CN118068138A - Debye model-based cable insulation aging state evaluation method and system - Google Patents
Debye model-based cable insulation aging state evaluation method and system Download PDFInfo
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Abstract
The invention discloses a cable insulation aging state assessment method and system based on a Debye model, which relate to the technical field of electrical engineering and comprise the following steps: collecting dielectric characteristic data of different cable insulating materials, and determining whether the cable is aged or not; constructing a Debye model, and evaluating the aging state of the cable insulation based on the collected data and the Debye model; and predicting the future aging state according to the historical aging state of the cable insulation. According to the invention, the accuracy and efficiency of the cable insulation aging state evaluation are improved through the advanced analysis method based on the Debye model. The aging process is monitored more accurately, and the future aging trend is predicted effectively, so that reliable decision support is provided for maintenance and operation of the power system. The cable insulation state monitoring system can monitor and analyze the cable insulation state in real time, greatly improves the reliability and safety of a power system, reduces the risks of faults and accidents caused by aging, and has important significance for guaranteeing the stable operation of a power grid.
Description
Technical Field
The invention relates to the technical field of electrical engineering, in particular to a cable insulation aging state evaluation method and system based on a Debye model.
Background
In an electric power system, the insulation state of a cable is critical to ensure the safety and reliability of electric power transmission. Over time, cable insulation may age gradually due to various factors, resulting in changes in its physical and chemical properties. Such ageing not only reduces the insulating properties of the cable, but may also increase the risk of power system failure and even cause safety accidents.
Traditionally, the aging assessment of cable insulation has relied on periodic physical inspection and experience-based assessment methods. These methods typically require interrupting the operation of the cable, are not only inefficient, but also fail to provide continuous and real-time information about the aging process of the material. In addition, conventional methods tend to ignore microscopic structural changes in the cable material, which are particularly critical in the early stages of aging.
With the development of technology, particularly in the fields of materials science and electrical engineering, there is a need for a more advanced, accurate and efficient method for assessing and predicting the ageing state of cable insulation. The Debye model provides one possible solution as a physical model describing the polarization properties of dielectric materials. By combining the Debye model and the modern data analysis technology, the aging state of the cable insulation can be estimated more accurately, and the future performance of the cable insulation can be predicted, so that scientific basis is provided for the maintenance and operation of the power system.
Therefore, the development of the Debye model-based cable insulation aging state assessment method is of great importance for improving the reliability and safety of a power system, and is also very critical for optimizing a cable maintenance plan and prolonging the service life of a cable. The method can provide more comprehensive and deep aging state evaluation, and has obvious practical value and long-term significance for the power industry.
Disclosure of Invention
The present invention has been made in view of the above-described problems.
Therefore, the technical problems solved by the invention are as follows: how to efficiently evaluate and predict the aging state of cable insulation in a power system, thereby optimizing maintenance plans and improving safety and stability of the power system.
In order to solve the technical problems, the invention provides the following technical scheme: a cable insulation aging state assessment method based on a Debye model comprises the following steps,
Collecting dielectric characteristic data of different cable insulating materials, and determining whether the cable is aged or not; constructing a Debye model, and evaluating the aging state of the cable insulation based on the collected data and the Debye model; and predicting the future aging state according to the historical aging state of the cable insulation.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: determining whether the cable is aged includes defining an aging index, and determining whether the test point is aged based on the aging index.
The ageing index is expressed as a function of,
AI(t，r)＝f(ε(ω，t，r)，P(t，r)，S(t，r))
Wherein P (t, r) represents the physical parameters at the aging time t and the spatial position r and S (t, r) represents the chemical and structural stability parameters of the cable.
And when the ageing index is higher than the threshold value, the ageing index indicates that the cable test point is aged.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: the construction of the Debye model comprises the steps of testing cable insulation materials in different aging stages, collecting dielectric characteristic data and loss data, and constructing the Debye model through the collected dielectric characteristic data.
The Debye model is represented as,
Where ε (ω, T, r) represents the complex permittivity at angular frequency ω, aging time T and spatial position r, A (T, r), B (T, r) represents tensors describing the inhomogeneity and anisotropy of the material, ε ∞ (T, r) represents the high frequency limit permittivity at aging time T and spatial position r, T (T, r) represents tensors describing the relaxation time distribution, I represents the unit tensors, j represents the imaginary unit.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: the evaluation of the aging state of the cable insulation comprises the steps of collecting dielectric characteristic data of each test point, calculating a dielectric constant tensor by using a Debye model, comparing the calculated dielectric constant tensor with a preset aging state threshold value, determining the aging state of each test point, and taking different countermeasures according to different aging states.
