Bifacial PV Research Articles

Design of ground-mounted grid-connected photovoltaic system with bifacial modules using PVsyst software

Bifacial photovoltaic module has gained significant traction in recent years due to its higher irradiation capture capabilities with cost-effective technology. This paper presents the design, simulation, and techno-economic evaluation of a 45MW fixed-tilt ground-mounted grid-connected photovoltaic system with bifacial photovoltaic modules. The site is located in Sungai Petani, Kedah, Malaysia. The PVsyst 7.2 software was used to design the system by selecting the rating of PV module, inverter and tilt angle of PV modules. In addition, shading and loss calculation, as well as performance evaluation, were also conducted using the software. The simulation of the optimal geometrical parameters had shown an optimal tilt angle of 5°, the pitch of 5.5m and PV array installation height of 1.5m with an albedo value of 0.25. Besides, the performance of system with bifacial and monofacial modules were compared in terms of techno-economic performance indicators. The results showed that the bifacial PV system produces higher energy output with a lower levelized cost of electricity when compared to the system with monofacial PV modules.

TECHNO-ECONOMIC COMPARISON OF BIFACIAL VS MONOFACIAL SOLAR PANELS

A techno-economic analysis is performed for a solar farm with a 35 MWe installed capacity using bifacial solar panels and compared with standard monofacial solar panels at the same installed capacity level. The bifacial panel usage gain from total panel efficiency is identified from 4-year measurements to be within a range of 7.9–16.8% depending on monthly yield. A Monte Carlo simulation is carried out to forecast electricity prices under uncertainty. In terms of Net Present Value, it is found that the bifacial farm yields 12.6% higher values than the monofacial options under reference assumptions. An incremental internal rate of return (IRR) analysis is carried out yielding an IRR for the bifacial panels of 44% under various scenarios. The sensitivity analysis reveals that results are highly sensitive to discount rate and lifetime, and less sensitive to electricity prices. SWOT analysis performed to compare the bifacial with the monofacial panel and evaluate panels according to internal and external factors. The study was concluded with a summary of the technical specifications based on the test results. The results were used to identify that 12.2% added net present value corresponding to $186.7 – $214.5 per unit MW (under various electricity price trajectories) can be used as a reference for assessing the benefit for usage of bifacial PV for 35 MW type medium-size projects. In summary, it is suggested that bifacial solar PV with its outstanding techno-economic results can be the driving force of the growing solar PV market.

Determination of Optimal Elevation of Silicon Bifacial Solar Panel

In this paper, bifacial PV module was characterized to investigate the optimum height and tilt angle of bifacial solar cells in Baghdad location. The module elevation is a key factor in bifacial PVs because of the effect of self-shading on the amount of diffuse and albedo that can hit the rear side of the panel. This elevation is a function of latitude, daylight time, and season, which is never been determined before in Baghdad location up to our knowledge. Various heights above the ground were used (100, 120, 140, and 160cm), and for each height several tilt angles were taken (0°, 12°, 30°, 49°, and 70°). Data were collected in several days of November, 2020. PV parameters were characterized at each condition. Rated power of the panel showed an increase when elevation increases from 100cm to 120cm then tends to level off at 140cm and 160cm heights. This result suggests that the optimal elevation of a bifacial PV panel in Baghdad city location is 120cm. The results also showed that 49° gives the best photovoltaic performance. This can be elucidated by the seasonal effect. Since the measurements were done in winter, the optimal tilt angle should be 49° according to Baghdad latitude.

Artificial neural networks for power output forecasting from bifacial solar PV system with enhanced building roof surface Albedo

The main objective of this research study is to evaluate the performance of bifacial solar PV systems (bPV) installed on flat roof buildings with controlled surface albedo and to develop forecasting models to anticipate the power output from bifacial solar PV systems due to the enhancement of surface albedo. The originality of this study and the novelty include integrating innovative bifacial solar PV and cool roof technologies to increase solar PV panel power output and anticipate electricity generation in advance to balance supply and demand. For the methodology, modeling and simulation analysis was used to test the performance of bPV system installed on a building with a surface albedo of 0.2–0.8. An Artificial Neural Network was used as a machine learning approach for bifacial solar PV power and energy forecasting. The significant findings show that an increase in surface albedo from 0.2 to 0.5 and 0.2 to 0.8 will help to boost the annual bifacial solar PV power production by 7.75% and 14.96%, respectively. The predictive models are exceptionally accurate in anticipating the bifacial solar PV power. The monthly power from bPV rose from 10.87 to 21.54%, with a 0.3 (from 0.2 to 0.5) to 0.6 (from 0.2 to 0.8) albedo increase. The coefficient of correlation R values for all of the power data ranges from 0.99145 to 0.99382 for the roof surface albedo, ranging from 0.2 to 0.8. The ANN models illustrate how effectively the model mimics the modeling and simulation data. For the research implications, the developed forecast models will assist the industry in predicting ahead of the power production, building operations and maintenance, demand-side management, and advanced energy purchases.

