Wake flow control method and system for wind turbine generator of wind power plant
By obtaining wind farm data and operating status data, determining wake characteristics and controlling the yaw rate and pitch angle of upstream units, the problem of limited wind farm power generation efficiency improvement caused by the operation of a single wind turbine is solved, and the overall power generation of the wind farm and the stable unit operation is achieved.
Patent Information
- Application Number
- CN202510500679.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-21
- Publication Date
- 2025-06-13
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
In the prior art, the optimal operation of a single wind turbine is mainly due to limited improvement in the overall power generation efficiency of the wind farm, and the downstream wind turbine is affected by wake flow, reducing power generation efficiency and increasing fatigue load.
By obtaining the wind farm data of the wind farm and the operating status data of the wind turbine, determining the wake distribution characteristics and estimating the wake characteristic parameters, generating wake control instructions, controlling the yaw rate and pitch angle of the upstream unit, and causing the wake to deviate from the downstream unit.
The average operation characteristics of wind farms have been optimized, the power generation is increased, the unit operation is ensured safe and stable, and the impact of wake flow on downstream units has been reduced.
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Figure CN120140145A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical field of wind power generation, and particularly to a wake control method and system for wind turbines in a wind farm. Background Art
[0002] While obtaining energy from the wind, a wind turbine forms a wake region downstream where the wind speed decreases. Compared with the free incoming flow, the air velocity in the wake region decreases and the turbulence intensity increases. If the downstream wind turbine is located in the wake region, it will be affected by the wake, resulting in a reduction in power generation efficiency, a decrease in power generation, an increase in fatigue loads, and an impact on the service life of the wind turbine.
[0003] Therefore, in the prior art, to reduce the impact caused by the wake effect, it is basically based on the optimal operation of a single wind turbine. In this way, although a single wind turbine can operate in an optimal state, for a wind farm, there are mutual influences among wind turbines. When the operating state of a single wind turbine changes, it will change its wake influence area, thereby affecting the performance of downstream wind turbines. Therefore, the current control strategy mainly based on the optimal operation of a single wind turbine is not conducive to improving the overall power generation efficiency of the wind farm, thus affecting the power generation of the wind farm. Summary of the Invention
[0004] The present application provides a wake control method and system for wind turbines in a wind farm, which can improve power generation and ensure the safe and stable operation of the turbines on the premise of optimizing the average operating characteristics of the wind farm.
[0005] A wake control method for wind turbines in a wind farm includes:
[0006] Obtaining wind farm data and the operating state data of the wind turbines;
[0007] Determining the wake distribution characteristics according to the wind farm data;
[0008] Estimating the wake characteristic parameters according to the wake distribution characteristics and the operating state data of the turbines;
[0009] Generating a wake control command according to the wake characteristic parameters;
[0010] Controlling the yaw rate and pitch angle of the upstream turbines according to the wake control command to deflect the wake from the downstream turbines.
[0011] Optionally, obtaining the wind farm data includes:
[0012] Obtaining at least one piece of wind farm data such as the wind speed, wind direction, temperature, and air pressure of the wind farm.
[0013] Optionally, the operating state data of the wind turbines includes:
[0014] Obtain at least one piece of operating state data of the power output, pitch angle, yaw angle, rotational speed, and mechanical load of the wind turbine.
[0015] Optionally, determine the wake distribution characteristics according to the wind farm data, including:
[0016] Determine the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate according to the wind farm data;
[0017] Determine the wake distribution characteristics according to the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate.
[0018] Optionally, estimate the characteristic parameters according to the wake distribution characteristics and the unit operating state data, including:
[0019] Estimate the wake velocity deficit according to the wake distribution characteristics and the unit operating state data;
[0020] Determine the wake deflection angle and the characteristic parameters of the power loss of the downstream unit according to the wake velocity deficit.
[0021] Optionally, estimate the wake velocity deficit according to the wake distribution characteristics and the unit operating state data, including:
[0022] According to Estimate the wake velocity deficit;
[0023] where C T is the thrust coefficient of the wind turbine, γ is the yaw angle of the upstream unit, D is the rotor diameter, x is the distance of the downstream unit; T is the temperature, and U is the wind speed.
[0024] Optionally, generate a wake control instruction according to the wake velocity deficit, including:
[0025] Generate a yaw control instruction and a pitch angle control instruction according to the wake velocity deficit, where the yaw control instruction includes: yaw rate; the pitch angle control instruction includes: pitch angle change rate.
