METHOD OF PERFORMANCE SIMULATION OF A SOLAR ENERGY SYSTEM

Technical Field

[0001] The present invention relates to the technical field of simulation of the performance of solar energy systems. More particularly, it relates to a computer-implemented method of such performance simulation which gives accurate results without requiring excessive computational power.

State of the art

[0002] When designing solar energy systems, whether for photovoltaic (PV) or solar thermal generation of electricity or for heat production, it is important at the planning stage to simulate the likely energy output the solar modules or collectors of the system will provide. In solar energy systems the production costs of energy are dominated by the initial investment so an accurate simulation of energy production at an early stage of design is very useful to determine the likely return on investment and the merits of a particular project. The simulations can also be used iteratively, to optimise the design of the system given the constraints of where it will be installed (e.g. the surface area available for installation, surrounding buildings and/or the surrounding geography leading to shading, and so on), and the types of solar modules available for installation. Moreover, repetitive simulations are useful when the state of a solar energy system is monitored in real time or forecast on a recurring basis. The iteration can also be performed over space rather than time when mapping the feasibility of a specific system design in a geographical area comprising multiple potential sites.

[0003] The report by Stein, Joshua S, and Boris Farnung.‘PV Performance Modelling Methods and Practices: Results from the 4 ^th PV Performance Modelling Collaborative Workshop’. IEA Photovoltaic Power Systems Program, March 2017. https://pypmc.sandia.gov/download/5789/. presents the standard, linear sequence of PV performance modelling steps as follows:

a. Define PV system design parameters b. Choose irradiance and weather data

c. Translate irradiance data to the plane of the array

d. Estimate optical losses from shading, soiling, and reflections on the surface of the array or module

e. Estimate“effective” irradiance

f. Estimate the cell temperature of the PV cells

g. Estimate the current (I) and voltage (V) characteristics of the PV module

h. Estimate the DC wiring and mismatch losses

i. Estimate the DC to AC conversion losses

j. Estimate the AC wiring and transformer losses.

[0004] In this standard sequence, all estimation steps depend on the irradiance and weather data selected on step b). These data are randomly variable as a function of the location of the solar energy system and of the time at which it is desired to know the output of the solar energy system. If either the location or the time changes e.g., if one wants to calculate the output of a solar energy system of identical design in another location or if one wants to regularly forecast the output of a solar energy system based on weather forecasts, then the entire computation flow needs to be run again. The marginal computation cost of simulating an extra day or an extra location therefore stays constant.

[0005] When bifacial PV modules are used, the problem is compounded further, since the shaded rear side of the module is also used for generating electricity from indirect light reflected or scattered from surrounding surfaces. This increases the computation power required for calculating the energy production since reflections from all neighbouring surfaces need to be taken into account rather than just the insolation received from the sky.

[0006] The paper B. Marion et aL, “A Practical Irradiance Model for Bifacial PV Modules,” presented at the 44th IEEE Photovoltaic Specialists Conference (PVSC), Washington, D.C., USA, 2017, describes a performance simulation model based around a two-dimensional analysis where the radiative interaction between the PV array and its surroundings is assumed to vary only in a single horizontal direction and in the vertical direction. Such a simplification limits the application of the model to fairly simple solar arrays, and may prevent the evaluation of systems comprising multiple absorber surfaces or utilising significant quantities of diffuse irradiance.

[0007] C. T. Li,“Development of Field Scenario Ray Tracing Software for the Analysis of Bifacial Photovoltaic Solar Panel Performance,” University of Ottawa, Ottawa, ON, Canada, 2016, describes a ray-tracing method for simulating the performance of a bifacial PV array. While this model appears to give excellent results by simulating the surroundings of the PV array, it is computationally extremely heavy. Furthermore, any changes to the PV array require re calculation of the entire model. This applies not only in the case of modifying e.g. the position or angle of a panel, but also in the case of panels arranged to track the sun, since each tracking movement represents a reconfiguration of the array. The computational requirements to simulate the long-term performance of a tracking array are hence so large as to be effectively impossible to carry out with this model.

[0008] Document US 2017/263047 discloses a method in which, in a first step, the array and its surroundings are CAD modelled, and then a solar access matrix is calculated for each of a plurality of sun positions. This approach requires individually CAD modelling each individual site, and also re-calculating all values in case of changes being made.

[0009] “High resolution shading modelling and performance simulation of sun-tracking photovoltaic systems”, H. Capdevila et al, AIP Conference Proceedings 1556, 201 (2013) describes a shading analysis tool for estimating the performance of one specific array at one specific location, and requires complete recalculation for different locations.

[0010] The aim of the present invention is thus to at least partially overcome the drawbacks of the above-mentioned prior art, and thereby provide a simulation which gives accurate results without requiring excessive computational power particularly in the case of an extra simulation being run for the same system at several locations, and which is compatible with bifacial and tracking solar modules. Disclosure of the invention

[001 1] More specifically, the invention relates to a computer-implemented method for performance simulation of a solar energy system, which may be actually- existing or at the planning stage. This solar energy system is (intended to be) situated at a predetermined location and comprises at least one solar absorber, which may be solar-thermal, photovoltaic or a hybrid PV/thermal collector.

