Method for quickly determining monthly optimal inclination angle of photovoltaic module

Through the relationship model established by the exponential attenuation function and the double Gaussian function, the optimal inclination angle of the photovoltaic module is quickly determined, which solves the complex calculation problems in the existing technology, and achieves the accuracy and calculation efficiency of the optimal inclination angle of the photovoltaic module, supporting the efficient operation of the photovoltaic power station.

CN120372937APending Publication Date: 2025-07-25FUZHOU UNIV
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202510455268.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-11
Publication Date
2025-07-25

AI Technical Summary

Technical Problem

The calculation method of determining the optimal monthly inclination angle of photovoltaic modules in the prior art is complex, difficult to meet actual engineering needs, and has low computing efficiency.

Method used

The relationship model between the latitude and the best inclination angle of the month is established by using the exponential attenuation function and the double Gaussian function, and the best inclination angle of the month of the photovoltaic module is quickly determined through curve fitting, including constructing a function of the total radiation received by the inclination plane, selecting the inclination angle corresponding to the maximum value as the best inclination angle of the month, and using the Solargis database to obtain the ratio of direct radiation to the total radiation.

Benefits of technology

It achieves rapid and accurate determination of the optimal monthly inclination angle of photovoltaic modules, significantly improves the calculation speed and practicality, ensures the maximum monthly total solar radiation on the inclined surface, and supports the refined design and efficient operation of photovoltaic power stations.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN120372937A_ABST
    Figure CN120372937A_ABST
Patent Text Reader

Abstract

The invention relates to a rapid determination method for a monthly optimal inclination angle of a photovoltaic module. The method comprises the following steps: acquiring the latitude of a place where a photovoltaic station is located; calculating the difference value between the latitude of the photovoltaic station and the optimal dip angle of each month under the ratio of different direct radiation quantities to the total radiation quantity; an exponential decay function is adopted to establish a first function relation between the difference value of the latitude and the monthly optimal inclination angle and the ratio of the direct radiation quantity to the total radiation quantity, and curve fitting is carried out; taking the month as an independent variable, respectively establishing a second function relation between the month and each parameter in the first function relation by adopting a double-Gaussian function, and carrying out curve fitting; constructing a monthly optimal inclination angle calculation model; acquiring the ratio of the direct radiation quantity to the total radiation quantity in each month of the latitude of the photovoltaic station; and substituting the monthly and the ratio of the direct radiation quantity to the total radiation quantity into the established monthly optimal inclination angle calculation model to obtain the monthly optimal inclination angle of the photovoltaic station in the corresponding month. According to the method, the monthly optimal inclination angle of the photovoltaic module can be quickly and accurately determined.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic arrays, and particularly relates to a method for quickly determining the monthly optimal inclination angle of a photovoltaic module. Background Art

[0002] As a clean and environmentally friendly green energy, solar photovoltaic power generation is an urgently needed energy supplement in the near future and is also the basis of the future energy structure. However, for a photovoltaic system, the installation inclination angle of the module is a key factor affecting the power station performance and economic benefits.

[0003] The optimal inclination angles of a photovoltaic panel can be mainly divided into three categories: monthly optimal inclination angle, quarterly optimal inclination angle, and annual optimal inclination angle, corresponding to the installation angles that maximize the total solar radiation received by the photovoltaic panel on the time scales of month, quarter, and year respectively. Engineering practice shows that adopting the monthly optimal inclination angle can significantly improve the power generation efficiency of a photovoltaic power station. The existing methods for determining the optimal inclination angle mainly calculate the total solar radiation received by the inclined plane at different inclination angles, and select the inclination angle corresponding to the maximum total radiation as the optimal inclination angle. However, this method involves a large amount of complex calculations, with low calculation efficiency and difficult to meet the actual engineering requirements. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for quickly determining the monthly optimal inclination angle of a photovoltaic module, which can quickly and accurately determine the monthly optimal inclination angle of the photovoltaic module.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a method for quickly determining the monthly optimal inclination angle of a photovoltaic module, including the following steps:

[0006] Step S1: Obtain the latitude of the location where the photovoltaic power station is located;

[0007] Step S2: Calculate the differences between the latitude of the location where the photovoltaic power station is located and the monthly optimal inclination angles of each month at different ratios of direct radiation to total radiation;

[0008] Step S3: Establish a first functional relationship between the difference between the latitude and the monthly optimal inclination angle and the ratio of direct radiation to total radiation using an exponential decay function, and perform curve fitting on the first functional relationship by month using the data obtained in Step S2;

