An iterative compensation method and device for synchronous phasor measurement

Abstract

The application discloses a kind of iterative compensation synchronous phasor measurement method, after window function windowing, discrete fourier transform and average processing, target DFT sequence is obtained, after cost parameter is obtained, first cost function is calculated, and then it is judged whether there is out-of-band interference in original data, then spectrum leakage compensation and setting cost function are carried out for different situations, with the increase of iteration number, cost function value is smaller and smaller, measurement accuracy is higher and higher, to obtain the optimal value of cost parameter, the most accurate fundamental wave and interference parameter are measured, improve the synchronous phasor measurement accuracy, and can meet P level and M level performance requirements simultaneously, only one device can complete synchronous phasor measurement, reduce use cost;Considering the influence of out-of-band interference on fundamental wave phasor, out-of-band interference compensation is carried out;Considering that the device will be deployed outdoors, there is temperature change, temperature drift compensation mechanism is added, to ensure the performance of synchronous phasor measurement.In addition, the effect of measuring device is as above.

Description

Technical Field

[0001] This invention relates to the field of power system measurement technology, and in particular to an iterative compensation synchronous phasor measurement method and apparatus. Background Technology

[0002] During the construction of new power systems, a large number of power electronic devices and nonlinear loads are being deployed, and distributed renewable energy sources are being continuously integrated, exacerbating interference problems in modern power grids and making the operating environment more complex. Synchronous phasor measurement technology, which obtains precise absolute time through the Global Positioning System (GPS) and measures high-precision synchronous phasor data, is increasingly becoming an important technical means for dynamic security monitoring of power grids, enhancing the grid's observation capabilities.

[0003] Existing synchronous phasor measurement algorithms include Discrete Fourier Transform (DFT), least squares method, and Kalman filtering. In practical synchronous phasor measurement unit development, DFT is widely used due to its low computational complexity, ease of implementation, and full harmonic cancellation advantages. However, DFT has many limitations and drawbacks, such as spectral leakage and picket fence effects, which severely affect the performance of synchronous phasor measurements. Furthermore, most existing synchronous phasor measurement algorithms can only meet the P-level or M-level requirements defined in IEEE STD.C37.118, necessitating the simultaneous placement of two devices in practical applications, thus increasing the cost. Summary of the Invention

[0004] The purpose of this application is to provide an iterative compensation method and apparatus for synchronous phasor measurement to solve the performance problems of synchronous phasor measurement.

[0005] To address the aforementioned technical problems, this application provides an iterative compensation method for synchronous phasor measurement, comprising:

[0006] Voltage and current are collected at a preset time as raw data. After selecting a window function that meets the requirements, the raw data is windowed in multiple segments and then subjected to Discrete Fourier Transform (DFT) to obtain multiple sets of DFT sequences of the windowed raw data. The average of the multiple sets of DFT sequences is calculated to obtain the final target DFT sequence.

[0007] A preliminary estimate of the cost parameters is performed on the target DFT sequence to reconstruct the fundamental wave sequence in the target DFT sequence;

[0008] Calculate a first cost function based on the cost parameters, and determine whether the original data has out-of-band interference based on the first cost function:

[0009] If there is no out-of-band interference, spectral leakage compensation is performed on the last fundamental wave sequence to estimate the fundamental wave parameters;

[0010] Calculate the second cost function based on the target DFT sequence and the fundamental sequence;

[0011] Determine whether the value of the second cost function is less than the accuracy threshold or whether the number of iterations n is greater than the maximum value N of the fundamental iteration;

[0012] If yes, then stop compensation; if no, then return to the steps of performing spectral leakage compensation on the last fundamental wave sequence and estimating the fundamental wave parameters, and increment the value of n by one.

[0013] If out-of-band interference exists, the interference sequence is separated from the target DFT sequence based on the last fundamental wave sequence, spectral leakage compensation is performed on the interference sequence, and the interference parameters are estimated.

[0014] The fundamental wave sequence is separated from the target DFT sequence based on the interference parameters, and spectral leakage compensation is performed on the fundamental wave sequence to estimate the fundamental wave parameters.

[0015] Calculate the third cost function based on the interference sequence and the fundamental frequency sequence;

[0016] Determine whether the value of the third cost function is less than the precision threshold or whether the number of iterations m is greater than the maximum value of the interference iterations M;

[0017] If yes, then stop compensation; if no, then return to the steps of separating the interference sequence from the target DFT sequence based on the last fundamental wave sequence, performing spectral leakage compensation on the interference sequence, estimating the interference parameters, and incrementing the value of m by one.

[0018] Based on the ambient temperature, the fundamental wave parameter, and the interference parameter, temperature drift compensation is performed on the fundamental wave parameter and the interference parameter respectively to obtain the target fundamental wave parameter and the target interference parameter.

