Transformer three-dimensional temperature field detection method and system based on improved inverse multi-quadratic and Tikhonov regularization

Abstract

The invention discloses a transformer three-dimensional temperature field detection method and system based on improved inverse multi-secondary and Tikhonov regularization, and the method comprises the steps: placing a plurality of groups of ultrasonic transducers at the outer side of a transformer oil tank, and obtaining the flight time of N ultrasonic propagation paths through a multichannel temperature detection method; the method comprises the following steps: dividing a three-dimensional area in a tested transformer into M subspaces, taking a geometric center point of each subspace as a center point of a radial basis function, and decomposing flight time of an ultrasonic propagation path according to the subspaces to obtain a time matrix; shape parameters are determined, a reconstruction matrix is solved according to a radial basis function of each subspace, singular value decomposition is introduced to solve a generalized inverse matrix, regularization parameters are determined, a coefficient matrix is solved through a standard Tikhonov regularization method, a reciprocal function of ultrasonic velocity is solved, and finally temperature field distribution of the whole space of the transformer is obtained. Compared with the prior art, nondestructive online detection of temperature distribution in the oil tank is realized.

Description

Technical Field

[0001] The invention relates to the technical field of transformer detection, and in particular to a transformer three-dimensional temperature field detection method and system based on improved inverse multi-quadratic and Tikhonov regularization. Background Art

[0002] Oil-immersed transformers are the main force of power transmission and transformation in power networks. According to the analysis of the causes of large-scale power outages in power grids, one of the main causes of power grid failures is internal transformer failures, and more than 85% of transformer accidents are caused by excessively high internal local temperatures. Once a transformer fails, due to its large coverage and high cost, it may cause huge economic losses and pose a serious threat to personal safety and environmental safety. Therefore, it is of great significance to improve the operating reliability of oil-immersed transformers and reduce the probability of their failures.

[0003] When the oil-immersed transformer is in normal operation, electrical energy is converted into thermal energy, causing the temperature of the winding and the core to rise, which extends outward in the form of metal heat conduction, and the temperature of the insulating oil is increased through convection heat exchange. The heat energy on the winding is the load loss, and the heat energy on the core is the no-load loss. The heat of the insulating oil is transferred to the inner wall of the oil tank through convection, and then to the outer wall through heat conduction, and finally dissipated to the surrounding air through convection and radiation. When the transformer is overloaded, the load current increases sharply, the winding loss will also increase, and a large amount of heat will be generated. The mechanical properties and insulation properties of the winding material will change to a certain extent under the influence of high temperature, showing a deterioration trend; the temperature of the insulating oil will rise sharply, and it is easy to crack and produce bubbles, which not only reduces the insulation performance of the insulating oil, but also reduces the overall insulation performance of the transformer, which has a great negative impact on the safe operation of the transformer, causing the transformer in operation to fail easily; the insulation performance will drop rapidly when a system failure such as a short circuit occurs, which is very likely to cause danger.

[0004] Therefore, temperature is a key factor affecting the safe operation, insulation performance and service life of oil-immersed transformers. Currently, there are ultrasonic temperature field reconstruction algorithms based on least squares, filtered back projection, algebraic iteration, Fourier regularization, and so on.

[0005] 1) The least squares method seeks the unknown solution set through the known solution set and differential operation, so that the sum of square errors between the unknown solution set and the actual solution set is minimized. The algorithm is simple in principle and has a fast reconstruction speed. It has a solid theoretical basis in temperature field reconstruction and is widely used. Its main features are: mining the intrinsic correlation between data from multidimensional and complex data, and expressing this regularity in the form of functions or curves. Although the least squares temperature field reconstruction algorithm has high reconstruction accuracy, the temperature interpolation range is limited due to the limited number of regional decompositions and the temperature values ​​obtained. Only a limited number of center point temperature values ​​can be obtained, and the temperature information at the boundary of the measured area is difficult to obtain. Therefore, in the reconstruction result, the temperature information at the boundary of the measured area is lost, and the least squares temperature field reconstruction algorithm cannot reflect the temperature distribution characteristics of the entire measured area.

[0006] 2) In practical applications, the filtered back-projection algorithm requires rotating the acoustic wave transceiver from different angles to obtain projection data, and the temperature field reconstruction algorithm is not easy to implement.

