Ph.D Alessandro Tibaldi

Msc F L Bonali

Fabio Vitello

Emanuel Delage

Pareskevi Nomikou

Varvara Antoniou

Ugo Becciani

Benjamin Van Wyk De Vries

Mel Krokos

Malcolm Whitworth

Van Wyk

Real world-based immersive Virtual Reality for research, teaching and communication in volcanology

Keywords: Volcanology, Teaching & Scientific Communication, Immersive Virtual Reality, Head-

Direct outcrop observation and field data collection are key techniques in research, teaching and outreach activities in volcanic areas. However, very often outcrops are of difficult or inaccessible access, such as in areas with active volcanoes or steep cliffs. Classical remote-sensing surveys by satellites or airplanes are expensive, rarely reach sufficient resolution to allow high quality 3D visualisation of volcanic features, and do not facilitate mapping of vertical cliffs. We describe a novel approach that uses the immersive Virtual Reality (VR) based on real world 3D Digital Outcrop Models (DOMs) from images surveyed by unmanned aerial vehicles (UAV). 3D DOMs are built up using the Structure from Motion (SfM) photogrammetry technique, and a Virtual Reality scene is created using game engine technologies. Immersive real-time exploration of the environment is possible through a head mounted display, e.g. Oculus Rift. Tools embedded in the VR environment allow the user to map polygons, lines, point features, measure orientation, dip, inclination, azimuth, area, thickness and even take virtual photographs. Using three examples of volcanic areas with different geological features, we demonstrate the potential of our approach to allow users to be able to virtually map and measure remotely, and to collect data for research and teaching. Our approach is of paramount importance also for outreach, as it allows non-specialist audiences (e.g. common citizens) to experience and appreciate highly complex volcanic features through customised, hands-on immersive VR tools.

Introduction

Research activity, teaching and learning in volcanological sciences need the collection and observation of data in the field, which typically constitute the backbone of any applied study in petrography, geochemistry, geohazard, and many other areas. Outcrops can often be difficult to access for logistical reasons, or even impossible to inspect, e.g. in the case of steep or vertical cliffs. Data collection can also be dangerous, as in active volcanic areas with explosions, gas, hot fumes, etc., or other areas prone to geological hazards. Also, teaching and learning is classically based on 2D images, although geological objects are 3D; to overcome this problem, university geoscience courses typically include extensive fieldwork programmes, but these involve expensive and time-consuming trips.

In the case of extra-university communication addressing audiences within the society at large, including administrators, politicians, media and individual citizens, immersive Virtual Reality (VR) can allow different target groups to experience volcanic features in inclusive and novel (or otherwise impossible) ways. The term immersive VR refers to the perception of being physically present in a non-physical world. The perception is obtained by surrounding the user with images, sound or other stimuli, providing the feeling of being immersed in the environment. In Earth Sciences, this is essentially achieved by surrounding images [START_REF] Granshaw | Virtual fieldwork in geoscience teacher education: Issues, techniques, and models[END_REF][START_REF] Trexler | Surface slip from the 2014 South Napa earthquake measured with Structure from Motion and 3-D Virtual Reality[END_REF][START_REF] Zhao | Harnessing the power of immersive virtual reality-visualization and analysis of 3D Earth science data sets[END_REF]. As immersive VR can be fun, and different, it also engages people and allows them to express their thoughts and feeling about natural sites. This results in outreach and embracing communication, a two-way process that can help scientists understand the needs and opinions of society. Moreover, game engines have reached a high level of technological maturity offering rich toolsets of mechanisms for implementing 2D/3D visualisation and exploration workflows in immersive VR environments realised on dedicated game consoles, personal computers or mobile platforms [START_REF] Andrade | Game Engines: A Survey[END_REF]Lawson, 2016;[START_REF] Christopoulou | Overview and Comparative Analysis of Game Engines for Desktop and Mobile Devices[END_REF].

Remote or dangerous volcanic areas have been classically studied by aerial or satellite remotely-sensed images, which have several limitations: 1) high-resolution data are very expensive to cover large-scale geological objects and the resolution can be poor for some targets, 2) it can be challenging to plan a specific survey by an airplane, due to high costs or remoteness of the site, 3) it is impossible to map steep to vertical slopes by images acquired in vertical nadir, and 4) images are mostly 2D. Recently, unoccupied aerial systems (UASs), due to their high imaging capabilities, have been used to study volcanic eruption sites [START_REF] Müller | High-resolution digital elevation modeling from TLS and UAV campaign reveals structural complexity at the 2014/2015 Holuhraun eruption site, Iceland[END_REF], dykes [START_REF] Dering | Review of drones, photogrammetry and emerging sensor technology for the study of dykes: Best practises and future potential[END_REF], volcano-tectonic relations [START_REF] Walter | Underwater and drone based photogrammetry reveals structural control at Geysir geothermal field in Iceland[END_REF][START_REF] Bonali | UAV-based surveying in volcano-tectonics: An example from the Iceland rift[END_REF] and active faults in volcanic areas [START_REF] Rust | A unique 12 ka subaerial record of rift-transform triple-junction tectonics[END_REF], as well as faults and landslides in non-volcanic environment [START_REF] Rathje | Remote sensing for geotechnical earthquake reconnaissance[END_REF][START_REF] Gao | High-resolution mapping based on an Unmanned Aerial Vehicle (UAV) to capture paleoseismic offsets along the Altyn-Tagh fault[END_REF]. UASs are also known as drones, aerial photography systems and unmanned aerial vehicles. Recently, some studies have used the Structure from Motion (SfM) technique to create 3D Digital Outcrop Models (DOMs) of UAS-mapped areas [START_REF] Benassi | Testing accuracy and repeatability of UAV blocks oriented with gnss-supported aerial triangulation[END_REF][START_REF] Burns | Comparison of commercial structure-from-motion photogrammety software used for underwater three-dimensional modeling of coral reef environments[END_REF][START_REF] Cook | An evaluation of the effectiveness of low-cost UAVs and structure from motion for geomorphic change detection[END_REF][START_REF] Pavlis | The new world of 3D geologic mapping[END_REF], but none of these approaches has fully exploited the 3D nature of the modelled structures to allow the user to interact with the full 3D geometry of the model for measurement and mapping purposes. An attempt in this sense has been done by [START_REF] Gonzaga | MOSIS -Multi-outcrop sharing & interpretation system[END_REF], although their approach is just focused on single, limited outcrops.

Here we present an approach that allows a more complete understanding of volcanic features for teaching, learning and research, using immersive VR based on real world 3D DOMs scenario. Our approach, in fact, establishes a framework that provides a unique blend of tools allowing: i) the study of geological or volcanological sites at a wide range of scales, from small outcrops to large areas, ii) wide range of measurements, and iii) wide range of exploration scenarios. Using three examples of volcanic areas with different features, we demonstrate the potential of this type of approach to optimize the users' geological experience by allowing them to move around outcrops and take quantitative measurements. Furthermore, this allows far more embracing contact and exchange with a wider audience; we started to present our immersive VR at schools, national and international exhibitions (e.g. Fig. 1a) open days, and with the public in all sorts of situations, provoking very positive feedbacks and popularizing volcanological sciences and geological features of volcanic areas. We also used the feedback from students and colleagues to improve our software and tools.

3D modelling and data input (Part I)

Our approach consists of creating immersive VR that provides scientists and students with virtual ways to study rock outcrops and collect measurements (e.g. Fig. 1b), replicating classical field activity. The first step consists of creating a high-resolution 3D DOM, which is based off a real world scene, with UAS surveys planned at a scale suitable for the research purposes and using the SfM workflow (e.g. [START_REF] James | Mitigating systematic error in topographic models derived from UAV and ground-based image networks[END_REF][START_REF] James | Optimising UAV topographic surveys processed with structure-from-motion: ground control quality, quantity and bundle adjustment[END_REF][START_REF] Bonali | UAV-based surveying in volcano-tectonics: An example from the Iceland rift[END_REF]. We would like to remark that 3D DOM can be also referred as "Virtual Outcrops (VO)" [START_REF] Xu | Real time and the virtual outcrop improve geological field mapping[END_REF][START_REF] Tavani | Building a virtual outcrop, extracting geological information from it, and sharing the results in Google Earth via OpenPlot and Photoscan: An example from the Khaviz Anticline (Iran)[END_REF] that, with our approach, can be studied in first person. A Wavefront Object File (OBJ) -in the form of a Tiled model -was selected to store the 3D geometry and texture, based on the UAS-collected high-resolution images, as it can be easily imported and managed in the Unity game engine (Unity is a cross-platform game engine developed by Unity Technologies, and a game engine is a software-development environment designed for people to build video games) [START_REF] Krokos | Workflows for virtual reality visualisation and navigation scenarios in earth sciences[END_REF].

