CN117233449B - Test method for realizing harmonic voltage measurement based on application quantum technology - Google Patents
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Abstract
The invention discloses a testing method for realizing harmonic voltage measurement based on an application quantum technology. The method analyzes several points in a harmonic voltage measurement method applying a programmable Josephson quantum voltage reference from two aspects; the method comprises the steps of discussion of important parameters such as the number N of steps, the number M of sampling points on each step, the number N of iterations and the like from the angle of differential sampling, the calculation of the error level of a measurement result from the angle of an improved quasi-synchronous sampling method, an error level calculation formula and an error estimation calculation example of a specific experiment are provided, and the method is helpful for setting related parameters better in actual use.
Description
Technical Field
The invention relates to the fields of electromagnetic measurement, signal processing and error analysis, in particular to a testing method for realizing harmonic voltage measurement based on an application quantum technology.
Background
In the field of electromagnetic metering, because of the excellent characteristics and mature application of programmable Josephson quantum voltage reference (PJVS), electrical parameters such as voltage, current and power become research hot spots. PJVS has been primarily applied to the measurement and analysis of harmonic voltages, and researchers at home and abroad have developed related works.
When the PJVS is applied to harmonic voltage measurement and analysis, the fundamental wave, each subharmonic component and frequency spectrum information of the measured harmonic voltage signal are generally calculated by performing discrete Fourier transform on the reproduced voltage signal after differential sampling of the measured harmonic voltage and the quantum step voltage. In this process, two main problems need to be solved, one is that the quantum ladder voltage cannot be switched instantaneously when switching steps, so that a transition process occurs, and an influence point of the transition process brings errors in a final measurement result. Secondly, the perfect synchronous sampling is difficult to realize in the sampling process, which brings about the problem of asynchronous sampling, so that the measured voltage signal has synchronous deviation from the ideal signal, and the leakage problem exists after discrete Fourier change, which also introduces small errors in the measurement result.
In order to solve the two problems, a secondary weighted Fourier transform method based on quasi-synchronous sampling is provided, and the method compensates leakage errors caused by asynchronous sampling on the basis of solving the problem of the influence points of the transition process, thereby effectively improving the accuracy of harmonic voltage measurement analysis.
Although the secondary weighted fourier transform method has ideal measurement accuracy, the lack of a test for the influence of the selection of each parameter of the method on the measurement result and calculation of the error level of the measurement result when determining the parameter results in that the method is not perfect and is not easy to actually use, and how to select a specific parameter for measurement is not clear. It is therefore necessary to propose a reasonable and comprehensive test method for this harmonic voltage measurement scheme applying quantum technology.
Disclosure of Invention
The invention provides a testing method for realizing harmonic voltage measurement based on application quantum technology, which analyzes the harmonic voltage measurement method applied with programmable Josephson quantum voltage reference from two aspects, comprises the steps of selecting different parameters to analyze the amplitude level and the final measurement result of differential signals and calculating the measurement result error level when determining the parameters and giving an error level calculation formula, so that the existing measurement scheme is more perfect and is easy to practically use.
According to a first aspect of the invention, analyzing differential signal amplitude and measurement result error from a differential sampling perspective for selected parameters in a harmonic voltage measurement method employing a programmable josephson quantum voltage reference, comprises: the number N of steps, the number M of sampling points on each step, the number L of total sampling points per period and the frequency synchronization error f Δ ；
The harmonic voltage measurement method using the programmable Josephson quantum voltage reference comprises the following steps: a secondary weighted fourier transform method based on quasi-synchronous sampling.
The number N of steps, the number M of sampling points on each step, the number L of total sampling points per period and the frequency synchronization error f are aimed at Δ The testing method comprises the following steps: by controlling the variable method, in which the frequency is synchronized with the error f Δ In the case of a per-cycle sampling point number L determination,respectively analyzing differential signals and measurement results according to different step numbers N and the number M of sampling points on each step; adopting a control variable method, and respectively aiming at different frequency synchronization errors f under the condition that the number N of steps, the sampling point number M on each step and the total sampling point number L of each period are determined Δ And analyzing the differential signals and the measurement results.
Wherein, the relationship between N, M and L is as follows: m=l/N, which means that in the case of L determination, N is determined once, and M is also determined therewith, so N and M do not have to be discussed separately.
According to a second aspect of the invention, the harmonic voltage measurement method to which the programmable josephson quantum voltage reference is applied from the point of view of the improved quasi-synchronous sampling method calculates the error level of the measurement result when determining the parameters and gives an error level calculation formula.
