A method for evaluating snow load of a photovoltaic structure based on a multi-layer snowmelt model

Abstract

This invention discloses a method for assessing the snow load of photovoltaic structures based on a multi-layer snow melting model, comprising the following steps: obtaining basic meteorological data of the target area, starting the simulation from adding new snowfall and updating the boundary conditions at the top of the snow cover; calculating the total energy absorbed by the snow layer and photovoltaic panels, as well as the temperature of each layer; calculating the cumulative positive energy of the snow cover and its critical value, the mass balance equation of the snow cover, and the snow compaction process; and calculating the design snow load of the photovoltaic structure in the target area. By using basic meteorological data to construct the energy balance equation of the snow layer and photovoltaic panels, and the mass balance equation of the snow cover, the cumulative positive energy is used as a condition for judging snowfall, simulating the snow evolution process on the photovoltaic panels over many years; the annual extreme values ​​of snow load are extracted from the snow simulation results as samples for statistical analysis, and then the photovoltaic snow load for the return period is calculated to guide the design of photovoltaic structures. This method can save time and economic costs in determining the snow load, improve the safety of photovoltaic power plants, and reduce construction costs.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic structure snow load detection technology, and specifically relates to a method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model. Background Technology

[0002] In snowy regions, snow load is a critical control load that photovoltaic (PV) structures must consider. Firstly, the most reliable and direct method for determining snow load is on-site measurement, but this is extremely time-consuming and costly, and data collection for snow accumulation observation is difficult, making it impractical in reality. Secondly, while PV structure design can rely on code values ​​for snow load, existing codes lack sufficient historical research data on PV snow load. Therefore, code provisions stipulate that the snow distribution coefficient on tilted PV panels should be taken from the coefficient for single-slope roofs in the building load code; that is, the steeper the slope, the smaller the snow distribution coefficient for the PV structure. This simplistic approach ignores the influence of the PV panel's thermodynamic properties, resulting in inaccurate estimations of the snow load on the structure, potentially jeopardizing the safety of the PV power station or increasing equipment construction costs. Summary of the Invention

[0003] The purpose of this invention is to provide a method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model, aiming to solve the technical problems of difficulty in obtaining measured data of photovoltaic snow load and insufficient provisions in existing photovoltaic snow load specifications.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for evaluating the snow load on photovoltaic structures based on a multi-layer snow melting model includes the following steps:

[0006] Step 1: Obtain historical basic meteorological data for the target area from meteorological websites;

[0007] Step 2: Select meteorological data for year k. When simulating the snow load on the photovoltaic structure in year k, the calculation of any time step t starts from adding new snowfall and updating the boundary conditions at the top of the snow cover.

[0008] Step 3: Solve the energy balance equations for the snow layer and photovoltaic panel at time step t, and calculate the total energy absorbed by the snow layer and photovoltaic panel, as well as the temperature of each layer;

[0009] Step 4: Calculate the cumulative positive energy of the snow and its critical value. When the cumulative positive energy is greater than or equal to the critical value, it indicates that the snow has slid off, so proceed to step 2; when the cumulative positive energy is less than or equal to the critical value, it indicates that the snow has not slid off, so proceed to step 5.

[0010] Step 5: Solve the mass balance equation for snow accumulation at time step t, and calculate the phase change of snow and the snow layer outflow.

[0011] Step 6: By calculating the snow compaction process, obtain the density and depth of each snow layer after compaction within the current time step t;

[0012] Step 7: Re-divide the snow layers and update the physical parameters of the snow layers;

[0013] Step 8: Compare the current time step t with the maximum time step t max Size; when t <t max If the time frame is not met, proceed to step 2 to begin the calculation of time step t+1; otherwise, the calculation for year k ends, and the time history of the photovoltaic structure snow load for year k and the annual extreme value sample S of the snow load are output. a，max ;

[0014] Step 9: Compare the calculated year k with the maximum year k max The size of k; when k <k max Proceed to step 1 to begin the snow load simulation calculation for year k+1; otherwise, the snow load calculation for all years is complete, and the design snow load S of the photovoltaic structure in the target area is calculated. R :

[0015] ;

[0016] In the formula, u is the location parameter of the distribution, α is the scale parameter of the distribution, and R is the return period.

[0017] Furthermore, in step 1, the basic meteorological data includes daily maximum and minimum temperatures and average temperatures, daily average relative humidity, daily average wind speed, and daily total precipitation.

[0018] Hourly data is obtained by interpolating daily data; hourly temperature is linearly interpolated based on the daily maximum and minimum temperatures; hourly relative humidity and wind speed are assumed to be consistent with the daily average; hourly precipitation is the hourly average of the daily total precipitation.

[0019] Precipitation P is divided into rainfall amount and snowfall The formulas for calculating precipitation and snowfall are as follows:

[0020]

[0021] In the formula: T a For air temperature, T b T r These are the boundary values ​​for separating rain and snow, with a value of T. b =-1、T r =3.

[0022] Furthermore, in step 2, the new snowfall is divided into multiple snow layers covering the top of the existing snow cover, with each snow layer having a thickness between 0.5 and 1.0 cm.

[0023] Snowfall at current time step t The water equivalent of solid water (ice) in fresh snow; assuming the temperature of the fresh snowfall is the same as the air temperature, the depth of fresh snow is determined by the density of fresh snow and the water equivalent of solid water. The density of fresh snow is calculated as follows:

[0024]

[0025] In the formula, ρ s Snow density;

[0026] When the liquid water content exceeds the maximum water-holding capacity of the snow layer, excess snow water seeps into the next snow layer:

[0027]

[0028] In the formula, The meaning is the outflow rate of the i-th snow layer; W represents the equivalent amount of liquid water in the i-th snow layer at time step t. i Let be the snow water equivalent of the i-th snow layer; This represents the maximum water-holding capacity of the i-th snow layer.

[0029] Furthermore, in step 3, the total energy absorbed by each snow layer The following energy balance equation is used for calculation;

[0030] The energy balance equation for the i-th snow layer at time step t is:

[0031] ;

[0032] In the formula, the superscript i represents the snow layer number; the subscript f represents the front of the tilted photovoltaic panel; and the subscript s represents snow. Snow density; The specific heat of snow; This refers to the thickness of the snow layer. Snow layer temperature; Physical time; The solar radiation absorbed by the snow layer acts on the front of the photovoltaic panel; This refers to the net longwave radiation acting on the front of the photovoltaic panel; Sensible heat; Latent heat; This refers to energy transfer caused by the temperature difference between adjacent snow layers. The energy brought by precipitation; This is the first snow layer at the bottom of the snow layer, used for heat exchange between the snow layer and the photovoltaic panels.

[0033] Solar radiation acting on the front of the photovoltaic panel ( It will penetrate into the snow, and most of the solar radiation will be absorbed. Absorbed by each snow layer, the rest Photovoltaic panel absorption;

[0034] , , and It exists only in the m-th snow layer, which is in direct contact with the air.

[0035] The sum of the terms on the right-hand side of the energy balance equation for the snow layer above represents the total energy absorbed by each snow layer at time step t. The total energy absorbed by the snow on the photovoltaic panel at time t is ΔE, which represents the total energy absorbed by each snow layer. sum;

[0036] Total energy absorbed by the photovoltaic panel at time step t The following energy balance equation is used for calculation: ;

[0037] In the formula, the subscript PV represents the photovoltaic panel; the subscript b represents the back of the tilted photovoltaic panel; and m is the number of snow layers. Photovoltaic panel density; Specific heat of photovoltaic panels; The thickness of the photovoltaic panel; Temperature of the photovoltaic panel; Solar radiation that acts on the front of the photovoltaic panel and penetrates into the photovoltaic panel; This refers to the net solar radiation acting on the back of the photovoltaic panel; This refers to the net longwave radiation acting on the back of the photovoltaic panel; The net long-wave radiation from the front of the photovoltaic panel; This refers to the convective heat loss on the front side of the photovoltaic panel; This refers to the heat loss caused by convection on the back of the photovoltaic panel; The energy carried away by photovoltaic panels as they absorb solar radiation to generate electricity; Energy exchange between snow and photovoltaic panels;

[0038] Based on the energy balance equations for the snow layer and photovoltaic panels described above, the total energy absorbed by each snow layer at time step t is obtained. and the total energy absorbed by the photovoltaic panel And the temperature of each layer.

