A distributed photovoltaic power prediction method and system based on time series data reconstruction

Abstract

The present invention discloses a distributed photovoltaic power prediction method and system based on time series data reconstruction, the method comprising the following steps: collecting a number of single-type distributed photovoltaic power curves; using improved photovoltaic power data empirical mode decomposition to decompose the several single-type distributed photovoltaic power curves into sub-power curves of different frequencies; reconstructing the sub-power curves of different frequencies; using a neural network to predict the reconstructed sub-power curves, and then superimposing and summing the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data; the present invention classifies photovoltaic power into single-type curves of different scenes according to different seasons and weather, and uses improved empirical mode decomposition to divide the sub-power curves, which can reduce the randomness and volatility of the original data to the greatest extent before prediction, facilitate the efficient training of the neural network, and output accurate photovoltaic power time series prediction data.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic power prediction, and in particular to a distributed photovoltaic power prediction method and system based on time series data reconstruction. Background Art

[0002] Distributed power sources are connected to low-voltage distribution networks in large quantities. As an important component of renewable energy, distributed photovoltaics are affected by weather, seasons, geographic location and other factors, and their power generation is highly uncertain and volatile. In this case, distributed energy storage power often follows photovoltaic power to a greater extent to carry out photovoltaic consumption and peak-shaving. Therefore, the power prediction of distributed photovoltaics is particularly important. First, accurate power prediction can help the grid dispatching department to reasonably arrange power production and transmission plans, and effectively deal with grid fluctuations caused by photovoltaic power access; second, distributed photovoltaic power prediction can also help promote the optimization and transformation of energy structure. With the continuous increase in the proportion of renewable energy, the power system's requirements for flexibility and intelligence are also increasing. Through accurate power prediction, the complementarity and synergy between photovoltaic power generation and other energy forms can be better achieved, promoting the diversification and sustainable development of energy structure.

[0003] Among the existing technical solutions, most of the research is based on single-feature time series prediction of traditional neural networks or long short-term memory neural networks. However, due to the high uncertainty and volatility of distributed photovoltaic power, the learning effect of its time series data is often poor, and it is impossible to train a photovoltaic power output model that meets all scenarios, resulting in poor photovoltaic power prediction accuracy. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a distributed photovoltaic power prediction method and system based on time series data reconstruction, which aims to solve the problems in the background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a distributed photovoltaic power prediction method based on time series data reconstruction, comprising the following steps:

[0006] Step S1: collect historical photovoltaic power data and corresponding weather data and classify them to obtain several single-class distributed photovoltaic power curves;

[0007] Step S2: using improved photovoltaic power data empirical mode decomposition to decompose a number of single-type distributed photovoltaic power curves into sub-power curves of different frequencies;

[0008] Step S3: reconstructing sub-power curves of different frequencies;

[0009] Step S4: using a long short-term memory neural network to predict the reconstructed sub-power curves to obtain predicted values ​​of each sub-power curve, and then superimposing and summing the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data;

[0010] Among them, the specific process of step S3 is: calculating the number of maximum values ​​of each sub-power curve of different frequencies, reconstructing and superimposing the sub-power curves whose maximum values ​​fall in the high-frequency area, low-frequency area or trend area into the corresponding high-frequency, low-frequency or trend sub-power curves, that is, the reconstructed sub-power curves.

[0011] Furthermore, the specific process of using the improved photovoltaic power data empirical mode decomposition to decompose several single-type distributed photovoltaic power curves into sub-power curves of different frequencies is as follows:

[0012] Step S2.1: Superimpose the time series white noise on the single type of distributed photovoltaic power curve to obtain the A single type of distributed photovoltaic power curve after superimposing white noise , expressed as:

[0013] ;

[0014] In the formula, Indicates unit time; Indicates The noise coefficient of the white noise added once; It represents the power curve of a single type of distributed photovoltaic power after superimposing white noise; Indicates White noise added during the second processing;

[0015] Step S2.2: conduct After repeated decomposition, the mean value is calculated to obtain the first sub-power component of different frequencies, that is, the first sub-power curve of different frequencies. , expressed as:

[0016] ;