[0009] Step S4: Take the month as the independent variable, establish a second functional relationship between the month and each parameter in the first functional relationship using a double Gaussian function respectively, and then perform curve fitting on the second functional relationship by parameter using the data obtained in Step S3;

[0010] Step S5: Based on the results obtained in Steps S3 and S4, construct a calculation model for the monthly optimal inclination angle at the latitude of the location where the photovoltaic power station is located;

[0011] Step S6: Obtain the ratio of the direct radiation amount to the total radiation amount for each month at the latitude where the photovoltaic power station is located;

[0012] Step S7: Substitute the month and the ratio of the direct radiation amount to the total radiation amount into the established monthly optimal tilt angle calculation model to obtain the monthly optimal tilt angle of the corresponding month for the photovoltaic power station.

[0013] Further, step S2 includes the following steps:

[0014] Step S2.1: Construct a calculation function for calculating the total radiation amount received by the inclined plane and selecting the tilt angle corresponding to the maximum total radiation amount received by the inclined plane as the monthly optimal tilt angle. Its inputs are latitude, month, and the ratio of the direct radiation amount to the total radiation amount. Then, calculate the total radiation amount received by different inclined planes according to the input data, and select the tilt angle corresponding to the maximum total radiation amount received by the inclined plane from the total radiation amounts received by different inclined planes as the output, that is, the monthly optimal tilt angle;

[0015] Step S2.2: Divide the ratio of the direct radiation amount to the total radiation amount from 0 to 1 into ten intervals, and input the ratio of the direct radiation amount to the total radiation amount of 0, 0.1, 0.2,..., 0.9, each month, and the latitude where the photovoltaic power station is located into the calculation function to obtain the monthly optimal tilt angles of each month under different ratios of the direct radiation amount to the total radiation amount, and calculate the difference between the latitude where the photovoltaic power station is located and the monthly optimal tilt angles of each month, that is, obtain the differences between the latitude where the photovoltaic power station is located and the monthly optimal tilt angles of each month under different ratios of the direct radiation amount to the total radiation amount.

[0016] Further, step S3 includes the following steps:

[0017] Step S3.1: Establish the first functional relationship between the difference between the latitude and the monthly optimal tilt angle and the ratio of the direct radiation amount to the total radiation amount by using an exponential decay function as follows:

[0018] φ - S = y + A e -x / t

[0019] In the formula, φ is the latitude, S is the monthly optimal tilt angle, y, A, and t are three parameters related to the month; x is the ratio of the direct radiation amount to the total radiation amount;

[0020] Step S3.2: Substitute the data obtained in step S2 into the first functional relationship established in step S3.1 by month, and perform curve fitting on the first functional relationship by month to obtain the specific expressions of the first functional relationships of each month, as well as the specific values of the corresponding parameters y, A, and t.

[0021] Further, step S4 includes the following steps:

[0022] Step S4.1: Establish the second functional relationships between the month and the parameters y, A, and t in the first functional relationship by using a double Gaussian function as follows:

[0023]

[0024] In the formula, z i represents the parameter in the first functional relation, i = 1, 2 or 3, z1 = y, z2 = A, z3 = t, m is the month, y0, H, x c , w1, and w2 are all fitting parameters;

[0025] Step S4.2: Substitute the specific values of the parameters y, A, and t in the specific expressions of the first functional relations for each month obtained in Step S3 into the second functional relation established in Step S4.1, and perform curve fitting on the second functional relation according to the parameters to obtain the specific expressions of the second functional relations corresponding to the parameters y, A, and t respectively.

[0026] Further, in Step S5, substitute the specific expressions of the second functional relations corresponding to the parameters y, A, and t obtained in Step S4 into the first functional relation to obtain the monthly optimal tilt angle calculation model at the latitude where the photovoltaic power station is located.

[0027] Further, in Step S6, the calculation method of the ratio of the direct radiation amount to the total radiation amount is as follows:

[0028]

[0029] In the formula, I b represents the direct irradiance on the horizontal plane, and I T represents the total irradiance on the horizontal plane.

[0030] The present invention also provides a computer device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, and when the computer program instructions are executed by the processor, the above method is implemented.

[0031] The present invention also provides a computer-readable storage medium, on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the above method is implemented.

