacity (NTC) approaches [START_REF] Birbalta | Application of a network reduction approach on an energy system model and the impact of different node aggregations on the curtailment of renewable energy generation[END_REF]. Depending on the applied power-flow calculation method, the required computational effort allows different degrees of detail of the system representation [10] [11]. This is one of the reasons why there are fewer AC approaches, which are used in particular for detailed technical analyses. For similar reasons, network reduction methods are becoming increasingly important [START_REF] Birbalta | Application of a network reduction approach on an energy system model and the impact of different node aggregations on the curtailment of renewable energy generation[END_REF]. In contrast to AC approaches, the other approaches (DC, PTDF, NTC) have a much lower computational cost allowing the consideration of more extensive systems at the expense of a lower accuracy of the results [Zhu]. In this respect, the range of existing approaches for modeling transmission grid has its justification and these approaches can complement each other [10] [11]. The same applies to the various methodological approaches to the use of power-flow controlling equipment such as Phase Shifting Transformers (PST) or High-Voltage Direct Current (HVDC) links, which according to the German national grid development plan [START_REF]zweiter Entwurf der Übertragungsnetzbetreiber[END_REF] will be increasingly integrated into the AC grid in the future [START_REF] Rüberg | Strategische Netzausbauplanung in vermaschten Drehstromnetzen unter besonderer Berücksichtigung der Hochspannungsgleichstromübertragung[END_REF].

A detailed comparison of transmission gird models (including regionalization, dispatch, power-flow and congestion management methods) has not been performed yet. One reason for this is that all input data and model results have to be available in high spatial and temporal resolution. Furthermore, modelling the relevant electrical and technical restrictions make the applied methodological approaches complex. Hence, the concept of accuracy or the level of detail must be understood and considered on several levels by modelling the electrical transmission grid. The first level is the width of the modeling in the sense of the geographical area of the real grid topology and in particular the modeling of the edge area. The second level is formed by the different voltage levels of the power system. This horizontal dimension of the grid infrastructure has to be represented in the transmission grid model by an appropriate modeling depth with suitable grid equivalents. The last level represents the system-specific abstraction level. Taking into account the diversity and heterogeneity of the grid's components (like busbars and breakers) in substations and switching stations, an exact component-specific modeling of the continental European transmission system is highly complex. For this reason, parts of the electrical systems or groups of components are typically merged and aggregated in power system models in order to be able to subsequently transfer them into a so-called bus-branch model [START_REF] Klein | Aggregation of large-scale electrical energy transmission networks[END_REF]. For this purpose, a number of simplifying assumptions have to be made, which have a significant influence on possible results and their informative value. In particular, the way in which switchgear, breakers and individual busbars are represented in the network model has an influence on the number of nodes and links. At this point, the situation is aggravated by the fact that transmission grid data is only publicly accessible to a limited extent, which makes validation virtually impossible, even though there are increasingly publicly accessible but unconfirmed data sources [START_REF] Medjroubi | Open Data in Power Grid Modelling: New Approaches Towards Transparent Grid Models[END_REF]. However, in recent years a trend towards open source modeling and more and more also open data begun and is further increasing. In the meantime, there are a whole range of open modeling and open data platforms, such as e.g., GitHub or Zenodo. The open energy platform specifically targeted towards modelling of energy systems [START_REF]Öko-Institut[END_REF]. Furthermore, an open source python package has just been released that provides software tools and methods for comparison and visualization of model results [START_REF] Huppmann | [END_REF].

Development of a comparison framework and definition of model experiments

Workflow of the comparison framework

This chapter describes the comparison framework. The MODEX-Net research project team developed and used the framework to analyze various power system models. The comparison framework consist of two consecutive workflows (Figure 1). As a starting point, the framework analyzes the model's inputs and methods in a qualitative manner. Therefore, the initial workflow collects basic information about the models. To do so it makes use of factsheets to gather information on the basic data sources and methods. The developed factsheets are available as supplementary material as well as at https://www.energiesystem-forschung.de/forschen/projekte/modex-net. The comparison framework considers the model's inputs for the regionalization of generation and demand as well as for existing power grid infrastructure in the field of data sources. With regard to the models inner workings, the comparison framework analyzes the methods applied for spatial disaggregation as well as time series generation, for unit commitment and dispatch optimization, for power flow calculations and for congestion management optimization. Based on the comparison of the models main inputs and processed data sources as well as applied methods across all models, the comparison framework identifies each model's key characteristics and highlights major differences and similarities.

In a second workflow, the comparison framework determines harmonization potentials as a basis for the quantitative comparison. Taking into account the model's key characteristics as well as major differences and similarities, the workflow identifies inputs and methods that can easily be harmonized, e.g., by using publicly available data that is already used by some models. Furthermore the workflow proposes a harmonization of participating model's individual features, such as methods on the consideration of power flow controlling devices or modelling the (n-1)-criterion in explicit or indirectly by a simplified security margin. To put it concisely, the qualitative comparison builds the foundation to parametrize the participating models in a way that input data and applied methods across all participating models represents the lowest common denominator that can be reached without models having to implement new features in advance. Against the background of performing a quantitative comparison of power system model's results especially with a focus on transmission grid utilization, it needs further steps to carry out detailed analysis in a structured procedure. After harmonizing the most relevant input data and methods of the models, the harmonization of the model experiment itself becomes crucial. Especially when real transmission grid infrastructure instead of test systems, like IEEE 118 Bus, are considered, the point in time of the study is important. On the one hand there are so called back testing studies that try to replicate the historic systems behavior as good as possible. On the other hand, there are system studies dedicated to forecast the future power system. The latter are heavily dependent on and driven by assumptions with regard to different components of the future energy systems. A key factor by analyzing future scenarios is the transmission grid infrastructure that is assumed to be built in the meantime (today until year of future scenario, e.g., 2030) forming the system studies reference grid. Hence, the (future) market and grid scenarios have to be defined in detail to serve as an adequate reference in a model comparison. The scenario definition workflow specifies the energy-economical framework in terms of installed generation capacities and electricity demand. Furthermore, the workflow defines the reference transmission grid by providing a list of already known grids expansion and reinforcement measures that are assumed to be realized until the point in time under assessment.

Based on the detailed market and grid scenarios as well as the harmonized data sources and methods so called model experiments (MODEX) are carried out. Each model experiments includes the parametrization of all participating models with the harmonized data and methods, whereby each model makes use of its own transmission grid data and grid modelling methods, the execution of a model run including a simulation of the power market, the transmission grid's utilization and congestion management measures, the upload of each simulation's results to the OEP clone, the automated analysis of all provided model results with a newly developed python framework and finally a discussion of possible adjustments that were tracked in an issue list.

Definition of model experiments

As mentioned before, the point in time (the scenario year) of a system study is essential, if real transmission grid infrastructure is analyzed. Hence, the model experiments in the MODEX-Net research project were designed in a way to incorporate the two most relevant types of system studies. The first model experiment will be a back testing study for the year 2016 and the second model experiment will analyze a future energy system for the year 2030 based on assumptions from the German grid development plan with regard to the system's development [START_REF]zweiter Entwurf der Übertragungsnetzbetreiber[END_REF]. The reference data sets for 2016 and 20130 used the model experiments are publicly available at https://www.energiesystemforschung.de/forschen/projekte/modex-net. In both model experiments Germany and its neighboring countries are considered as main focus region of the study. However, the complete area under assessment includes further countries the so-called satellite regions.

