High-precision vertical double-sided photovoltaic module irradiance calculation method and device

Abstract

This invention discloses a high-precision method and apparatus for calculating the irradiance of vertical bifacial photovoltaic modules, belonging to the field of photovoltaic irradiance calculation technology. This invention divides the module, ground, and wall into sub-blocks, uses a three-dimensional finite-length view factor to calculate the optical transmission relationship between each sub-block and the sky view factor, and combines shadow judgment and the solution of the multiple reflection matrix of the wall-ground cavity to achieve accurate calculation of the front and back sides of the module and the equivalent irradiance in a vertical bifacial photovoltaic fence / railway scenario. This invention breaks through the limitations of the traditional two-dimensional infinite length assumption, can adapt to any number of modules, requires no complex modeling, has high calculation efficiency, and meets industry standards in accuracy, effectively supporting the design, power prediction, and engineering promotion of vertical bifacial photovoltaic systems.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic module irradiance calculation technology, specifically to a high-precision irradiance calculation method and device applicable to scenarios such as vertical double-sided photovoltaic walls and photovoltaic railings with wall reflections on the back. Background Technology

[0002] As an innovative application of building-integrated photovoltaics (BIPV), bifacial photovoltaic wall systems can replace traditional building walls and roof railings with high-efficiency bifacial photovoltaic modules, achieving photovoltaic power generation without occupying additional land and building space. They have advantages such as high power generation efficiency, convenient installation and maintenance, strong adaptability to existing building renovation, local consumption, and a balance between enclosure and aesthetics. They are an important technical path for deep energy conservation and emission reduction in the building sector.

[0003] Currently, there are significant deficiencies in the industry's irradiance simulation calculation technology for vertical bifacial photovoltaic wall scenarios. In particular, there is a lack of accurate calculation of the irradiance reflected by multiple cavities between the back wall of the module and the ground, which cannot support subsequent power prediction and system design optimization, and seriously restricts the large-scale promotion of this technology.

[0004] The existing methods for calculating the irradiance of vertical bifacial photovoltaic modules have the following main drawbacks:

[0005] 1. The two-dimensional view factor method is only applicable to infinitely long photovoltaic arrays, cannot be adapted to scenarios with a limited number of components, and cannot take into account the complex lighting conditions of reflection from the back wall.

[0006] 2. Mainstream commercial photovoltaic simulation software such as PVsyst and SAM use simplified two-dimensional models, which make it difficult to reproduce complex scene light reflections;

[0007] 3. Although optical simulation tools such as Radiance can achieve three-dimensional simulation, they are complex to model, have low computational efficiency, and are costly to apply in engineering.

[0008] Therefore, a high-precision irradiance calculation method is needed that can adapt to finite-length vertical bifacial photovoltaic modules, accurately calculate multiple reflections from walls and the ground, and has low modeling and calculation costs. Summary of the Invention

[0009] This invention aims to solve the problems of existing technologies, such as the inability to accurately calculate the irradiance of vertical bifacial photovoltaic modules reflected from the back wall, poor adaptability of finite-length arrays, complex modeling, and low computational efficiency. It provides a high-precision, high-efficiency method and device for calculating the irradiance of vertical bifacial photovoltaic modules that is adapted to actual engineering scenarios.

[0010] To achieve the above objectives, this invention provides a high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module, comprising the following steps:

[0011] 1. Obtain basic parameters

[0012] Collect information on vertical bifacial photovoltaic walls: module model, geometric parameters, azimuth angle, ground clearance, distance from the wall, and lateral position; obtain ground reflectivity and wall reflectivity; input local latitude and longitude and meteorological data, including horizontal total irradiance (GHI) and horizontal diffuse irradiance (DHI).

[0013] 2. Calculate the position of the sun

[0014] The pvlib library is used to calculate the solar zenith angle and azimuth angle.

[0015] 3. Surface segmentation and view factor calculation

[0016] The photovoltaic modules, the ground, and the wall are each evenly divided into several sub-blocks;

[0017] Calculate the mutual viewing factors between each sub-block, including ground-wall, wall-ground, component-wall, wall-component, component-ground, and ground-component;

[0018] Calculate the sky view factor for each sub-block, i.e. the proportion of the sky visible to the sub-block.