Determining the aging state of each test point comprises the steps of indicating that the test point is in an unaged state if the dielectric constant tensor of the test point is smaller than a first-level threshold, indicating that the test point is in a mild aging state if the dielectric constant tensor of the test point is between the first-level threshold and a second-level threshold, indicating that the test point is in a moderate aging state if the dielectric constant tensor of the test point is between the second-level threshold and a third-level threshold, and indicating that the test point is in a severe aging state if the dielectric constant tensor of the test point is between the third-level threshold and a fourth-level threshold.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: the taking of different countermeasures includes, when the cable is in an unaged state, periodic cable quality inspection and supply chain management, ensuring the use of high quality materials and components, analyzing historical performance data of the cable with big data, finding potential weaknesses and improvement fields, and formulating personalized maintenance and inspection plans according to specific types and historical performances of the cable.
When the cable is in a light aging state, fault mode identification and influence analysis are carried out on cable insulation, potential fault reasons are identified, preventive maintenance measures such as encryption monitoring frequency are enhanced, and the light damaged part is repaired or replaced in time aiming at the detected light damage.
When the cable is in a moderate aging state, performing comprehensive systematic risk assessment, and taking the influence of cable aging on the whole power system into consideration, making a detailed emergency response plan including the influence on the surrounding environment and the system, and making a corresponding emergency response plan.
When the cable is in a severely aged state, comprehensive system performance reevaluation is performed, including power demand, operation efficiency and safety, cost benefit analysis is performed, whether to replace aged cables or upgrade systems is determined, when the cable replacement is determined, critical areas and high-risk parts are prioritized, temporary enhancement monitoring and protection measures are implemented, and system faults caused by aged cables are prevented.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: the predicting of the future aging state comprises the steps of collecting historical data and corresponding aging states, evaluating the current aging state according to a Debye model to obtain a current aging index AI (t, r), predicting the future aging state based on a prediction model, and making countermeasures based on the predicted aging state.
The predicting of the future aging state based on the predictive model is expressed as,
AI Prediction (t+Δt, r) =ai (t, r) +aging rate (t, r) ×Δt+environmental factor influence (r)
Where Δt represents the time interval, and the aging rate is derived from the historical data.
If AI Prediction is above the aging index threshold AI Early warning or the aging rate exceeds the threshold, it indicates that aging will occur in the future.
As a preferable scheme of the cable insulation aging state evaluation method based on the Debye model, the invention is characterized in that: the method comprises the steps of encrypting monitoring frequency of a cable when the test point predicts and displays future aging, tracking the running state of the cable in real time, implementing dynamic load management, adjusting the load level of the cable according to the real-time state of the cable, arranging periodic cable cleaning work, checking and replacing the insulation material which is worn or damaged, periodically performing insulation test and resistance measurement, ensuring the integrity of the insulation material, preparing an emergency plan, quickly responding according to the emergency plan when the test point is aged, including a rapid repair of cable faults and a temporary power grid reconfiguration strategy, and starting a standby power supply or adjusting load distribution of adjacent cables.
Another object of the present invention is to provide a system for evaluating the aging state of cable insulation based on the Debye model, which can more accurately and finely evaluate the aging state of cable insulation material by using advanced data analysis and real-time monitoring technology, so as to solve the problems of insufficient precision and lack of real-time monitoring of the aging process evaluation in the existing method.
In order to solve the technical problems, the invention provides the following technical scheme: the cable insulation aging state evaluation system based on the Debye model comprises a data acquisition module, an aging state evaluation module and a future aging prediction module.
The data acquisition module is responsible for collecting dielectric characteristic data of different cable insulating materials.
The aging state evaluation module is responsible for evaluating the current aging state of the cable insulation using the constructed Debye model.
The future aging prediction module is responsible for predicting a future aging state based on the current aging state and the historical aging trend.
A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the cable insulation ageing state assessment method based on the Debye model as described above.
A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the cable insulation ageing state assessment method based on the Debye model as described above.