[0019] The target fundamental frequency parameter, the target interference parameter, and the target time stamp are reported to the main station, wherein the target time stamp is the average value of time information collected within a preset time period.

[0020] Based on the above embodiments, as a preferred implementation, the sequence x'(n) after multi-segment windowing of the original data using a window function that meets the requirements is:

[0021]

[0022] Among them, the first to fifth segments of windowed raw data, x(n) represents the nth raw data, w(n) represents the window function, and L represents the length of a single segment of windowed raw data.

[0023] Based on the above embodiments, as a preferred implementation, the multiple sets of DFT sequences x'(k) are:

[0024]

[0025]

[0026] Based on the above embodiments, as a preferred implementation, the target DFT sequence X(k) is:

[0027] X(k) = average(X′(k)).

[0028] Based on the above embodiments, as a preferred implementation, the step of performing a preliminary estimation of the cost parameter δ on the target DFT sequence to reconstruct the fundamental wave sequence in the target DFT sequence specifically involves:

[0029] Find the maximum sequence k based on the distribution of the target DFT sequence. max Location, k max =argmax(X(k)) calculates the trend factor ε and cost parameter δ; the cost parameter δ needs to be determined based on the specific window function chosen.

[0030] The fundamental frequency, amplitude, and phase are obtained based on the cost parameter δ and the window function type.

[0031] The restored fundamental frequency sequence for:

[0032]

[0033] in, This indicates the first fundamental frequency sequence. This represents the positive component of the first fundamental frequency sequence. This represents the negative component of the first fundamental frequency sequence. T represents the amplitude of the first fundamental frequency. total Indicates the preset time.

[0034] It should be further noted that the first cost function c(δ) is:

[0035] Where X(k) represents the target DFT sequence.

[0036] Based on the above embodiments, as a preferred implementation, the spectral leakage compensation of the final fundamental wave sequence specifically involves:

[0037] Here, spec-compens represents spectral leakage compensation.

[0038] It should be further noted that, in the absence of out-of-band interference, the fundamental frequency parameters are:

[0039]

[0040] The second cost function is:

[0041]

[0042] It should be further noted that when out-of-band interference is present, the interference parameters are:

[0043] Where m is the number of iterations;

[0044] The fundamental wave parameters are:

[0045]

[0046] The third cost function c(δ) is:

[0047]

[0048] To address the aforementioned technical problems, this application also provides an iteratively compensated synchronous phasor measurement device corresponding to the iteratively compensated synchronous phasor measurement method, comprising:

[0049] It includes a data acquisition module, a transformation module, a first compensation module, a second compensation module, and a reporting module.

[0050] The acquisition module is used to acquire voltage, current and ambient temperature for a preset time. The acquisition module integrates a time synchronization module, which is used to acquire time information.

[0051] The transformation module is used to select a window function that meets the requirements to perform multi-segment windowing on the original data and then perform discrete Fourier transform to obtain multiple sets of DFT sequences of the windowed original data. The average of the multiple sets of DFT sequences is then calculated to obtain the final target DFT sequence.

[0052] The first compensation module is used to perform spectral leakage compensation on the target DFT sequence;

[0053] The second compensation module is used to perform temperature drift compensation on the fundamental wave parameter and the interference parameter according to the ambient temperature, the fundamental wave parameter and the interference parameter, respectively, to obtain the target fundamental wave parameter and the target interference parameter;

[0054] The reporting module is used to report the target fundamental wave parameter, the target interference parameter, and the target time stamp to the main station, wherein the target time stamp is the average value of time information collected within a preset time period.

[0055] Compared with existing technologies, the iterative compensation synchronous phasor measurement method provided by this invention obtains the target DFT sequence through windowing, discrete Fourier transform, and averaging. After obtaining the cost parameters, a first cost function is calculated to determine whether out-of-band interference exists in the original data. Then, spectral leakage compensation and cost function settings are performed for different situations. As the number of iterations increases, the cost function value becomes smaller and the measurement accuracy becomes higher, thus obtaining the optimal value of the cost parameters and measuring the most accurate fundamental and interference parameters. This improves the accuracy of synchronous phasor measurement and can simultaneously meet P-level and M-level performance requirements. Synchronous phasor measurement can be completed with only one device, reducing usage costs. The influence of out-of-band interference on the fundamental phasor is considered, and out-of-band interference compensation is performed on the signal. Considering that the device will be deployed outdoors and subject to drastic temperature changes, a temperature drift compensation mechanism is added to ensure the performance of synchronous phasor measurement. In addition, this application also provides an iterative compensation synchronous measurement device with the same effects. Attached Figure Description

[0056] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0057] Figure 1 A flowchart of an iterative compensation synchronous phasor measurement method provided in an embodiment of this application;

[0058] Figure 2 A schematic diagram of an iterative compensation synchronous phasor measurement device provided in an embodiment of this application;

[0059] Figure 3 This is a diagram illustrating the experimental results of a fundamental frequency signal provided in an embodiment of this application.

