Optimal Tilt Angle Design Method Based on Planar Roof Photovoltaic Systems

Abstract

This invention discloses an optimal tilt angle design method for a planar rooftop photovoltaic (PV) system. Using historical local load demand data as a reference, it combines a long short-term memory (LSTM) artificial neural network algorithm to predict the local electricity load demand for the next year. Based on this predicted load demand, the optimal tilt angle is optimized. The obtained optimal tilt angle improves the annual electricity load utilization rate and avoids excessive power shortages in certain months. Furthermore, this invention considers the PV device capacity per unit area under actual installation costs and calculates the PV tilt angle that maximizes the PV device capacity per unit area. Finally, game theory is used to optimize the two schemes, ensuring that the final optimal tilt angle improves both the annual electricity load utilization rate and the PV device capacity per unit area.

Description

Technical Field

[0001] This invention relates to the field of power grid data processing technology, and is particularly applicable to the optimal tilt angle design method based on planar roof photovoltaic systems. Background Technology

[0002] Against the backdrop of a "dual carbon" environment, solar energy, as a viable alternative to traditional energy sources, has seen large-scale distributed photovoltaic (PV) power generation being integrated into the grid, driven by the energy crisis. In PV power generation systems, photovoltaic modules, commonly known as solar panels, are the core and most valuable component. Their function is to convert solar radiation into electrical energy, which is either stored in batteries or used to power loads. Currently, the most widely used PV power plants in my country are fixed grid-connected PV power plants. In the use and design of fixed grid-connected PV power plants, the array surface needs to be tilted at a certain angle, ensuring the installation tilt angle is equal to or close to the optimal tilt angle to obtain the maximum annual solar radiation. Therefore, the optimal tilt angle is one of the key design parameters for fixed grid-connected PV power plants.

[0003] In practical applications, many experts have found a correlation between the installation tilt angle and its geographical latitude. With the equator as the orientation, the optimal tilt angle for photovoltaic installations is generally approximately equal to the local latitude. Furthermore, the optimal tilt angle is also affected by solar radiation. Some scholars have quantified the uniformity of radiation distribution throughout the year, calculating the tilt angle while considering both uniformity and maximum radiation, and calculating the percentage increase in radiation relative to the horizontal plane based on the assumption of clear skies. However, this method can lead to reduced photovoltaic power generation in winter, potentially causing severe power shortages in certain months. Simultaneously, by focusing too much on the maximum solar radiation obtained at the optimal tilt angle of the photovoltaic panels, and neglecting the impact of factors such as different load demands, system usage frequency, centralized installation, and subsequent operation and maintenance, this method reduces its guiding significance for engineering practice. Summary of the Invention

[0004] The purpose of this invention is to provide an optimal tilt angle design method for planar roof photovoltaic systems. This method aims to provide a multi-objective optimization approach to optimize the tilt angle of planar roof photovoltaic systems, avoid excessive power shortages in certain months, and improve the power conversion efficiency of distributed photovoltaic systems on planar pitched roofs and reduce the investment and maintenance costs of the "source-grid-load-storage" system by taking into account factors such as usage frequency, centralized installation, and subsequent operation and maintenance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] The optimal tilt angle design method for a planar roof photovoltaic system described in this invention includes the following steps:

[0007] S1, based on the sunshine percentage of ground meteorological stations or satellite remote sensing data, establish the correlation between solar radiation and slope surface;

[0008] S2, obtain the declination angle, hour angle and solar time of the installation site;

[0009] S3, obtain the parameters of the photovoltaic modules to be installed and the historical electricity load demand data of the installation site;

[0010] S4. Based on the data from steps S1 and S2, establish a planar slope solar radiation calculation model to obtain the optimal photovoltaic tilt angle without considering load demand.

[0011] S5, based on the historical electricity load demand data of the installation site, uses a long short-term memory artificial neural network algorithm to predict the electricity load demand of the installation site for the next year; in order to avoid excessive power shortages in certain months of the next year, the optimal photovoltaic tilt angle is optimized to obtain the optimal installation tilt angle that takes into account the load demand.

