A method, medium and terminal for fast analysis of power signal harmonics

Abstract

The application is suitable for the field of electric energy metering technology and relates to a fast analysis method for power signal harmonics, a medium and a terminal. The periodical property of the phase rotation factor of the discrete Fourier transform is used to construct a linear convolution system of the sample value sequence and the phase rotation factor of the discrete Fourier transform, the discrete Fourier transform of the sample value sequence is expressed in the form of digital filtering, and finally the harmonic spectrum analysis is completed through the recursive iteration calculation in the form of only real number operation and difference equation. The application effectively solves the problems of spectrum leakage and fence effect caused by non-synchronous sampling and non-integer period truncation during the fundamental / harmonic analysis, and has the advantages of high harmonic analysis accuracy and efficiency, low resource consumption and high real-time property compared with the prior art.

Description

Technical Field

[0001] This invention belongs to the field of power metering technology, and particularly relates to a rapid analysis method, medium and terminal for power signal harmonics. Background Technology

[0002] The combined effects of large-scale integration of new energy sources and widespread use of nonlinear loads have led to the power grid signal exhibiting wide dynamic range and multi-characteristic fluctuations, placing higher demands on the metering accuracy of electricity meters under nonlinear conditions.

[0003] To effectively reduce spectral leakage and picket fence effects caused by asynchronous sampling and non-integer period truncation, the commonly used harmonic analysis method is the windowed interpolation FFT algorithm. This algorithm reduces spectral leakage by using a high-performance window function in the time domain and reduces the picket fence effect by interpolating the spectral calculation results. However, the computational load involved in windowing and interpolation is very large, resulting in low accuracy and efficiency of harmonic analysis of power signals, making it unsuitable for power metering devices with very limited computing resources, such as power meters. Patent application CN102128982A provides a harmonic analysis method based on windowed interpolation FFT fundamental frequency tracking technology. This analysis method includes the following steps: a. Obtaining a high-precision fundamental frequency: Sampling the power signal at a low frequency sampling rate, performing FFT calculation on the sampled data after applying a Hanning window, and then obtaining a high-precision fundamental frequency f through interpolation; b. Fundamental frequency tracking and synchronous frequency doubling: Re-sampling the power signal at a frequency of 128×f, performing FFT calculation on the sampled data, and calculating the amplitude and phase of each harmonic. This patent application also uses windowed interpolation, which involves a large amount of computation and has the same drawbacks as existing technologies.

[0004] Therefore, how to provide an accurate and efficient method for harmonic analysis of power signals is a technical problem that urgently needs to be solved by those in the field. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a rapid analysis method for power signal harmonics, thereby solving the problems of low accuracy and efficiency in power signal harmonic analysis in existing technologies. In addition, this invention also provides a rapid analysis medium and terminal for power signal harmonics.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a rapid analysis method for harmonics in power signals, comprising the following steps:

[0008] S10. Acquire the input electrical signal and obtain the sampled value sequence of the electrical signal;

[0009] S20. Utilizing the periodicity of the discrete Fourier transform phase rotation factor, based on the discrete Fourier transform of the sampled value sequence obtained after acquisition, construct a linear convolution system between the sampled value sequence and the discrete Fourier transform phase rotation factor, and express the discrete Fourier transform in the form of digital filtering.

[0010] S30. Based on the constructed linear convolution system, obtain the system unit sample response corresponding to the convolution kernel function, and the form of the single-pole system function and the corresponding difference equation, so as to realize recursive iterative calculation.

[0011] S40. Merge complex conjugate poles to convert the single-pole system function into the form of a two-pole system function so that the recursive iterative calculation only includes real number operations.

[0012] S50. Using the difference equation form corresponding to the obtained double-pole system function, perform recursive iterative calculation on the sampled value sequence obtained after acquisition to obtain the spectral components of the specified harmonic frequency.

[0013] S60. Calculate the corresponding harmonic amplitude and harmonic phase based on the spectral components of the specified harmonic frequency.

[0014] Furthermore, the following expression is specifically used in S20:

[0015]

[0016]

[0017]

[0018] Where N is the number of sampling points within the time window corresponding to the Discrete Fourier Transform; W N y is the discrete Fourier transform phase rotation factor; x(m) is the sample value at the m-th point in the sample value sequence obtained after S10 acquisition; X(k) is the spectral component output at the k-th point after the sample value sequence undergoes discrete Fourier transform, where k ranges from 0 to N-1; k (n) is the phase rotation factor between the sampled value sequence and the discrete Fourier transform of the sampled value sequence. The nth point convolution output after the linear convolution system.