The resolution and accuracy of the resulting model depends on the UAS camera resolution, UAS distance to target during photo acquisition, number of established ground control points and level of quality during SfM processing (details in Westboy et al., 2012;[START_REF] Bonali | UAV-based surveying in volcano-tectonics: An example from the Iceland rift[END_REF]. For example, when flying about 25 m above the target, we achieve a resolution of 8 mm/pixel, as shown in our example of the Greek Metaxa mine that will be described below. All surveys in the present work have been done using a quadcopter equipped with a 20 MPX camera, including EXIF (Exchangeable Image file Format) information and GPS coordinates, provided by the integrated Satellite Positioning Systems GPS/GLONASS (referred to the WGS84 datum). Thanks to a built-in high precision 3-axis gimbal, flights are smooth, and the image collection is steady. The model we used provides constantly stable flights thanks to the integrated GPS system, including position holding, altitude lock and stable hovering. Hereunder we summarise the overall steps to produce a high-resolution 3D DOM (Part I of the overall workflow shown in Figure 1c). The first step is to define the area to be surveyed, the UAS flight missions, including paths orientations and flight height, that can be planned and managed using dedicated software, particularly for pictures acquired in nadir orientation. The UAS has been manually driven to collect pictures with oblique orientation of the camera and to detail vertical cliffs. Photo overlap has also to be defined, as suggested by [START_REF] Gerloni | Immersive Virtual Reality for Earth Sciences[END_REF]), Bonali et al. (2019), [START_REF] Krokos | Workflows for virtual reality visualisation and navigation scenarios in earth sciences[END_REF] and [START_REF] Antoniou | The story map for Metaxa Mine (Santorini, Greece): A unique site where history and volcanology meet each other[END_REF]. In fact, it is recommended that UAS-captured photos should have an overlap of 90% along the path and 80% in lateral direction, in order to obtain a greater alignment of images and to reduce the distortions on the resulting texture. The photos have been captured every 2 seconds (equal time interval mode), with a constant velocity of 3 m/s (low speed) and in optimal light conditions suitable for the camera ISO range (100-1600) [START_REF] Bonali | UAV-based surveying in volcano-tectonics: An example from the Iceland rift[END_REF].

In order to allow for the co-registration of datasets and the calibration of models resulting from SfM processing (e.g. Orthomosaics and DSMs), World Geodetic System (WGS84) coordinates of, at least, four artificial Ground Control Points (GCPs) must be established near each corner within each surveyed area and one in the central part (e.g. James and Robson, 2012;Turner et al., 2012;[START_REF] Westoby | Structure-from-Motion' photogrammetry: A low-cost, effective tool for geoscience applications[END_REF][START_REF] James | Optimising UAV topographic surveys processed with structure-from-motion: ground control quality, quantity and bundle adjustment[END_REF] for reducing the 'doming' effect resulting from SfM processing. Wherever possible, GCPs were surveyed with the Emlid Reach RS©, low-cost single frequency receivers (Rover and Base) in RTK configuration (with centimetre-level accuracy), finally correcting the z (altitude above the sea level ) values of the GCPs using the regional geoid model to obtain the orthometric height for the models.

Focusing on data processing aimed at 3D DOM production, photos have been processed with the use of Agisoft Metashape (http://www.agisoft.com/). This is a SfM software becoming increasingly widely used in the geological community for both UAS and field based SfM studies for its user-friendly interface, intuitive workflow and high quality of points clouds [START_REF] Benassi | Testing accuracy and repeatability of UAV blocks oriented with gnss-supported aerial triangulation[END_REF][START_REF] Burns | Comparison of commercial structure-from-motion photogrammety software used for underwater three-dimensional modeling of coral reef environments[END_REF][START_REF] Cook | An evaluation of the effectiveness of low-cost UAVs and structure from motion for geomorphic change detection[END_REF]. The SfM technique allowed to identify matching features in different photos, collected along a defined flight path (Fig. 5b), and combined them to create a sparse and dense cloud, and the Wavefront OBJ Tiled model (further details in Stal et al., 2012;[START_REF] Westoby | Structure-from-Motion' photogrammetry: A low-cost, effective tool for geoscience applications[END_REF]. The first step was to obtain an initial low-quality photo alignment, only considering measured camera locations (Reference preselection mode). After that, photos with quality value 0.5, or out of focus, were excluded from further photogrammetric processing, following the software user manual (Agisoft LLC, 2018). The focal length and photo dimensions were automatically detected by the software, after the import of digital images and then used for the subsequent calibration of the intrinsic parameters of the camera (principal point coordinates, distortion coefficients). After this first quality check, we added Ground Control Points (GCPs) in all photos, where available, in order to: i) scale and georeference the point cloud (and thus the resulting model); ii) optimize extrinsic parameters, such as estimated camera locations and orientations; iii) improve the accuracy of the final model. We then realigned the photos using high accuracy settings: as a result of this step, camera location and orientation were better established, and the sparse point cloud was computed by the software. The next step consisted in reconstructing the dense point cloud, calculated from the sparse point cloud, using a Mild depth filtering and medium/high quality settings.

The 3D tiled model was then reconstructed using the dense cloud as source data for a Medium number of Face count and exported in the format OBJ tiled model. The information provided with the OBJ Tiled Model must be imported in the Unity game engine in order to replicate a real-world reference system.

Building Immersive VR (Part II)

The target of our approach is to comprehensively simulate field experiences and observational behaviours of geoscientists using high-resolution datasets and models. Our approach provides interaction experiences realising navigation/exploration workflows that may not even be possible in the actual field, thus giving unique spatial awareness insights in comprehending complex volcanological processes. An example can be the monitoring of a steep slope on an active volcano, where uprising magma, intrusions, or earthquake shaking can destabilise the slope with the possibility of slope failure. These multiple hazards create a complex scenario that requires field inspection and collection of reliable field measures, but this can be impossible for the impending threats.

We developed a software that provides end users with a holistic view of an area of interest, by allowing exploration of specific features from several points of view and at a range of different scales (see supplemental videos 1, 2 and 3), starting from technologies commonly used in entertainment applications (such as video games). Those include modern game engines (Unity, https://unity.com) combined with Virtual Reality devices (Oculus Rift, https://www.oculus.com/). Unity supports modularity and extensibility to build modular assets that are easily expanded and sustained long term. Furthermore, Unity supports several file formats as used in industry-leading 3D applications (e.g. 3DS Max, Blender). Unity is also well documented as it is supported by large numbers of communities of software developers. Although the development of our software framework is based on the Unity game engine and Oculus, we have deployed generic functionalities of game engines and head mounted displays abstracting as much as possible from specific realisations.

Our system supports a high-performance visualisation layer underpinning a comprehensive set of navigation, interaction and accurate measurement tools to allow geoscientists full appreciation of on-shore settings. Unlike other software for handling digital outcrops (VRGS, www.vrgeoscience.com, or MOSIS of Gonzaga et al., 2017), our focus has been on developing a fully integrated software suite for seamless VR navigation of wide areas. Moreover, our software enables, via appropriate controls, rich user interactions and on-the-fly visualisation adjustments. The uniqueness of our framework lies on the modularity of its underlying architecture enabling support for multiple mechanisms to select and deploy navigation approaches. It enables incorporation of several import and export mechanisms to ensure the creation of data products with long-term sustainability. The 3D DOM/Tiled model approach is built upon UAS-based SfM techniques and is thus able to provide centimetric pixel size resolution for textures. The use of Wavefront OBJ Tiled model was successfully designed and tested by [START_REF] Krokos | Workflows for virtual reality visualisation and navigation scenarios in earth sciences[END_REF] who applied it to areas of different extents and resolutions, respectively ranging 50-1000 m (along the longest) and 0.8-4 cm, also considering the present work. The use of 3D DOM allows improved representations of geometrical features especially around regions that are vertical to the terrain.