[0012] S6. Based on the data from step S2, establish a dynamic shadow area calculation model; based on the dynamic shadow area calculation model, obtain the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area.

[0013] S7. The evaluation factors are the optimal installation tilt angle considering load demand and the optimal installation tilt angle corresponding to the maximum photovoltaic device capacity per unit area. The subjective weight of the evaluation factors is determined by the network hierarchy analysis method, and the objective weight of the evaluation factors is determined by the entropy weight method.

[0014] S8. The evaluation factors are combined and weighted according to the game theory algorithm to obtain the combined weights of the evaluation factors.

[0015] S9. The installation tilt angles corresponding to the combined weights of the evaluation factors are weighted and summed to obtain the optimal installation angle.

[0016] Furthermore, the expression for the planar slope solar radiation calculation model described in step S4 is as follows:

[0017]

[0018] In the formula, This refers to direct radiation. This refers to the amount of scattered radiation from the sky. Design the tilt angle for photovoltaic panels, For the latitude of the installation location; The solar declination of the installation location; is the hour angle; n is the number of days in a year starting from New Year's Day; The ground reflectivity is taken as 0.2.

[0019] Furthermore, the optimization of the optimal photovoltaic tilt angle in step S5 includes calculating the average absolute error S between the monthly photovoltaic power generation rate and the monthly electricity load demand for the next year for different tilt angles within ±10° of the optimal photovoltaic tilt angle determined in step S4. The tilt angle corresponding to the minimum value of S is the optimal installation tilt angle considering the load demand.

[0020] Further, in step S7, the network hierarchical analysis method determines the subjective weights of the evaluation factors, including S7.1.1, constructing the pairwise comparison matrix X of the evaluation factors, and calculating the weight vector M of each evaluation factor;

[0021] S7.1.2 Multiply the comparison matrix X with the weight vector M of each evaluation factor to obtain the super-weighted matrix;

[0022] S7.1.3 Calculate the super-weighted matrix by continuous powers until the matrix tends to stabilize, and obtain the limit super matrix. Each column of the limit super matrix corresponds to the subjective weight of each evaluation factor.

[0023] Furthermore, in step S8, according to the game theory algorithm, the difference between subjective weights and objective weights is minimized to obtain the weight coefficient of subjective weights for each evaluation factor; and the combined weight of each evaluation factor is calculated.

[0024] The advantage of this invention lies in its ability to predict the local electricity load demand for the next year based on existing research on optimal photovoltaic installation tilt angles, using historical local load demand data as a reference and employing a Long Short-Term Memory (LSTM) algorithm. The optimal tilt angle is then optimized based on this predicted load demand, resulting in a higher annual electricity load utilization rate and preventing excessive power shortages in certain months. Furthermore, when the shading time of the front and rear rows of modules is consistent, the distance from the leading edge of the front row fixed support module to the leading edge of the adjacent rear row fixed support module decreases accordingly. This results in a different footprint for a 1 MW photovoltaic array, which, considering factors such as actual installation costs, affects the photovoltaic device capacity per unit area. This patent calculates the photovoltaic tilt angle that maximizes the photovoltaic device capacity per unit area. Finally, game theory is used to optimize the two schemes, ensuring that the final optimal tilt angle improves both the annual electricity load utilization rate and the photovoltaic device capacity per unit area. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method described in this invention.

[0026] Figure 2 This is a flowchart illustrating the determination of the optimal installation tilt angle considering load requirements in the method described in this invention. Detailed Implementation

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0028] like Figure 1 As shown, the optimal tilt angle design method for a planar roof photovoltaic system according to the present invention includes the following steps:

[0029] S1, based on the sunshine percentage of ground meteorological stations or satellite remote sensing data, establish the correlation between solar radiation and slope surface.

[0030] S2, obtains geographical data such as the declination angle δ, hour angle ω, and solar time at the installation site.