Thermo-electro-hydraulic analysis of jet impingement bifacial photovoltaic thermal (JIBPVT) solar air collector

The effects of impinging air jet on the thermo-electro-hydraulic performance of a bifacial PVT with different packing factors are entirely unclear. Here, we have proposed a dual-functional jet plate reflectors are introduced to induce jet air cooling and increase the light absorption at the rear part of the bifacial PV module. The effects of jet plate reflectors with different configurations on the system's performance are investigated and studied. The simulation results were verified and validated with the experimental findings. Increasing the distance between jet holes reduces the interference and enhances the heat transfer, which led to higher friction and greater pumping power. Net energy gain is the key to calculate hydraulic efficiency, by subtracting the pumping power from the energy output. Therefore, the system's best performance can be explained by the lowest Re to generate max efficiencies. Jet impingement bifacial photovoltaic thermal (JIBPVT) with 36 jet-holes has the greatest jet spacing between the jet holes and optimum performance. The maximum thermal energy gain and electrical energy produced were achieved at lower critical values of Re, which are 9929 and 5667, respectively. JIBPVT has the optimum thermal, electro, and thermo-electro-hydraulic efficiencies, with 57.3%, 10.36%, and 83.93%, respectively.

View Factors in Horizontal Plane Fixed-Mode Solar PV Fields

In solar PV fields, solar photovoltaic panels are typically arranged in parallel rows one after the other. This arrangement introduces variations in the distribution of solar irradiance over the entire field, compared to measurements recorded at meteorological weather stations and data obtained from climatic database platforms. This is due to the difference in the view factors between the rows of the solar PV field and a single surface, as well as the presence of shade on rear sides and in the space separating the rows. These phenomena combined will reduce the intensity of solar irradiance incident on the PV solar field; consequently will reduce the energy yields. Accurate estimation of solar radiation on solar fields requires knowledge of the sky, ground, and rear side of the preceding row view factors, and an estimation of the time and space occupied by the row’s shadow. Prior literature has addressed this issue using two-dimensional (2-D) techniques such as the crossed-strings method (CSM). This study developed a novel three-dimensional (3-D) analysis in addition to numerical analysis to determine the view factors associated with solar fields. The study uses both isotropic and anisotropic transposition analyses to determine solar irradiance incident on the solar field with varying tilt angles of solar panels and distance separating the rows (distance aspect ratio) for several latitudes. The present research also tested the validity of the CSM for wide ranges of distance separating rows and length aspect ratios, the obtained results show that the CSM shows good agreements in both sky and ground view factor in the range of length aspect ratio greater than one. But the CSM fails in rear-side view factor in the design ranges of PV solar fields, where the error rate was found about 11%, this result is important in the case of bifacial PV solar systems. Also, the present work compared the solar irradiance calculated for a single surface with that incident on a PV solar field for wide range of sky conditions and latitudes. The obtained results ensure the accuracy of using the solar irradiance incident on a single surface data for low latitudes and for most sky conditions for PV rooftop solar systems as well as PV solar fields. While it has remarked a large error in the case of cloudy skies, where the error rate exceeded 17% in the case of aspect ratio equals to 1.5 and about 15.5% in the aspect ratio of 2.0.