[0019] Furthermore, the following expression is specifically used in S30:

[0020]

[0021]

[0022]

[0023] Among them, h k u(n) represents the nth point of the unit sampled response of the linear convolutional system constructed in S20; u(n) represents the nth point of the unit step sequence; H k (z) represents the system's unit sample response as h. k The single-pole form of the linear convolution system of (n); z is the independent variable of the system function; y k (n) and y k (n-1) are the nth and n-1th data points after recursive iteration calculation by the difference equation, respectively; x(n) is the sampling point value of the nth point in the sampling value sequence obtained after S10 acquisition.

[0024] Furthermore, the following expression is specifically used in S40:

[0025]

[0026] Among them, H k (z) represents the system's unit sample response as h. k The bipolar form of the linear convolution system of (n); z is the independent variable of the system function.

[0027] Furthermore, the following expression is specifically used in S50:

[0028]

[0029]

[0030]

[0031] Among them, w k (n), w k (n-1), w k (n-2), w k (N) and w k (N-1) represent the nth, n-1th, n-2th, Nth, and N-1th data points after recursive iterative calculation of the difference equation corresponding to the double-pole system function; X(k) is the specified harmonic frequency. Spectral components at that location.

[0032] Furthermore, the following expression is specifically used in S60:

[0033]

[0034]

[0035] Where |X(k)| and arg[X(k)] are the specified harmonic frequencies. The harmonic amplitude and harmonic phase at the point; Re[X(k)] and Im[X(k)] represent the real and imaginary parts of X(k), respectively.

[0036] Furthermore, the frequency corresponding to the spectral component at point k is... The values ​​of m, k, and n all range from 0 to N-1.

[0037] Furthermore, the sampling frequency is f s =12800Hz, fundamental frequency is f1=50±2.5Hz, fundamental frequency amplitude is A1=1A, fundamental frequency phase is φ1=0°, harmonic frequency amplitude is A h =1A, harmonic frequency phase φ h =60°, harmonic order is 2 to 41.

[0038] In a second aspect, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0039] Thirdly, the present invention also provides an electronic terminal, comprising: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the terminal to perform the method described above.

[0040] The rapid analysis method, medium, and terminal for power signal harmonics provided by this invention have at least the following advantages compared with existing technologies:

[0041] Currently, the commonly used harmonic analysis method is the windowed interpolation FFT algorithm. This algorithm reduces spectral leakage by using a high-performance window function in the time domain and reduces the picket fence effect by interpolating the spectral calculation results. However, the computational load involved in windowing and interpolation is very large, resulting in low accuracy and efficiency in power signal harmonic analysis. This invention has a simple process and is easy to operate. It utilizes the periodicity of the discrete Fourier transform phase rotation factor to construct a linear convolution system of the sampled value sequence and the discrete Fourier transform phase rotation factor, representing the discrete Fourier transform of the sampled value sequence as a digital filter. Finally, it completes the harmonic spectrum analysis through recursive iterative calculations in the form of difference equations, involving only real number operations. This invention effectively solves the problems of spectral leakage and picket fence effect caused by asynchronous sampling and non-integer period truncation in fundamental / harmonic analysis. Compared with existing methods, it has the advantages of high accuracy and efficiency in harmonic analysis, low resource consumption, and high real-time performance. Attached Figure Description

[0042] To more clearly illustrate the solution of the present invention, a brief introduction will be given to the drawings used in the description of the embodiments below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0043] Figure 1 A flowchart illustrating a rapid analysis method for power signal harmonics provided in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram illustrating the harmonic analysis principle of a rapid analysis method for power signal harmonics provided in an embodiment of the present invention. Detailed Implementation

[0045] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0047] This invention provides a rapid analysis method for power signal harmonics, applied to the analysis of fundamental / harmonic waves in power signals. The rapid analysis method for power signal harmonics includes the following steps:

[0048] S10. Acquire the input electrical signal to obtain a sequence of sampled electrical signal values; S20. Utilize the periodicity of the discrete Fourier transform phase rotation factor, and construct a linear convolution system between the sampled value sequence and the discrete Fourier transform phase rotation factor based on the discrete Fourier transform of the acquired sampled value sequence, expressing the discrete Fourier transform in the form of digital filtering; S30. Based on the constructed linear convolution system, obtain the system unit sample response corresponding to the convolution kernel function, and the form of the single-pole system function and the corresponding difference equation, to achieve recursive iterative calculation; S40. Merge complex conjugate poles, converting the single-pole system function into the form of a double-pole system function, so that the recursive iterative calculation only includes real number operations; S50. Use the difference equation form corresponding to the obtained double-pole system function to perform recursive iterative calculation on the acquired sampled value sequence to obtain the spectral components of the specified harmonic frequency; S60. Calculate the corresponding harmonic amplitude and harmonic phase based on the spectral components of the specified harmonic frequency.