[0017] In the formula, express The first eigenmode components;

[0018] Step S2.3: Calculate after the first decomposition The residual component , and conduct Repeat the solution and take the average to obtain the second sub-power component with different frequencies , expressed as:

[0019] ;

[0020] ;

[0021] In the formula, represents the first component generated by the improved empirical mode decomposition of photovoltaic power data; Indicates the noise coefficient of the first addition of white noise;

[0022] Step S2.4: Repeat step S2.3 until the improved PV power data empirical mode decomposition reaches the final condition and obtains sub-power components of different frequencies, residual components It is expressed as:

[0023] ;

[0024] In the formula, Indicates Sub-power components;

[0025] The power curve of a single type of distributed photovoltaic power generation after the final superposition of white noise Decomposed into several sub-power curves of different frequencies and a residual component :

[0026] .

[0027] Furthermore, the number of maximum values ​​of the sub-power curves of each different frequency is calculated, which is expressed as:

[0028] ;

[0029] ;

[0030] In the formula, For the The number of maxima of the sub-power curves of different frequencies, Initial value of is 0; express Sub-power curves at different frequencies The weight of the moment; express Sub-power curves at different frequencies The weight of moment.

[0031] Furthermore, the sub-power curves whose maximum values ​​fall in the high-frequency area, low-frequency area or trend area are reconstructed and superimposed into the corresponding high-frequency, low-frequency or trend sub-power curves, i.e., the reconstructed sub-power curves, which are expressed as:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, , , Respectively represent High frequency, low frequency and trend sub-power curves; Initial value of is 0, Initial value of is 0, Initial value of is 0; , , Respectively represent High frequency, low frequency and trend sub-power curves; is the number boundary of the maximum values ​​of the high-frequency sub-power curve and the low-frequency sub-power curve, It is the boundary of the number of maximum values ​​of the low-frequency sub-power curve and the trend sub-power curve.

[0037] Furthermore, the specific process of step S4 is as follows:

[0038] The forget gate of the long short-term memory neural network is used to selectively remove the weakly correlated information in the reconstructed sub-power curve, which is expressed as:

[0039] ;

[0040] In the formula, express The output of the hidden layer at each moment; express The input at the moment is the reconstructed sub-power curve; express Activation function; express Always forget the output of the gate; represents the forget gate weight matrix; Represents the forget gate offset value matrix;

[0041] Through the input gate of the long short-term memory neural network, The activation function and the hidden layer together update the state of the memory unit in the long short-term memory neural network, which is expressed as:

[0042] ;

[0043] ;

[0044] ;

[0045] In the formula, express The output of the input gate at any time; represents the weight matrix of the input gate; Represents the input gate offset value matrix; express The state of candidate memory units at each moment; , The neuron weight matrix and bias value matrix represent the memory unit state respectively; express Keep track of the unit status at all times;

[0046] Calculate output gate , expressed as:

[0047] ;

[0048] In the formula, and Represent the weight matrix and offset value matrix of the output gate respectively;

[0049] Calculate the hidden layer state , that is, the predicted data of the reconstructed sub-power curve, is expressed as:

[0050] ;

[0051] The prediction data of the multiple reconstructed sub-power curves are superimposed and summed to obtain a certain type of distributed photovoltaic power data.

[0052] Furthermore, the specific process of step S1 is as follows:

[0053] Step S1.1: Collect the output photovoltaic power data of the distributed photovoltaic system at preset time intervals through the fusion terminal or collector, and synchronously obtain the weather data of the same time period, including light intensity, temperature, and humidity information, by connecting with the meteorological station or online weather service interface;

[0054] Step S1.2: Based on the collected photovoltaic power data time and weather data, the data is classified according to the four seasons of spring, summer, autumn and winter, and the four weather conditions of sunny, rainy, cloudy and overcast, to obtain several single-type distributed photovoltaic power curves.