Starting from the processed datasets (see Part I), the user must perform few preliminary operations in order to make the scene navigable: an invisible object called "collider" must be assigned to each mesh for the purposes of physical collisions, and the scene has to be properly referenced and scaled by employing information derived from SfM processing. Thus, the scene dimension (in meters) and the corresponding geographic coordinates must be defined, as well as the altitude referred to the 3D reconstructed model. All informations are included in the Tiled Model folder, in Wavefront OBJ format, provided by SfM software we used. Finally, to optimize the rendering performance of the scene, we also suggest the use of Unity Levels of Detail (LODs) methodology to reduce the number of details shown when the model is far away from the camera. For this case, in the Tiled Model folder different level of details for the model that can be set up in Unity engine are already provided.

First of all, the user will see the scenario in first person and walk on a "solid ground surface" to allow them to move around within the virtual scene, or the user can fly over the area, allowing him to have a different view of the outcrop that may open perspectives that are not possible to experience during real fieldwork (see supplemental video 1).

Our software also includes a series of tools embedded in the VR environment, represented by symbols that appear on the screen by pressing a button of the joystick (Fig. 1d) (see supplemental video 2). Such tools have been developed by our research team that comprises also software developers and required some months of work in strict collaboration with geologists. The tools were in fact customized on the classical needs of geologists and volcanologists in the field, which are of paramount importance to quantitatively describe the features of a given area. Directly on the screen you can choose the tool you need. The tools have been developed with the idea of allowing the user to take measurements like being in the field, but with the advantage that the user can change the angle of view in order to better select the proper perspective to take measures. Once you have selected the tool, you point with the joystick the object to be analysed. A tool allows to assess geographic location by coordinates. Another tool allows to select a point feature. By other tools it is possible to map polygons and lines, and measure areas. In these cases, it is necessary to click with the joystick in different points on the virtual ground. Other tools allow the measurement of dip, inclination, and azimuth of an object. By clicking on two points with another tool, it is possible to measure thickness of volcanological objects such as bedding, dykes, etc, and with another tool it is possible to reconstruct the topographic profile. Finally, the system allows to take virtual photographs and notes.

Case studies

The Dallol Volcano, Ethiopia

The active Dallol Volcano was one of the most inaccessible places on Earth, but recently has opened up due to a new road, and there is rapid increase of tourists visiting the incredible geothermal manifestations. This has led to increased risk from multiple geohazards and from the extreme climate. Assessing hazards requires detailed topographic and geologic information, but the area is dangerous and hard to access. Thus, the area was surveyed by UAS and data was processed following our approach (Fig. 2a). Particularly, the 3D DOM is based on 229 pictures acquired with nadir camera orientation, at a flight height of 113 m, obtaining a texture resolution of 2.87 cm/pixel over an area of 0.176 km². Photo alignment has been processed with high quality setting and using Generic and Reference preselection. The dense cloud has also been built up using high quality, whereas GCPs have been not collected in the field due to hard logistic condition. In the VR environment, we have been able to access areas impossible in the field, making measurements and observing features. We have detected different types of dykes and found erupted products (Fig. 2b). We have also characterized and quantified salt karst structures, to start integrating measurements into a hydrogeologicalvolcanological model. Tower morphologies are topped by a 3-m thick white eruption deposit. A tower of salt layers has a vertical sided doline (sink hole) which is 6 m across, and at least 5 m deep, set on a flat area above a 17-m high cliff. Dykes of red clay, possibly filled karst pathways, from Dallol's central hydrothermal area, are mapped and selected measurements shown. A white dyke, made of salt and magma is up to 17 m wide outcropping over 1000 m 2 . A small dry river channel between source and sink holes is 53 m long. This Dallol reconstruction has already been shown in Ethiopia and internationally, and has been used to get opinions of stakeholders on the nature of the geological object, its use in geotourism and possibilities of protection. Users who know the area, mostly geologists so far, have expressed amazement at the ability to see the geological features that they have missed in the field. Prospective visitors (non geologists) have also expressed amazement and wonder at being able to fly around such a landscape.

The Metaxa mine, Greece

The Metaxa Mine is a unique geotope of Santorini volcano (Greece) where the pumice layers of the famous Late Bronze Age (LBA) (well-known also as Minoan) eruption are exposed (see supplemental video 3). It is nowadays abandoned and it is located in the central part of Santorini island, overlooking the famous Santorini caldera (Figs. 3a,b). The latter was created after the catastrophic Minoan eruption [START_REF] Friedrich | Santorini eruption radiocarbon dated to 1627-1600 BC[END_REF][START_REF] Druitt | New insights into the initiation and venting of the Bronze-Age eruption of Santorini (Greece), from component analysis[END_REF], which has influenced the decline of the Minoan civilization on Crete, making it an iconic event in both volcanology and archaeology disciplines. The mine contains the so-called "Famous section" which shows the pumice layers of the eruption along a length of 150 m (see the pictures collected from our immersive VR in Fig. 3c) and classical field activity (Fig. 3d). From the area which is located on the east side of the Famous section, about 1.3 million m 3 were excavated in the early years of mining. A total of 4.5 million m 3 is estimated to have been extracted from the Metaxa mine, according to 3D digital model of the terrain [START_REF] Antoniou | The story map for Metaxa Mine (Santorini, Greece): A unique site where history and volcanology meet each other[END_REF]. Our approach provides an excellent way to access the vertical and overhanging cliffs in immersive VR and to analyse it in detail in a way that was not possible before. The resulting 3D DOM has a pixel resolution of 8 mm and allows the recognition and measurement of the thickness not only of the main different pyroclastic layers, but also of the single eruptive pulse events (Fig. 3d), and even the diameter (down to 1-2 cm) of the lithic clasts embedded in the vertical exposure (Fig. 3e). Pictures have been taken in two main different missions: the first was devoted to capture a set of photos in nadir camera view (n=1121) to cover the whole selected area; in the second we collected photos (n=992) of the vertical outcrops with the camera oriented orthogonal to the vertical cliff, in order to add as much details as possible to the resulting model.

Photo alignment has been processed with high quality setting and both using Generic and Reference preselection, the dense cloud has also been built up using medium quality, considering the extent and resolution of the final model, and a set of 20 uniformly distributed Ground Control Points have been included in order to co-register the 3D model to the World Geodetic System (WGS84) [START_REF] Smith | Structure from motion photogrammetry in physical geography[END_REF][START_REF] Esposito | Application of UAV photogrammetry for the multi-temporal estimation of surface extent and volumetric excavation in the Sa Pigada Bianca open-pit mine, Sardinia, Italy[END_REF].

The resulting 3D DOM is as large as 349 x 383 m.

In Figure 3c, we can distinguish: a) The 103-cm-thick Pre-Minoan base, b) a reverse-graded pumice fall deposit of 258 cm thickness from the first main Plinian eruption (Phase 1, P1), c) the 731-cm-thick pyroclastic surge deposits with multiple bedsets, dune-like bedforms with wavelengths of several meters or more and bomb sag horizons (Phase 2, P2) [START_REF] Bond | The Minoan eruption of Santorini, Greece[END_REF]Heiken and McCoy, 1984;McClelland and Thomas,1990), and d) within eruptive Phase 2, it is easy to distinguish the lowest fine-grained bedset (P2a) from the overlying coarse grained sequence of multiple bedsets (P2b) and the 498-cm-thick fine-grained, nonwelded ignimbrite (P4). The precursory explosion phase (P0) is characterized by a thin lapilli fallout layer of 10 cm in thickness, shown in the field-panoramic view of the Famous section (Fig. 3f). These measures have been obtained by our VR approach and similar detailed values did not exist for the site. At general, Phase 1 corresponds to a Plinian eruption, whereas Phase 2 was characterized by syn-plinian pyroclastic surges. In Phase 3, eruption of 'cold' phreatomagmatic pyroclastic flows constructed a large tuff cone that filled the old caldera, cutting it off from the sea. In Phase 4, eruption of hot pyroclastic flows took place from multiple subaerial vents, associated with caldera collapse that enlarged and deepened the ancient caldera [START_REF] Nomikou | Posteruptive flooding of Santorini caldera and implications for tsunami generation[END_REF].

