Transformer fault current and inrush current distinguishing method based on VMD and box dimension

Abstract

The invention belongs to the technical field of power systems, and discloses a transformer fault current and inrush current distinguishing method based on VMD and box dimension, and the method comprises the following steps: obtaining an original time domain signal, setting VMD parameters, and optimizing the span; step-by-step correction is carried out in the specified span, and VMD decomposition is carried out on the original signal; the optimized VMD parameters are decomposed, and an effective IMF component sum is obtained through a kurtosis index in combination with a correlation coefficient method; further calculating a box dimension of the sum of the effective IMF components obtained by calculation; and calculating various fault conditions of the transformer and the box dimension during excitation surge current of the transformer, and judging the current type. By optimizing the VMD parameters, screening the effective IMF components, calculating the box dimension of the effective IMF components and combining threshold judgment, high-precision distinguishing is achieved, the problems that a traditional method is poor in adaptability and complex in calculation are solved, and the method is suitable for the differential protection device of the power transformer.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and particularly relates to a method for distinguishing transformer fault current and inrush current based on VMD and box dimension. Background Art

[0002] Power transformers play a crucial role in power systems. They are one of the core components of the power grid. They are not only highly regarded due to their high cost but also have irreplaceable strategic significance in power transmission and distribution. To protect power transformers from internal faults during operation, differential protection units are widely used in transformer protection systems. The main function of the differential protection unit is to quickly detect and isolate internal faults of the transformer by monitoring current changes, thereby ensuring the stable operation of the power system. However, at the moment of no-load closing of the power transformer, due to the electromagnetic characteristics of the transformer itself, a special current phenomenon - inrush current - will occur. Inrush current is a temporary current fluctuation, and its amplitude may be very large, even exceeding the rated current of the transformer. This inrush current has certain similarities with fault current in characteristics. Therefore, when inrush current appears, the differential relay may misidentify it as fault current, triggering the protection action and causing the transformer to trip. This misoperation not only affects the normal operation of the power system but also may have a negative impact on the stability and reliability of the power grid. To avoid mis-tripping caused by inrush current, the differential relay must have the ability to quickly, accurately, and reliably distinguish inrush current from fault signals to ensure correct judgment when inrush current appears and avoid unnecessary power outages.

[0003] To effectively solve the problem of distinguishing inrush current from fault current, numerous scholars and researchers have conducted extensive and in-depth studies and proposed various solutions. Among them, the harmonic suppression method is one of the most direct and simple technical means. The core idea of this method is to analyze based on the harmonic components in the current, and distinguish inrush current and fault current by detecting the characteristics of second and fifth harmonic currents. In early power transformers, due to the relatively stable characteristics of the core material, the harmonic suppression method could relatively effectively distinguish inrush current from fault current. However, with the continuous development of modern power transformer technology, the application of new core materials has caused significant changes in the harmonic content of transformers. This change has led to a significant decrease in the accuracy of traditional harmonic suppression methods in distinguishing inrush current and fault current, thus limiting its application in modern power systems. In addition to the harmonic suppression method, the method based on flux constraint also provides a new idea for inrush current identification. This method accurately calculates parameters such as the flux constraint, induced voltage, and instantaneous inductance of the transformer, and uses the variation laws of these parameters to judge the nature of the current. This method has high accuracy in theory, but its disadvantages are obvious. Since precise measurement and calculation of the internal parameters of the transformer are required, it has extremely high requirements for the accuracy and performance of transformer accessories. This not only increases the cost of the equipment, but also poses higher requirements for maintenance and debugging, making it restricted in practical applications. In recent years, with the rapid development of computer technology, pattern recognition and artificial intelligence methods have gradually been introduced into the field of inrush current identification. These methods are based on the principle of pattern recognition and can learn and identify the characteristics of inrush current and fault current by constructing complex neural networks and fuzzy logic models. In practical applications, these methods can distinguish inrush current and fault current according to multi-dimensional information such as the waveform characteristics, amplitude variation laws, and time characteristics of the current. However, these methods are not perfect either. When the parameters of the test system change, such as the type of transformer, operating environment, or connection method changes, the original neural network or fuzzy logic model may no longer be applicable. At this time, the algorithm needs to be retrained to establish a model adapted to the new conditions. This process is not only time-consuming and laborious, but also increases the complexity and maintenance cost of the system. In addition, the ratio-based method is also a class of innovative solutions. These methods analyze the relationship between current and voltage signals and use the ratio change of current and voltage to identify inrush current and fault signals. The advantage of this method is that it can directly use the existing current and voltage measurement data without additional equipment or complex calculations. However, it also has some obvious disadvantages. First, this method is sensitive to decaying DC components, which may lead to inaccurate identification of inrush current in some cases. Second, it has a strong dependence on current and voltage information. If there are errors or noise interferences in the measurement data, it may lead to misjudgment. Finally, since this method usually performs signal processing based on the discrete Fourier transform, there is an inherent one-cycle delay.This delay may affect the rapidity of the protection device, thereby reducing its effectiveness in practical applications.