[0060] Figure 4 A diagram showing the experimental results of harmonic distortion provided in an embodiment of this application;

[0061] Figure 5 This is a diagram showing the results of an out-of-band interference experiment provided in an embodiment of this application;

[0062] Figure 6 This is an experimental result diagram of another fundamental frequency signal provided in an embodiment of this application;

[0063] Figure 7 This is another diagram showing the experimental results of harmonic distortion provided in an embodiment of this application;

[0064] Figure 8 This is another out-of-band interference experimental result diagram provided in an embodiment of this application.

[0065] In the diagram: 201, Acquisition Module; 2011, Time Synchronization Module; 202, Transformation Module; 203, First Compensation Module; 204, Second Compensation Module; 205, Reporting Module. Detailed Implementation

[0066] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0067] The core of this application is to provide an iterative compensation method and apparatus for synchronous phasor measurement, which solves the problem of synchronous phasor measurement performance.

[0068] Figure 1 This is a flowchart of an iterative compensation synchronous phasor measurement method provided in an embodiment of this application. Figure 2 A schematic diagram of an iterative compensation synchronous phasor measurement device provided in an embodiment of this application; Figure 3 This is a diagram showing the experimental results of a fundamental frequency signal provided in an embodiment of this application. Figure 4 This is a diagram showing the experimental results of harmonic distortion provided in an embodiment of this application. Figure 5 This is a diagram showing the results of an out-of-band interference experiment provided in an embodiment of this application. Figure 6 This is an experimental result diagram of another fundamental frequency signal provided in an embodiment of this application. Figure 7 This is another diagram showing the experimental results of harmonic distortion provided in an embodiment of this application. Figure 8 For another out-of-band interference experimental result diagram provided in this application embodiment, see [link to diagram]. Figures 1 to 8 As shown.

[0069] A synchronous phasor measurement method with iterative compensation includes the following steps:

[0070] S1. Collect voltage and current at a preset time as raw data. Select a window function that meets the requirements to apply multiple windows to the raw data and then perform Discrete Fourier Transform to obtain multiple sets of DFT sequences of the windowed raw data. Calculate the average of the multiple sets of DFT sequences to obtain the final target DFT sequence.

[0071] S2, perform a preliminary estimation of the cost parameters to reconstruct the fundamental wave sequence in the target DFT sequence;

[0072] S3, calculate the first cost function based on the cost parameters, and determine whether the original data has out-of-band interference based on the first cost function:

[0073] If there is no out-of-band interference, proceed to step S4; if there is out-of-band interference, proceed to step S9.

[0074] S4, perform spectral leakage compensation on the final fundamental wave sequence and estimate the fundamental wave parameters;

[0075] S5, calculate the second cost function based on the target DFT sequence and the fundamental sequence;

[0076] S6, determine whether the value of the second cost function is less than the precision threshold or whether the number of iterations n is greater than the maximum value of the fundamental iteration N;

[0077] If yes, proceed to step S7; otherwise, proceed to step S8.

[0078] S7, stop compensation;

[0079] S8, return to step S4, and increment the value of n by one;

[0080] S9. Based on the last fundamental wave sequence, the interference sequence is separated from the target DFT sequence, spectral leakage compensation is performed on the interference sequence, and the interference parameters are estimated.

[0081] S10, Based on the interference parameters, separate the fundamental wave sequence from the target DFT sequence, perform spectral leakage compensation on the fundamental wave sequence, and estimate the fundamental wave parameters;

[0082] S11, Calculate the third cost function based on the interference sequence and the fundamental sequence;

[0083] S12, determine whether the value of the third cost function is less than the precision threshold or whether the number of iterations m is greater than the maximum value of the interference iteration M;

[0084] If yes, proceed to step S13; otherwise, proceed to step S14.

[0085] S13, Stop compensation;

[0086] S14, return to step S9, and increment the value of m by one;

[0087] S15. Based on the ambient temperature, fundamental wave parameter, and interference parameter, temperature drift compensation is performed on the fundamental wave parameter and interference parameter respectively to obtain the target fundamental wave parameter and target interference parameter.

[0088] S16, report the target fundamental wave parameters, target interference parameters and target timestamp to the main station, where the target timestamp is the average of the time information collected within a preset time period.

[0089] As a preferred implementation, the sequence x'(n) after applying multiple windowing steps to the original data using a window function that meets the requirements is:

[0090]

[0091] Where x1(n)-x5(n) represent the first to fifth windowed original data segments, x(n) represents the nth original data segment, w(n) represents the window function, and L represents the length of the windowed original data segment.

