Method and apparatus for temperature control of electrical room in apartment

Abstract

A method for controlling the temperature of an electrical room in a multi-unit dwelling and a device thereof are disclosed. The temperature control device identifies spatial information including the temperature within the electrical room of a multi-unit dwelling where a transformer is located, identifies power equipment information including the transformer load rate, and inputs spatial information and power equipment information collected over a certain past period from the present time into a temperature prediction model that predicts the temperature at a future point in time based on time-series data regarding the spatial information and power equipment information to determine the predicted temperature, and controls the cooling equipment of the electrical room based on the identified predicted temperature.

Description

Technology Field

[0001] An embodiment of the present invention relates to a method and apparatus for controlling the temperature of an electrical room in a multi-unit dwelling, and more specifically, to a method and apparatus for controlling the temperature of an electrical room in a multi-unit dwelling in which a transformer that converts high voltage to low voltage is installed. Background Technology

[0002] To use high-voltage power provided by a power company for residential purposes, it must be converted into low-voltage power. In some cases, power companies directly convert high-voltage power to low-voltage power and supply it to multi-unit dwellings. However, this has the disadvantage of higher electricity rates because the power company installs and manages the transformers that convert high-voltage to low-voltage power. Consequently, most multi-unit dwellings install the transformers that convert the power supplied by the power company into low-voltage power in their electrical rooms and manage them directly.

[0003] Electrical rooms in multi-unit dwellings are densely packed with various power equipment, such as transformers, circuit breakers, and distribution panels, that supply electricity to each household. The prolonged continuous operation of these devices generates persistent heat within the electrical room. Particularly during the summer or peak load hours, the amount of heat generated inside transformers increases rapidly; consequently, if air circulation within the electrical room is inadequate, a temperature imbalance may occur, resulting in localized temperature increases near the transformers. Overheating within the electrical room can cause the deterioration of transformer insulating oil, increased coil resistance, and reduced efficiency, potentially leading to a risk of insulation breakdown in the long term.

[0004] To prevent such overheating phenomena inside the electrical room of a multi-unit dwelling, ventilation fans or air conditioners are installed and operated. However, existing cooling systems operate continuously until the target temperature is reached, manually operated by a manager. For example, it is a repetitive on / off control structure in which air conditioners (air conditioners, fans, ventilation fans, etc.) are turned on when the temperature inside the electrical room exceeds the target temperature (e.g., 35℃), and the air conditioners are stopped when the temperature inside the electrical room drops below the target temperature.

[0005] However, since these cooling systems begin cooling only after the temperature inside the electrical room has already risen, they fail to suppress thermal stress inside the transformer in advance. Furthermore, frequent switching of the air conditioner on and off increases power consumption, and there is a problem with the cooling operating repeatedly even when it is not actually needed. In addition, uneven airflow within the electrical room causes overheating to concentrate in specific areas, which becomes a factor that shortens the lifespan of the transformer in the long term. The problem to be solved

[0006] The technical problem that the embodiments of the present invention aim to solve is to provide a method and apparatus for controlling temperature based on temporal prediction and / or spatial heat distribution regarding the temperature inside the electrical room of a multi-unit dwelling where a transformer is located, rather than a simple temperature-based feedback control method. means of solving the problem

[0007] An example of a temperature control method for an electrical room of a multi-unit dwelling according to an embodiment of the present invention, for achieving the above technical objectives, comprises: a step of identifying spatial information including the temperature within the electrical room of a multi-unit dwelling where a transformer is located; a step of identifying power equipment information including the transformer load rate; a step of identifying a predicted temperature by inputting spatial information and power equipment information collected over a certain past period from the present time into a temperature prediction model that predicts the temperature at a future point in time based on time-series data regarding spatial information and power equipment information; and a step of controlling a cooling device of the electrical room based on the predicted temperature.