[0007] 3) The Fourier regularized temperature field reconstruction algorithm is related to the quality of the reconstructed image and the area covered by the sound wave propagation path. Increasing the number of sensors can improve the reconstruction quality. However, the prior knowledge of temperature in the actual environment is difficult to obtain, which limits its practicality. At the same time, the reconstruction result will be affected by the regularization parameters. Summary of the invention

[0008] Purpose of the invention: In view of the problems in the background technology, the present invention provides a transformer three-dimensional temperature field detection method and system based on improved inverse multi-quadratic and Tikhonov regularization, adopting radial basis function which is inverse multi-quadratic function, solves the problem of missing temperature distribution reconstruction result near the boundary of the detected area; the shape of the detected area can be arbitrary, and the radial basis function reconstruction is not constrained by the shape of the area; the required calculation time and the accuracy range that can be achieved by the reconstruction result can be adjusted to each other, at the cost of calculation time, the accuracy of the reconstruction result is significantly improved, or at the cost of the accuracy of the reconstruction result, the calculation time is significantly reduced; Tikhonov regularization suppresses the influence of noise on the solution, so as to obtain higher reconstruction accuracy.

[0009] Technical solution: The present invention discloses a transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization, comprising the following steps:

[0010] Step 1: multiple groups of transmitting and receiving transducers are placed outside the transformer oil tank, and the transformer temperature data is measured by a multi-channel temperature detection method. The multi-channel temperature detection method uses a unidirectional multi-channel method to detect the parts around the oil tank where ultrasonic wave propagation is unobstructed, and uses a reflection multi-channel method to detect the parts that the winding and the core cannot penetrate, and obtains the flight time of N ultrasonic wave propagation paths;

[0011] Step 2: The transformer oil tank is equivalent to a three-dimensional cuboid, and the three-dimensional area inside the transformer under test is divided into M subspaces with uniform temperature. The average temperature is used as the center point temperature of the subspace, and the geometric center point of each subspace is used as the center point of the radial basis function. The flight time of the N ultrasonic propagation paths is decomposed according to the subspace to obtain the time matrix t;

[0012] Step 3: Determine the shape parameter η of the inverse multi-quadratic radial basis function, find the reconstruction matrix H based on the radial basis function of each subspace, and introduce singular value decomposition to find the generalized inverse matrix H + Solve the ill-posed problem of ill-conditioned matrices;

[0013] Step 4: Determine the regularization parameter μ, obtain the coefficient matrix ε through the standard Tikhonov regularization method, obtain the inverse function f(x, y, z) of the ultrasonic velocity, and finally obtain the temperature field distribution T(x, y, z) of the transformer in the entire space.

[0014] Furthermore, in step 1, the unidirectional multi-channel method is specifically as follows:

[0015] Two ultrasonic transducers are used as the transmitting end and the receiving end respectively, working independently of each other. According to the actual volume structure of the transformer under test, multiple groups of ultrasonic transducers are composed of unidirectional multi-channel to simultaneously measure the area penetrated by ultrasonic waves. The ultrasonic transducer on one side is responsible for transmission and the other side is responsible for reception. The time difference method is used to obtain the flight time of the ultrasonic wave, that is, the time difference between the transducer transmitting signal and the receiving signal. The temperature distribution of the surroundings, bottom layer and top layer is obtained on both sides of each surface of the transformer.

[0016] Furthermore, in step 1, the reflection multi-channel method is specifically as follows:

[0017] An ultrasonic transducer is responsible for transmitting and receiving signals. When the transmitted signal encounters the winding or the core, it is reflected and the echo is received by the ultrasonic transducer. Multiple groups of ultrasonic transducers form a reflective multi-channel to simultaneously measure the parts that the winding core cannot penetrate.

[0018] Furthermore, a high-frequency ultrasonic transducer is selected to transmit the signal, and an ultrasonic coupling agent is applied between the box wall and the transducer to reduce the measurement error.

[0019] Furthermore, the step 1 also includes sorting out specific coordinates according to the location of the ultrasonic transducer, clarifying the ultrasonic flight path, calculating the ultrasonic flight time of each subspace according to the flight time corresponding to each collected flight path, and calculating the geometric center coordinates of each subspace when determining the geometric center point in step 2.