[0039] Furthermore, in step 3, the calculation process for each energy term in the energy balance equation for solving the total energy absorbed by each snow layer and photovoltaic panel is as follows:

[0040] 1) Solar shortwave radiation

[0041] The total radiation from the sun reaching the ground at a horizontal surface is called diffuse radiation. and direct radiation The sum of the solar radiation and the solar radiation reflected from the ground onto the tilted surface of the photovoltaic panel, in addition to the scattered and direct radiation acting on the tilted surface, also includes the scattered radiation acting on the tilted surface. The scattered radiation acting on the front and back of the tilted surface of the photovoltaic panel are expressed as follows: and The direct radiation acting on the front and back sides of the tilted surface of the photovoltaic panel are respectively represented as: and The reflected radiation from the ground to the front and back of the tilted surface of the photovoltaic panel is represented as follows: and ;

[0042] The sum of all radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front side of the inclined surface. Total radiation from the back of the inclined surface , respectively represented as: , ;

[0043] The albedo of the front and back sides of the inclined surface is expressed as follows: and Under the influence of albedo, a portion of the total radiation leaves the surface of the inclined surface, including the total radiation that leaves the front of the inclined surface due to albedo. and the total radiation amount away from the back of the inclined surface due to albedo , respectively represented as: , The remaining portion represents the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and net solar radiation acting on the back side of the inclined surface , respectively represented as: , ;

[0044] Net solar radiation acting on the front of the tilted surface of the photovoltaic panel The amount of radiation received by the snow layer and the photovoltaic panel are respectively expressed as: , ;

[0045] Potential extraterrestrial solar radiation on a certain day The calculation formula is:

[0046]

[0047] In the formula, It is the solar constant; Solar declination; Latitude;

[0048] Daily total horizontal radiation The relationship between daily potential extraterrestrial solar radiation and the daily clear sky index can be used. To assess; daily total horizontal radiation ; The calculation formula is:

[0049]

[0050] In the formula, The daily temperature difference is represented by a, b, and c, which are empirical coefficients.

[0051] After obtaining the total daily horizontal radiation, it needs to be further decomposed into the direct radiation components on the daily horizontal surface. and scattered radiation components The ratio of daily scattered radiation to daily total horizontal radiation; Scattering fraction The daily clear sky index The function of daily horizontal scattered radiation; The daily direct radiation at the horizontal surface is ; The calculation formula is:

[0052] ;

[0053] In the formula, The sunset angle, with the 81.4° dividing line used in the formula. Seasonal correlation;

[0054] Photovoltaic structure snowmelt models require hourly radiation data to accurately simulate snow accumulation time histories. Hourly radiation data can be obtained from daily radiation data. Hourly total radiation is used. Total daily radiation ratio To characterize the relationship between the two. Hourly total radiation , hour angle The function is calculated using the following formula:

[0055]

[0056] Similarly, hourly scattered radiation Sun-scattered radiation ratio The hourly scattered radiation can be calculated using the following formula. Hours of direct radiation ; The calculation formula is as follows:

[0057]

[0058] Solar radiation acting on the front of the tilted surface of the photovoltaic panel Direct radiation including inclined surfaces Scattered radiation from inclined surfaces Inclined surface reflects radiation Three components; each component can be directly radiated through the horizontal plane. Scattered radiation This invention uses the HDKR model (the Hay, Davies, Klucher, Reindl model) to calculate the total radiation on the inclined surface. The calculation method is as follows:

[0059]

[0060] In the formula, geometric factor ,in Angle of incidence Zenith angle;

[0061] is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; The direct score; Ground albedo; The tilt angle of the photovoltaic panel;

[0062] For tilted photovoltaic panels that are raised by supports, both the front and back sides will receive solar radiation from the sky. , The solar radiation received by the back panel is generally low and does not participate in power generation, but it will slightly increase the temperature of the photovoltaic panel. This is calculated when determining the solar radiation received by the back panel. When this occurs, it can be calculated using the following formula; unlike frontal radiation, only the contributions of scattered and reflected radiation components are considered here. Furthermore, the calculation... The tilt angle of the back of the photovoltaic panel is taken :

[0063]

[0064] For a photovoltaic panel covered by snow, the net solar radiation absorbed by both the photovoltaic panel and the snow surface ( , The albedo of the front snow cover and the photovoltaic backsheet should also be considered separately. , The impact of:

[0065] ;

[0066] In the formula, The effect of snow-covered photovoltaic panels on absorbing net solar radiation on the front; The effect of the snow-covered photovoltaic panel on absorbing solar radiation on the back side; The albedo is the reflectance of the front of the snow-covered photovoltaic panel, i.e., the albedo of the snow surface; The albedo is the reflectance on the back of the snow-covered photovoltaic panel, i.e., the reflectance on the back of the photovoltaic panel.

[0067] The net solar radiation acting on the front of the photovoltaic panel penetrates into the snow layer and is gradually absorbed. The amount of solar radiation absorbed by each snow layer... The expression is as follows:

[0068]

[0069] In the formula, m represents the total number of snow layers; c1 and c2 are empirical coefficients; after removing the solar radiation absorbed by the snow, the remaining radiation is absorbed by the photovoltaic panels at the bottom of the snow layer. Solar radiation absorbed by the photovoltaic panels. Calculate according to the following formula:

[0070]

[0071] When covered by snow, very little solar radiation penetrates to the photovoltaic panel, and a small proportion of this penetrated radiation is reflected back into the snow. Therefore, it is assumed that the photovoltaic panel absorbs all the solar radiation that penetrates to it. When there is no snow on the photovoltaic panel, the following formula is used to consider the impact of the photovoltaic panel's absorption and transmission capabilities on solar radiation:

[0072]

[0073] In the formula, , and It is the product of transmittance and absorptivity at the effective incident angles of direct, scattered, and reflected radiation.

[0074] 2) Net longwave radiation

[0075] Incident or outgoing longwave radiation can be calculated using the Stefan-Boltzmann equation:

[0076]

[0077] In the formula, the subscript j refers to the main body emitting long-wave radiation, and sky, gr, f and b represent the sky, the ground, the front and back of the tilted surface of the photovoltaic panel, respectively. Represents the long-wave radiation emitted by j; Let j be the temperature; For Stefan Boltzmann constant, Let j be the emissivity;

[0078] The long-wave radiation between the front and back surfaces of the tilted photovoltaic panel and the sky and ground needs to be considered separately. The net long-wave radiation of each surface is calculated according to the following formula:

[0079]

[0080] In the formula, L sky Long-wave radiation emitted from the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Long-wave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f F represents the apparent factor from the sky to the front of the photovoltaic panel. gr-f F is the apparent factor from the ground to the front of the photovoltaic panel. sky-b F represents the apparent factor from the sky to the back of the photovoltaic panel. gr-b The apparent factor is the distance from the ground to the back of the photovoltaic panel;

[0081] 3) Sensible heat

[0082] The sensible heat exchange between the upper surface of the snow and the air is calculated according to the following formula:

[0083]

[0084] In the formula, air density; The specific heat of air; This is the adjusted turbulence exchange coefficient; To measure wind speed at an altitude; The convective heat transfer coefficient of sensible heat flux under windless conditions; Air temperature; This refers to the surface temperature of the snow.

[0085] 4) Latent heat

[0086] The formula for calculating the latent heat flux exchange between the snow surface and the air is as follows:

[0087]

[0088] In the formula, To sublimate latent heat; The constant for dry air; The adjusted turbulent exchange coefficient, ; It is the vapor pressure of air; The vapor pressure of the snow surface;

[0089] 5) Heat transfer between snow layers

[0090] The energy transfer between adjacent snow layers due to temperature differences is calculated by the following formula:

[0091]

[0092] In the formula, Temperature of snow cover; The coordinates of the snow along the depth direction; The effective heat transfer coefficient of the snow layer;

[0093] 6) Heat brought by precipitation

[0094] The energy that precipitation brings to snow accumulation can be expressed in the following form:

[0095]

[0096] In the formula, This refers to the amount of snowfall. The specific heat of snow; c w The specific heat of liquid water; The density of liquid water; Rainfall; It is the latent heat of melting of snow.

[0097] 7) Electricity generated by photovoltaics

[0098] The formula for calculating photovoltaic capacity is as follows:

[0099]

[0100] In the formula, The solar radiation received on the front of the tilted photovoltaic panel; This represents the maximum efficiency of the photovoltaic module under standard test conditions. The maximum power temperature coefficient; Temperature of the photovoltaic module; The reference temperature for standard test conditions; solar radiation not used for power generation is converted into heat inside the photovoltaic panel. ;

[0101] 8) Heat loss due to convection

[0102] The formulas for calculating heat loss due to convection on the front and back of a photovoltaic panel are as follows:

[0103]

[0104] In the formula, The forced convection heat transfer coefficient; The free convection heat transfer coefficient; This refers to the temperature difference at the photovoltaic-air boundary; when snow accumulates on the surface of the photovoltaic panel, the heat loss on the front of the panel due to convection is also considered. It is zero;

[0105] The forced convection heat transfer coefficient is calculated using the following formula:

[0106]

[0107] In the formula, It is the Reynolds number; For Prandtl numbers, The thermal conductivity of air; The length of the module along the natural airflow direction;

[0108] The free convection heat transfer coefficient is calculated using the following formula:

[0109]

[0110] In the formula, Rayleigh number;

[0111] 9) Heat exchange between photovoltaic panels and snow accumulation

[0112] The heat transfer between the photovoltaic panel and the snow is determined by the temperature difference between the photovoltaic panel and the lower surface of the snow, and the calculation formula is as follows:

[0113]

[0114] In the formula, This refers to the surface temperature beneath the snow cover. The thermal conductivity of the photovoltaic panel; This refers to the thickness of the photovoltaic panel.