[0008] An example of a temperature control device for an electrical room of a multi-unit dwelling according to an embodiment of the present invention for achieving the above technical objectives comprises: a spatial analysis unit for identifying spatial information including the temperature within the electrical room of a multi-unit dwelling where a transformer is located; an equipment analysis unit for identifying power equipment information including the transformer load rate; a temperature prediction model for predicting a temperature at a future point in time based on time-series data regarding the spatial information and the power equipment information; a temperature prediction unit for identifying a predicted temperature by inputting the spatial information and the power equipment information collected over a past period from the present point in time into the temperature prediction model; and a control unit for controlling the operation of a cooling device in the electrical room based on the predicted temperature. Effects of the invention

[0009] According to an embodiment of the present invention, it is possible to predict the internal temperature of an electrical room. Through this, real-time temperature peaks can be mitigated by partially operating the cooling equipment before the internal temperature of the electrical room reaches a predefined threshold, thereby preventing overloading of the cooling equipment, increasing the efficiency of the cooling equipment, and reducing the power consumption of the cooling equipment. In addition, by performing multi-objective control through an integrated evaluation of the transformer efficiency degradation rate, insulation oil degradation rate, and cooling energy consumption, it is possible to simultaneously prevent excessive cooling operation or insufficient cooling. In another embodiment, hot spots can be suppressed by adjusting the airflow and direction for each section using data from multiple temperature sensors inside the electrical room. Furthermore, by linking with an Energy Management System (EMS), the cooling load of the electrical room can be distributed in advance during peak power hours, and cooling can be concentrated during periods of low electricity rates, thereby reducing operating costs and obtaining benefits for Demand Response (DR). Brief explanation of the drawing

[0010] FIG. 1 is a drawing illustrating an example of an electrical room in a multi-unit dwelling in which a temperature control method according to an embodiment of the present invention is implemented. FIG. 2 is a flowchart illustrating an example of a temperature control method for an electrical room in a multi-unit dwelling according to an embodiment of the present invention. FIG. 3 is a drawing illustrating an example of a temperature prediction model according to an embodiment of the present invention. FIG. 4 is a drawing illustrating an example of a method for controlling a cooling device in an electrical room according to an embodiment of the present invention. FIG. 5 is a diagram illustrating an example of a method for dynamically setting a target temperature according to an embodiment of the present invention. FIG. 6 is a diagram illustrating an example of a method for calculating a control value of a cooling device according to an embodiment of the present invention, and, FIG. 7 is a diagram illustrating the configuration of an example of a temperature control device according to an embodiment of the present invention. Specific details for implementing the invention

[0011] Hereinafter, a temperature control method and apparatus for an electrical room of a multi-unit dwelling according to an embodiment of the present invention will be examined in detail with reference to the attached drawings.

[0012] FIG. 1 is a drawing illustrating an example of an electrical room in a multi-unit dwelling in which a temperature control method according to an embodiment of the present invention is implemented.

[0013] Referring to FIG. 1, the electrical room (110) of a multi-unit dwelling contains a transformer (120), a distribution board (130), a cooling device (150), and at least one sensor (140). The transformer (120) converts high-voltage power supplied by a power company into low-voltage power. The distribution board (130) distributes power to each household within the multi-unit dwelling. The cooling device (150) includes various devices for lowering the temperature within the electrical room (110) of the multi-unit dwelling. For example, the cooling device (150) may include various devices such as air conditioners, fans, vents, and air conditioning units. The types and number of cooling devices within the electrical room may vary depending on the embodiment and are not limited to specific examples.

[0014] The sensor (140) measures spatial information, including the temperature inside the electrical room (110). In one embodiment, various types of sensors, such as at least one temperature sensor and at least one humidity sensor, may be located in various places within the electrical room (110). In another embodiment, sensors for measuring the outside temperature or outside humidity outside the electrical room (110) may be further included. In yet another embodiment, various sensors for measuring the load or power loss of the transformer (120) may exist. In addition, sensors for collecting various data necessary for the embodiments of the present invention may exist inside or outside the electrical room (110).

[0015] The temperature control device (100) controls the cooling device (150) based on spatial information, such as the temperature inside the electrical room collected through the sensor (140), and power equipment information, such as the load of the transformer. The temperature control device (100) does not simply control the on / off of the cooling device by comparing the target temperature set in advance by the user with the actual temperature inside the electrical room, but rather identifies the predicted temperature at a certain future point in time based on various environmental information (temperature, transformer load, etc.) of the electrical room (110), and controls the cooling device according to the predicted temperature. A specific method for controlling based on the predicted temperature inside the electrical room is described below in FIG. 2.

[0016] FIG. 2 is a flowchart illustrating an example of a temperature control method for an electrical room in a multi-unit dwelling according to an embodiment of the present invention.

