A method for improving the accuracy of clustering in photovoltaic power generation systems

Abstract

This invention discloses an accuracy improvement method for photovoltaic (PV) power generation system clustering, belonging to the field of equivalent modeling technology for PV power generation systems. The method includes the following steps: Step S1, establishing a mathematical model of the PV cell; Step S2, performing theoretical analysis on the mathematical model of the PV cell to obtain the nonlinear characteristics of the PV cell's maximum power in relation to light intensity and temperature; Step S3, introducing a correction weight function based on the error loss caused by the nonlinear characteristics. This invention employs the above-mentioned accuracy improvement method for PV power generation system clustering, which can effectively improve the simulation accuracy of the PV power generation system clustering model.

Description

Technical Field

[0001] This invention relates to the field of equivalent modeling technology for photovoltaic power generation systems, and in particular to a method for improving the accuracy of clustering of photovoltaic power generation systems. Background Technology

[0002] Based on the distribution of photovoltaic (PV) clusters, the equivalent methods for regional centralized PV systems mainly include single-unit equivalent methods and multi-unit equivalent methods. When the environmental conditions of centralized PV systems are relatively uniform, the single-unit equivalent method, due to its simplicity, usually meets the requirements in situations where high accuracy is not necessary. This method compares the differential equations of the detailed model and the equivalent model, lists the equations for each component, and compares the parameters to determine the component parameters of the equivalent model. The equivalent model parameters can usually be directly calculated using formulas. The multi-unit equivalent method seeks a balance between simulation accuracy and efficiency. It classifies PV power generation units using clustering algorithms and then calculates the equivalent model. When focusing on the dynamic response of the PV system, inverter parameters, such as the product of control parameters and sensitivity, are often chosen as clustering indices. If the requirement for dynamic accuracy is slightly lower, and only steady-state accuracy is considered, environmental parameters such as light intensity and temperature can be used as clustering indices.

[0003] However, when clustering based on the light intensity and temperature of photovoltaic power generation systems, it is found that the output of the clustering model has a certain error compared to the actual system. For large-scale photovoltaic power generation systems, whose power levels are typically in the millions of kilowatts to tens of megawatts, even a small error can result in a significant discrepancy in reality. Therefore, further improving the accuracy of the equivalent model is crucial. Currently, the general solution in this field is to propose more complex clustering algorithms or use deep learning and other methods to improve the simulation accuracy of the clustering model. However, the implementation process is extremely complex and not easy to implement. Summary of the Invention

[0004] The purpose of this invention is to provide a method for improving the accuracy of photovoltaic power generation system clustering, which can effectively improve the simulation accuracy of photovoltaic power generation system clustering models.

[0005] To achieve the above objectives, this invention provides a method for improving the accuracy of clustering in photovoltaic power generation systems, comprising the following steps:

[0006] Step S1: Establish a mathematical model for photovoltaic cells;

[0007] Step S2: Perform theoretical analysis on the mathematical model of the photovoltaic cell to obtain the nonlinear characteristics of the maximum power of the photovoltaic cell in relation to light intensity and temperature;

[0008] Step S3: Based on the error loss caused by nonlinear characteristics, a corrected weighting function is introduced.

[0009] Preferably, the mathematical model of the photovoltaic cell in step S1 is as follows:

[0010]

[0011] Where I represents the output current of the photovoltaic cell; I sc V represents the photocurrent generated by the photovoltaic panel; V represents the output voltage of the photovoltaic cell; V oc V represents the open-circuit voltage of a photovoltaic cell. m Indicates the maximum power point voltage of the photovoltaic cell; I m I represents the maximum power point current of the photovoltaic cell; sc Represents the short-circuit current of the photovoltaic cell; a, b, and c represent compensation coefficients; S represents the actual illumination temperature; T represents the actual operating temperature; I scref Indicates the reference value of photocurrent; I mref This indicates the reference value of the maximum power point current of the photovoltaic cell; V ocref This indicates the reference value for the open-circuit voltage of a photovoltaic cell; V mref This represents the reference value for the maximum power point voltage of a photovoltaic cell; ΔT = TT ref T represents the difference between the actual temperature and the reference temperature. ref This represents the temperature under standard operating conditions, which is 25 degrees Celsius; ΔS = SS ref S represents the difference between the actual illumination and the reference illumination. ref This indicates the ambient temperature under standard operating conditions, which is 1000 W / m. 2 ;