For science popularization and communication, the VR reconstruction of Metaxa mine is being used in a UNESCO Geosciences Programme project (IGCP project 692 "Geoheritage for Geohazard Resilience") to raise awareness in the geological community and in the more general public about the value of this site, which is in urgent need of protection and development as a unique heritage demonstration of the powerful volcanic eruptions of Santorini. Moreover, this site has great value in regards to the relations between volcanic activity and humans: this mine is part of Santorini history, especially in relation to the economic development of local populations, who in difficult times were able to find income opportunities thanks to the extraction of pumice materials. The Metaxa mine is not only a site of international scientific relevance, but also an industrial heritage site that, as every monument, deserves special attention. The VR model has also been presented at Santorini administrations in order to explain in a more effective way the features present in the field.

Outstanding dykes along the Santorini s caldera wall, Greece

Santorini is a unique place where it is possible to study outstanding feeder and non-feeder dykes (e.g. Figs. 4ab), cropping out along the northern part of the caldera wall. Their study is of paramount importance for better understanding processes related to the propagation paths of fractures/dykes through layers with dissimilar mechanical properties, since they are emplaced in a highly heterogeneous and anisotropic host rock. Their mapping could provide valuable insights on the topic. In fact, [START_REF] Browning | Forecasting magma-chamber rupture at Santorini volcano, Greece[END_REF] started this work collecting detailed measurements of dykes at the sea level in some accessible sites. The problem is that most dykes crop out along inaccessible vertical cliffs (up to 300 m high) or dangerous areas with hard logistic conditions (continuous rockfalls), and thus their characterisation can only be done very locally, at the sea level, and cannot be measured along their whole outcropping range. We give here an example to illustrate how it is possible to overcome such difficulties. We also emphasize that this is just an example, but a full study of the whole cliff is underway by VR and will be published in another paper. This represents measurements at a site that was previously inaccessible. We reconstructed a text-book case of a dyke (Figs. 4c-e) using UAS-collected pictures and SfM processing, obtaining a model with a texture resolution of 4 cm/pixel. Pictures have been collected with oblique orientation of the camera using a quadcopter equipped with a 20 MPX camera. It has been manually driven, at a constant velocity of 3 m/s and capturing pictures every 2 seconds (equal time interval mode), flying between the sea level and a maximum height of 130 m. Regarding the processing, photo alignment has been processed with high quality setting and both using Generic and Reference preselection.

The dense cloud has been built up using medium quality, and a set of 5 GCPs have been included in order to co-register the 3D model to the World Geodetic System (WGS84) [START_REF] Smith | Structure from motion photogrammetry in physical geography[END_REF][START_REF] Esposito | Application of UAV photogrammetry for the multi-temporal estimation of surface extent and volumetric excavation in the Sa Pigada Bianca open-pit mine, Sardinia, Italy[END_REF].

The resulting 3D DOM is as large as about 1000 x 340 m.

Different from the two examples described before, in this case quantitative data have been collected flying in front and around the dyke, instead of walking within the 3D DOM. Using the measurement tools, we collected dyke inclination and thickness from the sea level up to an altitude of 100 m, providing unique and new data (Figs. d-e). The selected dyke is characterised by a dip angle of about 80° at the sea level, with a NW dip, becoming vertical between 30-50 m a.s.l. Between 50-90 m a.s.l., its inclination decreases to 70-80°. The thickness is between 1.0-1.5 m from sea level to an altitude of 20 m, and increases up to 2-2.5 m at 80-90 m a.s.l. These results demonstrate that the immersive VR we developed has a great potential to fully study the dyke swarm emplaced in the Santorini volcano, as well as any other magma plumbing system exposed at vertical cliffs. Even though field studies are vital for mapping and understanding the geological processes on Earth, in several cases, like the one here shown, classical surveys are impossible, whereas our approach represents a solution.

Discussion

Volcanic areas are of high interest for scientific and economic reasons, such as minerals, soil fertility and tourism. In the case of active volcanoes, they can pose significant threats to large populations and infrastructures, and the latter can be temporarily or permanently interrupted with significant repercussions for economic and social stability. Volcanic areas can also have spectacular features that attract the attention of the wider public, who is keen to experience and know more about them, but that is also a risk if people go close to hazardous sites. Therefore, the reconnaissance, mapping, quantification and understanding of volcanic areas is increasingly important, together with the communication of volcanic hazards.

To date, the study of volcanic areas has relied largely upon standard field data collection techniques, but these can be affected by logistic and time constraints or difficulties in accessing dangerous sites. For example, an impending eruption requires immediate data collection or observations of the crater zone, which can be inaccessible or extremely dangerous to approach. Similarly, very rugged terrains and steep slopes represent hard logistic conditions. The approach described here links together geoscience, remote sensing and game engine technologies with an innovative, integrated software solution to create opportunities to collect data in remote areas or dangerous zones, using a fully immersive VR environment.

The three case sites presented, show how important and useful our approach can be. We have focused here on onshore examples, but we stress that our approach can also be applied to offshore environments. The Dallol Volcano shows a case where several complex characteristics can be detected and measured in an extremely inhospitable environment. The magma and karst paths of the volcano are now 3D objects that stand out from a highly dissected landscape. The approach here allows careful measurement of dyke thickness, length, strike, and dip angle, allowing a complete reconstruction of the karst and volcanic plumbing system. It is also possible to immediately calculate the area of exposures from these various outcrops, and to inspect inaccessible cliffs and deep hollows, allowing other 3D objects, such as sink holes to be explored and measured. The Dallol example also shows how visually attractive such an experience can be for engaging with the greater public. This is particularly true in the case of spectacular natural features that otherwise would be impossible to visit.

The Metaxa mine provides exposure of the Minoan eruption and illustrates how detailed measurements can be obtained along inaccessible vertical cliff sections. It has been possible to measure bed thickness and dimensions of single cm-size lithic clasts hosted in the volcanic strata. Furthermore, this example shows that our approach can be used to demonstrate the value of the site and the need for its protection and future development. VR acts as a motor for a wider appreciation of this site, and can be used in political and administrative meetings to effectively communicate with decision makers.

The Santorini dyke we presented (Fig. 4) is part of a large dyke swarm affecting the northern part of the caldera where it is mostly impossible to collect quantitative measures to characterize dyke geometry and thickness, except for near the sea level. This is due to the continuous rock falling and the absence of safe paths to reach the dykes along the 300-m-high caldera wall. Using the immersive VR, we provided, for the first time, measurements characterizing dyke thickness and geometry with continuity from the sea level upwards. We demonstrated that this approach is fundamental to fully study the dyke swarm and to provide new outcomes related to diking process in highly heterogeneous and anisotropic host rock, a topic of paramount importance for volcanic hazard assessment [START_REF] Gudmundsson | How local stresses control magma-chamber ruptures, dyke injections, and eruptions in composite volcanoes[END_REF].

The three cases of 3D rendering in immersive VR are also examples of how this approach can be used for outreach purposes; for example, a Santorini committee is currently using the model as part of its proposal to classify the mine as a unique example of the Minoan eruption, serving as an open-air museum. This 3D model records important scientific and cultural heritage and will virtually preserve the integrity of the site. This permanent record of the site will allow future scientists to interact with the original outcrops, and inform a non-academic audience about the historical and volcanological aspects of this site that provides a unique window of the Minoan eruption [START_REF] Antoniou | The story map for Metaxa Mine (Santorini, Greece): A unique site where history and volcanology meet each other[END_REF]. Equally, the Dallol example is being used to communicate the unknown and un-valued nature of the site to both locals, authorities and tourists, in order to protect this natural heritage [START_REF] Vereb | Remote sensing monitoring and geosite assessment of Dallol, Ethiopia. Putting an isolated and deserted area on map with geoheritage and resilience Geophysical Research Abstracts[END_REF]. Santorini dyke swarm is a unique example to popularize the concept of magmatic intrusions, feeder and non-feeder dyke and volcanic eruptions. This showcases how a volcano interior is.

In general, our approach enables anyone to create models based on real world images with unprecedented detail, georeferenced, and fully explorable. This allows the operator to take measurements in an immersive VR 3D environment. Moreover, since outcrops can also change over time, our approach allows to make a quick and direct comparison of the area development. For example, it is possible to quantitatively compare pre-and post-eruption craters. This approach allows collection of quantitative data similar to standard field data collection. This represents a scenario where the experience of the geologist/volcanologist, which is critical in carrying out the interpretation, can be fully exploited, and fully communicated to all end users. Of course, VR cannot substitute field survey where this is feasible (but it can contribute to collect more geometric data), and cannot replace field trips for students where they can also take samples and see finer rock textures and minerals.