[0017] Referring to FIG. 2, the temperature control device (100) identifies spatial information including the temperature inside the electrical room using at least one sensor (S200). In one embodiment, the temperature control device can identify the temperature distribution inside the electrical room (i.e., spatial temperature distribution) through temperature sensors located in multiple spaces inside the electrical room.

[0018] The temperature control device (100) identifies power equipment information including the transformer load rate (S210). In one embodiment, the temperature control device (100) can collect power equipment information such as the transformer temperature or current along with the transformer load rate.

[0019] The temperature control device (100) predicts the temperature inside the electrical room at a future point in time based on spatial information such as the temperature inside the electrical room and power equipment information such as the transformer load rate (S220). The predicted temperature may be the temperature after a certain period of time from the current point in time (e.g., after 1 hour or after 3 hours, etc.) or a continuous temperature change from the current point in time to a certain period of time. Alternatively, the predicted temperature may be the predicted temperature for multiple spaces inside the electrical room or the predicted temperature at a single point.

[0020] The temperature control device (100) can predict the temperature at a future point in time using a temperature prediction model. In one embodiment, the temperature prediction model may be generated based on a time series analysis model. The temperature prediction model for this embodiment is examined again in FIG. 3.

[0021] The temperature control device (100) controls the cooling device based on the predicted temperature (S230). In one embodiment, the temperature control device (100) can operate the cooling device in advance if the predicted temperature is higher than the target temperature, even if the current temperature in the electrical room is lower than the target temperature. Various methods for controlling the cooling device based on the predicted temperature are examined again in FIG. 4.

[0022] In another embodiment, the temperature control device (100) can dynamically adjust the target temperature. A method for dynamically setting the target temperature is shown in FIG. 5. In yet another embodiment, the temperature control device (100) can calculate an optimal cooling device control value by considering the energy consumption of the cooling device and the power loss of the transformer together when operating the cooling device. This is shown again in FIG. 6.

[0023] FIG. 3 is a diagram illustrating an example of a temperature prediction model according to an embodiment of the present invention.

[0024] Referring to FIG. 3, the temperature prediction model (300) has input data (310) that includes time series data such as spatial information (312) such as the temperature inside the electrical room and power equipment information (314) such as the load rate of the transformer, and output data that is a predicted temperature (320) for a future time point or a future period.

[0025] The temperature prediction model (300) can be implemented as a time series analysis model such as LSTM (Long Short-Term Memory model), ARIMA (Autoregressive Integrated Moving Average), or gradient boosting. In addition, the temperature prediction model (300) can be implemented as various types of artificial intelligence models.

[0026] The spatial information (312) may further include information such as humidity inside the electrical room, outside temperature, or solar radiation along with the temperature inside the electrical room. The power equipment information may further include various types of information such as transformer temperature, transformer power loss, or insulation degradation indicator along with the transformer load.

[0027] When a temperature prediction model (300) is generated, the temperature control device (100) inputs spatial information (312) and power equipment information (314) from the present time to a certain past period into the temperature prediction model (300) to predict the temperature inside the electrical room at a certain future time (or period) from the present time. Additionally, if the spatial information included in the input data (310) includes temperature information for multiple spaces inside the electrical room, the temperature predicted by the temperature prediction model (300) may be the predicted temperature for multiple points inside the electrical room.

[0028] FIG. 4 is a diagram illustrating an example of a method for controlling a cooling device in an electrical room according to an embodiment of the present invention.

[0029] Referring to FIG. 4, the temperature control device (100) can compare the predicted temperature (400) at a certain future point in time (or period) identified through a temperature prediction model with a preset target temperature (410), and if the predicted temperature (400) is greater than or equal to the target temperature (410), the cooling device can be operated in advance.

[0030] In one embodiment, when the predicted temperature (400) is the predicted temperature for a plurality of spaces within the electrical room, the temperature control device (100) can control the air direction and air speed of the cooling device by comparing the predicted temperature (400) of the plurality of spaces with the target temperature (410). For example, if the predicted temperature (400) of a first point (e.g., a transformer area) within the electrical room is greater than or equal to the target temperature (410), the temperature control device (100) can adjust the direction of the cooling device toward the transformer area and adjust the intensity of the cooling device based on the difference between the predicted temperature (400) and the target temperature (410).

