Voltage transformer error evaluation method considering harmonic influence

Abstract

The invention discloses a voltage transformer error evaluation method considering harmonic influence, which comprises the following steps of: analyzing the short-time invariant characteristic of the unbalance degree of voltage output by a voltage transformer, and quantifying the measurement error of a three-phase voltage transformer according to the amplitude of the three-phase unbalance degree; based on a robust-principal component analysis algorithm, a matrix formed by the three-phase voltage signals of the voltage transformer is decomposed into a principal component space and a residual space, the principal component space corresponds to the actual measurement value of the voltage transformer, and the residual space corresponds to the measurement error; and monitoring the offset size of the principal component space and the residual space by using statistical magnitude, and taking the offset size as an evaluation basis of the measurement error of the voltage transformer. According to the mutual inductor error evaluation method based on the robust-principal component analysis algorithm provided by the invention, accurate identification of sudden change and gradual change of the phase difference of the mutual inductor can be realized, and accurate early warning can be carried out on a fault phase.

Description

Technical Field

[0001] The invention relates to the field of voltage transformers, and in particular to a voltage transformer error evaluation method taking harmonic influence into consideration. Background Art

[0002] The new distribution network under the background of "double high" has serious harmonic pollution, which leads to the decline of power quality and seriously affects the accuracy of metering devices such as transformers. As an important component of power metering devices in the new distribution network, the accuracy and reliability of voltage transformers' measurement data are the basis for ensuring the safe and stable operation of the power system. Therefore, the development of new distribution networks urgently needs to realize the online evaluation of transformer errors without power outages.

[0003] With the high proportion of new energy grid connection and the increase of nonlinear loads in distribution networks, new distribution networks are facing challenges from harmonic injection with diverse frequencies and uncertain contents. However, the current electromagnetic transformers mainly rely on electromagnetic coils to transmit signals, which are particularly sensitive to high-order harmonics, and can easily cause PT (Potential Transformer) to enter saturation, which may lead to errors in measurement results and affect the reliability and stability of the system. At the same time, due to the limited working range of PT and the transient, wide frequency domain and high frequency characteristics of harmonics themselves, it is difficult for traditional equivalent models to describe the harmonic transmission characteristics of PT. At present, the harmonic factors that cause errors in the measurement of voltage transformers in new distribution networks are mainly harmonic frequency, harmonic content and multi-harmonic superposition.

[0004] Traditional voltage transformer error assessment methods usually ignore the impact of harmonics and only consider the error under fundamental conditions. This method may lead to large measurement errors in practical applications, affecting the stability and safety of the power system.

[0005] The disclosure of the above background technology content is only used to assist in understanding the concept and technical solution of the present application. It does not necessarily belong to the prior art of the present application, nor does it necessarily provide technical guidance. In the absence of clear evidence that the above content has been disclosed before the filing date of the present application, the above background technology should not be used to evaluate the novelty and creativity of the present application. Summary of the invention

[0006] The purpose of the present invention is to provide a transformer error evaluation model based on robust PCA, so as to accurately evaluate whether the transformer measurement error considering the influence of harmonics is abnormal.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A voltage transformer error evaluation method considering harmonic influence comprises the following steps:

[0009] The short-time invariance characteristics of the voltage imbalance output by the voltage transformer are analyzed, and the measurement error of the three-phase voltage transformer is quantified by the amplitude of the three-phase imbalance.

[0010] Based on the robust principal component analysis algorithm, the matrix composed of the three-phase voltage signals of the voltage transformer is decomposed into a principal component space and a residual space, wherein the principal component space corresponds to the actual measurement value of the voltage transformer, and the residual space corresponds to the measurement error; and statistics are used to monitor the offset size of the principal component space and the residual space as a basis for evaluating the measurement error of the voltage transformer.

[0011] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, using statistics to monitor the offset between the principal element space and the residual space as a basis for evaluating the measurement error of the voltage transformer includes:

[0012] quantifying the extent to which the actual measurement value of the voltage transformer to be evaluated at a certain moment is projected into the subspace of the residual space by using a Q statistic;

[0013] If the quantized result of the projection degree is greater than a preset statistical threshold, it is determined that the voltage transformer measurement error is abnormal; otherwise, it is determined that the measurement error is within a normal range.