Conclusions

Collecting in-situ data from field localities is essential in geological and volcanological sciences for teaching and research. We proposed an approach that ensures that studies can be as effective as possible even where areas are difficult or impossible to access (e.g. active volcanic areas or vertical slopes). We combine existing technologies of remote sensing, UAS, SfM, game engines and gaming headsets (e.g. Oculus Rift) with new software that allows real-time navigation in real world-based immersive VR and quantitative measurements using specially designed tools for typical geological mapping. This method has been showcased using three sites with different volcanological and volcanotectonic features to illustrate how relevant quantitative field data can be collected in inaccessible areas using VR. The results indicate significant potential for recording sites for virtual research and also for educational purposes and exploration by future generations. There is a high potential for improving communication between scientists and the public about the shared experience of natural objects; "bringing" the field in a room through immersive VR means that non-scientists can have a real perception of natural phenomena. This is scientific awareness and understanding of the ongoing volcanological processes in a way that previously was not possible, an essential step for making informed choices and behaviours.

Figure 1

 1 Figure 1. a) International outreach event using immersive VR in the framework of the the EGU General Assembly 2019; b) Example of teacher and student activity using immersive VR.; c) Processing workflow overview; d) VR headset on the left and sticks used to interact with the scene, on the right.

Figure 2 .

 2 Figure 2. a) 3D representation of an area of the Dallol volcano (Ethiopia) captured using camera tool in Immersive VR. (distances show the measured length of the edges of the perspective). Inset shows full view of Dallol volcano and locates the area described, with arrow for view direction. b) Interpretation with some examples of quantitative measurements taken in Immersive VR environment. Selected features mapped in this area include red dykes related to infilling of the karst system, a white dyke magmatic-hydrothermal intrusion, white eruptive layers, and sink holes.

  Finally, in regards to teaching, our VR model has been used to train Msc and PhD students of different European countries during a series of International Summer Schools organized in the framework of the 2018-2020 project Erasmus+ KA2 "3DTeLC: Bringing the 3D-world into the classroom: a new approach to Teaching, Learning and Communicating the science of geohazards in terrestrial and marine environments".

Figure 3 .

 3 Figure 3. Metaxa mine example: a) Location in Santorini island. b) Location of the reconstructed outcrop used in this example. c) 3D view of the "Famous section" showing the main strata of the various Minoan eruptive phases and measured thickness in immersive VR. d) and e) Examples of measurement of lithic clasts at vertical outcrops by VR. f) Field-panoramic view of the "Famous section" (modified after Antoniou et al., 2019).

Figure 4 .

 4 Figure 4. a) Boat-collected picture of a vertical dyke outcropping along the NW part of the caldera wall, in correspondence of the Oia village; houses for scale, the location is provided in Figure 3a. b) UAS-collected picture of a mostly vertical NE-striking dyke, outcropping in the NE part of the caldera wall, location is marked in Figure 4a (picture courtesy of Luca Fallati). c) and e) show the same dyke of Figure 4b but the pictures have been collected in immersive VR, as well as all measurements regarding dyke inclination and thickness presented in figures d) and f).

Acknowledgements

We greatly appreciated the useful comments on an early version of the manuscript of the Editor, Jacopo Taddeucci, and two anonymous reviewers. The UAS survey of the Dallol volcano was made in collaboration with Olivier Grunewald (https://www.oliviergrunewald.com/). Funded by project ACPR15T4_00098

Agisoft Metashape is acknowledge for photogrammetric data processing.


Andy Varais
email: andy.varais@hotmail.fr

Xavier Roboam

Fabien Lacressonnière

Eric Bru

Nicolas Roux
email: nicolas.roux@laplace.univ-tlse.fr

Keywords: Batteries, power conversion systems, power hardware in the loop, real time emulation, reduced scale systems

published or not. The documents may come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

LECTRIC power conversion systems usually involve a complex and time consuming experimental phase. The experimental cost is huge especially for high power systems as for wind power systems. Furthermore, environment dynamics in renewable powered systems (solar irradiation, thermal conditions, and wind speed) are "naturally unpredictable" making difficult if not illusory to reproduce mastered conditions in order to compare several design concepts or several energy management strategies (EMS) with the same environment. Furthermore, these unpredictable dynamics usually lead to long time range of experiments to cover the whole combinatory cases.

In this context, many papers are related to power hardware in the loop (PHIL) concept [START_REF] Lauss | Characteristics and Design of Power Hardware-in-the-Loop Simulations for Electrical Power Systems[END_REF] which consists in real-time simulations which conjoin software and hardware testing coupling simulations that are used for designing, analyzing, and testing of electrical power system components. This concept is sometimes also called "real time emulation". Several studies apply this concept in the framework of microgrids [START_REF] Jeon | Development of Hardware In-the-Loop Simulation System for Testing Operation and Control Functions of Microgrid[END_REF] electric drives [START_REF] Bouscayrol | Different types of hardware-in-the-loop simulation for electric drives[END_REF] and transport systems [START_REF] Allegre | Reduced-scale-power hardware-in-the-Loop simulation of an innovative subway[END_REF]. In this paper, this concept is applied to electric power conversion systems, for instance wind turbine power conversion systems, coupled with battery storage. The complexity, the cost and the risk when using this latter device make also very interesting to simulate it by means of real time emulated devices (RTED) which consists in replacing the physical component by a power hardware device that emulates it at real time [START_REF] Seitl | Power hardware-in-the-loop implementation and verification of a real time capable battery model[END_REF].

The PHIL real time emulation process is usually developed by "reduced scale experiments" with a device sizing adapted to the rating of the reduced scale test bench. Therefore, it is advisable to use scaled models both to decrease the experiment cost and to adapt device sizing to the reduced scale test bench. As numerical simulations make possible to deduce the characteristics of the phenomena at real size, reduced scale real time emulation based on PHIL experiments minimize the risks associated with the experiments even in extreme conditions [START_REF] Khazaei | Real-time simulation and hardware-in-the-loop tests of a battery system[END_REF] and decrease associated costs [START_REF] Taksale | Low cost hardware-in-loop for automotive application[END_REF]. Such process aims at experimentally validate the simulations especially dynamic (real time) aspects related to control and management of power systems [START_REF] Yi | Hardware-in-loop simulation for the energy management system development of a plug-in hybrid electric bus[END_REF].

In the paper, we mainly focus on RTED applied to battery storage. Battery emulation for PHIL real time simulation are used in several applications. In electric vehicles [START_REF] König | Battery Emulation for Power-HIL Using Local Model Networks and Robust Impedance Control[END_REF][10], battery emulators are developed in order to test performance of powertrain. A hybrid storage emulator (battery/supercapacitor) can also be realised for testing dynamics behaviours of a storage device and the energy management strategy implemented in the electric vehicle [START_REF] Mesbahi | Dynamical modelling and emulation of Li-ion batteriessupercapacitors hybrid power supply for electric vehicle applications[END_REF]. For studying the influence of the thermal environment on battery emulator, a thermal model is coupled with the electric model [START_REF] Thanheiser | Battery emulation considering thermal behaviour[END_REF]. For grid applications, battery energy storage systems (BESS) is emulated by a model, which includes the battery and power electronics interface [START_REF] Boles | Converter-Based Emulation of Battery Energy Storage Systems (BESS) for Grid Applications[END_REF]. To test functions implemented in a battery management system (BMS), multicell battery emulator allows reproducing electrical and thermal behaviour [START_REF] Collet | Multi-cell battery emulator for advanced battery management system benchmarking[END_REF][START_REF] Buccolini | Cell Battery Emulator for Hardware-in-the-Loop BMS Test[END_REF][START_REF] Dai | Cell-BMS validation with a hardware-in-the-loop simulation of lithium-ion battery cells for electric vehicles[END_REF][START_REF] Barreras | An Advanced HIL Simulation Fig. 12. Time acceleration for "model based" (a) and "image based" (b) RTEDs. (a) (b) Battery Model for Battery Management System Testing[END_REF][START_REF] Zhang | Robust and Adaptive Estimation of State of Charge for Lithium-Ion Batteries[END_REF][START_REF] Rahimi-Eichi | Battery management system: An overview of its application in the smart grid and electric vehicles[END_REF]. Sometimes, a real battery is connected to the PHIL test bench. In this case, the method is called battery in the loop [START_REF] Tara | Battery-in-the-Loop Simulation of a Planetary-Gear-Based Hybrid Electric Vehicle[END_REF][START_REF] Shidore | Battery in the loop: Battery evaluation in a systems context[END_REF].