The error level calculation object of the measurement result is a measurement amplitude, and the error level calculation formula is as follows:
Δ＝|γ m | n ≈ξ n
wherein, gamma m And xi are respectively:
wherein L is the number of sampling points per cycle, m is the harmonic frequency, T Δ Is a period synchronization error, T Δ ＝1/f-1/f r F is the ideal fundamental frequency. f (f) r Is the actual fundamental frequency, n is the number of sampling cycles, and also represents the number of iterations.
In the error level calculation formula, gamma m Determined by a recurrence formula defined by quasi-synchronous sampling, the recurrence formula is:
wherein t is 0 For sampling starting point y (t) as the harmonic voltage signal sequence to be measured, ρ t The weight coefficient corresponding to the selected complex product formula (the complex trapezoidal product formula is taken as an example in the invention).
The invention has the advantages that:
the method is more perfect and is easy to use in actual measurement, and provides convenience for selection and determination of each parameter in actual measurement and calculation of error level.
Drawings
The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of exemplary embodiments of the invention, as illustrated in the accompanying drawings.
Fig. 1 shows an overall test scheme block diagram of a test method for implementing harmonic voltage measurement based on application of quantum technology according to the invention.
Fig. 2a, 2b and 2c show graphs of relative positions of a quantum step voltage signal and a harmonic signal to be measured in a certain period, in case of other parameter determination, according to an embodiment of the present invention, of a differential sampling example when N is 20, a differential sampling example when N is 40 and a frequency synchronization deviation.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are illustrated in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows an overall test scheme block diagram of a test method for implementing harmonic voltage measurement based on application of quantum technology according to the invention.
The harmonic voltage measurement scheme applying the quantum technology comprises the following steps: a secondary weighted fourier transform method based on quasi-synchronous sampling.
According to a first aspect of the invention, analyzing the selected important parameters from a differential sampling point of view, comprises: the number N of steps, the number M of sampling points on each step, the number L of total sampling points per period and the frequency synchronization error f Δ ；。
In one example, the test method performed for the number of steps N and the number of sampling points M on each step is:
(1) The number of sampling points per cycle L is set, because the following relationship exists between L, N and M: m=l/N, which means that in the case of L determination, N is once determined, M is also determined therewith, and in the case of each cycle of sampling point determination, the more the number of steps, the fewer the number of step up-sampling points.
(2) Eliminating the influence of asynchronous sampling, and setting the fundamental wave frequency f of the actual harmonic voltage signal to be detected r For ideal fundamental frequency f=50 Hz, i.e. f Δ =0; sampling frequency f s 50L Hz; setting harmonic frequency, amplitude and phase angle of each subharmonic contained in the harmonic voltage to be tested; the iteration number n is set.
(3) Different N and M are respectively set, for example, N is set to be 20 and N is set to be 40, so that M corresponds to 100 and 50 respectively, and a secondary weighted Fourier transform method based on quasi-synchronous sampling is applied to measure the harmonic voltage signals to be measured. Fig. 2a and 2b show schematic diagrams of differential sampling at N of 20 and at N of 40, respectively, and phase modulation is generally performed during differential sampling, as shown by the arrow in fig. 2a, where the harmonic voltage signal to be measured and the quantum step voltage signal intersect at the midpoint of the step, which can reduce the amplitude of the differential signal. .
(4) And measuring the fitting degree of the two waveforms, the differential signal size and the difference of the measurement results, and giving the measurement results of the two parameters N and M.
In one example, for a frequency synchronization error f Δ The testing method comprises the following steps:
(1) Setting sampling points L of each cycle; setting N and M; setting the fundamental wave frequency f of an actual harmonic voltage signal to be measured r If a certain frequency synchronization deviation exists, f Δ ＝|f r -f|; and setting harmonic frequency, amplitude and phase angle of each subharmonic contained in the harmonic voltage to be tested.
(2) Respectively setting frequency synchronization errors f with different magnitudes Δ For 0.02, 0.03, 0.05, 0.1, 0.3 and 0.5 (in Hz), a secondary weighted fourier transform method based on quasi-synchronous sampling is applied to measure the above harmonic voltage signals to be measured.
(3) Measuring the fitting degree of the two waveforms, the difference signal size and the difference of the measurement results, and giving the synchronization error f for different frequencies Δ Is a measurement result of (2); fig. 2c shows that in the presence of a frequency synchronization error, the harmonic voltage signal to be measured and the quantum step voltage signal cannot cross the step midpoint like the arrow shown in fig. 2a even through the phase modulation operation, and the cross point position is more and more shifted from the step midpoint as the sampling time increases, which causes an increase in the amplitude of the differential signal.