[0032] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for quickly determining the monthly optimal tilt angle of a photovoltaic module, which can quickly and accurately determine the monthly optimal tilt angle of the photovoltaic module, ensure that the total solar radiation amount on the inclined plane reaches the maximum value every month, and at the same time quickly respond to the requirements of different latitudes and month changes, significantly improving the calculation speed and practicality, and providing strong technical support for the refined design and efficient operation of photovoltaic power stations. Description of the Drawings

[0033] Figure 1It is the flowchart of the method implementation in the embodiment of the present invention;

[0034] Figure 2 It is the Python code diagram in the embodiment of the present invention;

[0035] Figure 3 It is the fitting diagram of the proportion of direct radiation from January to June in City A in the embodiment of the present invention with respect to the latitude and the difference in monthly optimal inclination angles;

[0036] Figure 4 It is the fitting diagram of the proportion of direct radiation from July to December in City A in the embodiment of the present invention with respect to the latitude and the difference in monthly optimal inclination angles;

[0037] Figure 5 It is the fitting diagram of the parameter y in the first functional relationship in the embodiment of the present invention;

[0038] Figure 6 It is the fitting diagram of the parameter A in the first functional relationship in the embodiment of the present invention;

[0039] Figure 7 It is the fitting diagram of the parameter t in the first functional relationship in the embodiment of the present invention;

[0040] Figure 8 It is the monthly optimal inclination angle diagram of City A in the embodiment of the present invention;

[0041] Figure 9 It is the monthly optimal inclination angle diagram of City B in the embodiment of the present invention. Detailed implementation manners

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0044] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0045] As Figure 1 shown, this embodiment provides a method for quickly determining the monthly optimal inclination angle of a photovoltaic module, including the following steps:

[0046] Step S1: Obtain the latitude of the location where the photovoltaic power station is located.

[0047] Step S2: Calculate the difference between the latitude where the PV power station is located and the monthly optimal tilt angle for each month at different ratios of direct radiation to total radiation.

[0048] Specifically, step S2 includes the following steps:

[0049] Step S2.1: By analyzing the existing Python code or obtaining it from other existing technologies, construct a calculation function for calculating the total radiation received by the inclined plane and selecting the tilt angle corresponding to the maximum total radiation received by the inclined plane as the monthly optimal tilt angle. The input of this calculation function is latitude, month, and the ratio of direct radiation to total radiation. Then, calculate the total radiation received by different inclined planes based on the input data, and select the tilt angle corresponding to the maximum total radiation received by the inclined plane from the total radiation received by different inclined planes as the output, that is, the monthly optimal tilt angle.

[0050] Step S2.2: Divide the ratio of direct radiation to total radiation from 0 to 1 into ten intervals, and input the ratios of direct radiation to total radiation of 0, 0.1, 0.2,..., 0.9, each month, and the latitude where the PV power station is located into the calculation function to obtain the monthly optimal tilt angle for each month at different ratios of direct radiation to total radiation, and subtract the latitude where the PV power station is located to obtain the difference between the latitude where the PV power station is located and the monthly optimal tilt angle for each month at different ratios of direct radiation to total radiation.

[0051] Step S3: Establish a first functional relationship between the difference between the latitude and the monthly optimal tilt angle and the ratio of direct radiation to total radiation using an exponential decay function (ExpDec1), and use the data obtained in step S2 to perform curve fitting on the first functional relationship by month.

[0052] Specifically, step S3 includes the following steps:

[0053] Step S3.1: Establish a first functional relationship between the difference between the latitude and the monthly optimal tilt angle and the ratio of direct radiation to total radiation using an exponential decay function as follows:

[0054] φ - S = y + A e -x / t

[0055] In the formula, φ is the latitude, S is the monthly optimal tilt angle, y, A, and t are three parameters related to the month; x is the ratio of direct radiation to total radiation.

[0056] Step S3.2: Substitute the data obtained in step S2 into the first functional relationship established in step S3.1 by month, and perform curve fitting on the first functional relationship by month to obtain the specific expression of the first functional relationship for each month, and the specific values of the corresponding parameters y, A, and t.

[0057] Step S4: Using the month as the independent variable, establish second functional relationships between the month and the parameters in the first functional relationship respectively by means of the Bigaussian function, and then use the data obtained in Step S3 to perform curve fitting on the second functional relationship according to the parameters.

[0058] Specifically, Step S4 includes the following steps:

[0059] Step S4.1: Establish second functional relationships between the month and the parameters y, A, and t in the first functional relationship respectively by means of the Bigaussian function as follows:

[0060]

[0061] In the formula, z i represents the parameter in the first functional relationship, i = 1, 2, or 3, z1 = y, z2 = A, z3 = t, m is the month, and y0, H, x c , w1, and w2 are all fitting parameters.