[0014] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the projection degree is calculated by the following formula:

[0015] Among them, Q(j) is the projection degree, e j is the j-th row vector of the residual matrix E, e j T for e j The inverted matrix of is the standard matrix The i-th row vector of for The inverted matrix, I is the identity matrix, P is the principal element load matrix, P T is the inverse matrix of matrix P;

[0016] Among them, the standard matrix The standardized matrix is ​​formed after preprocessing and standardizing the data set X composed of the amplitudes of the three-phase imbalance degree: The data set X is composed of n rows and m columns, M = [μ1,…,μ m ], μ1 is the mean of the first column of the data set X, μ m is the mean of the mth column of the data set X, 1 n is the n-order identity matrix, D σ is the variance of the data set X.

[0017] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the preset statistical threshold is obtained by the following formula:

[0018]

[0019] Among them, Q α is the statistical threshold, k is the number of principal components, λ j i is the standard matrix The i-th power of the j-th item in the eigenvalue set of the covariance C matrix; C α is the critical value of the standard normal distribution with confidence level α.

[0020] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the residual matrix E is obtained by the following method:

[0021] The standard matrix Decomposed into score vector t i and the load vector p i The inner product of

[0022] Define P as the principal element load matrix, P e is the residual loading matrix, T is the principal component score matrix, T e is the residual score matrix;

[0023] The standard matrix Converts to: Among them, k is the number of principal components, TP T is the principal element matrix, E = T e P e T is the residual matrix.

[0024] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the load vector p i By dividing the standard matrix The covariance C matrix of is obtained by singular value decomposition;

[0025] According to the principal element space and the residual space, the load vector p i Divided into principal component load matrix P and residual load matrix P e .

[0026] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the standard matrix is ​​selected The weighted covariance matrix NewC of is expressed as:

[0027] in:

[0028]

[0029] in, is the standard matrix The i-th row vector, u n for The ideal response value of , β is a regulation parameter greater than 0;

[0030] According to the characteristic equation of the weighted covariance matrix NewC, solving the matrix characteristic roots of the weighted covariance matrix NewC;

[0031] Combined with the decomposition formula of the weighted covariance matrix NewC, NewC = PΛP T / (n-1), calculate the principal component load matrix P.

[0032] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the number of principal components k is determined by using the cumulative variance contribution rate method:

[0033] Set the expected threshold T H ;

[0034] Solution To calculate the number of the main components k, where λ i is the standard matrix The i-th item in the eigenvalue set of the covariance C matrix of .

[0035] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, if it is evaluated that the measurement error of the voltage transformer is abnormal, the following steps are further performed:

[0036] The contribution rate of each phase in the three phases to the measurement error of the voltage transformer is calculated by the following formula:

[0037] Among them, Cont i Q is the corresponding contribution rate of the ith i is the column vector of the subspace of the residual space corresponding to the ith is the standard matrix corresponding to the ith , is the column vector of the subspace of the principal element space corresponding to the i-th element;

[0038] Compare the contribution rates of the three phases;

[0039] Determine the phase with the largest contribution rate as the fault phase.

[0040] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the measurement error of the three-phase voltage transformer is quantified in the following manner:

[0041]

[0042] , where U At , U Bt , U Ct is the amplitude of each phase voltage of the three-phase voltage transformer at time t, cosθ At 、cosθ Bt 、cosθ Ct is the cosine value of the initial phase angle of each phase, is the amplitude of the three-phase unbalance degree taking into account the influence of harmonics at time t, which is used as the measurement error of the three-phase voltage transformer.

[0043] The beneficial effects brought by the technical solution provided by the present invention are as follows:

[0044] a. The present invention provides a method for accurately evaluating the voltage transformer measurement error under harmonic interference. This method can more accurately evaluate the error level of the voltage transformer in the new distribution network and improve the robustness of the voltage transformer measurement;

[0045] b. By evaluating the transformer online, its working status and performance indicators can be monitored in real time, potential problems can be discovered in time and corresponding measures can be taken, thereby effectively improving the reliability and accuracy of the measurement and ensuring the efficient operation of the power system. This is of great significance to the reliability and stability of the new distribution network and helps to improve the intelligence level of system operation and management efficiency;