[0031] Formula (1)

[0032] n is the number of days in a year starting from New Year's Day.

[0033] Formula (2)

[0034] Formula (3)

[0035] Local standard time; Local longitude; The standard longitude is DS; DS represents daylight saving time, which is 1 when it is in effect, otherwise it is 0.

[0036] Based on formula (2) and the specific sunrise and sunset times, the sunrise and sunset angles can be calculated.

[0037] S3, obtain the parameters of the photovoltaic modules to be installed and the historical electricity load demand data of the installation site.

[0038] S4. Based on the data from steps S1 and S2, establish a planar slope solar radiation calculation model to obtain the optimal photovoltaic tilt angle without considering load demand.

[0039] The expression for the solar radiation calculation model of a flat slope is:

[0040] Formula (4)

[0041] In the formula, H T Total daily radiation This refers to direct radiation. This refers to the amount of scattered radiation from the sky. Design the tilt angle for photovoltaic panels, For the latitude of the installation location; The solar declination of the installation location; is the hour angle; n is the number of days in a year starting from New Year's Day; The ground reflectivity is taken as 0.2.

[0042] S5, based on historical electricity load demand data of the installation site, uses a long short-term memory artificial neural network algorithm to predict the electricity load demand of the installation site for the next year; in order to avoid excessive power shortages in certain months of the coming year, the optimal photovoltaic tilt angle is optimized to obtain the optimal installation tilt angle that takes load demand into account. The specific process is as follows: Figure 2 As shown.

[0043] like Figure 2 As shown, the specific steps for establishing a long short-term memory artificial neural network algorithm to predict the electricity load demand of the installation site for the next year are as follows:

[0044] S5.1 collects monthly power load data for the installation site over the years, preprocesses the collected data, and divides the sample data into training and test sets.

[0045] S5.2, Use the training set data to train the long short-term memory artificial neural network algorithm to obtain a prediction model for predicting the electricity load demand of the installation site in the next year, and determine whether the accuracy of the prediction model has reached the preset value. If it has not reached the preset accuracy, update the prediction model parameters and continue training until the prediction accuracy of the prediction model reaches the preset value.

[0046] S5.3, use test set data to verify the prediction results of the prediction model, and obtain the final prediction model, which is used to output the electricity load demand of the installation site for the next year.

[0047] Then, based on the optimal photovoltaic tilt angle obtained from S4 without considering load demand, the average absolute error S between the monthly photovoltaic power generation rate and the monthly electricity load demand for each different tilt angle within a range of ±10° is calculated. The tilt angle corresponding to the minimum value of S is taken as the optimal installation tilt angle considering load demand. The expression for S is:

[0048] Formula (5)

[0049] in, Let be the predicted load demand value for the i-th month; Let n be the power generation of the photovoltaic panel at a certain tilt angle in the i-th month. n is the total number of natural months.

[0050] S6. Based on the data from step S2, establish a dynamic shadow area calculation model; based on the dynamic shadow area calculation model, obtain the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area.

[0051] When the shading time of the front and rear rows of modules is the same, the distance from the leading edge of the front row fixed support module to the leading edge of the adjacent rear row fixed support module will decrease accordingly, resulting in a different footprint for a 1 MW photovoltaic array. Considering factors such as actual installation costs, the photovoltaic device capacity per unit area will also be affected. Using PVsyst software for shading simulation, the shading formation mechanism is analyzed based on the spatial projection method, and a dynamic shading area calculation model is established. The specific steps are as follows:

[0052] S6.1, Calculate the width C of the photovoltaic array shadow in the planar slope model;

[0053] Formula (6)

[0054] The width of the photovoltaic array; L represents the height difference between the foundations of the photovoltaic strings; L represents the height of the photovoltaic array support. Let S be the slope angle of the plane slope. S6.2, calculate the shadow length D of the photovoltaic array in the plane slope model;

[0055] Formula (7)

[0056] The length of the photovoltaic array;

[0057] S6.3 refers to the area occupied by the photovoltaic panels when the photovoltaic arrays do not block each other. :

[0058] Formula (8)

[0059] S6.4, using PVsyst simulation software for analysis and calculation to make The photovoltaic panel installation tilt angle that achieves the minimum value is denoted as β.