[0055] A distributed photovoltaic power prediction system based on time series data reconstruction, comprising:

[0056] A collection module is used to collect and classify historical photovoltaic power data and corresponding weather data to obtain several single-class distributed photovoltaic power curves;

[0057] A decomposition module, used for decomposing a number of single-type distributed photovoltaic power curves into sub-power curves of different frequencies by using improved photovoltaic power data empirical mode decomposition;

[0058] A reconstruction module, used to reconstruct sub-power curves of different frequencies;

[0059] The prediction module is used to predict the reconstructed sub-power curve using a long short-term memory neural network to obtain the predicted value of each sub-power curve, and then superimpose and sum the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data.

[0060] An electronic device comprises a processor, a memory and a bus, wherein the processor and the memory are connected via the bus, wherein the memory is used to store a set of program codes, and the processor is used to call the program codes stored in the memory to execute a distributed photovoltaic power prediction method based on time series data reconstruction.

[0061] A non-volatile computer storage medium stores computer executable instructions, which can execute a distributed photovoltaic power prediction method based on time series data reconstruction.

[0062] Compared with the existing technology, the present invention has the following beneficial effects:

[0063] (1) The present invention classifies photovoltaic power into single-type curves for different scenarios according to different seasons and weather conditions, and uses improved empirical mode decomposition to divide the sub-power curves. This can minimize the randomness and volatility of the original data before prediction, facilitate efficient training of the neural network, and output accurate photovoltaic power time series prediction data.

[0064] (2) In order to solve the problem that too many sub-power curves after decomposition may lead to increased errors after multiple predictions and increased model calculation time, the present invention reconstructs the sub-power curves after decomposition, calculates the number of maximum values ​​of each sub-power curve through an algorithm, and reconstructs the sub-power curves whose maximum values ​​fall in the same area and superimposes them into high-frequency, low-frequency and trend sub-power curves, thereby achieving a better balance between the problem of accurate model training and the problem of excessive model training time. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 The figure is a flow chart of the method of the present invention.

[0066] Figure 2 This is a schematic diagram of the reconstruction and superposition of sub-power curves of the present invention. DETAILED DESCRIPTION

[0067] like Figure 1 As shown, the present invention provides a technical solution: a distributed photovoltaic power prediction method based on time series data reconstruction, comprising the following steps:

[0068] Step S1: collect historical photovoltaic power data and corresponding weather data and classify them to obtain several single-type distributed photovoltaic power curves.

[0069] Step S2: using improved photovoltaic power data empirical mode decomposition to decompose several single-type distributed photovoltaic power curves into sub-power curves of different frequencies.

[0070] Step S3: reconstructing sub-power curves of different frequencies.

[0071] Step S4: Use the long short-term memory neural network to predict the reconstructed sub-power curve to obtain the predicted value of each sub-power curve, and then superimpose and sum the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data.

[0072] The specific process of step S1 is:

[0073] Step S1.1: Collect the output photovoltaic power data of the distributed photovoltaic system at preset time intervals through the fusion terminal or collector, and synchronously obtain the weather data of the same time period by connecting with the meteorological station or online weather service interface, including light intensity, temperature, and humidity information.

[0074] Step S1.2: Based on the collected photovoltaic power data time and weather data, the data are classified according to the four seasons of spring, summer, autumn and winter, and the four weather conditions of sunny, rainy, cloudy and overcast, to obtain 16 single-type distributed photovoltaic power curves.

[0075] Among them, Empirical Mode Decomposition (EMD) is a new adaptive signal time-frequency processing method, which is particularly suitable for the analysis and processing of nonlinear and non-stationary signals. This patent has been optimized and improved on the basis of EMD. By adding white noise, it can effectively suppress the modal aliasing of photovoltaic data, change the extreme point characteristics of distributed photovoltaic power, and more efficiently divide high-frequency data and low-frequency data during the decomposition process, thereby improving the accuracy and reliability of photovoltaic data decomposition, so as to better adapt to photovoltaic power prediction.

[0076] Step S2.1: Superimpose the time series white noise on the single type of distributed photovoltaic power curve to obtain the A single type of distributed photovoltaic power curve after superimposing white noise , expressed as:

[0077] (1);

[0078] In the formula, Indicates the unit time, usually 15 minutes; Indicates The noise coefficient of the white noise added once; It represents the power curve of a single type of distributed photovoltaic power after superimposing white noise; Indicates White noise added during the second processing.