[0046] c. After fully considering the influence of harmonics on the metering error of the voltage transformer, the present invention proposes a transformer evaluation method based on the robust-principal component analysis algorithm by analyzing the short-time invariant characteristics of the imbalance of the voltage output by the voltage transformer. On the voltage transformer metering error evaluation test platform, the error simulation device is used to further simulate the abnormal metering state of the transformer caused by the harmonics of the new distribution network. The obtained test data is used to verify that the transformer error online evaluation model based on robust-PCA proposed in the present invention can accurately identify voltage transformers with excessive ratio difference and angle difference, and can accurately warn the faulty phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0048] Figure 1 A basic flow chart of a voltage transformer error evaluation method considering harmonic influence provided by an exemplary embodiment of the present invention;

[0049] Figure 2 A schematic diagram of an R-PCA algorithm provided as an exemplary embodiment of the present invention for converting raw data into linearly independent statistics by rotating coordinate axes;

[0050] Figure 3 A schematic diagram of a specific flow chart of a mutual inductor error evaluation algorithm provided by an exemplary embodiment of the present invention;

[0051] Figure 4 A diagram of the R-CPA model amplitude detection process provided for an exemplary embodiment of the present invention;

[0052] Figure 5 A diagram of the R-CPA model amplitude detection process provided for an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0054] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, device, product or equipment that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or equipment.

[0055] The present invention aims to provide a voltage transformer error evaluation method considering the influence of harmonics, establish an online evaluation model to evaluate the transformer online, monitor its working status and performance indicators in real time, discover potential problems in time and take corresponding measures, so as to effectively improve the reliability and accuracy of the measurement and ensure the efficient operation of the power system. This technical means is of great significance to the reliability and stability of the new distribution network, and helps to improve the intelligence level and management efficiency of the system operation.

[0056] In one embodiment of the present invention, a voltage transformer error evaluation method considering harmonic influence is provided, such as Figure 1 As shown, the evaluation method includes the following steps:

[0057] The short-time invariance characteristics of the voltage imbalance output by the voltage transformer are analyzed, and the measurement error of the three-phase voltage transformer is quantified by the amplitude of the three-phase imbalance.

[0058] Based on a robust principal component analysis algorithm, decomposing a matrix composed of three-phase voltage signals of a voltage transformer into a principal component space and a residual space, wherein the principal component space corresponds to an actual measurement value of the voltage transformer, and the residual space corresponds to the measurement error; and

[0059] The offset between the principal element space and the residual space is monitored by using statistics as a basis for evaluating the measurement error of the voltage transformer, as follows: Figure 1 As shown:

[0060] quantifying the extent to which the actual measurement value of the voltage transformer to be evaluated at a certain moment is projected into the subspace of the residual space by using a Q statistic;

[0061] If the quantization result of the projection degree, i.e., the statistic Q(j), is greater than the preset statistic threshold Q α , it is determined that the voltage transformer measurement error is abnormal, otherwise it is determined that the measurement error is within the normal range.

[0062] Based on the above, in order to implement an embodiment of the present invention, the first step is to analyze the short-time invariant characteristics of the unbalanced output voltage of the three-phase voltage transformer, and then determine / quantify the measurement error of the voltage transformer; the second step is to establish an online evaluation model of the PT error of the voltage transformer based on the robust principal component analysis algorithm, i.e., the R-PCA algorithm, to obtain the Q statistic representing the offset between the principal component space and the residual space, and then use the Q statistic as an evaluation basis to determine whether the measurement error of the PT quantified in the first step exceeds the normal range.

[0063] The following are detailed descriptions of these two steps:

[0064] The first step is to analyze the short-time invariant characteristics of the output voltage imbalance of the three-phase voltage transformer.

[0065] From the operating characteristics of the power system itself, it can be seen that the phase voltage signals on the primary side of the transformer have the following relationship:

[0066] Where: is the phasor of each phase voltage on the primary side, A phasor defined as the degree of unbalance of the three-phase voltage. The real part of satisfies the following formula (2), that is:

[0067]

[0068] Where U At , U Bt , U Ct is the amplitude of each phase voltage of the three-phase voltage transformer at time t, cosθ At 、cosθ Bt 、cosθ Ct is the cosine value of the initial phase angle of each phase, is the amplitude of the three-phase unbalance degree taking into account the influence of harmonics at time t, which is used as the measurement error of the three-phase voltage transformer.