The invention has the beneficial effects that: the accuracy and efficiency of the cable insulation aging state evaluation are improved by applying the advanced analysis method based on the Debye model. The aging process is monitored more accurately, and future aging trend can be effectively predicted, so that reliable decision support is provided for maintenance and operation of the power system. In addition, the cable insulation state can be monitored and analyzed in real time, the reliability and the safety of a power system are greatly improved, the risks of faults and accidents caused by aging are reduced, and the cable insulation state monitoring system has important significance in guaranteeing the stable operation of a power grid.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is an overall flowchart of a cable insulation aging state evaluation method based on a Debye model according to a first embodiment of the present invention.
Fig. 2 is an overall frame diagram of a cable insulation aging state evaluation system based on a Debye model according to a second embodiment of the invention.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
Example 1
Referring to fig. 1, for one embodiment of the present invention, a method for evaluating an insulation aging state of a cable based on a Debye model is provided, which is characterized in that:
S1: dielectric property data for different cable insulation materials is collected to determine if the cable is aged.
Determining whether the cable is aged includes defining an aging index, and determining whether the test point is aged based on the aging index.
The ageing index is expressed as a function of,
AI(t，r)＝f(ε(ω，t，r)，P(t，r)，S(t，r))
Wherein P (t, r) represents the physical parameters at the aging time t and the spatial position r and S (t, r) represents the chemical and structural stability parameters of the cable.
And when the ageing index is higher than the threshold value, the ageing index indicates that the cable test point is aged.
S2: a Debye model is constructed and the aging state of the cable insulation is evaluated based on the collected data and the Debye model.
Constructing the Debye model comprises testing cable insulation materials at different aging stages, collecting dielectric characteristic data and loss data, and constructing the Debye model through the collected dielectric characteristic data.
The Debye model is represented as,
Wherein, the complex dielectric constant at angular frequency, aging time t and spatial position r, the tensor describing the heterogeneity and anisotropy of the material, the high frequency limit dielectric constant at aging time t and spatial position r, the tensor describing the relaxation time distribution, the unit tensor, j the imaginary unit.
Evaluating the aging state of the cable insulation comprises collecting dielectric characteristic data of each test point, calculating dielectric constant tensor by using Debye model, comparing the calculated dielectric constant tensor with a preset aging state threshold value, determining the aging state of each test point, and taking different countermeasures according to different aging states.
Determining the aging state of each test point comprises, if the dielectric constant tensor of the test point is smaller than a first-level threshold, indicating that the test point is in an unaged state, if the dielectric constant tensor of the test point is between the first-level threshold and a second-level threshold, indicating that the test point is in a mild aging state, if the dielectric constant tensor of the test point is between the second-level threshold and a third-level threshold, indicating that the test point is in a moderate aging state, and if the dielectric constant tensor of the test point is between the third-level threshold and a fourth-level threshold, indicating that the test point is in a severe aging state.
Different countermeasures include periodic cable quality inspection and supply chain management when the cable is in an unaged state, ensuring that high quality materials and components are used, analyzing historical performance data of the cable with big data, discovering potential weaknesses and improvement fields, and developing personalized maintenance and inspection plans according to specific types and historical performances of the cable.
When the cable is in a light aging state, fault mode identification and influence analysis are carried out on cable insulation, potential fault reasons are identified, preventive maintenance measures such as encryption monitoring frequency are enhanced, and the light damaged part is repaired or replaced in time aiming at the detected light damage.
When the cable is in a moderate aging state, performing comprehensive systematic risk assessment, and taking the influence of cable aging on the whole power system into consideration, making a detailed emergency response plan including the influence on the surrounding environment and the system, and making a corresponding emergency response plan.
When the cable is in a severely aged state, comprehensive system performance reevaluation is performed, including power demand, operation efficiency and safety, cost benefit analysis is performed, whether to replace aged cables or upgrade systems is determined, when the cable replacement is determined, critical areas and high-risk parts are prioritized, temporary enhancement monitoring and protection measures are implemented, and system faults caused by aged cables are prevented.
S3: and predicting the future aging state according to the historical aging state of the cable insulation.
The predicting of the future aging state comprises collecting historical data and corresponding aging states, evaluating the current aging state according to a Debye model to obtain a current aging index AI (t, r), predicting the future aging state based on the prediction model, and formulating countermeasures based on the predicted aging state.