[0062] Step S4.2: Substitute the specific values of the parameters y, A, and t in the specific expressions of the first functional relationships of each month obtained in Step S3 into the second functional relationships established in Step S4.1, and perform curve fitting on the second functional relationships according to the parameters to obtain the specific expressions of the second functional relationships corresponding to the parameters y, A, and t respectively.

[0063] Step S5: Based on the results obtained in Steps S3 and S4, construct a monthly optimal tilt angle calculation model for the latitude where the photovoltaic power station is located.

[0064] Specifically, substitute the specific expressions of the second functional relationships corresponding to the parameters y, A, and t obtained in Step S4 into the first functional relationship to obtain a monthly optimal tilt angle calculation model for the latitude where the photovoltaic power station is located.

[0065] Step S6: Through the Solargis database, obtain the ratio of the direct radiation amount to the total radiation amount for each month at the latitude where the photovoltaic power station is located.

[0066] Among them, the calculation method of the ratio of the direct radiation amount to the total radiation amount is:

[0067]

[0068] In the formula, I b represents the direct irradiance on the horizontal plane, and I T represents the total irradiance on the horizontal plane.

[0069] Step S7: Substitute the month and the ratio of the direct radiation amount to the total radiation amount into the established monthly optimal tilt angle calculation model to obtain the monthly optimal tilt angle of the photovoltaic power station for the corresponding month.

[0070] Example 1

[0071] Select City A at a latitude of 38°, and the Python code for analyzing the relationship between the ratio of different direct radiation amounts to the total radiation amount and the difference in the monthly optimal inclination angle in this latitude area is as Figure 2 shown.

[0072] Use the exponential decay function (ExpDec1) to establish the functional relationship between the proportion of direct radiation and the latitude and the difference in the monthly optimal inclination angle as Figures 3-4 shown.

[0073] Taking the month as the independent variable, use the double Gaussian function (Bigaussian) to fit the three parameters in the exponential decay function as Figures 5-7 shown.

[0074] Construct the monthly optimal inclination angle calculation model for City A at a latitude of 38° based on the ratio of direct radiation to total radiation as follows:

[0075]

[0076] S = φ - y - A e -x / t

[0077] In the formula, S is the monthly optimal inclination angle; m is the month; x is the ratio of direct radiation to total radiation. w a , w y and w t are piecewise functions, as follows:

[0078]

[0079] Through the Solargis database, obtain the ratio of direct radiation to total radiation in City A as shown in Table 1 below:

[0080] Table 1

[0081]

[0082] Substitute into the constructed monthly optimal inclination angle calculation model for City A to obtain the monthly optimal inclination angle as Figure 8 shown.

[0083] Example 2

[0084] Select City B at a latitude of 29° as the area for constructing the monthly optimal inclination angle model. The implementation steps are the same as those in Example 1, and the obtained monthly optimal inclination angle calculation model is as follows:

[0085]

[0086] S = φ - y - A e -x / t

[0087] In the formula, S is the monthly optimal inclination angle; m is the month; x is the ratio of direct radiation to total radiation. w a 、w y and w t are piecewise functions, as shown below:

[0088]

[0089] Through the Solargis database, the ratio of direct radiation to total radiation in City B is obtained as shown in Table 2 below:

[0090] Table 2

[0091]

[0092] Substituting into the constructed calculation model of the monthly optimal inclination angle in City B, the monthly optimal inclination angle is as Figure 9 shown.

[0093] This embodiment also provides a computer device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, which implement the above method when the computer program instructions are executed by the processor.

[0094] This embodiment also provides a computer-readable storage medium, on which computer program instructions are stored, which implement the above method when the computer program instructions are executed by a processor.

[0095] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0096] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowcharts and / or block diagrams, and the combination of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, so that the instructions executed by the processors of the computer or other programmable data processing devices generate for implementing in the process Figure 1 each process or multiple processes and / or blocks Figure 1means for the functions specified in one or more boxes.

[0097] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one Figure 1 process or more processes and / or boxes Figure 1 one box or more boxes.

[0098] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one Figure 1 process or more processes and / or boxes Figure 1 one box or more boxes.