[0019] 4. Shadow identification and initial irradiance calculation

[0020] Determine the shadow occlusion status of each sub-block;

[0021] Calculate the irradiance of the front of the component, the initial irradiance of the ground sub-block, and the initial irradiance of the wall sub-block.

[0022] 5. Calculation of multiple reflections in wall-to-ground cavity

[0023] Construct a set of linear equations for the reflected irradiance of each sub-block on the ground and wall, and solve for the final reflected irradiance after multiple reflections in matrix form.

[0024] 6. Calculation of the back of the component and equivalent irradiance

[0025] Substituting the results of multiple reflections, the irradiance on the back of the module is calculated; combined with the bifacial coefficient, the equivalent irradiance of the module is obtained.

[0026] The present invention also provides a high-precision vertical bifacial photovoltaic module irradiance calculation system for implementing the above method, the system comprising:

[0027] Parameter acquisition module: used to acquire geometric and optical parameters of photovoltaic modules, walls, and ground, as well as meteorological data;

[0028] Solar position calculation module: used to solve for the solar zenith angle and azimuth angle;

[0029] Viewpoint Factor Calculation Module: Used to calculate the viewpoint factor between sub-blocks and the sky viewpoint factor;

[0030] Irradiance calculation module: used to calculate the irradiance of the front, back, ground, and wall surfaces, as well as multiple reflections from the cavity.

[0031] Output module: Used to output the component's equivalent irradiance and power prediction results.

[0032] The key technical points of this invention are as follows:

[0033] A method for calculating the viewing factor between a three-dimensional finite-length photovoltaic module, a wall, and a ground surface;

[0034] Method for calculating the sky view factor of each sub-block of a vertical double-sided component;

[0035] A method for solving the irradiance matrix of multiple reflections in cavities between walls and floors;

[0036] A method for calculating the full-link irradiance of vertical bifacial photovoltaic modules applicable to photovoltaic fences and railings.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. High precision: The view factor model of a three-dimensional finite-length surface is used to accurately depict the complex radiation transfer relationship between a finite number of photovoltaic modules and the ground and walls, overcoming the large error caused by the traditional two-dimensional infinite length assumption.

[0039] 2. Considering complex reflections: For the first time in the irradiance calculation of vertical bifacial photovoltaic modules, the multiple reflection effects of the cavity formed between the ground and the wall were accurately simulated by constructing and solving a system of linear equations, which significantly improved the calculation accuracy of back irradiance.

[0040] 3. High efficiency: Compared with optical simulation software such as Radiance, which requires complex 3D modeling, this invention is based on analytical formulas and linear equations, which does not require the establishment of a 3D geometric model. It has a fast calculation speed and is suitable for engineering applications.

[0041] 4. Strong scene adaptability: It can flexibly adapt to photovoltaic fence or guardrail scenarios with different numbers of components, different spacing, and different position offsets. Attached Figure Description

[0042] Figure 1 This is a schematic diagram showing the coordinate definitions and spatial relationships of the three radiation receiving surfaces in this invention: vertical bifacial photovoltaic module, ground surface, and wall surface.

[0043] Figure 2 This is a schematic diagram illustrating the relevant angle definitions involved in the irradiance calculation in this invention.

[0044] Figure 3 The following are meteorological data and a comparison chart of equivalent irradiance and power generation during the test period in the experimental verification of this invention; (a) Meteorological data during the test period; (b) Comparison of predicted and experimental values ​​of equivalent irradiance and power generation on the same day.

[0045] Figure 4 The following is a comparison and verification diagram of meteorological data, irradiance, and power under cloudy to overcast weather conditions for the present invention; (a) shows the total horizontal irradiance and horizontal scattered irradiance data; (b) shows the ambient temperature and wind speed; (c) shows the comparison between measured and predicted irradiance on the front and back sides; and (d) shows the comparison between measured and predicted maximum power.

[0046] Figure 5 The following is a comparison and verification diagram of meteorological data, irradiance, and power under sunny to cloudy weather conditions for the present invention; (a) shows the total horizontal irradiance and horizontal scattered irradiance data; (b) shows the ambient temperature and wind speed; (c) shows the comparison between measured and predicted irradiance on the front and back sides; (d) shows the comparison between measured and predicted maximum power. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0048] Example:

[0049] A high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module, the specific steps of which are as follows:

[0050] Information for vertical bifacial photovoltaic fences includes module model, module geometry, module azimuth angle, ground reflectivity, wall reflectivity, distance between the module and the wall, module height above the ground, lateral position of the module relative to the wall, and local latitude and longitude, and meteorological data (horizontal diffuse irradiance, horizontal total irradiance).

