Transformer fault identification method and system based on fitting weight and equivalent inductance

Abstract

The present invention discloses a transformer fault identification method and system based on fitting weights and equivalent inductance. The method selects the voltage across the primary winding and the current across the primary and secondary windings as sampling points in the transformer to generate a matrix of the voltage and current across the primary winding within each unit data window. The method performs equivalent inductance normalization calculations to obtain an unweighted equivalent inductance. The method accumulates the equivalent inductance within the weighted data window to obtain a weighted equivalent inductance. A fault protection criterion is designed based on the weighted equivalent inductance. The fault protection criterion is used to identify transformer faults and design a protection criterion. If the equivalent inductance value consistently meets the protection criterion within the time window, the fault is determined to be within the transformer's fault zone. Compared with existing technologies, the method overcomes the drawback of large fluctuations in traditional time-domain calculations and improves the stability and reliability of protection.

Description

Technical Field

[0001] The present invention belongs to the field of power system relay protection, and in particular relates to a transformer fault determination method and system based on the transformer's time-domain equivalent inductance. Background Art

[0002] In renewable energy transmission systems, transformers play a key role in voltage conversion and energy transmission. Rapid fault identification and protection are crucial for equipment safety and system stability. Currently, current differential protection based on Kirchhoff's law is widely used as the primary transformer protection in projects. This system calculates the second harmonic content of the three-phase differential current to determine the magnetizing inrush current, thereby achieving timely protection lockout and preventing false trips. With the integration of large-scale power electronic equipment, transformer fault characteristics exhibit high harmonic characteristics, exacerbating the difficulty of identifying transformer magnetizing inrush currents. Traditional transformer protection systems carry the risk of refusal to operate or false trips.

[0003] When the transformer fault current contains high harmonic content, the second harmonic criterion can easily lock out the protection, which will not re-open until the second harmonic content drops below the threshold. To better distinguish between normal transformer operation, magnetizing inrush current, and fault conditions, the transformer's equivalent inductance is calculated in the time domain using parameter identification. This intuitively reflects the transformer's operating status, quickly identifies faults, and ensures reliable protection. Summary of the Invention

[0004] To address the difficulty in identifying transformer faults and magnetizing inrush currents under the access of new energy, the present invention proposes a transformer fault determination method and system based on fitting weights and equivalent inductance. The weighted equivalent inductance is obtained in the time domain, and the judgment criteria are formed based on the weighted equivalent inductance to quickly identify internal faults occurring in the operating state of the transformer and achieve reliable protection action.

[0005] In order to achieve the above-mentioned object of the invention, the present invention proposes the following technical solutions:

[0006] A transformer fault identification method based on fitting weight and equivalent inductance includes:

[0007] Step 1: Select the voltage across the primary winding and the current across the primary and secondary windings as sampling points in the transformer, and read any sampling point. The voltage across the primary winding , the original secondary double-end winding current sampling value 、 , calculate the differential current of each unit data window converted to the acquisition voltage side , generate the voltage matrix in each unit data window , current matrix ;

[0008] Get sampling point The voltage equation across the primary winding is as follows:

[0009] ;

[0010] Where, is the sampling point sequence index, is the sampling period, For sampling points The differential current, The next sampling point The differential current, The previous sampling point The differential current;

[0011] Select sampling period The combination of multiple sampling points in the primary winding voltage matrix U and current matrix I are obtained, and the expressions are as follows:

[0012] ;

[0013] Set the least squares window length n, the primary winding voltage matrix within the least squares window length n and current matrix It is expressed as follows:

[0014] ;

[0015] , ;

[0016] Where, , ,... ..., is the current sampling sequence within the unit data window length n, , ,... ..., is the differential derivative sequence of the current sampling points within the unit data window length n, where n is the least squares calculation window length. is the data index within the least squares calculation window;

[0017] The sampling sequence equations are obtained, which can be expressed as:

[0018] ;