Figure 2 shows the countries that were considered in the model experiments. Germany's neighboring countries as well as Norway and Sweden, which are linked via sea cables to the German transmission grid, are considered in all models. Therefore we harmonized the input data for these countries. The maximum spatial extent of individual models covers all ENTSO-E countries, excluding Cyprus and Iceland. Both model experiments include the simulation of the European power market, the simulation of the transmission grid's utilization as well relevant congestion management measures to resolve congestions in Germany by conventional redispatch and curtailment of renewable energy sources. The power plants dispatch, the power flows in the transmission grid as well as the congestion management measures are determined on an hourly basis for a complete year, resulting in 8,760 consecutive snapshots of the system providing the raw input data for the comparison framework.

Technical implementation of the comparison framework

The comparison framework is implemented at a cloud server, which is a self hosted linux server with a postgresql database as backend.

The database consists of several predefined tables and views, which take into account the spatial and time resolution (e.g., country code, region code and timestamp) of the selected key figures from the quantitative model results. The selected key figures are defined within a given data structure including foreign key constraints for dimensions to enforce integrity. The tables use fixed naming conventions for each parameter and model. All key figures shown in Figure 3 refer to market results (dispatch). For the upload procedure we developed a python client for communicating with the API as well as additional helper functions to parse csv files into proper data structures. Following this, each model maintainer uploads their own model data into their designated tables as defined by the naming convention.

The linkage to the open data community is given by using a clone of the open energy platform (https://github.com/OpenEnergyPlatform/oeplatform) as middleware stack (django) with public API for data upload and download. At the end of the project, we will upload the final model results and all input data which is available under an open data license to the open energy platform (https://openenergyplatform.org/). From this point on, other models can add their own model results and compare them with our results. The chosen comparing methods are described in section 5.

Designing the proper model experiments requires the identification of the key modeling aspects and differences among the various models. Moreover, such a process becomes essential for determining the harmonization potential of the modeling components, which may also play a significant role in designing the experiments and the final comparison of the models as well. Therefore, a systematic investigation of their properties and parameters is deemed necessary. Such a task can be typically accomplished by designing and filling appropriate factsheets, where all the necessary information can be conveniently consolidated, hence providing a way to more easily compare the models and gain further insight about their most critical discrepancies.

The process of transmission grid planning typically consists of the following methodological steps:  Definition of Scenarios,  Regionalization of generation and demand,  Generation of time series of inflexible loads and variable renewable energy sources,  Power Market Simulation for unit commitment and economic dispatch as well as commercial exchanges in Europe,  Power Flow studies to calculate the grid's utilization (considering power flow controlling devices) and identify congestions,  Congestion Management Simulations to preventively avoid potential overload situations.

Comparison of input data

As each of the steps mentioned before make use of individual specialized input data and methods, the comparison framework clearly differentiates between data and methods. Furthermore, the comparison framework's factsheets consider the input data and methods of each step separately. Table 4-1 provides an overview on the most important model's characteristics considered to compare input data and data sources. The factsheets consider the methodological steps of simulating the transmission grid's utilization before and after the application of congestion management measures in an aggregated manner, as the main data sources are typically identical in these steps.

 Basic grid topology and its electrical parameters  Grid expansion and reinforcement projects

As the methodological steps of regionalization and time series generation is covered in detail in [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF], this paper sets the focus on modelling power generation in the step of the market simulation. At first, all models are compared with regard to the inclusion or neglect of fuel types and generation technologies. It is found that the corresponding agreement among the models is high, hence this aspect may be disregarded as a source of discrepancy. Further invariant subcategories include the spatial resolution of power plants, where these are modeled as single power plants or units and are usually connected to the nearest substation. The operational parameters of hydro and VRES power plants, as well as the spatial distribution of the electricity demand which follows the nearest substation principle as well. Therefore, although these aspects may strongly influence the modeling outputs, this influence cannot be examined by this study, since there is no discrepancy among the models. Furthermore, it is worth noticing that although all models include the same operational parameters for hydro and VRES generation or the same principle for connecting the demand or the power plants to the grid, these aspects cannot be subject to harmonization, since they constitute core modeling elements whose differences are under investigation (e.g., the variable capacity factors of wind generation).

Despite the partial agreement on several sub-categories of generation data, the models show significant discrepancies with respect to primary data sources, the spatial distribution of VRES as well as the operational parameters of conventional power plants. The data of the primary sources may contain information regarding the geographical locations, parameters like the commissioning year or the year of the latest retrofitting, fuel type, technology or even more technical ones like overall efficiency. Due to their significant role in the model, these data are also not suitable for harmonization. Nevertheless, a further quantitative description is deemed necessary. Similar conclusions apply for the spatial distribution of the VRES as well, which is discussed further in [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF] in order to identify the key differences between the models with the corresponding methodologies considered unsuitable for harmonization.

On the contrary, the operational parameters of conventional power plants provide one of the highest potentials for harmonization among the various models. It can be observed, that besides the parameters related to the combined heat and power (CHP) plants operation, the ones related to unit commitment formulation as well as the part-load efficiencies, all other parameters are shared by the majority of the models. Therefore, for the cases where these parameters can be harmonized (e.g., CO 2 costs), a respective harmonization of them can render them invariant among all models. In addition, this finding highlights the necessity of each parameter with regard to modeling power systems as well as the diversity in modeling the flexibility of thermal power plants.

In contrast to generation, comparing the modeling of the transmission grid requires fewer sub-categories, namely topology data and grid data. However, despite the lower number of sub-categories, more differences can be identified among the models. Similarly, to the comparison of the primary data sources for power plants, little information can be extracted with respect to the grid topology data from the factsheets alone, while also a corresponding harmonization is considered undesirable for the purposes of this study as well. Nevertheless, it can be noticed from the factsheets that most of the models consider ENTSO-E and the German Network Development Plans as data sources. Moreover, it can be observed that almost all models apply special considerations to Germany in contrast the rest of Europe.

Regarding the grid data, it can be observed that most models consider typical line parameters for the European grid outside Germany. Although not all models share the same assumptions, many of them do not include any modeling of transformers. On the other hand, the line parameters for Germany show a higher diversity among the models and thus an increased difficulty for harmonization. Finally, modeling the connections to offshore wind generation shows discrepancies that cannot be easily evaluated by the factsheets alone, therefore further comparison is deemed necessary [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF].

Comparison of methods

Besides input data related to generation and demand as well as the grid infrastructure, various methodologies and assumptions regarding the spatial distribution of generation and demand (regionalization), the operation of conventional power plants (market simulation), the operational concept of power flow controlling devices (grid simulation) as well as the sequence of costly and non-costly remedial actions (congestion management simulation) are compared, since these are expected to play a vital role in the overall behavior of each model. Table 4-2 provides an overview on the most important model's characteristics considered to compare the applied data processing techniques and simulation methods. Regarding the regionalization methods used to simulate the spatial distribution of VRES and demand the basic working principle of the models looks quite similar. On the one hand, there are models that make use of top-down approaches using distribution factors to break down national capacities to smaller regions, e.g., NUTS or LAU regions. On the other hand, some models make use of bottom-up approaches by explicitly considering land usage and land cover data to simulate the spatial distribution of installed VRES capacities. Furthermore, this observation can be extended to data processing and simulation methods in the field of time series generation. Models applying top-downs regionalization approaches typically scale historical generation profiles to simulate the hourly VRES feed-in, whereas models that apply a bottom-up regionalization approach tend to use numerical weather models to simulate the hourly feed-in of VRES. However, all models consider historical load profiles to simulate the inflexible demand that is extended by additional load profiles of flexible consumers. Further details on the topic of regionalization and time series generation can be found in [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF].

