Harmonic metering method, medium, system and harmonic energy meter

Abstract

The application discloses a kind of harmonic metering method, medium, system and harmonic watt-hour meter, method includes the following steps: S1, the voltage and current of three-phase power grid are obtained, obtain the discrete voltage sample value sequence and current sample value sequence, and the period value of voltage is calculated;S2, according to the period value of voltage, voltage sample value sequence and current sample value sequence are interpolated and resampled;S3, the voltage sample value sequence and current sample value sequence after interpolation and resampling are analyzed by FFT transform, and FFT analysis result is obtained;S4, according to FFT analysis result, harmonic voltage, harmonic current and total harmonic active power are calculated.The application realizes sampling synchronization processing by Lagrange polynomial interpolation and resampling technology, improves harmonic analysis accuracy;And the corresponding compensation is carried out to harmonic amplitude error, further improves harmonic analysis accuracy.

Description

Technical Field

[0001] This invention relates to the field of electricity meter technology, specifically to a harmonic metering method, medium, system, and harmonic electricity meter. Background Technology

[0002] The continuous integration of new energy sources and novel nonlinear loads into the current power grid has made the operating conditions of electricity meters more complex, manifested in more dynamic changes in current, more complex waveform envelopes, and numerous impacts. Unstable energy sources such as wind and solar power bring dynamic changes to the power grid, while high-energy-consuming loads such as electrified railways, electrolytic aluminum equipment, electric arc furnaces, and rolling mills bring even more impacts. These loads not only exhibit instability and randomness but also complex characteristics such as three-phase balance, harmonics, interharmonics, and dramatic voltage and current fluctuations, directly affecting the accuracy of electricity metering. This means that electricity metering instruments designed based on sinusoidal circuit power theory or traditional non-sinusoidal circuit power theory cannot accurately reflect the electrical energy absorbed from the power system. In a nonlinear power consumption environment, the accuracy of electricity metering not only affects the economic interests of power investors and operators but also the interests of every user. The accuracy of reactive power metering directly affects the accuracy of voltage levels, power factors, and electricity metering data. Therefore, it is necessary to study metering methods under nonlinear load access of electricity meters, including harmonic measurement, harmonic and fundamental energy metering, and reactive energy methods, in order to adapt to the non-steady-state and non-sinusoidal working environment of the power grid.

[0003] In harmonic analysis of nonlinear loads, asynchronous sampling is the main cause of errors in electricity metering. Methods to reduce the impact of asynchronous sampling mainly fall into two categories: windowed interpolation algorithms and synchronous sampling techniques. Applying a cosine window in the time domain can effectively reduce spectral leakage, and performing spectral interpolation on the FFT results in the frequency domain can reduce errors caused by the picket fence effect. However, windowing and spectral interpolation involve large amounts of computation, including solving high-order linear equations, division operations, and spectral peak searches, which places high demands on CPU performance and makes them unsuitable for electricity meter platforms.

[0004] There are two types of synchronous sampling techniques: hardware synchronous sampling and software synchronous sampling. Hardware synchronous sampling uses a phase-locked loop (PLL) to track the fundamental frequency with the sampling frequency. However, it requires low-pass filtering of the input signal to remove DC and harmonic components other than the power frequency. When the sampling frequency is high, the PLL has a large division factor, resulting in a delay of several hundred milliseconds. Moreover, this technique can only be used on ADCs based on successive approximation (SAR) and can be hardware-triggered for sampling. Some other types of ADCs, such as Σ-Δ ADCs, cannot use this technique because their sampling interval cannot be finely adjusted.