Simulations of Luminescent Solar Concentrator Bifacial Photovoltaic Mosaic Devices Containing Four Different Organic Luminophores

In this article, various design configurations of luminescent solar concentrator photovoltaic (LSC-PV) devices have been simulated using Monte Carlo raytracing. These LSC PV devices are composed of mono-crystalline silicon solar cells and cubical poly (methyl methacrylate) lightguides, each containing one of the following dyes: Lumogen F Red 305, Lumogen F Orange 240, Perylene Green, or Perylene-diimide di-tert-butylphenyl, which results in different device colors. In these devices, mono-crystalline silicon bifacial PV cell are placed in between the vertical edge(s) of neighboring cubical lightguides whereas monofacial PV cells are positioned at the bottom of a lightguide. Each device is made out of five cubical 10 × 10 × 10 mm³ lightguides, meaning that the PV cells measure 10 × 10 mm². The main research goal of this article is to evaluate the optical and electrical performance of five of such configured LSC-PV devices. Hence, the spectral distribution of irradiance received by the edges and bottom of the devices has been simulated as well as the optical efficiency of these surfaces and the power conversion efficiency of each device. The theoretical results for power conversion efficiency are in the range of 13.3% to 18% under irradiance of 1000 W/m² and depend on the dyes applied. Hence, this article demonstrates the potential for energy generation by these colorful LSC-PV technologies, which we have called Mosaic devices.

A comprehensive assessment of electrical performance and mismatch losses in bifacial PV module under different front and rear side shading scenarios

Bifacial modules are expected to enable greater energy generation at reduced cost owing to their dual face absorption nature, however this requires an in-depth understanding of the inherent self-shading of module. A cumulative effect of front and rear side inhomogeneity of irradiance may lead to difference in electrical performance of a bifacial module with respect to monofacial module, under similar shading scenarios. In this research work, an extensive analysis has been carried out through ray tracing simulations and a cell level electrical model of a bifacial module to evaluate the effect of front and rear side inhomogeneity in irradiance. The results for front side shading present a likeness to monofacial modules under similar shading conditions. The more critical and inherent rear-side inhomogeneity along with associated mismatch losses have been quantified through a novel linear model, developed to predict the mismatch loss in a bifacial PV module with high accuracy (R2 91.4%, MAE 1.63% and RMSE 1.91%). Using the model, discussion has been presented on mismatch losses in a 3x3 bifacial PV array, demonstrating the impact of rear inhomogeneity induced mismatch losses on overall system performance. A novel sensitivity study is also carried out to assess the impact of installation parameters on mismatch losses. The significance of this study is the importance of such in-depth assessment for future reliability studies as well as developing standard procedures for hotspot testing and mitigation for a bifacial PV module.

3D-thermal modelling of a bifacial agrivoltaic system: a photovoltaic module perspective

This study presents a 3D computational fluid dynamic model to evaluate the temperature distribution and energy performances of a vertical bifacial photovoltaic module for agrivoltaic applications. This last is compared to a conventionally tilted bifacial photovoltaic module for ground-mounted applications. The simulations are performed in SolidWorks Flow Simulation® and validated with measured data gathered from the first experimental agrivoltaic system in Sweden. Additionally, four more simulations scenarios were defined to compare the performances of vertically mounted and conventionally tilted bifacial photovoltaic modules under different operating conditionsThe validation of the computational fluid dynamic model shows that the model tends to underestimate the readings performed with the thermal camera in the order of 3°C to 4°C for the vertical bifacial PV module. The comparison of the results obtained from the computational fluid dynamic model with existing models available in literature shows a good agreement. The comparison of the heat distribution from the computational fluid dynamic model and the thermal images also shows a good agreement. In all the scenarios investigated, the vertical bifacial photovoltaic module's overall efficiency was higher than that of the ground-mounted module due to lower average operating temperatures. The use of the computational fluid dynamic approach for studying the performance of a single photovoltaic module showed promising results that can be extended to study the system performance and microclimatic conditions.

Performance evaluation of bifacial solar PV modules under different climatic regions in Nigeria

Nigeria's annual solar radiation is estimated to be between 1400 and 2500 kWh/m2. This has made the use of solar energy to generate power in the country feasible. We investigated the performance of a bifacial solar PV system in Nigeria under various climatic regions in this study because bifacial PV modules are known to be location-dependent. The In-Plane solar radiation received by tilted monofacial and bifacial PV modules was calculated and compared using an analytical model. In all climatic regions, the bifacial PV system receives more in-plane solar irradiance. The systems were simulated on PVsyst to determine the energy yield, and the results show that under natural ground (vegetation and sand) of the various regions and optimization of the tilt angle, the bifacial PV system yielded more energy than the monofacial system. The bifacial gain varies depending on location, and system parameters must be optimized to improve the bifacial energy gain.