[0092] In one preferred embodiment, the multiple DFT sequences x'(k) are:

[0093]

[0094]

[0095] In one preferred embodiment, the target DFT sequence X(k) is:

[0096] X(k) = average(X(k)).

[0097] As a preferred implementation, the cost parameter δ is initially estimated from the target DFT sequence to reconstruct the fundamental wave sequence in the target DFT sequence, specifically as follows:

[0098] Find the maximum sequence k based on the distribution of the target DFT sequence. max Location, k max =argmax(X(k)) calculates the trend factor ε and cost parameter δ; the cost parameter δ needs to be determined based on the specific window function chosen.

[0099] The fundamental frequency, amplitude, and phase are obtained based on the cost parameter δ and the window function type.

[0100] The restored fundamental frequency sequence for:

[0101]

[0102] in, This indicates the first fundamental frequency sequence. This represents the positive component of the first fundamental frequency sequence. This represents the negative component of the first fundamental frequency sequence. T represents the amplitude of the first fundamental frequency. total Indicates the preset time.

[0103] In a preferred embodiment, the first cost function c(δ) is:

[0104] Here, X(k) represents the target DFT sequence. The presence of out-of-band interference in the original data is determined based on the first cost function c(δ). If the value of the first cost function is less than the out-of-band interference threshold, it indicates that there is no out-of-band interference, and only fundamental frequency compensation is needed; otherwise, out-of-band interference compensation is required.

[0105] As a preferred embodiment, if there is no out-of-band interference, spectral leakage compensation for the final fundamental sequence specifically involves:

[0106] Here, spec-compens represents spectral leakage compensation.

[0107] Find the position k of the maximum sequence based on the distribution of the target DFT sequence X(k). max The trend factor ε and cost parameter δ are obtained.

[0108] The frequency, amplitude, and phase of the target DFT sequence X(k) are obtained based on the cost parameters, and spectral leakage compensation is completed.

[0109] In a preferred embodiment, when there is no out-of-band interference, the fundamental parameters of the restored input sequence's positive frequency, negative frequency, and combined sequences are estimated as follows:

[0110]

[0111] The second cost function is:

[0112]

[0113] Preferably, if out-of-band interference exists, the interference sequence is separated from the original DFT sequence based on the final fundamental frequency sequence. Spectral leakage compensation was performed on it, and the interference parameters were:

[0114] Where m is the number of iterations, and m is used for counting, serving as a criterion for whether to stop compensation. The value is incremented by one for each iteration.

[0115] Reconstruct the positive frequency, negative frequency, and combined frequency sequences of the interference sequence:

[0116]

[0117] Preferably, when out-of-band interference exists, the fundamental frequency parameters are:

[0118] The subscripts i and 0 are used to distinguish between interference and fundamental frequency. The subscript i indicates interference, and the subscript 0 indicates fundamental frequency.

[0119] Reconstruct the positive frequency sequence, negative frequency sequence, and combined sequence of the input sequence:

[0120]

[0121] The third cost function c(δ) is:

[0122]

[0123] E after temperature drift compensation R E represents the amplitude temperature drift compensation coefficient. P Indicates the phase temperature drift compensation coefficient:

[0124] Where T represents the ambient temperature.

[0125] If there is no out-of-band interference, then both the amplitude and phase of the interference are 0:

[0126] The subscript 0 represents the fundamental frequency parameter, the subscript i represents the interference parameter, and A and φ represent the amplitude and phase, respectively.

[0127] If out-of-band interference exists, the corresponding parameters are as follows:

[0128]

[0129] like Figure 2 As shown, an iteratively compensated synchronous phasor measurement device includes an acquisition module 201, a transformation module 202, a first compensation module 203, a second compensation module 204, and a reporting module 205.

[0130] The data acquisition module 201 is used to acquire voltage, current, and ambient temperature over a preset time. It samples a set of voltage and current values ​​every 78.125 µs and the current ambient temperature every 20 ms. The data acquisition module 201 integrates a time synchronization module 2011, which is used to acquire time information. The time synchronization module 2011 uses a combination of the Global Positioning System (GPS) and IEEE 1588, determining the current time based on the precise rising edge of a 1 pps second signal (one cycle is 1 second, and the rising edge marks the start of the current second).

[0131] Transformation module 202 is used to select a window function that meets the requirements to perform multi-segment windowing on the original data and then perform discrete Fourier transform to obtain multiple sets of DFT sequences of the windowed original data. The average of the multiple sets of DFT sequences is calculated to obtain the final target DFT sequence.