[0031] FIG. 5 is a diagram illustrating an example of a method for dynamically setting a target temperature according to an embodiment of the present invention.

[0032] Referring to FIG. 5, the temperature control device (100) can dynamically set (520) the target temperature according to the transformer load rate (500) in the electrical room or the outside temperature (510). For example, if the outside temperature is high and the transformer load rate is high during the day, the temperature control device (100) can lower the target temperature. Conversely, if it is night or the transformer load is low, the temperature control device (100) can raise the target temperature.

[0033] The relationship between various variables such as the transformer load rate (500) or the ambient temperature (510) and the target temperature can be defined in advance using a table or graph, or by the following mathematical formula.

[0034]

[0035] Here, f base is the reference target temperature (e.g., a predefined temperature (35℃) or the transformer design temperature), ΔL(t) is the transformer load factor variation (relative to the reference, %), and ΔT out (t) is the deviation of the ambient temperature from the reference (°C), and ΔI sol(t) is the change in solar radiation (in units of W / m², deviation from the average), Δt is the time period weight (e.g., peak time = +1, night = -1, etc.), and α and β are correction factors (determined by experiment or simulation). α and β can be predefined to various values ​​depending on the embodiment.

[0036] In one embodiment, the temperature control device (100) can periodically determine the target temperature using the above mathematical formula 1.

[0037] In another embodiment, the temperature control device (100) may use some of the variables of Equation 1 above as predicted values. For example, the amount of change in the transformer load rate may be a predicted value for a certain future point in time (e.g., 30 minutes later) rather than the current point in time. The temperature control device (100) may predict the change in the load rate at a certain future point in time (30 minutes later) by inputting the transformer load rate collected over a certain past period (e.g., 24 hours) from the current point in time into a time series analysis model (e.g., LSTM model). In addition, various types of analysis models that predict data at a future point in time based on time series data over a certain past period may be used to predict the transformer load rate.

[0038] Alternatively, the temperature control device (100) may use the outside air temperature as a predicted value in Equation 1. The temperature control device (100) may use the outside air temperature at a certain future point in time (e.g., 30 minutes, etc.) identified by connecting to a weather agency server, etc. Alternatively, the temperature control device (100) may predict the outside air temperature at a certain future point in time, such as 30 minutes later, through time series analysis based on the outside air temperature collected over a certain past period (e.g., 1 hour, etc.).

[0039] The temperature control device (100) can also use predicted values ​​for solar radiation. The temperature control device (100) can predict solar radiation at a certain future point in time using a location-based solar radiation model (clear sky model) or predict solar radiation at a certain future point in time based on an average solar radiation pattern by time period.

[0040] The temperature control device (100) can perform preemptive control of the cooling device by using a predicted value at a future point in time to set the target temperature. That is, when the predicted temperature identified through the temperature prediction model is higher than the target temperature and the cooling device is operated in advance, the temperature control device can optimize the operation of the cooling device by preemptively changing the target temperature according to future conditions (e.g., transformer load rate, ambient temperature, solar radiation, etc. at a future point in time). For example, if the target temperature decreases over time, the temperature control device can gradually decrease the intensity of the cooling device, and conversely, if the target temperature increases over time, the temperature control device can gradually increase the intensity of the cooling device.

[0041] FIG. 6 is a diagram illustrating an example of a method for calculating a control value of a cooling device according to an embodiment of the present invention.

[0042] Referring to FIG. 6, the temperature control device (100) can calculate an operation method that minimizes the energy consumption (600) of the cooling device while minimizing the power loss (610) of the transformer or the insulation degradation index (620) when operating the cooling device. In one embodiment, the temperature control device (100) can calculate an optimal control value, such as the intensity of the cooling device, using an objective function (J) (630).

[0043]

[0044] Here, E cool is the energy consumption of the cooling device, and P c(θ,L) represents the power loss of the transformer according to the transformer temperature (θ) and load factor (L) (relative to rating, 0~1 or %), AF(θ) represents the insulation degradation index according to the temperature (θ), and λ is a weighting factor.

[0045] The temperature control device (100) can determine the transformer power loss (610) or insulation degradation index (620) by measuring the temperature or current of the transformer through various sensors. Since the method for determining the transformer power loss (610) and insulation degradation index (620) is already widely known, further explanation regarding this is omitted.