Impact of the Thicknesses of the p and p+ Regions on the Electrical Parameters of a Bifacial PV Cell

The present paper is about a contribution to the bifacial PV cell performances improvement. The PV cell efficiency is weak compared to the strong energy demand. In this study, the base thickness impacts and the p+ zone size influence are evaluated on the rear face of the polycrystalline back surface field bifacial silicon PV cell. The photocurrent density and photovoltage behaviors versus thickness of these regions are studied. From a three-dimensional grain of the polycrystalline bifacial PV cell, the magneto-transport and continuity equations of excess minority carriers are solved to find the expression of the density of excess minority carriers and the related electrical parameters, such as the photocurrent density, the photovoltage and the electric power for simultaneous illumination on both sides. The photocurrent density, the photovoltage and electric power versus junction dynamic velocity decrease for different thicknesses of base and the p+ region increases for simultaneous illumination on both sides. It is found that the thickness of the p+ region at 0.1 μm and the base size at 100 μm allow reaching the best bifacial PV cell performances. Consequently, it is imperative to consider the reduction in the thickness of the bifacial PV cell for exhibition of better performance. This reduced the costs and increase production speed while increasing conversion efficiency.

Investigation of indoor environment and thermal comfort of building installed with bifacial PV modules

In comparison with common PV module, bifacial PV module can increase energy output by installing cells on both sides of the module. Due to the thermoelectric effect in the rear, the impact of bifacial PV module on indoor environment is more complex. To study indoor environment of bifacial PV module as building envelope, a building integrated bifacial PV module was established. Through the experiments and simulation of the PV building, it is found that thermal stratification is obvious at noon in summer, which indicates the bifacial PV module causes a large influence on the indoor temperature. PMV is between -1 and +1 in summer nights and winter days but it becomes poor in sunny days due to the large solar radiation intensity. Additionally, the indoor light environment is studied. The indoor lighting is ideal in general but overlarge when the solar radiation is too strong. For the purpose of improving the indoor comfort, the coverage of PV module was changed and the heat insulation reflective layer was installed behind the PV modules. With the optimization design, the indoor environment has been significantly improved, and the period of annual thermal comfort has increased by 8%.

Study on the optimum orientation of bifacial photovoltaic module

The idiosyncrasy of bifacial photovoltaic devices by means of its ambivalent nature in absorbing irradiation demarcates this technology from conventional monofacial modules. The performance of bifacial PV devices is primarily a function of the orientation of the device, that is, its tilt angle (β), the elevation of the module above the ground (E), the albedo of the location (ρg) and the azimuth angle (γ). The current work, focusing on determining the optimum setting for module installation, takes into consideration three factors, namely, β°, E(m) and γ°, concentrated on maximizing the power generation from the test bifacial PV module at Jaipur, India (26.91°N, 75.78°E) using full factorial design experiment through Taguchi method. Based on Taguchi analysis, the optimal parameter setting for maximizing response obtained is β° = 40°, E = 0.8 m and γ° = 22.5°. Adequacy of the design was determined through ANOVA, which presented a high R2 value of 88.7%. The results for optimal parameter setting obtained using Taguchi design are validated through experiment, and the error in computed value and experimentally determined value of response is 2.64%. The PR of the module installed at optimum orientation, upon investigation, was highest among test orientations (84.76%) due to greater rear side irradiance collection. Further results show that increasing albedo increases the output for modules installed at optimum orientation. The results are also verified against empirical relations presented in the literature to highlight the competency of the results.

Design and analysis of a new renewable-nuclear hybrid energy system for production of hydrogen, fresh water and power

