Multi-energy collaborative power grid new energy consumption capability assessment method and system
The multi-energy collaborative grid new energy consumption capacity evaluation model is established through the particle swarm algorithm, which solves the accuracy of grid new energy consumption capacity evaluation and achieves more efficient power system scheduling and resource utilization.
Patent Information
- Application Number
- CN202510452117.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-11
- Publication Date
- 2025-07-25
AI Technical Summary
It is difficult for the existing technology to accurately evaluate the ability to absorb new energy from the perspective of power grid operation risks, resulting in waste of resources such as wind and electricity scrapping, and reducing power generation efficiency.
A multi-energy synergistic power grid new energy consumption capacity evaluation model is used to establish a multi-energy collaboration power grid new energy consumption capacity evaluation model, combining the operating data of new energy such as wind power and photovoltaics and grid risks, and solving the evaluation model through the particle swarm algorithm to optimize the new energy consumption capacity.
It improves the accuracy of the assessment of the power grid's new energy consumption capacity, reduces operating risk costs, improves power generation efficiency and reduces resource waste.
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Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of new energy power systems, and particularly relates to a method and system for evaluating the new energy consumption capacity of a power grid with multi-energy collaboration. Background Art
[0002] In the current field of power grid energy utilization, the utilization rate of new energy represented by wind power, photovoltaic power, and hydropower has been significantly improved. When new energy is connected to the power system, it can effectively save the power generation cost. However, its significant uncertainty and volatility bring risks to the operation of the power grid, posing new challenges to the regulation ability and support ability of the power system. An inaccurate assessment of the power grid's new energy consumption capacity will cause situations such as wind and photovoltaic power abandonment, reducing the power generation efficiency and resulting in waste of resources. Therefore, how to improve the accuracy of the power grid's new energy consumption capacity assessment is an urgent problem to be solved.
[0003] Existing research on dealing with the uncertainty problem of new energy usually includes: scenario method, conditional value-at-risk method, data mining technology method, robust optimization algorithm, and other methods. The new energy consumption capacity is mostly evaluated from different angles such as peak shaving, frequency stability, and unit regulation performance, but there are few studies on evaluating from the perspective of power grid operation risk. Summary of the Invention
[0004] Object of the Invention: The present invention proposes a method for evaluating the new energy consumption capacity of a power grid with multi-energy collaboration, evaluates and models the new energy consumption capacity of the power grid from the perspective of power grid operation risk, and solves the evaluation model based on the particle swarm algorithm.
[0005] Technical Solution:
[0006] The present invention discloses a method for evaluating the new energy consumption capacity of a power grid with multi-energy collaboration, including:
[0007] Collecting the operation data of new energy from new energy sensors, power grid monitoring systems, and historical records to calculate the new energy acceptance risk value;
[0008] Calculating the predicted output of new energy, and establishing a new energy consumption capacity evaluation model in combination with the new energy acceptance risk value;
[0009] Solving the evaluation model based on the particle swarm algorithm to obtain the evaluation result of the new energy consumption capacity.
[0010] Furthermore, the new energy acceptance risk value is denoted as R, and is expressed as:
[0011]
[0012]
[0013] Among them, π1 represents the cost of wind curtailment, π2 represents the cost of PV curtailment, π3 represents the cost of load shedding caused by wind power, and π4 represents the coefficient of load shedding caused by PV; after the prediction error of the wind turbine is discretized, the number of risk units greater than the predicted value is denoted as and the number of risk units less than the predicted value is After the prediction error of the PV unit is discretized, the number of risk units greater than the predicted value is and the number of risk units less than the predicted value is
[0014] The u1-th risk unit of the wind turbine at the m-th time period t is The corresponding risk value is The interval of the l1-th risk unit of the wind turbine at the m-th time period t is The corresponding risk value is
[0015] The u2-th risk unit of the PV unit at the e-th time period t The corresponding risk values of each unit are The interval of the l2-th risk unit of the PV unit at the e-th time period t The corresponding risk values of each unit are The number of wind turbines is N w , and the number of PV units is N pv .