[0012] The method comprises carrying out on at least one programmable computer the steps of:

[0013] a) generating, in the spatial domain:

[0014] - a mesh of sun positions in the sky for multiple (i.e. at least two different) locations, said predetermined location being one of these. This mesh either contains all possible sun positions at a given angular resolution or only a subset of these positions for the predetermined location and at least one other location;

[0015] - a geometric model of said solar energy system at any convenient resolution and level of detail;

[0016] - a geometric model of surfaces and objects external to said solar energy system which interact radiatively therewith, e.g. buildings, foliage, the ground, and so on.

[0017] b) mapping radiative interaction between said solar energy system and said surfaces, with said objects, with the sun and with the sky at at least some of said sun positions to generate a set of system-solar geometric maps of geometry-dependent radiative interactions of said at least one solar absorber

[0018] c) for a predetermined time period of interest, which may be one or more years, or a shorter period such as a day, week, month, season or multiple thereof, generating a time-dependent series of maps, on the basis of said system-solar geometric maps, by correlating the position of the sun in the sky at predetermined times to the nearest point in said mesh of sun positions and extracting the corresponding radiative interactions as mentioned above from said system-solar geometric maps. It should be noted that the time-dependent series of maps (which include temporal-domain information) are distinct from the system-solar geometric maps (which only contain spatial-domain information); and

[0019] d) simulating the performance of said solar energy system based on said time- dependent series of maps and on meteorological data generated for said at least one location for said predetermined time period of interest.

[0020] This enables giving accurate performance simulations using significantly simplified and accelerated processing for complex solar energy systems, since the spatial-domain steps describing the system in function of the position of the sun in the sky independently of time only need to be carried out once for any given system, whereas in conventional approaches, the spatial aspects must be re-calculated in parallel with the track of the sun each time the model is run.

[0021] Advantageously, said solar geometric mesh may comprise datapoints representing the whole sky covering all possible geographic locations, one of which naturally corresponds to said predetermined location. This geometric mesh ideally comprises datapoints at a resolution of between 2° and 5°, preferably between 2.5° and 3.5°, further preferably substantially 3°, which represents an optimum compromise between accuracy and computing power requirements.

[0022] Advantageously, step b) may comprise substeps of:

• Mapping ground shadows;

• Mapping cross-shading between absorbers;

• Mapping cross-blocking between absorbers;

• Mapping specular absorber reflection (i.e. light being reflected from one absorber to another);

• Estimating view factors between absorbers and, if appropriate, a view factor estimation for said objects external to said solar energy system.

• Estimating view factors between absorbers and the sky

[0023] Advantageously, step b) may further comprise substeps of:

• Estimating required backtracking;

• Calculating backtracked beam incidence angles; [0024] wherein said backtracked beam incidence angles are used to update the geometric model of said solar energy system.

[0025] By so doing, the system can provide calculations in respect of tracking solar absorbers.

[0026] Advantageously, the system-solar geometric maps can be generated by a computer server, enabling the computationally-heavy steps to be carried out by a powerful server. The remaining steps can either be carried out on a server, or on a different computer, e.g. the user’s personal computer.

[0027] Advantageously, the system-solar geometric maps can be stored on a non volatile computer-readable storage medium, such as the hard drive of a server.

Brief description of the drawings

[0028] Further details of the invention will appear more clearly upon reading the description below, in connection with the following figures which illustrate:

- Fig.1 : a schematic representation of a solar energy system in a particular environment;

- Fig. 2: a schematic flow diagram of the principle steps of the method of the invention;

- Fig. 3: a component diagram illustrating in more detail the method of the invention;

- Fig. 4: examples of solar meshes for a) Winterthur, b) Abu Dhabi, and c) a combined solar mesh for both Winterthur and Abu Dhabi;

- Fig. 5: a graph illustrating the impact of angular resolution on the grid size of an all-sky geometric mesh;

- Fig. 6 a-c: the solar meshes of figures 4 a-c respectively in two- dimensional representation;

- Fig. 7: graphs of comparisons of computational performance between the method of the invention and conventional approaches;

- Fig. 8: a graph of the impact of angular resolution on plane-of- absorber irradiance estimation;

- Fig. 9: a graph of the impact of angular resolution on ground-reflected front plane-of-absorber irradiance estimation; - Fig. 10: an example of algorithmic design for the method of the invention, applied to a ground-mounted bifacial PV array in a large multiple-array system with a fixed mount at a flat site;

- Fig. 11 : an example of algorithmic design for the method of the invention, applied to a ground-mounted bifacial PV array in a large multiple-array system with solar tracking at a flat site;

- Fig. 12: an example of algorithmic design for the method of the invention, applied to a building-applied solar water heating system in a multiple-collector system at an urban site;

- Fig. 13: a graph of the number of solar mesh grid points at 3° resolution for various combinations of sites of interest; and

- Fig. 14: a graph of the number of solar mesh grid points at 3° resolution for various combinations of sites of interest.