[0020] Furthermore, in step 2, the flight time of the N ultrasonic propagation paths is decomposed according to the subspace to obtain the time matrix t, and the specific process is as follows:

[0021] The inverse multi-quadratic radial basis function is used to reconstruct the global temperature field inside the transformer, and its formula is expressed as:

[0022]

[0023] Where: is the standard Euclidean norm of the inverse multi-quadratic function, which represents the distance from any point (x, y, z) in the three-dimensional measured space to the center point (x i ,y i ,z i ), that is, η is the shape parameter. After the shape parameter is determined, the radial basis function only connects the point (x, y, z) to the function center point (x i ,y i ,z i ) is related to the distance;

[0024] The inverse of the propagation speed of the ultrasonic wave in the three-dimensional space of the transformer oil tank is recorded as f(x, y, z), then along the path l k The propagation flight time t k for:

[0025]

[0026] Where: N is the number of effective propagation paths between ultrasonic transducers; f(x, y, z) is also expressed as the number of radial basis functions h on this path in three-dimensional coordinate form i (x i ,y i ,z i ), then:

[0027]

[0028] but:

[0029]

[0030] Where: ε i is the weight coefficient of the i-th basis function, which represents the distribution characteristics of f(x, y, z) in the i-th subspace;

[0031] In determining the basis function h i (x i ,y i ,z i ), the center point of the basis function is the geometric center point of the subspace, then the i-th (x i ,y i,z i ) coordinates are the center coordinates of the i-th subspace. After determining the center point of the basis function, the i-th inverse multi-quadratic function is constructed as follows:

[0032]

[0033] make The integral of the inverse multi-quadratic radial basis function on the ultrasonic propagation path is expressed as h ki If t k This breaks down into:

[0034]

[0035] Rewritten in matrix form:

[0036] t=Hε (7)

[0037] Where: t=(t1,t2,...t k ) T ,ε=(ε1,ε2,...,ε i ) T , t is the ultrasonic flight time matrix, which is obtained by measuring the flight time of N ultrasonic propagation paths; ε is the coefficient matrix of M subspace basis functions; H is the reconstruction matrix, which is a constant matrix and the integral matrix of M subspace basis functions on N ultrasonic propagation paths.

[0038] Furthermore, the specific process of step 3 is as follows:

[0039] Singular value decomposition is used for improvement, and the eigenvectors of the pseudo-inverse ill-conditioned matrix are extracted to simplify the calculation process, specifically:

[0040] The reconstruction matrix H is expressed as:

[0041]

[0042] Where: Matrix U and Matrix Q are two orthogonal matrices, j is the rank of matrix H, σ j are the non-zero singular values ​​of the matrix H, and σ j >0;

[0043] The generalized inverse matrix of matrix H can be expressed as:

[0044]

[0045] Where:

[0046] The generalized inverse matrix of matrix H is:

[0047] H + =QS + UT (10)

[0048] Furthermore, the specific process in step 4 is:

[0049] The coefficient matrix ε is rewritten as:

[0050] ε=H + t=QS + U T t (11)

[0051] Assume that the ultrasonic flight time t contains noise e. The Tikhonov regularization method is used to improve it, reduce the influence of noise e on the reconstruction result, and solve the following minimization problem:

[0052]

[0053] Where: μ is the regularization parameter, A is the regularization matrix, the standard Tikhonov regularization is taken as A unit matrix I, the solution of the above formula is:

[0054] ε=(H T H+μA T A) -1 H T t=(H T H+μI) -1 H T t (13)

[0055] Perform singular value decomposition on the reconstruction matrix H and the regularization matrix I, and the standard Tikhonov regularization solution is:

[0056]

[0057] Where: Matrix u and Matrix q are the left and right singular value vectors of the reconstruction matrix H, γ j are the non-zero singular values ​​of the regularization matrix I, and γ j >0.

[0058] Then the standard Tikhonov regularized filter function g is:

[0059]

[0060] After determining the coefficient matrix ε, the inverse function of the ultrasonic velocity f(x, y, z) is obtained by formula (3), and finally the temperature field distribution T(x, y, z) of the transformer in the whole space is obtained, which is expressed as:

[0061]

[0062] The present invention also discloses a transformer temperature field ultrasonic detection system, comprising hardware equipment, an ultrasonic transducer and a host computer, wherein the hardware equipment comprises a main control module, an ultrasonic transmitting module, an ultrasonic receiving module, a data acquisition module and a power supply module, wherein the main control module comprises an FPGA chip and a transceiver control circuit; the ultrasonic transmitting module comprises a high-voltage driving circuit; the ultrasonic receiving module comprises a signal processing circuit;