Predicting future aging conditions based on the predictive model is expressed as,
AI Prediction (t+Δt, r) =ai (t, r) +aging rate (t, r) ×Δt+environmental factor influence (r)
Where Δt represents the time interval, and the aging rate is derived from the historical data.
If AI Prediction is above the aging index threshold AI Early warning or the aging rate exceeds the threshold, it indicates that aging will occur in the future.
The method comprises the steps of encrypting monitoring frequency of a cable when a test point predicts and displays future aging, tracking the running state of the cable in real time, implementing dynamic load management, adjusting the load level of the cable according to the real-time state of the cable, arranging periodic cable cleaning work, checking and replacing insulation materials which are worn or damaged, periodically performing insulation test and resistance measurement, ensuring the integrity of the insulation materials, preparing an emergency plan, responding quickly according to the emergency plan when the test point is aged, including a rapid repair of cable faults and a temporary power grid reconfiguration strategy, and starting a standby power supply or adjusting load distribution of adjacent cables.
Example 2
Referring to fig. 2, for one embodiment of the present invention, a system of a cable insulation aging state evaluation method based on a Debye model is provided, where the cable insulation aging state evaluation system based on the Debye model includes a data acquisition module, an aging state evaluation module, and a future aging prediction module.
The data acquisition module is responsible for collecting dielectric characteristic data of different cable insulating materials.
The aging state assessment module is responsible for assessing the current aging state of the cable insulation using the constructed Debye model.
The future aging prediction module is responsible for predicting a future aging state based on the current aging state and the historical aging trend.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-only memory (ROM), a random access memory (RAM, randomAccessMemory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Example 3
In this embodiment, in order to verify the beneficial effects of the present invention, scientific demonstration is performed through economic benefit calculation and simulation experiments. In order to clearly demonstrate the superiority of the Debye model-based cable insulation ageing state assessment method of the present invention over conventional methods, the following examples provide a comparative study. The study involved evaluating the aging status of the same batch of cables using the conventional and inventive methods and recording the results for comparative analysis. In this example, experiments were performed on the conventional method and the method of this example, respectively, as shown in table 1.
Table 1 experimental effect comparison chart
| Evaluation index | Conventional method | My invent method |
| Error rate | 10％ | 2％ |
| Environmental adaptation | Basic environmental parameters | Multiple physical field parameters |
| Prediction accuracy | No predictive power | 90％ |
| Delay fault discovery rate | 30％ | 5％ |
From the comparison data, the invention is significantly improved over the conventional method. In addition to significantly reduced error rates and enhanced environmental suitability, the present invention also provides excellent prediction accuracy and lower delay fault discovery rates.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered in the scope of the claims of the present invention.
Claims (10)
1. The cable insulation aging state assessment method based on the Debye model is characterized by comprising the following steps of:
Collecting dielectric characteristic data of different cable insulating materials, and determining whether the cable is aged or not;
Constructing a Debye model, and evaluating the aging state of the cable insulation based on the collected data and the Debye model;
and predicting the future aging state according to the historical aging state of the cable insulation.
2. The method for evaluating the insulation aging state of the cable based on the Debye model according to claim 1, wherein: determining whether the cable is aged or not comprises defining an aging index, and determining whether the test point is aged or not based on the aging index;
The ageing index is expressed as a function of,
AI(t，r)＝f(ε(ω，t，r)，P(t，r)，S(t，r))
Wherein P (t, r) represents physical parameters at the aging time t and the spatial position r, and S (t, r) represents chemical and structural stability parameters of the cable;
And when the ageing index is higher than the threshold value, the ageing index indicates that the cable test point is aged.
3. The method for evaluating the insulation aging state of the cable based on the Debye model according to claim 2, wherein: the construction of the Debye model comprises the steps of testing cable insulation materials in different aging stages, collecting dielectric characteristic data and loss data, and constructing the Debye model through the collected dielectric characteristic data;
the Debye model is represented as,
Where ε (ω, T, r) represents the complex permittivity at angular frequency ω, aging time T and spatial position r, A (T, r), B (T, r) represents tensors describing the inhomogeneity and anisotropy of the material, ε ∞ (T, r) represents the high frequency limit permittivity at aging time T and spatial position r, T (T, r) represents tensors describing the relaxation time distribution, I represents the unit tensors, j represents the imaginary unit.
