Photovoltaic structure snow load assessment method based on multi-layer snow melting model

Abstract

The invention discloses a photovoltaic structure snow load evaluation method based on a multi-layer snow melting model, and the method comprises the following steps: obtaining basic meteorological data of a target region, and starting simulation from the adding of new snowfall and the updating of snow top boundary conditions; calculating the total energy absorbed by the snow layer and the photovoltaic panel and the temperature of each layer; calculating accumulated positive energy of the accumulated snow and a critical value thereof, a mass balance equation of the accumulated snow and an accumulated snow compaction process; and calculating the design snow load of the photovoltaic structure of the target area. Constructing an energy balance equation of a snow layer and a photovoltaic panel and a mass balance equation of accumulated snow by using the basic meteorological data, and simulating the evolution process of the accumulated snow on the photovoltaic panel for many years by taking accumulated positive energy as a condition for judging the falling of the accumulated snow; according to the method, the annual extreme value of the snow load is extracted from the accumulated snow simulation result as a sample for statistical analysis, and then the photovoltaic snow load in the return period is calculated for guiding the photovoltaic structure design, so that the time cost and the economic cost for determining the snow load can be saved, the safety of a photovoltaic power station is improved, and the construction cost is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of photovoltaic structure snow load detection, and in particular relates to a photovoltaic structure snow load assessment method based on a multi-layer snowmelt model. Background Art

[0002] In snowy areas, snow load is a controlling load that must be considered for photovoltaic structures. First, the most reliable and direct way to determine snow load is on-site measurement, but on-site measurement is extremely time-consuming and financially intensive, and snow observation data collection is difficult, making it impractical in reality. Second, when designing photovoltaic structures, snow loads can be determined based on code values. However, existing codes lack sufficient historical research data on photovoltaic snow loads, so the code stipulates that the snow distribution coefficient on inclined photovoltaic panels shall be determined based on the coefficient for single-slope roofs in the building load code, i.e., the greater the slope, the smaller the snow distribution coefficient of the photovoltaic structure. This simple method of determining the value ignores the influence of the thermodynamic properties of the photovoltaic panels themselves, and does not accurately estimate the snow load on the structure, thereby endangering the safety of photovoltaic power stations or increasing equipment construction costs. Summary of the Invention

[0003] The purpose of the invention is to provide a photovoltaic structure snow load assessment method based on a multi-layer snowmelt model, aiming to solve the technical problems in the existing technology that it is difficult to obtain actual photovoltaic snow load data and the existing photovoltaic snow load specification provisions are insufficient.

[0004] To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0005] A method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model comprises the following steps:

[0006] Step 1: Obtain basic meteorological data of the target area over the years from the meteorological website;

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

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

[0009] Step 4: Calculate the accumulated positive energy of the snow and its critical value. When the accumulated positive energy is greater than or equal to the critical value, it indicates that the snow has fallen, and the process goes to step 2. When the accumulated positive energy is less than or equal to the critical value, it indicates that the snow has not fallen, and the process goes to step 5.

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

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

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

[0013] Step 8: Compare the current time step t with the maximum time step t max The size of t <t max When , jump to step 2 to start the calculation of time step t+1; otherwise, the calculation of the kth year is completed, and the snow load history of the photovoltaic structure in the kth year and the annual extreme value sample of snow load S are output. a，max ;

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

[0015] ;

[0016] Where 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, minimum and average temperatures, daily average relative humidity, daily average wind speed and daily total precipitation;

[0018] Daily data were interpolated to obtain hourly data; hourly temperatures were linearly interpolated based on the daily maximum and minimum temperatures; hourly relative humidity and wind speed were assumed to be consistent with the daily averages; hourly precipitation was the hourly average of the daily total precipitation;

[0019] Precipitation P is divided into rainfall and snowfall , the calculation formulas for precipitation and snowfall are as follows:

[0020]

[0021] Where: T a is the air temperature, T b 、T r are the boundary values ​​of rain and snow separation, and their values ​​are T b =-1, T r =3.

[0022] Furthermore, in step 2, the new snowfall is divided into multiple snow layers covering the upper part of the original snow accumulation, and the thickness of each snow layer is between 0.5 and 1.0 cm;

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

[0024]

[0025] Where, ρ s is the snow layer density;

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

[0027]

[0028] Where, The meaning of is the outflow of the i-th snow layer; is the liquid water equivalent in the i-th snow layer at time step t; W i is the snow water equivalent of the i-th snow layer; is 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 of the i-th snow layer at time step t is:

[0031] ; Where, superscript i is the snow layer number; subscript f represents the front of the tilted photovoltaic panel; subscript s represents snow; is the snow layer density; is the specific heat of snow; is the thickness of the snow layer; is the snow layer temperature; is physical time; is the solar radiation absorbed by the snow layer i acting on the front of the photovoltaic panel; is the net longwave radiation acting on the front of the photovoltaic panel; is sensible heat; is latent heat; Energy transfer caused by temperature differences between adjacent snow layers; Energy brought to precipitation; The first snow layer at the bottom of the snowpack is the heat exchange between the snow layer and the photovoltaic panels;

[0032] Solar radiation acting on the front of the photovoltaic panel ( ) will penetrate into the snow, and most of the solar radiation Absorbed by each snow layer, the rest Photovoltaic panel absorption;

[0033] 、 、 and Only exists in the mth snow layer in direct contact with the air;

[0034] The sum of the right-hand side of the energy balance equation for the above snow layer is 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 △E, which is the total energy absorbed by each snow layer. sum;

[0035] The total energy absorbed by the photovoltaic panel at time step t The following energy balance equation is used for calculation: ; Where, subscript PV represents photovoltaic panel; subscript b represents the back side of the tilted photovoltaic panel; m is the number of snow layers; is the density of photovoltaic panels; is the specific heat of the photovoltaic panel; is the thickness of the photovoltaic panel; is the photovoltaic panel temperature; It is the solar radiation that acts on the front of the photovoltaic panel and penetrates into the photovoltaic panel; is the net solar radiation acting on the back of the photovoltaic panel; is the net longwave radiation acting on the back of the photovoltaic panel; is the net longwave radiation on the front of the photovoltaic panel; is the convective heat loss from the front of the photovoltaic panel; The heat loss caused by convection on the back of the photovoltaic panel; It is the energy taken away by photovoltaic panels when they absorb solar radiation to generate electricity; For energy exchange between snow and photovoltaic panels;

[0036] According to the energy balance equation of the snow layer and photovoltaic panels above, the total energy absorbed by each snow layer at time step t is obtained and the total energy absorbed by the photovoltaic panels and the temperature of each layer.

[0037] Furthermore, in step 3, the energy balance equation for the total energy absorbed by each snow layer and photovoltaic panel is solved by calculating the energy terms as follows:

[0038] 1) Solar shortwave radiation

[0039] The total horizontal radiation from the sun reaching the ground is diffuse radiation and direct radiation The front and back of the photovoltaic panel's inclined surface, in addition to the scattered and direct radiation acting on the inclined surface, also need to consider the solar radiation reflected from the ground to the inclined surface. The scattered radiation acting on the front and back of the photovoltaic panel's inclined surface is expressed as and , the direct radiation acting on the front and back of the inclined surface of the photovoltaic panel is expressed as and , the reflected radiation from the ground to the front and back of the inclined surface of the photovoltaic panel are expressed as and ; The sum of the radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front of the inclined surface and the total radiation on the back side of the inclined surface , respectively expressed as: , ; The albedo of the front and back sides of the inclined surface are expressed as and ; Due to the effect of albedo, part 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 leaving the back of the inclined surface due to albedo , respectively expressed as: , The remaining part is the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and the net solar radiation acting on the back of the inclined surface , respectively expressed as: , ; Net solar radiation acting on the front of the inclined surface of the photovoltaic panel The radiation received by the snow layer and the photovoltaic panel are expressed as , ;