With regard to the market simulation methods applied to optimize the operation of conventional power plants and storages as well as commercial exchanges between the European bidding zones, it can be observed that the models cover different regions but all have a strong focus on Germany. All models consider Germany and its neighboring countries in the market simulation, but some models do not consider the countries behind the direct neighbors, e.g., Italy, Great Britain or Spain. Besides the regional scope of the models the basic working principle of the market or dispatch simulation shows some discrepancies between the models. On the one hand, there are models following a consecutive approach starting with a zonal market simulation that considers each bidding zone as a copper plate having no transmission constraints. Hence, the grid's transmission capacities are considered in a very simplified way (typically by bilateral NTC values) in the market simulation. This represents today's consecutive market and system operation processes. On the other hand, there are models that apply an integrated market and grid simulation by considering grid's transmission capacities directly inside their dispatch optimization. Such kind of approaches are often used in academics or non-European system studies where Independent System Operators (ISO) typically perform Optimal Power Flow (OPF) simulations.

The methods used to simulate transmission grid's utilization are quite different in the models. At first, it has to be noted that the electrical power flow can be described in different ways going along with different levels of complexity. The full AC power flow equations are non-linear making it challenging to integrate them in optimization problems. Thus, linearization techniques and iterative methods to solve the non-linear equations are typically used to formulate and solve optimization problems in the field of power system analysis.

Regarding the modeling methods for the transmission grid, it can be observed that the discrepancy is high. It is worth mentioning that for redispatch a more elaborate comparison is required since the various approaches cannot be easily consolidated in the form of simplified factsheets. Due to the high diversity in transmission methodologies, further analysis is considered necessary to understand the differences between the various models and can be found in [START_REF] Hobbie | Impact of model parametrization and formulation on the explorative power of electricity network congestion management models. Insights from a grid model comparison experiment[END_REF].

The detailed comparison of the different models with the assistance of the factsheets has provided significant insight into the various modeling aspects and the corresponding discrepancies. Nevertheless, further conclusions may be extracted out of this analysis. Such conclusions may include the identification of the most crucial modeling aspects that can form the guidelines for designing the scenario frameworks, upon which the individual model experiments can be carried out.

The aim of the qualitative comparison consists of identifying and interpreting the differences between the various models and more specifically the influence of the different modeling methodologies. Therefore, the model experiments are designed in such a way that the impact of the most critical aspects can be adequately isolated and hence be better estimated and quantified as well as interpreted with respect to the model behaviors. To this end, the modeling aspects that constitute the primary candidates for the potential discrepancies in the models' behavior and outputs are collected and classified by the application of a quantitative model comparison making use of different key performance indicators and means of visualization (cf. section 5).

Identified Harmonization Potentials and Applied Harmonization

Based on the qualitative model comparison using the presented factsheets the relevant input parameters that should be harmonized to generate a unified data basis were identified. The objective here is to harmonize the model's input parameters only to a certain degree, so that the methodological differences applied by each model regarding the regionalization and the modelling of the transmission grid can continue to take effect. For these reasons, the input data for electricity grid parameters were not harmonized at all and electricity demand, energy carrier-specific generation capacities and storage capacities were only harmonized at country level (NUTS-0). The further topics concerning regionalization of input data [START_REF] Raventós | Comparison of different methods of spatial disaggregation of electricity generation and consumption time series[END_REF] as well as grid simulation and redispatch calculation [START_REF] Hobbie | Impact of model parametrization and formulation on the explorative power of electricity network congestion management models. Insights from a grid model comparison experiment[END_REF] are discussed in two associated papers of this project.

As relevant input data to harmonize we selected fuel type specific installed generation capacities, storage capacities, availabilities of these capacities, full load hours of renewable energies, annual total demand and NTC values. A comparison of model data with a variety of literature sources showed similar trends in terms of agreement in generation capacity values. The most challenging generation type was found to be hydropower, where significant discrepancies were observed both within the models as well as the literature, while also the distinction to the different types of hydropower may differ or be ignored. This differentiation, however, was deemed significant for the harmonization, where the three types were distinguished based on the individual flexibilities, namely run of river, reservoir and pumped hydro storages. The harmonized values for the selected input data were decided to be independent of any models and only based on the literature survey, where it was attempted to use as few sources as possible and mostly official sources, such that consistent scenarios could be maintained. The main data sources for these input parameters for the reference scenario 2016 and 2030 are:

Reference scenario 2016  ENTSO-E Statistical fact sheet [START_REF] Entso-E | Statistics and Data[END_REF]  Joint Research Centre (JRC) Hydro-power database [START_REF] De Felice Und | energy-modelling-toolkit/hydro-power-database: JRC Hydropower database -release 05[END_REF]  List of power plant from the German Federal Network Agency [START_REF] Bundesnetzagentur | Power plant list[END_REF]  NTC as maxima of forecasted year ahead transfer capacities from ENTSO-E Transparency Platform [START_REF] Entso-E | ENTSO-E Transparency Platform[END_REF] Reference scenario 2030  TYNDP 2018, scenario "Sustainable transition" [START_REF] Entso-E | Ten Year Network Development Plan 2018[END_REF]  Network development plan for Germany 2030 (version 2019), scenario "B 2030" [START_REF] Amprion | Netzentwicklungsplan Strom 2030, Version 2019[END_REF]  Mid-term adequacy forecast 2019 from ENTSO-E [START_REF] Entso-E | Mid-term Adequacy Forecast 2019[END_REF] Imprecise information was collected in an issue list in order to finally develop a common understanding and use a uniform definition of the data. Whenever necessary, additional literature sources were included, such as historical data for technical availabilities of thermal power plants or the JRC data base for hydro power plants. For pumped storage power plants, we have made the assumption that the pumping capacity is equal to the turbine capacity and the storage capacity is eight times the turbine capacity.

In addition, harmonized default values were also provided for individual input parameters from the MODEX thematic network. These include energy carrier-specific CO 2 emission factors, fuel and CO 2 prices as well as country-specific standardized profiles for load and variable renewable energies for the weather year 2016 [START_REF] Gardian | Data harmonization in heterogeneous energy system models -Example of the MODEX project cluster[END_REF].

Besides the identification of input parameters that should be harmonized for the model comparison, the qualitative model comparison shows harmonization potentials in the field of the applied methods. As the developed framework has a strong focus on comparing the transmission grids utilization as well as overloads and congestions management volumes needed to remove the overloads, the following methodological steps were harmonized to ensure a better comparability of the model's results. As not all participating models were able to consider Dynamic Line Rating (DLR) in their power-flow studies it was decided that no models will consider it. However, it has to be noted that DLR significantly increases transmission capacities and therefore can reduce redispatch and VRES curtailment drastically. Most of the participating models were not able to consider the effects of PST in their power-flow or congestion management simulations, as a consequence no model will consider PST. Only two models have methods implemented to explicitly simulate outages and to perform power-flow studies in the (n-1)-case. The other models typically apply static security margins by reducing the maximum power-flow of all lines.

Therefore, the method to model the (n-1)-criterion was harmonized in all models by applying a static security margin of 70 %.

Quantitative model comparison

Definition of key performance indicators

Comparing methodologies and input data provides significant understanding of similarities and differences among models, nevertheless, the comparison of their outputs can provide additional useful insight to their inner workings. Using both sources of information can provide a better understanding of the differences between models. However, comparing results only also carries its own merit. Since different models may generate a variety of different types of output data, a process similar to input data harmonization can be applied, where all models should be able to provide the selected output in comparable format. Moreover, this selection should incorporate sufficient complexity for analyzing the models, while also be simple enough, such that the data are intuitive to interpret as well as easier to be linked to the differences in input and methods. To that end, appropriate visualization methods should be designed as well as key performance indicators be derived.