[0115] Furthermore, in step 4, the formula for calculating the cumulative positive energy of snow accumulation during the time interval from the initial time t0 to any time t is as follows:

[0116]

[0117] In the formula, ΔE is the total energy absorbed by the snow on the photovoltaic panel at time step t; Positive energy for the accumulation of snow;

[0118] Photovoltaic panels with different slopes The corresponding formula for calculating the cumulative positive energy threshold is as follows:

[0119]

[0120] In the formula, The cumulative positive energy threshold is defined by A, B, and C, which are empirical coefficients determined from actual snow cover measurements or experimental data.

[0121] Furthermore, in step 5, the phase change between liquid and solid water within the snow and the calculation process for snow layer outflow are as follows:

[0122] The evaporation or sublimation of liquid water within snow will cause a change in snow mass. Substituting precipitation and snowfall into the following formula yields the amount of sublimation and evaporation. The formula for calculating the change is as follows:

[0123]

[0124] In the formula, This is the equivalent of snow water in the liquid water layer at the top; The latent heat of snow evaporation; h s For the latent heat of snow sublimation; W e E1 is the amount of sublimation evaporation; ρ is the latent heat; w Let be the density of water; when there is liquid water in the snow layer, the phase change of water due to latent heat is considered only for evaporation; when there is no liquid water in the snow layer, the phase change of water due to latent heat is considered only for sublimation.

[0125] The outflow of snowmelt from the snowpack is controlled by the snow layer's maximum water-holding capacity; when the liquid water content exceeds the snow layer's maximum water-holding capacity, excess snowmelt seeps into the next snow layer.

[0126]

[0127] In the formula, Let be the snow water equivalent of the i-th snow layer; This represents the maximum water-holding capacity of the i-th snow layer;

[0128] When the snow layer absorbs energy, a phase change occurs between solid water (ice) and liquid water within the snow layer, resulting in their interconversion; the change in solid water due to the phase change at time step t. and changes in liquid water Calculated according to the following formula:

[0129]

[0130] In the formula, This represents the total energy absorbed by the i-th snow layer. The density of liquid water, The latent heat of melting ice, Let be the equivalent water volume of solid water in the i-th snow layer. Let t be the equivalent amount of liquid water in the i-th snow layer, t represent the current time step, and t-1 represent the previous time step.

[0131] Liquid water equivalent in the i-th snow layer at time step t Water equivalent to solid water Calculate using the following formula:

[0132]

[0133]

[0134] The phase change between liquid and solid water in the snow and the snow layer outflow are calculated using the above formulas. Then, the mass balance equation of the snow layer at time step t is solved to obtain the change in mass of each snow layer.

[0135] The mass balance equation for snow accumulation on photovoltaic panels is shown below:

[0136]

[0137] In the formula, This represents the water equivalent of the i-th snow layer. Rainfall. Snowfall snow melt outflow Snow sublimation or evaporation This will cause changes in the quality of the top snow layer.

[0138] Furthermore, in step 6, for densities less than 150 kg·m³ -3 For fresh snow, the destructive deformation of the internal structure of the snow layer is the main cause of snow compaction. The compaction rate can be calculated using the following empirical formula:

[0139]

[0140] After the initial destructive deformation stage, the rate of snow compaction decreases significantly. At this point, the main reason for snow compaction is the gravity compaction of the accumulated snow. The compaction rate can be calculated using the following formula:

[0141]

[0142] The total rate of snow compaction is the sum of the compaction rates of the two stages mentioned above:

[0143]

[0144] The change in snow density due to snow compaction can be obtained from the following formula:

[0145]

[0146] In the formula, γ represents the temperature of snow layer i; i The density of snow layer i; P s η is the pressure of the snow accumulation on the upper part of the snow layer; η0 is an empirical parameter.

[0147] Furthermore, in step 7, the snow layers are re-divided, completely melted snow layers are removed, snow layers less than 0.5 cm are merged with adjacent snow layers, and snow layers greater than 1.0 cm are further subdivided so that each layer meets the thickness requirements.

[0148] The physical parameters of the snow layer, such as density, depth, water content, and temperature, are updated using a weighted average method.

[0149] Furthermore, in step 8, the snow load is the product of snow depth and snow density; the time history of the photovoltaic structure snow load in year k is output, and the maximum snow load value is extracted as the annual extreme value sample of snow load. .

[0150] Furthermore, in step 9, the snow load of the photovoltaic structure under a certain guarantee rate is calculated using snow load samples from all years. ;

[0151] "Snow load with a return period of R" means that the magnitude is The snow load occurs on average once every R years, meaning that in any given year, the guarantee rate of 1-1 / R will not exceed [a certain value]. Snow load;

[0152] "A certain guarantee rate" refers to the snow load during the return period R. The probability of not exceeding the limit in a given year. Generally, the snow load return period for photovoltaic structures is taken as 25 years, in which case the "certain guarantee rate" is 1 - 1 / 25 = 96%;

[0153] The statistical sample of snow load uses the annual maximum value, and it is assumed that the sample distribution follows a type I extreme value distribution, with the distribution function being:

[0154]

[0155] In the formula, This is a sample of annual extreme values ​​of snow load. The location parameter of the distribution is the scale parameter of the distribution. denoted as the sample standard deviation, and μ as the sample mean.

[0156] The technological advancements achieved by this invention compared to existing technologies are as follows:

[0157] This invention utilizes basic meteorological data from the target region to construct energy balance equations for snow layers and photovoltaic panels, as well as mass balance equations for snow accumulation. Accumulated positive energy is used as a condition for determining snowfall, simulating the multi-year snow accumulation evolution process on photovoltaic panels. Subsequently, annual extreme values ​​of snow load are extracted from the snow accumulation simulation results as samples for statistical analysis. The photovoltaic snow load under a certain guarantee rate is then calculated to guide photovoltaic structure design. This significantly reduces the time and economic costs required to determine snow load and improves the accuracy of snow load estimation on photovoltaic structures. This invention considers the energy balance process of photovoltaic panels, especially the impact of tilted surface radiation on snow melting on photovoltaic panels. It is particularly suitable for accurate simulation of snow load on photovoltaic structures in areas lacking snow accumulation observation data, improving the safety of photovoltaic power plants and reducing construction costs. Attached Figure Description

[0158] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0159] In the attached diagram:

[0160] Figure 1 A flowchart illustrating a method for evaluating the snow load on photovoltaic structures based on a multi-layer snow melting model, provided in an embodiment of the present invention;

[0161] Figure 2 This is a schematic diagram illustrating the various energy and mass exchanges between snow accumulation on the photovoltaic panel and the environment in an embodiment of the present invention;

[0162] Figure 3 This is a schematic diagram illustrating the exchange of interlayer energy between layers when there is snow accumulation on the photovoltaic panel in an embodiment of the present invention;

[0163] Figure 4 This is a schematic diagram illustrating the energy exchange between the photovoltaic panel and the natural environment through radiation and convection when there is no snow accumulation on the panel, according to an embodiment of the present invention.

[0164] Figure 5 This is a schematic diagram of the solar shortwave radiation components on the tilted surface of the photovoltaic panel in an embodiment of the present invention;

[0165] Figure 6 This is a flowchart illustrating the calculation of solar shortwave radiation on a snow-covered photovoltaic panel in an embodiment of the present invention.

[0166] Figure 7 This is a schematic diagram illustrating the use of accumulated positive energy to determine snowfall in an embodiment of the present invention. Detailed Implementation

[0167] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0168] Currently, determining the snow load on photovoltaic (PV) structures mainly relies on experimental testing and values ​​derived from design specifications. Experimental testing is difficult to control due to challenging external conditions, consuming significant time, money, and manpower costs, and its limited scale restricts the amount of data obtained. Furthermore, the snow load calculation methods for PV structures recommended by design specifications, referencing building structure codes, are overly conservative, significantly increasing construction costs. Moreover, code provisions rely on engineering experience, and due to a lack of sufficient case studies of PV structure snow loads, the code methods are inaccurate. In contrast, the numerical simulation method provided by this invention is more flexible and efficient.