This paper investigates an integrated system where solar energy system (with 75 MWp bifacial PV arrays) and nuclear power plant (with 2 × 10 MWt HTR-10 type pebble bed reactors) are hybridized and integrated with a 72 MWe capacity high-temperature solid oxide electrolysis (SOE) unit to produce hydrogen, fresh water, and electrical power. The bifacial PV plant is integrated into the system for supplying electricity with a low LCOE and zero-carbon system. A Rankine cycle is integrated to generate power from the steam that generated from nuclear heat. According to the available irradiance, the steam is diverted between the steam turbine and high-temperature electrolyzer for hydrogen and power generation. A multi-effect desalination unit is also integrated to exploit the excess heat to generate fresh water. A system performance assessment is carried out by energy and exergy efficiencies thermodynamically. The bifacial PV plant is analyzed in six selected latitudes in order to assess the feasibility and applicability of the system. Numerous time-dependent analyzes are carried out to study the effects of varying inputs, such as solar radiation intensity. For 20 MWt nuclear, 75 MWp solar capacity; hydrogen productions are found to be between 0.036 and 0.562 kg/s. Among the Northern Hemisphere latitudes, the peak daily hydrogen production rate is obtained to reach 25.9 tons of hydrogen per day for the 75 °N case, mostly with the influence of low temperature and high albedo. The pitch distance change increased the hydrogen production rate by 28% between 3 m and 7 m tracker spacing. The overall system energy efficiency is obtained between 21.8% and 24.2%, where the overall system exergy efficiency is found to be between 18.6% and 21.1% under the actual dynamic conditions for the 45 °N latitude case.

Solar Architecture Integrated Bi-Facial Photovoltaic System as a Shade

Solar architecture is defined as a kind of building integrated photovoltaic (BIPV) in which the PV modules are deployed to passive solar concepts, to minimize the heating and cooling load, to upgrade the indoor environment, and to be adjustable for regional weather and to continuously succeed architectural culture. Solar architecture needs to consider the architectural culture and climate of the region through an ecological convergence. The ecological criteria lead to optimizing solar architecture through an ecological convergence of a passive intelligence and renewable energy system. The optimal angle of the bi-facial PV module as a shade is 23.5° considering the physical interaction and the traditional architecture in Korea according to the ecological criteria. The shading concept of the PV module reduces 27.5~34% of the building cooling load. Effective solar irradiance (ESR) is very important not only for PV efficiency but also for the system usage rate. This ESR should be controlled depending on the climate condition to maximize the total energy elimination factor and total energy transmittance factor for a window. The MB-BIPVS play an excellent role to maximize the total energy elimination factor and total energy transmittance factor for a window.

Modelling and Simulation of Bifacial PV Production Using Monofacial Electrical Models

In this paper, we investigate the use of monofacial PV models to simulate the production of bifacial PV systems over different albedos. Analytical and empirical models were evaluated using measured data obtained from three identical bifacial PV arrays: (1) with the backside covered by white plastic, (2) with normal albedo, and (3) with high albedo. The front-and rear-side irradiances were measured in order to integrate bifaciality of the modules into the models. The models showed good performance for non-real-time monitoring, especially under clear skies, and the analytical model was more accurate than the empirical model. The heatmap visualization technique was applied to six months of data in order to investigate the site conditions on the rear side of the modules as well as the accuracy of the models. The heatmap results of the rear- and front-sides irradiances showed that the installation conditions, such as the azimuth angles of the sun and the surrounding obstacles, had a strong impact on the energy received from the back of the modules. The heatmap results of the models validated the performance of the analytical model. The average daily errors for the analytical model were less than 1% and 3% for normal and high albedos, respectively.

A software-based approach in designing a rooftop bifacial PV system for the North Hall of Residence, IUT

Abstract Bifacial rooftop photovoltaic panels appear to be an excellent means of power generation in this era of urbanization, especially for land-limited countries like Bangladesh. This paper presents a software-based approach to design and simulate a bifacial solar-panel-based energy model on the rooftop of the North Hall of Residence of the Islamic University of Technology, Gazipur. This vertically mounted model investigates the feasibility and applicability of such an energy model in a university residence, situated in a load-shedding-prone area. Hence, three prominent software platforms, namely PVSOL, PVsyst and System Advisor Model (SAM), are brought into action and rigorous simulations are performed for three different orientations; promising outcomes are observed in terms of annual energy yield, bifacial gain (BG) and consumption coverage of the grid and PV model. The annual energy demand of the North Hall is ~444 733.5 kWh. The three orientations can generate annually 92 508.62, 94 643.48 and 86 758.94 kWh, respectively. Hence, it is evident that the proposed orientations can supply almost 19–21% of the site’s annual demand. Monthly BG analysis shows an overall increase in energy gain of 13%, 15.6% and 6% for Orientation-1, Orientation-2 and Orientation-3, respectively. A rigorous comparative analysis and deviation analysis among the software results has been accomplished to gain more insight into the feasibility of the proposed system. Thus, we have focused on a detailed software-based estimation of energy production for different orientations of the PV panels, considering several factors, which will provide prior knowledge and assessment before going for hardware implementation in the future.