[0026] An embodiment of the present application further provides a wake control system for wind turbines in a wind farm, including:
[0027] An acquisition module for acquiring the wind farm data and the unit operating state data of the wind turbine;
[0028] A processing module for determining the wake distribution characteristics according to the wind farm data; estimating the wake characteristic parameters according to the wake distribution characteristics and the unit operating state data; generating a wake control instruction according to the wake characteristic parameters;
[0029] A control module, configured to control the yaw rate and pitch angle of an upstream unit according to the wake control instruction, so as to deflect the wake away from a downstream unit.
[0030] An embodiment of the present application further provides an electronic device, including: a processor and a memory; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory, so that the processor executes the method as described above.
[0031] An embodiment of the present application further provides a readable storage medium, including: a program or an instruction, when the program or the instruction runs on a computer, the method as described above is executed.
[0032] The wind farm wake control method and system provided by the present application obtain wind farm data and unit operation status data of wind turbines; determine wake distribution characteristics according to the wind farm data; estimate wake characteristic parameters according to the wake distribution characteristics and unit operation status data; generate wake control instructions according to the wake characteristic parameters; control the yaw rate and pitch angle of an upstream unit according to the wake control instruction, so as to deflect the wake away from a downstream unit. Therefore, on the premise of optimizing the average operation characteristics of the wind farm, the power generation is increased and the safe and stable operation of the unit is ensured. Description of the Drawings
[0033] Figure 1 It is a flowchart of a wind farm wake control method provided by an embodiment of the present application;
[0034] Figure 2 It is a schematic diagram of a wake area of a wind farm provided by an embodiment of the present application;
[0035] Figure 3 It is a schematic diagram of modules of a wind farm wake control system provided by an embodiment of the present application. Detailed Embodiments
[0036] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below. Apparently, the described embodiments are some but not all of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall also fall within the protection scope of the present application.
[0037] The wake effect refers to the formation of a wake region downstream of a wind turbine after it absorbs a portion of the incoming wind energy. The wake develops dynamically downstream of the turbine, and for onshore wind farms with flat terrain, the wake influence range can exceed 20 times the rotor diameter, and the wake influence range of offshore wind farms is even larger. Wind turbines in a wind farm are affected by the wakes of upstream turbines, and there are two main physical mechanisms for this influence: (1) momentum deficit (velocity deficit), which reduces the power generation efficiency of downstream wind turbines and thus decreases the power output; (2) increased turbulence intensity, which increases the unsteady loads on downstream wind turbines. According to relevant statistical data, due to site and capacity limitations, the power generation loss caused by the wakes of a wind farm after reasonable layout accounts for approximately 10%-20% of the annual power generation; the fatigue load increases by approximately 5%-15%, affecting the service life of wind turbines.
[0038] In the prior art, to reduce the influence of wakes on wind turbines, the optimal operation of a single wind turbine is generally the main focus. However, for a wind farm, there are mutual influences among wind turbines. When the operating state of a single wind turbine changes, it will change its wake influence area, thereby affecting the performance of downstream wind turbines. Therefore, the control method based on the optimal operation of a single wind turbine is not conducive to improving the overall power generation efficiency of the wind farm.
[0039] As Figure 1 shown, an embodiment of the present application provides a wake control method for wind turbines in a wind farm, including:
[0040] Step 11, obtaining the wind field data of the wind farm and the unit operation state data of the wind turbines;
[0041] Step 12, determining the wake distribution characteristics according to the wind field data;
[0042] Step 13, estimating the wake characteristic parameters according to the wake distribution characteristics and the unit operation state data;
[0043] Step 14, generating a wake control instruction according to the wake characteristic parameters;
[0044] Step 15, controlling the yaw rate and pitch angle of the upstream unit according to the wake control instruction to deflect the wake away from the downstream unit.
[0045] The wake control method provided by this application aims to optimize the energy capture efficiency of the entire wind farm. Based on the real-time wind direction, wind speed data of the wind farm and the operating states of each unit, combined with the high-precision flow field simulation data in the early stage, it dynamically adjusts the target unit to operate in the optimal posture, thereby reducing the wake influence between units, realizing the global flow field optimization of the wind farm, improving the overall power generation of the wind farm and achieving the fatigue load balance of all units in the field. Specifically, it obtains the wind field data of the wind farm and the operating state data of the wind turbines; determines the wake distribution characteristics according to the wind field data; estimates the wake characteristic parameters according to the wake distribution characteristics and the operating state data of the units; generates wake control instructions according to the wake characteristic parameters; and controls the yaw rate and pitch angle of the upstream units according to the wake control instructions to make the wake deviate from the downstream units. Thus, on the premise of ensuring the optimization of the average operating characteristics of the wind farm, the power generation is increased and the safe and stable operation of the units is ensured.