In the case study considered in this paper, the battery device is associated to a wind turbine power conversion system. More

Reduced scale PHIL emulation concepts applied to power conversion systems with battery storage

Andy Varais, Xavier Roboam, Fabien Lacressonnière, Eric Bru and Nicolas Roux E generally, renewable energy systems and smart grids or microgrids are other typical fields of application; due to the complexity of these systems, it becomes essential to apply PHIL real time simulation for testing and validating controls and EMS [START_REF] Vijay | Real-Time Testing Approaches for Microgrids[END_REF]. In [START_REF] Kumar | Alternative Hardware-In-the-Loop (HIL) Setups for Real-Time Simulation and Testing of Microgrids[END_REF], some alternative HIL setups are proposed for real-time simulation and testing of microgrids. Limitation of numerical simulation and advantages of PHIL in distributed generation testing are emphasized in [START_REF] Kotsampopoulos | The Limitations of Digital Simulation and the Advantages of PHIL Testing in Studying Distributed Generation Provision of Ancillary Services[END_REF]. For the development and testing of microgrids control and protection functions, a model (including diesel generators, battery storage, PV plant and wind turbine) in a PHIL environment has been developed [START_REF] Baccino | Real-time Hardware-in-the-Loop Modeling for Microgrid Applications[END_REF]. In [START_REF] Mai | Comprehensive Electric-Thermal Photovoltaic Modeling for Power-Hardware-in-the-Loop Simulation (PHILS) Applications[END_REF], an electro-thermal photovoltaic model is developed for PHIL simulation. In [START_REF] Schechner Andc | Scaling of the Drive Train Dynamics of Large-Scale Wind Turbine Systems for Real-Time Emulation in Small-Scale Laboratory Setups[END_REF], authors have recently presented a real time emulation scaled from a large scale wind turbine system and power reduced for a small-scale laboratory setups. Other scaling process consist in per unit approaches [START_REF] Gauchía | A per-unit hardware-in-the-loop simulation of a fuel cell/battery hybrid energy system[END_REF].

Complementary to these studies, the main contribution of this paper is related to the concepts for PHIL real time simulation especially in the context of device scale reduction for accelerated PHIL tests. Two different concepts of RTED are also compared and discussed in Section II. The reduced scale process by means of a similitude approach is presented in section III allowing to rigorously identify the scaling factors given the degrees of freedom for reduction. The fourth section finally presents the proposed concepts of RTED applied to a wind turbine power conversion system hybridized with a lithium-ion battery (LIB). Beyond the system model derivation and its scaling, experimental analysis by means of PHIL real time emulation are proposed on a reduced power scale test bench. The time compression effect on both RTED for a LIB at different thermal conditions are finally compared.

II. TWO CONCEPTS FOR PHIL REAL TIME EMULATION

In order to achieve a PHIL process, the RTEDs are associated with physical hardware and software components. Classically, RTEDs are based on a model of the actual device from which the real time behavior can be simulated: this concept is named "model based" RTED (see Fig. 1 upper part). Another (less classical) approach consists of a copy of a signal from a physical device : this concept is named "image based" RTED (see Fig. 1 lower part) : the "image" of an actual physical device whose behavior is copied and amplified through "adaptation factors" from electrical cabinets usually made of programmable sources and loads. An example (Fig. 1) of both concepts is provided in the particular case of a battery device (a bidirectional power DC supply is used for power amplification). Of course, these concepts can be generalized to any physical devices such as sources (PV arrays, wind turbines, fuel cells, etc), storage devices (flywheel, ultracapacitors, batteries, H2 storage, etc) or load. The classical "model based" RTED only based on numerical modelling has the advantage of being safer as only a programmable source or load has to be used during real time testing. The cost is also lower than in the case of the "image based" RTED for which the cost of the physical device to be copied must be included. Another benefit of the "model based" RTED is the repeatability of behavior allows testing the performance of different EMS under the same conditions (solar irradiation for photovoltaic arrays, wind speed for wind turbine, state of health for storage device). The flexibility of numerical models is another advantage: the "model based" RTED can be used whatever the scaling input variables. In particular, section IV will show how it is possible to compress the time if a reference model is considered in a "model based" RTED. Contrarily, the same similitude may not be achieved in an "image based" RTED due to characteristics of the physical devices. For instance, in the case of electrochemical batteries, the battery current has to be increased in order to reduce the discharging time. Thereby, the discharging time is accelerated but the actual capacity of the physical device decrease. Thus, the similitude is not respected on that nonlinear actual device. However, the real and clear advantage of the "image based" RTED concept is related to its accuracy. Indeed, as illustrated in the example of a battery, all technological and environmental (temperature) conditions can be taken into account in the "physical image" device. The aging mechanisms of this physical image is also naturally enclosed.

Table I summarizes these characteristics for both concepts.

III. REDUCED SCALE PHIL SIMULATION: THE SIMILITUDE REDUCTION PROCESS

The purpose of dimensional modelling is to carry out experiments on a scaled-model system and then to be able to project the obtained results on the full-scaled system. Similitude theory is a branch of engineering science concerned with establishing the necessary and sufficient conditions of similarity among phenomena. The invariance property (similarity) allows defining the behavior of a physical system

TABLE I COMPARISON OF RTED CONCEPTS

by a complete set of dimensionless variables formed by relevant physical variables. According to this theory, two systems have the same behaviour (under the same experimental conditions) if their dimensionless variables have the same values. Then, it is possible to compare the systems with each other by comparing their dimensionless quantities. The Vaschy-Buckingham theorem [START_REF] Buckingham | On physically similar systems: illustrations of the use of dimensional equations[END_REF] (or theorem), basic theorem of dimensional analysis, allows setting how many independent dimensionless variables can be constructed in a physical problem that involves variables. Reader may find the detailed reduction process in [START_REF] Varais | Scaling of wind energy conversion system for timeaccelerated and size-scaled experiments[END_REF].

The first step of the process is the "dimensional analysis" related to the relationships between different physical quantities by identifying their fundamental dimensions in

[m], [kg], [s], [A], [°K], [mol].
For example, a simple RL circuit (Fig. 2) involves r=3 fundamental dimensions (i.e. m 2 •kg, s, A). r is the number of independent variables, chosen among all variables of the system that can be scaled for the dimensional analysis. The r selected variables are the "degrees of freedom" for the scaling process. In the RL circuit, both voltage and current can be selected as scaling inputs in order to reduce the system power. The time variable t can be chosen as the third degree of freedom. Note that the time being a physical variable among others, this scaling process allows compressing time by creating a "virtual compressed time" that may accelerate testing: this original idea is the main contribution in [START_REF] Varais | Scaling of wind energy conversion system for timeaccelerated and size-scaled experiments[END_REF].

The application of the Vaschy-Buckingham theorem involves k=n-r dimensionless variables (also named  groups). In the RL circuit case involving 5 variables with 3 fundamental dimensions, 5-3=2 dimensionless variables can be defined setting 2  groups assigned to R and L parameters. As detailed in [START_REF] Shidore | Battery in the loop: Battery evaluation in a systems context[END_REF], the systematic derivation of the dimensionless variables leads to the derivation of the similitude factors which sets the ratio between "scaled" and "original" (reference) system variables as in [START_REF] Lauss | Characteristics and Design of Power Hardware-in-the-Loop Simulations for Electrical Power Systems[END_REF] In the RL circuit, the  groups are:

(2) From ( 2), the similitude factors are obtained knowing that these latter are equal to 1 (by definition) for the dimensionless variables:

(3) Equations ( 3) are well known relationships for the RL simple circuit.