[0005] Software-synchronized sampling achieves frequency tracking by fine-tuning the ADC sampling interval using a timer or other programmable delay module based on the measured input signal frequency. However, this algorithm is only applicable to SAR ADCs. High-resolution, highly integrated, and low-cost Σ-Δ ADCs have excessively long startup times, making this technique unsuitable. Furthermore, analog sampling in high-precision power metering systems typically requires Σ-Δ ADCs. Therefore, asynchronous sampling of Σ-Δ ADCs and their application in power metering for harmonic analysis using FFT are pressing issues that need to be addressed. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a harmonic metering method, medium, system and harmonic energy meter with high analysis accuracy, addressing the technical problems existing in the prior art.

[0007] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows:

[0008] A harmonic measurement method, characterized by comprising the following steps:

[0009] S1. Obtain the voltage and current of the three-phase power grid, obtain discrete voltage sample value sequences and current sample value sequences, and calculate the periodic value of the voltage;

[0010] S2. Interpolate and resample the voltage and current sample value sequences based on the voltage period value;

[0011] S3. Perform harmonic analysis on the interpolated and resampled voltage and current sample sequences using FFT transformation to obtain the FFT analysis results;

[0012] S4. Calculate the harmonic voltage, harmonic current and total harmonic active power based on the FFT analysis results.

[0013] Preferably, in step S2, the voltage sample value sequence and the current sample value sequence are interpolated using a Lagrange interpolation polynomial.

[0014] Preferably, in step S3, the FFT analysis results include the amplitude and phase values ​​corresponding to each harmonic.

[0015] Preferably, in step S3, the harmonic amplitude error caused by interpolation is curve-fitted to establish an amplitude compensation model based on univariate linear regression, and the harmonic amplitude error after interpolation is compensated accordingly.

[0016] Preferably, the specific process of harmonic amplitude error compensation is as follows:

[0017] Using the frequency offset Δf as the variable and the harmonic amplitude error e as the dependent variable, n corresponding frequency offsets and harmonic amplitude errors are used as independent observation samples (Δf). i ,e i Performing univariate linear regression analysis on i = 1, 2, ..., n, we obtain the best estimates of parameters a and b in the following formula. and Right now:

[0018]

[0019] In the above formula, the optimal estimates of parameters a and b can be calculated using the following formula:

[0020]

[0021] in:

[0022]

[0023]

[0024] Finally, the theoretical error of each harmonic amplitude is calculated based on the real-time frequency and the fitting curve obtained by the above formula, and the measured value is corrected.

[0025] Preferably, in step S4, the periodic average power obtained by shifting the phase of each harmonic voltage by 90° using a Hilbert filter is taken as the total reactive power, that is, the algebraic sum of the reactive power of each harmonic.

[0026] Preferably, in step S4, the Hilbert filter is an IIR type Hilbert filter, which is designed using an elliptic half-band filter.

[0027] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, the computer program performing the steps of the method described above when run by a processor.

[0028] The present invention further discloses a harmonic metering system, including a memory and a processor, wherein the memory stores a computer program, and the computer program executes the steps of the method described above when run by the processor.

[0029] This invention also discloses a harmonic energy meter, comprising a metering module, a management module, and a power supply module. The metering module includes an A / D converter and a control unit. The A / D converter is connected to the control unit and is used to receive phase voltage and current signals, perform analog-to-digital conversion, and send them to the control unit. The control unit is used to complete the metering of electrical energy according to the harmonic metering method as described in any one of claims 1-7. The management module is connected to the control unit and is used to complete data statistics, storage, communication, and display.

[0030] Compared with the prior art, the advantages of the present invention are as follows:

[0031] This invention achieves sampling synchronization through Lagrange polynomial interpolation and resampling techniques, thereby improving the accuracy of harmonic analysis. Curve fitting is performed on the harmonic amplitude error caused by the Lagrange interpolation synchronization process to establish an amplitude compensation model based on univariate linear regression. This model compensates for the harmonic amplitude error after interpolation, further improving the accuracy of harmonic analysis. Furthermore, by designing an IIR-type Hilbert filter using an elliptic half-band filter, the periodic average power obtained after shifting each harmonic voltage by 90° is used as the total reactive power. This achieves higher amplitude and phase shift accuracy over a wide frequency range and has the advantages of lower order, smaller computational load, and smaller data storage requirements. Attached Figure Description

[0032] Figure 1 This is a flowchart of an embodiment of the harmonic measurement method of the present invention.