[0046] The temperature control device (100) finds the energy consumption of the cooling device at which the objective function (J) (630) is minimized. For example, when the temperature inside the electrical room rises, the power loss (610) of the transformer increases and the insulation degradation index (620) rises, so the operation of the cooling device must be increased, but in this case, the energy consumption (600) of the cooling device increases. Therefore, a point where the objective function (J) (630) is minimized is found so that the energy consumption (600) of the cooling device is minimized while the power loss (610) of the transformer is minimized and the rise in the insulation degradation index (620) due to the temperature rise can be suppressed. Various existing optimization algorithms can be used in the optimization process of finding the optimal combination of conflicting variables included in the objective function (630). For example, Model Predictive Control (MPC) / Model Predictive Control (PI) and gradient-based optimization techniques can be used.

[0047] When the energy consumption amount is determined through the objective function (630), the temperature control device (100) operates the cooling device within the limit of the energy consumption amount.

[0048] FIG. 7 is a diagram illustrating the configuration of an example of a temperature control device according to an embodiment of the present invention.

[0049] Referring to FIG. 7, the temperature control device (100) includes a spatial analysis unit (700), an instrument analysis unit (710), a temperature prediction model (720), a temperature prediction unit (730), a control unit (740), an optimization unit (750), and a target temperature setting unit (760). Depending on the embodiment, some components may be omitted or additional components may be included. Additionally, the temperature control device (100) may be implemented as a computing device including memory, a processor, and an input / output device. In this case, each component may be implemented as software (program), loaded into memory, and then executed by the processor.

[0050] The spatial analysis unit (700) identifies spatial information including the temperature inside the electrical room of the multi-unit dwelling where the transformer is located. In one embodiment, the spatial analysis unit (700) may generate spatial information including information such as humidity, outside temperature, and solar radiation, along with the temperature (or temperature distribution) inside the electrical room.

[0051] The device analysis unit (710) identifies power equipment information including the transformer load rate. In one embodiment, the device analysis unit (710) measures the transformer (winding, etc.) temperature, current, etc. along with the transformer load rate to identify the transformer's power loss, insulation degradation index, etc., and generates power equipment information including the above.

[0052] The temperature prediction model (720) is a time series analysis model that predicts the temperature at a future point in time based on time series data regarding spatial information and power equipment information. An example of the temperature prediction model (720) is illustrated in FIG. 3.

[0053] The temperature prediction unit (730) inputs spatial information and power equipment information collected over a certain period in the past from the current point in time into a temperature prediction model to determine the predicted temperature.

[0054] The control unit (740) controls the operation of the cooling device in the electrical room based on the predicted temperature. For example, the control unit (740) can pre-operate the cooling device if the predicted temperature is higher than the target temperature. An example of a method for controlling the cooling device based on the predicted temperature is illustrated in FIG. 4.

[0055] The optimization unit (750) finds the point where the objective function is minimized, which is defined as the power loss according to the load and temperature of the transformer, the insulation degradation index according to the temperature of the transformer, and the weighted sum of the energy consumption of the cooling device to lower the temperature of the electrical room to the target temperature. An example of a method for finding the optimal control value of the cooling device is illustrated in FIG. 6. The control unit (740) can control the cooling device based on the energy consumption of the cooling device identified through the optimization process of the objective function.

[0056] The target temperature setting unit (760) dynamically sets the target temperature according to the load rate of the transformer and the ambient temperature. An example of a method for dynamically setting the target temperature is illustrated in FIG. 5. The control unit (740) can control the cooling device based on the periodically changing target temperature and the predicted temperature.

[0057] The present invention can also be implemented as computer-readable program code on a computer-readable recording medium. A computer-readable recording medium includes all types of recording devices in which data that can be read by a computer system is stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc. Additionally, computer-readable recording media can be distributed across networked computer systems, allowing computer-readable code to be stored and executed in a distributed manner.

[0058] The present invention has been described above with reference to its preferred embodiments. Those skilled in the art will understand that the present invention may be embodied in modified forms without departing from the essential characteristics of the invention. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the invention is defined by the claims, not by the foregoing description, and all variations within the scope of the claims should be interpreted as being included in the invention.