[0132] The first compensation module 203 is used to perform spectral leakage compensation on the target DFT sequence;

[0133] The second compensation module 204 is used to perform temperature drift compensation on the fundamental wave parameter and the interference parameter according to the ambient temperature, fundamental wave parameter and interference parameter respectively, so as to obtain the target fundamental wave parameter and the target interference parameter;

[0134] The reporting module 205 is used to report the target fundamental wave parameters, target interference parameters and target timestamp to the main station. The target timestamp is the average value of the time information collected within a preset time period.

[0135] To enable those skilled in the art to better understand this solution, the following detailed description is provided using specific embodiments:

[0136] Example 1

[0137] Voltage or current data are collected over 500 ms to form a discrete sequence x(n) of length 5L.

[0138] Apply a window to the raw data using the Hanning window function:

[0139]

[0140] Performing a Discrete Fourier Transform (DFT) on x′(n) yields multiple DFT sequences of the original data with windowed input:

[0141]

[0142] X(k) = average(X′(k)).

[0143] At this point, the maximum sequence k can be found based on the distribution of the target DFT sequence. max Location k max =argmax(X(k)), to obtain the trend factor ε and cost parameter δ:

[0144]

[0145] The fundamental frequency, amplitude, and phase are obtained from the cost parameter δ:

[0146]

[0147] Reconstruct the fundamental positive frequency, negative frequency sequences, and fundamental frequency sequence:

[0148]

[0149] Calculate the value of the first cost function:

[0150]

[0151] The presence of out-of-band interference in the original data is determined based on the value of the first cost function, and the out-of-band interference threshold θ is used. inter If the first cost function value is set to 0.0033, and the value is less than the out-of-band interference threshold, it means that there is no out-of-band interference and only fundamental frequency compensation is needed; otherwise, out-of-band interference compensation is required.

[0152] The specific steps for fundamental frequency compensation are as follows:

[0153] Spectral leakage compensation for the final fundamental sequence

[0154] Find the position k of the maximum sequence based on the distribution of the target DFT sequence X(k). max The trend factor ε and cost parameter δ are obtained:

[0155]

[0156] Based on the cost parameters, the frequency, amplitude, and phase of the input sequence are obtained, and spectral leakage compensation is completed.

[0157]

[0158] Finally, the positive frequency sequence, negative frequency sequence, and combined sequence of the input sequence are restored:

[0159]

[0160] Calculate the value of the second cost function:

[0161]

[0162] If the value of the second cost function is less than the precision threshold θ accur If the number of iterations n is greater than the maximum value N of the fundamental wave iterations, stop the compensation. Otherwise, repeat the above steps, incrementing n by one, and θ... accur The values ​​of N are 1e-4 and 2, respectively.

[0163] The specific steps for out-of-band interference compensation are as follows:

[0164] The interference sequence is separated from the original DFT sequence based on the final fundamental frequency sequence. Perform spectral leakage compensation and estimate interference parameters:

[0165]

[0166] Reconstruct the positive frequency, negative frequency, and combined frequency sequences of the interference sequence:

[0167]

[0168] Based on the interference estimation results, the fundamental wave sequence is separated from the target DFT sequence. Spectral leakage compensation is performed on this sequence, and the fundamental wave parameters are estimated.

[0169]

[0170] Reconstruct the positive frequency sequence, negative frequency sequence, and combined sequence of the input sequence:

[0171]

[0172] Calculate the value of the third cost function based on the above results:

[0173]

[0174] If the cost function value is less than the precision threshold θ accur If the number of iterations m is greater than the maximum value of the interference iteration M, stop the compensation. Otherwise, repeat the above steps, incrementing the value of m by one, and θ... accur The values ​​of M are 1e-4 and 28, respectively.

[0175] Finally, temperature drift compensation is performed. Based on the temperature of the placement location, the amplitude and phase of the fundamental wave and the interference are compensated. After temperature drift compensation, the target fundamental wave parameter E... R and target interference parameter E P They are respectively:

[0176]

[0177] If there is no out-of-band interference, then both the amplitude and phase of the interference are 0:

[0178]

[0179] If out-of-band interference exists, the corresponding parameters are as follows:

[0180]

[0181] Next, tests were conducted. Based on the IEEE Std C37.118 measurement standard, signals from low-temperature, normal, and high-temperature environments were collected for simulation tests. Specifically, the signals were three types of signals with different frequencies: those containing only the fundamental frequency, those containing harmonics, and those containing out-of-band interference.

[0182] 1. Only includes fundamental frequency signal testing

[0183] The signal model x(t) is:

[0184] Where t represents time t, and the value of f0 ranges from 45 to 55 Hz.

[0185] according to Figure 3 It can be seen that the errors TVE, FE, and RFE are all within the allowable range of Class P and Class M. TVE, FE, and RFE represent the total vector error, frequency error, and frequency change rate error, respectively. This meaning is defined by the IEEE STD.C37.118 standard.