[0169] The snow load assessment method for photovoltaic structures proposed in this invention, based on snow melting models and statistical analysis of snow load samples, can rapidly, economically, and accurately simulate the multi-year snow load of photovoltaic structures in a target area using readily available basic meteorological data from weather stations. It also obtains snow loads under a certain guarantee rate to guide photovoltaic structure design, improve structural safety, and reduce construction costs. Ordinary snow melting models are mostly used for runoff prediction, water resource management, and avalanche early warning; a few can simulate snow loads on building structures. Compared to ordinary snow melting models, the multi-layer snow melting model for photovoltaic structures constructed in this invention considers the energy balance process of photovoltaic panels, especially the influence of tilted surface radiation on snow melting on photovoltaic panels, making it particularly suitable for accurate simulation of snow loads on photovoltaic structures in areas lacking snow accumulation observation data. The following is the specific assessment process of this invention:

[0170] 1. Model Introduction

[0171] The multi-layer snow melting model of photovoltaic structures simulates snow accumulation and photovoltaic panels as a complete system. Figure 2 This model demonstrates the various energy and mass exchanges between the snow accumulation above the photovoltaic panel and the environment. In this calculation, the snow accumulation is divided into multiple snow layers capable of phase transitions along the normal direction of the photovoltaic panel plane. The temperature and density within each snow layer are linearly distributed, and its thickness ranges from 0.5 to 1.0 cm. Due to physical phenomena such as melting and condensation within the snow, it is considered to be composed of three phases: ice, water, and air. The sum of the volume fractions of the three phases is 1.0. Compared to the snow accumulation, the photovoltaic panel is considered a special layer that does not undergo phase transitions and is in direct contact with the underlying snow layer. Figure 3 There is heat conduction and energy exchange between the layers. When there is no snow cover on the top of the photovoltaic panel, both its upper and lower surfaces are directly exposed to the air, exchanging energy with the natural environment through radiation and convection. Figure 4 For ease of description, this invention defines the surface of the photovoltaic panel facing the sky as the front and the surface of the tilted surface facing the ground as the back. In the formula, the subscript f represents the front and b represents the back, respectively.

[0172] 1.2 Energy Balance Equation

[0173] Depend on Figure 2 It can be seen that the energy absorbed by each snow layer is different, and the energy balance equation of the i-th snow layer is as follows: As shown:

[0174]

[0175] In the formula, the superscript i represents the snow layer number; the subscript f represents the front of the tilted photovoltaic panel; and the subscript s represents snow. Snow density; The specific heat of snow; This refers to the thickness of the snow layer. Snow layer temperature; Physical time. Net longwave radiation acting on the front. Energy brought by precipitation and sensible heat and latent heat This exists only in the m-th snow layer, which is in direct contact with the air. Heat exchange between the snow layer and the photovoltaic panel... The first snow layer at the bottom of the snowpack. Energy transfer (heat conduction) occurs between adjacent snow layers due to temperature differences. ;

[0176] Net solar (shortwave) radiation acting on the front It will penetrate into the snow, and most of the solar radiation will be absorbed. Absorbed by each snow layer, the rest Photovoltaic panel absorption.

[0177] The energy transfer process of photovoltaic panels is as follows Figure 3 and Figure 4 As shown, its energy balance equation is expressed as follows:

[0178]

[0179] In the formula, the subscript PV represents the photovoltaic panel; the subscript b represents the back of the tilted photovoltaic panel; and m is the number of snow layers. Photovoltaic module density; Specific heat of photovoltaic modules; The thickness of the photovoltaic panel; The temperature of the photovoltaic panel. When the upper part of the photovoltaic panel is covered by snow (m>1), the energy exchange between the module and the surrounding environment includes solar radiation acting on the front and penetrating into the photovoltaic panel. Energy exchange between snow and photovoltaic panels Net longwave radiation acting on the back of the photovoltaic panel Heat loss due to convection on the back of the photovoltaic panel Net solar radiation acting on the back of the photovoltaic panel And the energy carried away by photovoltaic panels due to absorbing solar radiation to generate electricity. When there is no snow cover on the photovoltaic panel (m=0), the front of the photovoltaic panel will be in contact with the atmosphere, and the heat conduction between the snow and the photovoltaic panel will be affected. It will not exist. At this point, the net longwave radiation acting on the front must also be considered. and positive convective heat loss The following section introduces the calculation formulas for each energy term.

[0180] (1) Solar shortwave radiation

[0181] Figure 5 It displays various shortwave (solar) radiation components on the inclined plane. Figure 6 This is a flowchart for calculating shortwave radiation.

[0182] extraterrestrial solar radiation emitted by the sun Due to the scattering, absorption, and transmission effects of the atmosphere, it is attenuated and converted into scattered radiation. and direct radiation Reaching the ground, the sum of the two is the total horizontal radiation ( The radiation component on the inclined surface can be calculated from the radiation component on the horizontal surface using a radiation model. For the front and back sides of the inclined surface, in addition to the scattered and direct radiation acting on the inclined surface, the solar radiation reflected from the ground to the inclined surface must also be considered. The scattered radiation acting on the front and back sides of the photovoltaic panel's inclined surface are expressed as follows: and The direct radiation acting on the front and back sides of the tilted surface of the photovoltaic panel are respectively represented as: and The reflected radiation from the ground to the front and back of the tilted surface of the photovoltaic panel is represented as follows: and Generally, in the Northern Hemisphere winter, the sun is always in the front of a south-facing photovoltaic panel, and the back of the panel cannot be directly exposed to sunlight. Therefore, the direct radiation incident on the back is limited. This can be ignored. The sum of all radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front side of the inclined surface. Total radiation from the back of the inclined surface , respectively represented as: , The albedo of the front and back sides of the inclined surface is expressed as follows: and Under the influence of albedo, a portion of the total radiation leaves the surface of the inclined surface, including the total radiation that leaves the front of the inclined surface due to albedo. and the total radiation amount away from the back of the inclined surface due to albedo , respectively represented as: , The remaining portion represents the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and net solar radiation acting on the back side of the inclined surface , respectively represented as: , Net solar radiation acting on the front of the tilted surface of the photovoltaic panel. The effects of transmission and absorption by snow and photovoltaic panels need to be further considered. The final amount of radiation received by the snow layer and photovoltaic panels is expressed as follows: , .

[0183] Potential extraterrestrial solar radiation on a certain day The calculation formula is as follows:

[0184]

[0185] In the formula, It is the solar constant; Solar declination; Latitude.

[0186] Daily total horizontal radiation The relationship between daily potential extraterrestrial solar radiation and the daily clear sky index can be used. To assess. Daily total horizontal radiation. This article uses the following formula for calculation. :

[0187]

[0188] In the formula, denoted as , where a, b, and c are empirical coefficients.

[0189] After obtaining the total daily horizontal radiation, it needs to be further decomposed into the direct radiation components on the daily horizontal surface. and scattered radiation components The ratio of daily scattered radiation to daily total horizontal radiation. Scattering fraction The daily clear sky index A function of daily scattered radiation on a horizontal surface. The daily direct radiation at the horizontal surface is . and relational formula Adopt the following form:

[0190]

[0191] In the formula, The sunset angle, with the 81.4° dividing line used in the formula. Seasonal correlation.

[0192] Multi-layer snow melting models for photovoltaic structures require hourly radiation data to accurately simulate snow accumulation time histories. Hourly radiation data can be obtained from daily radiation data. The total hourly radiation is used. Total daily radiation ratio To characterize the relationship between the two. Hourly total radiation . hour angle The function is calculated using the following formula:

[0193]

[0194] Similarly, hourly scattered radiation Sun-scattered radiation ratio Formulas can be used Calculate hourly scattered radiation. Hours of direct radiation . The calculation formula is as follows:

[0195]

[0196] Solar radiation acting on the front of the inclined surface Direct radiation including inclined surfaces Scattered radiation from inclined surfaces Inclined surface reflects radiation Three components. Each component can be directly radiated through the horizontal plane. Scattered radiation This invention uses the HDKR model (the Hay, Davies, Klucher, Reindl model) to calculate the total radiation on the inclined surface. The calculation method is as follows: As shown, the three terms in the formula correspond to the three components of the radiation from the inclined surface:

[0197]

[0198] In the formula, geometric factor ,in Angle of incidence Zenith angle; is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; The direct score; Ground albedo; The tilt angle of the photovoltaic panel.