[0069] This embodiment also includes the following further analysis to illustrate the impact of harmonics:

[0070] Under the condition of considering the influence of harmonics, based on the characteristics of three-phase symmetrical operation in the power grid, the relationship between the variables can be transformed into the state equation as shown in formula (3):

[0071]

[0072] Where t is the time when the voltage is collected; U(t+1)=[U At ,U Bt ,U Ct ] T ,θ(t+1)=[θ At ,θ Bt ,θ Ct ] T ;p U 、p θ is a network element parameter. In an embodiment where network parameters are not considered, p U 、p θ All can be regarded as 0; A U =A θ Represents the physical characteristics of the operation, and its value remains unchanged; S U (t), D U (t+1) and S θ (t), Dθ (t+1) causes the three-phase voltage to be asymmetric, where S U (t) is the voltage parameter caused by the switching device, D U (t+1) is the voltage parameter caused by the load, S θ (t) is the phase parameter caused by the switching device, D θ (t+1) Phase parameter caused by load; H U , H θ is the component generated by harmonics. Therefore, formula (3) can be simplified as:

[0073]

[0074] Among them, Ref U (t) is S U (t), D U (t+1), Ref θ (t) is S θ (t), D t (t+1).

[0075] At this time, the voltage signal output by the metering winding of the three-phase PT contains the following information:

[0076]

[0077] In the formula, u at 、u bt 、u ct is the amplitude of the a / b / c three-phase output voltage of PT at time t, θ at ,θ bt ,θ ct is the initial phase angle of each phase, k is the number of principal elements, v fat is the voltage component of phase a generated by wind power generation in the distribution network, v fbt is the b-phase voltage component generated by wind power generation in the distribution network, v fct is the c-phase voltage component generated by wind power generation in the distribution network; s fax is the voltage component of phase a generated in photovoltaic power generation, s fbx is the b-phase voltage component generated in photovoltaic power generation, s fcx is the c-phase voltage component generated in photovoltaic power generation; h fat is the harmonic interference component of phase a, h fbt is the b-phase harmonic interference component, h fct is the c-phase harmonic interference component;

[0078] v θat is the initial phase angle of phase a in wind power generation under the distribution network, v θbt is the initial phase angle of phase b in wind power generation under the distribution network, vθct is the initial phase angle of phase c in wind power generation under the distribution network; s θax is the initial phase angle of phase a in photovoltaic power generation, s θbx is the initial phase angle of phase b in photovoltaic power generation, s θcx is the initial phase angle of phase c in photovoltaic power generation; h θat is the initial phase angle of the a-phase harmonic interference component, h θbt is the initial phase angle of the b-phase harmonic interference component, h θct is the initial phase angle of the c-phase harmonic interference component.

[0079] Therefore, when there is harmonic interference, the PT output information is shown in formula (7):

[0080]

[0081] In formula (7), u(t+1)=[u at ,u bt ,u ct ] T ,θ(t+1)=[θ at ,θ bt ,θ ct ] T , Ref U (t), Ref θ (t), H U , H θ is the disturbance amount that causes asymmetry.

[0082] The above disturbances reflect the three-phase imbalance and measurement error information. Under harmonic interference, the measurement error of the three-phase PT is mainly caused by harmonics; similarly, the three-phase imbalance of the power system can also be regarded as a constant in a short time, that is, in addition to u(t+1), θ(t+1), H U , H θ , other parameters remain basically unchanged and can be regarded as constants. When the PT is running, the linear relationship between the secondary output voltage signal and the primary voltage physical signal of the power system is the key, that is, the transformer presents this linear relationship under normal working conditions, so this linear relationship can be used as a key evaluation criterion, and then the correlation of the secondary output information is further analyzed to distinguish the data errors caused by the harmonic fluctuations of the power system and the PT itself. Through numerical analysis and the establishment of statistical features, the measurement error of the three-phase PT can be quantified, and its measurement error status can be evaluated according to the feature changes.

[0083] The second step is to establish an online evaluation model of the PT error of the voltage transformer based on the robust principal component analysis algorithm, namely the R-PCA algorithm.

[0084] Through the above analysis, even with the influence of harmonics, the secondary side and the primary side of the voltage transformer are still in a linear relationship during operation. The existence of this linear relationship leads to the robust principal component analysis algorithm.

[0085] The R-PCA algorithm aims to rotate the coordinate axes of the data set so that the new coordinate axes can more accurately reflect the deviation degree of the abnormal statistical variables and the amplitude of the three-phase imbalance degree including the influence of harmonics in the above formula (2). The greater the influence of harmonics in the distribution network, the greater the deviation degree reflected. Therefore, the R-PCA algorithm is suitable for the error evaluation of voltage transformers in distribution networks.