[0060] S7. The subjective weights of the evaluation factors are determined by the analytic hierarchy process (AHP) and the objective weights by the entropy weight method, respectively, using the optimal installation tilt angle considering load demand and the optimal installation tilt angle corresponding to the maximum photovoltaic device capacity per unit area as evaluation factors.

[0061] The network analytic hierarchy process (AHP) determines the subjective weights of the evaluation factors by including:

[0062] S7.1.1 Construct the pairwise comparison matrix X of the evaluation factors and calculate the weight vector M of each evaluation factor.

[0063] Among them, four evaluation factors are determined based on the optimal installation tilt angle considering load demand and the optimal installation tilt angle corresponding to the maximum photovoltaic device capacity per unit area, which is related to the initial investment of photovoltaic power generation projects.

[0064] The revenue corresponding to the optimal installation tilt angle considering load demand is an important indicator for measuring the feasibility of photovoltaic power generation projects. The single-panel installation cost corresponding to the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area reflects the cost required to maximize the power generation capacity per unit area, which is related to land resource utilization efficiency and cost control. The revenue corresponding to the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area represents the profitability that can be obtained when the capacity per unit area is maximized at a specific installation angle, and is extremely crucial for comprehensively evaluating the economic benefits of the installation scheme.

[0065] The pairwise comparison matrix X of the evaluation factors is constructed as follows:

[0066]

[0067] In the formula, a ij This indicates the importance of the i-th factor compared to the j-th factor. w1 represents the importance weight of the cost of a single photovoltaic panel considering the installation angle based on load demand; w2 represents the importance weight of the profitability of a single photovoltaic panel considering the installation angle based on load demand; w3 represents the importance weight of the cost of the maximum installation angle per unit area capacity; and w4 represents the importance weight of the profitability of the maximum installation angle per unit area capacity.

[0068] S7.1.2 Multiply the comparison matrix X with the weight vector M of each evaluation factor to obtain the super-weighted matrix.

[0069] The pairwise comparison matrix X of the above evaluation factors is a reciprocal matrix, having a ij =1 / a ji The characteristic is that the elements are consistent.

[0070] Suppose there exists a positive vector M of the same order as matrix X;

[0071]

[0072] Let M be the largest eigenvalue of matrix X. The eigenvectors are used to solve for the matrix X, and the resulting solution is the weight vector corresponding to each evaluation factor. Multiplying matrix X by the priority weights generated from the criteria, denoted as W=X×M, yields the super-weighted matrix. Each element in the super-weighted matrix represents the relative importance of each factor in the network hierarchy, denoted as Mi'=(v1,v2,v3,v4). v1,v2,v3,v4 represent the relative importance of each factor.

[0073] S7.1.3 Calculate the super-weighted matrix by continuous powers until the matrix tends to stabilize, and obtain the limit super matrix. Each column of the limit super matrix corresponds to the subjective weight of each evaluation factor.

[0074] To capture all the influence paths between these evaluation factors, including direct and indirect influences, the super-weighted matrix needs to be upgraded to a limit supermatrix.

[0075] This can be achieved by calculating successive powers of the superweighted matrix. For example, you can first calculate the square of the superweighted matrix and then observe the changes in the matrix; then calculate the cube and observe again; and so on, until the matrix tends to stabilize.

[0076] In this process, we notice that the element values ​​of the matrix change as the power increases, reflecting the dynamics and complexity of the influence between the evaluation factors. When the super-weighted matrix reaches its limit, we obtain the limit hypermatrix. This limit hypermatrix contains all the direct and indirect influence paths between the evaluation factors. The relative limit order of each element in the lower network layer of the control element in the limit hypermatrix with respect to element i is the subjective weight of the evaluation factor.