IV. APPLICATION OF PHIL REAL TIME TESTING OF REDUCED SCALE POWER CONVERSION SYSTEM WITH BATTERY

In order to illustrate the main concepts related to the PHIL real time simulation by applying the similitude theory to reduced (power and time) scale power conversion systems, a simplified case study that has relatively few physical variables has been selected.

A. Architecture and modelling of the case study 1) Architecture of the case study

A wind turbine (WT) power conversion system connected to a LIB has been chosen (see Fig. 3). In order to make this case study as simple (but realistic) as possible, actual generator (GEN) and its power electronic association has been replaced by an "energetically equivalent" DC generator supplying a DC-DC chopper. The source device thus consists of a WT including its rotating inertia J driving a generator. Through a DC-DC chopper, this electromechanical sub-system feeds a DC bus hybridized with a battery storage device. The rest of the system is simplified to an "equivalent DC grid" which absorbs the produced power. Symbols used in Fig. 3 are defined in Table II.

2) Modelling of the wind turbine power conversion chain

The torque produced by the WT blades depends on the wind velocity :

(4)

The power coefficient is a non-linear function of the tip speed ratio , a dimensionless quantity depending on , the shaft speed and the blade radius :

(5)

The swept area of the WT is a function of the blade radius:

In our case study, we take into account the torque drop caused by the WT inertia , but friction effects are neglected:

In this simplified case study, the electromechanical conversion is provided by a permanent magnet DC equivalent generator instead of the AC machine classically used in wind generation system. Let us note that the DC machine is seen as energetically equivalent to a vector controlled inverter fed permanent magnet synchronous machine or induction machine but with a simpler model. A classical modelling is used for the generator:

In the same way the DC-DC chopper is simply defined by its duty cycle  through a classical average model of converter:

(9)
3) Reduced scale model of the wind turbine power subsystem The similitude reduction process described in section III is applied in order to derive a reduced scale model. More details on the similitude reduction process are in [START_REF] Varais | Scaling of wind energy conversion system for timeaccelerated and size-scaled experiments[END_REF].

In the sub-system associating the WT, the generator and the DC-DC chopper, 4 independent fundamental dimensions ([m], [kg], [s], [A]) exist as emphasized in Table II. Thus, 4 degrees of freedom have to be selected as the inputs of the reduction process. For this subsystem, we have chosen to scale the quantities , , and .

Practically, the air density  will not be modified and the system power will be scaled through both voltages v (V) and currents i (A). The time t (s) may also be reduced in order to accelerate PHIL tests. The "scaled" parameters are calculated from the parameters of the original (ori) model through scaling factors (S x ): [START_REF] Mesbahi | Li-Ion Battery Emulator for Electric Vehicle Applications[END_REF] In the same way the control parameters have to be adapted to conserve dynamic properties (stability, time response) after scale reduction. In our case, for a PI current controller, these adaptation equations on the control are: [START_REF] Mesbahi | Dynamical modelling and emulation of Li-ion batteriessupercapacitors hybrid power supply for electric vehicle applications[END_REF] Kp, Ti being the proportional and integral coefficients.

4) Electro-thermal model of an electrochemical battery

This subsection summarizes the main issues related to an electro-thermal model of a LIB. Readers may find more details related to this model and parameters characterization in [START_REF] Lacressonnière | Scaling electro-thermal model of a lithium-ion battery for time-accelerated experiments in a HIL system[END_REF].

The electrical model presented in this study is based on an extended modified Shepherd model [START_REF] Tremblay | A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles[END_REF] in which several modifications have been made [START_REF] Cabello | Battery dynamic model improvement with parameters estimation and experimental validation[END_REF]. This model is commonly used in the modelling of multi-physical energy systems incorporating a battery and in particular for studies of EMS of hybrid systems [START_REF] Motapon | A Comparative Study of Energy Management Schemes for a Fuel-Cell Hybrid Emergency Power System of More-Electric Aircraft[END_REF] or for health monitoring [START_REF] Lee | Reduction of Li-ion Battery Qualification Time Based on Prognostics and Health Management[END_REF].

Several assumptions are linked with this model. Among them, Peukert effect, aging and battery self-discharge are neglected in our case study. The battery model is described by the following equations: [START_REF] Thanheiser | Battery emulation considering thermal behaviour[END_REF] (13) [START_REF] Collet | Multi-cell battery emulator for advanced battery management system benchmarking[END_REF] where the variables are the battery current i bat (A), the filtered battery current i * bat (A), the battery capacity Q (

), the battery constant voltage E 0 (V), , the polarization constant K (V/

), the internal resistance R 1 (Ω), the polarization resistance R 2 (Ω), the current filter time constant T f = R 2 C 2 (s), the discharge logic variable and the charge logic variable . The logic variable is equal to 1 in discharging mode while in charging mode, it is equal to 0. The logic variable is equal to 1 in charging mode while in discharging mode, it is equal to 0. The i * bat current filtered through the R 2 C 2 parallel network in the Fig. 4 allows taking into account the dynamic behavior on the battery voltage response. From the battery capacity Q, the state of charge (SOC) is calculated by using the common Coulomb counting method (with a coulombic efficiency equal to 1 which is convenient for LIB [START_REF] Chang | A New State of Charge Estimation Method for LiFePO4 Battery Packs Used in Robots[END_REF]): [START_REF] Buccolini | Cell Battery Emulator for Hardware-in-the-Loop BMS Test[END_REF] where SOC 0 is the initial battery SOC.

It is possible to translate these equations by an Equivalent Circuit Model as shown in Fig. 4.

In order to take into account the influence of the ambient temperature on the battery performance, a thermal model can be associated with the electrical part. As for the electrical model, a series of assumptions are made for the thermal model, detailed in [START_REF] Lacressonnière | Scaling electro-thermal model of a lithium-ion battery for time-accelerated experiments in a HIL system[END_REF]. As for instance, the temperature inside the cell is uniform, the predominant head mode transport in the cell is the conduction (convection and radiation modes are neglected) and the parameters of the thermal model are independent of the temperature.

The thermal model of the cell (as shown in Fig. 5) is composed by a heat source p (W), a specific heat capacity C p (J/K), an internal heat transfer resistance R thc (K/W) and an external heat transfer resistance R thv (K/W).

The heat source p and R thv can be expressed as:

(16) (17)
where h v (W/m²/K) is the thermal convection coefficient and S cell (m²) is the cell surface area (surfaces of negative and positive terminals of the cell are neglected).

The surface temperature Ts (K) can be calculated by: [START_REF] Zhang | Robust and Adaptive Estimation of State of Charge for Lithium-Ion Batteries[END_REF] where Tamb (K) is the ambient temperature of the cell (being also the ambient temperature of the battery).

The estimated temperature influences both resistances R 1 and R 2 of the equivalent circuit model (Fig. 4) which values are governed from Arrhenius laws: [START_REF] Rahimi-Eichi | Battery management system: An overview of its application in the smart grid and electric vehicles[END_REF] where R is the perfect gas constant (8.314 J•mol -1 •K -1 ), K 1,2 is the pre-exponential factor, and E a1,2 is the activation energy.

As the state of charge has a prime importance in energy management process, its estimation must be as accurate as possible. According to the state of the art [START_REF] Zhang | Improved Realtime State-of-Charge Estimation of LiFePO4 Battery Based on a Novel Thermoelectric Model[END_REF], the SOC estimation can be refined by taking into account the temperature effects on the capacity (Q) derivation. A polynomial fitting is possible as emphasized in Fig. 6. The thermal parameter identification is detailed in [START_REF] Lacressonnière | Scaling electro-thermal model of a lithium-ion battery for time-accelerated experiments in a HIL system[END_REF]. In our case study, experimental data are extracted from 18650 format 1.6Ah Li-ion cells with lithium iron phosphate (LFP) cathode and graphite anode. As shown in Fig. 7, these cells are assembled in several modules (connected in series and parallel) in order to obtain the characteristics of the battery. The surface temperature of the battery is measured by using a thermocouple attached on the cell. Hence, the thermal model of the battery is based on the thermal cylindrical cell.

5) Scaling of the electro-thermal battery model

As for the WT power conversion sub-system, the similitude reduction process can be applied to the electrothermal battery model. The SI Units of variables are summarized in Table III. III. Hence, there are 6 degrees of freedom used as the inputs of the battery reduced scale electro-thermal model. In this study, we have chosen to scale the quantities v, i, t, T, R, and S cell. The perfect gas constant R and the cell surface S cell will be fixed and the battery power will be scaled through its voltage v and current i variations. The time t may also be reduced in order to accelerate PHIL tests. The "scaled" model parameters (see Table IV) are calculated from the parameters of the original ("ori") model.