[0186] 2. Testing for the presence of harmonic distortion

[0187] The signal model x(t) is:

[0188]

[0189] Where n iThe harmonic order is measured, with a range of 2nd to 50th harmonics. Figure 4 It can be seen that the errors of TVE, FE, and RFE are all within the allowable range of p-class and m-class.

[0190] 3. Testing under out-of-band interference conditions

[0191] The signal model x(t) is:

[0192]

[0193] Where f i The out-of-band interference frequency is measured in the range of 2nd-50th harmonics. Figure 5 It can be seen that the errors of TVE, FE, and RFE are all within the allowable range of p-class and m-class.

[0194] Table 1 compares the maximum error values ​​under all temperature conditions with the requirements of Class P and Class M. As can be seen from the table, all maximum error values ​​are far below the standard requirements.

[0195] Table 1. Error Statistics of Hanning Window

[0196]

[0197] Example 2

[0198] Voltage or current data are collected over 500 ms to form a discrete sequence x(n) of length 5L.

[0199] Apply a sine window function to the raw data:

[0200]

[0201] Performing a Discrete Fourier Transform on x(n) yields multiple DFT sequences of the original data with a window:

[0202]

[0203] X(k) = average(X′(k))

[0204] At this point, the location k of the maximum sequence can be found based on the distribution of the target DFT sequence. max =argmax(X(k)), to obtain the trend factor ε and cost parameter δ:

[0205]

[0206] The fundamental frequency, amplitude, and phase are obtained from the cost parameters:

[0207]

[0208] Reconstruct the fundamental positive frequency, negative frequency sequences, and fundamental frequency sequence:

[0209]

[0210] Calculate the value of the first cost function:

[0211]

[0212] The presence of out-of-band interference is determined based on the value of the first cost function, and the out-of-band interference threshold θ is used. inter If the first cost function value is set to 0.0033, and the value is less than the out-of-band interference threshold, it means that there is no out-of-band interference and only fundamental frequency compensation is needed; otherwise, out-of-band interference compensation is required.

[0213] The specific steps for fundamental frequency compensation are as follows:

[0214] Spectral leakage compensation for the final fundamental sequence

[0215] Find the position k of the maximum sequence based on the distribution of the target DFT sequence X(k). max The trend factor ε and cost parameter δ are obtained:

[0216]

[0217] Based on the cost parameters, the frequency, amplitude, and phase of the input sequence are obtained, and spectral leakage compensation is completed.

[0218]

[0219] Finally, the positive frequency sequence, negative frequency sequence, and combined sequence of the input sequence are restored:

[0220]

[0221] Calculate the value of the second cost function:

[0222]

[0223] If the value of the second cost function is less than the precision threshold θ accur If the number of iterations n is greater than the maximum value N of the fundamental wave iterations, stop the compensation. Otherwise, repeat the above steps, incrementing n by one, and θ... accur The values ​​of N are 1e-4 and 2, respectively.

[0224] The specific steps for out-of-band interference compensation are as follows:

[0225] The interference sequence is separated from the original DFT sequence based on the final fundamental frequency sequence. Perform spectral leakage compensation and estimate interference parameters:

[0226]

[0227] Reconstruct the positive frequency, negative frequency, and combined frequency sequences of the interference sequence:

[0228]

[0229] Based on the interference estimation results, the fundamental wave sequence is separated from the target DFT sequence. Spectral leakage compensation is performed on this sequence, and the fundamental wave parameters are estimated.

[0230]

[0231] Reconstruct the positive frequency sequence, negative frequency sequence, and combined sequence of the input sequence:

[0232]

[0233] Calculate the value of the third cost function based on the above results:

[0234]

[0235] If the value of the third cost function is less than the precision threshold θ accur If the number of iterations m is greater than the maximum value of the interference iteration M, stop the compensation. Otherwise, repeat the above steps, incrementing the value of m by one, and θ... accur The values ​​of M are 1e-4 and 16, respectively.

[0236] Finally, temperature drift compensation is performed. Based on the temperature of the placement location, the amplitude and phase of the fundamental wave and the interference are compensated. After temperature drift compensation, the target fundamental wave parameter E is... R and target interference parameter E P They are respectively:

[0237]

[0238] If there is no out-of-band interference, then both the amplitude and phase of the interference are 0:

[0239]

[0240] If out-of-band interference exists, the corresponding parameters are as follows:

[0241]

[0242] Next, tests were conducted. Based on the IEEE Std C37.118 measurement standard, signals from low-temperature, normal, and high-temperature environments were collected for simulation tests. Specifically, the signals were three types of signals with different frequencies: those containing only the fundamental frequency, those containing harmonics, and those containing out-of-band interference.