[0012] The maximum power of a photovoltaic cell is expressed as: P m =V m ·I m V in the mathematical model of photovoltaic cells m I m Substitute into formula P m =V m ·I m get:

[0013]

[0014] Among them, P m (S,T) represents the maximum power of a photovoltaic cell as a function of light intensity and temperature.

[0015] Preferably, in step S2, the temperature T is set as a constant to obtain the nonlinear characteristic P of the maximum output power of the photovoltaic cell versus the light intensity. m (S) is shown below:

[0016]

[0017] Similarly, when the light intensity is stable, the nonlinear characteristic P of the maximum output power versus temperature is obtained. m (T) is shown below:

[0018]

[0019] Preferably, the error loss in step S3 is: for function P m (S), its second derivative is:

[0020]

[0021] In the interval where the light intensity S > 0, P″ m (S)>0; therefore, the function P is obtained. m (S) is a strictly convex function. For a strictly convex function, the following inequality is satisfied for any x1, x2, and λ∈[0,1]:

[0022] f(λx1+(1-λ)x2)<λf(x1)+(1-λ)f(x2);

[0023] when At that time, there were:

[0024]

[0025] Where f(x) represents any strictly convex function; the above equation proves that when clustering two data points, the maximum power corresponding to the cluster center of the light intensity is smaller than the average power corresponding to the actual two light intensities.

[0026] Preferably, according to the general probability theory form of the Chinsen inequality:

[0027]

[0028] The expected value of a function representing a random variable; This represents the expected value of a function of a random variable;

[0029] Prove that the following equation holds true:

[0030]

[0031] Where, x n This indicates the nth variable; it means that for any cluster of illumination data points, using the illumination intensity of the cluster center as the average illumination intensity of the entire cluster will reduce the output power of the aggregation model.

[0032] Preferably, the modified weight function w(S) in step S3 is:

[0033] w(S)=1+a·Sln(e+0.0005*(S-1000));

[0034] Where α represents the coefficient of the weighting function.

[0035] Therefore, this invention employs the aforementioned accuracy improvement method for photovoltaic power generation system clustering. By conducting an in-depth analysis of the relationship between the maximum power of photovoltaic cells and light intensity, and introducing a modified weighting function, it effectively eliminates the errors caused by the failure to consider the nonlinear relationship between light intensity and power in traditional clustering methods. This modification significantly improves the simulation accuracy of the photovoltaic power generation system clustering model, especially when light intensity varies greatly, enabling more accurate prediction of the photovoltaic system's power output.

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0037] Figure 1 This is a flowchart of an embodiment of a method for improving the accuracy of clustering in photovoltaic power generation systems according to the present invention;

[0038] Figure 2 This is a diagram showing the maximum power output characteristics of a photovoltaic cell in an embodiment of the accuracy improvement method for clustering of photovoltaic power generation systems according to the present invention. Figure 2 (a) in the figure is the curve of maximum power versus illumination characteristics; Figure 2 (b) in the figure is the maximum power versus temperature characteristic curve;

[0039] Figure 3 This is a schematic diagram of two illumination data clustering methods in an embodiment of the present invention, which is applied to the accuracy improvement method of clustering in photovoltaic power generation systems.