[0063] The transceiver control circuit pre-sets the working modes of multiple groups of ultrasonic transducers, namely, only transmit, only receive, transmit first and then receive, and receive first and then transmit. The FPGA chip transmits a 3.3V 400kHz square wave pulse signal to the ultrasonic transmitting module, and the high-voltage driving circuit converts it into a pulse high voltage to excite the ultrasonic transducer to generate a 400kHz signal. At the moment of ultrasonic transmission, the internal timer Timer of the FPGA chip is started, the ultrasonic receiving module receives the signal, the timing stops, and the flight time of the ultrasonic wave in each propagation path is obtained. The signal processing circuit filters, amplifies, and integrates the echo signal; the data acquisition module transmits the detected data information to the host computer, and the hardware device, the ultrasonic transducer and the host computer implement the above-mentioned transformer three-dimensional temperature field detection method based on improved inverse multi-secondary and Tikhonov regularization to realize online non-destructive detection of the temperature field of the oil-immersed transformer.

[0064] Preferably, the host computer also performs visual display through MATLAB GUI software to perform online non-destructive testing of the oil tank temperature of the oil-immersed transformer.

[0065] Beneficial effects:

[0066] 1. The radial basis function used in the present invention is an inverse multi-quadratic function, which is a global radial basis function. When the shape parameter of the inverse multi-quadratic function changes slightly, the shape of the function presents a variety of forms, so it is often used to solve convection-diffusion problems. The advantages of the algorithm proposed in the present invention are: it solves the problem of missing temperature distribution reconstruction results near the boundary of the detected area; the shape of the detected area can be arbitrary, and the radial basis function reconstruction algorithm is not constrained by the shape of the area; the calculation time required by the radial basis function reconstruction algorithm and the accuracy range that can be achieved by the reconstruction result can be adjusted to each other, at the cost of calculation time, the accuracy of the reconstruction result is significantly improved, or at the cost of the accuracy of the reconstruction result, the calculation time is significantly reduced; Tikhonov regularization suppresses the influence of noise on the solution, so as to obtain higher reconstruction accuracy.

[0067] 2. The present invention is based on ultrasonic temperature measurement technology, takes the transformer oil tank as the research object, and uses insulating oil as the propagation medium. It proposes a combined multi-channel transformer detection method. The unidirectional multi-channel method is used to detect the area where ultrasonic propagation is unobstructed in the transformer, and the reflection multi-channel method is used to detect the winding core area where ultrasonic propagation is obstructed, thereby obtaining the flight time of ultrasonic waves in a larger range.

[0068] 3. The present invention divides the internal space of the transformer into several subspaces, calculates and processes the flight time, fits the temperature of the entire space according to the average temperature of the subspace, and reconstructs the three-dimensional temperature field of the transformer, thereby solving the problem of missing temperature in the part of the transformer where ultrasonic waves are blocked and the ill-posed matrix ill-posed problem in which the number of cut subspaces is greater than the propagation path, thereby realizing non-destructive online detection of the temperature distribution inside the oil tank; a three-dimensional temperature field ultrasonic detection system for the transformer is developed, and the effectiveness of the system's reconstruction of the temperature field is verified by comparing the results of the embedded thermocouple test with the system reconstruction, thereby providing a temperature basis for transformer fault diagnosis and analysis, and providing a reference for thermal fault detection and positioning of other power equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is the overall flow chart of the detection method of the present invention;

[0070] Figure 2 This is a block diagram of the transformer temperature field ultrasonic detection system of the present invention;

[0071] Figure 3 This is a schematic diagram of the unidirectional multi-channel measurement principle of the present invention;

[0072] Figure 4 This is a schematic diagram of the reflected multi-channel measurement principle of the present invention;

[0073] Figure 5 A specific layered structure diagram and a three-dimensional temperature field diagram of a transformer according to an embodiment of the present invention;

[0074] Figure 6 It is a three-dimensional temperature field analysis of different characteristic layers in the embodiment of the present invention, wherein a to d are respectively a bottom layer temperature analysis diagram, a middle layer temperature analysis diagram, a maximum temperature analysis diagram, and a top layer temperature analysis diagram;

[0075] Figure 7 This is a temperature comparison diagram of a characteristic layer in an embodiment of the present invention;

[0076] Figure 8 Graph 1 shows the comparison of temperature variation with height in the embodiments of the present invention. DETAILED DESCRIPTION

[0077] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0078] The present invention discloses a transformer three-dimensional temperature field detection method and system based on improved inverse multi-quadratic and Tikhonov regularization. The transformer temperature field ultrasonic detection system includes hardware equipment, ultrasonic transducer and host computer. Figure 2The hardware equipment includes a main control module, an ultrasonic transmitting module, an ultrasonic receiving module, a data acquisition module and a power module. The main control module includes an FPGA chip and a transceiver control circuit; the ultrasonic transmitting module includes a high-voltage driving circuit; and the ultrasonic receiving module includes a signal processing circuit.