Despite the narrow context of this paper, power systems can be modeled in a variety of ways, hence the output selected for comparison should be generic enough that almost all models should be able to produce, regardless of their inner structure. To that end, it is selected to follow the existing paradigm of operating the European power system in a relatively coarse manner and providing data for two levels: the results of a day ahead market level and of a grid level where the whole transmission grid is taken into account for redispatch calculation. For each of these two levels a collection of minimal output can be selected as shown in Table 5-1.

Comparison of market results

In this paper the focus lies more on the discussion of the market level, since the comparison of grid model formulations and corresponding conclusions (see [START_REF] Hobbie | Impact of model parametrization and formulation on the explorative power of electricity network congestion management models. Insights from a grid model comparison experiment[END_REF]) requires a more detailed discussion that goes beyond the mere description of a comparison framework. Regarding the market results, the results of the corresponding list in Table 5-1 can used for the model comparison. As it can be observed, besides the options in the secondary results list, all other results constitute time series data, thus resulting in comparing two-dimensional data for each model, e.g., a temporal and a spatial dimension for electricity prices. Therefore, the main goal of the comparison of models' output consists of deriving meaningful values for the differences of these data.

Extracting information from the market level results can be achieved by calculating indicators that reduce the dimensions of the original data such that they provide insight on their properties and ultimately reveal properties of the models as well. In this framework, four main ways are suggested for achieving this goal, accompanied with additional visualizations for better comprehension:

 Reduction of each time series independently by deriving additional results.  Reduction of each time series independently based on an operator.  Reduction of pairs of time series based on a distance metric.  Elimination of the spatial dimension by focusing on a single region of interest.

The application of each method and its interpretation depends on the original result including its properties and its significance analyzing the model's behavior. Similarly, the selection of the specific operators and distance metrics depends on each case and the corresponding usefulness. Figure 4 summarizes the reduction methods of the time series results suggested by the existing framework. The recommendations stem primarily from the applicability as well as their usefulness to interpreting model behavior. In fact, in many cases comparing the full time series is not necessarily more useful than comparing the respective averages. In addition, some of the results are more important for model comparison than others that may be more sensitive or too complicated to interpret. The percentile converter operator can be understood as an alternative to the kurtosis of the respective probability density function (PDF) that can provide a value with more direct interpretation for energy systems. It can be essentially viewed as a metric of the curvature of the corresponding duration curve and measures the area for a given percentile as shown in Figure 5. For the case of VRES curtailments this would indicate whether the corresponding energy is concentrated over a few incidents with high volume or are more uniformly distributed over time. Regarding the indicators that measure the distance of time series, two different categories can be distinguished: distance metrics applied on the original time series data (time series metrics) and metrics applied on the derived probability density function (PDF metrics). Both categories can provide different information that may be useful depending on the measured result. For instance, the correlation coefficient may show how similarly two time series fluctuate over time, while measuring the similarity of the shapes of the corresponding PDF can show whether the two data sets exhibit similar distributions in a more averaged manner. A better understanding is given in Table 5-2, where they are also applied to exemplary results.

A better understanding of the suggested indicators and metrics can be achieved via a discussion over data produced by market simulations rather than random time series. In this way the indicators can be viewed within the respective context, hence illustrating their usefulness and potential limitations for power system comparison. Moreover, the analysis will focus only the generation output and electricity prices results, since these are proven to be the most relevant for model comparison and can also sufficiently illustrate the relevance for most of the afore-mentioned operators and metrics. This is not entirely unexpected, since the information of how much energy each unit will produce and each time and what price it will receive constitutes the primary result of every dispatch model. Nevertheless, it also appears that these results are the most useful for model comparison, since model behavior can be more easily tracked via them, while also patterns in how similarly models behave become easier to identify.

Generation

Generation output constitutes an extensive set of data that is both very difficult and not useful to compare in its primary form. Since models do not use the same input data or methods for generation units, it becomes more advantageous to aggregate them in both time and space. The most popular and useful way to accomplish that consist of the energy mix, where power units are grouped based on their fuel or technology type, e.g., onshore wind or natural gas CCGT. The corresponding classification depends on the context of the desired information and one obvious selection can be the classification of the harmonization process, nevertheless, the number of generation types can be further reduced for better visualization purposes.

Figure 6 shows the annual energy mix for all investigated models and their common countries including the respective data from ENTSO-E [START_REF] Entso-E | Statistics and Data[END_REF] for the year 2016 in both absolute and relative values. It is considered the most important indicator regarding a model's performance with respect to the market behavior since it is comprehensive enough as well as easily comprehensible to use for interpretation and comparison. For instance, it can become relatively easy to observe that most models exhibit high nuclear production in France because of overestimation of the available capacity or low production from natural gas because of simplistic market methods or limited modeling of CHP units. Nevertheless, a more quantitative indicator can also be derived by measuring the average difference of the energy mix, weighted over all countries and generation types such that differences in small categories, e.g., oil in Denmark, do not skew the results. Figure 7 shows a heatmap of this indicator, where it can become more apparent which models behave more similar than others.

Electricity prices

Electricity prices constitute the second most important result since it also includes comprehensive information about a model's behavior, while also it is relatively easy to compare since each biding zone only has one time series. Using electricity prices, we can also demonstrate some of the main aspects of time series comparison in power system modeling as well as evaluating the various types of results for model comparison. Covering all indicators on all results in Table 5-1 and their respective interpretation would go beyond the description of a comparison framework, while also the corresponding prioritization may depend on the results themselves as well as the context of the comparison. Therefore, the primary aspects of time series comparison can be illustrated via electricity prices, where the main conclusions can be then extended to the other types of results as well.

Time series reduction by descriptive statistics

The most direct approach to comparing time series consists of the independent reduction into a single value via descriptive statistics or derivation of secondary results. Besides the 'sum' or the 'percentile converter' operators that do not generate any useful value, all other operators can provide values that can be used for comparing electricity prices. Some of the most directly comprehensible operators for electricity prices consist of the first two moments that can measure the average behavior and spread over the mean value correspondingly. An additional advantage of this type of time series reduction consists of the ability to use hierarchical clustering in order to identify clusters of models with respect to that operator and measure a respective distance between the clusters. After reduction, a single vector with the various countries as coordinates corresponds to each model. These data can then be clustered using hierarchical clustering for a given distance metric, such as Euclidean, and a linkage criterion, such as minimization of the cluster variance.

Figure 8 shows the mean and standard deviation of electricity prices for all models and the harmonized countries, including data from ENTSO-E [START_REF] Entso-E | ENTSO-E Transparency Platform[END_REF]. Since models tend to behave similarly, it becomes easier to extract conclusion from these visualizations. For instance, it can be observed that, for the mean value, most models have small variations among the countries and similar to each other as well as ENTSO-E. However, for the standard deviation value, it can be seen that models tend to have significantly less spread in comparison to the ENTSO-E values, which may be an indicator that models do not sufficiently capture all the temporal dynamics involved as well as strategic behavior. The dendrogram produced for the 'mean' operator further shows which models are closer to each other over all countries.

Time series comparison in pairs by distance metrics

The third way of comparing model results consists of the comparison of pairs of time series. As discussed earlier, there are two main categories for computing distance or similarity indicators, one applied directly on the original time series and the second applied on the respective PDF. In order to better understand the nuances behind each approach and the respective metric, we consider the electricity price results for Germany using the model PoweFlex as reference and compare to the corresponding results from the models ISAaR and Europower. The reason for this selection is illustrated in Table 5-2, where it can be seen that different indicators can show different, even opposite, results with respect to the distance (closer marked with green) to the two models.