[0019] Step 2: Perform normalized calculation of the equivalent inductance to obtain the unweighted equivalent inductance. The specific description is as follows:

[0020] The least squares method is used to estimate and solve the sampling sequence equations, that is, the fitting coefficient matrix The calculated value of the voltage matrix in the data window is The primary winding voltage matrix with least squares The actual value has the smallest distance in Euclidean space, and the Euclidean distance between the two is The expression is:

[0021] ;

[0022] The Euclidean distance The formula is used to find the partial derivative and set it equal to 0 to obtain the fitting coefficient matrix in each unit data window. , the expression is as follows:

[0023] ;

[0024] The solution to the equation is , r and L are the primary winding voltage equations respectively The unfitted equivalent resistance and equivalent inductance in ;

[0025] Step 3: Accumulate and calculate the weighted data window The equivalent inductance inside is calculated to obtain the weighted equivalent inductance, which is described as follows:

[0026] Define the fitting error for a single fitting calculation The expression is as follows:

[0027] ;

[0028] in, 、 Represents any sampling point in the data window The corresponding primary winding voltage matrix and current matrix;

[0029] Set the weighted data window length m, and select any sampling point in the weighted data window according to the corresponding unit data window. The weight coefficient Perform weighted summation and normalization as the calculation result of equivalent inductance output. At this time, the equivalent inductance calculation formula is:

[0030]

[0031] ;

[0032] Cumulative calculation weighted data window The fitted equivalent inductance of the corresponding weighted data window length m is used to obtain the weighted equivalent inductance, which is expressed as follows:

[0033] ;

[0034] Where, The fitting weight of the result is calculated for each unit inductance of the weighted data window, is the weight matrix composed of all weights, is the weighted data window index, m is the weighted data window length, 1< <m, is the equivalent inductance value in the weighted data window, is the weighted equivalent inductance, is the fitting weight corresponding to 1, 2, 3, ...m in the weighted data window;

[0035] Step 4: design a fault protection criterion based on the weighted equivalent inductance, and use the fault protection criterion to identify transformer faults:

[0036] The design protection criterion is expressed as:

[0037] ;

[0038] Where, is the weighted data window index The equivalent inductance, , is the inductance threshold, is the coefficient of fluctuation, To protect the time window of the criterion, if the value of the equivalent inductance is If the criterion is met within the time window, it is determined that the transformer has an internal fault.

[0039] A transformer fault identification system based on fitting weight and equivalent inductance includes:

[0040] Transformer information acquisition module, used to select the voltage at both ends of the primary winding and the current at both ends of the primary and secondary windings as sampling points in the transformer, and read any sampling point The voltage across the primary winding , the original secondary double-end winding current sampling value 、 , calculate the differential current of each unit data window converted to the acquisition voltage side , generate the voltage matrix in each unit data window , current matrix , the primary winding voltage matrix within the least squares window length n is and current matrix , we get the sampling sequence equations ;

[0041] The equivalent inductance normalization calculation module is used to use the least square method to calculate the sampling sequence equation group. Perform an estimated solution and normalize the equivalent inductance to obtain the unfitted equivalent resistance and unfitted equivalent inductance in the primary winding voltage equation;

[0042] Weighted equivalent inductance calculation module, used to accumulate and calculate weighted data window The equivalent inductance inside is used to obtain the weighted equivalent inductance;

[0043] The fault identification module is used to design a fault protection criterion based on the weighted equivalent inductance, use the fault protection criterion to identify transformer faults, and design a protection criterion. The expression is:

[0044] ;

[0045] Where, Any unit data window The equivalent inductance calculated value within, is the inductance threshold, for

[0046] Volatility coefficient, The value ranges from -0.1 to -0.05. The time window of the protection criterion is long. If the equivalent inductance meets the protection criterion, it is determined that an internal fault has occurred in the transformer.