[0033] Figure 2 This is a schematic diagram of the Lagrange quadratic interpolation method of the present invention.

[0034] Figure 3 This is a schematic diagram illustrating the errors of linear interpolation and Lagrange interpolation in this invention; where (a) represents linear interpolation and (b) represents Lagrange interpolation.

[0035] Figure 4 This is an error curve diagram after harmonic amplitude compensation in this invention.

[0036] Figure 5 The diagram shows the amplitude and phase characteristics of the Hilbert filter in this invention; where (a) is the amplitude frequency characteristic and (b) is the phase frequency characteristic.

[0037] Figure 6 This is a hardware structure topology diagram of the harmonic energy meter in this invention.

[0038] Figure 7 This is a software design architecture diagram of the harmonic energy meter in this invention.

[0039] Figure 8 This is a graph showing the comparative test results of the harmonic performance in this invention.

[0040] Figure 9 The diagram shows the reactive power measurement error of the Hilbert filter in this invention; where (a) is the current-metering error diagram and (b) is the harmonic order-metering error diagram.

[0041] Figure 10 This is a diagram of the on-site current signal of a traction station in this invention; where (a) is the current signal when the locomotive enters the section; and (b) is the current signal when the locomotive leaves the section. Detailed Implementation

[0042] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0043] like Figure 1 As shown, the harmonic measurement method of this invention includes the following steps:

[0044] S1. Obtain the voltage and current of the three-phase power grid through Σ-ΔADC to obtain discrete voltage sample value sequences and current sample value sequences, and calculate the periodic value of the voltage.

[0045] S2. Interpolate and resample the voltage and current sample value sequences based on the voltage period value;

[0046] S3. Perform harmonic analysis on the interpolated and resampled voltage and current sample sequences using FFT transformation to obtain the FFT analysis results;

[0047] S4. Calculate the harmonic voltage, harmonic current and total harmonic active power based on the FFT analysis results.

[0048] In one specific embodiment, in step S2, the voltage sample value sequence and the current sample value sequence are interpolated using a Lagrange interpolation polynomial. Polynomial interpolation is a method of constructing new data points by interpolating a set of discrete given data points using a polynomial. The simplest method is to use the Lagrange interpolation polynomial. The known data points are obtained by ADC measurement, and the new data points are calculated by software interpolation. Assume there are r+1 discrete data points (x0, y0), (x1, y1), ..., (x... r ,y r If ), then the general formula for the Lagrange interpolation polynomial is as follows:

[0049]

[0050] Where r is the order of the polynomial, L i(x) is the fundamental Lagrange polynomial, and its expression is:

[0051]

[0052] From the above equation, we can see that the fundamental polynomial L i (x) has the following properties:

[0053]

[0054] Obviously, according to L i The properties of (x) are such that the interpolation polynomial y = L(x) passes through these (r+1) data points;

[0055] Let r = 2, then we obtain the Lagrange quadratic interpolation polynomial, which calculates the unknown value y at x using three adjacent data points, as shown below:

[0056]

[0057] Where L i (x) is the basic Lagrange quadratic polynomial.

[0058] Where f s f is the sampling frequency; in A is the fundamental frequency; A1 and φ1 are the fundamental amplitude and phase, respectively. h and φ h Here, h represents the amplitude and phase of the hth harmonic; h is the harmonic order; and k is the data sequence number.