There exist a variety of metrics to measure the similarity of time series and they have been in a variety of contexts. Such metrics for instance may focus on measuring the correlation, error or apply geometric or more complex approaches. Table 5-2 includes a non-exhaustive selection of such metrics for both time series and their PDF. Except for the Wasserstein metric that appears to show insignificant differences and hence is not deemed useful for model comparison in this context, the remaining metrics show a similar behavior. That behavior consists of the expected dependency on the difference between the mean values. Figure 9 shows all three time series for the month September. It can be observed that Europower correlates to PowerFlex better than ISAaR, nevertheless with a clear positive offset, while ISAaR remains in the similar range but with significantly less correlation.

It follows that two main indicators can be extracted that are mostly useful for model comparison. The first indicator consists of the difference of the mean values of the two time series and the second indicator consists of one or more metrics that measure the distance of the normalized time series (i.e., centered around their mean values). The first indicator measures the average distance and can be connected to the input data such as the bidding prices of generators. The second indicators can also be related to the input data, e.g., the distribution of bids, however, it also reveals additional information about the behavior of the model, assuming a harmonized residual load. For instance, high correlation and high shape similarity of the time series and the corresponding PDF may indicate a higher similarity of the model methodologies. Apart from error scores which are not particularly useful, since a close match is not expected, all other metrics exhibit the same trend, i.e., exhibit shorter distances for more similar shapes. However, it is not straightforward to compare the results of different metrics since they can be interpreted differently and have different "units". For that reason, it is recommended to use the most intuitive ones for the specific context. For instance, the "max difference" metric is easier to interpret, whereas Frechet and DTW distances are less intuitive for power system modeling and more difficult to compute. Comparing PDFs instead of the time series directly, additionally holds the advantage of capturing a more average behavior that can be more robust to rare but high differences in the time series or to the modeling of VRES production. As it was shown earlier using reduction operators, even average results can differ substantially and may pose difficulties in comparing models. Hence, analyzing in higher detail is unlikely to provide useful information for the models. Comparing PDFs constitutes a recommended compromise of analyzing time series in detail and usefulness for understanding. Figure 10 shows the PDFs of the three selected time series as well as ENTSO-E. It can be observed here as well, that PowerFlex and ISAaR are closer on average, however PowerFlex and Europower have a more similar shape. One of the most intuitive methods to quantify that consists of the Bhattacharyya distance applied on the normalized curves, a metric which is based on measuring the curves overlap.

Discussion of grid model formulations and their impacts

Besides market results, an important aspect of comparing power system models also consists of comparing results from grid simulation and redispatch calculation. Such results may include line loadings, congestion work or amount and cost of redispatch and curtailments. A similar approach is also recommended for this case, where the focus is primarily on average values and visualizations, since the various models may have different grid data, regionalization methodologies, market results as well as congestion management methods. However, a more detailed discussion is necessary, which lies beyond the scope of this paper. Hence, different model formulations and its impact on grid results are presented in further detail in [START_REF] Hobbie | Impact of model parametrization and formulation on the explorative power of electricity network congestion management models. Insights from a grid model comparison experiment[END_REF]. Furthermore, the learnings of grid modelers in the process of model development concerning the validity of network congestion management results are also discussed in [START_REF] Hobbie | Impact of model parametrization and formulation on the explorative power of electricity network congestion management models. Insights from a grid model comparison experiment[END_REF].

Discussion and Conclusions

It can be observed that despite all models attempt to describe the same real world system, the variety of the different methods and input data (cf. section 3) for the different modeling contexts result in significant differences in model output. Moreover, model output consists of a variety of results that also not necessarily coincide. Therefore, a detailed quantitative comparison such as deriving a single distance or error-like value between two models becomes impossible. Similarly, to how each model is developed within a specific context, model comparison may also depend on the comparison context. For instance, whether prices or curtailments are considered more important. Nevertheless, even in such cases, a detailed comparison may still not be straightforward due to significant modeling differences. Hence, it can be concluded that the German/European transmission grid models considered in this comparison have been built against the background of different research questions going along with different model requirements. As a consequence, the models might look quite similar by comparing the grid topology in Germany or by comparing the number of nodes and lines considered, but individual line's parameters or the spatial distribution of generation and load can differ significantly from one model to another leading to a mismatch in line specific power flows and nodal redispatch volumes. Additionally, the regions/countries covered by the participating transmission grid models have been identified as an important influencing factor. The harmonization process needs some kind of fallback solutions to ensure that all models see a comparable reference situation. On the one hand, this was ensured by the harmonization process. On the other hand, this can be ensured by considering additional exchanges with countries that are not explicitly considered in the transmission grid model for models that only cover a smaller region.

Because of the afore-mentioned challenges, the proposed framework consists of a flexible workflow and a variety of tools (cf. section 5) instead of a rigorous algorithm. Regarding the part of results comparison, it is similarly recommended to concentrate on average behavior and on the results that are easier to interpret, for example prioritize the energy mix and electricity prices, instead of the cross-border exchanges. It may be possible to also compare time series, rather than only averages; nevertheless, it is also recommended to use metrics that only measure the average distance and the shape similarity of either the original time series or the respective PDF, instead of quantifying the differences via measuring an error metric. The various indicators that are proposed are demonstrated for a specific context and only discussed for electricity prices as well as merely recommended, since each individual comparison may be applied in a different context and the necessary tools to reach useful conclusions may depend on the results themselves. This implies that a significant amount of freedom is left to the researcher, nevertheless, this framework can provide a specific structure on how to approach such a task as well as valuable lessons learned and a catalog of tools that are discussed and may be considered useful.

Finally, it can be concluded that the developed model comparison framework is able to deliver insights in the inner working principles of the considered models as well as in the interactions of different modelling techniques and results. Hence, the presented framework to compare power system models can be considered as a proof of concept. Furthermore, the framework is based on the open energy platform to ensure future interoperability. By using the OEP as a basis the developed framework ensures transparency in the total workflow and supports the idea of openness in power system modelling.

ELMOD

The model ELMOD uses optimal power flow calculations to analyze the interaction between generation and the transmission system regarding the operation of the grid and investment decisions [START_REF] Schönheit | Elmod documentation: Modeling of flow-based market coupling and congestion management[END_REF] [32] [START_REF] Hobbie | Where to Install Wind Capacities? -Optimal Deployment from an Energy System Perspective[END_REF]. The model was developed at the chair of energy economics of Technische Universität Dresden -Chair of Energy Economicsand has been used for several energy system studies. The European transmission system and the corresponding generation infrastructure is modelled in a great detail at a level of transmission grid nodes. The load flow calculations are approximated by a direct current approach. In its basic version the main aim of ELMOD is to analyze effects of renewable energy integration on the European transmission system. This includes various aspects regarding market design, congestion management, and future developments of the electricity sector. Moreover, latest research conducted with ELMOD involve studying flow-based market coupling. [START_REF] Mueller | The eGo grid model: An open source approach towards a model of german high and extra-high voltage power grids[END_REF]. The model was developed by several institutions in the context of the openeGo project [START_REF] Mueller | The eGo grid model: An open source approach towards a model of german high and extra-high voltage power grids[END_REF]. eTraGo uses PyPSA [START_REF] Brown | PyPSA: Python for Power System Analysis[END_REF] for DC load flow calculations to determine the cost-optimized dispatch of power plants and optimal storage capacities. The German transmission grid is modeled together with the 110 kV grid level with a total of about 11,300 grid notes and neighboring countries are represented by a single grid node. The model calculates weather-dependent generation data and uses standardized load profiles to derive demand data. The share of renewable energy sources varies in three scenarios for the years 2016, 2035 and 2050. In addition to the optimized costs for the transmission grid, eTraGo also calculates the hourly time series of the active power for each grid node (from 110 kV to 380 kV). [START_REF] Tlili | Role of electricity interconnections and impact of the geographical scale on the french potential of producing hydrogen via electricity surplus by 2035[END_REF]. It models the European electricity system in high temporal and spatial resolution, with approximately 4000 grid nodes, and includes constraints on thermal, hydro and RES generation as well as load shifting. The model consists of a set of linear optimization problems where the total cost of the system's operation is minimized considering grid constraints, where the DC approximation is used for modeling the power flows. For future scenarios, an upgraded European grid can be used, as well as future electricity consumers like battery electric vehicles and heat pumps.