[0047] Compared with the prior art, the present invention is not affected by power supply characteristics, can effectively eliminate the influence of harmonics and inrush current, and quickly and accurately identify internal and external faults and excitation inrush currents in the transformer area. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is an overall flow chart of a transformer fault identification method based on fitting weights and equivalent inductance according to the present invention;

[0049] Figure 2 This is an example diagram of the transformer structure;

[0050] Figure 3 This is a module diagram of a transformer fault identification system based on fitting weight and equivalent inductance of the present invention. DETAILED DESCRIPTION

[0051] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0052] Example 1:

[0053] like Figure 1 As shown, a transformer fault identification method based on fitting weight and equivalent inductance of the present invention has the following specific steps:

[0054] Step 1: Select the voltage across the primary winding and the current across the primary and secondary windings as sampling points in the transformer, and read any sampling point. The voltage across the primary winding , the original secondary double-end winding current sampling value 、 , calculate the differential current of each unit data window converted to the acquisition voltage side , generate the voltage matrix in each unit data window , current matrix , the steps are described in detail as follows:

[0055] like Figure 2 As shown in the figure, when the transformer has an internal fault, the short-circuited part is used as the third winding, which is equivalent to a three-winding transformer with a short circuit in the third winding, that is, the original excitation inductance A small fault inductor is connected in parallel Combining the principle of equivalent inductance, we can examine the instantaneous inductance of the transformer primary side based on the primary voltage and differential current. Under normal operating conditions, the equivalent inductance is the sum of the primary leakage inductance and the magnetizing inductance. Under fault conditions, the equivalent inductance consists of two components: the magnetizing inductance in parallel with the fault winding, and the leakage inductance of the primary winding. The sum of these two components gives the equivalent instantaneous inductance.

[0056] Ignoring the voltage drop of the secondary current on the primary leakage resistor, the voltage equation across the primary winding is constructed as follows:

[0057] ; (1)

[0058] Where, is the voltage across the primary winding, is the equivalent resistance, is the equivalent magnetizing inductance, is the differential current;

[0059] Using difference instead of differentiation, the sampling point is obtained according to formula (1): The primary winding voltage equation is as follows:

[0060] ;(2)

[0061] ;

[0062] ;

[0063] Where, is the sampling point sequence index, is the sampling period, For sampling points The differential current, The next sampling point The differential current, The previous sampling point The differential current, For sampling points The primary double-ended winding current sampling value, For sampling points The secondary double-ended winding current sampling value, The previous sampling point The primary double-ended winding current sampling value, The previous sampling point The secondary double-end winding current sampling value;

[0064] Select sampling period The primary winding voltage matrix U and current matrix I of multiple sampling points within are expressed as follows:

[0065] ; (3)

[0066] Set the least squares window length n. According to formula (3), the primary winding voltage matrix within the least squares window length n is and current matrix It is expressed as follows:

[0067] ; (4)

[0068] , ; (5)

[0069] Where, , ,... ..., is the current sampling sequence within the window length n, , ,... ..., is the differential derivative sequence of the current sampling points within the window length n, 、 The primary winding voltage matrix constructed above is and current matrix The least squares result of , the subscript represents the dimension of the matrix, n is the calculation window length of the least squares, is the data index within the least squares calculation window;

[0070] in:

[0071] ; (6)

[0072] ; (7)

[0073] in, is the sampling period, For sampling points The differential current, The next sampling point The differential current, The previous sampling point The differential current;

[0074] According to equations (3), (4), and (5), the following sampling sequence equations are obtained:

[0075] ; (8)

[0076] Step 2: perform normalized calculation of the equivalent inductance to obtain the unweighted equivalent inductance. This step is described in detail as follows:

[0077] 2.1, based on certain redundant data and using the least squares method to estimate and solve the equation group (8), that is, the fitting coefficient matrix The calculated value of the voltage matrix in the data window is The primary winding voltage matrix with least squares The actual value has the smallest distance in Euclidean space, and the Euclidean distance between the two is The expression is:

[0078] ; (9)

[0079] The above-mentioned certain redundant data means that the least squares window length n is set to at least 2. When the computation load allows, the value of n is as large as possible to satisfy the primary winding voltage matrix within the least squares window length n. and current matrix There are multiple redundant data involved in the least squares method.