[0079] Step S2.2: conduct After repeated decomposition, the mean value is calculated to obtain the first sub-power component of different frequencies (the first sub-power curve of different frequencies) , expressed as:

[0080] (2);

[0081] In the formula, express The first eigenmode components.

[0082] Step S2.3: Calculate after the first decomposition The residual component , and conduct Repeat the solution and take the average to obtain the second sub-power component with different frequencies , expressed as:

[0083] (3);

[0084] (4);

[0085] In the formula, represents the first component generated by the improved empirical mode decomposition of photovoltaic power data; Indicates the noise coefficient of the first addition of white noise.

[0086] Step S2.4: Repeat step S2.3 until the improved PV power data empirical mode decomposition reaches the final condition and obtains sub-power components of different frequencies, residual components It is expressed as:

[0087] (5);

[0088] In the formula, Indicates Sub-power components.

[0089] The power curve of a single type of distributed photovoltaic power generation after the final superposition of white noise Decomposed into several sub-power components of different frequencies (several sub-power curves of different frequencies) and a residual component :

[0090] (6).

[0091] The specific process of step S3 is as follows: after the time series data is decomposed, the distributed photovoltaic power curve is divided into several sub-power curves. Since there are many sub-power curves after the above decomposition, if too many feature vectors are predicted during the model training process, the training time will be too long. At the same time, the superposition of multiple feature vectors after separate prediction will also lead to excessive data errors. In order to reduce the error accumulation caused by the sum of multiple predictions and reduce the calculation time of the model, the decomposed sub-power curves are reconstructed, such as Figure 2 As shown, the number of maximum values ​​of the sub-power curves of each different frequency is calculated, which is expressed as:

[0092] (7);

[0093] (8);

[0094] In the formula, For the The number of maxima of the sub-power curves of different frequencies, Initial value of is 0; express Sub-power curves at different frequencies The weight of the moment; express Sub-power curves at different frequencies The weight of moment.

[0095] The sub-power curves whose maximum values ​​fall in the high-frequency area, the low-frequency area or the trend area are reconstructed and superimposed into the corresponding high-frequency, low-frequency and trend sub-power curves, i.e., the reconstructed sub-power curves; Figure 2 middle, is the number boundary of the maximum values ​​of the high-frequency sub-power curve and the low-frequency sub-power curve, It is the number boundary of the maximum values ​​of the low-frequency sub-power curve and the trend sub-power curve; is the first sub-power component of different frequencies, is the second sub-power component of different frequency, is the third sub-power component of different frequency, For the sub-power components of different frequencies, For the sub-power components of different frequencies; is the residual component.

[0096] (9);

[0097] (10);

[0098] (11);

[0099] (12);

[0100] In the formula, , , Respectively represent High frequency, low frequency and trend sub-power curves; Initial value of is 0, Initial value of is 0, Initial value of is 0; , , Respectively represent High frequency, low frequency and trend sub-power curves.

[0101] The specific process of step S4 is:

[0102] Through the forget gate of the long short-term memory neural network, the weakly correlated information in the reconstructed sub-power curve can be selectively removed to more effectively extract features and improve the training quality.

[0103] (13);

[0104] In the formula, express The output of the hidden layer at each moment; express Input at time (reconstructed sub-power curve); express Activation function; express Always forget the output of the gate; represents the forget gate weight matrix; Represents the forget gate offset value matrix.

[0105] Through the input gate of the long short-term memory neural network, The activation function and the hidden layer together update the state of the memory unit in the long short-term memory neural network.

[0106] (14);

[0107] (15);

[0108] (16);

[0109] In the formula, express The output of the input gate at any time; represents the weight matrix of the input gate; Represents the input gate offset value matrix; express The state of candidate memory units at each moment; , The neuron weight matrix and bias value matrix represent the memory unit state respectively; express Memory unit status at all times.

[0110] Calculate output gate , expressed as:

[0111] (17);

[0112] In the formula, and Represent the weight matrix and bias value matrix of the output gate respectively.