Embodiments of the invention

[0029] Figure 1 illustrates schematically the problems associated with modelling a solar energy system 1 situated at a predetermined location. The system 1 may already exist, or may simply be in the planning phase, the modelling being carried out as part of a feasibility study, to predict or hindcast short or long term performance, or similar.

[0030] The system 1 comprises a number of absorbers 3 such as monofacial or bifacial photovoltaic (PV) modules of any type, solar thermal collectors e.g. for heating water, or photovoltaic thermal-hybrid collectors for combined heat and electrical power applications. These are typically formed as absorber planes, and are mounted on the ground (as illustrated here), or on horizontal, vertical or inclined surfaces of buildings (e.g. on a flat or sloped roof, on a wall, or on any convenient surface) or of the terrain. The absorbers may be fixed or may be arranged to track the sun around one or two axes of rotation as is generally known. As illustrated, the absorbers 3 are mounted on the ground where their insolation is affected by a nearby building 5, but the situation illustrated in Figure 1 can also apply in the case in which the absorbers 3 are mounted on the roof of a building. [0031] Typically, ground-mounted solar energy systems are configured such that only a small fraction of the absorbed solar radiation is reflected onto the active surface(s) from the ground or other objects surrounding the surface. The performance simulation of such systems is commonly based on three separately modelled irradiance sources: sun disk, sky, and ground. In doing so, it is usually sufficient to consider the ground as a homogenous, isotropic irradiance source covering the entire visible part of the below-horizon zone as opposed to the sky above the horizon. In the case of systems with radiatively complex surroundings however, this is not the case and more complex modelling is carried out. Examples of such systems include urban solar energy systems and bifacial PV systems particularly in multiple-array configurations. In the case of the building-applied bifacial PV system 1 , or in PV systems mounted close to buildings as depicted in figure 1 , accurate performance simulation requires careful consideration of the radiative interaction between the absorbers 3 and their surroundings. The computational weight of the purely geometric modelling steps increases when the impact of obstructions blocking the absorber surfaces’ view to the sky or the ground cannot be neglected or when the contribution of surface-reflected irradiance becomes more significant as in the case of bifacial PV systems.

[0032] Figure 1 illustrates clearly the issue of shading of the absorbers 3, either from adjacent absorbers casting a shadow 7 on the active surface thereof, or of objects external to the system such as buildings 5, hills, mountains, foliage or similar casting their own shadows 7a when the sun is at certain angles in the sky. Furthermore, in the case of bifacial PV modules 3, the shadows 7, 7a cast on the ground also have an impact on the light incident on the rear side of the modules 3 since they will influence the amount of back-reflected light arriving from nearby surfaces and objects.

[0033] In the case of systems comprising tracking absorbers 3, system geometry is continuously adjusted following the path of the sun, which also changes the shadows cast on the active surfaces of the absorbers 3 and on the ground. Moreover, when the performance impact of ground shading is significant as in the case of a system of multiple bifacial PV arrays, in radiative terms, the geometric parameters even change with fixed mount (FM) configurations as the sun tracks across the sky.

[0034] Figure 2 illustrates in its most generic form the simulation method of the invention.

[0035] In a first step 101 , geometric mapping is carried out in the spatial domain with spatially-determinate parameters, namely the positions of the sun in the sky expressed in spherical coordinates and taking into account solar positions for at least two possible locations for the system, the geometry of the system 1 , the geometry of surrounding object such as buildings which affect the radiation incident on the system 1 , the diffuse irradiation of the sky, albedo and so on. It should be noted that the positions of the sun in the sky are determined at arbitrary predetermined angular positions, without necessarily making any reference at this stage to the times at which the sun occupies these positions. The optical interactions which cause light to impinge on active surfaces of the absorbers 3 are mapped in function of the angular position of the sun in the sky, and the result is one or more system-solar geometric maps, typically expressed in the form of matrices in function of the geometric position of the sun. This geometric mapping only has to be carried out once for a given system design since all of said interactions can be determined exclusively in terms of the angular position of the sun rather than requiring calculation of the position of the sun at given times. This is extremely advantageous in respect of reducing processing requirements when simulating the same system in various locations, or the same system at the same location but at different times. We will return to these points in more detail below while discussing specific implementations.

[0036] It should be noted that“map” is a generic term which includes for instance multidimensional data arrays, lookup tables, datasets (whether indexed or not), matrices and so on, containing the corresponding data.

[0037] The system-solar geometric maps generated in step 101 hence contain geometry-dependent radiative interactions of the absorbers 3 with the sun, the sky and other objects. These can be stored in permanent computer memory, such as on a hard drive, computer server or similar, and re-used multiple times since they do not need to be re-calculated each time.

[0038] In step 102, domain transformation is performed on the mapping results of step 101 in order to convert these spatial-domain geometric maps into a model in the geospatiotemporal domain, i.e. a model which is dependent on time and the geographic location of the system.