[0199] For tilted PV systems that are elevated by supports, both the front and back sides receive solar radiation from the sky. , The solar radiation received by the back panel is generally low and does not participate in power generation, but it will slightly increase the temperature of the photovoltaic panel. This is calculated when determining the solar radiation received by the back panel. At that time, you can follow the formula Calculations are performed. Unlike frontal radiation, only the contributions of scattered and reflected radiation components are considered here. Furthermore, calculations are performed... The tilt angle of the back of the photovoltaic panel is taken :

[0200]

[0201] For a photovoltaic panel covered by snow, the net solar radiation absorbed by both surfaces is ( , The albedo of the front snow cover and the photovoltaic backsheet should also be considered separately. , The impact of:

[0202]

[0203] The net solar radiation acting on the front penetrates into the snow layer and is gradually absorbed. Referenced studies indicate the amount of solar radiation absorbed by each snow layer. The expression is as follows:

[0204]

[0205] In the formula, m represents the total number of snow layers; c1 and c2 are empirical coefficients. After removing the solar radiation absorbed by the snow, the remaining radiation is absorbed by the photovoltaic panels at the bottom of the snow layer. The solar radiation absorbed by the photovoltaic panels... It can be calculated using the following formula:

[0206]

[0207] When covered by snow, very little solar radiation penetrates to the photovoltaic panel, and a small proportion of this penetrated radiation is reflected back into the snow. Therefore, it is assumed that the photovoltaic panel absorbs all the solar radiation that penetrates to it. When there is no snow on the photovoltaic panel, the following formula is used to consider the impact of the photovoltaic panel's absorption and transmission capabilities on solar radiation:

[0208]

[0209] In the formula, , and It is the product of transmittance and absorptivity at the effective incident angle of direct, scattered, and reflected radiation.

[0210] (2) Net longwave radiation

[0211] Incident or outgoing longwave radiation can be calculated using the Stefan-Boltzmann equation:

[0212]

[0213] In the formula, the subscript j represents the main body emitting long-wave radiation, which can be sky, gr, f, and b, representing the sky, the ground, the front of the tilted surface, and the back of the tilted surface, respectively. Represents the long-wave radiation emitted by j; Let j be the temperature; For Stefan Boltzmann constant, Let j be the emission rate.

[0214] The long-wave radiation between the front and back of the inclined surface and the sky and the ground needs to be considered separately. The net long-wave radiation of each surface is calculated according to the following formula:

[0215]

[0216] In the formula, L sky Long-wave radiation emitted from the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Long-wave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f F represents the apparent factor from the sky to the front of the photovoltaic panel. gr-f F is the apparent factor from the ground to the front of the photovoltaic panel. sky-b F represents the apparent factor from the sky to the back of the photovoltaic panel. gr-b The apparent factor is the distance from the ground to the back of the photovoltaic panel.

[0217] (3) Sensible heat

[0218] The sensible heat exchange between the upper surface of the snow and the air is calculated according to the following formula:

[0219]

[0220] In the formula, air density; The specific heat of air; This is the adjusted turbulence exchange coefficient; To measure wind speed at an altitude; The convective heat transfer coefficient of sensible heat flux under windless conditions; Air temperature; This represents the surface temperature of the snow.

[0221] (4) Latent heat

[0222] The formula for calculating the latent heat flux exchange between the snow surface and the air is as follows:

[0223]

[0224] In the formula, To sublimate latent heat; The constant for dry air; The adjusted turbulent exchange coefficient, ; It is the vapor pressure of air; This is the vapor pressure of the snow surface.

[0225] (5) Heat transfer between snow layers

[0226] The energy transfer between adjacent snow layers due to temperature differences is calculated by the following formula:

[0227]

[0228] In the formula, Temperature of snow cover; The coordinates of the snow along the depth direction; is the effective heat transfer coefficient of the snow layer.

[0229] (6) Heat brought by precipitation

[0230] The energy that precipitation brings to snow accumulation can be expressed in the following form:

[0231]

[0232] In the formula, This refers to the amount of snowfall. The specific heat of snow; The density of liquid water; Rainfall; This is the latent heat of melting of snow.

[0233] (7) Electricity generated by photovoltaics

[0234] The formula for calculating photovoltaic capacity is as follows:

[0235]

[0236] In the formula, The solar radiation received on the front side of the tilted photovoltaic panel; This represents the maximum efficiency of the photovoltaic module under standard test conditions. The maximum power temperature coefficient; Temperature of the photovoltaic module; This is the reference temperature for standard test conditions. Solar radiation not used for power generation is converted into heat inside the photovoltaic panel. .

[0237] (8) Heat loss caused by convection

[0238] The formulas for calculating heat loss due to convection on the front and back of a photovoltaic panel are as follows:

[0239]

[0240] In the formula, The forced convection heat transfer coefficient; The free convection heat transfer coefficient; This refers to the temperature difference at the photovoltaic-air boundary; when snow accumulates on the surface of the photovoltaic panel, the heat loss on the front of the panel due to convection is also considered. It is zero.

[0241] The forced convection heat transfer coefficient is calculated using the following formula:

[0242]

[0243] In the formula, It is the Reynolds number; For Prandtl numbers, The thermal conductivity of air; The length of the photovoltaic panel along the natural airflow direction;

[0244] The free convection heat transfer coefficient is calculated using the following formula:

[0245]

[0246] In the formula, It is a Rayleigh number.

[0247] (8) Heat exchange between photovoltaics and snow cover

[0248] The heat transfer between the photovoltaic panels and the snow is determined by the temperature difference between the photovoltaic panels and the lower surface of the snow, and the calculation formula is as follows:

[0249]

[0250] In the formula, This refers to the surface temperature beneath the snow cover. The thermal conductivity of the photovoltaic panel; This refers to the thickness of the photovoltaic panel.

[0251] 1.3 Mass Balance Equation

[0252] When snow accumulates on top of a photovoltaic (PV) module, the mass balance equation for the snow needs to be solved. Compared to the snow particles and water inside the snow layer, the phase change and diffusion of water vapor have a smaller impact on the mass change of the snow layer; therefore, its influence on the mass balance equation is ignored. The mass balance equation for snow accumulation on a photovoltaic (PV) module is shown in the formula. As shown:

[0253]

[0254] In the formula, This represents the water equivalent of the i-th snow layer. Rainfall. Snowfall snow melt outflow Snow sublimation or evaporation This will cause changes in the mass of the top snow layer. The mass changes of the middle and bottom snow layers are determined by the outflow of the preceding and current snow layers. The calculation formulas for each mass term are introduced below.

[0255] (1) Rainfall and snowfall

[0256] Precipitation and snowfall are calculated based on temperature using the following formula:

[0257]

[0258] (2) Evaporation and sublimation

[0259] The evaporation or sublimation of liquid water within snow will cause a change in the mass of the snow. The amount of change can be calculated using the following formula:

[0260]

[0261] In the formula, This is the equivalent of snow water in the liquid water layer at the top; The latent heat of snow evaporation is considered. When there is liquid water in the snow layer, the phase change of water caused by latent heat is only considered as evaporation; when there is no liquid water in the snow layer, the phase change of water caused by latent heat is considered as sublimation.

[0262] (3) Outflow rate

[0263] The outflow of meltwater from snowpack is controlled by the snow layer's maximum water-holding capacity. When the liquid water content exceeds the snow layer's maximum water-holding capacity, excess meltwater seeps into the next snow layer.

[0264]

[0265] In the formula, Let be the snow water equivalent of the i-th snow layer; This represents the maximum water-holding capacity of the i-th snow layer.

[0266] 1.4 Phase Transition Process

[0267] When the snow layer absorbs energy, a phase transition occurs between solid water (ice) and liquid water within it, resulting in their interconversion. The change in solid water volume due to the phase transition at time step t is shown. and changes in liquid water Calculated according to the following formula:

[0268]

[0269] In the formula, This represents the total energy absorbed by the i-th snow layer. The density of liquid water, The latent heat of melting ice, Let be the equivalent water volume of solid water in the i-th snow layer. Let t be the equivalent amount of liquid water in the i-th snow layer, t represent the current time step, and t-1 represent the previous time step.

[0270] Liquid water equivalent in the i-th snow layer at time step t Water equivalent to solid water Calculate using the following formula:

[0271]

[0272]

[0273] 1.5 snow density

[0274] (1) New snow density

[0275] The bulk density of fresh snow varies greatly under different climatic conditions. It is generally considered that the density of fresh snow is a function of air temperature, and the formula is expressed as follows:

[0276]

[0277] (2) Snow compaction

[0278] Snow is constantly subjected to compaction after it falls. Snow compaction can be divided into two stages: the stage where fresh snow is compacted due to deformation and breakage, and the stage where snow is compacted due to gravity or pressure from above.