[0086] By linearly combining the original coordinates, new statistics are obtained, thereby effectively detecting and describing abnormal data. From a geometric point of view, the original data is converted into linearly independent statistics by rotating the coordinate axes, so that abnormal variables can be effectively detected, such as Figure 2 In the new coordinate system, the abnormal data shows obvious deviation, which makes the main factors (such as y1) prominent, while the minor factors (such as y2) can be ignored, reducing the constraints and improving the evaluation efficiency.

[0087] Assume that the deviation after the three-phase unbalance is added is There are n rows and m columns in the data set X n×m , which is the three-phase unbalance degree obtained after executing the above formula analysis. Due to the large differences between the data and the possibility of data missing, in order to facilitate R-PCA analysis, the data set needs to be preprocessed and standardized to form a standardized matrix as shown in formula (8) to ensure the accuracy and reliability of the analysis.

[0088]

[0089] in, is a standard matrix, the data set X is a matrix with n rows and m columns, is the variance of the data set X; M=[μ1,…,μ m ], 1 n is the n-order identity matrix to highlight that M is in matrix form, μ1 is the mean of the first column of the data set X, μ m is the mean of the mth column of the data set X.

[0090] In one embodiment, the standard matrix It can be decomposed into the score vector t i and the load vector p i The inner product of P is defined as the principal component load matrix, P e is the residual loading matrix, T is the principal component score matrix, T eis the residual score matrix. The standard matrix It can be transformed into formula (8):

[0091]

[0092] Where, k≤m is the number of principal components; TP T is the principal element matrix, E = T e P e T is the residual matrix.

[0093] If the standard matrix The covariance C matrix of can be decomposed by singular value to obtain the load vector p i , thus obtaining the P matrix and P e Matrix, which can be specifically a matrix that converts the load vector p into i Divided into principal component load matrix P and residual load matrix P e .

[0094]

[0095] In the formula, Λ σ =diag(λ1,…,λ m ), where λ1,λ2,…,λ m is the standard matrix The eigenvalues ​​of the covariance C matrix, and λ1>λ2>…>λ m , each eigenvalue λ i The corresponding eigenvector is p i .

[0096] In order to further improve the robustness of the R-PCA algorithm, enhance the algorithm's ability to handle abnormal outliers, and improve the performance in the face of complex data, the present invention uses a weighted covariance matrix NewC to replace the original covariance matrix C. The expression of its weighted covariance matrix is ​​as follows:

[0097]

[0098] In the formula, and Among them, β is a regulating parameter, which is greater than 0. Its purpose is to reduce the impact of outlier data on the principal component model. is the standard matrix The i-th row vector, u n for The ideal response value.

[0099] NewC matrix eigenvalue λ i The size of is closely related to the correlation degree of the corresponding quantity. The detailed solution process is given below:

[0100] variable x i 、x j The correlation between them can be expressed by unbiased estimation, as shown in the following formula:

[0101]

[0102] r ij ^ is the variable x i 、x j The correlation between them, x ki 、x kj The data in the i-th row and k-th column and the data in the k-th row and j-th column are respectively are the average values ​​of the i-th row and the j-th column, respectively, s i 、s j are the standard deviation of the i-th row and the j-th column, respectively, ski For x ki - A simplified representation of x skj For x kj - A simplified representation of .

[0103] From formula (11), we can further calculate

[0104] Therefore, the standard matrix The NewC matrix can be expressed as:

[0105]

[0106] In the formula, Then, through the characteristic equation |NewC-λI|=0, where I is the unit matrix, the characteristic roots of the NewC matrix can be obtained, and finally the principal element load matrix P is solved. Then, the load vector p is converted into i Divided into principal component load matrix P and residual load matrix P e matrix.

[0107] In addition, the criterion for selecting the number of principal components is whether the critical value of the principal component and the residual space can be accurately and quickly identified, so as to make the state monitoring threshold more reasonable. In the present invention, the number of principal components k is determined by the Cumulative Percent of Variance (CPV), that is, the number of principal components k is determined by the variance contribution ratio of the first p principal components. The specific formula is:

[0108]

[0109] Among them, λ iis the standard matrix The i-th item in the eigenvalue set of the covariance C matrix / weighted covariance matrix NewC. The method discussed in the present invention uses only three voltage amplitude variables when making error predictions, and the influence of subjective selection can be ignored. Therefore, although the expected value of 85% is subjectively selected, this method can still select the number of principal components simply, reliably and efficiently, and the present invention does not limit the expected threshold value T of the variance contribution ratio. H is 85%.