[0039] This is carried out e.g. by taking a time period of interest for the system, e.g. a day, a week, a month, a season, a year or even longer, and generating time- domain series by correlating the position of the sun in the sky at given times (such as every 15 minutes, 30 minutes or hour over the period of interest) for each location of interest. Essentially, at a given timestep (e.g. 12:00 pm on a given date at a given location), the corresponding position of the sun in the sky can be used as a reference to look up in the purely spatially-determined system-solar geometric maps generated in step 101 and thereby obtain the geometric parameters and hence the light received by the absorbers at that time (assuming no meteorological interference). This can be carried out for all timesteps of interest at any desired resolution, resulting in a time-dependent series of maps, with one or more maps for each timestep in the period of interest. This step only needs to be carried out once for a given system 1.

[0040] Finally, in step 103, system performance simulation is carried out based on the time-dependent series generated in step 102, which can also be (and typically indeed is) combined with meteorological data, whether real, predicted, or extracted from a dataset comprising a so-called“typical meteorological year” (TMY) for a given site at a predetermined number of time steps for each system 1 of interest. This meteorological data incorporates one or more of cloudiness, temperature, wind speed and so on. Furthermore, other aspects which influence system performance such as soiling and cleaning schedule can be incorporated as well. Use of real meteorological data has a particular application in detecting faults in an existing system 1 , by modelling over a period of time which has passed and comparing the real energy production with the simulated production. A large difference in these two values would indicate a problem with the system. Predicted meteorological or TMY-based data are useful for performance prediction over the long-term or the short-term, for instance to predict how much energy will be produced in a given period.

[0041] The generalities of the principle of the method of the invention having now been explained, more concrete details of execution are given below. It should be noted that a large number of individual steps described both above and below are known to the skilled person, for instance in the publication’’Planning and Installing Photovoltaic Systems A Guide For Installers, Architects and Engineers”, DGS - Deutsche Gesellschaft fiir Sonnenergie, Third Edition, Routledge 2013, and also in other similar publications. However, the multistep dual-domain approach of first modelling the system and mapping its optical parameters and interactions exclusively in function of solar position and independent of time before constructing time-series on the basis of the solar- system geometric maps previously generated is, to the best of the applicant’s knowledge, unknown in the prior art.

[0042] Figure 3 illustrates a component diagram containing more detailed building blocks and sub-blocks of the method according to the invention, this method being carried out by means of a general purpose computer, by means of a computer program product stored on a non-volatile computer-readable storage medium (hard disk, CD-ROM, memory stick or similar) comprising instructions arranged to cause the computer to carry out the method of the invention. These blocks will be described generally below, and then later in more detail in the context of more specific examples.

[0043] The box marked“geometric mapping” corresponds to step 101 of figure 2, and illustrates the various inputs and processes that can be used for geometric mapping in the spatial domain and hence the generation of the system-solar maps mentioned above.

[0044] Starting at the top left of figure 3, geospatial domain parameters relating to the geographic location of the system 1 (i.e. its longitude, latitude and elevation) are used, together with information relating to the timeframe of interest (e.g. a whole year, or only a part thereof), to generate a solar geometric mesh in substep 101a. A“solar geometric mesh” is a mesh of sun positions in the sky for at least two given locations, and contains a series of points expressed in spherical coordinates at an arbitrary predetermined spatial resolution. The mesh may be square, rectangular, triangular, hexagonal, or any other polygonal form, and may be regular or irregular.

[0045] Figure 4 illustrates such solar geometric meshes generated for Winterthur (a), (47.50°N, 8.73°E), and for Abu Dhabi (b), (24.44°N, 54.61 °E).

[0046] In the spherical coordinate system, the two-dimensional (unit spherical) solar position in the sky is determined by solar zenith angle (q _z ) and solar azimuth angle (y _s ). In order to construct the 0z-y _s meshes in respect to the location of the system(s) concerned for the time period of interest, an initial high- resolution time series can be generated, e.g. by means of the computationally efficient SG2 algorithm disclosed in P. Blanc and L. Wald,“The SG2 algorithm for a fast and accurate computation of the position of the Sun for multi-decadal time period,” Sol. Energy, vol. 86, no. 10, pp. 3072-3083, Oct. 2012. Other methods for generating solar geometric meshes are of course equally possible. In the present example, each mesh illustrated in figures 4a and 4b is expressed at a spatial resolution of 3° of both azimuth and zenith (i.e. a square mesh), which corresponds to a time resolution of 12 minutes. Generally, angular resolution can be chosen arbitrarily such that the estimation accuracy of the geometric parameters is not notably reduced while the number of the resulting simulation points is a fraction of the combined number of the sites and time steps of interest for performance simulation. With an angular resolution of 3° as illustrated, the implemented approach results in a reduction of 54-79 per cent in data points compared to the traditional time series-based simulation based on yearly data at an hourly resolution for a single site. An important aspect of the present approach is that, when generated for any two given sites on Earth at a given angular resolution, a certain number of the points in the solar mesh are common to both sites. This is clearly shown in figure 4c, which illustrates the solar meshes for Winterthur and Abu Dhabi superimposed one on top of the other. It can clearly be seen that a large number of these points are in common (about 45%), and that the variation in the extent of the meshes (i.e. where their boundaries lie) is merely dependent upon latitude. Furthermore, the same angular position of the sun in the sky can correspond to the sun position at different times of different days of the year e.g. depending on season; at a practical angular resolution, the sun’s position at a given time is not necessarily unique for the entire time period considered.