Six independent fundamental dimensions ([m], [kg], [s], [A], [K], [mol]) of the battery subsystem appear in Table

TABLE IV DIMENSIONAL ANALYSIS THE BATTERY DEVICE

The scaling process has been validated through numerical transient simulations by comparing "original" sizing with a "scaled" model and by considering several reductions on variables such as voltages, currents and also on the time.

B. Comparison of two reduced scale PHIL simulation concepts for battery device

A test bench (Fig. 8) has been developed for PHIL experiments. A dSPACE supervisor is used in order to manage the PHIL simulation experiments. EMS are implemented in the supervisor while emulator models are developed with matlab-simulink. Scaling factors are set by a user interface developed with Controldesk. Experiments are performed with a common DC bus set at 300V. The DC grid is emulated by a programmable DC loads connected to the DC bus. The battery is emulated with a bidirectional DC power supply whereas the wind turbine is emulated using a 15kW DC supply. These physical emulators are connected to the DC bus through two DC/DC boost choppers. A resistive load is coupled to the DC bus in order to improve the stability of the test bench.

The issue here is to compare the performance of both concepts of RTED as presented in section II. Two different adaptations must be done in order to scale conveniently both the WT power conversion subsystem and the battery storage device (Li-ion battery 25.6V -13Ah) to obtain a PHIL simulation with the correct rating for our system test bench (Fig. 9):

-For the "model based" RTED related to the 2MW reference wind turbine system, voltage and current scaling factors are used: S v * =1/5 and S i * =1/50. Hence, the power is reduced by 250.

-For the battery sub-system, both concepts of RTED are implemented in the test bench. The voltage and current are amplified respectively by S v =6 and S i =7, which makes a battery emulator with a 42 power amplification.

In order to compare the performance of both RTED concepts, a typical EMS is used for the real time PHIL simulation. This EMS detailed in [START_REF] Hernandez-Torres | Technoeconomical optimization of wind power production including Lithium and/or Hydrogen sizing in the context of the day ahead market in island grids[END_REF] is related to a "power commitment problem" in the context of the day ahead market for a WT (rated at 2MW) associated with a LIB. As illustrated on Fig. 10, a commitment power (red curve) is forecasted the day ahead. At real time, given the actual wind profile (upper curve), the actual production power (blue curve) from the WT can be inside or outside a tolerance band (black lines) around the commitment power. Note that wind speed data are sampled at 0.1s which is enough rapid with respect to the inertia constant of the initial (scale 1) turbine but also in the case of the reduced scale WT (reduced inertia). Depending on SOC conditions, the EMS drives the battery power in order to keep the grid feeding power (i.e. the sum of WT and battery powers) inside the tolerance band to avoid penalties due to "commitment failure". In order to compare both RTED concepts, we have zoomed on a typical portion of time with 4 hour of duration for which low production conditions with respect to a higher commitment power provokes a quasicontinuous discharge of the battery.

In the following tests, the initial SOC is set at 40%. When the SOC achieves 10%, the EMS stops the battery power.

1) Comparison of "model based" with "image based" RTED for the battery device at different thermal conditions

Both RTED concepts are compared in this subsection for two different thermal conditions 20°C and 0°C. Fig. 11 shows the battery voltage for several RTED concepts and the relative error (between the experimental battery voltage measurements of the "image based" RTED Vbat I and the "model based" RTED Vbat M ) calculated by: [START_REF] Tara | Battery-in-the-Loop Simulation of a Planetary-Gear-Based Hybrid Electric Vehicle[END_REF] As emphasized on Fig. 11, the electro-thermal battery model allows keeping a good accuracy even if the ambient temperature decreases (Error is lower than 1%). It is not the case for the "electrical battery model" based RTED at 0°C (for this model, the temperature dependence on the parameters is not taken into account [START_REF] Lacressonnière | Scaling electro-thermal model of a lithium-ion battery for time-accelerated experiments in a HIL system[END_REF]). However, some differences occur on the battery voltages with respect to the experimental measures on the "image" especially at low temperature. This confirms that an "image based" RTED keeps a better accuracy when environment conditions vary. It may certainly be the same with aging effects, especially if the model does not take into account of these effects accurately. These effects can be included in "model based" RTED by coupling an aging model with the Li-ion electro-thermal model. Equations modelling the influence of the number of cycles on capacity and resistances can be implemented in the battery model [START_REF] Beltran | Lithium ion batteries ageing analysis when used in a PV power plant[END_REF].

2) Time compression effect on both RTED concepts

Another aspect of the comparison is related to the time compression concept. For the "model based" RTED, a virtual compressed time with accelerated PHIL tests can be achieved by also scaling the time variable in the model. As illustrated on Fig. 12(a), for 2 thermal conditions, battery voltage and SOC are perfectly in accordance if the time is accelerated by S t =1/10 and S t =1/60. Note that 3 different time scales are displayed on Fig. 12(a). In the case of the "image based" RTED, no model scaling is possible. The time acceleration consists in increasing the charging/discharging current (C-rate) in the battery. In the Fig. 12(b), a "nominal C-rate" battery current I is compared with a current multiplied by 10 to fasten the transient. However, the loss balance increases if the C-rate is higher and the voltages and SOC are also different, especially at low temperature (the battery is stopped by the EMS when the SOC reached 10%). This latter analysis shows that the "image based" RTED concept cannot be applied with time accelerated tests.

V. CONCLUSION

In this paper, the main contribution was related to PHIL real time simulation with a scaling methodology. This methodology allows adapting all model parameters when a reduced scale real time simulation has to be achieved with a reduced power test bench. In such a process, RTED can be associated with actual hardware devices and with a real time EMS. If similitude laws are correctly fulfilled in these RTEDs by applying the appropriate theory, dynamics of the physical system are "by definition" conserved after scaling. Thus, dynamic conditions and consequently the stability of the scale 1 system should be the same as for the reduced scale system, if dynamics (time constants, etc) of the control algorithms are also adapted with respect to the process scaling. Two different concepts of RTED have been compared: the classical "model based" and the "image based" RTED. This latter offers the advantage of its accuracy as the RTED is based on measurements on an actual technological device (the "image") which dimensions can be adapted (scaled) to obtained a RTED correctly rated with respect to the test bench sizing. This concept also allows reducing costs and risks as the "image" size can be reduced. In our case study the "image" was a LIB which size is adequate to be inserted inside a climatic chamber, allowing to test the device under different ambient temperatures. However, the "image based" RTED does not allow accelerating the experimental time which is also a very interesting concept to test rapidly several EMS over long term profile conditions. In that case, we have shown that the "model based" RTED can perfectly operate. We are currently thinking about a new RTED concept that would mix both previous concepts, allowing to accelerate tests but keeping at the same time the accuracy advantage in terms of information of the physical "image".

Fig. 1 .

 1 Fig. 1. Two concepts of RTED: (up) "model based" RTED, (down) "image based" RTED.

Fig. 2 .

 2 Fig. 2. Dimensional analysis of a RL circuit in the SI units.

Fig. 3 .

 3 Fig. 3. Simplified case study for reduced scale PHIL real time simulation.

Fig. 6 .

 6 Fig. 6. Polynomial fitting of the battery capacity versus temperature.

Fig. 5 .Fig. 4 .

 54 Fig. 5. Simpified thermal model of the cell.

Fig. 8

 8 Fig. 8 Test bench for PHIL simulation experiments.

Fig. 7 .

 7 Fig.7. Module of 8 Li-ion LFP cells developped by TYVA ENERGY.

Fig. 10 .

 10 Fig. 10. Test profile for actual wind and powers.

Fig. 11 .

 11 Fig. 11. Comparison of "model based" vs "image based" RTED concept under different thermal environments.

Fig. 9 .

 9 Fig. 9. Voltage and current adaptations from the battery (left part) and from the actual wind turbine system.

ACKNOWLEDGMENT

The authors thank SCLE-SFE (ENGIE Group) and the OCCITANIE Region for their financial support.

This work was supported in part by SCLE-SFE (ENGIE Group) and OCCITANIE region.