[0059] Figure 2 This is a schematic diagram illustrating a Lagrange quadratic interpolation example. Lagrange quadratic interpolation refers to polynomial interpolation of order r = 2. Compared to linear interpolation, this method offers superior computational performance and accuracy, making it particularly suitable for real-time, efficient calculations in electricity metering applications and for current waveforms with significant distortion under nonlinear loads. First, three adjacent data points (n+p, u) are known. n+p (n+p+1,u) n+p+1 ) and (n+p+2,u n+p+2 The interpolation point is n+p+q. Substituting these three data points and x = n+p+q into equation (5) and simplifying, we obtain the unknown value u' at n+p+q. n The calculation results. Figure 2 The three data points, i.e., the ADC sample values, are marked with solid lines, and the interpolation function passing through these data points is a dashed parabola. By repeating the same process using multiple new adjacent data points, a complete periodic data sequence suitable for FFT can be obtained.

[0060] Simulation Verification: The provided Lagrange harmonic algorithm was simulated using MATLAB software to verify the accuracy of harmonic analysis, especially higher harmonic analysis, using this method, and the impact of fundamental frequency fluctuations on the harmonic algorithm. The corresponding simulation model is as follows:

[0061] (1) The following expression is used to generate a data sequence of fundamental wave superimposed with single harmonic:

[0062]

[0063] Among them, f s f is the sampling frequency. s =12.8kHz; f in The fundamental frequency is defined as φ1, which increases by 0.5 Hz within the range of 47.5–52.5 Hz to verify the impact of fundamental frequency fluctuations on the harmonic algorithm; A1 and φ1 represent the fundamental amplitude and phase, respectively. h and φ h Let A be the amplitude and phase of the h-th harmonic. h =0.1A1, φ1=φ h =0; h is the harmonic order, ranging from 2 to 63; k is the data sequence number;

[0064] (2) The above methods are used to perform linear interpolation and Lagrange quadratic interpolation on the above data sequence (e.g., ...). Figure 3 (as shown);

[0065] (3) Perform FFT analysis on the N-point data sequence obtained by interpolation to calculate the amplitude and phase values ​​corresponding to each harmonic;

[0066] (4) Compare the calculated values ​​of the amplitude and phase of each harmonic with the original value A. h and φ h The comparisons are made, and the harmonic errors caused by interpolation are calculated.

[0067] from Figure 3 It is easy to see that, under the simulation conditions of superimposed 2nd to 63rd harmonics and the fundamental frequency changing from 47.5Hz to 52.5Hz, the harmonic analysis method based on Lagrange quadratic interpolation has an error within ±0.65%, which is nearly 10 times more accurate than that using linear interpolation.

[0068] In one specific embodiment, in step S3, to further improve the accuracy of harmonic analysis, the harmonic amplitude error caused by the Lagrange interpolation synchronization process is curve-fitted, and an amplitude compensation model based on univariate linear regression is established to compensate for the harmonic amplitude error after interpolation. The specific process is as follows:

[0069] The amplitude error compensation method mainly borrows the idea of ​​data regression analysis in statistics, using the frequency offset Δf as the variable (where Δf is the offset between the actual frequency and 50Hz), and the harmonic amplitude error value e as the dependent variable. It uses n corresponding frequency offsets and harmonic amplitude error values ​​as independent observation samples (Δf...). i ,e i Performing univariate linear regression analysis on i = 1, 2, ..., n, we obtain the best estimates of parameters a and b in the following formula. and Right now:

[0070]

[0071] In the above formula, the optimal estimates of parameters a and b can be calculated using the following formula:

[0072]

[0073] in:

[0074]

[0075]

[0076] Finally, based on the real-time frequency, the theoretical error of each harmonic amplitude can be calculated according to the fitting curve obtained by the above formula, and then the measured value can be corrected.

[0077] The effect after amplitude compensation is as follows Figure 4 As shown, the harmonic energy metering error limit has been reduced from ±0.65% to within ±0.25%.