[0110] At this point, we can get the principal element matrix TP T and the residual matrix

[0111] Then, the statistics and thresholds are calculated to make the evaluation results. The statistics are calculated as follows:

[0112] The embodiment of the present invention uses R-PCA to process the standard matrix X and decompose it into a principal component space and a residual space, wherein the principal component space corresponds to the actual measurement value of the voltage transformer and the residual space corresponds to the measurement error of the voltage transformer. The weighted covariance NewC matrix will also undergo corresponding changes, affecting the mapping area of ​​the subspace of the principal component space (hereinafter referred to as the principal component subspace) or the subspace of the residual space (hereinafter referred to as the residual subspace). In order to measure the accuracy fluctuation of the secondary output data of the transformer, the data deviation degree statistics are provided as a reference, and the key is to use the Q statistic to monitor the offset size of the principal component and residual space. Therefore, the present invention processes the standard matrix through R-PCA, and uses the Q statistic to monitor the accuracy fluctuation of the voltage transformer output data, so as to achieve the goal of transformer metering state evaluation.

[0113] The Q statistic (Squared Prediction Error, SPE) can quantify the projection degree of the estimated data in the residual subspace at a certain moment, and its calculation formula is expressed as:

[0114]

[0115] Where Q(j) is the projection degree, e j is the j-th row vector of the residual matrix E, e j T for e j The inverted matrix of is the standard matrix The i-th row vector of for The inverted matrix, I is the identity matrix, P is the principal element load matrix, P T is the inverse matrix of the matrix P.

[0116] Under the condition of confidence α, the threshold Q of the Q statistic can be obtained α , as follows:

[0117]

[0118] In the formula, Q α is the statistical threshold, k is the number of principal components, λ j i is the standard matrix The i-th power of the j-th term in the eigenvalue set of the covariance C matrix, C α is the critical value of the standard normal distribution with a confidence level of α, and the value of α is usually 0.99.

[0119] The condition for determining whether the measurement is wrong is shown in formula (16), that is, when the sample data Q statistic of the transformer secondary output is lower than the threshold Q α When , it indicates that the transformer measurement error is within the normal range, otherwise it is abnormal.

[0120] Q(j)≤Q α (16)

[0121] Most of the data that cause the measurement error of the transformer are generally mapped in the residual subspace. Therefore, Q statistical feature is an effective way to characterize the abnormal situation of the transformer measurement deviation and its deviation degree, so as to monitor the measurement status of the transformer.

[0122] Although the Q statistic can be used to detect metering anomalies, it cannot determine the specific source of the three-phase mutual inductor fault, that is, it cannot determine which phase the metering error comes from. The present invention analyzes the correlation between the three-phase voltage amplitude and the Q statistic, establishes the over-limit contribution rate of each phase data, and displays the degree statistics of each relative to the projected area of ​​the residual subspace. Finally, by comparing the contribution ratio of each phase data, the phase of the metering fault can be determined.

[0123] The specific contribution rate calculation formula after the metering error occurs in each phase is as follows:

[0124]

[0125] Among them, Cont i Q is the corresponding contribution rate of the ith i is the column vector of the subspace of the residual space corresponding to the ith is the standard matrix corresponding to the ith , is the column vector of the subspace of the principal element space corresponding to the i-th element.

[0126] Compare the contribution rates of the three phases; determine the phase with the largest contribution rate as the fault phase; and

[0127] After further determining the fault phase of the transformer using the contribution diagram method, a fault alarm is issued and online calibration is performed.

[0128] In summary, the transformer error evaluation algorithm process is as follows: Figure 3 As shown, the specific process is as follows:

[0129] First, the model is established offline, including: ① obtaining offline raw data and standardizing it; ② calculating or presetting the adjustment parameter β (for formula (10)) that can reduce the influence of outliers based on empirical values; ③ calculating the weighted covariance matrix NewC according to formula (12) to complete the establishment of the initial offline R-PCA model; ④ calculating the Q statistic and control threshold using formulas (14) and (15);

[0130] Secondly, online evaluation includes: ① collecting real-time operation data and performing standardization processing; ② calculating the Q statistic of the new data through formula (14) and comparing it with the statistic threshold Q α ③ Compare, if it does not exceed the threshold, it is judged to be operating normally, and return to update the R-PCA model with new data; if it exceeds the threshold, it is judged to be operating abnormally; ③ Use the contribution graph method to further determine the fault phase of the transformer; ④ Issue a fault alarm and perform online calibration.