[0040] Potential extraterrestrial solar radiation on a certain day's horizontal surface The calculation formula is:

[0041]

[0042] Where, is the solar constant; is the solar declination; is latitude;

[0043] Daily horizontal total radiation The relationship between the daily potential extraterrestrial solar radiation and the daily clear sky index can be used To evaluate; daily horizontal total radiation ; The calculation formula is:

[0044]

[0045] Where, is the daily temperature difference, a, b, c are empirical coefficients;

[0046] After obtaining the daily horizontal surface total radiation, it needs to be further decomposed into the direct radiation component on the daily horizontal surface and the diffuse radiation component ; The ratio of daily diffuse radiation to daily horizontal total radiation is the scattering fraction , is the daily clear sky index function of daily horizontal diffuse radiation , and the daily direct radiation on the horizontal surface is ; The calculation formula is:

[0047] ; Where, is the sunset angle, and the 81.4° boundary is used to represent the seasonal correlation;

[0048] The photovoltaic structure snowmelt model requires hourly radiation data to accurately simulate the snow accumulation time course. Hourly radiation data can be obtained from daily radiation data. Using hourly total radiation Total daily radiation Ratio To characterize the relationship between the two. , Hour angle The function is calculated as follows:

[0049]

[0050] Similarly, hourly scattered radiation Diffuse radiation from the sun Ratio The following formula can be used to calculate the hourly scattered radiation , hours of direct radiation ; The calculation formula is as follows:

[0051]

[0052] Solar radiation acting on the front of the inclined surface of the photovoltaic panel Including direct radiation from inclined surfaces , inclined surface scattered radiation , inclined surface reflected radiation Three components; each component can be directly radiated by the horizontal plane , diffuse radiation The present invention uses the HDKR model (the Hay, Davies, Klucher, Reindl model) to calculate the total radiation of the inclined surface. , the calculation method is as follows:

[0053]

[0054] Where, the geometric factor ,in is the angle of incidence, is the zenith angle;

[0055] is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; is the direct score; is the ground albedo; is the inclination angle of the photovoltaic panel;

[0056] For tilted photovoltaic panels raised by brackets, both the front and back sides receive solar radiation from the sky ( , ). The solar radiation received by the back panel is generally small and does not participate in power generation, but it will slightly increase the temperature of the photovoltaic panel. When , it can be calculated according to the following formula; different from the front radiation, only the contribution of scattered and reflected radiation components is considered. In addition, the calculation The inclination angle of the back of the photovoltaic panel is :

[0057]

[0058] For a snow-covered photovoltaic panel, the net solar radiation absorbed by both the photovoltaic panel and the snow is ( , )Albedo of the front snow and photovoltaic back panel should also be considered separately ( , )

[0059] ;

[0060] Where, The net solar radiation absorbed by the snow-covered photovoltaic panels acting on the front; The solar radiation absorbed by the snow-covered photovoltaic panels acting on the back side; is the albedo of the front side of the snow-covered photovoltaic panel, that is, the albedo of the snow surface; is the albedo of the back side of the snow-covered photovoltaic panel, that is, the albedo of the back side of the photovoltaic panel.

[0061] The net solar radiation acting on the front of the photovoltaic panel will penetrate into the snow layer and be gradually absorbed. The amount of solar radiation absorbed by each snow layer is The expression is as follows:

[0062]

[0063] Where m is 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. Calculate according to the following formula:

[0064]

[0065] When covered with snow, very little solar radiation penetrates the photovoltaic panels, and a very small proportion of this penetrating radiation is reflected back to the snow. Therefore, it is assumed that the photovoltaic panels absorb all the solar radiation that penetrates them. When there is no snow on the photovoltaic panels, the following formula is used to consider the impact of the photovoltaic panels' absorption and transmission capabilities on solar radiation:

[0066]

[0067] Where, , and is the product of transmittance-absorption at the effective incident angle of direct, scattered and reflected radiation;

[0068] 2) Net longwave radiation

[0069] The incoming or outgoing longwave radiation can be calculated using the Stefan-Boltzmann equation:

[0070]

[0071] Where, the subscript j refers to the subject emitting long-wave radiation, sky, gr, f, and b represent the sky, the ground, the front side, and the back side of the photovoltaic panel’s tilt, respectively; represents the long-wave radiation emitted by j; is the temperature of j; is the Stefan-Boltzmann constant, is the emissivity of j;

[0072] The long-wave radiation between the front and back of the photovoltaic panel's 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:

[0073]

[0074] Where, L sky The long-wave radiation emitted by the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Longwave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f is the viewing factor from the sky to the front of the photovoltaic panel, F gr-f F is the viewing factor from the ground to the front of the photovoltaic panel; sky-b is the viewing factor from the sky to the back of the photovoltaic panel, F gr-b is the viewing factor from the ground to the back of the photovoltaic panel;

[0075] 3) Sensible heat

[0076] The sensible heat exchange between the upper surface of the snow and the air is calculated as follows:

[0077]

[0078] Where, is the air density; is the specific heat of air; is the adjusted turbulent exchange coefficient; is the wind speed at the measuring height; Convective heat transfer coefficient for sensible heat flux in the absence of wind; is the air temperature; is the surface temperature of the snow cover;

[0079] 4) Latent heat

[0080] The latent heat flux exchange between the snow surface and the air is calculated as follows:

[0081]

[0082] Where, is the latent heat of sublimation; is the dry air constant; is the adjusted turbulent exchange coefficient, ; is the air vapor pressure; is the vapor pressure of the snow surface;

[0083] 5) Heat transfer between snow layers

[0084] The energy transfer due to temperature difference between adjacent snow layers is calculated by the following formula:

[0085]

[0086] Where, is the snow temperature; is the coordinate of the snow along the depth direction; is the effective heat transfer coefficient of the snow layer;

[0087] 6) Heat from precipitation

[0088] The energy brought by precipitation to snow accumulation can be expressed as follows:

[0089]

[0090] Where, is the amount of snowfall; is the specific heat of snow; c w is the specific heat of liquid water; is the density of liquid water; is the rainfall; is the latent heat of melting of snow.

[0091] 7) Electricity generated by photovoltaics

[0092] The calculation formula for photovoltaic production capacity is as follows:

[0093]

[0094] Where, is the solar radiation received by the front of the tilted photovoltaic panel; It is the maximum efficiency of photovoltaic modules under standard test conditions; is the maximum power temperature coefficient; is the 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. ;

[0095] 8) Heat loss due to convection

[0096] The calculation formula for heat loss due to convection on the front and back of photovoltaic panels is as follows:

[0097]

[0098] Where, is the forced convection heat transfer coefficient; is the free convection heat transfer coefficient; is the temperature difference between the photovoltaic panel and the air boundary; when there is snow on the photovoltaic panel surface, the heat loss caused by convection on the front of the photovoltaic panel is zero;

[0099] The forced convection heat transfer coefficient is calculated using the following formula:

[0100]

[0101] Where, is the Reynolds number; is the Prandtl number, is the thermal conductivity of air; is the length of the module along the direction of natural air flow;

[0102] The free convection heat transfer coefficient is calculated by the following formula:

[0103]

[0104] Where, is the Rayleigh number;

[0105] 9) Heat exchange between photovoltaic panels and snow

[0106] The heat transfer between the photovoltaic panel and the snow is determined by the temperature difference between the photovoltaic panel and the surface under the snow, and the calculation formula is as follows:

[0107]

[0108] Where, is the surface temperature under the snowpack; is the thermal conductivity of the photovoltaic panel; is the thickness of the photovoltaic panel.

[0109] Furthermore, in step 4, the cumulative positive energy of snow from the initial time t0 to any time t is calculated as follows:

[0110]

[0111] Where △E is the total energy absorbed by the snow on the photovoltaic panel at time step t; Positive energy for the accumulation of snow;

[0112] Photovoltaic panels with different slopes The corresponding cumulative positive energy critical value calculation formula is as follows:

[0113]

[0114] Where, is the critical value of cumulative positive energy, and A, B, and C are empirical coefficients determined by actual snow measurement or experimental data.