[0047] To further expand on this point, since the solar-geometric meshes are determined in the spatial domain purely on the basis of arbitrary pre determined azimuth and zenith angles without reference at this stage to the time at which the sun occupies any of the given positions, a part of each mesh is common to any two given sites. In essence, by using angular azimuth and zenith angles at arbitrary, predetermined spacings, the question for any given point in the mesh is“at a given site, does the sun pass through this point at any point in the year or not?” without regard yet as to when it does so. On the other hand, in for instance US 2017/263049, sun tracks in function of the actual path of the sun through the sky at the site of interest in function of discrete time steps are generated, rather than simply a mesh of possible spatial sun positions. This is the key to the present invention.

[0048] The effect of this approach is further illustrated by the graphs of figures 13 and 14, which illustrate the total number of required solar mesh points at 3° and 1 ° angular resolution respectively. From these graphs it can clearly be seen that the number of solar mesh points required for Winterthur and Abu Dhabi combined is significantly less than the sum of the points required to treat each site individually, and hence computation can be more efficient for the two sites combined, rather than computing each site individually. Furthermore, any Swiss (CFI) site requires only 3.5% more points than Winterthur alone, since most Swiss sites will share the overwhelming majority of points in common, and other comparisons can be made by consulting the graphs.

[0049] Due to the commonality of spatial positions of the sun at multiple different locations, and as a simplification in the case in which the same system 1 might be installed at any one of a large number of locations, it is even possible to generate a whole sky solar mesh which includes every possible sun position for any position on Earth at the desired resolution (see“any site” of figures 13 and 14). On this basis, all the geometry-dependent radiative interactions can be mapped for any possible solar mesh point in the spatial domain, a number of these points being eliminated when modelling at a given location where these sun positions do not occur. This is essentially impossible to achieve with a conventional time-and-location based approach, since the number of datapoints would be vast, and the proportion of points in common between various sites would be relatively small in proportion to the number of points. In this latter case, the combination of azimuth, zenith and time would only be the same for very few points, if any, rendering computation for a large number of possible sites extremely difficult.

[0050] The approach of the invention hence means that all possible sites on earth can be modelled simultaneously with a maximum of 3,600 solar mesh points at 3° angular resolution, or with a maximum of 32,400 points at 1 ° angular resolution, which shows how the method of the invention can be significantly more computationally-efficient than modelling the solar path for a large number of sites individually.

[0051] In substep 101 b, the absorber configuration is modelled based on parameters relating to the system dimensions, such as the type of absorbers 3, their orientation, their spacing, their ground clearance and any other useful parameters. It should be noted that the absorbers 3 can be modelled as monolithic, or in more detail in the case in which it is desired to take into account e.g. light passing through the absorber 3 between individual cells thereof. In essence, the complexity of the model can be adapted according to need, with more complex models naturally requiring more computing power to process. It should be further noted that this type of modelling has been well- described in the literature, such as in“Planning and Installing Photovoltaic Systems A Guide For Installers, Architects and Engineers” mentioned above, and hence need not be described in detail here.

[0052] On the basis of the outputs of substeps 101a and 101 b, and on a model of the coordinates of objects external to the system 1 but liable to interact radiatively therewith (such as building 5, foliage, ground surfaces etc.), in substep 101c, radiative interaction between the absorbers 3 and surrounding surfaces are mapped, at least for the parts in common between the at least two possible sites. This substep outputs: • the view factor (the fraction of radiation leaving a first surface which is incident on a second surface when considered from the first to the second surface) from each absorber 3 to surrounding surfaces and vice versa;

• incidence angles of impinging light at each absorber 3 from surrounding surfaces and vice versa;

• absorber/ground/external object shading;

• absorber/ground/external object blocking; and

• specular solar beam reflection from surfaces.

[0053] This mapping may optionally be fed back to the substep 101 b if the configuration of absorbers 3 is re-adjusted after mapping absorber cross shading or beam reflections, for instance in the case of sun-tracking PV arrays or in an iterative design of the configuration of the system 1.

[0054] In substep 101 d, radiative interaction between each absorber 3 and the sky is mapped. As is described in e.g. R. R. Perez, P. Ineichen, R. D. Seals, J. Michalsky, and R. Stewart, “Modelling daylight availability and irradiance components from direct and global irradiance,” Sol. Energy, vol. 44, no. 5, pp. 271-289, 1990 to estimate incident sky diffuse irradiance, or“PV Performance Modelling Methods and Practices”, Report IEA-PVPS T13-06:2016, or indeed countless other publications, the diffuse irradiance of the sky can be modelled, dividing the sky up into a grid of finite sky elements. The radiation emanating from each finite sky element can be calculated based on the sun positions calculated in the solar geometric mesh generated in substep 101a. Furthermore, impinging light not coming from the sun or the sky can be modelled based on the model of the coordinates of objects external to the system 1 but liable to interact radiatively therewith as mentioned above, and the view factors from each absorber 3 to surrounding surfaces output by step 101c.