[0080] 2.2, calculate the partial derivative of the above formula (9) and set it equal to 0 to obtain the data within the least squares calculation window The fitting coefficient matrix of , the expression is as follows:

[0081] ; (10)

[0082] From formula (10), we can get the solution of the equation: , r and L are the equivalent resistance and equivalent inductance that are not fitted in formula (2);

[0083] The actual magnetization curve of a transformer is a curve with a continuously changing slope, which means that the solution equation for the equivalent inductance is nonlinear. Even when using the least squares linear method with a shorter window length, the calculation results will have large errors and fluctuations, which is not conducive to constant value setting and fault identification. It is necessary to improve the accuracy and reliability of the calculation.

[0084] Step 3: Accumulate and calculate the weighted data window The equivalent inductance inside is calculated to obtain the weighted equivalent inductance, which is described as follows:

[0085] The size of the Euclidean distance in formula (9) directly reflects the accuracy of the calculation. The smaller the Euclidean distance, the better the fitting calculation effect. That is, the calculated value of the fault distance is closer to the steady-state calculated value. Otherwise, the fitting effect is poor. Based on this, the fitting error of a single fitting calculation is defined as The expression is as follows:

[0086] ; (11)

[0087] in, 、 Represents any sampling point in the data window The corresponding primary winding voltage matrix and current matrix;

[0088] Fitting error It reflects the effect of the fault distance fitting calculation in the unit data window. The smaller the value of the fitting error, the higher the matching degree between the coefficient matrix obtained by the solution and the voltage and current matrix obtained by sampling. In other words, it is believed that the voltage matrix and current matrix in the data window of the fitting calculation are more stable, and the confidence of the calculation result based on this is higher. Therefore, the reciprocal of the fitting error is As the weight coefficient of the fitting calculation result, the larger the weight coefficient is, the higher the confidence of the fitting calculation result is. To this end, the present invention proposes to calculate the fault distance fitting calculation result in each unit data window. .

[0089] Set the weighted data window length m, and select any sampling point in the weighted data window according to the corresponding unit data window. The weight coefficient Perform weighted summation and normalization as the calculation result of equivalent inductance output. At this time, the equivalent inductance calculation formula is:

[0090] ; (12)

[0091] ; (13)

[0092] Cumulative calculation weighted data window The fitted equivalent inductance of the corresponding weighted data window length m is used to obtain the weighted equivalent inductance, which is expressed as follows:

[0093] ; (14)

[0094] Where, The fitting weight of the result is calculated for each unit inductance of the weighted data window, is the weight matrix composed of all weights, is the weighted data window index, m is the weighted data window length, , is the equivalent inductance, is the weighted equivalent inductance, is the fitting weight corresponding to the data window index 1, 2, 3, ..., k'', ...m in the weighted data window;

[0095] In summary, by performing fast calculations based on a sliding short-time data window and fitting the error weight coefficient, the weight of the equivalent inductance calculation value with low confidence can be greatly reduced, thereby reducing its impact on the overall result. Based on historical calculation data, the equivalent inductance calculation results are weighted and accumulated, thereby accelerating the calculation convergence while improving the stability of the overall calculation results.