[0046] In an optional embodiment of this application, in step 11, obtaining the wind field data of the wind farm includes: obtaining at least one item of wind field data such as wind speed, wind direction, temperature, and air pressure of the wind farm.
[0047] In this embodiment, the wind speed, wind direction, etc. can be monitored in real time by lidar, and parameters such as temperature and air pressure can be collected by relevant sensors to obtain high-precision wind field data and further determine the wake intensity.
[0048] In an optional embodiment of this application, in step 11, the operating state data of the wind turbines includes:
[0049] Obtaining at least one item of operating state data such as the power output, pitch angle, yaw angle, rotational speed, and mechanical load of the wind turbines.
[0050] In this embodiment, the operating state data such as the generator rotational speed ω, power output, pitch angle, yaw angle, and mechanical load (blade bending moment, tower vibration) of the wind turbines can be obtained by relevant sensors.
[0051] In an optional embodiment of this application, in step 12, determining the wake distribution characteristics according to the wind field data includes:
[0052] Step 121, determining the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate according to the wind field data;
[0053] Step 122, determining the wake distribution characteristics according to the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate.
[0054] In this embodiment, in step 121, determining the turbulence intensity according to the wind field data includes:
[0055] By Determine the turbulence intensity I;
[0056] where U is the horizontal wind speed (east - west direction), V is the horizontal wind speed (north - south direction), and W is the vertical wind speed (height direction);
[0057] where the fluctuating velocity:
[0058] Average velocity distribution:
[0059] t is a variable and N is a positive integer.
[0060] In step 121, according to the wind field data, determine the turbulent kinetic energy, including:
[0061] According to Determine the turbulent kinetic energy k, thereby quantifying the turbulent energy and predicting the wake recovery speed;
[0062] In step 121, according to the wind field data, determine the stress, including:
[0063] According to τ = -ρ<u'u'>, obtain the stress τ, where ρ is the air density, p is the air pressure, T is the temperature, and R is the gas constant;
[0064] In step 121, according to the wind field data, determine the turbulent dissipation rate, including:
[0065] According to ε = 2v<s ij s ij >, determine the turbulent dissipation rate, s ij is the strain rate tensor, evaluate the small - scale turbulent energy dissipation, and optimize the numerical simulation accuracy.
[0066] In step 122, according to the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate, determine the wake distribution characteristics, including:
[0067] Combine the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate together to obtain the wake distribution characteristics.
[0068] In an optional embodiment of the present application, in step 13, according to the wake distribution characteristics and the unit operation state data, estimate the characteristic parameters, including:
[0069] Step 131, estimate the wake velocity deficit according to the wake distribution characteristics and the unit operation state data;
[0070] Step 132, determine the wake deflection angle and the characteristic parameters of the downstream unit power loss according to the wake velocity deficit.
[0071] Among them, in step 131, estimating the wake velocity deficit according to the wake distribution characteristics and the unit operation status data includes:
[0072] According to estimating the wake velocity deficit; thereby quantifying the power loss of the downstream unit and optimizing the layout of the wind farm;
[0073] Among them, C T is the thrust coefficient of the wind turbine, γ is the yaw angle of the upstream unit, D is the rotor diameter, x is the distance of the downstream unit; T is the temperature, U is the wind speed;
[0074] Step 132, determining the wake deflection angle and the characteristic parameters of the power loss of the downstream unit according to the wake velocity deficit, includes:
[0075] According to determining the wake deflection angle δ;
[0076] According to determining the power loss P of the downstream unit loss ;
[0077] Among them, ΔU is the wake velocity deficit, P is the power of the wind turbine, U is the wind speed,
[0078] In an optional embodiment of the present application, in step 14, generating a wake control instruction according to the wake velocity deficit includes:
[0079] Step 141, generating a yaw control instruction and a pitch angle control instruction according to the wake velocity deficit, where the yaw control instruction includes: yaw rate; the pitch angle control instruction includes: pitch angle change rate.
[0080] In an optional embodiment of the present application, in step 15, controlling the yaw rate and pitch angle of the upstream unit according to the wake control instruction to make the wake deviate from the downstream unit includes:
[0081] Controlling the upstream unit to actively yaw according to the wake deflection angle δ and the yaw rate; where the yaw rate is less than or equal to 0.5° / s, so as to reduce mechanical shock;
[0082] According to the equivalent wind speed U eff = U∞ - ΔU, adjusting the pitch angle to maintain the maximum power coefficient Cp, P is the power, U is the wind speed, ρ is the air density, A is a constant.