[0055] This substep 101 d estimates the proportion of each absorber 3’s sky view obstructed by other absorbers or objects external to the system. This substep does not need inputs from the solar geometric meshing substep 101a if anisotropic sky blocking analysis is not performed, for instance in the case in which a simplifying assumption of isotropic sky radiance is made. Whether or not the mapping of the radiative interaction between the absorbers is dependent on solar geometry is determined by direct links to the sub-step ’’Solar geometric meshing” 101a. For mapping absorber cross-shading for instance, both the absorber configuration and the sun’s position need to be known but for absorber-to-absorber view factor estimation or mapping of absorber cross blocking (i.e. where an object blocks diffuse irradiation from a given source such as the sky, the ground or another object from impinging on a particular absorber), information about the absorber configuration is sufficient - regardless of the possible dependence of the configuration on solar geometry. The sub-step“Mapping of radiative interaction between absorbers and surrounding surfaces” 101c can also include ground meshing (i.e. modelling the ground as a series of discrete points arranged in a mesh), absorbers’ ground shadow mapping, and absorber sky and cross-blocking estimation for mesh points on the ground.

[0056] This substep 101 d outputs the following:

• View factors from each absorber 3 to the sky;

• Incidence angles at each absorber 3 from radiation emanating from each finite element of the sky; and

• Sky blocking, i.e. when objects block light rays coming from the sky from being incident on an absorber 3 or ground points.

[0057] The final output of first step 101 is a set of system-solar geometric maps incorporating the solar geometric mesh and the outputs of substeps 101c and 101 d mentioned above.

[0058] Again, it should be noted that such calculations and mapping are well-explored in the literature and it is not necessary to describe them in detail from first- principles here, particularly in view of the fact that they can be carried out in many different manners with very similar results.

[0059] These system-solar geometric maps are then domain-transformed by being data-fused in step 102 with geospatiotemporal design parameters such as the geographic coordinates of the system 1 , its elevation, and time steps in a time- period of interest so as to generate geolocated system-solar time series of maps, referred to here as a time-dependent series of maps.

[0060] This simply involves correlating the nearest solar positions in the solar mesh with the sun’s positions at predetermined times at the location in question, so as to generate a time-dependent series of maps of all the various radiative interactions previously calculated, while excluding points in the solar mesh which do not occur at this location. In other words, for each time step (e.g. one for every 15, 30 or 60 minutes during the time period in question which may be e.g. a day, a week, a month, a season or a year), a corresponding system- solar geometric map is extracted from the maps generated in step 101 , giving a time-dependent sequence of such maps.

[0061] This time-dependent series of maps is then fed into a system performance simulation in step 103, together with technological parameters of the system 1 (e.g. relating to efficiency of the absorbers 3, their spectral response to incident light and so on), meteorological information relating to insolation, and other weather conditions (cloudiness etc.) and so on. This meteorological information may be historical, predicted or based on the Typical Meteorological Year (TMY) for the location of the system 1. The final output is one or more performance time series.

[0062] In the case of radiatively complex geometric simulations, the step of geometric mapping 101 may be computationally very demanding i.e. take several hours of computation time on a standard personal computer.

[0063] The algorithmic design can hence be implemented such that the computational processes involved in this first step can be run with a high-performance work station acting as a server. The resulting system-solar geometric maps resulting from step 101 are saved as file types of the user’s preference on the server’s hard disk. When moving on to simulate system performance, these files can be processed by the domain transformation step 102, either on the server or after transferring the files on another computer referred to as the client here. The client-side domain transformation is reasonable if sufficient space is available in the client computer and several simulations based on different timeframes and/or system locations can be performed based on the same system-solar geometric maps e.g. when regularly forecasting the performance of an operational system 1. In terms of the requirements for digital space and memory, the final step of system performance simulation 103 is the least demanding when standard optical, thermal, and electrical system performance modelling tools are deployed. Step 103 can be performed either on a server, or on a normal multipurpose computer.

[0064] Another manner in which to describe the step of domain transformation 102 more mathematically is as follows. It can be considered that the output of step 101 represents one or more maps of optical factors O(0z, y _s ), indexed by discrete values of solar azimuth angle and solar zenith angle. Each indexed node O(0z, y _s ) is itself a complex data structure which comprises one or several multi-dimensional matrices, incorporating at least one of:

• Sky view factors

• Ground view factors

• Absorber view factors

• Surrounding object view factors

• Specular absorber reflection (i.e. light being reflected from one absorber to another)

• Absorber cross-shading binary modifiers

• Absorber cross-blocking binary modifiers

[0065] These maps of optical factors can be stored e.g. on a hard disk or other computer-readable medium (whether volatile or non-volatile). In step 102, these stored maps are transferred from the spatial domain into the temporal domain, for instance by means of the following algorithm or any other suitable method:

• For each site S of interest

• For each time t of interest

• Calculate solar zenith angle 0 _Z (S, t)Calculate solar azimuth angle y _s (S, t)

• Locate closest pair (0 _Z ^' , y _s ^' ) to (0 _Z (S, t), y _s (S, t)) in the index of the stored maps of optical factors

• Retrieve the optical factors 0(S, t) = O(0 _Z (S, t), y _s (S, t)) = O(0 _Z ^' , y _s ^' ) from the stored map of optical factors [0066] This results in the optical factors 0(S, t) in the geospatiotemporal domain, i.e. corresponding to a specific location at a plurality of times.