[0049] This invention effectively solves the problems of spectral leakage and picket fence effect caused by asynchronous sampling and non-integer period truncation during fundamental / harmonic analysis, and also features high accuracy, low resource consumption, and high real-time performance in harmonic analysis.

[0050] This invention provides a rapid analysis method for power signal harmonics, applied to the analysis of fundamental / harmonic frequencies in power signals, combined with... Figure 1 and Figure 2 In this embodiment, the rapid analysis method for power signal harmonics includes the following steps:

[0051] S10. Acquire the input electrical signal and obtain the sampled value sequence of the electrical signal.

[0052] S20. Utilizing the periodicity of the discrete Fourier transform phase rotation factor, based on the discrete Fourier transform of the sampled value sequence obtained after acquisition, construct a linear convolution system between the sampled value sequence and the discrete Fourier transform phase rotation factor, and express the discrete Fourier transform in the form of digital filtering.

[0053] Specifically, in this embodiment, the discrete Fourier transform of the sampled value sequence obtained after acquisition is:

[0054]

[0055] in .

[0056] Using the discrete Fourier transform phase rotation factor W N periodicity This yields the linear convolution form of the sampled value sequence and the discrete Fourier transform phase rotation factor:

[0057]

[0058] sequence y k (n) is defined as:

[0059]

[0060] according to Another representation of the spectral component at the k-th point after the discrete Fourier transform of the sampled value sequence is obtained:

[0061]

[0062] Where N is the number of sampling points within the time window corresponding to the Discrete Fourier Transform; W NLet be the discrete Fourier transform phase rotation factor; x(m) is the sample value at the m-th point in the sample value sequence obtained after step S10, where m ranges from 0 to N-1; X(k) is the output spectral component at the k-th point after the discrete Fourier transform of the sample value sequence, and the frequency corresponding to the spectral component at the k-th point is . k takes values ​​from 0 to N-1; y k (n) is the phase rotation factor between the sampled value sequence and the discrete Fourier transform of the sampled value sequence. The nth point convolution output after the linear convolution system, where n ranges from 0 to N.

[0063] S30. Based on the constructed linear convolution system, obtain the system unit sample response corresponding to the convolution kernel function, and the form of the single-pole system function and the corresponding difference equation, so as to realize recursive iterative calculation.

[0064] Specifically, in this embodiment, because The unit sample response of the linear convolution system of the sampled value sequence and the discrete Fourier transform phase rotation factor is obtained:

[0065]

[0066] Because of the system function definition of sequences The system function in single-pole form of the linear convolution system of the sampled value sequence and the discrete Fourier transform phase rotation factor is obtained:

[0067]

[0068] Based on the mapping relationship between the system function and the difference equation, the difference equation form of the linear convolution system of the sampled value sequence and the discrete Fourier transform phase rotation factor is obtained:

[0069]

[0070] Among them, h k u(n) represents the nth point of the unit sampled response of the linear convolutional system constructed in step S20; u(n) represents the nth point of the unit step sequence; H k (z) represents the system's unit sample response as h. k The single-pole form of the linear convolution system of (n); z is the independent variable of the system function; y k (n) and y k (n-1) are the nth and n-1th data points after recursive iteration calculation by the difference equation, respectively; x(n) is the sampling point value of the nth point in the sampling value sequence obtained after step S10.

[0071] S40. Merge complex conjugate poles to transform the single-pole system function into a two-pole system function so that the recursive iterative calculation only involves real number operations, thereby avoiding complex number operations.

[0072] Specifically, in this embodiment, based on the single-pole system function, a resonator pair with complex conjugate poles is constructed and merged to obtain the two-pole form of the system function of the linear convolution system of the sampled value sequence and the discrete Fourier transform phase rotation factor:

[0073]

[0074] Among them, H k (z) represents the system's unit sample response as h. k The bipolar form of the linear convolution system of (n); z is the independent variable of the system function.

[0075] S50. Using the difference equation form corresponding to the obtained double-pole system function, perform recursive iterative calculation on the sampled value sequence obtained after acquisition to obtain the spectral components of the specified harmonic frequency.