[0099] As described above, it is only the preferred embodiment of the present invention, and it is not a limitation of the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for quickly determining the monthly optimal tilt angle of a photovoltaic module, characterized in that, including the following steps: Step S1: Obtain the latitude of the location where the photovoltaic power station is located; Step S2: Calculate the difference between the latitude of the photovoltaic power station and the monthly optimal inclination angle for each month at different ratios of direct radiation to total radiation; Step S3: Establish a first functional relationship between the difference between the latitude and the monthly optimal inclination angle and the ratio of direct radiation to total radiation using an exponential decay function, and perform curve fitting on the first functional relationship by month using the data obtained in Step S2; Step S4: Using the month as the independent variable, establish second functional relationships between the month and each parameter in the first functional relationship using a double Gaussian function, and then perform curve fitting on the second functional relationships by parameter using the data obtained in Step S3; Step S5: Based on the results obtained in Steps S3 and S4, construct a calculation model for the monthly optimal inclination angle at the latitude where the photovoltaic power station is located; Step S6: Obtain the ratio of direct radiation to total radiation for each month at the latitude where the photovoltaic power station is located; Step S7: Substitute the month and the ratio of direct radiation to total radiation into the established calculation model for the monthly optimal inclination angle to obtain the monthly optimal inclination angle for the corresponding month of the photovoltaic power station.

2. A method for quickly determining the monthly optimal tilt angle of a photovoltaic module according to claim 1, characterized in that, Step S2 includes the following steps: Step S2.1: Construct a calculation function for calculating the total radiation received by the inclined plane and selecting the inclination angle corresponding to the maximum total radiation received by the inclined plane as the monthly optimal inclination angle. Its inputs are latitude, month, and the ratio of direct radiation to total radiation. Then, calculate the total radiation received by different inclined planes according to the input data, and select the inclination angle corresponding to the maximum total radiation received by the inclined plane from the total radiation received by different inclined planes as the output, that is, the monthly optimal inclination angle; Step S2.2: Divide the ratio of direct radiation to total radiation from 0 to 1 into ten intervals, and input the ratio of direct radiation to total radiation of 0, 0.1, 0.2,..., 0.9, each month, and the latitude of the photovoltaic power station into the calculation function to obtain the monthly optimal inclination angle for each month at different ratios of direct radiation to total radiation, and calculate the difference from the latitude of the photovoltaic power station, that is, obtain the difference between the latitude of the photovoltaic power station and the monthly optimal inclination angle for each month at different ratios of direct radiation to total radiation.

3. A method for quickly determining the monthly optimal inclination angle of a photovoltaic module according to claim 1, characterized in that, Step S3 includes the following steps: Step S3.1: Establish a first functional relationship between the difference between the latitude and the monthly optimal inclination angle and the ratio of direct radiation to total radiation using an exponential decay function as follows: φ - S = y + A e -x / t In the formula, φ is the latitude, S is the monthly optimal inclination angle, y, A, and t are three parameters related to the month; x is the ratio of direct radiation to total radiation; Step S3.2: Substitute the data obtained in Step S2 into the first functional relationship established in Step S3.1 by month, and perform curve fitting on the first functional relationship by month to obtain the specific expression of the first functional relationship for each month, and the specific values of the corresponding parameters y, A, and t.

4. A method for quickly determining the monthly optimal tilt angle of a photovoltaic module according to claim 3, characterized in that, Step S4 includes the following steps: Step S4.1: Establish second functional relationships between the month and the parameters y, A, and t in the first functional relationship using a double Gaussian function as follows: where z i represents the parameter in the first functional relation, i = 1, 2, or 3, z1 = y, z2 = A, z3 = t, m is the month, and y0, H, x c , w1, and w2 are all fitting parameters; Step S4.2: Substitute the specific values of parameters y, A, and t in the specific expressions of the first function relationships for each month obtained in Step S3 into the second function relationship established in Step S4.1, and perform curve fitting on the second function relationship according to the parameters to obtain the specific expressions of the second function relationships corresponding to parameters y, A, and t respectively.

5. A method for quickly determining the monthly optimal tilt angle of a photovoltaic module according to claim 4, characterized in that In Step S5, substitute the specific expressions of the second function relationships corresponding to parameters y, A, and t obtained in Step S4 into the first function relationship to obtain the monthly optimal inclination angle calculation model at the latitude where the photovoltaic power station is located.

6. The method for quickly determining the monthly optimal tilt angle of a photovoltaic module according to claim 1, wherein In Step S6, the calculation method of the ratio of direct radiation to total radiation is as follows: Where, I b represents the direct irradiance on the horizontal plane, and I T represents the total irradiance on the horizontal plane.

7. A computer device, characterized in that, Including: At least one processor, at least one memory, and computer program instructions stored in the memory, which implement the method according to any one of claims 1-6 when the computer program instructions are executed by the processor.

8. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, the method according to any one of claims 1-6 is implemented.