[0051] The sun's position (zenith angle, azimuth angle) can be calculated using Python's pvlib library.

[0052] Figure 1 This document lists three radiation receiving surfaces on the back of a vertical bifacial photovoltaic module and their coordinate definitions for calculating the viewing factor of the back side. The viewing factor of the front side can be calculated using the same method. An approximate calculation has been performed for a typical photovoltaic fence scenario (half from the ground and half from the sky). The sky viewing factor of the front side is also provided. and ground perspective factor All are 0.5. Where A1 represents a certain segment surface on the component; A2 represents a certain segment surface on the ground; A3 represents a certain segment surface on the wall.

[0053] View factor from ground A2 to wall A3 Calculate as shown in equations (1)-(2)

[0054] (1)

[0055] (2)

[0056] In the formula, the subscript "R" represents the back of the component; x, y, z represent the coordinates on the coordinate axes, the subscripts "1, 2" represent the points closer and farther from the origin of this segment vertex, and the superscripts "pv, gnd, wall" represent the surfaces on which the segment is located. Here, the English terms are used: pv represents the surface on the component, gnd represents the surface on the ground, and wall represents the surface on the wall. In this formula, i, j, k, l are defined as the traversal of subscripts 1 and 2; G and K have no special meaning. For detailed definitions, please refer to [link to definition]. Figure 1 .

[0057] View factor from wall A3 to ground A2 As shown in equation (3):

[0058] (3)

[0059] In the formula, η represents the coordinate on the coordinate axis, the subscripts "1, 2" represent the points that are closer to and farther from the origin, respectively, and the superscript represents the surface on which the block is located, which is represented in English here.

[0060] View factor of component A1 to wall A3 As shown in equations (4)-(5):

[0061] (4)

[0062] (5)

[0063] In the formula, D is the distance between the component and the wall; the definitions of other formulas are the same as above.

[0064] View factor of wall A3 to component A1 As shown in equation (6):

[0065] (6)

[0066] View factor of component A1 to ground A2 As shown in equations (7)-(8):

[0067] (7)

[0068] (8)

[0069] In this formula, G and K have no special meaning, and the other definitions are the same as above.

[0070] View factor from ground A2 to component A1 As shown in equation (9):

[0071] (9)

[0072] The sky view factor of component A1 is as shown in equation (10):

[0073] (10)

[0074] The sky view factor of ground A2 is as shown in equation (11):

[0075] (11)

[0076] The sky view factor of wall A3 is as shown in equation (12):

[0077] (12)

[0078] The calculation of irradiance models requires meteorological data, especially the total horizontal irradiance (GHI) and the horizontal diffuse irradiance (DHI), which can be obtained from databases such as Meteonorm or through field measurements. Figure 2 The definition of angles related to irradiance calculation is shown.

[0079] Component front irradiance G F As in equations (13)-(16):

[0080] (13)

[0081] (14)

[0082] In the formula, the uppercase subscript "F" refers to the variables on the front of the component, and the subsequent subscript "R" refers to the variables on the back of the component; G b It is direct irradiance; G d It is diffuse irradiance; G r It is reflected irradiance; G circ It is the irradiance in the circumpolar region; G iso It is isotropic irradiance; G hor This refers to the horizon brightening irradiance; the above can be calculated using the well-known Perez model in the industry; GHI is the total horizontal irradiance; DHI is the horizontal diffuse irradiance; IAM b It is a direct incident angle correction; IAM d It is a correction for the incident angle of scattering; It is the ground reflectivity; S b It is the component's shadow occlusion ratio; Rb It is the ratio of tilted direct irradiance to horizontal direct irradiance, as shown in the formula. .

[0083] (15)

[0084] In the formula, the uppercase subscript "F" refers to the variables on the front of the component, and the subsequent subscript "R" refers to the variables on the back of the component; θ is the angle of incidence, as shown in formula (16); θ zen γ is the solar zenith angle. pv ω is the component's azimuth angle; w is the hour angle.