[0078] In one specific embodiment, in step S3, to further improve the accuracy of harmonic analysis and reduce the computational load, the following method is adopted:

[0079] (1) A standard-compliant 10-cycle measurement time window is used;

[0080] (2) Design a Lagrange quadratic interpolation resampling algorithm for synchronization, and interpolate the 10-cycle data into 2560 fixed sampling points within the 10-cycle for easy Fourier analysis.

[0081] (3) Based on the conjugate symmetry of the real sequence DFT, the 2560-point real sequence DFT is converted into a 1280-point complex sequence DFT, reducing the computational load by half.

[0082] (4) Design and implement Winograd Fourier Transform (subscript mapping algorithm) to convert the 1280-point complex DFT into five 256-point complex FFTs, reducing the computational load by 40%.

[0083] In one specific embodiment, based on the orthogonality between the fundamental wave and each harmonic, it is known that no active or reactive power is generated between the fundamental wave and the harmonics, but it exists in the apparent power. This part of the power is called the Budeau distortion power.

[0084]

[0085] Where S is apparent power, P is active power, and Q is reactive power.

[0086] Under non-sinusoidal conditions, active power is the algebraic sum of fundamental active power and harmonic active power, and reactive power is the algebraic sum of fundamental reactive power and harmonic reactive power. The calculation method mainly involves performing FFT decomposition on voltage and current respectively, calculating the power of fundamental and harmonics, and then obtaining the total power by algebraic summation.

[0087] A common method for calculating reactive power is a 90° phase shift, which involves shifting the voltage or current signal by 90° and then calculating the average instantaneous reactive power over one cycle or an integer number of cycles. Under sinusoidal conditions, this method theoretically produces reactive power without any error. However, under non-sinusoidal conditions, i.e., when the voltage and current waveforms are severely distorted, the reactive power obtained using the 90° phase shift method is not equal to the actual reactive power; instead, it is a combination of odd-harmonic reactive power and even-harmonic active power, resulting in a larger calculation error.

[0088] Therefore, in step S4, the periodic average power obtained by shifting the phase of each harmonic voltage by 90° using a Hilbert filter is taken as the total reactive power, which is the algebraic sum of the reactive power of each harmonic. The Hilbert filter is an all-pass filter with an amplitude-frequency characteristic of 1. After the signal passes through the Hilbert filter, it undergoes a +90-degree phase shift at the negative frequency (-π, 0) and a -90-degree phase shift at the positive frequency (0, π).

[0089] In non-sinusoidal cases, the periodic average power obtained by shifting the phase of each harmonic voltage by 90° using a Hilbert filter is the reactive power, which is the algebraic sum of the reactive power of each harmonic. This calculation result also applies to sinusoidal signals, except that only the fundamental reactive power is available in this case.

[0090] In practical design, IIR filters are commonly used to implement the Hilbert filtering algorithm. IIR Hilbert filters typically employ two sets of digital phase-shifting filters, F1 and F2, to perform phase-shifting filtering on voltage and current signals respectively. IIR filters can be designed based on different principles; they can be designed using all-pass filters or half-band filters. Analysis has shown that combining both—designing an IIR Hilbert filter using an elliptic half-band filter—can achieve higher amplitude and phase-shifting accuracy over a wide frequency range, and also has the advantages of lower order, less computational load, and less data storage.

[0091] Based on the reactive power metering accuracy and hardware platform requirements, the normalized digital frequency range of the Hilbert filter is set to [0.006, 0.994], Fs = 12800Hz. Therefore, the effective bandwidth of the Hilbert filter is 38Hz to 6362Hz. Under the condition that the phase shift error is no greater than 0.006°, the transfer functions of the designed phase-shifting filters F1 and F2 are shown below:

[0092]

[0093]

[0094] According to the design H F1 (z) and H F2 (z), the amplitude and phase characteristics of the Hilbert filter are obtained as follows: Figure 5 As shown. From Figure 5 As shown in (a) and (b), within the frequency range of 38Hz to 6372Hz, the filter gain is close to 0dB, and the phase remains within the range of -90.006° to 89.994°, meaning that the designed IIR digital filter meets the accuracy requirements for reactive power metering. Furthermore, the designed Hilbert filter employs a fixed-point, two-stage cascaded structure, improving computational efficiency and meeting the requirements of practical systems.