[0131] The embodiment of the present invention can evaluate the mutual inductor measurement error through amplitude analysis and phase analysis.

[0132] I. Amplitude Analysis

[0133] The traditional PCA and R-PCA evaluation models use residuals and principal component spaces to distinguish the measurement errors caused by the transformer itself and the secondary output voltage data of the primary voltage through the transformer when processing data. The goal is to separate the transformer's own errors from random errors such as primary side fluctuations, so as to more accurately understand the structure of the data and extract effective information. In the R-PCA evaluation, the choice of setting the number of principal components to 1 is to highlight the main components or features in the data and effectively separate the transformer error from random errors such as primary side fluctuations, thereby improving the robustness and accuracy of the model.

[0134] For a transformer with an accuracy level of 0.2, the present invention analyzes and processes the voltage sample data collected by the transformer to be estimated within its error limit, and obtains that when α is 0.99, the Q statistical threshold Q of the traditional PCA and R-PCA models is α They are 0.00186 and 0.00169 respectively. The model parameters are shown in Table 1.

[0135] Table 1 Parameters of the principal component model of three-phase PT amplitude information

[0136]

[0137] The R-CPA model amplitude detection process is shown in the figure Figure 4 As shown in the figure, it can be seen from the analysis of the figure that the R-PCA method mentioned in the present invention has strong robust performance, and the Q statistic threshold Q of the R-PCA model α It is smaller, indicating that the R-PCA model has a higher sensitivity in identifying the state error of the transformer.

[0138] The sudden ratio error and gradual ratio error of the voltage transformer are simulated and analyzed to obtain the error evaluation result summary table shown in Table 2. When the voltage amplitude data measured by the PT show sudden ratio error and gradual ratio error, the R-PCA-based transformer error online evaluation model proposed in the present invention can accurately identify the voltage transformer with excessive ratio error and can accurately warn the fault phase.

[0139] Table 2 Summary of the results of the ratio error evaluation

[0140]

[0141] II. Phase Analysis

[0142] Similar to the amplitude analysis, the collected voltage phase test data were imported into the R-PCA evaluation model and the traditional PCA model for comparative analysis. The principal component model parameters are shown in Table 3.

[0143] Table 3 Parameters of the principal element model of three-phase PT phase information

[0144]

[0145] The phase detection process diagram of the R-PCA model is shown in the attached figure. Figure 5 Then, the sudden and gradual angular difference errors of the voltage transformer are simulated and analyzed, and the error evaluation result summary table shown in Table 4 is obtained. When the voltage amplitude data measured by the PT shows sudden angular difference and gradual angular difference, the R-PCA-based transformer error online evaluation model proposed in the present invention can accurately identify the voltage transformer with excessive angular difference, and can accurately warn the fault phase.

[0146] Table 4 Summary of angular error evaluation results

[0147]

[0148] From the above amplitude analysis and phase analysis, it can be seen that the results obtained by the R-PCA evaluation model are consistent with the results of the sudden and gradual changes of the transformer phase difference simulated by the voltage transformer measurement error evaluation test platform in terms of both the sudden change time and the gradual change trend, and the calculation results of the fault phase are also completely consistent with the experiment.

[0149] Therefore, the online evaluation model of mutual inductor error based on the robust principal component analysis algorithm proposed in the present invention can accurately identify the sudden and gradual changes of the mutual inductor phase difference, and can accurately warn the faulty phase.

[0150] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0151] The above is only a specific implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A voltage transformer error evaluation method considering harmonic influence, characterized in that: The following steps are involved: The short-time invariance characteristics of the voltage imbalance output by the voltage transformer are analyzed, and the measurement error of the three-phase voltage transformer is quantified by the amplitude of the three-phase imbalance. Based on the robust principal component analysis algorithm, the matrix composed of the three-phase voltage signals of the voltage transformer is decomposed into a principal component space and a residual space, wherein the principal component space corresponds to the actual measurement value of the voltage transformer, and the residual space corresponds to the measurement error; and statistics are used to monitor the offset size of the principal component space and the residual space as a basis for evaluating the measurement error of the voltage transformer.