[0016] Furthermore, calculating the predicted output of new energy, including wind power output and PV output, the formula is:
[0017]
[0018] Among them, represents the wind power output, represents the PV output; the predicted output of the wind turbine at the m-th time period t is The predicted positive error is The predicted negative error is The predicted value of the PV unit at the e-th time period t is The predicted positive error is The predicted negative error is Ω w represents the uncertainty of the wind turbine, and Ω pv represents the uncertainty of the PV unit, and T represents the total dispatching time period; respectively represent the state variables of the wind turbine at the m-th time period t, respectively represent the state variables of the PV unit at the e-th time period t.
[0019] Furthermore, when , the corresponding wind power output takes the upper limit of the wind turbine output When When the corresponding wind power output value is the lower limit of the wind turbine output
[0020] Furthermore, the operation data collected for new energy includes: wind speed data of the wind farm, solar irradiance data of the photovoltaic station, load demand data, output of hydropower units and conventional units, wind rejection amount, light rejection amount, and load shedding amount.
[0021] Furthermore, the optimization objective function of the new energy accommodation capacity evaluation model is expressed as:
[0022]
[0023] where represents the start-up cost of thermal power unit g at time period t, represents the shutdown cost of thermal power unit g at time period t, represents the operation cost of thermal power unit g at time period t; x represents the binary variable of the operation state of the thermal power unit; p W+ represents the predicted positive error of the wind turbine, p W- respectively represent the predicted negative error of the wind turbine; p v+ represents the predicted positive error of the photovoltaic unit, p v- represents the predicted negative error of the photovoltaic unit; denote the wind rejection cost coefficient at time period t as δ t and the light rejection cost coefficient as σ t and the load shedding cost coefficient as ω t ; P represents the output of hydropower units and conventional units; represents the wind rejection amount of the unit, represents the light rejection amount of the unit, respectively represent the load shedding amount of the unit; N d represents the total number of loads.
[0024] Furthermore, the particle swarm algorithm abstracts the solution of the objective function as particles, and obtains the optimal solution through calculating the velocity and position of the particles and continuous iteration;
[0025] The velocity calculation formula is:
[0026]
[0027] The position calculation formula is:
[0028]
[0029] where represents the d-th dimension component of the flight velocity of particle i in the k-th iteration, representing the output magnitude of different energy forms; is the d - th dimensional component of the position vector of particle i in the k - th iteration, pb id is the personal best value of particle i in the d - th dimension, gb id is the global best value of particle i in the d - th dimension; c1 and c2 are the personal learning factor and social learning factor of the particle, and r1 and r2 are two random numbers in the range of 0 to 1; w is the inertia weight, which is zero or a positive number.
[0030] Furthermore, take the optimal solution obtained by the particle swarm algorithm as the optimal output, calculate the average consumption rate based on the predicted output in the corresponding time period, and set the rating standard according to the magnitude of the consumption rate to evaluate the new - energy consumption capacity of the power grid.
[0031] The present invention also discloses a multi - energy collaborative evaluation system for the new - energy consumption capacity of the power grid, including a memory, a processor, and a computer program stored on the memory. The processor executes the computer program to implement the steps of the foregoing method.
[0032] The present invention also discloses a computer - readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the foregoing method.
[0033] Beneficial effects:
[0034] The present invention provides a multi - energy collaborative evaluation method for the new - energy consumption capacity of the power grid. Starting from the perspective of power - grid operation risks, an evaluation model for the new - energy consumption capacity of the power grid is established, taking into account various new - energy power - generation forms such as wind power and photovoltaic power, as well as power - grid operation risks. Compared with the existing evaluation methods for the new - energy consumption capacity of the power grid, it reduces the operation - risk cost and has higher accuracy.
[0035] The present invention also uses the particle swarm algorithm to improve the calculation and response speed of the system model, achieve fast and accurate power - system scheduling, improve the power - generation efficiency of the power grid, and reduce resource waste. Specific embodiments
[0036] The following combines specific embodiments to further clarify the present invention. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification of the present invention by those skilled in the art all fall within the scope defined by the appended claims of this application.
[0037] The present invention discloses a multi - energy collaborative evaluation method and system for the new - energy consumption capacity of the power grid. In a specific embodiment, the method includes the following steps:
[0038] (1) Collect the operation data of new energy from new - energy sensors, power - grid monitoring systems, and historical records to calculate the new - energy acceptance risk value.