[0095] This invention achieves sampling synchronization through Lagrange polynomial interpolation and resampling techniques, thereby improving the accuracy of harmonic analysis. Curve fitting is performed on the harmonic amplitude error caused by the Lagrange interpolation synchronization process to establish an amplitude compensation model based on univariate linear regression. This model compensates for the harmonic amplitude error after interpolation, further improving the accuracy of harmonic analysis. Furthermore, by designing an IIR-type Hilbert filter using an elliptic half-band filter, the periodic average power obtained after shifting each harmonic voltage by 90° is used as the total reactive power. This achieves higher amplitude and phase shift accuracy over a wide frequency range and has the advantages of lower order, smaller computational load, and smaller data storage requirements.

[0096] The present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program executing the steps of any of the methods described above when run by a processor. The present invention further provides a harmonic measurement system, including a memory and a processor, the memory having a computer program stored thereon, the computer program executing the steps of any of the methods described above when run by a processor. The medium and system of the present invention correspond to the above-described measurement methods and also possess the advantages described above.

[0097] like Figure 6 As shown in the figure, this embodiment of the invention also provides a harmonic energy meter, including a metering module, a management module, and a power supply module. The metering module includes an A / D converter and a control unit. The A / D converter is connected to the control unit and is used to receive voltage and current signals of each phase and perform analog-to-digital conversion, and send them to the control unit. The control unit is used to complete the metering of electrical energy according to the harmonic metering method described above. The management module is connected to the control unit and is used to complete data statistics, storage, communication, and display.

[0098] The specific working principle of the above-mentioned electricity meter is as follows:

[0099] (1) The A / D converter and DSP sample the current and voltage of each phase;

[0100] (2) Through corresponding mathematical calculations, the DSP part completes the work of measuring electrical parameters, measuring electrical energy, analyzing power quality, and calculating harmonic energy.

[0101] (3) The metering module exchanges data with the management MCU through a high-speed SPI communication interface;

[0102] (4) The management MCU mainly completes tasks such as display, data statistics, storage, communication, selection of electricity meter functions, and initialization data settings.

[0103] like Figure 7 As shown, the software design follows a hierarchical and modular design philosophy, and can be divided into three layers from bottom to top: the driver layer, the system layer, and the application layer. Each layer is further divided into modules based on functional implementation, as described below:

[0104] Driver Layer: The hardware driver layer is primarily responsible for the operation of DSP chip peripherals and external devices. This includes the driver layer for internal modules and peripheral interfaces of the DSP chip, as well as the drivers for external devices attached to the DSP chip, which require calling certain interfaces.

[0105] System Layer: The operating system layer is primarily responsible for task creation and scheduling, interrupt service management, etc., to support the operation of related programs in the application layer. The system uses TI's built-in real-time kernel SYS / BIOS, which supports preemptive multi-task scheduling, timely hardware response, and synchronization and communication between tasks. Interrupts mainly involve AD data ready interrupt, AD data transmission completion interrupt, MCU communication request interrupt, DSP receive / acknowledge completion interrupt, and second pulse signal interrupt. Among them, AD data ready interrupt and transmission completion interrupt complete the data acquisition function.