[0279] For densities less than 150 kg·m -3For fresh snow, the destructive deformation of the internal structure of the snow layer is the main cause of snow compaction. The compaction rate can be calculated using the following empirical formula:

[0280]

[0281] After the initial destructive deformation stage, the rate of snow compaction decreases significantly. At this point, the main reason for snow compaction is the gravity compaction of the accumulated snow. The compaction rate can be calculated using the following formula:

[0282]

[0283] The total rate of snow compaction is the sum of the compaction rates of the two stages mentioned above:

[0284]

[0285] The change in snow density due to snow compaction can be obtained from the following formula:

[0286]

[0287] 2. Criteria for determining snow rollover

[0288] Snow accumulated on photovoltaic panels will gradually melt or even slide off under the influence of external conditions such as radiation and temperature. This invention uses a method of accumulating positive energy to determine snow sliding off. Figure 7 Figure (a) and Figure 7 As shown in Figure (b), after fresh snow falls onto the photovoltaic panels, the snow absorbs energy from the environment. The total energy absorbed by the snow at a certain moment (Formula) (The sum of all the energies involved) When the value is greater than zero, it is said that the snow has absorbed positive energy. The so-called accumulation of positive energy This refers to the positive energy absorbed by the photovoltaic panels at every moment during the period when snow covers them. Integral over time, i.e. Figure 7 The area of ​​the shaded region under the curve in figure (b) is calculated using the following formula:

[0289]

[0290] like Figure 7 Figure (c) in the middle and Figure 7 In Figure (d), there is a critical value for the cumulative positive energy of snow accumulation on the sloping surface. When positive energy accumulates Reaching the critical value Snow slides off the solar panels, snow load The snow load quickly drops to zero. Conversely, the snow melts naturally in the environment. The snow load on the photovoltaic panels in a given year... The maximum value is the annual extreme value of the snow load on the photovoltaic structure. Different slopes Corresponding cumulative positive energy threshold (unit: MJ·m) -2 The following formula can be used for calculation:

[0291]

[0292] In the formula, The cumulative positive energy threshold is defined by A, B, and C, which are empirical coefficients determined from actual snow cover measurements or experimental data.

[0293] 3. Meteorological data

[0294] The meteorological data required for the photovoltaic structure snow melting model consists of basic meteorological elements collected by weather stations, which can be obtained from meteorological data websites. Specifically, it requires the daily maximum and minimum temperatures, average daily relative humidity, average daily wind speed, and total daily precipitation. The snow melting model is calculated in one-hour increments. Hourly temperatures are interpolated based on the daily maximum and minimum temperatures. Hourly relative humidity and wind speed are assumed to be consistent with the daily averages. Hourly precipitation is the hourly average of the total daily precipitation. When inputting into the snow melting model, according to the formula Precipitation is divided into rainfall and snowfall .

[0295] 4. Statistical analysis of extreme annual snow load samples

[0296] By combining historical meteorological data, a snow melting model for photovoltaic structures can simulate the variation of snow load on photovoltaic structures over time. Statistical analysis of the snow load over the years yields the snow load on the photovoltaic structure under a certain guarantee rate. The statistical sample of the snow load uses the annual maximum value, and it is assumed that the sample distribution conforms to a Type I extreme value distribution, with the distribution function as follows:

[0297]

[0298] In the formula, This is a sample of annual extreme values ​​of snow load. The location parameter of the distribution is the scale parameter of the distribution. denoted as the sample standard deviation, and μ as the sample mean.

[0299] Snow load with a return period of R used in structural design It can be calculated using the following formula:

[0300]

[0301] In the formula, R is the return period.

[0302] 5. Beneficial effects compared to existing technologies

[0303] Determining the snow load on photovoltaic (PV) structures can rely on field tests, code values, and numerical simulations. Field tests are difficult to control due to challenging external conditions, requiring significant time, money, and manpower, and their limited scale restricts the amount of data obtained. Code-recommended methods for calculating PV structure snow loads, referencing building structure codes, tend to be overly conservative, significantly increasing construction costs. Furthermore, code provisions rely on engineering experience, and the lack of sufficient case studies supporting PV structure snow loads renders these code methods inaccurate. In contrast, simulation methods are more flexible and efficient.

[0304] This invention proposes a method for assessing the snow load on photovoltaic structures based on snow melting models and statistical analysis of snow load samples. This method utilizes readily available basic meteorological data from weather stations to rapidly, economically, and accurately simulate the multi-year snow load on photovoltaic structures in a target area. It also obtains snow loads with a certain guarantee rate to guide photovoltaic structure design, improve structural safety, and reduce construction costs. Ordinary snow melting models are mostly used for runoff prediction, water resource management, and avalanche early warning; a few can simulate the snow load on building structures. Compared to ordinary snow melting models, the multi-layer snow melting model for photovoltaic structures constructed in this invention considers the energy balance process of the photovoltaic panels, especially the influence of tilted surface radiation on snow melting on the photovoltaic panels. This makes it particularly suitable for accurate simulation of the snow load on photovoltaic structures in areas lacking snow accumulation observation data.

[0305] The following are specific embodiments of the present invention, and the evaluation process is as follows: Figure 1 As shown.

[0306] This embodiment provides a method for evaluating the snow load on photovoltaic structures based on a multi-layer snow melting model, which includes the following steps:

[0307] Step 1: Obtain historical basic meteorological data for the target area from a weather website, including daily maximum and minimum temperatures, average daily relative humidity, average daily wind speed, and total daily precipitation. Interpolate the daily data to obtain hourly data. Hourly temperatures are linearly interpolated based on the daily maximum and minimum temperatures. Hourly relative humidity and wind speed are assumed to be consistent with the daily averages. Hourly precipitation is the hourly average of the total daily precipitation. According to the formula Divided into rainfall and snowfall Select meteorological data from year k and input it into the photovoltaic structure snow melting model to simulate the snow load on the photovoltaic structure in year k.

[0308] Step 2: The calculation of snow load at any time step t in year k begins with the addition of new snowfall and updating the boundary conditions at the top of the snow cover. The new snowfall is divided into multiple snow layers covering the existing snow cover, each with a thickness between 0.5 and 1.0 cm, to balance computational efficiency and accuracy. The snowfall amount at the current time step t is... This represents the equivalent water volume of solid water (ice) in fresh snow. Assuming the temperature of the fresh snowfall is the same as the air temperature, the density of the fresh snow is calculated using the formula... Values ​​are determined by the density of fresh snow and the water equivalent of solid water. The liquid water content is related to precipitation and the maximum water holding capacity of snow cover, according to the formula... calculate.

[0309] Step 3: Solve the energy balance equations for the snow layer and photovoltaic panel at time step t (formula) and formula The energy terms in the energy balance equation are calculated according to the formula. -formula Calculation. Based on the energy equation, obtain the total energy absorbed by each snow layer and photovoltaic panel at time step j. and (and the temperature of each layer.)

[0310] Step 4: According to the formula and formula Calculate the cumulative positive energy of the snow accumulation separately. and its critical value When positive energy accumulates ≥Centralized positive energy threshold Snow slid off the solar panels, at which point the snow load... If the value is reduced to 0, proceed to step 2 to begin the calculation for time step t+1. Conversely, if the snow on the photovoltaic panel does not slide off, proceed to step 5 to continue the snow melting calculation for time step t.

[0311] Step 5: Substitute the total energy absorbed by each snow layer obtained in Step 3 into the formula. -formula The phase transition between liquid and solid water within the snow and the snow layer outflow are calculated, and then the mass balance equation of the snow layer at time step t is solved (formula). This allows us to obtain information on the changes in the mass of each snow layer.

[0312] Step 6: Using the formula -formula The snow compaction process is calculated to obtain the density and depth of each snow layer after compaction within the current time step t.

[0313] Step 7: Re-divide the snow layers. Remove completely melted snow layers, merge snow layers less than 0.5 cm with adjacent snow layers, and further subdivide snow layers greater than 1.0 cm to ensure that each layer meets the thickness requirements. Update the physical parameters of the snow layers, such as density, depth, water content, and temperature, using a weighted average method.

[0314] Step 8: Compare the current time step t with the maximum time step t max The size of t. <t max If the timer fails, proceed to step 2 to begin the calculation at time step t+1. Otherwise, the calculation for year k ends. Snow load is the product of snow depth and snow density. Output the time history of the photovoltaic structure snow load for year k, and extract the maximum snow load value as the annual extreme value sample of snow load. .

[0315] Step 9: Compare the calculated year k with the maximum year k max The size of k; when k <k max If the snow load simulation is initiated in step 1, proceed to step k+1; otherwise, the snow load calculation for all years is complete. According to the formula... and formula Using snow load samples of photovoltaic structures from all years, the snow load with a return period R under a certain guarantee rate is calculated. . The snow load for the photovoltaic structure in the target area is now determined. This concludes the snow load assessment process for the photovoltaic structure.