[0039] The operating data refers to the actual operating information of new energy and the real-time or historical data of the power grid, including:
[0040] New energy operating information: Collected from sensors in new energy power stations (such as anemometers, irradiance sensors) and weather forecast services. For example, the wind speed data of a wind farm and the solar irradiance data of a photovoltaic station are the basis for model input.
[0041] Load demand data: Obtained from the monitoring system of the power grid (such as the SCADA system) or historical records, reflecting the electricity demand of each load point in the power grid.
[0042] Output of hydroelectric units and conventional units: From the operating records or dispatching plans of the power grid. The output of hydroelectric units is based on reservoir water level and water flow data, while the output of conventional units (such as thermal power units) depends on fuel supply and operating status.
[0043] Wind curtailment volume, light curtailment volume, and load shedding volume: Decision variables in the optimization model, and their possible ranges or constraints are derived from historical operating data. For example, the wind curtailment volume may be limited by the installed capacity of the wind farm, and the load shedding volume is constrained by the power grid reliability standard.
[0044] Define the new energy acceptance risk value as R, then there is:
[0045]
[0046] Among them, π1 represents the wind curtailment cost coefficient, π2 represents the light curtailment cost coefficient, π3 represents the load shedding cost coefficient caused by wind power, and π4 represents the load shedding cost coefficient caused by photovoltaic power; after discretizing the prediction error of the wind turbine, record the number of risk units greater than the predicted value as and the number of risk units less than the predicted value as After discretizing the prediction error of the photovoltaic unit, the number of risk units greater than the predicted value is and the number of risk units less than the predicted value as
[0047] The u1-th risk unit of the wind turbine at the m-th time period t is The corresponding risk value is The interval of the l1-th risk unit of the wind turbine at the m-th time period t is The corresponding risk value is
[0048] The u2-th risk unit of the photovoltaic unit at the e-th time period t The corresponding risk value of each unit is The interval of the l2-th risk unit of the photovoltaic unit at the e-th time period t The corresponding risk value of each unit is The number of wind turbines is N w, the number of photovoltaic units is N pv .
[0049] (2) Establish an evaluation model for new energy consumption capacity. It includes calculating the predicted output of new energy, and establishing an evaluation model for new energy consumption capacity by combining the predicted output of the new energy and the new energy acceptance risk value.
[0050] The predicted output of new energy includes wind power and photovoltaic output, and the calculation formula is:
[0051]
[0052] Among them, represents the wind power output, represents the photovoltaic output; the predicted output of wind turbine m at time t is The predicted positive error is The predicted negative error is Ω w represents the uncertainty of the wind turbine, and Ω pv represents the uncertainty of the photovoltaic unit, and T represents the total scheduling period.
[0053] respectively represent the state variables of wind turbine m at time t. When , the corresponding wind power output takes the upper limit of the wind turbine output When , the corresponding wind power output takes the lower limit of the wind turbine output The predicted value of photovoltaic unit e at time t is The predicted positive error is The predicted negative error is Similarly, respectively represent the state variables of photovoltaic unit e at time t.
[0054] Taking wind power as an example, when , due to the excess wind power output, the problem of wind curtailment occurs; when , due to the insufficient wind power output, the problem of load shedding occurs.
[0055] The above parameters are preset values, usually determined based on industry standards, grid operation specifications, economic data or physical constraints, specifically including:
[0056] Uncertainty: Obtained by statistically analyzing the historical data of new energy output (including wind power and photovoltaic), comparing the difference between the past predicted output and the actual output, and constructing a probability distribution model. The new energy predicted output follows a normal distribution, denoted by P r(x) represents the corresponding probability value, where x represents the actual output p of wind power w or the actual output p of photovoltaic power pv , and the cumulative distribution function or confidence interval is calculated through P r (x) to obtain the predicted output of new energy. The probability value provides key basic analysis and problem identification for the optimization of new energy integration and energy management. A probability model is constructed using the characteristics of the normal distribution to predict the output range and uncertainty of new energy and improve the prediction accuracy.
[0057] Prediction error: Also originating from historical data, it calculates the deviation between the predicted value and the actual value of new energy output, usually expressed by statistical indicators.