[0004] In summary, there are still some problems to be solved urgently in the existing technologies for inrush current identification:

[0005] 1. The problem of being unable to accurately distinguish internal fault current from inrush current remains one of the greatest challenges faced by current technologies. Although various methods have been proposed and applied in practice, in the complex operating environment of power systems, the characteristics of inrush current and fault current may change due to various factors, resulting in misjudgments of existing identification methods in some cases.

[0006] 2. To achieve more accurate inrush current identification, some methods require higher device costs. For example, the method based on flux constraint has extremely high requirements for device accuracy, increasing the procurement and maintenance costs of equipment; while pattern recognition and artificial intelligence methods require complex computing devices and professional technical personnel for model training and maintenance. These factors limit the application of these technologies in a wider range.

[0007] 3. The difficulty of model training is also an issue that cannot be ignored. With the development and change of power systems, the operating conditions and parameters of transformers may be continuously adjusted, which requires existing identification models to be updated and optimized in a timely manner. However, the process of retraining the model is not only time-consuming and laborious, but also may require a large amount of data support, which is a huge challenge for practical applications. Therefore, how to reduce device costs and simplify the model training process while ensuring the accuracy of inrush current identification will be the key research direction in the future. Summary of the Invention

[0008] Aiming at the problem that it is difficult to distinguish the fault current and inrush current of existing transformers and it is difficult to meet the existing practical application requirements, the present invention proposes a method for distinguishing the fault current and inrush current of transformers based on VMD and box dimension to solve the above problems existing in the prior art.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A method for distinguishing the fault current and inrush current of transformers based on VMD and box dimension, the method comprising the following steps:

[0011] S1. Obtain the original time-domain signal, set the VMD parameters and the optimization span;

[0012] S2. Perform step-by-step correction within the span specified in step S1, and perform VMD decomposition on the original signal;

[0013] S3. Obtain the optimized VMD parameters according to step S2, perform VMD decomposition, and obtain the effective IMF components through the kurtosis index combined with the correlation coefficient method;

[0014] S4. Further calculate the box dimension of the effective IMF components sum obtained according to the calculation in step S3;

[0015] S5. Determine the current type according to the box dimension sizes under various fault conditions of the transformer and the transformer inrush current calculated in step S4.

[0016] As a further scheme of the present invention: Step S1 specifically includes:

[0017] Set α and K and their optimization spans: α n = α a : Δα: α z , K m = K a : 1: K z , where Δα is the optimization span of α, and the subscripts m and n are respectively the loop counters within the optimization spans of parameters K and α, where m = 1, n = 1, the subscripts α and z respectively represent the start and end of the considered span, and the optimization spans of parameters K and α are 3:8 and 1000:5000 respectively, and the span Δα = 50.

[0018] As a further scheme of the present invention: Step S2 specifically includes:

[0019] Within the span specified in step 1, gradually correct α for each fixed K, and decompose the original signal according to the fixed K and the changing α. The best performance of the VMD algorithm in signal decomposition is highly proportional to minimizing the bandwidth of the acquisition mode. The bilateral bandwidth of the mode u k (t)

[0020]

[0021] E represents energy, u k represents the modal component, ω represents the signal frequency. The effective decomposition of VMD is directly related to the sparse bandwidth of the acquired mode. In VMD signal decomposition, a specific K and α can be found, where the extracted mode bandwidth has the minimum sparsity and the maximum sparsity. Establish the optimal values of K and α according to the exponential mean of adjacent modes NM:

[0022]

[0023] As a further scheme of the present invention: Step S3 specifically includes:

[0024] The kurtosis index formula is as follows:

[0025]

[0026] In the formula, the variable x represents the structural damage parameter; the parameter N represents the total duration of the acquired signal, in time units, and n is the discrete time node index corresponding to the signal sampling;

[0027] The correlation coefficient can quantify the statistical correlation characteristics between two signals and can effectively identify the non-uniform distribution characteristics of the component amplitudes. Its formula is as follows:

[0028]

[0029] In the formula, the variable X is the structural damage state signal, including damage characteristics; Y is the reference healthy state signal, without damage reference; the operator COV represents the covariance operation, used to measure the linear correlation between signals; σ represents the execution of the standard deviation calculation, reflecting the signal fluctuation intensity; E represents the implementation of the expected value solution, representing the central tendency of the signal probability distribution;

[0030] A weighted kurtosis index is constructed by fusing the statistical characteristics of signal kurtosis and correlation coefficient. This method uses a dynamic weighting mechanism to enhance the sensitivity to non-Gaussian features. The formula is as follows:

[0031]

[0032] In the formula, K EW,i is the dynamic weighted kurtosis value corresponding to the i-th IMF component, where K i and K j respectively represent the kurtosis measurement values of the i-th and j-th order intrinsic modes; C i and C j are the correlation coefficients between each IMF component; the parameter N represents the number of IMF decompositions, and sum is the sum, realizing the aggregation of multi-component parameters;

[0033] A feature-enhanced signal is constructed by dynamically fusing the selected intrinsic mode function IMF components. Its parametric integration process can be calculated by the following formula. This method is based on the optimization of multi-scale feature entropy values to achieve adaptive allocation of component contribution degrees;

[0034]

[0035] According to the above formula, the sum of the effective IMF components is calculated. In the formula, EPA is the sum of the effective IMF components, and t is time.

[0036] As a further solution of the present invention: the box dimension calculation formula in step S4 is as follows:

[0037]

[0038] In the formula, N(δ) is the grid count of the set x on the discrete space with a grid width of δ.

[0039] As a further solution of the present invention: Step S5 is specifically as follows: According to the various fault conditions of the transformer and the box dimension sizes during the inrush current of the transformer calculated in Step 4, the D box is compared with the calculated threshold TH 2 According to the obtained simulation analysis, the criterion is set as: when D box < TH 2 = 1.705, at this time it is a fault current. When D box > TH 2 = 1.705, at this time it is an inrush current.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] The present invention applies VMD variational mode decomposition, performs optimized variational mode decomposition and screens out effective IMF components, calculates the box dimension of the effective IMF components, distinguishes inrush current and internal and external fault currents through the difference in box dimension sizes, combines threshold determination to ensure the accuracy of inrush current identification, realizes high-precision discrimination, reduces equipment costs and simplifies the model training process at the same time, solves the problems of poor adaptability and complex calculation of traditional methods, and is applicable to power transformer differential protection devices. Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the structures shown in these drawings. Among them:

[0043] Figure 1 is the flow chart of the method for distinguishing transformer fault current and inrush current in the embodiment of the present invention;

[0044] Figure 2 is the transformer current sampling topology diagram in the embodiment of the present invention;

[0045] Figure 3 is the simulation waveform diagram of the short-circuit current of the maximum current phase when an internal fault occurs in the transformer;

[0046] Figure 4 is the simulation waveform diagram of the short-circuit current of the maximum current phase when an internal fault occurs in the transformer after optimized VMD decomposition;

[0047] Figure 5 is the simulation waveform diagram of the maximum current phase when inrush current occurs in the transformer;

[0048] Figure 6The optimized VMD decomposition simulation waveform diagram of the phase with the maximum magnetizing inrush current of the transformer;

[0049] Figure 7 It is a schematic diagram for calculating the box dimension of the phase with the maximum current during internal short - circuit and magnetizing inrush of the transformer to distinguish between transformer magnetizing inrush and internal short - circuit. Specific implementation manners

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0051] Embodiment

[0052] Please refer to Figure 1-7 As shown, the present invention provides a method for distinguishing transformer fault current and inrush current based on VMD and box dimension, and the method includes the following steps:

[0053] Step 1: Obtain the original time - domain signal, set the VMD parameters and the optimization span

[0054] Set α and K and their optimization spans: α n =α a :Δα:α z , K m =K a :1:K z , where Δα is the optimization span of α, and the subscripts m and n are the loop counters within the optimization spans of parameters K and α respectively, where m = 1, n = 1, the subscripts α and z represent the start and end of the considered spans respectively, and the optimization spans of parameters K and α are 3:8 and 1000:5000 respectively, and the span Δα = 50.