[0085] (16)

[0086] In the formula θ azm θ is the solar azimuth angle. sazm This refers to the azimuth angle of the component.

[0087] Component backside irradiance G R As in equation (17):

[0088] (17)

[0089] The components, ground, and wall are divided into i, j, and k uniform sub-blocks, respectively, representing the defined pv, gnd, and wall surface sub-blocks. The shadow situation of each sub-block and the viewing angle factor F between them are determined, and then the irradiance received by the ground, wall, and components is calculated. The irradiance received by the back of the components is shown in Equation (18).

[0090] (18)

[0091] In the formula, the capital "R" refers to the back of the component; R b It is the ratio of tilted direct irradiance to horizontal direct irradiance, as shown in the formula. ; It is the irradiance received by the ground sub-block; It is the irradiance received by the wall sub-blocks; other variables are defined as follows: - The definitions are the same.

[0092] (19)

[0093] The cavity between the floor and the wall reflects light multiple times, and the floor... and walls The calculation of received irradiance needs to be approached from the perspective of optics and heat transfer.

[0094] Initial irradiance of ground sub-block j As in equation (20):

[0095] (20)

[0096] Initial irradiance of wall sub-block k , as shown :

[0097] (twenty one)

[0098] definition Let the total energy density of the ground sub-block j ultimately reflected outward be as shown in equation (22):

[0099] (twenty two)

[0100] In the formula This refers to the ground reflectivity.

[0101] definition The total energy density of the ground sub-block k ultimately reflected outwards is given by equation (23):

[0102] (twenty three)

[0103] In the formula This refers to the ground reflectivity.

[0104] The irradiance reflected by each sub-block between the wall and the ground depends on the irradiance reflected by all other sub-blocks. It is a linear system of equations containing N=j+k unknowns, which can be expressed in matrix form, such as (24)-(25).

[0105] (twenty four)

[0106] (25)

[0107] In the formula, G is the irradiance vector of all sub-blocks ( G0 is the initial irradiance vector for all sub-blocks (); ); ρ is a diagonal matrix composed of the reflectivities of all sub-blocks ( F is the square matrix of perspective factors among all sub-blocks ( ).

[0108] Irradiance ultimately reflected by each sub-section of the ground and walls , The final irradiance of the component can be calculated by disassembling G and substituting it into equation (17).

[0109] The formula for calculating the equivalent irradiance of a vertical bifacial photovoltaic module is as follows:

[0110] (26)

[0111] In the formula This is the bifacial coefficient of the component.

[0112] Experimental verification example:

[0113] The power comparison involved in the experimental verification can be calculated using the single diode model and five-parameter model commonly used in the industry.

[0114] Figure 3 Meteorological data from the nine-day test period from March 6 to March 14, 2026 were presented. By observing the proportion of scattering in the total radiation, it can be seen that the entire experimental period included multiple working conditions such as sunny, cloudy and overcast days, and the ambient temperature gradually increased. Figure 3 (b) shows the measured and predicted equivalent irradiance (i.e., front irradiance + bifacial coefficient * back irradiance) and power generation during the test period.

[0115] The overall data for multiple days showed that the RMSD of the front and back irradiance and power errors was less than 30% for all indicators, with the RMSD error of the maximum power being 10.36%, which meets the requirements of "ASHRAE Guideline 14". In terms of correlation coefficient R, the correlation coefficients of all three dimensions reached above 0.94, with the "maximum power" showing the highest correlation (0.9854).

[0116] To comprehensively evaluate the accuracy of the photovoltaic power prediction model, this invention selects a measured dataset with typical meteorological abrupt changes for model validation. Minute-by-minute data from March 6th (sunny turning cloudy turning overcast) and March 11th (sunny turning cloudy) were used as the validation set. Comparative results from the measured data show that under these weather conditions, the RMSD of the maximum power predicted by the model is 11.87% and 11.51%, respectively, both meeting the requirements of "ASHRAE Guideline 14," indicating that the theoretical model can be considered validated by experimental data.

[0117] March 6th is a highly representative test sample, such as... Figure 4 This weather pattern, characterized by sunny skies turning cloudy and then overcast, means that the light source received by the photovoltaic array changes abruptly from highly directional direct sunlight to omnidirectional scattered light, and finally to low-energy, weakly scattered light. This poses a significant challenge to any photovoltaic power prediction model.