Claims

Claim 1 A temperature control method performed by a temperature control device including a processor, memory, and input / output device, comprising: a step of identifying spatial information including the temperature within the electrical room of a multi-unit dwelling where a transformer is located; a step of identifying power equipment information including the transformer load rate; a step of identifying a predicted temperature by inputting spatial information and power equipment information collected over a past period from the present time into a temperature prediction model that predicts the temperature at a future point in time based on time-series data regarding spatial information and power equipment information; and a step of controlling a cooling device in the electrical room based on the predicted temperature. Claim 2 A method for controlling the temperature of an electrical room in a multi-unit dwelling, characterized in that, in claim 1, the step of identifying spatial information includes the step of identifying the spatial temperature distribution within the electrical room through temperature sensors located at a plurality of points within the electrical room. Claim 3 A method for controlling the temperature of an electrical room in a multi-unit dwelling, characterized in that, in claim 1, the step of identifying spatial information includes the step of collecting spatial information including humidity, outside temperature, or solar radiation along with the temperature inside the electrical room, and the step of identifying power equipment information includes the step of collecting power equipment information including the temperature or current of the transformer along with the transformer load rate. Claim 4 A method for controlling the temperature of an electrical room in a multi-unit dwelling, wherein, in claim 1, the temperature prediction model is a time series analysis model that predicts data at a future point in time based on time series data, and is implemented using LSTM (Long Short-Term Memory model), ARIMA (Autoregressive Integrated Moving Average), or gradient boosting. Claim 5 A method for controlling the temperature of an electrical room in a multi-unit dwelling, wherein, in claim 1, the controlling step includes the step of operating the cooling device in advance if the current internal temperature of the electrical room has not reached the target temperature but the predicted temperature is higher than the target temperature. Claim 6 A method for controlling the temperature of an electrical room in a multi-unit dwelling, characterized in that, in claim 1, the controlling step comprises adjusting the wind direction and wind speed of the cooling device based on the predicted temperature of a plurality of points within the electrical room. Claim 7 A method for controlling the temperature of an electrical room in a multi-unit dwelling, characterized in that, in claim 1, it further comprises the step of optimizing an objective function defined as the power loss according to the load and temperature of the transformer, the insulation degradation index according to the temperature of the transformer, and the weighted sum of the energy consumption of the cooling device for lowering the temperature of the electrical room to a target temperature; and the controlling step comprises the step of controlling the cooling device according to the energy consumption of the cooling device identified through the optimization process of the objective function. Claim 8 A method for controlling the temperature of an electrical room in a multi-unit dwelling, characterized in that, in claim 1, it further includes the step of dynamically setting a target temperature according to the load rate of the transformer and the ambient temperature, and the controlling step includes the step of operating the cooling device if the predicted temperature is greater than or equal to the target temperature. Claim 9 delete Claim 10 A temperature control device for an electrical room of a multi-unit dwelling, characterized by comprising: a spatial analysis unit for identifying spatial information including the temperature inside the electrical room of a multi-unit dwelling where a transformer is located; an equipment analysis unit for identifying power equipment information including the transformer load rate; a temperature prediction model for predicting a future temperature based on time series data regarding the spatial information and the power equipment information; a temperature prediction unit for identifying a predicted temperature by inputting the spatial information and the power equipment information collected over a past period from the present time into the temperature prediction model; and a control unit for controlling the operation of a cooling device in the electrical room based on the predicted temperature. Claim 11 A temperature control device for an electrical room of a multi-unit dwelling, further comprising, in claim 10, an optimization unit that finds a point where an objective function is minimized, defined as the power loss according to the load and temperature of the transformer, the insulation degradation index according to the temperature of the transformer, and the weighted sum of the energy consumption of the cooling device for lowering the temperature of the electrical room to a target temperature; and wherein the control unit controls the cooling device based on the energy consumption of the cooling device identified through the optimization process of the objective function. Claim 12 A temperature control device for an electrical room of a multi-unit dwelling, wherein, in claim 10, it further comprises a target temperature setting unit that dynamically sets a target temperature according to the load rate of the transformer and the ambient temperature, and wherein the control unit operates the cooling device if the predicted temperature is greater than or equal to the target temperature. Claim 13 A computer-readable recording medium storing a computer program for performing the method described in paragraph 1.

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