[0077] The specific process of determining the objective weights of the evaluation factors using the entropy weight method is as follows:

[0078] By collecting actual values ​​from photovoltaic power plants that have been built and put into use, an evaluation set X2 = (x ij ) 4×4 , where x ij This represents the actual value of the i-th evaluation factor on the j-th sample. The evaluation factors include the cost per photovoltaic panel considering the installation angle based on load demand, the profit per photovoltaic panel considering the installation angle based on load demand, the cost per unit area capacity at the maximum installation angle, and the profit per unit area capacity at the maximum installation angle.

[0079] Then, the evaluation set is normalized. The standardized formula for the profit evaluation factors (denoted as indicators i=2,4) is: Here x i This represents the value of the i-th profitability evaluation factor across all samples. The purpose of this formula is to map profitability data to the [0,1] interval, making the profitability data of different power plants comparable; the larger the value, the better the profitability.

[0080] For cost indicators (let's say indicator i=1,3), the standardized formula is: After this processing, the cost data is also mapped to the [0,1] interval; however, unlike profit, smaller values ​​indicate lower costs. Through these standardization processes, the standardized matrix C2 = (c ij ) 4×4 ,c ij Let be the standard value of the i-th indicator on the j-th sample.

[0081] Then, the proportion f of the j-th sample under the i-th indicator. ij The calculation method is as follows For example, for the data of the first indicator (cost of a single photovoltaic panel considering the installation angle of load demand) in the four photovoltaic power plant samples, the standardized cost value corresponding to each power plant is divided by the sum of the standardized cost values ​​of the four power plants for this indicator to obtain the proportion of each power plant under this indicator.

[0082] Then calculate the entropy value H of the i-th index. i The calculation method is as follows Entropy reflects the degree of disorder or uncertainty of indicator data. The larger the entropy value, the more uniform the data distribution of the indicator, and the less information it provides.

[0083] Finally, the difference coefficient 1-Hi is calculated. The difference coefficient represents the degree of information difference of the i-th indicator; the larger the difference coefficient, the more effective information the indicator provides. Then, the entropy weight Ni of the i-th indicator is determined: In fact, this is the normalization of differences, which is consistent with the normalization logic above.

[0084] S8. The evaluation factors are weighted using a game theory algorithm to obtain their combined weights. This means that when considering the actual installation situation of photovoltaic panels, both load demand and installation costs must be taken into account. To comprehensively consider multiple factors and make the weight determination more scientific and reasonable, a combined weighting method that combines subjective weighting factors with entropy weighting factors is adopted in determining the optimal tilt angle of the photovoltaic panels.

[0085] Subjective weights are derived from the limit hypermatrix Mi'=(v1,v2,v3,v4). Objective weights are derived from the entropy weight method weight N. i Therefore, we can conclude that... ξ ξ is a weighting coefficient, ranging from 0 to 1, used to balance the relative importance of subjective weights and entropy weights in the combined weights. Based on game theory, the algorithm aims to minimize the sum of the deviations between subjective and objective weights, achieved by constructing a specific optimization objective function. This is done by calculating the combined weighting coefficient ξ, according to... Calculate the combined weights of each evaluation factor.

[0086] S9, the installation tilt angles corresponding to the combined weights of the evaluation factors are weighted and summed to obtain the optimal installation angle. The calculation formula is as follows: , The optimal angle for a single photovoltaic panel, taking into account load demand; To take into account the maximum installation angle per unit area (i.e., including the shaded area).