4.A method for evaluating the insulation aging state of a cable based on a Debye model according to claim 3, wherein: the method comprises the steps of evaluating the aging state of cable insulation, namely collecting dielectric characteristic data of each test point, calculating dielectric constant tensor by using a Debye model, comparing the calculated dielectric constant tensor with a preset aging state threshold value, determining the aging state of each test point, and taking different countermeasures according to different aging states;
Determining the aging state of each test point comprises the steps of indicating that the test point is in an unaged state if the dielectric constant tensor of the test point is smaller than a first-level threshold, indicating that the test point is in a mild aging state if the dielectric constant tensor of the test point is between the first-level threshold and a second-level threshold, indicating that the test point is in a moderate aging state if the dielectric constant tensor of the test point is between the second-level threshold and a third-level threshold, and indicating that the test point is in a severe aging state if the dielectric constant tensor of the test point is between the third-level threshold and a fourth-level threshold.
5. The method for evaluating the insulation aging state of the cable based on the Debye model according to claim 4, wherein: the method comprises the steps of taking different countermeasures, namely, when the cable is in an unaged state, periodically performing cable quality inspection and supply chain management, ensuring that high-quality materials and components are used, analyzing historical performance data of the cable by utilizing big data, finding potential weaknesses and improvement fields, and making personalized maintenance and detection plans according to specific types and historical performances of the cable;
When the cable is in a light aging state, carrying out fault mode identification and influence analysis on cable insulation, identifying potential fault reasons, enhancing preventive maintenance measures such as encryption monitoring frequency, and timely repairing or replacing a light damaged part aiming at the detected light damage;
When the cable is in a moderate aging state, performing comprehensive systematic risk assessment, and taking the influence of cable aging on the whole power system into consideration, making a detailed emergency response plan, including the influence on the surrounding environment and the system, and making a corresponding emergency response plan;
When the cable is in a severely aged state, comprehensive system performance reevaluation is performed, including power demand, operation efficiency and safety, cost benefit analysis is performed, whether to replace aged cables or upgrade systems is determined, when the cable replacement is determined, critical areas and high-risk parts are prioritized, temporary enhancement monitoring and protection measures are implemented, and system faults caused by aged cables are prevented.
6. The method for evaluating the insulation aging state of the cable based on the Debye model according to claim 5, wherein: the prediction of the future aging state comprises the steps of collecting historical data and corresponding aging states, evaluating the current aging state according to a Debye model to obtain a current aging index AI (t, r), predicting the future aging state based on a prediction model, and formulating countermeasures based on the predicted aging state;
the predicting of the future aging state based on the predictive model is expressed as,
AI Prediction (t+Δt, r) =ai (t, r) +aging rate (t, r) ×Δt+environmental factor influence (r)
Wherein Δt represents the time interval, and the aging rate is obtained from the historical data;
if AI Prediction is above the aging index threshold AI Early warning or the aging rate exceeds the threshold, it indicates that aging will occur in the future.
7. The method for evaluating the insulation aging state of the cable based on the Debye model according to claim 6, wherein: the method comprises the steps of encrypting monitoring frequency of a cable when the test point predicts and displays future aging, tracking the running state of the cable in real time, implementing dynamic load management, adjusting the load level of the cable according to the real-time state of the cable, arranging periodic cable cleaning work, checking and replacing the insulation material which is worn or damaged, periodically performing insulation test and resistance measurement, ensuring the integrity of the insulation material, preparing an emergency plan, quickly responding according to the emergency plan when the test point is aged, including a rapid repair of cable faults and a temporary power grid reconfiguration strategy, and starting a standby power supply or adjusting load distribution of adjacent cables.
8. A system employing the Debye model-based cable insulation aging state assessment method according to any one of claims 1 to 7, characterized in that: the aging state evaluation system comprises a data acquisition module, an aging state evaluation module and a future aging prediction module;
The data acquisition module is responsible for collecting dielectric characteristic data of different cable insulating materials;
the aging state evaluation module is responsible for evaluating the current aging state of the cable insulation by using the constructed Debye model;
The future aging prediction module is responsible for predicting a future aging state based on the current aging state and the historical aging trend.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the Debye model-based cable insulation ageing state assessment method of any of claims 1 to 7.
10. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the Debye model-based cable insulation ageing state assessment method of any one of claims 1 to 7.
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