[0115] Furthermore, in step 5, the phase change between liquid water and solid water in the snow and the snow layer outflow rate are calculated as follows:

[0116] The evaporation or sublimation of liquid water in the snow will cause the mass of the snow to change. Substituting precipitation and snowfall into the following formula, we can get the amount of sublimation and evaporation. The change is calculated as follows:

[0117]

[0118] Where, is the snow water equivalent of the liquid water in the top snow layer; is the latent heat of evaporation of snow; h s W is the latent heat of snow sublimation; e is the amount of sublimation evaporation; E1 is the latent heat; ρ w is the density of water; when there is liquid water in the snow layer, the phase change of water due to latent heat only considers evaporation; when there is no liquid water in the snow layer, the phase change of water due to latent heat considers sublimation.

[0119] The outflow of snow water from the snowpack is controlled by the maximum water holding capacity of the snow layer; when the liquid water content exceeds the maximum water holding capacity of the snow layer, the excess snow water seeps into the next snow layer:

[0120]

[0121] Where, is the snow water equivalent of the i-th snow layer; is the maximum water holding capacity of the i-th snow layer;

[0122] When the snow layer absorbs energy, a phase change occurs between solid water (ice) and liquid water in the snow layer, and the phase change is converted into each other; the change in solid water due to the phase change at time step t is and liquid water change is calculated according to the following formula:

[0123]

[0124] Where, is the total energy absorbed by the i-th snow layer, is the density of liquid water, is the latent heat of melting of ice, is the water equivalent of solid water in the i-th snow layer, is the equivalent of liquid water in the i-th snow layer, t represents the current time step, and t-1 represents the previous time step;

[0125] The liquid water equivalent in the i-th snow layer at time step t and water equivalent to solid water Calculate using the following formula:

[0126]

[0127]

[0128] The above formulas are used to calculate the phase change between liquid water and solid water in the snow and the outflow of the snow layer, and then the mass balance equation of the snow at time step t is solved to obtain the change in the mass of each snow layer;

[0129] The mass balance equation for snow accumulation on photovoltaic panels is as follows:

[0130]

[0131] Where, is the water equivalent of the i-th snow layer. , snowfall , snow melt outflow , snow sublimation or evaporation This will cause changes in the mass of the top snow layer.

[0132] Furthermore, in step 6, for density less than 150 kg·m -3 For fresh snow, the destructive deformation of the internal structure of the snow is the main cause of snow compaction. At this time, the compaction rate is calculated using the following empirical relationship:

[0133]

[0134] After the snow layer has gone through the initial destructive deformation stage, the rate of snow layer compaction will significantly decrease. The main reason for the snow layer compaction at this time is the gravity compaction of the snow. The compaction rate can be calculated by the following formula:

[0135]

[0136] The total rate of snow compaction is the sum of the compaction rates of the above two stages:

[0137]

[0138] The change in snow density caused by snow compaction can be obtained from the following formula:

[0139]

[0140] Where, is the temperature of snow layer i; γ i is the weight of snow layer i; P s is the pressure of snow on the upper part of the snow layer; η0 is an empirical parameter.

[0141] Furthermore, in step 7, the snow layers are re-divided, the completely melted snow layers are removed, the snow layers less than 0.5 cm are merged with the adjacent snow layers, and the snow layers exceeding 1.0 cm are further subdivided so that each layer meets the thickness requirements;

[0142] The density, depth, water content, temperature and other physical parameters of the snow layer are updated using a weighted average method.

[0143] Furthermore, in step 8, the snow load is the product of snow depth and snow density; the snow load time history of the photovoltaic structure in the kth year is output, and the maximum snow load is extracted as the annual extreme value sample of the snow load. .

[0144] Furthermore, in step 9, the snow load samples of PV structures in all years are used to calculate the snow load with a return period R under a certain guarantee rate. ; "Snow load with return period R" means the magnitude of The snow load occurs once every R years on average, that is, in any year, there is a guaranteed rate of 1-1 / R that does not exceed Snow load; “A certain guarantee rate” refers to the snow load with a return period of R The probability of not exceeding the limit in a certain year. The snow load recurrence period for general photovoltaic structures is 25 years, at which time the "certain guarantee rate" is 1-1 / 25=96%;

[0145] The statistical sample of snow load adopts the annual maximum value, and it is assumed that the sample distribution conforms to the extreme value type I distribution, and its distribution function is:

[0146]

[0147] Where, is the annual extreme value sample of snow load, is the location parameter of the distribution, is the scale parameter of the distribution, is the sample standard deviation, and μ is the sample mean.

[0148] Compared with the prior art, the present invention has the following technical advances:

[0149] The present invention utilizes basic meteorological data from the target area, constructs an energy balance equation for the snow layer and photovoltaic panels, and a mass balance equation for snow accumulation, and uses accumulated positive energy as a condition for determining whether snow will slide off, thereby simulating the evolution of snow accumulation on photovoltaic panels over many years. The annual extreme values ​​of snow load are then extracted from the snow accumulation simulation results as samples for statistical analysis, and the photovoltaic snow load under a certain guarantee rate is calculated to guide the design of photovoltaic structures. This can greatly save the time and economic costs required to determine the snow load, and improve the accuracy of snow load estimation on photovoltaic structures. The present invention takes into account the energy balance process of photovoltaic panels, especially the impact of inclined surface radiation on snowmelt on photovoltaic panels. It is particularly suitable for accurate simulation of snow loads on photovoltaic structures in areas where snow accumulation observation data is lacking, thereby improving the safety of photovoltaic power stations and reducing construction costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0150] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0151] In the attached figure:

[0152] Figure 1 A schematic flow chart of a method for snow load assessment of photovoltaic structures based on a multi-layer snowmelt model provided in an embodiment of the present invention;

[0153] Figure 2 Schematic diagram of the exchange of various energies and masses between snow accumulated on a photovoltaic panel and the environment in an embodiment of the present invention;

[0154] Figure 3 Schematic diagram of interlayer energy exchange between layers when snow accumulates on a photovoltaic panel according to an embodiment of the present invention;

[0155] Figure 4 Schematic diagram of energy exchange between a photovoltaic panel and the natural environment through radiation and convection when there is no snow on the photovoltaic panel according to an embodiment of the present invention;

[0156] Figure 5 Schematic diagram of solar shortwave radiation components on the inclined surface of a photovoltaic panel in an embodiment of the present invention;

[0157] Figure 6 This is a flow chart for calculating solar shortwave radiation on snow-covered photovoltaic panels in an embodiment of the present invention;

[0158] Figure 7 Schematic diagram of using accumulated positive energy to determine snowfall in an embodiment of the present invention. DETAILED DESCRIPTION

[0159] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments. The embodiments of the present invention will be described below with reference to the accompanying drawings.

[0160] At present, the determination of the snow load on photovoltaic structures mainly relies on field tests and values ​​based on design specifications. The external conditions of field tests are difficult to control, and they consume a lot of time, money, and manpower costs. In addition, they cannot be carried out on a large scale, resulting in a limited amount of data obtained. The calculation method for the snow load on photovoltaic structures recommended by the design specifications refers to the building structure specifications, and the values ​​are too conservative, which will greatly increase the construction cost of photovoltaic structures. In addition, the provisions of the specifications rely on engineering experience and judgment. Due to the lack of sufficient support from photovoltaic structure snow load cases, the specification method is not accurate. In comparison, the numerical simulation method provided by the present invention is more flexible and efficient.