[0106] Application Layer: Based on the driver layer and system layer, the application layer is responsible for data acquisition, data calculation, data recording and storage, and data communication operations involved in power metering and power quality monitoring, in the form of task modules. According to functional and performance requirements, the application layer mainly includes four major task modules: real-time data calculation, periodic data calculation, data communication, and second-time tasks, as well as software function modules such as basic metering, system clock, transient monitoring, flicker, harmonic analysis, and communication processing. The real-time data calculation task is mainly responsible for half-cycle / single-cycle basic data calculation, flicker calculation, and transient monitoring. The periodic data calculation task is mainly responsible for 10-cycle data calculation and other time cumulative value calculations such as 150-cycle and 10-minute. Data communication is responsible for data interaction between the DSP and MCU. The second-time task provides a 1-second timing processing interface. Each task completes its corresponding operation by calling interface functions in the software function modules. The priority of each task, from highest to lowest, is: real-time data calculation task, data interaction task, periodic data calculation task, and second-time task.

[0107] Test and application effect analysis:

[0108] (1) Laboratory testing

[0109] The performance of the harmonic algorithm under nonlinear conditions was tested. A harmonic performance testing platform based on the FLUKE6100A standard harmonic source was constructed. The developed harmonic energy meter was compared with several representative energy meters in terms of harmonic performance. Voltage harmonic content: 10%, current harmonic content: 40%, harmonics were added sequentially. The test results are as follows: Figure 8 As shown, the designed energy meter has a maximum harmonic measurement error of no more than 0.4% within a wide frequency range of 2-50, with the fundamental frequency varying from 47.5-52.5Hz, which is superior to the performance of similar products.

[0110] The test results of the reactive power metering error of the Hilbert filter are as follows: Figure 9 As shown, under sinusoidal signal conditions, the reactive power metering error data are all within ±0.05%, which is very small. Under harmonic conditions, the Hilbert algorithm exhibits superior harmonic performance; although the error gradually increases with the harmonic order, it does not exceed ±0.4% at most.

[0111] (2) Practical application effect

[0112] Trial operation was conducted at metering points such as electric railway traction substations and wind farms. These trial operation points generally exhibit nonlinear characteristics, and the trial operation at these points can more comprehensively test the scientific and rational design of the nonlinear load metering device.

[0113] The harmonic energy meter was put into trial operation for about 5 months at Bianshan Substation, a traction substation for electric railways. During the trial period, the meter operated stably without any crashes or malfunctions, reflecting that the meter's stability had withstood the test. Meanwhile, the meter's energy measurement results were compared with those of a regular three-phase energy meter connected to the same metering line. The comparison results are shown in Table 1.

[0114] Table 1 Comparison Data of Trial Coupling Operations of Electrified Railway Traction Stations

[0115]

[0116]

[0117] The reasons for the discrepancy between the above-mentioned accumulated electricity readings and those of ordinary meters warrant analysis. The traction transformer's field current signal exhibits significant transient impact characteristics. Under no-load conditions, the current is very small (around ten mA). When a high-speed train passes, the current rapidly rises to 1 A or even higher within 1 to 2 seconds, then reaches the balanced operating state under load. After the train passes, the current drops back to the normal no-load state of around ten mA within 1 to 2 seconds and maintains a balanced operating state. The traction transformer's field current continuously changes between these two balanced states. Figure 10 This refers to the current signal data measured at the traction transformer site when the locomotive enters and leaves the track section.

[0118] The harmonic content of the voltage and current waveforms at the field metering points is shown in Tables 2 and 3 through FFT analysis.

[0119] Table 2 Harmonic Content of Current at Traction Station Metering Points

[0120] Harmonic number Harmonic amplitude percentage Harmonic number Harmonic amplitude percentage fundamental wave 1.131788 100.00％ 14 times 0.001483 0.13％ 2 times 0.005831 0.52％ 15 times 0.002744 0.24％ 3 times 0.019434 1.72％ 16 times 0.001281 0.11％ 4 times 0.005446 0.48％ 17 times 0.006298 0.56％ 5 times 0.00566 0.50％ 18 times 0.000833 0.07％ 6 times 0.003723 0.33％ 19 times 0.0049 0.43％ 7 times 0.000809 0.07％ 20 times 0.000316 0.03％ 8 times 0.002957 0.26％ 21 times 0.000366 0.03％ 9 times 0.003126 0.28％ 22 times 2.32E-05 0.00％ 10 times 0.001902 0.17％ 23 times 0.003453 0.31％ 11 times 0.0043 0.38％ 24 times 0.000183 0.02％ 12 times 0.001478 0.13％ 25 times 0.003839 0.34％ 13 times 0.001603 0.14％