MarS/ZKNOT

The model MarS from the RWTH Aachen University -Institute for High Voltage Equipment and Grids, Digitalization and Energy Economicsdetermines the optimal dispatch of hydrothermal power plants in the ENTSO-E region under the consideration of flexibility options [START_REF] Alvarez | Novel Methodology for Selecting Representative Operating Points for the TNEP[END_REF] [45] [START_REF] Bongers | Impact of curtailment of renewable energy sources on high voltage network expansion planning[END_REF]. To this end, it uses the results of a regionalization approach for determining the generation of renewable energy sources and the electricity demand [START_REF] Lück | Bewertung regulatorischer Steuerungsinstrumente zur Synchronisierung des Zubaus von Anlagen auf Basis erneuerbarer Energien mit dem deutschen Übertragungsnetz[END_REF]. Using this information for all grid nodes the operation of the transmission grid is simulated by the model ZKNOT [START_REF] Eickmann | Simulation der Engpassbehebung im deutschen Übertragungsnetzbetrieb[END_REF]. The model uses AC load flow calculations to determine the use of the network capacity both in conventional operation scenarios and in the (N-1) scenario. Thus, ZKNOT can identify technical constraint violations. ZKNOT uses optimization to control network elements like phase shifters with variable modulation degrees and high-voltage direct-current power lines. Moreover, power plants and facilities for generating renewable energy are controlled such that they are capable to compensate for the constraint violations with minimal costs and a minimal number of interventions.

MILES

The model MILES from TU Dortmund University -Institute of Energy Systems, Energy Efficiency and Energy Economics (ie3)is a tool for simulating the European electricity market and transmission grid to answer technoeconomical questions regarding the energy system [START_REF] Teuwsen | Gegenüberstellung divergenter Zukunftsszenarien des Energieversorgungssystems[END_REF] [50] [START_REF] Spieker | Europäische Strommarkt-und Übertragungsnetzsimulation zur techno-ökonomischen Bewertung der Netzentwicklung[END_REF]. The modules of MILES cover the whole process chain of the strategical network development planing. For this purpose the tool determines the electricity demand and the decentralized generation on an hourly basis considering sector coupling with new electrical consumers. Further, MILES calculated the cost optimal dispatch of conventional power plant to serve the residual load and the result of electricity trading based on the dispatch decisions. MILES uses a detailed model of the transmission grid to consider technical restrictions of the grid by determining the status of grid elements. To this end, the model uses load flow calculations. Thus, it is possible to identify necessary congestion management actions for resolving bottlenecks in the transmission grid.

Figure 16 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the MLES simulation framework. The German transmission grid 2016 consist of 414 AC lines at 380 kV level, 378 AC lines at 220 kV level and 10 HVDC lines (wind offshore and cross-border connections). In 2030, the German transmission grid consist 583 AC lines at 380 kV level, 174 AC lines at 220 kV level as well as 36 HVDC lines (wind offshore connections, cross-border connections and internal HVDC lines in Germany). -Energy & Climate Divisionis a European electricity market model that determines an optimal dispatch of the power plants and the optimal operation of storage systems and flexibility options minimizing generation costs in order to serve the electricity demand and the need for balancing power [START_REF] Koch | Modellgestützte Bewertung von Netzausbau im europäischen Netzverbund und Flexiblitätsoptionen im deutschen Stromsystem im Zeitraum 2020 -2050[END_REF] [START_REF] Koch | Dispatch of Flexibility Options, Grid Infrastructure and Integration of Renewable Energies Within a Decentralized Electricity System[END_REF] [57] [START_REF] Ritter | Effects of a delayed expansion of interconnector capacities in a high res-e european electricity system[END_REF]. It models the transmission grid of Germany with about 320 grid nodes and, depending on the scenario framework, it includes also the planed highvoltage direct current lines. The load flows in the German grid are approximated using a linear DCapproach and a PTDF-matrix. The required redispatch is determined using an optimization model for minimizing line congestion at the lowest possible cost. The specific costs for line congestion are determined as part of a sensitivity analysis. For pumped storage power plants, intertemporal constraints are considered. PowerFlex represents the single ENTSO-E countries by using one grid node. The countries are coupled through interconnection point (transport-model approach).

Figure 1 :

 1 Figure 1: Workflow of the comparison framework

Figure 2 :

 2 Figure 2: Geographical scope of data harmonization and maximum spatial extent of individual models

Figure 3 :

 3 Figure 3: Predefined tables and views of the database for market results

Figure 4

 4 Figure 4 Sketch for possible reduction methods of primary market results in order to derive suitable comparison indicators.

Figure 5 :

 5 Figure 5: Exemplary illustration of different percentile converter indicators for different duration curves and percentiles. The data corresponds to the wind offshore profiles of Germany for the models miles and europower.

Figure 6 :

 6 Figure 6: Annual energy mix for all investigated models and their common countries including the respective data from ENTSO-E for the year 2016 in both absolute and relative values.

Figure 7 :

 7 Figure 7: Heat map of the average difference of the energy mix, weighted over all countries and generation types

Figure 8 :

 8 Figure 8: Mean (a) and standard deviation (b) of electricity prices for all models and the harmonized countries as well as dendrogram (c) for the electricity prices reduced by the mean operator.

Figure 9

 9 Figure 9 Electricity prices for Germany in September for the models PowerFlex, ISAaR and Europower as well as ENTSO-E.

Figure 10

 10 Figure 10 Probability density function for the electricity prices of Germany for the models PowerFlex, ISAaR and Europower as well ENTSO-E.

Figure 11

 11 Figure 11 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the ELMOD model. The 2016 model includes 609 nodes and 975 lines (966 AC and 9 DC). The 2030 model includes 646 nodes and 1077 lines (1020 AC and 57 DC).

Figure 11

 11 Figure 11 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the ELMOD model

Figure 12

 12 Figure 12 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the eTraGo model.

Figure 12

 12 Figure 12 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the eTraGo model

Figure 13

 13 Figure 13 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the Europower model.

Figure 13

 13 Figure 13 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the Europower model

Figure 14

 14 Figure 14 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the ISAaR model.

Figure 14

 14 Figure 14 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the ISAaR model

Figure 15

 15 Figure 15 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the MarS/ZKNOT model.

Figure 15

 15 Figure 15 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the MarS/ZKNOT model

Figure 16

 16 Figure 16 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the MILES model PERSEUS The model family PERSEUS from Karlsruhe Institute of Technology (KIT) -Institute for Industrial Production (IIP)is based on a bottom-up energy system model that minimizes system costs [52] [53] [54]. It comprises the EU28 countries and it can determine the power plant expansions until the year 2050. It has different modules that can be classified based on applications they are used for and applied methodologies. Based on the strategic research question, PERSEUS determines optimal energy balances and flows. It models the individual nodes of the German transmission grid (220 kV/380 kV) and the cross-border transmission lines to the neighbouring countries. The grid model is coupled to a NTC based 1-node transport problem of the European electricity trading. Under the consideration of grid constraints (DC approach) and cross-border power line capacities, PERSEUS determines the optimal power plant dispatch. The TANGO grid model is used to simulate the transmission grid operation [20]. It includes the expansion path for the transmission grid (220/380 kV) of the Core Capacity Calculation Region (core CCR) from 2016 until 2035. The model uses AC optimal power flow to determine feasible operation points and necessary measures for congestion management. Countries outside the Core region are modelled with a single node per country and coupled through the interconnectors with each other and to the grid region.