[0243] 1. Only includes fundamental frequency signal testing

[0244] The signal model x(t) is:

[0245] Where t represents time t, and the value of f0 ranges from 45 to 55 Hz.

[0246] according to Figure 6 It can be seen that the errors TVE, FE, and RFE are all within the allowable range of the p-class and m-class errors, respectively. TVE, FE, and RFE represent the total vector error, frequency error, and frequency change rate error, respectively.

[0247] 2. Testing for the presence of harmonic distortion

[0248] The signal model x(t) is:

[0249]

[0250] Where n i The harmonic order is measured, with a range of 2nd to 50th harmonics. Figure 7 It can be seen that the errors of TVE, FE, and RFE are all within the allowable range of p-class and m-class.

[0251] 3. Testing under out-of-band interference conditions

[0252] The signal model x(t) is:

[0253]

[0254] Where f i The out-of-band interference frequency is measured in the range of 2nd-50th harmonics. Figure 8 It can be seen that the errors of TVE, FE, and RFE are all within the allowable range of p-class and m-class.

[0255] Table 2 compares the maximum error values ​​under all temperature conditions with the requirements of Class P and Class M. As can be seen from the table, all maximum error values ​​are far below the standard requirements.

[0256] Table 2. Sine Window Error Statistics

[0257]

[0258] The iterative compensation synchronous phasor measurement method provided in this embodiment has at least the following beneficial effects: 1. By using spectral leakage compensation and setting a cost function, the cost function value decreases with the increase of the number of iterations, resulting in higher measurement accuracy. This leads to the optimal value of the cost parameter, the most accurate measurement of the fundamental wave and interference parameters, and improved synchronous phasor measurement accuracy. Furthermore, it simultaneously meets the P-level and M-level performance requirements defined in IEEE STD.C37.118. 2. It considers the application of two typical window functions, Hanning and sine, and proposes different calculation formulas and rules for different window functions. 3. It takes into account the influence of out-of-band interference on the fundamental phasor and performs out-of-band interference compensation for the signal. 4. Considering that the device may be deployed outdoors and subject to drastic temperature changes, a temperature drift compensation mechanism is added. This ensures the performance of synchronous phasor measurement, requiring only one device to complete the measurement, thus reducing operating costs.

[0259] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the application disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and incorporate common knowledge or customary techniques in the art disclosed herein. The specification and examples are to be considered exemplary only, and the true scope of this application is indicated by the claims.

[0260] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The embodiments of this application described above do not constitute a limitation on the scope of protection of this application.

Claims

1. A synchronous phasor measurement method with iterative compensation, characterized in that, Applicable to any synchronous phasor measurement device, including: The voltage and current at a preset time are collected as raw data, and ambient temperature and time information are also collected. After selecting a window function that meets the requirements, the original data is windowed in multiple segments and then subjected to Discrete Fourier Transform (DFT) to obtain multiple sets of DFT sequences of the original data with windowing. The average of the multiple sets of DFT sequences is then calculated to obtain the final target DFT sequence. A preliminary estimate of the cost parameters is performed on the target DFT sequence to reconstruct the fundamental wave sequence in the target DFT sequence; Calculate a first cost function based on the cost parameters, and determine whether the original data has out-of-band interference based on the first cost function: If there is no out-of-band interference, spectral leakage compensation is performed on the last fundamental wave sequence to estimate the fundamental wave parameters; Calculate the second cost function based on the target DFT sequence and the fundamental sequence; Determine whether the value of the second cost function is less than the accuracy threshold or whether the number of iterations n is greater than the maximum value N of the fundamental iteration; If yes, then stop compensation; if no, then return to the steps of performing spectral leakage compensation on the last fundamental wave sequence and estimating the fundamental wave parameters, and increment the value of n by one. If out-of-band interference exists, the interference sequence is separated from the target DFT sequence based on the last fundamental wave sequence, spectral leakage compensation is performed on the interference sequence, and the interference parameters are estimated. The fundamental wave sequence is separated from the target DFT sequence based on the interference parameters, and spectral leakage compensation is performed on the fundamental wave sequence to estimate the fundamental wave parameters. Calculate the third cost function based on the interference sequence and the fundamental frequency sequence; Determine whether the value of the third cost function is less than the precision threshold or whether the number of iterations m is greater than the maximum value of the interference iterations M; If yes, then stop compensation; if no, then return to the steps of separating the interference sequence from the target DFT sequence based on the last fundamental wave sequence, performing spectral leakage compensation on the interference sequence, estimating the interference parameters, and incrementing the value of m by one. Based on the ambient temperature, the fundamental wave parameter, and the interference parameter, temperature drift compensation is performed on the fundamental wave parameter and the interference parameter respectively to obtain the target fundamental wave parameter and the target interference parameter. The target fundamental wave parameter, the target interference parameter, and the target time stamp are reported to the main station, wherein the target time stamp is the average value of time information collected within a preset time period.