[0113] Calculate the hidden layer state , which is the output of the long short-term memory neural network (the predicted data of the reconstructed sub-power curve), is expressed as:

[0114] (18).

[0115] Finally, the prediction data of multiple reconstructed sub-power curves are obtained, and the prediction data of multiple reconstructed sub-power curves are superimposed and summed to obtain a certain type of distributed photovoltaic power data.

[0116] A distributed photovoltaic power prediction system based on time series data reconstruction, comprising:

[0117] A collection module is used to collect and classify historical photovoltaic power data and corresponding weather data to obtain several single-class distributed photovoltaic power curves;

[0118] A decomposition module, used for decomposing a number of single-type distributed photovoltaic power curves into sub-power curves of different frequencies by using improved photovoltaic power data empirical mode decomposition;

[0119] A reconstruction module, used to reconstruct sub-power curves of different frequencies;

[0120] The prediction module is used to predict the reconstructed sub-power curve using a long short-term memory neural network to obtain the predicted value of each sub-power curve, and then superimpose and sum the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data.

[0121] An electronic device comprises a processor, a memory and a bus, wherein the processor and the memory are connected via the bus, wherein the memory is used to store a set of program codes, and the processor is used to call the program codes stored in the memory to execute a distributed photovoltaic power prediction method based on time series data reconstruction.

[0122] A non-volatile computer storage medium stores computer executable instructions, which can execute a distributed photovoltaic power prediction method based on time series data reconstruction.

[0123] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A distributed photovoltaic power prediction method based on time series data reconstruction, characterized in that: The steps include: Step S1: collect historical photovoltaic power data and corresponding weather data and classify them to obtain several single-class distributed photovoltaic power curves; Step S2: using improved photovoltaic power data empirical mode decomposition to decompose a number of single-type distributed photovoltaic power curves into sub-power curves of different frequencies; Step S3: reconstructing sub-power curves of different frequencies; Step S4: using a long short-term memory neural network to predict the reconstructed sub-power curves to obtain predicted values ​​of each sub-power curve, and then superimposing and summing the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data; The specific process of step S3 is as follows: calculating the number of maximum values ​​of each sub-power curve with different frequencies, reconstructing and superimposing the sub-power curves with the number of maximum values ​​falling in the high-frequency area, low-frequency area or trend area into the corresponding high-frequency, low-frequency or trend sub-power curves, i.e., the reconstructed sub-power curves; The specific process of using the improved empirical mode decomposition of photovoltaic power data to decompose several single-type distributed photovoltaic power curves into sub-power curves of different frequencies is as follows: Step S2.1: Superimpose the time series white noise on the single type of distributed photovoltaic power curve to obtain the A single type of distributed photovoltaic power curve after superimposing white noise , expressed as: ； In the formula, Indicates unit time; Indicates The noise coefficient of the white noise added once; It represents the power curve of a single type of distributed photovoltaic power after superimposing white noise; Indicates White noise added during the second processing; Step S2.2: conduct After repeated decomposition, the mean value is calculated to obtain the first sub-power component of different frequencies, that is, the first sub-power curve of different frequencies. , expressed as: ； In the formula, express The first eigenmode components; Step S2.3: Calculate after the first decomposition The residual component , and conduct Repeat the solution and take the average to obtain the second sub-power component with different frequencies , expressed as: ； ； In the formula, represents the first component generated by the improved empirical mode decomposition of photovoltaic power data; Indicates the noise coefficient of the first addition of white noise; Step S2.4: Repeat step S2.3 until the improved PV power data empirical mode decomposition reaches the final condition and obtains sub-power components of different frequencies, residual components It is expressed as: ； In the formula, Indicates Sub-power components; The power curve of a single type of distributed photovoltaic power generation after the final superposition of white noise Decomposed into several sub-power curves of different frequencies and a residual component : 。 2. According to claim 1, a distributed photovoltaic power prediction method based on time series data reconstruction is characterized in that: Calculate the number of maximum values ​​of each sub-power curve of different frequencies, expressed as: ； ； In the formula, For the The number of maxima of the sub-power curves of different frequencies, Initial value of is 0; express Sub-power curves at different frequencies The weight of the moment; express Sub-power curves at different frequencies The weight of moment.