[0058] Scheduling period: Set based on the operating planning habits of the power grid, usually a scheduling cycle divided by the hour within 24 hours.
[0059] The optimization objective function of the new energy consumption capacity evaluation model is as follows:
[0060]
[0061] Among them, represents the start-up cost of thermal power unit g at time t, represents the shutdown cost of thermal power unit g at time t, represents the operating cost of thermal power unit g at time t; x represents the binary variable of the operating state of the thermal power unit; p W + represents the predicted positive error of the wind turbine, p W- respectively represent the predicted negative error of the wind turbine; p v+ represents the predicted positive error of the photovoltaic unit, p v- represents the predicted negative error of the photovoltaic unit; Denote the curtailment cost coefficient of wind power at time t as δ t , the curtailment cost coefficient of photovoltaic power as σ t , and the load shedding cost coefficient as ω t ; P represents the output of hydropower units and conventional units; represents the curtailment volume of the unit, represents the curtailment volume of the unit, respectively represent the load shedding volume of the unit; N d represents the total load.
[0062] The above parameters are pre-set values, usually determined based on industry standards, power grid operation specifications, economic data or physical constraints, specifically including:
[0063] Cost coefficient: Obtained from unit operators or energy market data, including economic parameters such as fuel costs and maintenance costs. For example, the operating cost of a thermal power unit is directly related to the fuel price.
[0064] Number of risk units: Usually refers to the number of units with uncertain output, such as wind power and photovoltaic units, and the data is from the asset database of the power grid.
[0065] Number of units: The total number of all generating units in the power grid, including thermal power, hydropower, wind power and photovoltaic units, and it comes from the configuration information of the power grid.
[0066] Start / stop / operation cost of thermal power units: Provided by the unit operator or estimated based on the industry standards of the same type of units. For example, the start-up cost is related to equipment characteristics, fuel preheating, etc.
[0067] Total load: Determined based on the number of load points in the power grid model, usually corresponding to the number of load buses in the power grid network model.
[0068] (3) Solve the evaluation model based on the particle swarm algorithm to obtain the evaluation results.
[0069] Since the model cannot be directly solved by the solver, the particle swarm algorithm is introduced to find the optimal solution. The particle swarm algorithm (Particle Swarm Optimization, PSO) is a bio-inspired algorithm that mimics the foraging behavior of bird flocks, that is, the process of a population searching for the optimal value within the domain, and each particle in the population represents a solution. The population in the particle swarm algorithm is stable during the optimization process and has parallelism. In each iteration step of optimization in the particle swarm, the particles communicate with each other to determine the optimal value found by the entire population (global optimal value) and the optimal value found by each particle itself (individual extreme value). Then, each particle will learn, both learning the distance between itself and the global optimum, and learning the distance between itself and the individual extreme value, and then continue to optimize with the combined velocity of flying in both directions.
[0070] The velocity attribute of the particle describes the moving speed, and the position attribute describes the moving direction. The calculations of velocity and position are as follows respectively:
[0071]
[0072] Where represents the d-th dimensional component of the flying speed of particle i in the k-th iteration, which corresponds to the output magnitude of different energy forms in the present invention. is the d-th dimensional component of the position vector of particle i in the k-th iteration. pb id is the individual extreme value of particle i in the d-th dimension, gb idIt is the global optimal value of particle i in the d-th dimension. c1 and c2 are the individual learning factor and social learning factor of the particle, which regulate the maximum step size of learning. r1 and r2 are two random numbers in the range of 0 to 1, which increase the randomness of search and optimization. w is the inertia weight, which is zero or a positive number and is used to regulate the search range.
[0073] The optimal solution obtained through the particle swarm algorithm reflects the optimal output level of the new energy. In this embodiment, the optimal solution of the new energy consumption capacity evaluation model is obtained through PSO, and the specific evaluation steps are as follows:
[0074] Obtain the optimal output: The PSO model provides the optimal output levels of new energies such as wind energy and solar energy, that is, the optimal solution of PSO.
[0075] Calculate the consumption rate: Based on the predicted output in each time period and the optimal output obtained by PSO, calculate the average consumption rate (the ratio of the optimal output to the predicted output). For example, if the predicted wind energy output is 1000 MW and the PSO optimal output is 900 MW, the consumption rate is 90%.