[0067] In respect of calculating the system performance, the optical factors 0(S, t) described above are combined with time-independent, system specific factors influencing the state of the solar energy system (e.g., nominal power) Po, and weather data, either measured, forecast or estimated, at site S at time t (e.g., solar irradiance, ambient air temperature, wind speed) W(S,t), to give the state of the solar energy system at site S and at time t according to the following equation

P(S,t) = f(W(S,t), 0(S,t), Po)

[0068] Where P(S,t) is the state of the solar energy system (i.e. power output, temperature or similar) at site S at time t.

[0069] P can be calculated for a plurality of timesteps at a desired resolution (e.g. hourly) and integrated to calculate the estimated performance for any given time period.

[0070] The main advantages of this dual-domain (spatial for the geometric mapping step 101 and geospatiotemporal for the subsequent steps 102 and 103) are as follows.

[0071] When digital memory is not a limiting factor, the computation time required for the geometric mapping step 101 is directly proportional to the number of data points regardless of whether the data are distributed in a solar angular domain or a geospatiotemporal domain. This does not necessarily apply to very simple systems such as solitary absorbers 3 in which case the construction of the solar geometric mesh itself accounts for a major part of the time consumed.

[0072] Figure 5 is a graph illustrating that the number of grid points in a solar geometric mesh is inversely proportional to the square of the angular resolution of the solar mesh. As can be seen from the figure, the 3° angular resolution illustrated in figures 4 a-c but applied to an all-sky mesh covering all possible sites and time steps would result in a lower number of data points (A/ _db =3600) than the annual number of daytime hours at an average site (A/ _db =4426). In other words, the system-solar geometric maps constructed based on a 3°-angular-resolution all-sky mesh are faster to generate than an annual hourly time series of the same solar geometric variables for a single site, illustrating clearly how the present method reduces the computation power required compared to prior art methods based on brute-force calculation in the time domain.

[0073] Solar geometric meshing and the conversion of system-solar geometric maps into geolocated time dependent series of system-solar maps are processes in the proposed dual-domain approach that do not exist in a comparable conventional, single-domain time-series-based approach.

[0074] Figure 7 presents the results of a comparative analysis of computational performance between the proposed approach and the conventional, time- series-based approach. In this case, the dual-domain approach of the invention is applied to a horizontal single axis tracking bifacial PV system with a 3° angular resolution and all possible time steps in Abu Dhabi (3°-angular resolution all-time, 1 site in Figure 7) or all possible sites and time steps (i.e. for an all-sky solar mesh, represented by the line marked 3°-angular resolution all-sky in Figure 7). In this specific case, the switch to the dual-domain approach results in reduced computation time at a number of geospatiotemporal grid points (i.e. number of sites times number of time steps) of 1500 and above with the multiple-absorber configurations (Figure 7a) and at that of 6100 and above with a solitary absorber (Figure 7b). As a reference, the most common type of solar system simulation is to compute day-time performance over one typical year with a one-hour resolution and thus represents a number of geospatiotemporal grid points of 4340-4600 depending on the site of interest. It should be noted, however, that if some of the yearly time steps will not be simulated at any point, the all-time solar geometric meshing would not be necessary and the time required for carrying out the dual-domain approach could be further reduced by simply excluding a priori such non-occurring points from consideration.

[0075] Figure 8 and Figure 9 present the performance of the proposed dual-domain approach in terms of accuracy. More specifically, Figure 8 illustrates the impact of angular resolution on plane-of-absorber irradiance estimation by means of the proposed dual-domain approach in the case of a ground-mounted system with multiple adjacent and parallel fixed absorbers on March 20, 2012, and Figure 9 likewise represents the impact of angular resolution on ground- reflected front plane-of-absorber irradiance estimation by means of the proposed dual-domain approach in the case of a ground-mounted system with multiple adjacent and parallel fixed absorbers on March 20, 2012.

[0076] As can be seen from the figures, accuracy naturally strongly depends on angular resolution but also on the site and the output variable of interest. Overall, Figure 8 shows that the error due to finite angular resolution does not significantly affect the accuracy of plane-of-absorber irradiance estimation even at quite low angular resolution levels. Flowever, the impact on the estimation of the ground-reflected component of plane-of-absorber irradiance is notable at angular resolution > 3°. As per these results, the angular resolution of 3° seems a well-justified trade-off between accuracy and computation speed.

[0077] Figure 10, Figure 11 , and Figure 12 illustrate as activity diagrams specific embodiments of the proposed algorithmic design applied to the output power estimation of a bifacial PV array in a system of multiple identical arrays with fixed mount (Figure 10) and tracking (Figure 11) and that of a building-applied solar water heating system comprising multiple parallel collectors in an urban environment (Figure 12). The process chain is dependent on the number of absorbers (i.e. arrays (A/ _a ) or collectors (A/ _c )).