[0040] Figure 4 This is a schematic diagram of two temperature data clustering methods in an embodiment of the present invention, which is applied to improve the accuracy of clustering in photovoltaic power generation systems. Detailed Implementation

[0041] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0043] Example 1

[0044] In this embodiment, the mathematical model of the photovoltaic cell uses twenty photovoltaic power generation units, the aggregation model adopts the K-means algorithm, and the number of aggregated equivalent models is three. For example... Figure 1As shown, this invention provides a method for improving the accuracy of clustering in photovoltaic power generation systems, comprising the following steps:

[0045] Step S1: Establish a mathematical model of the photovoltaic cell. As the energy source of the entire photovoltaic power generation system, the output power of the photovoltaic cell directly determines the grid-connected power. When the system is operating stably in grid-connected mode, due to the MPPT algorithm, it can be assumed that all photovoltaic arrays in the entire photovoltaic power station are operating at their maximum power point. Therefore, studying the maximum power characteristics of the photovoltaic cell is crucial for analyzing the errors generated in the clustering process. The mathematical model of the photovoltaic cell is shown below:

[0046]

[0047] Where I represents the output current of the photovoltaic cell; I sc V represents the photocurrent generated by the photovoltaic panel; V represents the output voltage of the photovoltaic cell; V oc V represents the open-circuit voltage of a photovoltaic cell. m Indicates the maximum power point voltage of the photovoltaic cell; I m I represents the maximum power point current of the photovoltaic cell; sc Represents the short-circuit current of the photovoltaic cell; a, b, and c represent compensation coefficients; S represents the actual illumination temperature; T represents the actual operating temperature; I scref Indicates the reference value of photocurrent; I mref This indicates the reference value of the maximum power point current of the photovoltaic cell; V ocref This indicates the reference value for the open-circuit voltage of a photovoltaic cell; V mref This represents the reference value for the maximum power point voltage of a photovoltaic cell; ΔT = TT ref T represents the difference between the actual temperature and the reference temperature. ref This represents the temperature under standard operating conditions, which is 25 degrees Celsius; ΔS = SS ref S represents the difference between the actual illumination and the reference illumination. ref This indicates the ambient temperature under standard operating conditions, which is 1000 W / m. 2 ;

[0048] The maximum power of a photovoltaic cell is expressed as: P m =V m ·I m V in the mathematical model of photovoltaic cells m I m Substitute into formula P m =V m ·I m get:

[0049]

[0050] Among them, P m(S,T) represents the maximum power of a photovoltaic cell as a function of light intensity and temperature.

[0051] Step S2: Perform theoretical analysis on the mathematical model of the photovoltaic cell to obtain the nonlinear characteristics of the photovoltaic cell's maximum power with respect to light intensity and temperature; assuming a constant temperature T, the nonlinear characteristics P of the photovoltaic cell's maximum output power with respect to light intensity are obtained. m (S) is shown below:

[0052]

[0053] From the above equation, it can be seen that when the temperature T remains constant and the coefficient k1 is constant, there is a significant nonlinear relationship between the maximum power of the photovoltaic cell and the light intensity. Similarly, when the light intensity is stable, the nonlinear characteristic P of the maximum output power versus temperature can be obtained. m (T) is shown below:

[0054]

[0055] Therefore, it can be seen that the maximum power of a photovoltaic cell has a nonlinear relationship with both light intensity and temperature. This nonlinearity depends on the characteristics of the photovoltaic cell model and is affected by the compensation coefficients a, b, and c. It is independent of the specific photovoltaic cell model. Therefore, the parameters of a certain photovoltaic cell model can be selected to study the nonlinear output characteristics of its maximum power, and this method is applicable to all photovoltaic cell models.

[0056] When the temperature is 25℃, P m (S) with illumination of 1000W / m 2 P at time m The expression for (T) is as follows:

[0057]

[0058] To illustrate the relationship more intuitively, the characteristic curves of the photovoltaic cell's maximum power versus light intensity and power can be obtained from this formula, as shown below. Figure 2 As shown.

[0059] Step S3: Based on the error loss caused by nonlinear characteristics, a corrected weighting function is introduced.