[0161] The photovoltaic structure snow load assessment method proposed in the present invention, which is based on a snowmelt model and statistical analysis of snow load samples, can use the basic meteorological data that is easily obtained from meteorological stations to quickly, economically and accurately simulate the photovoltaic structure snow load in the target area for many years, and obtain snow loads under a certain guarantee rate to guide the design of photovoltaic structures, improve structural safety and reduce construction costs. Ordinary snowmelt models are mostly used for runoff prediction, water resource management, and avalanche warning, and a few can simulate snow loads on building structures. Compared with ordinary snowmelt models, the photovoltaic structure multi-layer snowmelt model constructed by the present invention takes into account the energy balance process of photovoltaic panels, especially the impact of inclined surface radiation on the melting of snow on photovoltaic panels, and is particularly suitable for accurate simulation of photovoltaic structure snow loads in areas where snow observation data is lacking. The following is the specific assessment process of the present invention:

[0162] 1. Model Introduction

[0163] The multi-layer snowmelt model of photovoltaic structures simulates snow and photovoltaic panels as a complete system. Figure 2 The various energy and mass exchanges between the snow on the upper part of the photovoltaic panel and the environment are demonstrated. In the model calculation, the snow is divided into multiple snow layers along the normal direction of the photovoltaic panel plane, which can undergo phase changes. The temperature and density inside each snow layer are linearly distributed, and the thickness is between 0.5-1.0 cm. Due to physical phenomena such as melting and condensation inside the snow, the snow is regarded as consisting of three phases: ice, water, and air. The sum of the volume fractions of the three phases is 1.0. Compared with the snow, the photovoltaic panel is regarded as a special layer that does not undergo phase change and is in direct contact with the bottom snow layer ( Figure 3 ), there is heat conduction and interlayer energy exchange between each layer. When there is no snow covering the upper part of the photovoltaic panel, its upper and lower surfaces are directly exposed to the air and exchange energy with the natural environment through radiation and convection ( Figure 4 For ease of description, the present invention defines the surface of the photovoltaic panel's inclined surface facing the sky as the front side, and the surface of the inclined surface facing the ground as the back side. In the formulas, the subscripts f and b are used to represent the front side and the back side, respectively.

[0164] 1.2 Energy balance equation

[0165] 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:

[0166]

[0167] Where, superscript i is the snow layer number; subscript f represents the front of the tilted photovoltaic panel; subscript s represents snow; is the snow layer density; is the specific heat of snow; is the thickness of the snow layer; is the snow layer temperature; is the physical time. The net long-wave radiation acting on the front , energy from precipitation , and sensible heat and latent heat , only exists in the mth snow layer that is in direct contact with the air. Heat exchange between the snow layer and the photovoltaic panel The first layer of snow exists at the bottom of the snowpack. There is energy transfer (heat conduction) between adjacent snow layers due to the temperature difference between each layer. ;

[0168] Net solar (shortwave) radiation acting on the front ) will penetrate into the snow, and most of the solar radiation Absorbed by each snow layer, the rest Photovoltaic panels absorb.

[0169] The energy transfer process of photovoltaic panels is as follows Figure 3 and Figure 4 As shown, the energy balance equation is expressed as follows:

[0170]

[0171] Where, subscript PV represents photovoltaic panel; subscript b represents the back side of the tilted photovoltaic panel; m is the number of snow layers; is the PV module density; is the specific heat of the photovoltaic module; is the thickness of the photovoltaic panel; is the temperature of the photovoltaic panel. When the upper part of the photovoltaic panel is covered with snow (m>1), the energy exchange between the module and the surrounding environment includes the solar radiation acting on the front and penetrating into the photovoltaic panel. Energy exchange between snow and photovoltaic panels , the net long-wave radiation acting on the back of the photovoltaic panel , heat loss caused by convection on the back of the photovoltaic panel , Net solar radiation acting on the back of the photovoltaic panel And the energy taken away by photovoltaic panels due to absorbing solar radiation to generate electricity When there is no snow 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 It will not exist. At this time, we must also consider the net long-wave radiation acting on the front and convective heat loss from the front The calculation formulas for each energy term are introduced below.

[0172] (1) Solar shortwave radiation

[0173] Figure 5 Shows the various components of shortwave (solar) radiation on the inclined surface, Figure 6 Flowchart for calculating shortwave radiation.

[0174] Extraterrestrial solar radiation emitted by the Sun Affected by the scattering, absorption and transmission 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 the radiation model. For the front and back 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 of the photovoltaic panel inclined surface is expressed as and , the direct radiation acting on the front and back of the inclined surface of the photovoltaic panel is expressed as and , the reflected radiation from the ground to the front and back of the inclined surface of the photovoltaic panel are expressed as and Generally speaking, in the winter in the northern hemisphere, the sun is always in front of the photovoltaic panels installed facing south. The back of the photovoltaic panels cannot be directly exposed to the sun, so the direct radiation incident on the back is The sum of the radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front of the inclined surface. and the total radiation on the back side of the inclined surface , respectively expressed as: , The albedo of the front and back sides of the inclined surface are expressed as and ; Due to the effect of albedo, part 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 leaving the back of the inclined surface due to albedo , respectively expressed as: , The remaining part is the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and the net solar radiation acting on the back of the inclined surface , respectively expressed as: , The net solar radiation acting on the front of the photovoltaic panel's inclined surface The effects of transmission and absorption of snow and photovoltaics need to be further considered. The radiation received by the snow layer and photovoltaic panels can be expressed as , .

[0175] Potential extraterrestrial solar radiation on a certain day's horizontal surface The calculation formula is as follows:

[0176]

[0177] Where, is the solar constant; is the solar declination; is the latitude.

[0178] Daily horizontal total radiation The relationship between the daily potential extraterrestrial solar radiation and the daily clear sky index can be used To evaluate. Daily horizontal total radiation This paper uses the following formula to calculate :

[0179]

[0180] Where, is the daily temperature difference, a, b, c are empirical coefficients.

[0181] After obtaining the daily horizontal surface total radiation, it needs to be further decomposed into the direct radiation component on the daily horizontal surface and the diffuse radiation component The ratio of daily diffuse radiation to daily horizontal total radiation is is the scattering fraction , is the daily clear sky index Daily diffuse radiation on the horizontal surface , and the daily direct radiation on the horizontal surface is . and The relationship Take the following form:

[0182]

[0183] Where, is the sunset angle, and the 81.4° boundary is used to represent the seasonal correlation.

[0184] The multi-layer snowmelt model for photovoltaic structures requires hourly radiation data to accurately simulate the snow accumulation process. 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. . Hour angle The function is calculated as follows:

[0185]

[0186] Similarly, hourly scattered radiation Diffuse radiation from the sun Ratio You can use the formula Calculation. Hourly diffuse radiation , hours of direct radiation . The calculation formula is as follows:

[0187]

[0188] Solar radiation acting on the front of the inclined surface Including direct radiation from inclined surfaces , inclined surface scattered radiation , inclined surface reflected radiation Three components. Each component can be directly radiated by the horizontal plane , diffuse radiation The present invention uses the HDKR model (the Hay, Davies, Klucher, Reindl model) to calculate the total radiation of 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:

[0189]

[0190] Where, the geometric factor ,in is the angle of incidence, is the zenith angle; is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; is the direct score; is the ground albedo; is the inclination angle of the photovoltaic panel.