[0096] Step 3: Design a fault protection criterion based on the equivalent inductance, and use the fault protection criterion to identify transformer faults. The specific steps are as follows:

[0097] The design protection criterion is expressed as:

[0098] ; (15)

[0099] Where, is the weighted data window index The calculated value of equivalent inductance is: is the inductance threshold value (is the inductance setting value), is the coefficient of fluctuation, The value ranges from -0.1 to -0.05. To protect the time window of the criterion, if the value of the equivalent inductance is If the formula (10) is satisfied within the time window, it is determined that the transformer has an internal fault. It is set to 8~12ms; that is, under normal circumstances, when the transformer is closed under no-load, the time the iron core is in the saturation zone within one cycle will not exceed 8~12ms. Therefore, if the equivalent inductance value is within a small value range within the time span of 8~12ms in one cycle, it is determined that the transformer has an internal fault; otherwise, it is determined that the transformer has an external fault.

[0100] Furthermore, the threshold value in formula (15) The setting principle is to be able to distinguish whether the core is in a saturated state and avoid the interference of the excitation inrush current on fault identification. The calculation method is:

[0101] ; (16)

[0102] Where, is the equivalent inductance value at no load, It is the ratio of the unsaturated magnetic permeability to the saturated magnetic permeability of the core material. It can be set by referring to the silicon steel sheet model. It is generally between 50 and 200. is the reliability coefficient, which is set between 0.5 and 1.0. In summary, the time domain transformer protection action process based on fitting weights is as follows: Figure 2 shown.

[0103] Example 2

[0104] like Figure 3 As shown, a transformer fault identification system based on fitting weights and equivalent inductance of the present invention includes a transformer information acquisition module, an equivalent inductance normalization calculation module, a weighted equivalent inductance calculation module and a fault identification module.

[0105] The transformer information acquisition module is used to execute step 1, the equivalent inductance normalization calculation module is used to execute step 2, the fitting weight equivalent inductance calculation module is used to execute step 3, and the fault identification module is used to execute step 4.

[0106] In response to the problem of delayed transformer protection caused by the high harmonic characteristics of new energy systems, it has been verified that the transformer time-domain equivalent inductance protection based on fitting weights proposed in the present invention is not affected by the power supply characteristics, can effectively eliminate the influence of harmonics and inrush currents, and quickly and accurately identify internal and external faults and excitation inrush currents in the transformer area.

[0107] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

Claims

1. A transformer fault identification method based on fitting weight and equivalent inductance, characterized in that: include: Step 1: Select the voltage across the primary winding and the current across the primary and secondary windings as sampling points in the transformer, and read any sampling point. The voltage across the primary winding , the original secondary double-end winding current sampling value 、 , calculate the differential current of each unit data window converted to the acquisition voltage side , generate the voltage matrix in each unit data window , current matrix ; Get sampling point The voltage equation across the primary winding is as follows: ; Where, is the sampling point sequence index, is the sampling period, For sampling points The differential current, The next sampling point The differential current, The previous sampling point The differential current; Select sampling period The combination of multiple sampling points in the primary winding voltage matrix U and current matrix I are obtained, and the expressions are as follows: ; Set the least squares window length n, the primary winding voltage matrix within the least squares window length n and current matrix It is expressed as follows: ; ， ; Where, , ,... ..., is the current sampling sequence within the unit data window length n, , ,... ..., is the differential derivative sequence of the current sampling points within the unit data window length n, where n is the least squares calculation window length. is the data index within the least squares calculation window; The sampling sequence equations are obtained, which can be expressed as: ; Step 2: Perform normalized calculation of the equivalent inductance to obtain the unweighted equivalent inductance. The specific description is as follows: The least squares method is used to estimate and solve the sampling sequence equations, that is, the fitting coefficient matrix The calculated value of the voltage matrix in the data window is The primary winding voltage matrix within the least squares window length n The actual value has the smallest distance in Euclidean space, and the Euclidean distance between the two is The expression is: ; The Euclidean distance The formula is used to find the partial derivative and set it equal to 0 to obtain the fitting coefficient matrix in each unit data window. , the expression is as follows: ; The solution to the equation is , r and L are the primary winding voltage equations respectively The unfitted equivalent resistance and equivalent inductance in ; Step 3: Accumulate and calculate the weighted data window The equivalent inductance inside is calculated to obtain the weighted equivalent inductance, which is described as follows: Define the fitting error for a single fitting calculation The expression is as follows: ; in, 、 Represents any sampling point in the data window The corresponding primary winding voltage matrix and current matrix; Set the weighted data window length m, and select any sampling point in the weighted data window according to the corresponding unit data window. The weight coefficient Perform weighted summation and normalization as the calculation result of equivalent inductance output. At this time, the equivalent inductance calculation formula is: ; Cumulative calculation weighted data window The fitted equivalent inductance of the corresponding weighted data window length m is used to obtain the weighted equivalent inductance, which is expressed as follows: ; Where, The fitting weight of the result is calculated for each unit inductance of the weighted data window, is the weight matrix composed of all weights, is the weighted data window index, m is the weighted data window length, 1≤ ≤m, is the equivalent inductance value in the weighted data window, is the weighted equivalent inductance, is the fitting weight corresponding to 1, 2, 3, ...m in the weighted data window; Step 4: design a fault protection criterion based on the weighted equivalent inductance, and use the fault protection criterion to identify transformer faults: The design protection criterion is expressed as: ; Where, is the weighted data window index The equivalent inductance, , is the inductance threshold, is the coefficient of fluctuation, To protect the time window of the criterion, if the value of the equivalent inductance is If the criterion is met within the time window, it is determined that the transformer has an internal fault.