[0083] In this embodiment, as Figure 2As shown, through the above method, the power influence of the wake of the upstream wind turbine on the downstream wind turbine is reduced or no longer affects. Through real-time flow field cooperative control, the wind farm is upgraded from "single-machine isolated operation" to "agent network cooperation", and more than 10% of the power generation increase and 20% of the fatigue load balance optimization can be achieved in a typical wind farm. Global energy optimization: Maximize wind energy capture through wake redirection. Dynamic safety balance: Multi-objective optimization ensures the service life of the unit and grid requirements.
[0084] In the above embodiments of the present application, the wake control aims at the optimal energy capture efficiency of the entire wind farm. It uses lidar intelligent wind measurement sensors to capture accurate information of the oncoming wind domain, uses positioning and orientation devices to obtain the true north orientation of each unit's nacelle, and uses the wind farm controller to achieve data transmission and control instruction generation. According to the real-time wind parameters such as wind direction and wind speed in the wind farm and the operating status of each unit, it cooperatively controls the operating postures of each unit to achieve the optimization goal:
[0085] A series of intelligent sensors such as lidar are used, combined with advanced three-dimensional flow field reconstruction technology, to accurately invert the real-time three-dimensional wind domain flow field information of the entire wind farm, especially near each unit, providing important wind farm flow field data input for wake control. High-precision flow field simulation data can accurately evaluate the flow field characteristics and the operating characteristics of each unit. Combined with the dynamic wake control algorithm, the operating postures of each unit under the optimal power generation efficiency of the wind farm can be obtained.
[0086] The wind farm controller comprehensively manages all sensor and unit operation data in the wind farm, and issues wake control instructions to each unit to achieve the wake control goal.
[0087] The basic starting point of the dynamic wake control algorithm is to comprehensively consider the influence of the actual on-site wind conditions and the dynamic characteristics of the unit wake on the premise of ensuring the optimization of the average operating characteristics of the wind farm, so as to further improve the power generation, make the wake control instructions continuous and stable, and ensure the safe and stable operation of the unit.
[0088] As Figure 3 shown, the embodiment also provides a wake control system 30 for wind turbines in a wind farm, including:
[0089] An acquisition module 31, configured to acquire wind farm data and unit operation status data of the wind turbines;
[0090] A processing module 32, configured to determine the wake distribution characteristics according to the wind farm data; estimate wake characteristic parameters according to the wake distribution characteristics and unit operation status data; generate wake control instructions according to the wake characteristic parameters;
[0091] A control module 33, configured to control the yaw rate and pitch angle of the upstream unit according to the wake control instructions to deflect the wake from the downstream unit.
[0092] Optionally, obtain the wind farm data, including:
[0093] Obtain at least one of the wind speed, wind direction, temperature, and air pressure in the wind farm as the wind farm data.
[0094] Optionally, the unit operation status data of the wind turbine includes:
[0095] Obtain at least one of the power output, pitch angle, yaw angle, rotational speed, and mechanical load of the wind turbine as the operation status data.
[0096] Optionally, determine the wake distribution characteristics according to the wind farm data, including:
[0097] Determine the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate according to the wind farm data;
[0098] Determine the wake distribution characteristics according to the turbulence intensity, turbulent kinetic energy, stress, and turbulent dissipation rate.
[0099] Optionally, estimate the characteristic parameters according to the wake distribution characteristics and the unit operation status data, including:
[0100] Estimate the wake velocity deficit according to the wake distribution characteristics and the unit operation status data;
[0101] Determine the wake deflection angle and the characteristic parameters of the power loss of the downstream unit according to the wake velocity deficit.
[0102] Optionally, estimate the wake velocity deficit according to the wake distribution characteristics and the unit operation status data, including:
[0103] According to Estimate the wake velocity deficit;
[0104] where C T is the thrust coefficient of the wind turbine, γ is the yaw angle of the upstream unit, D is the rotor diameter, x is the distance of the downstream unit; T is the temperature, and U is the wind speed.
[0105] Optionally, generate a wake control command according to the wake velocity deficit, including:
[0106] Generate a yaw control command and a pitch angle control command according to the wake velocity deficit. The yaw control command includes: yaw rate; the pitch angle control command includes: pitch angle change rate.
[0107] For the wake control system of the wind farm wind turbine provided by the embodiments of the present application, the specific implementation process can refer to the above method embodiments, and its implementation principle and technical effects are similar, which will not be elaborated here in this embodiment.
[0108] An electronic device provided by an embodiment of the present application includes: a processor and a memory. Among them, the memory stores computer-executable instructions. The processor executes the computer-executable instructions stored in the memory, so that the processor executes the method described in any of the above embodiments.