[0191] For tilted PV systems that are elevated by brackets, both the front and back sides receive solar radiation from the sky ( , ). The solar radiation received by the back panel is generally small and does not participate in power generation, but it will slightly increase the temperature of the photovoltaic panel. When Calculation. Unlike the front radiation, only the contribution of the scattered and reflected radiation components is considered. In addition, the calculation The inclination angle of the back of the photovoltaic panel is :

[0192]

[0193] For a snow-covered photovoltaic panel, the net solar radiation absorbed by the two surfaces ( , )Albedo of the front snow and photovoltaic back panel should also be considered separately ( , )

[0194]

[0195] The net solar radiation acting on the front will penetrate into the snow layer and be gradually absorbed. The expression is as follows:

[0196]

[0197] Where m is 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. It can be calculated as follows:

[0198]

[0199] When covered with snow, very little solar radiation penetrates the photovoltaic panels, and a very small proportion of this penetrating radiation is reflected back to the snow. Therefore, it is assumed that the photovoltaic panels absorb all the solar radiation that penetrates them. When there is no snow on the photovoltaic panels, the following formula is used to consider the impact of the photovoltaic panel's absorption and transmission capacity on solar radiation:

[0200]

[0201] Where, , and It is the transmittance-absorption product of direct, scattered and reflected radiation at the effective incident angle.

[0202] (2) Net longwave radiation

[0203] The incoming or outgoing longwave radiation can be calculated using the Stefan-Boltzmann equation:

[0204]

[0205] Where the subscript j represents the entity emitting long-wave radiation, which can be sky, gr, f, and b, representing the sky, the ground, the front of the light-inclined surface, and the back of the inclined surface, respectively. represents the long-wave radiation emitted by j; is the temperature of j; is the Stefan-Boltzmann constant, is the emissivity of j.

[0206] 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:

[0207]

[0208] Where, L sky The long-wave radiation emitted by the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Longwave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f is the viewing factor from the sky to the front of the photovoltaic panel, F gr-f F is the viewing factor from the ground to the front of the photovoltaic panel; sky-b is the viewing factor from the sky to the back of the photovoltaic panel, F gr-b is the viewing factor from the ground to the back of the photovoltaic panel.

[0209] (3) Sensible heat

[0210] The sensible heat exchange between the upper surface of the snow and the air is calculated as follows:

[0211]

[0212] Where, is the air density; is the specific heat of air; is the adjusted turbulent exchange coefficient; is the wind speed at the measuring height; Convective heat transfer coefficient for sensible heat flux in the absence of wind; is the air temperature; is the surface temperature of the snow cover.

[0213] (4) Latent heat

[0214] The latent heat flux exchange between the snow surface and the air is calculated as follows:

[0215]

[0216] Where, is the latent heat of sublimation; is the dry air constant; is the adjusted turbulent exchange coefficient, ; is the air vapor pressure; is the vapor pressure of the snow surface.

[0217] (5) Heat transfer between snow layers

[0218] The energy transfer due to temperature difference between adjacent snow layers is calculated by the following formula:

[0219]

[0220] Where, is the snow temperature; is the coordinate of the snow along the depth direction; is the effective heat transfer coefficient of the snow layer.

[0221] (6) Heat from precipitation

[0222] The energy brought by precipitation to snow accumulation can be expressed as follows:

[0223]

[0224] Where, is the amount of snowfall; is the specific heat of snow; is the density of liquid water; is the rainfall; is the latent heat of melting of snow.

[0225] (7) Electricity generated by photovoltaics

[0226] The calculation formula for photovoltaic production capacity is as follows:

[0227]

[0228] Where, is the solar radiation received by the tilted photovoltaic front; It is the maximum efficiency of photovoltaic modules under standard test conditions; is the maximum power temperature coefficient; is the temperature of the photovoltaic module; The reference temperature for standard test conditions. Solar radiation that is not used for power generation is converted into heat inside the photovoltaic panel. .

[0229] (8) Heat loss due to convection

[0230] The calculation formula for heat loss due to convection on the front and back of photovoltaic panels is as follows:

[0231]

[0232] Where, is the forced convection heat transfer coefficient; is the free convection heat transfer coefficient; is the temperature difference between the photovoltaic panel and the air boundary; when there is snow on the photovoltaic panel surface, the heat loss caused by convection on the front of the photovoltaic panel is zero.

[0233] The forced convection heat transfer coefficient is calculated using the following formula:

[0234]

[0235] Where, is the Reynolds number; is the Prandtl number, is the thermal conductivity of air; is the length of the photovoltaic panel along the direction of natural air flow;

[0236] The free convection heat transfer coefficient is calculated by the following formula:

[0237]

[0238] Where, is the Rayleigh number.

[0239] (8) Heat exchange between photovoltaics and snow

[0240] The heat transfer between the photovoltaic panel and the snow is determined by the temperature difference between the photovoltaic panel and the surface under the snow, and the calculation formula is as follows:

[0241]

[0242] Where, is the surface temperature under the snowpack; is the thermal conductivity of the photovoltaic panel; is the thickness of the photovoltaic panel.

[0243] 1.3 Mass balance equation

[0244] When snow accumulates on top of a photovoltaic module, the mass balance equation for the snow must be solved. Compared to the snow particles and water inside the snow layer, the phase change and diffusion of water vapor have less impact on the mass change of the snow layer, so the balance equation ignores its influence on the mass balance equation. The mass balance equation for snow on a photovoltaic (PV) module is as follows: As shown:

[0245]

[0246] Where, is the water equivalent of the i-th snow layer. , snowfall , snow melt outflow , snow sublimation or evaporation This causes a change in the mass of the top snow layer. The mass changes in the middle and bottom snow layers are determined by the outflow from the previous and current snow layers. The calculation formulas for each mass term are described below.

[0247] (1) Rainfall and snowfall

[0248] Precipitation and snowfall are calculated based on the temperature using the following formula:

[0249]

[0250] (2) Evaporation and sublimation amount

[0251] The evaporation or sublimation of liquid water in the snow will cause the mass of the snow to change. The change can be calculated according to the following formula:

[0252]

[0253] Where, is the snow water equivalent of the liquid water in the top snow layer; is the latent heat of evaporation of snow. When liquid water exists 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 for sublimation.

[0254] (3) Outflow

[0255] The outflow of snow water from the snowpack is controlled by the maximum water holding capacity of the snow layer. When the liquid water content exceeds the maximum water holding capacity of the snow layer, the excess snow water seeps into the next snow layer:

[0256]

[0257] Where, is the snow water equivalent of the i-th snow layer; is the maximum water holding capacity of the i-th snow layer.

[0258] 1.4 Phase change process

[0259] When the snow layer absorbs energy, a phase change occurs between solid water (ice) and liquid water in the snow layer, and the change in solid water due to phase change at time step t is and liquid water change is calculated according to the following formula:

[0260]

[0261] Where, is the total energy absorbed by the i-th snow layer, is the density of liquid water, is the latent heat of melting of ice, is the water equivalent of solid water in the i-th snow layer, is the equivalent of liquid water in the i-th snow layer, t represents the current time step, and t-1 represents the previous time step.

[0262] The liquid water equivalent in the i-th snow layer at time step t and water equivalent to solid water Calculate using the following formula:

[0263]

[0264]

[0265] 1.5 snow density

[0266] (1) New snow density

[0267] The volume density of fresh snow varies greatly under different climatic conditions. It is generally believed that the density of fresh snow is a function of the air temperature as the independent variable, and the calculation formula is expressed as follows:

[0268]

[0269] (2) Snow compaction

[0270] Snow is subject to compaction from the moment it falls. Snow compaction can be divided into two stages: the stage where new snow compacts due to deformation and destruction, and the stage where accumulated snow compacts due to gravity or pressure from above.