3. The distributed photovoltaic power prediction method based on time series data reconstruction according to claim 2 is characterized in that: The sub-power curves whose maximum values ​​fall in the high-frequency area, low-frequency area or trend area are reconstructed and superimposed into the corresponding high-frequency, low-frequency or trend sub-power curves, that is, the reconstructed sub-power curves, which are expressed as: ； ； ； ； In the formula, , , Respectively represent High frequency, low frequency and trend sub-power curves; Initial value of is 0, Initial value of is 0, Initial value of is 0; , , Respectively represent High frequency, low frequency and trend sub-power curves; is the number boundary of the maximum values ​​of the high-frequency sub-power curve and the low-frequency sub-power curve, It is the boundary of the number of maximum values ​​of the low-frequency sub-power curve and the trend sub-power curve.

4. The distributed photovoltaic power prediction method based on time series data reconstruction according to claim 3 is characterized in that: The specific process of step S4 is: The forget gate of the long short-term memory neural network is used to selectively remove the weakly correlated information in the reconstructed sub-power curve, which is expressed as: ； In the formula, express The output of the hidden layer at each moment; express The input at the moment is the reconstructed sub-power curve; express Activation function; express Always forget the output of the gate; represents the forget gate weight matrix; Represents the forget gate offset value matrix; Through the input gate of the long short-term memory neural network, The activation function and the hidden layer together update the state of the memory unit in the long short-term memory neural network, which is expressed as: ； ； ； In the formula, express The output of the input gate at any time; represents the weight matrix of the input gate; Represents the input gate offset value matrix; express The state of candidate memory units at each moment; , The neuron weight matrix and bias value matrix represent the memory unit state respectively; express Keep track of the unit status at all times; Compute output gate , expressed as: ； In the formula, and Represent the weight matrix and offset value matrix of the output gate respectively; Calculate the hidden layer state , that is, the predicted data of the reconstructed sub-power curve, is expressed as: ； The prediction data of the multiple reconstructed sub-power curves are superimposed and summed to obtain a certain type of distributed photovoltaic power data.

5. The distributed photovoltaic power prediction method based on time series data reconstruction according to claim 1 is characterized in that: The specific process of step S1 is: Step S1.1: Collect the output photovoltaic power data of the distributed photovoltaic system at preset time intervals through the fusion terminal or collector, and synchronously obtain the weather data of the same time period, including light intensity, temperature, and humidity information, by connecting with the meteorological station or online weather service interface; Step S1.2: Based on the collected photovoltaic power data time and weather data, the data is classified according to the four seasons of spring, summer, autumn and winter, and the four weather conditions of sunny, rainy, cloudy and overcast, to obtain several single-type distributed photovoltaic power curves.

6. A distributed photovoltaic power prediction system based on time series data reconstruction, applied to a distributed photovoltaic power prediction method based on time series data reconstruction as claimed in any one of claims 1 to 5, characterized in that: include: A collection module is used to collect and classify historical photovoltaic power data and corresponding weather data to obtain several single-class distributed photovoltaic power curves; A decomposition module, used for decomposing a number of single-type distributed photovoltaic power curves into sub-power curves of different frequencies by using improved photovoltaic power data empirical mode decomposition; A reconstruction module, used to reconstruct sub-power curves of different frequencies; The prediction module is used to predict the reconstructed sub-power curve using a long short-term memory neural network to obtain the predicted value of each sub-power curve, and then superimpose and sum the predicted values ​​of each sub-power curve to obtain a certain type of distributed photovoltaic power data.

7. An electronic device, characterized in that: It includes a processor, a memory and a bus, wherein the processor and the memory are connected via the bus, wherein the memory is used to store a set of program codes, and the processor is used to call the program codes stored in the memory to execute a distributed photovoltaic power prediction method based on time series data reconstruction as described in any one of claims 1-5.

8. A non-volatile computer storage medium storing computer executable instructions, characterized in that: The computer executable instructions execute a distributed photovoltaic power prediction method based on time series data reconstruction as described in any one of claims 1-5.

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