[0078] The substeps mentioned in the box labelled“solar angular domain” correspond to substeps 101a, 101 b, 101c and 101 d of figure 3 as indicated.“Domain transformation” corresponds to step 102 of figure 3, and the system performance simulation 103 comprises the indicated substeps. The activities performed by the component“System performance simulation” (corresponding to step 103 of figures 2 and 3) vary between the different implementation examples and are not affected by the introduction of the dual-domain approach of the invention. Flence, only the activities performed in the solar angular domain i.e. the ones involved in“Geometric mapping” (see Figure 3) are described in detail below.

[0079] Starting with the activity diagram of figure 10, which is for the simplest situation of an array of fixed-mount photovoltaic panels.

[0080] As discussed, in substep 101a, the sun position is mapped in angular terms on the basis of a solar mesh at e.g. 3° spatial resolution, as described above. Also, the array configuration is modelled in step 101 b.

[0081] The outputs of these steps are then used to calculate, for each appropriate angular position of the sun in the sky, maps of ground shadows cast by absorbers 3 and other objects, and cross-shading where one absorber casts a shadow on the other are also mapped.

[0082] Subsequently, cross-blocking mapping is carried out if the number of absorbers is greater than 3, if not then it is not necessary. Also, specular reflections coming off of the various absorbers are mapped.

[0083] On the basis of the foregoing, the view factors of each of the absorbers of the array are estimated, as are the sky view factors and ground view factors.

[0084] Subsequently, step 102 of domain transformation is carried out as described above, correlating the sun’s position at various times to its angular position (i.e. to the nearest point in the solar mesh) and creating a series of maps for each of these times based on the corresponding angle of the sun. This is then combined with meteorological data to estimate the irradiance at the absorption plane of each absorber in the array (known in the field of solar system modelling as“plane-of-array irradiance”) and the power output of the array can be estimated taking into account e.g. estimates of the effective irradiance of each absorber 3, the temperature of the individual cells of each absorber, and any other desired factors.

[0085] It should be noted that the modelling discussed above can be carried out for each absorber 3 in an array, or various simplifying assumptions can be carried out, for instance if the array comprises a large number of absorbers 3 (e.g. more than 100) arranged in a regular pattern and not subject to any significant shading by e.g. buildings or topographical features. In such a case, the modelling and calculation can be simplified by considering only a single absorber 3 at or near the centre of the array, and considering its interaction with other absorbers liable to interact optically therewith to any significant degree, e.g. the immediately-surrounding absorbers, and possibly also some or all the absorbers adjacent to these latter. Or, only absorbers within a predetermined distance to the single absorber 3 in question can be considered. In such a case, the entire system’s performance can be modelled as the output of this single absorber 3 multiplied by the number of absorbers 3 in the array, since the error due to the different situation of the relatively small number of absorbers 3 at or near the edge of the array can often be neglected.

[0086] Figure 1 1 shows an activity diagram of the situation with a system 1 comprising an array of tracking absorbers rather than fixedly-mounted absorbers 1. This differs from the diagram of figure 1 1 in that the tracking has to be taken account in step 101 b for each angular position of the sun, since the absorbers track this latter so as to maximise energy production at each solar position. As a result, there is feedback from step 101c into step 101 b as this tracking occurs. Furthermore, backtracking of the absorbers 3 must be taken into account if they are sufficiently close to each other for some absorbers to cast significant shadows on others. Typically, a tracking absorber 3 is piloted to maintain its absorber plane as close to perpendicular as possible to the axis of incident light coming from the sun, since this represents an optimal angle for maximising power output, particularly if the absorber is on its own or is sufficiently far from its neighbours to not cast shadows thereupon. Flowever, above a certain number of absorbers 3 per unit surface area in the system significant shading of absorbers 3 from other absorbers can occur when the angle of the absorbers is perpendicular to the axis of the incident light coming from the sun. As a result the optimum output for the array sometimes occurs with the absorbers 3 tilted backwards (hence“backtracking”) away from the theoretical optimum for a single, solitary absorber 3. Although this backtracking reduces the power density of light received by an unshaded absorber 3, it reduces shading on other absorbers to a degree that more than compensates for the fact that the angle of the absorber plane would not be optimal for an absorber 3 which was not shaded by another. This principle is well-described in the literature, such as in“Planning and Installing Photovoltaic Systems A Guide For Installers, Architects and Engineers” mentioned above. [0087] Figure 12 represents an activity diagram in which the absorbers 3 are solar- thermal collectors mounted on a building. The differences with the activity diagram of figure 10 are that surrounding objects which interact radiatively with the absorbers 3 are also modelled in step 101 b, and that the performance simulation is adapted to thermal collectors. Again, the implementation of these differences with respect to the diagram of figure 10 are well-explored in the literature and hence do not need to be discussed in detail here.

[0088] Although the invention has been described with reference to specific examples, variations are of course possible without departing from the scope of the invention as defined in the appended claims. For instance, other calculation methods can be used other than those mentioned above in reference to specific publications.