2. The transformer fault identification method based on fitting weight and equivalent inductance according to claim 1 is characterized in that: in, Threshold The setting calculation formula is: ; Where, is the equivalent inductance value at no load, is the ratio of the unsaturated magnetic permeability to the saturated magnetic permeability of the core material, is the reliability coefficient.

3. The transformer fault identification method based on fitting weight and equivalent inductance according to claim 1 is characterized in that: in, When the transformer is switched on without load, the core will not be in the saturation zone for more than , Set to 8~12ms.

4. The transformer fault identification method based on fitting weight and equivalent inductance according to claim 1 is characterized in that: in, Next sampling point The differential current , the previous sampling point The differential current The expression is as follows: ; 。 5. The transformer fault identification method based on fitting weight and equivalent inductance according to claim 1 is characterized in that: in, Current sampling sequence within window length n , differential derivative sequence of current sampling points within window length n The expression is as follows: ; ; in, is the sampling period, For sampling points The differential current, The next sampling point The differential current, The previous sampling point The differential current.

6. A transformer fault identification system based on fitting weights and equivalent inductance that implements the transformer fault identification method based on fitting weights and equivalent inductance according to any one of claims 1 to 5, characterized in that: include: Transformer information acquisition module, used to select the voltage at both ends of the primary winding and the current at both ends of the primary and secondary windings as sampling points in the transformer, and read any sampling point The voltage across the primary winding , the original secondary double-end winding current sampling value 、 , calculate the differential current of each unit data window converted to the acquisition voltage side , generate the voltage matrix in each unit data window , current matrix , the primary winding voltage matrix within the least squares window length n is and current matrix , we get the sampling sequence equations ; The equivalent inductance normalization calculation module is used to use the least square method to calculate the sampling sequence equation group. Perform an estimated solution and normalize the equivalent inductance to obtain the unfitted equivalent resistance and unfitted equivalent inductance in the primary winding voltage equation; Fitting weighted equivalent inductance calculation module, used to accumulate and calculate weighted data window The equivalent inductance inside is used to obtain the weighted equivalent inductance; The fault identification module is used to design a fault protection criterion based on the weighted equivalent inductance, use the fault protection criterion to identify transformer faults, and design a protection criterion. The expression is: ; Where, Any unit data window The equivalent inductance calculated value within, is the inductance threshold is the coefficient of fluctuation, The value ranges from -0.1 to -0.

05. The time window of the protection criterion is long. If the equivalent inductance meets the protection criterion, it is determined that an internal fault has occurred in the transformer.

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