2. The synchronous phasor measurement method with iterative compensation according to claim 1, characterized in that, The sequence x after multi-segment windowing of the original data by selecting a window function that meets the requirements. ’ (n) is: ； Where x1(n)-x5(n) represent the first to fifth windowed original data segments, x(n) represents the nth original data segment, w(n) represents the window function, and L represents the length of the windowed original data segment.

3. The synchronous phasor measurement method with iterative compensation according to claim 2, characterized in that, The multiple sets of DFT sequences x ’ (k) is: ； in, L represents the normalization factor, and N represents the original data length. This represents the rotation factor.

4. The synchronous phasor measurement method with iterative compensation according to claim 3, characterized in that, The target DFT sequence X(k) is: 。 5. The synchronous phasor measurement method with iterative compensation according to claim 4, characterized in that, The specific steps for performing a preliminary estimation of the cost parameter δ to reconstruct the fundamental wave sequence in the target DFT sequence are as follows: Find the maximum sequence k based on the distribution of the target DFT sequence. max Location The trend factor ε and cost parameter δ are obtained; and the cost parameter δ needs to be determined based on the specific window function chosen. ; The fundamental frequency, amplitude, and phase are obtained based on the cost parameter δ and the window function type. ; The restored fundamental frequency sequence for: ； Wherein, parameter K represents the frequency index. This indicates the first fundamental frequency sequence. This represents the positive component of the first fundamental frequency sequence. This represents the negative component of the first fundamental frequency sequence. T represents the amplitude of the first fundamental frequency. total Indicates the preset time.

6. The synchronous phasor measurement method with iterative compensation according to claim 5, characterized in that, The first cost function c(δ) is: , where X(k) represents the target DFT sequence.

7. The synchronous phasor measurement method with iterative compensation according to claim 1, characterized in that, The specific steps for spectral leakage compensation of the final fundamental wave sequence are as follows: Where spec-compens represents spectral leakage compensation. The fundamental frequency, amplitude, phase, and DFT sequence of the nth iteration are represented sequentially.

8. The synchronous phasor measurement method with iterative compensation according to claim 7, characterized in that, When there is no out-of-band interference, the fundamental frequency parameters are: ;in, Represents the positive component of the n+1th fundamental wave sequence, This represents the negative component of the (n+1)th fundamental wave sequence. T represents the (n+1)th fundamental wave dft sequence. total Here, k represents the preset time, k represents the frequency index, W represents the DFT sequence of the window function, and j is the imaginary unit. This represents the amplitude of the (n+1)th fundamental wave sequence. This represents the frequency of the (n+1)th fundamental wave sequence, with the subscript 0 indicating the fundamental wave and the superscript indicating the iteration number. The second cost function is: , where X(k) represents the target DFT sequence.

9. The synchronous phasor measurement method with iterative compensation according to claim 1, characterized in that, When out-of-band interference is present, the interference parameters are: , where m is the number of iterations. The frequency, amplitude, and phase of the (m+1)th interference are represented sequentially. The fundamental wave parameters are: ； The third cost function c(δ) is: ,in, Let X(k) represent the target DFT sequence, the fundamental DFT sequence of the (m+1)th iteration, and the interference DFT sequence of the (m+1)th iteration, respectively. The subscript 0 represents the fundamental, i represents the interference, the superscript represents the iteration number, and X(k) represents the target DFT sequence.

10. A synchronous phasor measurement device with iterative compensation for applying the synchronous phasor measurement method with iterative compensation according to any one of claims 1-9, characterized in that, It includes a data acquisition module, a transformation module, a first compensation module, a second compensation module, and a reporting module. The acquisition module is used to acquire voltage, current and ambient temperature for a preset time. The acquisition module integrates a time synchronization module, which is used to acquire time information. The transformation module is used to select a window function that meets the requirements to perform multi-segment windowing on the original data and then perform discrete Fourier transform to obtain multiple sets of DFT sequences of the windowed original data. The average of the multiple sets of DFT sequences is then calculated to obtain the final target DFT sequence. The first compensation module is used to perform spectral leakage compensation on the target DFT sequence; The second compensation module is used to perform temperature drift compensation on the fundamental wave parameter and the interference parameter according to the ambient temperature, the fundamental wave parameter and the interference parameter, respectively, to obtain the target fundamental wave parameter and the target interference parameter; The reporting module is used to report the target fundamental wave parameter, the target interference parameter, and the target time stamp to the main station, wherein the target time stamp is the average value of time information collected within a preset time period.

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