[0109] For the electronic device provided by the embodiment of the present application, the specific implementation process can refer to the above method embodiment, and its implementation principle and technical effect are similar, which will not be elaborated here.
[0110] In the above embodiment, it should be understood that the processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.
[0111] The memory may include high-speed RAM memory and may also include non-volatile storage NVM, such as at least one disk memory.
[0112] The bus may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, the bus in the drawings of the present application is not limited to only one bus or one type of bus.
[0113] The embodiment of the present application also provides a computer-readable storage medium, in which computer-executable instructions are stored. When the processor executes the computer-executable instructions, the method shown in the above method embodiment is implemented.
[0114] The above-mentioned computer-readable storage medium may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disk. The readable storage medium may be any available medium accessible by a general-purpose or special-purpose computer.
[0115] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium may also be a component of the processor. The processor and the readable storage medium may be located in an application specific integrated circuit (ASIC). Of course, the processor and the readable storage medium may also exist as discrete components in a device.
[0116] Those of ordinary skill in the art can understand that all or part of the steps for implementing the above method embodiments can be completed by hardware related to program instructions. The foregoing program may be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments; and the foregoing storage medium includes various media that can store program codes, such as ROM, RAM, magnetic disks, or optical disks.
[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not intended to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.
Claims
1. A method for controlling the wake of a wind turbine in a wind farm, characterized in that: include: Obtain wind farm data of the wind farm and unit operation status data of the wind turbines; Determining wake distribution characteristics according to the wind field data; estimating wake characteristic parameters according to the wake distribution characteristics and the unit operation status data; generating a wake control instruction according to the wake characteristic parameter; According to the wake control instruction, the yaw rate and pitch angle of the upstream unit are controlled to make the wake deviate from the downstream unit.
2. The wake control method for a wind turbine generator set in a wind farm according to claim 1, characterized in that: Obtain wind farm data of wind farms, including: At least one wind farm data of the wind speed, wind direction, temperature and air pressure of the wind farm is obtained.
3. The wake control method for a wind turbine generator set in a wind farm according to claim 1, characterized in that: Wind turbine unit operating status data, including: Obtain at least one operating status data of the wind turbine generator set: power output, pitch angle, yaw angle, rotation speed, and mechanical load.
4. The wake control method for a wind turbine generator set in a wind farm according to claim 1, characterized in that: Determine wake distribution characteristics according to the wind field data, including: determining turbulence intensity, turbulence kinetic energy, stress, and turbulence dissipation rate based on the wind field data; The wake distribution characteristics are determined based on turbulence intensity, turbulent kinetic energy, stress and turbulence dissipation rate.
5. The wake control method for a wind turbine generator set in a wind farm according to claim 1, characterized in that: According to the wake distribution characteristics and the unit operation status data, characteristic parameters are estimated, including: estimating the wake velocity loss according to the wake distribution characteristics and the unit operation status data; According to the wake velocity loss, the wake deflection angle and the characteristic parameters of the downstream unit power loss are determined.
6. The wake control method for a wind turbine in a wind farm according to claim 5, characterized in that: According to the wake distribution characteristics and the unit operation status data, the wake velocity loss is estimated, including: according to Estimated wake speed loss; Among them, C T is the thrust coefficient of the wind turbine, γ is the yaw angle of the upstream unit, D is the rotor diameter, x is the distance to the downstream unit; T is the temperature, and U is the wind speed.
7. The wake control method for a wind turbine generator set in a wind farm according to claim 1, characterized in that: Generating a wake control instruction according to the wake velocity loss includes: A yaw control instruction and a pitch angle control instruction are generated according to the wake velocity loss. The yaw control instruction includes: a yaw rate; and the pitch angle control instruction includes: a pitch angle change rate.
8. A wake control system for a wind turbine in a wind farm, characterized in that: include: An acquisition module is used to acquire wind farm data of a wind farm and unit operation status data of a wind turbine; A processing module, used to determine the wake distribution characteristics according to the wind field data; estimate the wake characteristic parameters according to the wake distribution characteristics and the unit operation status data; and generate a wake control instruction according to the wake characteristic parameters; The control module is used to control the yaw rate and pitch angle of the upstream unit according to the wake control instruction, so that the wake deviates from the downstream unit.
9. An electronic device, characterized in that: include: Processor and memory; Memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory, so that the processor performs the method according to any one of claims 1 to 7.
10. A readable storage medium, characterized in that: include: A program or instruction, when the program or instruction is run on a computer, executes the method according to any one of claims 1 to 7.
Citation Information
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