[0316] The above scheme utilizes readily available basic meteorological data from weather stations to quickly, economically, and accurately simulate the snow load on photovoltaic structures in the target area over many years, and obtains snow loads with a certain guarantee rate to guide the design of photovoltaic structures, thereby improving the safety of photovoltaic structures and reducing construction costs.

[0317] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for evaluating the snow load on photovoltaic structures based on a multi-layer snow melting model, characterized in that, Includes the following steps: Step 1: Obtain historical basic meteorological data for the target area from meteorological websites; Step 2: Select meteorological data for year k. When simulating the snow load on the photovoltaic structure in year k, the calculation of any time step t starts from adding new snowfall and updating the boundary conditions at the top of the snow cover. Step 3: Solve the energy balance equations for the snow layer and photovoltaic panel at time step t, and calculate the total energy absorbed by the snow layer and photovoltaic panel, as well as the temperature of each layer; Step 4: Calculate the cumulative positive energy of the snow and its critical value. When the cumulative positive energy is greater than or equal to the critical value, it indicates that the snow has slid off, so proceed to step 2; when the cumulative positive energy is less than or equal to the critical value, it indicates that the snow has not slid off, so proceed to step 5. Step 5: Solve the mass balance equation for snow accumulation at time step t, and calculate the phase change of snow and the snow layer outflow. Step 6: By calculating the snow compaction process, obtain the density and depth of each snow layer after compaction within the current time step t; Step 7: Re-divide the snow layers and update the physical parameters of the snow layers; Step 8: Compare the current time step t with the maximum time step t max Size; when t <t max If the time frame is not met, proceed to step 2 to begin the calculation of time step t+1; otherwise, the calculation for year k ends, and the time history of the photovoltaic structure snow load for year k and the annual extreme value sample S of the snow load are output. a，max ; Step 9: Compare the calculated year k with the maximum year k max The size of k; when k <k max Proceed to step 1 to begin the snow load simulation calculation for year k+1; otherwise, the snow load calculation for all years is complete, and the design snow load S of the photovoltaic structure in the target area is calculated. R : ； In the formula, u is the location parameter of the distribution, α is the scale parameter of the distribution, and R is the return period.

2. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 1, characterized in that: In step 1, the basic meteorological data includes daily maximum and minimum temperatures and average temperatures, daily average relative humidity, daily average wind speed, and daily total precipitation. Hourly data is obtained by interpolating daily data; hourly temperature is linearly interpolated based on the daily maximum and minimum temperatures; hourly relative humidity and wind speed are assumed to be consistent with the daily average; hourly precipitation is the hourly average of the daily total precipitation. Precipitation P is divided into rainfall amount and snowfall The formulas for calculating precipitation and snowfall are as follows: ； In the formula: T a For air temperature, T b T r These are the boundary values ​​for separating rain and snow, with a value of T. b =-1、T r =3.

3. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 2, characterized in that: In step 2, the new snowfall is divided into multiple snow layers covering the top of the existing snow cover, with each snow layer having a thickness between 0.5 and 1.0 cm. Snowfall at current time step t Let be the water equivalent of solid water in fresh snow. Assuming the temperature of the fresh snowfall is the same as the air temperature, the depth of fresh snow is determined by the density of fresh snow and the water equivalent of solid water. The density of fresh snow is calculated as follows: ； In the formula, ρ s Snow density; When the liquid water content exceeds the maximum water-holding capacity of the snow layer, excess snow water seeps into the next snow layer: ； In the formula, The meaning is the outflow rate of the i-th snow layer; W represents the equivalent amount of liquid water in the i-th snow layer at time step t. i Let be the snow water equivalent of the i-th snow layer; This represents the maximum water-holding capacity of the i-th snow layer.

4. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 3, characterized in that: In step 3, the total energy absorbed by each snow layer The following energy balance equation is used for calculation; The energy balance equation for the i-th snow layer at time step t is: ； In the formula, the superscript i represents the snow layer number; the subscript f represents the front of the tilted photovoltaic panel; and the subscript s represents snow. Snow density; The specific heat of snow; This refers to the thickness of the snow layer. Snow layer temperature; Physical time; The net solar radiation absorbed by the snow layer on the front of the photovoltaic panel; This refers to the net longwave radiation acting on the front of the photovoltaic panel; Sensible heat; Latent heat; This refers to energy transfer caused by the temperature difference between adjacent snow layers. The energy brought by precipitation; This is the first snow layer at the bottom of the snow layer, used for heat exchange between the snow layer and the photovoltaic panels. The solar radiation acting on the front of the photovoltaic panel is: ; , , and It exists only in the m-th snow layer, which is in direct contact with the air. The sum of the terms on the right-hand side of the energy balance equation for the snow layer above represents the total energy absorbed by each snow layer at time step t. The total energy absorbed by the snow on the photovoltaic panel at time t is ΔE, which represents the total energy absorbed by each snow layer. sum; Total energy absorbed by the photovoltaic panel at time step t The following energy balance equation is used for calculation: ; In the formula, the subscript PV represents the photovoltaic panel; the subscript b represents the back of the tilted photovoltaic panel; and m is the number of snow layers. Photovoltaic panel density; Specific heat of photovoltaic panels; The thickness of the photovoltaic panel; Temperature of the photovoltaic panel; Solar radiation that acts on the front of the photovoltaic panel and penetrates into the photovoltaic panel; This refers to the net solar radiation acting on the back of the photovoltaic panel; This refers to the net longwave radiation acting on the back of the photovoltaic panel; The net long-wave radiation from the front of the photovoltaic panel; This refers to the convective heat loss on the front side of the photovoltaic panel; This refers to the heat loss caused by convection on the back of the photovoltaic panel; The energy carried away by photovoltaic panels as they absorb solar radiation to generate electricity; Energy exchange between snow and photovoltaic panels; Based on the energy balance equations for the snow layer and photovoltaic panels described above, the total energy absorbed by each snow layer at time step t is obtained. and the total energy absorbed by the photovoltaic panel And the temperature of each layer.

5. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 4, characterized in that: In step 3, the calculation process for each energy term in the energy balance equation for solving the total energy absorbed by each snow layer and photovoltaic panel is as follows: 1) Solar shortwave radiation The total radiation from the sun reaching the ground at a horizontal surface is called diffuse radiation. and direct radiation The sum of the solar radiation reflected from the ground to the tilted surface of the photovoltaic panel, including the front and back sides, must be considered in addition to the scattering and direct radiation acting on the tilted surface. The scattered radiation acting on the front and back sides of the tilted surface of the photovoltaic panel are respectively represented as follows: and The direct radiation acting on the front and back sides of the tilted surface of the photovoltaic panel are respectively represented as: and The reflected radiation from the ground to the front and back of the tilted surface of the photovoltaic panel is represented as follows: and ; The sum of all radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front side of the inclined surface. Total radiation from the back of the inclined surface , respectively represented as: , ; The albedo of the front and back sides of the inclined surface is expressed as follows: and ; Under the influence of albedo, a portion of the total radiation leaves the surface of the inclined plane, including the total radiation that leaves the front of the inclined plane due to albedo. and the total radiation amount away from the back of the inclined surface due to albedo , respectively represented as: , The remaining portion represents the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and net solar radiation acting on the back side of the inclined surface , respectively represented as: , ; Net solar radiation acting on the front of the tilted surface of the photovoltaic panel The amount of radiation received by the snow layer and the photovoltaic panel are respectively expressed as: and ; Potential extraterrestrial solar radiation on a certain day The calculation formula is: ； In the formula, It is the solar constant; Solar declination; Latitude; Daily total horizontal radiation The relationship between the daily potential extraterrestrial solar radiation and the daily clear sky index was used. To assess; daily total horizontal radiation ; The calculation formula is: ； In the formula, The daily temperature difference is represented by a, b, and c, which are empirical coefficients. After obtaining the total daily horizontal radiation, it is decomposed into the direct radiation components on the daily horizontal surface. and scattered radiation components The ratio of daily scattered radiation to daily total horizontal radiation; Scattering fraction The daily clear sky index The function of daily horizontal scattered radiation; The daily direct radiation at the horizontal surface is ; The calculation formula is: ； In the formula, The sunset angle, with the 81.4° dividing line used in the formula. Seasonal correlation; Total radiation per hour , hour angle The function is calculated using the following formula: ； Similarly, hourly scattered radiation Hours of direct radiation ; The calculation formula is as follows: ； Solar radiation acting on the front of the tilted surface of the photovoltaic panel Direct radiation including inclined surfaces Scattered radiation from inclined surfaces Inclined surface reflects radiation Three components, The calculation method is as follows: ； In the formula, geometric factor ,in Angle of incidence Zenith angle; is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; The direct score; Ground albedo; The tilt angle of the photovoltaic panel; For tilted photovoltaic panels raised by supports, both the front and back sides receive solar radiation from the sky, respectively. and ; Calculate the solar radiation received on the back side At that time, the tilt angle of the back of the photovoltaic panel is taken as The calculation formula is as follows: ； For a photovoltaic panel covered by snow, the net solar radiation absorbed by the two surfaces of the photovoltaic panel and the snow are respectively and The calculation formula is as follows: ； The net solar radiation acting on the front of the photovoltaic panel penetrates into the snow layer and is gradually absorbed. The amount of solar radiation absorbed by each snow layer... The expression is as follows: ； In the formula, m is the total number of snow layers; c1 and c2 are empirical coefficients; Solar radiation absorbed by photovoltaic panels Calculate according to the following formula: ； When there is no snow accumulation on the photovoltaic panel, the following formula is used to consider the impact of the photovoltaic panel's absorption and transmission capabilities on solar radiation: ； In the formula, , and It is the product of transmittance and absorptivity at the effective incident angles of direct, scattered, and reflected radiation. 2) Net longwave radiation The incident or emitted longwave radiation is calculated using the Stefan-Boltzmann equation: ； In the formula, the subscript j refers to the main body emitting long-wave radiation, and sky, gr, f and b represent the sky, the ground, the front and back of the tilted surface of the photovoltaic panel, respectively. Represents the long-wave radiation emitted by j; Let j be the temperature; For Stefan Boltzmann constant, Let j be the emissivity; The net longwave radiation of the front and back sides of the inclined plane is calculated according to the following formula: ； In the formula, L sky Long-wave radiation emitted from the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Long-wave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f F represents the apparent factor from the sky to the front of the photovoltaic panel. gr-f F is the apparent factor from the ground to the front of the photovoltaic panel. sky-b F represents the apparent factor from the sky to the back of the photovoltaic panel. gr-b The apparent factor is the distance from the ground to the back of the photovoltaic panel; 3) Sensible heat The sensible heat exchange between the upper surface of the snow and the air is calculated according to the following formula: ； In the formula, air density; The specific heat of air; This is the adjusted turbulence exchange coefficient; To measure wind speed at an altitude; The convective heat transfer coefficient of sensible heat flux under windless conditions; Air temperature; This refers to the surface temperature of the snow. 4) Latent heat The formula for calculating the latent heat flux exchange between the snow surface and the air is as follows: ； In the formula, To sublimate latent heat; The constant for dry air; The adjusted turbulent exchange coefficient, ; It is the vapor pressure of air; The vapor pressure of the snow surface; 5) Heat transfer between snow layers The energy transfer between adjacent snow layers due to temperature differences is calculated by the following formula: ； In the formula, Temperature of snow cover; The coordinates of the snow along the depth direction; The effective heat transfer coefficient of the snow layer; 6) Heat brought by precipitation The energy that precipitation brings to snow accumulation can be expressed in the following form: ； In the formula, This refers to the amount of snowfall. The specific heat of snow; c w The specific heat of liquid water; The density of liquid water; Rainfall; The latent heat of melting of snow; 7) Electricity generated by photovoltaics The formula for calculating photovoltaic capacity is as follows: ； In the formula, The solar radiation received on the front of the tilted photovoltaic panel; This represents the maximum efficiency of the photovoltaic module under standard test conditions. The maximum power temperature coefficient; Temperature of the photovoltaic module; The reference temperature for standard test conditions; solar radiation not used for power generation is converted into heat inside the photovoltaic panel. ; 8) Heat loss due to convection The formulas for calculating heat loss due to convection on the front and back of a photovoltaic panel are as follows: ； In the formula, The forced convection heat transfer coefficient; The free convection heat transfer coefficient; This refers to the temperature difference at the photovoltaic-air boundary; when snow accumulates on the surface of the photovoltaic panel, the heat loss on the front of the panel due to convection is also considered. Zero; The forced convection heat transfer coefficient is calculated using the following formula: ； In the formula, It is the Reynolds number; For Prandtl numbers, The thermal conductivity of air; The length of the module along the natural airflow direction; The free convection heat transfer coefficient is calculated using the following formula: ； In the formula, Rayleigh number; 9) Heat exchange between photovoltaic panels and snow accumulation The heat transfer between the photovoltaic panel and the snow is determined by the temperature difference between the photovoltaic panel and the lower surface of the snow, and the calculation formula is as follows: ； In the formula, This refers to the surface temperature beneath the snow cover. The thermal conductivity of the photovoltaic panel; This refers to the thickness of the photovoltaic panel.

6. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 5, characterized in that: In step 4, the formula for calculating the cumulative positive energy of snow accumulation during the time interval from the initial time t0 to any time t is as follows: ； In the formula, ΔE is the total energy absorbed by the snow on the photovoltaic panel at time step t; Positive energy for the accumulation of snow; Photovoltaic panels with different slopes The corresponding formula for calculating the cumulative positive energy threshold is as follows: ； In the formula, The cumulative positive energy threshold is defined by A, B, and C, which are empirical coefficients determined from actual snow cover measurements or experimental data.

7. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 6, characterized in that: In step 5, the phase change between liquid and solid water within the snow and the calculation process for snow layer outflow are as follows: The evaporation or sublimation of liquid water within snow will cause a change in snow mass. Substituting precipitation and snowfall into the following formula yields the amount of sublimation and evaporation. The formula for calculating the change is as follows: ； In the formula, This is the equivalent of snow water in the liquid water layer at the top; The latent heat of snow evaporation; h s For the latent heat of snow sublimation; W e E1 is the amount of sublimation evaporation; ρ is the latent heat; w The density of water; The outflow of snowmelt from the snowpack is controlled by the snow layer's maximum water-holding capacity; when the liquid water content exceeds the snow layer's maximum water-holding capacity, excess snowmelt seeps into the next snow layer. ； In the formula, Let be the snow water equivalent of the i-th snow layer; This represents the maximum water-holding capacity of the i-th snow layer; When the snow layer absorbs energy, a phase transition occurs between solid and liquid water within the snow layer, resulting in their interconversion; the change in solid water due to the phase transition at time step t. and changes in liquid water Calculated according to the following formula: ； In the formula, This represents the total energy absorbed by the i-th snow layer. The density of liquid water, The latent heat of melting ice, Let be the equivalent water volume of solid water in the i-th snow layer. Let t be the equivalent amount of liquid water in the i-th snow layer, t represent the current time step, and t-1 represent the previous time step. Liquid water equivalent in the i-th snow layer at time step t Water equivalent to solid water Calculate using the following formula: ； ； The phase change between liquid and solid water in the snow and the snow layer outflow are calculated using the above formulas. Then, the mass balance equation of the snow layer at time step t is solved to obtain the change in mass of each snow layer. The mass balance equation for snow accumulation on photovoltaic panels is shown below: ； In the formula, Let be the water equivalent of the i-th snow layer.

8. The method for evaluating the snow load of photovoltaic structures based on a multi-layer snow melting model according to claim 7, characterized in that: In step 6, for densities less than 150 kg·m -3 For fresh snow, the compaction rate is calculated using the following formula: ； After the snow layer has undergone the initial destructive deformation stage, the compaction rate is calculated using the following formula: ； The total rate of snow compaction is the sum of the compaction rates of the two stages mentioned above: ； The change in snow density due to snow compaction is obtained by the following formula: ； In the formula, γ represents the temperature of snow layer i; i The density of snow layer i; P s η is the pressure of the snow accumulation on the upper part of the snow layer; η0 is an empirical parameter.

9. The method for evaluating the snow load of a photovoltaic structure based on a multi-layer snow melting model according to claim 8, characterized in that: In step 7, the snow layers are re-divided, completely melted snow layers are removed, snow layers less than 0.5 cm are merged with adjacent snow layers, and snow layers greater than 1.0 cm are subdivided so that each layer meets the thickness requirements.

10. The method for evaluating the snow load of a photovoltaic structure based on a multi-layer snow melting model according to claim 9, characterized in that: In step 9, the snow load for the return period R is calculated using snow load samples of the photovoltaic structure from all years. ; The statistical sample of snow load uses the annual maximum value, and it is assumed that the sample distribution follows a type I extreme value distribution, with the distribution function being: ； In the formula, This is a sample of annual extreme values ​​of snow load. The location parameter of the distribution is the scale parameter of the distribution. denoted as the sample standard deviation, and μ as the sample mean.

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