[0121] Table 3 Voltage Harmonic Content at Traction Station Metering Points

[0122]

[0123]

[0124] It can be seen that the harmonics of the on-site signal are mainly the 3rd, 5th, 11th and 17th harmonics.

[0125] The harmonic energy meter of this invention focuses on the accuracy of harmonic energy measurement. During the development process, the amplitude and phase of the fundamental wave and each harmonic were precisely calibrated and compensated, while conventional meters only calibrate and compensate for the fundamental wave component, resulting in a significant difference in the final measurement results. Therefore, in traction transformer sites with high harmonic content, the harmonic energy meter has a clear advantage over conventional meters, better matching the load characteristics of traction transformers and thus better reflecting the principles of fair and reasonable scientific measurement.

[0126] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A harmonic measurement method, characterized in that, Including the following steps: S1. Obtain the voltage and current of the three-phase power grid, obtain discrete voltage sample value sequences and current sample value sequences, and calculate the periodic value of the voltage; S2. Interpolate and resample the voltage and current sample value sequences based on the voltage period value; S3. Perform harmonic analysis on the interpolated and resampled voltage and current sample sequences using FFT transformation to obtain the FFT analysis results; S4. Calculate the harmonic voltage, harmonic current and total harmonic active power based on the FFT analysis results; In step S3, the harmonic amplitude error caused by interpolation is curve-fitted to establish an amplitude compensation model based on univariate linear regression, and the harmonic amplitude error after interpolation is compensated accordingly. The specific process of harmonic amplitude error compensation is as follows: With frequency offset Harmonic amplitude error value (as a variable) As the dependent variable, n corresponding frequency offset and harmonic amplitude error values ​​are used as independent observation samples. Performing a univariate linear regression analysis yields the following parameters. , Best estimate and ,Right now: In the above formula, , The optimal estimate of the parameter can be calculated using the following formula: in: Finally, the theoretical error of each harmonic amplitude is calculated based on the real-time frequency and the fitting curve obtained by the above formula, and the measured value is corrected.

2. The harmonic measurement method according to claim 1, characterized in that, In step S2, the voltage sample value sequence and the current sample value sequence are interpolated using a Lagrange interpolation polynomial.

3. The harmonic measurement method according to claim 1, characterized in that, In step S3, the FFT analysis results include the amplitude and phase values ​​corresponding to each harmonic.

4. The harmonic measurement method according to claim 1, 2, or 3, characterized in that, In step S4, the periodic average power obtained by shifting the phase of each harmonic voltage by 90° using a Hilbert filter is taken as the total reactive power, which is the algebraic sum of the reactive power of each harmonic.

5. The harmonic measurement method according to claim 4, characterized in that, In step S4, the Hilbert filter is an IIR type Hilbert filter, which is designed using an elliptic half-band filter.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program, when run by a processor, performs the steps of the method as described in any one of claims 1 to 5.

7. A harmonic metering system, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, The computer program, when run by a processor, performs the steps of the method as described in any one of claims 1 to 5.

8. A harmonic energy meter, characterized in that, The device includes a metering module, a management module, and a power supply module. The metering module includes an A / D converter and a control unit. The A / D converter is connected to the control unit and is used to receive voltage and current signals of each phase, perform analog-to-digital conversion, and send them to the control unit. The control unit is used to complete the metering of electrical energy according to the harmonic metering method described in any one of claims 1-5. The management module is connected to the control unit and is used to complete data statistics, storage, communication, and display.

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