2. The voltage transformer error evaluation method considering harmonic influence according to claim 1 is characterized in that: Using statistics to monitor the offset between the principal element space and the residual space as a basis for evaluating the measurement error of the voltage transformer includes: quantifying the extent to which the actual measurement value of the voltage transformer to be evaluated at a certain moment is projected into the subspace of the residual space by using a Q statistic; If the quantized result of the projection degree is greater than a preset statistical threshold, it is determined that the voltage transformer measurement error is abnormal; otherwise, it is determined that the measurement error is within a normal range.

3. The voltage transformer error evaluation method considering harmonic influence according to claim 2 is characterized in that: The projection degree is calculated by the following formula: Among them, Q(j) is the projection degree, e j is the j-th row vector of the residual matrix E, for e j The inverted matrix of is a standard matrix The i-th row vector of for The inverted matrix, I is the identity matrix, P is the principal element load matrix, P T is the inverse matrix of matrix P; Among them, the standard matrix The standardized matrix is ​​formed after preprocessing and standardizing the data set X composed of the amplitudes of the three-phase imbalance degree: The data set X is composed of n rows and m columns, M = [μ1,…,μ m ], μ1 is the mean of the first column of the data set X, μ m is the mean of the mth column of the data set X, 1 n is the n-order identity matrix, D σ is the variance of the data set X.

4. The voltage transformer error evaluation method considering harmonic influence according to claim 3 is characterized in that: The preset statistical threshold is obtained by the following formula: Among them, Q α is the statistical threshold, k is the number of principal components, is a standard matrix The i-th power of the j-th item in the eigenvalue set of the covariance C matrix; C α is the critical value of the standard normal distribution with confidence level α.

5. The voltage transformer error evaluation method considering harmonic influence according to claim 3 is characterized in that: The residual matrix E is obtained in the following way: The standard matrix Decomposed into score vector t i and the load vector p i The inner product of Define P as the principal element load matrix, P e is the residual loading matrix, T is the principal component score matrix, T e is the residual score matrix; The standard matrix Translates to: Among them, k is the number of principal components, TP T is the principal element matrix, E = T e P e T is the residual matrix.

6. The voltage transformer error evaluation method considering harmonic influence according to claim 5, characterized in that: The load vector p i By dividing the standard matrix The covariance C matrix of is obtained by singular value decomposition; According to the principal element space and the residual space, the load vector p i Divided into principal component load matrix P and residual load matrix P e .

7. The voltage transformer error evaluation method considering harmonic influence according to claim 5, characterized in that: Select the standard matrix The weighted covariance matrix NewC of is expressed as: in: in, is a standard matrix The i-th row vector, u n for The ideal response value of , β is a regulation parameter greater than 0; According to the characteristic equation of the weighted covariance matrix NewC, solving the matrix characteristic roots of the weighted covariance matrix NewC; Combined with the decomposition formula of the weighted covariance matrix NewC, NewC = PΛP T / (n-1), calculate the principal component load matrix P.

8. The voltage transformer error evaluation method considering harmonic influence according to claim 4 or 5, characterized in that: The number of principal components k is determined by the cumulative variance contribution method: Set the expected threshold T H ; Solution To calculate the number of the main components k, where λ i is a standard matrix The i-th item in the eigenvalue set of the covariance C matrix of .

9. The voltage transformer error evaluation method considering harmonic influence according to any one of claims 1 to 7, characterized in that: If it is assessed that the measurement error of the voltage transformer is abnormal, the following steps are further performed: The contribution rate of each phase in the three phases to the measurement error of the voltage transformer is calculated by the following formula: Among them, Cont i Q is the corresponding contribution rate of the ith i is the column vector of the subspace of the residual space corresponding to the ith is the standard matrix corresponding to the ith , is the column vector of the subspace of the principal element space corresponding to the i-th element; Compare the contribution rates of the three phases; Determine the phase with the largest contribution rate as the fault phase.

10. The voltage transformer error evaluation method considering harmonic influence according to any one of claims 1 to 7, characterized in that: The measurement error of the three-phase voltage transformer is quantified as follows: ， Among them, U At , U Bt , U Ct is the amplitude of each phase voltage of the three-phase voltage transformer at time t, cosθ At 、cosθ Bt 、cosθ Ct is the cosine value of the initial phase angle of each phase, is the amplitude of the three-phase unbalance degree taking into account the influence of harmonics at time t, which is used as the measurement error of the three-phase voltage transformer.

Images