[0055] Step 2: Within the span specified in Step 1, gradually correct α for each fixed K, and decompose the original signal according to the fixed K and the changing α. The best performance of the VMD algorithm in signal decomposition is highly proportional to minimizing the bandwidth of the obtained mode. The two - sided bandwidth k (t)

[0056]

[0057] E represents energy, u kIt represents the modal component, ω represents the signal frequency. The effective decomposition of VMD is directly related to obtaining the sparse bandwidth of the modulus. In the VMD signal decomposition, a specific K and α can be found, where the extracted modal bandwidth has the minimum sparsity and the maximum sparsity. The optimal values of K and α are established based on the exponential mean of the adjacent modal NM:

[0058]

[0059]

[0060] Step 3: According to the optimized VMD parameters obtained in Step S2, perform VMD decomposition and obtain the effective IMF components through the kurtosis index combined with the correlation coefficient method. The kurtosis index formula is as follows:

[0061]

[0062] In the formula, the variable x represents the structural damage parameter; the parameter N represents the total duration of the collected signal, in time units, and n is the discrete time node index corresponding to the signal sampling;

[0063] The correlation coefficient can quantify the statistical correlation characteristics between two signals and can effectively identify the non-uniform distribution characteristics of the component amplitudes. Its formula is as follows:

[0064]

[0065] In the formula, the variable X is the structural damage state signal, containing damage characteristics; Y is the reference healthy state signal, without damage reference; the operator COV represents the covariance operation, used to measure the linear correlation between signals; σ represents the execution of the standard deviation calculation, reflecting the signal fluctuation intensity; E represents the implementation of the expected value solution, representing the central tendency of the signal probability distribution;

[0066] Construct a weighted kurtosis index by fusing the statistical characteristics of the signal kurtosis and the correlation coefficient. This method adopts a dynamic weighting mechanism to enhance the sensitivity to non-Gaussian characteristics. The formula is as follows:

[0067]

[0068] In the formula, K EW,i is the dynamic weighted kurtosis value corresponding to the i-th IMF component, where K i and K j represent the kurtosis measurement values of the i-th and j-th order intrinsic modes respectively; C i and C j are the correlation coefficients between the IMF components; the parameter N represents the number of IMF decompositions, and sum is the sum, realizing the aggregation of multi-component parameters;

[0069] Construct a feature-enhanced signal by dynamically fusing the selected intrinsic mode function (IMF) components. The parametric integration process can be calculated by the following formula. This method is based on optimizing the multi-scale feature entropy value to adaptively allocate the contribution degree of components;

[0070]

[0071] Calculate the sum of the effective IMF components according to the above formula, where EPA is the sum of the effective IMF components and t is time.

[0072] Step 4: Further calculate the box dimension of the sum of the effective IMF components obtained in Step 3. The box dimension calculation formula is as follows:

[0073]

[0074] In the formula, N(δ) is the grid count of the set x in the discrete space with a grid width of δ.

[0075] Step 5: Calculate the box dimensions under various fault conditions of the transformer and during transformer inrush current according to Step 4. Compare D box with the calculated threshold TH 2 as shown in the schematic diagram for calculating the box dimension of the maximum current phase of the transformer internal short circuit and inrush current to distinguish the transformer inrush current and internal short circuit. According to the obtained simulation analysis, set the criterion as: when D Figure 7 <TH box 2 = 1.705, this is the fault current at this time. When D box >TH 2 = 1.705, this is the inrush current at this time.