Claims

1. A method for optimizing the tilt angle of a planar rooftop photovoltaic system, characterized in that: Includes the following steps, S1, based on the sunshine percentage of ground meteorological stations or satellite remote sensing data, establish the correlation between solar radiation and slope surface; S2, obtain the declination angle, hour angle and solar time of the installation site; S3, obtain the parameters of the photovoltaic modules to be installed and the historical electricity load demand data of the installation site; S4. Based on the data from steps S1 and S2, establish a planar slope solar radiation calculation model to obtain the optimal photovoltaic tilt angle without considering load demand. The expression for the solar radiation calculation model of the plane slope is: In the formula, H T This represents the total daily radiation. This refers to direct radiation. This refers to the amount of scattered radiation from the sky. Design the tilt angle for photovoltaic panels, For the latitude of the installation location; The solar declination of the installation location; is the hour angle; n is the number of days in a year starting from New Year's Day; The ground reflectivity is taken as 0.2; S5. Based on the historical electricity load demand data of the installation site, a long short-term memory artificial neural network algorithm is used to predict the electricity load demand of the installation site for the next year. In order to avoid excessive power shortages in certain months of the next year, the optimal photovoltaic tilt angle is optimized to obtain the optimal installation tilt angle considering the load demand. The optimization of the optimal photovoltaic tilt angle includes calculating the average absolute error S between the monthly photovoltaic power generation rate and the monthly electricity load demand for the next year for different tilt angles within ±10° of the optimal photovoltaic tilt angle determined in step S4. The tilt angle corresponding to the minimum value of S is the optimal installation tilt angle considering the load demand. S6. Based on the data from step S2, establish a dynamic shadow area calculation model; based on the dynamic shadow area calculation model, obtain the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area. The steps include the following: S6.1, Calculate the width C of the photovoltaic array shadow in the planar slope model; ； in, The width of the photovoltaic array; L represents the height difference between the foundations of the photovoltaic arrays; L represents the height of the photovoltaic array support structure. The slope angle of a plane slope; S6.2, Calculate the shadow length D of the photovoltaic array in the planar slope model; ； in, The length of the photovoltaic array; S6.3 refers to the area occupied by the photovoltaic panels when the photovoltaic arrays do not block each other. : ； S6.4, using PVsyst simulation software for analysis and calculation to make The photovoltaic panel installation tilt angle that achieves the minimum value is denoted as the optimal installation tilt angle that maximizes the photovoltaic device capacity per unit area. S7. The evaluation factors are the optimal installation tilt angle considering load demand and the optimal installation tilt angle corresponding to the maximum photovoltaic device capacity per unit area. The subjective weight of the evaluation factors is determined by the network hierarchy analysis method, and the objective weight of the evaluation factors is determined by the entropy weight method. S8. The evaluation factors are combined and weighted according to the game theory algorithm to obtain the combined weights of the evaluation factors. S9. The installation tilt angles corresponding to the combined weights of the evaluation factors are weighted and summed to obtain the optimal installation angle.

2. The optimal tilt angle design method for a planar roof photovoltaic system according to claim 1, characterized in that: In step S7, the network hierarchy analysis method determines the subjective weights of the evaluation factors, including S7.1.1, constructing the pairwise comparison matrix X of the evaluation factors, and calculating the weight vector M of each evaluation factor; S7.1.2 Multiply the comparison matrix X with the weight vector M of each evaluation factor to obtain the super-weighted matrix; S7.1.3 Calculate the super-weighted matrix by continuous powers until the matrix tends to stabilize, and obtain the limit super matrix. Each column of the limit super matrix corresponds to the subjective weight of each evaluation factor.

3. The optimal tilt angle design method for a planar rooftop photovoltaic system according to claim 2, characterized in that: In step S8, according to game theory algorithms, the sum of the deviations between subjective and objective weights is minimized to obtain the weight coefficients of the subjective weights of each evaluation factor; according to Calculate the combined weights of each evaluation factor; N i M represents the entropy weight of the i-th indicator, also known as the objective weight; i The subjective weight of the i-th indicator is derived from the limit hypermatrix; ξ is a weighting coefficient, ranging from 0 to 1, used to balance the relative importance of subjective weights and entropy weights in the combined weights; the indicators include profit evaluation factors, denoted as indicators i=2,4; and cost indicators, denoted as indicators i=1,3.

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