[0060] Clustering algorithms define the cluster center of each cluster as the Euclidean center of the data points within that cluster. For example, the basic principle of the K-means algorithm is to minimize the sum of the squares of the Euclidean distances from each data point to its corresponding cluster center, thereby achieving data clustering. This data clustering method assumes that all data points have the same weight, and therefore is suitable for linear processing.

[0061] However, in the clustering of photovoltaic systems, there is a nonlinear relationship between the power of photovoltaic cells and light intensity and temperature. This nonlinearity introduces errors into the clustering process. Figure 3 As shown, taking the parameters of a 100KW photovoltaic cell array as an example, assuming that light intensity A and B are two points belonging to the same cluster in a certain cluster, and assuming that the two have the same temperature, then according to the relationship between the maximum power curve of the photovoltaic cell and the light intensity, its maximum power can be obtained, and at the same time, the cluster center, that is, the midpoint C of the two light intensities, can be obtained.

[0062] The light intensity at points A and B is 850 W / m². 2 and 1150W / m 2 The corresponding maximum power is 83.22kW and 118.985kW respectively, and their total power is 202.178kW.

[0063] If we use the aggregate equivalent model, we can replace points A and B with a light intensity of 1000 W / m. 2 The equivalent point C is determined by doubling the capacity of the photovoltaic cells. The maximum power at point C is 201.448 kW. Compared to the sum of the actual power at points A and B, the aggregated equivalent model introduces a power loss of 730 W. This demonstrates that while clustering simplifies calculations, it also introduces a certain degree of power deviation.

[0064] We will discuss the case of clustering two or more datasets using mathematical analysis, for the function P. m (S), its second derivative is:

[0065]

[0066] From the above formula, it can be seen that in the interval where the light intensity S > 0, P″ m (S)>0; therefore, the function P is obtained. m (S) is a strictly convex function. For a strictly convex function, the following inequality is satisfied for any x1, x2, and λ∈[0,1]:

[0067] f(λx1+(1-λ)x2)<λf(x1)+(1-λ)f(x2);

[0068] when At that time, there were:

[0069]

[0070] Where f(x) represents any strictly convex function, the above equation proves that when clustering two data points, the maximum power corresponding to the cluster center of the light intensity is smaller than the average power corresponding to the actual two light intensities.

[0071] According to the general probability-theoretic form of Chinson's inequality:

[0072]

[0073] The expected value of a function representing a random variable; This represents the expected value of a function of a random variable;

[0074] Prove that the following equation holds true:

[0075]

[0076] Where, x n Let n represent the nth variable. The above formula shows that for any cluster of illumination data points, using the illumination intensity of the cluster center as the average illumination intensity of the entire cluster will reduce the output power of the aggregation model.

[0077] Similarly, we analyze the impact of temperature clustering on power error. Assume data points D and E belong to the same cluster, have the same light intensity but different temperatures, and their maximum power characteristics with temperature are as follows: Figure 4 As shown.

[0078] Depend on Figure 4 It is known that when two data points with temperatures of 15℃ and 25℃ are aggregated and equivalent, a power error of 27W will occur. This error is far smaller than the impact of light intensity on the power error. Furthermore, in actual photovoltaic systems, the difference in light intensity between different photovoltaic units is usually much greater than the temperature difference, and this temperature difference will be further reduced after clustering. Therefore, in the clustering process, the impact of light intensity on clustering accuracy is mainly considered, while the error caused by temperature data is ignored.

[0079] In photovoltaic (PV) power generation system clustering modeling, the clustering results based on illuminance directly affect the accuracy of the clustering model. However, since the maximum power output of PV cells exhibits a non-linear relationship with illuminance, and existing clustering algorithms such as K-means typically assume a linear relationship between data points, a significant error arises during the clustering process, especially under non-uniform illumination conditions. This error causes the power output of the clustering model to be significantly lower than that of the detailed model. To reduce this error, a data preprocessing method based on a weighting function to correct illuminance is proposed.