[0076] Specifically, in this embodiment, an intermediate sequence w is introduced. k (n) and the corresponding z-transform W k (z), let This yields the cascaded form of the two-pole system function:

[0077]

[0078]

[0079] Based on the mapping relationship between the system function and the difference equation, and as follows: Figure 2 The direct Type II signal flow graph of the two-pole system function shown is used to obtain the difference equation form corresponding to the two-pole system function:

[0080]

[0081]

[0082] The difference equation form corresponding to the obtained two-pole system function is used to perform recursive iterative calculations on the sampled value sequence obtained after acquisition. This yields the spectral components of the specified harmonic frequency.

[0083]

[0084] In the formula, w k (n), w k (n-1), w k (n-2), w k (N) and wk (N-1) represent the nth, n-1th, n-2th, Nth, and N-1th data points after recursive iterative calculation of the difference equation corresponding to the double-pole system function; X(k) is the specified harmonic frequency. Spectral components at that location.

[0085] S60. Calculate the corresponding harmonic amplitude and harmonic phase based on the spectral components of the specified harmonic frequency.

[0086] Specifically, in this embodiment, the following formula is used for calculation:

[0087]

[0088]

[0089] Where |X(k)| and arg[X(k)] are the specified harmonic frequencies. The harmonic amplitude and harmonic phase at the specified location; X(k) is the specified harmonic frequency obtained in step S50. The spectral components at the given location; Re[X(k)] and Im[X(k)] represent the real and imaginary parts of X(k), respectively.

[0090] In this embodiment, the specified harmonic frequency obtained in step S50 The spectral component X(k) at point X(k) = 0.5 + j0.866 yields the corresponding harmonic amplitude and harmonic phase.

[0091]

[0092]

[0093] The fundamental / harmonic rapid analysis method of this embodiment was verified under the following experimental conditions, where the sampling frequency was: f s =12800Hz; Fundamental frequency: f1=50±2.5Hz; Fundamental frequency amplitude: A1=1A; Fundamental frequency phase: φ1=0°; Harmonic frequency amplitude: A h =1A; Harmonic frequency phase: φ h =60°; harmonic order 2-41.

[0094] Under the above experimental conditions, the harmonic calculation errors of the power signal harmonic rapid analysis method in this embodiment are shown in Tables 3 and 4, respectively. Table 3 shows the harmonic error diagram at a frequency of 47.5Hz, and Table 4 shows the harmonic error diagram at a frequency of 52.5Hz. It is easy to see from the tables that when the fundamental frequency is f1=50±2.5Hz, the number of sampling points in one cycle is 243.8 and 269.5 points, respectively. That is, the number of sampling points in the time window corresponding to the discrete Fourier transform is a non-integer power of 2. After adopting the power signal harmonic rapid analysis method in this embodiment, the harmonic calculation error is within ±0.09%, and all errors are within 20% of the national standard error limit of Class 1 harmonic active energy meters. It effectively solves the problems of spectrum leakage and picket fence effect caused by asynchronous sampling and non-integer period truncation during harmonic analysis. Moreover, the harmonic calculation accuracy is high, and the calculation amount is only half that of the windowed interpolation FFT algorithm when analyzing a small number of harmonic orders.

[0095] Table 3

[0096] Serial Number Harmonic number Harmonic amplitude error (%) Harmonic phase error (°) 1 1 0.014 0.009 2 2 0.022 0.011 3 3 0.025 0.011 4 4 0.033 0.012 5 5 -0.035 0.012 6 10 -0.047 0.013 7 11 -0.048 0.014 8 20 -0.063 0.014 9 21 -0.066 0.014 10 30 -0.074 0.014 11 31 -0.077 0.015 12 40 -0.083 0.016 13 41 -0.086 0.016

[0097] Table 4

[0098] Serial Number Harmonic number Harmonic amplitude error (%) Harmonic phase error (°) 1 1 0.012 0.010 2 2 0.021 0.012 3 3 0.024 0.011 4 4 0.035 0.013 5 5 -0.034 0.012 6 10 -0.044 0.013 7 11 -0.046 0.014 8 20 -0.061 0.015 9 21 -0.062 0.014 10 30 -0.072 0.015 11 31 -0.075 0.015 12 40 -0.080 0.017 13 41 -0.084 0.017

[0099] This invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods in this embodiment.

[0100] This invention also provides an electronic terminal, including: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the terminal performs any of the methods in this embodiment.