[0118] Overall, the power RMSD on March 6 was 11.87%, which meets the requirements of "ASHRAE Guideline 14", and the R value was 0.9798. Looking at different phases, the period from 9:00 AM to 9:45 AM was the dominant period for direct sunlight. Figure 4 (c) The measured mean irradiance on the front side is 531.3 W / m², while the predicted mean is 522.2 W / m², with a relative error of 8.7%. The irradiance on the back side is somewhat underestimated compared to the radiometer reading, possibly because the uniform Lambertian plane assumption neglects the gain from specular reflection. Figure 4 (d) shows a high degree of fit in the final power. The period from 10:00 to 14:00 is dominated by scattering, with almost 100% scattered light. During this time interval, cloud cover causes a sharp drop in frontal illumination, leading to an overestimation of the frontal irradiance. However, the measured irradiance on the back side is 124.4 W / m², compared to the predicted 131.4 W / m², resulting in a dramatic drop in error to 6.4%. The period from 14:30 to 16:00 is a period of weak scattering, with predicted irradiance on both the front and back sides around tens of W / m², showing a small absolute deviation. However, the measured power still remained at 108.2 W, while the model predicted 87.7 W. This may be partly due to the strong low-light performance of the tested HJT module.

[0119] March 11th was a typical sunny day turning cloudy, such as... Figure 5 (a)-(b). The power RMSD on March 11 was 11.51%, which meets the requirements of "ASHRAE Guideline 14", with an R value of 0.9758. For example... Figure 5 As shown in (c), except for a certain deviation during the period from 11:30 to 13:00, the fit with the measured data is relatively high at other times; Figure 5 The power output during the period from 11:30 to 13:00 was also underestimated. This is because the east-facing modules have a larger solar incidence angle at noon, and the slight calculation error in the incident angle loss has a greater impact on the east-facing and west-facing modules.

[0120] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module, characterized in that, Includes the following steps: (1) Obtain the geometric parameters, optical parameters, azimuth angle, height above ground, spacing and meteorological data of the installation location of the vertical bifacial photovoltaic module, wall, and ground; (2) Calculate the position of the sun to obtain the zenith angle and azimuth angle; (3) Divide the components, ground, and walls into several sub-blocks, and calculate the mutual viewing angle factor between each sub-block and the sky viewing angle factor; (4) Determine the shadow status of each sub-block and calculate the initial irradiance of the front of the component, the ground, and the wall; (5) Construct a system of linear equations for multiple reflections of the wall and floor cavities, and solve for the final reflected irradiance; (6) Calculate the irradiance and equivalent irradiance on the back of the component.

2. The method for calculating the irradiance of a high-precision vertical bifacial photovoltaic module according to claim 1, characterized in that, The viewing factors include ground-wall, wall-ground, component-wall, wall-component, component-ground, and ground-component viewing factors.

3. The high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module according to claim 1, characterized in that, The multi-reflection irradiance of the wall and the ground is solved using matrix form.

4. The high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module according to claim 1, characterized in that, The irradiance on the front of the component was calculated using the Perez model combined with incident angle correction.

5. The high-precision method for calculating the irradiance of a vertical bifacial photovoltaic module according to claim 1, characterized in that, The equivalent irradiance combined with the bifacial coefficient of the component is obtained by weighting the irradiance of the front and back sides.

6. A high-precision vertical bifacial photovoltaic module irradiance calculation device, used to implement the method as described in any one of claims 1 to 5, characterized in that, include: The parameter acquisition module is used to acquire component, wall, and ground parameters, as well as meteorological data. The solar position calculation module is used to calculate the solar zenith angle and azimuth angle; The viewpoint factor calculation module is used to calculate the viewpoint factors between sub-blocks and the sky viewpoint factor; The irradiance calculation module is used to calculate the irradiance of the front, back, ground, and wall surfaces, as well as multiple reflections. The output module is used to output the equivalent irradiance and power prediction results.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 5.

8. An electronic device, characterized in that, include: processor; And a memory for storing executable instructions of the processor; wherein the processor is configured to perform the method of any one of claims 1 to 5 by executing the executable instructions.

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