[0076] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.​

Claims

1. A method for distinguishing transformer fault current and inrush current based on VMD and box dimension, characterized in that: The method comprises the following steps: S1. Obtain the original time domain signal to set VMD parameters and optimize span; S2, performing step-by-step correction within the span specified in step S1, and performing VMD decomposition on the original signal; S3, according to step S2, the optimized VMD parameters are obtained, VMD decomposition is performed, and the effective IMF components and are obtained by combining the kurtosis index with the correlation coefficient method; S4, further calculating the box dimension of the effective IMF component sum according to the effective IMF component sum calculated in step S3; S5. According to step S4, various fault conditions of the transformer and the dimension of the transformer excitation inrush current are calculated to determine the current type.

2. The method for distinguishing transformer fault current and inrush current based on VMD and box dimension according to claim 1, characterized in that: Step S1 specifically includes: Set α and K and their optimization span: α n =α a :Δα:α z , K m =K a :1:K z , Δα is the optimization span of α, subscripts m and n are loop counters within the optimization span of parameters K and α, respectively, where m=1, n=1, subscripts α and z represent the start and end of the considered span, respectively, the optimization spans of parameters K and α are 3:8, 1000:5000, and the span Δα=50.

3. The method for distinguishing transformer fault current and inrush current based on VMD and box dimension according to claim 2, characterized in that: Step S2 specifically includes: Within the span specified in step 1, α is modified step by step for each fixed K, and the original signal is decomposed according to the fixed K and the changing α. The best performance of the VMD algorithm in signal decomposition is highly proportional to the minimization of the bandwidth of the acquisition mode. The mode u k (t) is the bilateral bandwidth BW uk : E represents energy, u k represents the modal component, ω represents the signal frequency, and the effective decomposition of VMD is directly related to the sparse bandwidth of the obtained mode. In the VMD signal decomposition, a specific K and α can be found, where the extracted mode bandwidth has the minimum sparsity and maximum sparsity. The optimal values ​​of K and α are established based on the exponential mean of adjacent modes NM:

4. The method for distinguishing transformer fault current and inrush current based on VMD and box dimension according to claim 3, characterized in that: Step S3 specifically includes: The kurtosis index formula is as follows: Wherein, variable x is the parameter characterizing structural damage; parameter N represents the total duration of the acquired signal, measured in time units, and n is the discrete time node index corresponding to the signal sampling; The correlation coefficient can quantify the statistical correlation characteristics between two signals and effectively identify the non-uniform distribution characteristics of the component amplitudes. The formula is as follows: In the formula, variable X is the structural damage state signal, including damage characteristics; Y is the baseline healthy state signal, without damage reference; operator COV represents the covariance operation, which is used to measure the linear correlation between signals; σ represents the standard deviation calculation, which reflects the signal fluctuation intensity; E represents the expected value solution, which represents the central trend of the signal probability distribution; The weighted kurtosis index is constructed by integrating the statistical characteristics of signal kurtosis and correlation coefficient. This method uses a dynamic weighting mechanism to enhance the sensitivity to non-Gaussian features. The formula is as follows: In the formula, K EW,i is the dynamic weighted kurtosis value corresponding to the i-th IMF component, where K i With K j Respectively represent the kurtosis measurement value of the i-th and j-th order eigenmodes; C i , C j is the correlation coefficient between each IMF component; parameter N represents the number of IMF decompositions, and sum is the sum, which realizes multi-component parameter aggregation; The feature enhancement signal is constructed by dynamically fusing the selected intrinsic mode function IMF components. Its parameterized integration process can be calculated by the following formula. This method realizes adaptive allocation of component contribution based on multi-scale feature entropy optimization. The sum of the effective IMF components is calculated according to the above formula, where EPA is the sum of the effective IMF components and t is the time.

5. The method for distinguishing transformer fault current and inrush current based on VMD and box dimension according to claim 4, characterized in that: The box dimension calculation formula of step S4 is as follows: Where N(δ) is the grid count of the set x in the discrete space with a grid width of δ.

6. The method for distinguishing transformer fault current and inrush current based on VMD and box dimension according to claim 5, characterized in that: Step S5 is specifically as follows: According to Step 4, calculate the box dimension sizes under various fault conditions of the transformer and during transformer inrush current, and let D box be compared with the calculated threshold TH2. According to the obtained simulation analysis, set the criterion as: when D box < TH2 = 1.705, at this time it is a fault current; when D box > TH2 = 1.705, at this time it is an inrush current.

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