[0101] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0102] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0103] The fast analysis method, medium, and terminal for power signal harmonics described in the above embodiments, compared with existing technologies, address the challenges of the commonly used harmonic analysis method, which is the windowed interpolation FFT algorithm. This algorithm reduces spectral leakage by employing a high-performance window function in the time domain and reduces the picket fence effect by interpolating the spectral calculation results. However, the computational load involved in windowing and interpolation is very large, resulting in low accuracy and efficiency in power signal harmonic analysis. This invention features a simple process and convenient operation. Utilizing the periodicity of the discrete Fourier transform phase rotation factor, it constructs a linear convolution system between the sampled value sequence and the discrete Fourier transform phase rotation factor, representing the discrete Fourier transform of the sampled value sequence as a digital filter. Finally, it completes the harmonic spectrum analysis through recursive iterative calculations involving only real number operations and difference equations. This invention effectively solves the problems of spectral leakage and picket fence effect caused by asynchronous sampling and non-integer period truncation during fundamental / harmonic analysis. Compared with existing methods, it has the advantages of high accuracy and efficiency in harmonic analysis, low resource consumption, and high real-time performance.

[0104] Obviously, the embodiments described above are merely preferred embodiments of the present invention, and not all embodiments. The accompanying drawings illustrate preferred embodiments of the present invention, but do not limit the scope of the patent. The present invention can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this invention.

Claims

1. A rapid analysis method for harmonics in power signals, characterized in that, Includes the following steps: S10. Acquire the input electrical signal and obtain the sampled value sequence of the electrical signal; S20. Utilizing the periodicity of the discrete Fourier transform phase rotation factor, based on the discrete Fourier transform of the sampled value sequence obtained after acquisition, construct a linear convolution system between the sampled value sequence and the discrete Fourier transform phase rotation factor, and express the discrete Fourier transform in the form of digital filtering. The following expression is specifically used in S20: Where N is the number of sampling points within the time window corresponding to the Discrete Fourier Transform; W N y is the discrete Fourier transform phase rotation factor; x(m) is the sample value at the m-th point in the sample value sequence obtained after S10 acquisition; X(k) is the spectral component output at the k-th point after the sample value sequence undergoes discrete Fourier transform, where k ranges from 0 to N-1; k (n) is the phase rotation factor between the sampled value sequence and the discrete Fourier transform of the sampled value sequence. The nth point convolution output after a linear convolution system; S30. Based on the constructed linear convolution system, obtain the system unit sample response corresponding to the convolution kernel function, and the form of the single-pole system function and the corresponding difference equation, so as to realize recursive iterative calculation. The following expression is specifically used in S30: Among them, h k u(n) represents the nth point of the unit sampled response of the linear convolutional system constructed in S20; u(n) represents the nth point of the unit step sequence; H k (z) represents the system's unit sample response as h. k The single-pole form of the linear convolution system of (n); z is the independent variable of the system function; y k (n) and y k (n-1) are the nth and (n-1)th data points after recursive iterative calculation using the difference equation, respectively; x(n) is the sampling point value of the nth point in the sampling value sequence obtained after S10 acquisition; S40. Merge complex conjugate poles to convert the single-pole system function into the form of a two-pole system function so that the recursive iterative calculation only includes real number operations. The following expression is specifically used in S40: Among them, H k (z) represents the system's unit sample response as h. k The bipole form of the linear convolution system of (n); z is the independent variable of the system function; S50. Using the difference equation form corresponding to the obtained double-pole system function, perform recursive iterative calculation on the sampled value sequence obtained after acquisition to obtain the spectral components of the specified harmonic frequency. The following expression is specifically used in S50: Among them, w k (n), w k (n-1), w k (n-2), w k (N) and w k (N-1) represent the nth, n-1th, n-2th, Nth, and N-1th data points after recursive iterative calculation of the difference equation corresponding to the double-pole system function; X(k) is the specified harmonic frequency. spectral components at the location; S60. Calculate the corresponding harmonic amplitude and harmonic phase based on the spectral components of the specified harmonic frequency.

2. The method for rapid analysis of power signal harmonics according to claim 1, characterized in that, The specific expression used in S60 is as follows: Where |X(k)| and arg[X(k)] are the specified harmonic frequencies. The harmonic amplitude and harmonic phase at the point; Re[X(k)] and Im[X(k)] represent the real and imaginary parts of X(k), respectively.

3. The method for rapid analysis of power signal harmonics according to claim 1, characterized in that, The frequency corresponding to the spectral component at point k is The values ​​of m, k, and n all range from 0 to N-1.

4. The rapid analysis method for power signal harmonics according to claim 1, characterized in that, The sampling frequency is f s =12800Hz, fundamental frequency is f1=50±2.5Hz, fundamental frequency amplitude is A1=1A, fundamental frequency phase is φ1=0°, harmonic frequency amplitude is A h =1A, harmonic frequency phase φ h =60°, harmonic order is 2 to 41.

5. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 4.

6. An electronic terminal, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the terminal to perform the method as described in any one of claims 1 to 4.

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