Experimental observations in mismatch losses in monofacial and bifacial PV generators

AbstractMismatch losses ( ) in PV arrays have been experimentally investigated by observing the dispersion in the operating voltage of the individual modules under normal operating conditions, that is, with the inverter delivering energy to the grid, and by assuming that in the absence of mismatch, all the modules will have the same operating voltage which are equal to the observed average. For that, a quadratic relationship between relative power and relative voltage deviations derived from the power‐voltage curve of the modules is required. This has been carried out in two different PV generators: a 5.1 kWp with monofacial multicrystalline BSF modules installed in March 2013 and a 6.6 kWp with bifacial monocrystalline PERC modules, installed in May 2019. The respective coefficient of variation of the STC power is 1.6% and 0.3%. This decrease reflects the improvement between these two PV technologies and translates into a reduction in the component derived from intrinsic differences in the constitution of the module, from 0.09% to 0.01%, following theoretical considerations. The component due to the non‐uniformity of rear irradiance in the bifacial PV array is deduced by comparing its functioning with and without the rear side of the modules covered by opaque canvas and results in about 0.2–0.4%, which represents half of the total observed . The difference between these components and the total observed is attributed to differences in the module operating temperature. The aging of the monofacial PV array translates into an increase in at a ratio of 0.04% per year.

Sensitivity analysis of design parameters and power gain correlations of bi-facial solar PV system using response surface methodology

Sensitivity analysis of design parameters and power gain correlations of bi-facial solar PV system is presented in this paper. The main objectives are to study the effects of albedo, tilt angle and height from the ground on the performance of the system; determine the optimum operating conditions; and the development of new correlations for the annual energy yield and bifacial gain of bPV solar system. Three primarily significant installation parameters, albedo [10%, 50%, 90%], tilt angle [15°, 25°, 35°] and height [0.5 m, 1 m, 1.5 m] are investigated with PVSYST for bifacial and mono-facial PV modules. The response surface methodology (RSM) based optimization method is used to determine the optimum conditions and the interaction of these three parameters on the performance of bPV solar system. New quadratic equations or correlations are introduced to estimate the annual energy yield and bifacial gain of bPV. The results show that the albedo is the most significant parameter between tilt angle and height. The increase in albedo factor and height of bPV modules from ground increase the energy yield. In this study, the optimum tilt angle of bPV is found to be 35°for higher albedo and elevation of bPV from the ground as compared to 25° of mPV. An average daily bifacial gain of 35.68% can be achieved in clear sunny day with 90% albedo, tilt angle of 35° and at height of 1.5 m. The maximum specific productions of 192.4 kWh/kWp and 160.6 kWh/kWp are observed in May for bPV and mPV, respectively while the maximum bifacial gain of 21.93% is found in July.

Analysis of water environment on the performances of floating photovoltaic plants

There is an increasing interest in Floating PV (FPV) plants thanks to their advantages compared with ground and rooftop PV systems, mainly related to very limited land use, evaporation reduction, and improvement of the energy performance. The PV modules installed on water surfaces have a natural cooling due to the microclimate in which they operate, which reduces thermal power losses. Furthermore, they can be equipped with simple and effective forced active water cooling systems which further improve FPVs performance. The objective of this study is to develop and validate mathematical models capable of estimating the performance of bifacial and monofacial PV modules installed on water surfaces. Starting from the energy balances of the PV modules, different scenarios are simulated, such as mono and bifacial systems installed on the rooftop, mono, and bifacial FPV systems in presence of natural (or passive) and forced (or active) cooling. The models are validated against experimental data acquired in FPV systems installed in the Enel Innovation Lab by Enel Green Power, Catania (Italy). The obtained results show an energy gain due to bifaciality of 5.24%. The passive cooling in the FPV increases the energy collected by 3% (maximum obtainable of 6.4%) and 2.6% for the bifacial and monofacial technology respectively. Active cooling in FPVs increases the collected energy by 9.7% (maximum achievable of 13.5%) and 9.5% for the bifacial and monofacial respectively.