[0076] Allocate grades or scores: Set the rating criteria according to the consumption rate. The grade allocation used in this embodiment is shown in Table 1:
[0077] Table 1
[0078]
[0079] Optionally, further combine the normalized operating cost and curtailment rate, and adjust the weights to form a comprehensive score formula:
[0080] Comprehensive score = 0.4 × consumption rate + 0.3 × (1 - curtailment rate) + 0.2 × (1 - cost) + 0.1 × stability index
[0081] The stability index is an index that measures the ability of the power grid to maintain stable operation after connecting new energies (such as wind power and photovoltaic). Due to the volatility and uncertainty of the output of new energies, it may have an impact on key parameters such as the voltage and frequency of the power grid. The stability index reflects the response ability and robustness of the power grid in the face of these fluctuations. If a certain power grid has a high consumption rate, a low curtailment rate, a low cost, and a high stability index, its comprehensive score is relatively high, indicating that its new energy consumption capacity is relatively strong. On the contrary, if the stability index is relatively low, even if other indicators perform well, the comprehensive score will be affected to a certain extent, indicating that there are potential risks in the stability of the power grid. By comparing the calculated comprehensive scores, the high and low levels of the new energy consumption capacity of the power grid within different units can be accurately and quickly distinguished.
[0082] Next, a comparison is made between the embodiment of the method for evaluating the new energy consumption capacity of the power grid using the present invention and the commonly used deterministic scheduling method (DS) and robust scheduling method (RS) in the prior art.
[0083] In the deterministic scheduling method, the execution time, priority, and other constraints of tasks are known, and there is no possibility of any change. The scheduling strategy is usually based on precise calculations of known information to optimize resource allocation. This method assumes that the system behavior is completely predictable, so the scheduling is "deterministic". The robust scheduling method, on the other hand, responds to the uncertainties in the system. These uncertainties may come from fluctuations in task execution time, unpredictability of resources, or changes in external factors. The goal of robust scheduling is to maintain the efficient operation of the system in the face of these uncertainties, usually by designing scheduling strategies that can handle the worst-case scenario.
[0084] The new energy consumption capacity model established by using the method provided by the present invention is denoted as the PSO model. Similarly, the evaluation model established by using the deterministic method is denoted as the DS model, and the evaluation model established by using the robust scheduling method is denoted as the RS model. Based on the IEEE-9 node system, the scheduling costs of different models are calculated and compared, and the results are shown in Table 2.
[0085] Table 2
[0086]
[0087] As can be seen from Table 2, the DS model has the lowest operating cost, the PSO model has the second lowest operating cost, and the RS model has the highest operating cost. Since the RS model and the PSO model consider robustness, the corresponding operating costs will be higher; the DS model does not consider the output range of renewable energy, and the output of renewable energy is a predicted value, so the corresponding operating risk is the greatest, and it is easy to generate wind and light curtailment; although the RS model considers the output range of renewable energy, the corresponding operating risk of the fixed output range is relatively high. In the PSO model, the operating risk of the output of renewable energy is considered, and the corresponding optimized operating risk cost is relatively low. The output range of renewable energy optimized by the PSO model is larger than that of the RS model, and it can effectively evaluate the power grid consumption capacity.
Claims
1. A method for evaluating the new energy consumption capacity of a power grid with multi-energy collaboration, characterized in that, Including: Collecting the operation data of new energy from new energy sensors, power grid monitoring systems and historical records to calculate the new energy acceptance risk value; Calculating the predicted output of new energy, and establishing a new energy consumption capacity evaluation model in combination with the new energy acceptance risk value; Solving the new energy consumption capacity evaluation model based on the particle swarm algorithm to obtain the new energy consumption capacity evaluation result.