[0271] For density less than 150 kg·m -3For fresh snow, the destructive deformation of the internal structure of the snow is the main cause of snow compaction. At this time, the compaction rate is calculated using the following empirical relationship:

[0272]

[0273] After the snow layer has gone through the initial destructive deformation stage, the rate of snow layer compaction will significantly decrease. The main reason for the snow layer compaction at this time is the gravity compaction of the snow. The compaction rate can be calculated by the following formula:

[0274]

[0275] The total rate of snow compaction is the sum of the compaction rates of the above two stages:

[0276]

[0277] The change in snow density caused by snow compaction can be obtained from the following formula:

[0278]

[0279] 2. Determining conditions for snow slide

[0280] Snow on photovoltaic panels will gradually melt or even slide down under the influence of external conditions such as radiation and temperature. The present invention uses the method of accumulating positive energy to determine whether snow has fallen. Figure 7 Figure (a) and Figure 7 As shown in Figure (b), after the new snow falls on the photovoltaic panel, the snow absorbs energy from the environment. When the total energy absorbed by the snow at a certain moment (formula The sum of all energies involved) When it is greater than zero, the snow is said to have absorbed positive energy The so-called accumulation of positive energy , refers to the positive energy absorbed at each moment during the period when snow covers the photovoltaic panel The integral over time, Figure 7 The area of ​​the shaded part under the curve in Figure (b) is calculated as follows:

[0281]

[0282] like Figure 7 Figure (c) and Figure 7 In Figure (d), the accumulated positive energy of snow on the inclined surface has a critical value When positive energy is accumulated Reaching critical value , snow slides down from the photovoltaic panels, snow load Rapidly becomes zero. On the contrary, the snow melts naturally in the environment. Snow load on photovoltaic panels in a certain year The maximum value is the annual extreme value of the snow load on photovoltaic structures Different slopes The corresponding cumulative positive energy critical value (Unit: MJ·m -2 ) can be calculated using the following formula:

[0283]

[0284] Where, is the critical value of cumulative positive energy, and A, B, and C are empirical coefficients determined by actual snow measurement or experimental data.

[0285] 3. Weather data

[0286] The meteorological data required for the photovoltaic structure snowmelt model are the basic meteorological elements collected by the weather station and can be obtained from the meteorological data website. Specifically, it is necessary to obtain the daily maximum and minimum and average temperatures, daily average relative humidity, daily average wind speed, and daily total precipitation. The snowmelt model calculation time step is one hour. The hourly temperature is interpolated based on the daily maximum and minimum temperature values. The hourly relative humidity and wind speed are assumed to be consistent with the daily average. The hourly precipitation is the hourly average of the daily total precipitation. When the precipitation When input into the snowmelt model, according to the formula Classify precipitation as rain and snowfall .

[0287] 4. Statistical analysis of annual extreme snow load samples

[0288] Combined with historical meteorological data, the PV structure snowmelt model can simulate the temporal changes in the snow load on PV structures over the years. A statistical analysis of the snow load over the years was performed to obtain the snow load on PV structures under a certain guarantee rate. The statistical sample of snow load uses the annual maximum value, and the sample distribution is assumed to conform to the extreme value type I distribution, whose distribution function is:

[0289]

[0290] Where, is the annual extreme value sample of snow load, is the location parameter of the distribution, is the scale parameter of the distribution, is the sample standard deviation, and μ is the sample mean.

[0291] Snow load with a return period of R used in structural design , can be calculated as follows:

[0292]

[0293] Where R is the return period.

[0294] 5. Beneficial effects compared with existing technologies

[0295] Determining snow loads on photovoltaic structures can rely on field tests, standard values, and numerical simulations. Field tests are difficult to control due to external conditions, consume significant time, money, and labor costs, and cannot be carried out on a large scale, resulting in limited data. The standard-recommended snow load calculation method for photovoltaic structures refers to building structure standards, but the values ​​are overly conservative, significantly increasing the construction cost of photovoltaic structures. Furthermore, the standard provisions rely on engineering experience and judgment, and due to a lack of sufficient supporting case studies of photovoltaic structure snow loads, the standard method is not accurate. In comparison, simulation methods are more flexible and efficient.

[0296] The photovoltaic structure snow load assessment method proposed in the present invention, which is based on a snowmelt model and statistical analysis of snow load samples, can use basic meteorological data that is easily obtained from meteorological stations to quickly, economically and accurately simulate the photovoltaic structure snow load for many years in the target area, and obtain snow loads under a certain guarantee rate to guide the design of photovoltaic structures, improve structural safety and reduce construction costs. Ordinary snowmelt models are mostly used for runoff prediction, water resource management, and avalanche warning, and a few can simulate snow loads on building structures. Compared with ordinary snowmelt models, the photovoltaic structure multi-layer snowmelt model constructed by the present invention takes into account the energy balance process of photovoltaic panels, especially the impact of inclined surface radiation on snowmelt on photovoltaic panels, and is particularly suitable for accurate simulation of photovoltaic structure snow loads in areas where snow observation data is lacking.

[0297] The following is a specific embodiment of the present invention, and the evaluation process is as follows: Figure 1 shown.

[0298] This embodiment provides a method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model, comprising the following steps:

[0299] Step 1: Obtain basic meteorological data for the target area over the years from the meteorological website, including daily maximum, minimum and average temperatures, daily average relative humidity, daily average wind speed, and daily total 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 average. Hourly precipitation is the hourly average of the daily total precipitation. Precipitation According to the formula Divided into rainfall and snowfall The meteorological data of the kth year is selected to be input into the photovoltaic structure snowmelt model to simulate the snow load of the photovoltaic structure in the kth year.

[0300] Step 2: The calculation of any time step t in the snow load simulation of year k begins by adding new snowfall and updating the boundary conditions on the top of the snowpack. The new snowfall is divided into multiple snow layers covering the top of the original snowpack, and the thickness of each snow layer is between 0.5 and 1.0 cm to balance the calculation efficiency and accuracy. The snowfall amount at the current time step t is is the equivalent of solid water (ice) in fresh snow. Assuming that the temperature of fresh snowfall is consistent with the air temperature, the density of fresh snow is calculated according to the formula The depth of new snow is determined by the density of new snow and the equivalent of solid water. The content of liquid water is related to the precipitation and the maximum water holding capacity of snow. According to the formula calculate.

[0301] Step 3: Solve the energy balance equations for the snow layer and photovoltaic panels at time step t (Formula and formula ). Each energy term in the energy balance equation is calculated according to the formula -formula Calculation. According to the energy equation, the total energy absorbed by each snow layer and photovoltaic panel at time step j is obtained ( and ) and the temperature of each layer.

[0302] Step 4: Follow the formula and formula Calculate the accumulated positive energy of snow separately and its critical value When positive energy is accumulated ≥ Cumulative positive energy critical value , the snow on the photovoltaic panel slides down, and the snow load If it decreases to 0, the process jumps to step 2 to start the calculation of time step t+1. Otherwise, if the snow on the photovoltaic panel does not slide off, the process goes to step 5 to continue the snowmelt calculation at time step t.

[0303] Step 5: Substitute the total energy absorbed by each snow layer obtained in step 3 into the formula -formula , calculate the phase change between liquid water and solid water in the snow and the outflow of the snow layer, and then solve the mass balance equation of snow accumulation at time step t (Formula ), and obtain the changes in the quality of each snow layer.

[0304] Step 6: By formula -formula Calculate the compaction process of snow and obtain the density and depth of each snow layer after compaction in the current time step t.

[0305] Step 7: Re-divide the snow layers. Completely melted snow layers are removed, snow layers less than 0.5 cm are merged with adjacent layers, and snow layers greater than 1.0 cm are further subdivided so that each layer meets the required thickness. Physical parameters such as snow layer density, depth, moisture content, and temperature are updated using a weighted average method.

[0306] Step 8: Compare the current time step t with the maximum time step t max The size of t <t max When , jump to step 2 to start the calculation of time step t+1. Otherwise, the calculation of year k is completed. Snow load is the product of snow depth and snow density. Output the snow load time history of photovoltaic structure in year k, and extract the maximum snow load as the annual extreme value sample of snow load .

[0307] Step 9: Compare the calculated year k with the maximum year k max The size of k <k max , jump to step 1 to start the snow load simulation calculation for year k+1; otherwise, the snow load calculation for all years is completed. According to the formula and formula , using the snow load samples of photovoltaic structures in all years to calculate the snow load with a return period R under a certain guarantee rate . The design snow load for PV structures in the target area is now complete.