Figure 17

 17 Figure17shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the PERSEUS/TANGO simulation framework. The German transmission grid 2016 consist of 939 nodes at 505 substations, 602 AC lines at 380 kV level, 495 AC lines at 220 kV level and 15 HVDC lines (wind offshore and cross-border connections). In 2030, the German transmission grid consist of 1050 nodes at 561 substations, 884 AC lines at 380 kV level, 346 AC lines at 220 kV level as well as 48 HVDC lines (wind offshore connections, cross-border connections and internal HVDC lines in Germany).

Figure 17

 17 Figure 17 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the PERSEUS/Tango modelPowerFlexThe model PowerFlex from Öko-Institut e.V. -Energy & Climate Divisionis a European electricity market model that determines an optimal dispatch of the power plants and the optimal operation of storage systems and flexibility options minimizing generation costs in order to serve the electricity demand and the need for balancing power[START_REF] Koch | Modellgestützte Bewertung von Netzausbau im europäischen Netzverbund und Flexiblitätsoptionen im deutschen Stromsystem im Zeitraum 2020 -2050[END_REF] [START_REF] Koch | Dispatch of Flexibility Options, Grid Infrastructure and Integration of Renewable Energies Within a Decentralized Electricity System[END_REF] [57][START_REF] Ritter | Effects of a delayed expansion of interconnector capacities in a high res-e european electricity system[END_REF]. It models the transmission grid of Germany with about 320 grid nodes and, depending on the scenario framework, it includes also the planed highvoltage direct current lines. The load flows in the German grid are approximated using a linear DCapproach and a PTDF-matrix. The required redispatch is determined using an optimization model for minimizing line congestion at the lowest possible cost. The specific costs for line congestion are determined as part of a sensitivity analysis. For pumped storage power plants, intertemporal constraints are considered. PowerFlex represents the single ENTSO-E countries by using one grid node. The countries are coupled through interconnection point (transport-model approach).

Figure 18

 18 Figure 18 shows the topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the PowerFlex model. The German transmission grid 2016 consist of 310 nodes, 350 AC lines at 380 kV level, 118 AC lines at 220 kV level and 6 wind offshore connections. In 2030, the German transmission grid consist of 316 nodes, 413 AC lines at 380 kV level, 82 AC lines at 220 kV level, 7 DC lines and 6 wind offshore connections.

Figure 18

 18 Figure 18 Topology of the German transmission grid 2016 (left) and 2030 (right) as implemented in the PowerFlex model

Table 4 -1: Exemplary data points (excerpt) considered to compare input data and sources of each model Methodological step Exemplary data points considered in comparison of input data Scenario definition

 4

	Market	 Power plant data base, load profiles, NTC-Values
	simulation	 Commodity prices, outages & availabilities
	Grid
	simulation and
	congestion
	management
	simulation

 Model based endogenous scenario generation  External scenario data, e.g., NDP or TYNDP, as an input Regionalization  Current fleet / assets / portfolio in models' base year  Land cover / usage data for RES potential areas  Social and structural data, like GDP or population density Time-series generation  Profiles vs. weather data and historic full load hours (FLH)  Solar and wind power plant model to transform weather data  Social & structural data, like GDP, for sectoral demand forecasts

Table 4 -2: Exemplary data points (excerpt) considered to compare data processing and simulation methods of each model Methodological step Exemplary data points considered in comparison of methods Scenario definition

 4

	Congestion	 Consecutive steps (real world) vs. integrated OPF (academic)
	management	 Power flow controlling devices: HVDC, PST
	simulation	 Consideration of time coupling

 Model based endogenous scenario generation  External scenario data, e.g., NDP or TYNDP, as an input Regionalization  Top-down vs. bottom-up  Dis-/Aggregation methods from/to grid nodes Time-series generation  Weather data vs. profiles Market simulation  Regional scope  Nodal pricing (OPF) vs. zonal NTC energy only Grid simulation  AC vs. DC vs. PTDF  Consideration of grid losses  Dynamic line rating  (N-1)-criterion vs. security margins  Power flow controlling devices: PST, HVDC

Table 5 -1: Minimal model results for comparison framework at market level and grid level. Results marked in red are not shared, instead secondary results are used.

 5

	Market level	Grid level
	Time series	Time series
	 Generation per unit/timestep [MW]	 Upwards redispatch per node/timestep
	 Electricity price per zone/timestep	[MW]
	[€/MWh]	 Downwards redispatch per node/timestep
	 Cross-border power flow per	[MW]
	interconnection/timestep [MW]	 VRES curtailments per node/timestep
	 VRES curtailments per zone/timestep	[MW]
	[MW]	 Congestion work per line/timestep [MW]
	 CO 2 emissions per country/timestep	 Amount of congestion per line/timestep
	[Gtons]	[h]
	 Charging/discharging per zone/timestep	 Overload per line/timestep [%]
	[MW]
	 State of charge per zone/timestep [GWh]
	 Load curtailments per zone/timestep
	[MW]
	Secondary results	Secondary results
	 Energy mix per zone [TWh]	 Upwards redispatch per node [TWh]
	 Net balances per zone [TWh]	 Downwards redispatch per node [TWh]
	 Price convergence per region [%]
	 Price convergence per interconnection
	[€/MWh]

 VRES curtailments per node [TWh]  Congestion work per line [TWh]  Amount of congestion per line [h]  Maximum overload per line [%]

Table 5 -2: Exemplary distance metrics and their values when comparing isaar and europower to powerflex for the electricity prices in Germany. The green color indicates the lowest distance and the red color indicates that the numbers may be misleading.

 5

		Metric	Original	Normalized	Comments
			ISAaR	Europower	ISAaR	Europower
		Means difference	-0.36	-4.63	0	0	Distance between the
							mean values
		Correlation	0.16	0.83	0.16	0.83	Highest score shows
	series	coefficient					the highest correlation
	Time	Max difference	35.6	17.2	35.2	12.6	Maximum difference at any timestep
		MAPE	0.17	0.17	6.1	1.1	Linear error, small

Acknowledgements

Acknowledgements: We would like to thank all partners and project members for their contributions

Funding: This research was funded by the Federal Ministry for Economic Affairs and Energy in the 6. energy research funding program, grant number 03ET4074.

Appendix Description of the models included

The models under study belong to the partners involved in the MODEX-NET project. From all the information contained in each of the models, MODEX-NET focuses on the transmission grid in Germany. The transmission grids as implemented in the different models are considered in a status quo scenario for 2016 and a future scenario for 2030.


Isabelle Fobis-Loisy

Yvon Jaillais
email: yvon.jaillais@ens-lyon.fr

Feeling the pressure: a mechanical tale of the pollen tube journey through the pistil

The pollen tube grows inside the pistil to carry the male gametes to the ovule. During this journey, it invades diverse tissues and must sense and adapt to abrupt changes in its mechanical environment (mechanical transitions). In this issue, a study presents a Receptorlike-kinase/Rho-GTPase module that regulates such transition.