From the principle of differential sampling and the test result, in order to obtain an accurate harmonic voltage measurement result, the smaller the amplitude of the differential signal is, the better, and it should be noted that the amplitude refers to an absolute value, and in order to ensure an ideal measurement result, the amplitude of the differential signal should be controlled below 0.4V; by the testing method, proper parameters can be adjusted according to the steps, the amplitude of the differential signal is controlled in an ideal range, and then subsequent voltage measurement and analysis are carried out, so that the accuracy of a measurement result is ensured, and the influence of differential sampling on the error of the final measurement result is minimized.
According to the second aspect of the invention, namely from the perspective of the improved quasi-synchronous sampling method principle, the error level of the measurement result is calculated and an error calculation formula is given under the condition that each parameter is determined.
In one example, the error level for the measured amplitude is calculated as:
Δ＝|γ m | n ≈ξ n
wherein, gamma m And xi are respectively:
wherein, gamma m For a specific calculation, ζ is a calculation derived from the frequency synchronization error, L is the number of sampling points per cycle, m is the number of harmonics, T Δ Is a period synchronization error, T Δ ＝1/f-1/f r F is the ideal fundamental frequency. f (f) r Is the actual fundamental frequency, n is the number of sampling cycles, and also represents the number of iterations.
Wherein, gamma m Determined by a recurrence formula defined by quasi-synchronous sampling, the recurrence formula is:
wherein F is 1 And F n For iterative recursion formula under definition of quasi-synchronous sampling, t 0 For sampling starting point y (t) as the harmonic voltage signal sequence to be measured, ρ t The weight coefficient corresponding to the selected complex product formula (the complex trapezoidal product formula is taken as an example in the invention).
In order to facilitate understanding of the scheme and the effect of the embodiment of the present invention, a specific application example of calculating the error level of the measurement result using the error calculation formula is given below. It will be understood by those of ordinary skill in the art that the examples are for ease of understanding only and that any particular details thereof are not intended to limit the present invention in any way.
Application example 1
The table below gives the individual harmonic specific parameters, including amplitude and phase angle, for five sets of harmonics m, 1 (fundamental), 5, 10, 30 and 50, respectively.
| Harmonic order | 1 | 5 | 10 | 30 | 50 |
| amplitude/V | 1 | 0.3 | 0.2 | 0.02 | 0.01 |
| Phase angle/° | 30 | 48 | 35 | 56 | 84 |
Setting the ideal fundamental wave frequency f to 50Hz, and the actual fundamental wave frequency f r 50.1Hz, the frequency synchronization deviation f Δ Is 0.1Hz; setting the sampling point number L per cycle to 2000 points, and sampling frequency f s For fL, the number of steps per cycle of the quantum-step voltage signal N is 40, and the number of sampling points m=l/N on each step is 50. Through verification, under the experimental parameter setting, the differential signal amplitude can meet the requirements.
In the secondary weighted Fourier transform method based on quasi-synchronous sampling, the required component is increased by an attenuation factor Y due to the existence of synchronous deviation mm At the same time, there are many other unwanted components besides the desired componentComponents, which are also preceded by an attenuation factor Y mm '、Y ml And Y lm . Let omega Δ For angular frequency synchronous deviation omega LS =2pi f, K is the highest harmonic order. When the following condition is satisfied:
|Y mm i will be much larger than the other three attenuation factors, typically Y mm I will be several orders of magnitude higher than the other three attenuation factors. Therefore, when parameters such as amplitude and the like are calculated, only the main attenuation factor and the components thereof are taken into calculation, and other small values are discarded. Therefore, in actual error calculation, the ideal calculation formula |γ is used m | n To calculate the error level will not be accurate enough.
Thus, with xi n Instead of |gamma m | n To calculate the error level of the fundamental amplitude.
Under the above parameter setting, the period synchronization deviation T can be calculated Δ And xi has the value:
taking the absolute error of the amplitude of the highest harmonic measurement result reaching 1E-9 and above as a target, presetting the sampling period number n, namely the quasi-synchronous iteration number to be 3, and using xi in an error level calculation formula n To calculate the error level delta, and delta is approximately equal to zeta n ＝0.002 3 =8.0e-9, and at the same time, taking into account errors introduced in the differential sampling process and the one-time weighting calculation process, allowing a margin for measurement results, optionally increasing the number of iterations by one time, and allowing n=4 to perform the test, so that Δζ≡ n ＝0.002 4 =1.6e-11, and each group of single harmonics can meet the requirement that the absolute error of the amplitude reaches 1E-9 and above.