[0308] The above scheme uses basic meteorological data that is easily obtained from weather stations to quickly, economically and accurately simulate the snow load on photovoltaic structures in the target area for many years, and obtain snow loads under a certain guaranteed rate to guide the design of photovoltaic structures, thereby improving the safety of photovoltaic structures and reducing construction costs.

[0309] 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 aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model, characterized in that: The following steps are involved: Step 1: Obtain basic meteorological data of the target area over the years from the meteorological website; Step 2: Select the meteorological data of year k. When simulating the snow load on the PV structure in year k, the calculation of any time step t starts by adding new snowfall and updating the boundary conditions on the top of the snowpack. Step 3: Solve the energy balance equations of the snow layer and photovoltaic panels at time step t, and calculate the total energy absorbed by the snow layer and photovoltaic panels as well as the temperature of each layer; Step 4: Calculate the accumulated positive energy of the snow and its critical value. When the accumulated positive energy is greater than or equal to the critical value, it indicates that the snow has fallen, and the process goes to step 2. When the accumulated positive energy is less than or equal to the critical value, it indicates that the snow has not fallen, and the process goes to step 5. Step 5: Solve the mass balance equation of snow accumulation at time step t and calculate the phase change of snow and the outflow of snow layer; Step 6: By calculating the snow compaction process, the density and depth of each snow layer after compaction in the current time step t are obtained; Step 7: Re-divide the snow layer and update the physical parameters of the snow layer; Step 8: Compare the current time step t with the maximum time step t max The size of t <t max When , jump to step 2 to start the calculation of time step t+1; otherwise, the calculation of the kth year is completed, and the snow load history of the photovoltaic structure in the kth year and the annual extreme value sample of snow load S are output. a，max ; Step 9: Compare the calculated year k with the maximum year k max The size of k <k max , jump to step 1 to start the snow load simulation calculation for year k+1; otherwise, the snow load calculation for all years is completed, and the design snow load S of the photovoltaic structure in the target area is calculated. R : ； Where 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 snow load assessment of photovoltaic structures based on a multi-layer snowmelt model according to claim 1, characterized in that: In step 1, the basic meteorological data includes daily maximum, minimum and average temperatures, daily average relative humidity, daily average wind speed and daily total precipitation; Daily data were interpolated to obtain hourly data; hourly temperatures were linearly interpolated based on the daily maximum and minimum temperatures; hourly relative humidity and wind speed were assumed to be consistent with the daily averages; hourly precipitation was the hourly average of the daily total precipitation; Precipitation P is divided into rainfall and snowfall , the calculation formulas for precipitation and snowfall are as follows: ； Where: T a is the air temperature, T b 、T r are the boundary values ​​of rain and snow separation, and their values ​​are T b =-1, T r =3.

3. The method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model according to claim 2, characterized in that: In step 2, the new snowfall is divided into multiple snow layers covering the upper part of the existing snow, and the thickness of each snow layer is between 0.5 and 1.0 cm; Snowfall at the current time step t is the equivalent of solid water in fresh snow. Assuming that the temperature of fresh snowfall is consistent with the air temperature, the depth of fresh snow is determined by the density of fresh snow and the equivalent of solid water. The density of fresh snow is calculated as follows: ； Where, ρ s is the snow layer density; When the liquid water content is greater than the maximum water holding capacity of the snow layer, the excess snow water seeps into the next snow layer: ； Where, The meaning of is the outflow of the i-th snow layer; is the water equivalent of liquid water in the i-th snow layer at time step t; W i is the snow water equivalent of the i-th snow layer; is the maximum water holding capacity of the i-th snow layer.

4. The method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt 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 of the i-th snow layer at time step t is: ； Where, superscript i is the snow layer number; subscript f represents the front of the tilted photovoltaic panel; subscript s represents snow; is the snow layer density; is the specific heat of snow; is the thickness of the snow layer; is the snow layer temperature; is physical time; is the net solar radiation absorbed by snow layer i acting on the front of the photovoltaic panel; is the net longwave radiation acting on the front of the photovoltaic panel; is sensible heat; is latent heat; Energy transfer caused by temperature differences between adjacent snow layers; Energy brought to precipitation; The first snow layer at the bottom of the snowpack is the heat exchange between the snow layer and the photovoltaic panels; The solar radiation acting on the front of the photovoltaic panel is: ; 、 、 and Only exists in the mth snow layer in direct contact with the air; The sum of the right-hand side of the energy balance equation for the above snow layer is 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 △E, which is the total energy absorbed by each snow layer. sum; The total energy absorbed by the photovoltaic panel at time step t The following energy balance equation is used for calculation: ； Where, subscript PV represents photovoltaic panel; subscript b represents the back side of the tilted photovoltaic panel; m is the number of snow layers; is the density of photovoltaic panels; is the specific heat of the photovoltaic panel; is the thickness of the photovoltaic panel; is the photovoltaic panel temperature; It is the solar radiation that acts on the front of the photovoltaic panel and penetrates into the photovoltaic panel; is the net solar radiation acting on the back of the photovoltaic panel; is the net longwave radiation acting on the back of the photovoltaic panel; is the net longwave radiation on the front of the photovoltaic panel; is the convective heat loss from the front of the photovoltaic panel; The heat loss caused by convection on the back of the photovoltaic panel; It is the energy taken away by photovoltaic panels when they absorb solar radiation to generate electricity; For energy exchange between snow and photovoltaic panels; According to the energy balance equation of the snow layer and photovoltaic panels above, the total energy absorbed by each snow layer at time step t is obtained and the total energy absorbed by the photovoltaic panels and the temperature of each layer.