2. The power grid new energy consumption capacity evaluation method according to claim 1, wherein The new energy acceptance risk value is denoted as R and is expressed as: Among them, π1 represents the cost of wind curtailment, π2 represents the cost of PV curtailment, π3 represents the cost of load shedding caused by wind power, and π4 represents the coefficient of load shedding caused by PV; after the prediction error of the wind turbine is discretized, the number of risk units greater than the predicted value is denoted as and the number of risk units less than the predicted value is After the prediction error of the PV unit is discretized, the number of risk units greater than the predicted value is and the number of risk units less than the predicted value is The u1-th risk unit of the wind turbine at time t in the m-th period is The corresponding risk value is The risk unit interval of the l1-th of the wind turbine at time t in the m-th period is The corresponding risk value is The u2nd risk unit of the photovoltaic unit at time period t in period e The risk values corresponding to each unit are The l2nd risk unit interval of the photovoltaic unit at time period t in period e The risk values corresponding to each unit are The number of wind turbines is N w , and the number of photovoltaic units is N pv .
3. The method for evaluating the new energy consumption capacity of the power grid according to claim 2, wherein The calculation of the predicted output of new energy includes wind power output and photovoltaic output, and the formula is: Among them, represents the wind power output, represents the photovoltaic power output; the predicted output of the wind turbine at time t in period m is The predicted positive error is The predicted negative error is The predicted value of the photovoltaic unit at time t in period e is The predicted positive error is The predicted negative error is Ω w represents the uncertainty of the wind turbine, Ω pv represents the uncertainty of the photovoltaic unit, and T represents the total scheduling period; respectively represent the state variables of the wind turbine at time t in period m, respectively represent the state variables of the photovoltaic unit at time t in period e.
4. The method for evaluating the new energy consumption capacity of the power grid according to claim 3, characterized in that, When , the corresponding wind power output value is the upper limit of the wind turbine output When , the corresponding wind power output value is the lower limit of the wind turbine output 5. The method for evaluating the new energy consumption capacity of the power grid according to claim 4, wherein The collection of the operation data of new energy includes: wind speed data of wind farms, solar irradiance data of photovoltaic stations, load demand data, output of hydroelectric units and conventional units, wind rejection amount, light rejection amount and load shedding amount.
6. The method for evaluating the new energy consumption capacity of the power grid according to claim 5, characterized in that The optimization objective function of the new energy consumption capacity evaluation model is expressed as: Among them, represents the start-up cost of thermal power unit g at time period t, represents the shutdown cost of thermal power unit g at time period t, represents the operating cost of thermal power unit g at time period t; x represents the binary variable of the operating state of the thermal power unit; p W+ represents the predicted positive error of the wind power unit, p W- respectively represent the predicted negative error of the wind power unit; p v+ represents the predicted positive error of the photovoltaic unit, p v- represents the predicted negative error of the photovoltaic unit; denote the curtailment cost coefficient of wind power at time period t as δ t , the curtailment cost coefficient of photovoltaic power as σ t , and the load shedding cost coefficient as ω t ; P represents the output of the hydropower unit and the conventional unit; represents the curtailment amount of wind power of the unit, represents the curtailment amount of photovoltaic power of the unit, respectively represent the load shedding amount of the unit; N d represents the total load.
7. The method for evaluating the new energy consumption capacity of the power grid according to claim 6, characterized in that The particle swarm algorithm abstracts the solution of the objective function into particles, and obtains the optimal solution through continuous iteration by calculating the speed and position of the particles; The speed calculation formula is: The position calculation formula is: Among them represents the d-th dimensional component of the flight speed of particle i in the k-th iteration, representing the output magnitude of different energy forms; is the d-th dimensional component of the position vector of particle i in the k-th iteration, pb id is the individual extreme value of particle i in the d-th dimension, gb id is the global optimal value of particle i in the d-th dimension; c1 and c2 are the individual learning factor and social learning factor of the particle, and r1 and r2 are two random numbers in the range of 0 to 1; w is the inertia weight, which is zero or a positive number.
8. The method for evaluating the new energy consumption capacity of the power grid according to claim 7, wherein Taking the optimal solution obtained by the particle swarm algorithm as the optimal output of new energy in the power grid, calculating the average consumption rate based on the predicted output in the corresponding time period, and setting a rating standard according to the size of the consumption rate to evaluate the new energy consumption capacity of the power grid.
9. A multi-energy collaborative power grid new energy consumption capacity evaluation system, including a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to claims 1 to 8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, the steps of the method according to claims 1 to 8 are implemented.