The table below shows the measured simulation results.
| Harmonic order | 1 | 5 | 10 | 30 | 50 |
| Absolute error of amplitude | 2.3E-14 | 8.0E-14 | 5.5E-13 | 5.1E-11 | 1.5E-10 |
As can be seen from the experimental results, in five groups of single harmonic measurement experiments, the absolute errors of the amplitudes of the subharmonics reach the level of 1.5E-10 and above. This indicates that the above-described error level is calculated in a reasonable and accurate manner.
The technical solutions and examples described above in connection with the drawings are merely illustrative of the present invention, and various modifications or variations will be readily apparent to those skilled in the art based on the application methods and principles disclosed herein, without being limited to the methods described in the above-described specific embodiments of the present invention, therefore, the above-described modes are given by way of preference only and not by way of limitation.
Claims (4)
1. A testing method for realizing harmonic voltage measurement based on application of quantum technology comprises the following steps:
testing parameters in a harmonic voltage measurement method of a programmable Josephson quantum voltage reference, recording and analyzing differential signal levels after differential sampling under different parameter settings, and giving a numerical value level range which needs to be controlled for the amplitude of a differential signal when an ideal result is obtained, wherein the differential signal is a difference value between a harmonic voltage signal to be tested and a quantum ladder voltage signal;
calculating the error level of the measurement result by using an improved quasi-synchronous sampling method principle, and providing an error level calculation formula, wherein the error level calculation formula is as follows:
Δ＝|γ m | n ≈ξ n
wherein, gamma m And xi are respectively:
wherein, gamma m For a specific calculation, ζ is a calculation derived from the frequency synchronization error, L is the number of sampling points per cycle, m is the number of harmonics, T Δ Is a period synchronization error, T Δ ＝1/f-1/f r F is the ideal fundamental frequency, f r Is the actual fundamental frequency, n is the sampling period number and also represents the iteration number; and wherein gamma m Determined by a recurrence formula defined by quasi-synchronous sampling, the recurrence formula is:
wherein F is 1 And F n For iterative recursion formula under definition of quasi-synchronous sampling, t 0 For sampling starting point y (t) as the harmonic voltage signal sequence to be measured, ρ t And (3) calculating a weight coefficient corresponding to the selected complex product formula, wherein L is the total sampling point number of each cycle.
2. The test method for implementing harmonic voltage measurement based on application of quantum technology according to claim 1, wherein the harmonic voltage measurement method using the programmable josephson quantum voltage reference is: a secondary weighted fourier transform method based on quasi-synchronous sampling.
3. A test method for implementing harmonic voltage measurement based on application of quantum technology according to claim 1, wherein the parameters selected in the voltage measurement method comprise: the number N of steps, the number M of sampling points on each step, the number L of total sampling points per period and the frequency synchronization error f Δ 。
4. The method for testing harmonic voltage measurement based on application of quantum technology according to claim 1, wherein the object of calculating the error level of the measurement result is a measurement amplitude.
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| CN110632387A (en) * | 2019-09-23 | 2019-12-31 | 中国计量科学研究院 | Harmonic voltage measuring method based on alternating-current quantum voltage |
| CN115951286A (en) * | 2022-12-13 | 2023-04-11 | 沈阳化工大学 | Calibrating and detecting device for inductive voltage divider tracing to quantum voltage |
| WO2023071672A1 (en) * | 2021-10-25 | 2023-05-04 | 山东大学 | Rapid and precise power grid information sensing method based on nonlinear robust estimation |
| CN116359605A (en) * | 2023-04-21 | 2023-06-30 | 中国计量科学研究院 | Harmonic signal analysis method based on secondary weighting |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110632387A (en) * | 2019-09-23 | 2019-12-31 | 中国计量科学研究院 | Harmonic voltage measuring method based on alternating-current quantum voltage |
| WO2023071672A1 (en) * | 2021-10-25 | 2023-05-04 | 山东大学 | Rapid and precise power grid information sensing method based on nonlinear robust estimation |
| CN115951286A (en) * | 2022-12-13 | 2023-04-11 | 沈阳化工大学 | Calibrating and detecting device for inductive voltage divider tracing to quantum voltage |
| CN116359605A (en) * | 2023-04-21 | 2023-06-30 | 中国计量科学研究院 | Harmonic signal analysis method based on secondary weighting |
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