[0080] The error correction design is based on the characteristic function of the photovoltaic cell's maximum power and light intensity. A weighting function is constructed to preprocess the light intensity, enhancing the representativeness of the data in clustering. This is based on the nonlinear characteristics of the photovoltaic cell's maximum output power and temperature, P... m(T), construct a light intensity preprocessing weight function w(S). This function has a minimum value of 1 and exhibits the same nonlinear increasing characteristic as the maximum power characteristic of the photovoltaic cell as the light intensity increases, thereby increasing the weight of strong light intensity. Based on this rule, the expression for the weight function can be obtained as follows:

[0081] w(S)=1+α·Sln(e+0.0005*(S-1000));

[0082] Where α represents the coefficient of the weighting function.

[0083] Based on the aggregation model results obtained from the K-means clustering algorithm, the light intensity of the entire system is 500 W / m². 2 Up to 1500W / m 2 The average light intensity is 1000W / m² 2 The accuracy after clustering is 94.8%, meaning that clustering introduces approximately 5% simulation error. Therefore, a 5% compensation can be provided at the system's average illumination intensity to calculate the weighting coefficients, i.e.:

[0084] w(1000)≤1.05;

[0085] Therefore, the weight function coefficient α = 0.0005 is calculated, and the expression for w(S) is:

[0086] w(S)=1+0.0005·Sln(e+0.0005*(S-1000));

[0087] Using this weighting function to preprocess the light intensity before clustering corrects the power loss caused by the nonlinear characteristics of the maximum power of photovoltaic cells and light intensity, which can compensate for the results of the photovoltaic aggregation equivalent model and effectively improve its accuracy.

[0088] Therefore, the present invention employs the above-mentioned accuracy improvement method for clustering photovoltaic power generation systems, which can effectively improve the simulation accuracy of the photovoltaic power generation system cluster model.

[0089] It is worth noting that all the contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for improving the accuracy of clustering in photovoltaic power generation systems, characterized in that, Includes the following steps: Step S1: Establish the mathematical model of the photovoltaic cell; the mathematical model of the photovoltaic cell is shown below: ； ； in, I This indicates the output current of the photovoltaic cell; V This indicates the output voltage of the photovoltaic cell; V oc This indicates the open-circuit voltage of the photovoltaic cell; V m This indicates the voltage at the maximum power point of the photovoltaic cell; I m This indicates the maximum power point current of the photovoltaic cell; I sc Indicates the short-circuit current of the photovoltaic cell; Indicates the compensation coefficient; S Indicates the actual light intensity; T Indicates the actual operating temperature; I scref Indicates the reference value for photocurrent; I mref This indicates the reference value for the maximum power point current of a photovoltaic cell; V ocref This indicates the reference value for the open-circuit voltage of a photovoltaic cell; V mref This indicates the reference value for the maximum power point voltage of a photovoltaic cell; This represents the difference between the actual temperature and the reference temperature. T ref This indicates the temperature under standard operating conditions, which is 25 degrees Celsius. This represents the difference between the actual illumination and the reference illumination. S ref This indicates the light intensity under standard operating conditions, which is 1000 W / m². 2 ; The maximum power of a photovoltaic cell is expressed as: The mathematical model of photovoltaic cells , Substitute into the formula get: ； in, The maximum power of a photovoltaic cell is a function of light intensity and temperature. Step S2: Perform theoretical analysis on the mathematical model of the photovoltaic cell to obtain the nonlinear characteristics of the photovoltaic cell's maximum power in relation to light intensity and temperature; in step S2, the temperature is set. T Assuming the constant is used, the nonlinear characteristics of the maximum output power of the photovoltaic cell versus the light intensity are obtained. As shown below: ； Similarly, the nonlinear characteristics of the maximum output power versus temperature when the light intensity is stable are obtained. As shown below: ； Step S3: Based on the error loss caused by nonlinear characteristics, a corrected weighting function is introduced; the corrected weighting function... for: ； in, This represents the coefficients of the weighting function. This weighting function is used to preprocess the light intensity before clustering, correcting the power loss caused by the nonlinear characteristics of the maximum power of photovoltaic cells and light intensity.

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