5. The method for snow load assessment of photovoltaic structures based on a multi-layer snowmelt model according to claim 4, characterized in that: In step 3, the energy balance equation for the total energy absorbed by each snow layer and photovoltaic panel is solved as follows: 1) Solar shortwave radiation The total horizontal radiation from the sun reaching the ground is diffuse radiation and direct radiation The sum of the front and back sides of the photovoltaic panel's inclined surface, in addition to the scattered and direct radiation acting on the inclined surface, also needs to consider the solar radiation reflected from the ground to the inclined surface; The scattered radiation acting on the front and back of the inclined surface of the photovoltaic panel is expressed as and , the direct radiation acting on the front and back of the inclined surface of the photovoltaic panel is expressed as and , the reflected radiation from the ground to the front and back of the inclined surface of the photovoltaic panel are expressed as and ; The sum of the radiation components acting on the inclined surface is the total radiation of the inclined surface, including the total radiation on the front of the inclined surface and the total radiation on the back side of the inclined surface , respectively expressed as: , ; The albedo of the front and back sides of the inclined surface are expressed as and ; Due to the effect of albedo, part 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 leaving the back of the inclined surface due to albedo , respectively expressed as: , The remaining part is the net solar radiation acting on the inclined surface, including the net solar radiation acting on the front of the inclined surface. and the net solar radiation acting on the back of the inclined surface , respectively expressed as: , ; Net solar radiation acting on the front of the inclined surface of the photovoltaic panel The radiation received by the snow layer and the photovoltaic panel are expressed as and ; Potential extraterrestrial solar radiation on a certain day's horizontal surface The calculation formula is: ； Where, is the solar constant; is the solar declination; is latitude; Daily global horizontal radiation Relationship with daily potential extraterrestrial solar radiation using the daily clear sky index To evaluate; daily horizontal total radiation ; The calculation formula is: ； Where, is the daily temperature difference, a, b, c are empirical coefficients; After obtaining the daily horizontal surface total radiation, decompose it into the direct radiation component on the daily horizontal surface and the diffuse radiation component ; The ratio of daily diffuse radiation to daily horizontal total radiation is the scattering fraction , is the daily clear sky index function of daily horizontal diffuse radiation , and the daily direct radiation on the horizontal surface is ; The calculation formula is: ； Where, is the sunset angle, and the 81.4° boundary is used to represent the seasonal correlation; Hourly total radiation , Hour angle The function is calculated as follows: ； Similarly, hourly scattered radiation , hours of direct radiation ; The calculation formula is as follows: ； Solar radiation acting on the front of the inclined surface of the photovoltaic panel Including direct radiation from inclined surfaces , inclined surface scattered radiation , inclined surface reflected radiation Three components, The calculation method is as follows: ； Where, the geometric factor ,in is the angle of incidence, is the zenith angle; is the anisotropy index, which is a function of the atmospheric transmittance of direct radiation; is the direct score; is the ground albedo; is the inclination angle of the photovoltaic panel; For the tilted photovoltaic panels raised by the bracket, both the front and back sides receive solar radiation from the sky, which are and ; Calculate the solar radiation received by the back side When the inclination angle of the back of the photovoltaic panel is , the calculation formula is as follows: ； For snow-covered photovoltaic panels, the net solar radiation absorbed by the photovoltaic panels and snow is and , the calculation formula is as follows: ； The net solar radiation acting on the front of the photovoltaic panel will penetrate into the snow layer and be gradually absorbed. The amount of solar radiation absorbed by each snow layer is The expression is as follows: ； Where 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 on the photovoltaic panels, the following formula is used to consider the impact of the photovoltaic panels' absorption and transmission capabilities on solar radiation: ； Where, , and is the product of transmittance-absorption at the effective incident angle of direct, scattered and reflected radiation; 2) Net longwave radiation The incoming or outgoing longwave radiation is calculated according to the Stefan-Boltzmann equation: ； Where, the subscript j refers to the subject emitting long-wave radiation, sky, gr, f, and b represent the sky, the ground, the front side, and the back side of the photovoltaic panel’s tilt, respectively; represents the long-wave radiation emitted by j; is the temperature of j; is the Stefan-Boltzmann constant, is the emissivity of j; The net longwave radiation from the front and back of the inclined surface is calculated as follows: ； Where, L sky The long-wave radiation emitted by the sky, L f Long-wave radiation emitted from the front of the photovoltaic panel; L gr Longwave radiation emitted from the ground, L b Long-wave radiation emitted from the back of the photovoltaic panel; F sky-f is the viewing factor from the sky to the front of the photovoltaic panel, F gr-f F is the viewing factor from the ground to the front of the photovoltaic panel; sky-b is the viewing factor from the sky to the back of the photovoltaic panel, F gr-b is the viewing factor 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 as follows: ； Where, is the air density; is the specific heat of air; is the adjusted turbulent exchange coefficient; is the wind speed at the measuring height; Convective heat transfer coefficient for sensible heat flux in the absence of wind; is the air temperature; is the surface temperature of the snow cover; 4) Latent heat The latent heat flux exchange between the snow surface and the air is calculated as follows: ； Where, is the latent heat of sublimation; is the dry air constant; is the adjusted turbulent exchange coefficient, ; is the air vapor pressure; is the vapor pressure of the snow surface; 5) Heat transfer between snow layers The energy transfer due to temperature difference between adjacent snow layers is calculated by the following formula: ； Where, is the snow temperature; is the coordinate of the snow along the depth direction; is the effective heat transfer coefficient of the snow layer; 6) Heat from precipitation The energy brought by precipitation to snow accumulation can be expressed as follows: ； Where, is the amount of snowfall; is the specific heat of snow; c w is the specific heat of liquid water; is the density of liquid water; is the rainfall; is the latent heat of melting of snow; 7) Electricity generated by photovoltaics The calculation formula for photovoltaic production capacity is as follows: ； Where, is the solar radiation received by the front of the tilted photovoltaic panel; It is the maximum efficiency of photovoltaic modules under standard test conditions; is the maximum power temperature coefficient; is the 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 calculation formula for heat loss due to convection on the front and back of photovoltaic panels is as follows: ； Where, is the forced convection heat transfer coefficient; is the free convection heat transfer coefficient; is the temperature difference between the photovoltaic panel and the air boundary; when there is snow on the photovoltaic panel surface, the heat loss caused by convection on the front of the photovoltaic panel is zero; The forced convection heat transfer coefficient is calculated using the following formula: ； Where, is the Reynolds number; is the Prandtl number, is the thermal conductivity of air; is the length of the module along the direction of natural air flow; The free convection heat transfer coefficient is calculated by the following formula: ； Where, is the Rayleigh number; 9) Heat exchange between photovoltaic panels and snow The heat transfer between the photovoltaic panel and the snow is determined by the temperature difference between the photovoltaic panel and the surface under the snow, and the calculation formula is as follows: ； Where, is the surface temperature under the snowpack; is the thermal conductivity of the photovoltaic panel; is the thickness of the photovoltaic panel.

6. The method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model according to claim 5, characterized in that: In step 4, the cumulative positive energy of snow from the initial time t0 to any time t is calculated as follows: ； Where △E 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 cumulative positive energy critical value calculation formula is as follows: ； Where, is the critical value of cumulative positive energy, and A, B, and C are empirical coefficients determined by actual snow measurement or experimental data.

7. The method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model according to claim 6, characterized in that: In step 5, the phase change between liquid water and solid water in the snow and the snow layer outflow rate are calculated as follows: The evaporation or sublimation of liquid water in the snow will cause the mass of the snow to change. Substituting precipitation and snowfall into the following formula, we can get the amount of sublimation and evaporation. The change is calculated as follows: ； Where, is the snow water equivalent of the liquid water in the top snow layer; is the latent heat of evaporation of snow; h s W is the latent heat of snow sublimation; e is the amount of sublimation evaporation; E1 is the latent heat; ρ w is the density of water; The outflow of snow water from the snowpack is controlled by the maximum water holding capacity of the snow layer; when the liquid water content exceeds the maximum water holding capacity of the snow layer, the excess snow water seeps into the next snow layer: ； Where, is the snow water equivalent of the i-th snow layer; is the maximum water holding capacity of the i-th snow layer; When the snow layer absorbs energy, a phase change occurs between the solid water and liquid water in the snow layer, and the solid water and liquid water are transformed into each other. The change in the solid water due to the phase change at time step t is and liquid water change is calculated according to the following formula: ； Where, is the total energy absorbed by the i-th snow layer, is the density of liquid water, is the latent heat of melting of ice, is the water equivalent of solid water in the i-th snow layer, is the equivalent of liquid water in the i-th snow layer, t represents the current time step, and t-1 represents the previous time step; The liquid water equivalent in the i-th snow layer at time step t and water equivalent to solid water Calculate using the following formula: ； ； The above formulas are used to calculate the phase change between liquid water and solid water in the snow and the outflow of the snow layer, and then the mass balance equation of the snow at time step t is solved to obtain the change in the mass of each snow layer; The mass balance equation for snow accumulation on photovoltaic panels is as follows: ； Where, is the water equivalent of the ith snow layer.

8. The method for assessing snow loads on photovoltaic structures based on a multi-layer snowmelt model according to claim 7, characterized in that: In step 6, for density less than 150 kg·m -3 For fresh snow, the compaction rate is calculated using the following relationship: ； After the snow layer has gone through 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 above two stages: ； The change in snow density caused by snow compaction is given by the following formula: ； Where, is the temperature of snow layer i; γ i is the weight of snow layer i; P s is the pressure of snow on the upper part of the snow layer; η0 is an empirical parameter.

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

10. The method for snow load assessment of photovoltaic structures based on a multi-layer snowmelt model according to claim 9, characterized in that: In step 9, the snow load for the return period R is calculated using the snow load samples for the PV structures for all years. ; The statistical sample of snow load adopts the annual maximum value, and it is assumed that the sample distribution conforms to the extreme value type I distribution, and its distribution function is: ； Where, is the annual extreme value sample of snow load, is the location parameter of the distribution, is the scale parameter of the distribution, is the sample standard deviation, and μ is the sample mean.

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