The pollen tube is a tip growing cell that navigates thought the female tissues of the pistil to deliver the immobile sperm cells to the ovules. The pistil is a source of diffusible chemical attractants for the pollen tube [START_REF] Mizuta | Chemical signaling for pollen tube guidance at a glance[END_REF]. Mechanical cues also contribute to the proper pollen tube growth and guidance [START_REF] Reimann | Durotropic Growth of Pollen Tubes[END_REF][START_REF] Riglet | KATANIN-dependent mechanical properties of the stigmatic cell wall mediate the pollen tube path in Arabidopsis[END_REF][START_REF] Sanati Nezhad | Quantification of cellular penetrative forces using lab-on-a-chip technology and finite element modeling[END_REF]. In Arabidopsis, the pollen tube has to invade a series of tissues with different mechanical properties on its path to the ovule (Figure 1). It thus encounters several sharp "mechanical transitions", which correspond to boundary areas where the local mechanical environment of the pollen tube change drastically. For example, it first germinates on the open surface of stigmatic cells, but then penetrates the stigmatic cell walls to grow within this rigid layer, which provides guidance cues to the pollen tube [START_REF] Riglet | KATANIN-dependent mechanical properties of the stigmatic cell wall mediate the pollen tube path in Arabidopsis[END_REF] (Figure 1). The pollen tube then progresses within the intercellular space of the transmitting tract [START_REF] Mizuta | Chemical signaling for pollen tube guidance at a glance[END_REF]. Whereas the style transmitting tract is a compact tissue, the ovary transmitting tract is much more open as it undergoes program cell death to facilitate pollen tube passage [START_REF] Crawford | The NTT gene is required for transmitting-tract development in carpels of Arabidopsis thaliana[END_REF] (Figure 1). Other mechanical transitions include the pollen tube emergence from the transmitting tract into the septum, its growth on the funiculus surface (which is open on the ovary cavity), and ultimately its entrance in the narrow micropyle (Figure 1). It remains unclear how the pollen tubes sense and adapt to these drastic variations in their surrounding mechanical environment. In this issue of Developmental Cell, Zhou et al. (2021) describe a Receptor-Like-Kinase (RLK)/Rho-GTPase module, which allows the pollen tube of Arabidopsis thaliana to respond to the sharp mechanical transition encountered at the style/ovary boundary.

BUDDHA'S PAPER SEAL-1 (BUPS1) encodes a pollen-expressed RLK from the Catharanthus roseus RLK1L-like (CrRLK1L) subfamily, which is required for the transmission of the male gamete in Arabidopsis thaliana [START_REF] Ge | Arabidopsis pollen tube integrity and sperm release are regulated by RALF-mediated signaling[END_REF]. The tips of bups1 pollen tubes rupture when enter the ovary (Zhou et al., 2021). The style/ovary boundary corresponds to a sharp mechanical transition (Figure 1), which suggests that BUPS1 might be involved in sensing or responding to changes in the pollen tube local mechanical environment. To test this hypothesis, the authors used a semi-in-vitro assay where wild-type pollen tubes grow within pistils cut after the style, and then elongate in a culture medium. In this system, bups1 pollen tube tips ruptured when emerging from the cut. They also used three in planta situations (immature pistil, the pistil of Thellungiella salsuginea, and the pistil of the no transmitting tract (ntt) mutant) in which the transmitting tract of the ovary remains compact, similar to the style. Using these systems, they selectively removed the mechanical transition at the style/ovary boundary, which allowed the bups1 pollens to elongate much deeper within these pistils. Taken together, these data suggest that bups1 pollen tubes are fully functional in a mechanically stable environment but fail to maintain their integrity when their mechanical environment is changing.

To simulate the mechanical transition encountered by the pollen tube at the style/ovary boundary, Zhou et al. (2021) used an elegant microfluidic system with microchannels of varying diameters. This device recapitulates the mechanical situation of (i) the mature pistil (a narrow region that mimic the style followed by a wider microchannel that mimic the ovary), (ii) the immature, Thellungiella salsuginea or ntt pistils (a long narrow region) and (iii) a pressure-free control. When compared to the wild type, the bups1 tubes elongated longer in the long narrow region and exhibited a much higher rupture frequency when emerging from a narrow region into a wider microchannel. Importantly, in a constant mechanical environment, the bups1 and wild-type pollen tubes were identical (i.e. similar cell wall strength and composition, turgor pressure). However, only the wild-type but not bups1 pollen tubes were able to adjust their cell wall composition upon increased tensions/decreased compression. Indeed, in the microfluidic chips, demethyl-esterified pectins accumulate at the tip of Arabidopsis wild-type pollen tubes when emerging from a narrow channel. This is thought to enhance wall rigidity thereby allowing the tip to resist to mechanical changes [START_REF] Bidhendi | Relating the mechanics of the primary plant cell wall to morphogenesis[END_REF]. By contrast, in bups1 pollen tubes, this accumulation is not detected, suggesting that BUPS1 might regulate demethyl-esterified pectin polar secretion and hence cell wall rigidity during this mechanical transition (Zhou et al., 2021).

Rho-of-plant-1 (ROP1) integrates tip-localized polar secretion of wall polymers and mechanics of the pollen tube [START_REF] Luo | Exocytosis-coordinated mechanisms for tip growth underlie pollen tube growth guidance[END_REF]. Zhou et al. (2021), found that the kinase domain of BUPS1 interacts with all pollen-expressed ROP Guanidine Exchange Factors (GEF), which are direct ROP1 activators. Accordingly, ROP1 activity is rapidly induced, in a BUPS1-dependent manner, upon acute tensile stress at the pollen tube tips (e.g. induced by pectinase treatment or emergence of the tube from the narrow region of the microchannel). Furthermore, when a constitutive active ROP1 is expressed in bups1 pollen tube, it partially restored pollen tube growth and fertility. Together, these results show that BUPS1 acts upstream of GEFs/ROP1 to regulate pollen tip rigidity and support tube growth at the style/ovary boundary. BUPS1/ROP1 not only induce local pectin secretion, but also the polar exocytosis of RAPID , which are required for pollen tube integrity during the style-to-ovary transition (Zhou et al., 2021). RALF4/19 are extracellular ligands that bind to and activate BUPS1 [START_REF] Ge | Arabidopsis pollen tube integrity and sperm release are regulated by RALF-mediated signaling[END_REF]. Thus, stimulating RALF4/19 polar secretion triggers a positive feedback loop that self-amplifies BUPS1-dependent signaling at the pollen tube tips. The RALFs/BUPS1/ROP1 module could work downstream of a yet uncharacterized tensile stress sensor, such as for example RLKs, stretch-activated channels or cytoskeleton components [START_REF] Bacete | The Role of Mechanoperception in Plant Cell Wall Integrity Maintenance[END_REF]. In this scenario, such unknown mechanosensor would initiate the feedback loop within the RALFs/BUPS1/ROP1 module and the self-amplifying properties of this module would then be used to execute rapid and local cell wall rearrangements. Moreover, because both RALFs and CrRLK1L receptors directly interact with cell wall components [START_REF] Bacete | The Role of Mechanoperception in Plant Cell Wall Integrity Maintenance[END_REF], it is also tempting to speculate that they could directly act as mechanosensors at the pollen tip. However, in this case, the molecular mechanisms that would enable to physically sense the mechanical stimuli within the pollen cell wall remain to be determined. et al., 2020;Zhou et al., 2021;[START_REF] Mizuta | Chemical signaling for pollen tube guidance at a glance[END_REF]. SEM: scanning electron microscopy, TT: transmitting tract.

Figure 1 :

 1 Figure 1: Mechanical transition encountered by the pollen tube on its way to the ovule. Schematic representation of an Arabidopsis pistil, highlighting boundary regions with "mechanical transition" (i.e. abrupt changes in mechanical environment). Yellow stars represent transition toward a higher compressive environment, orange stars represent the reverse situation. Micrographs on the right represent pollen tube growth in wild type and/or mechanically challenged mutants: katanin pistil or bups1 pollens (images modified from Rigletet al., 2020;Zhou et al., 2021;[START_REF] Mizuta | Chemical signaling for pollen tube guidance at a glance[END_REF]. SEM: scanning electron microscopy, TT: transmitting tract.