[0079] The transceiver control circuit pre-sets the working modes of multiple groups of ultrasonic transducers, namely, only transmit, only receive, transmit first and then receive, and receive first and then transmit. The FPGA chip transmits a 3.3V 400kHz square wave pulse signal to the ultrasonic transmitting module, and the high-voltage driving circuit converts it into a pulse high voltage to excite the ultrasonic transducer to generate a 400kHz signal. At the moment of ultrasonic transmission, the internal timer of the FPGA chip is started, the ultrasonic receiving module receives the signal, the timing stops, and the flight time of the ultrasonic wave in each propagation path is obtained. The signal processing circuit filters, amplifies, and integrates the echo signal; the data acquisition module transmits the detected data information to the host computer. After the data is uploaded to the host computer, the three-dimensional temperature field of the whole space is obtained according to the transformer three-dimensional temperature field algorithm based on improved inverse multi-quadratic and Tikhonov regularization (IMQ-TR). Finally, the results are displayed through MATLAB GUI software to realize the online non-destructive detection of the temperature field of oil-immersed transformers.

[0080] Based on the improved inverse multi-quadratic and Tikhonov regularization transformer three-dimensional temperature field detection method, based on ultrasonic temperature measurement technology, with transformer oil tank as the research object and insulating oil as the propagation medium, a joint multi-channel transformer detection method is proposed. The one-way multi-channel method is used to detect the area where ultrasonic propagation is unobstructed in the transformer, and the reflection multi-channel method is used to detect the winding core area where ultrasonic propagation is obstructed, so as to obtain the flight time of ultrasonic waves in a larger range; a transformer three-dimensional temperature field algorithm based on improved inverse multi-quadratic and Tikhonov regularization (IMQ-TR) is proposed, which divides the internal space of the transformer into several subspaces, calculates and processes the flight time, fits the temperature of the entire space according to the average temperature of the subspace, and reconstructs the three-dimensional temperature field of the transformer, solves the problem of missing temperature in the obstructed part of the transformer and the ill-posed problem of ill-conditioned matrix when the number of cut subspaces is greater than the propagation path, and realizes non-destructive online detection of the temperature distribution inside the oil tank. The specific process is:

[0081] Step 1: Place multiple sets of transmitting and receiving transducers outside the transformer oil tank, and use a multi-channel temperature detection method to measure the transformer temperature data. The multi-channel temperature detection method uses a unidirectional multi-channel method to detect the parts around the oil tank where ultrasonic wave propagation is unobstructed, and uses a reflection multi-channel method to detect the parts that the winding and the core cannot penetrate, and obtain the flight time of N ultrasonic wave propagation paths.

[0082] Ultrasonic waves are sound waves with a frequency higher than 20KHz, which can propagate in solids, liquids, and gases. Ultrasonic temperature measurement technology is based on the characteristic that its propagation speed changes with the temperature of the medium, and it can measure the temperature of different media. Due to its high temperature sensitivity, non-destructive internal detection safety, good electrical insulation and anti-electromagnetic interference ability, it has become an emerging temperature measurement method that has attracted much attention in recent years.

[0083] The propagation speed c of ultrasound in liquid is:

[0084]

[0085] Where: λ is the adiabatic compressibility coefficient of the liquid, which is the ratio of the specific heat capacity of ultrasound under equal pressure conditions and equal volume conditions in the liquid medium; p is the pressure; ρ is the liquid density.

[0086] From the state equation pV=BT, we know that:

[0087]

[0088] In the formula: B is the ideal gas constant, which is 8.314; G is the molecular mass; T is the liquid temperature.

[0089] When the propagation distance L and flight time t of the ultrasonic wave are known:

[0090]

[0091] According to formula (2) and formula (3),

[0092]

[0093] Aiming at the problem that the structure inside the transformer oil tank is complex and ultrasound cannot penetrate internal windings, cores and other devices, this paper proposes a multi-channel temperature detection method, which combines the two detection methods of unidirectional measurement and reflection measurement. The unidirectional multi-channel method is used to detect the parts around the oil tank where ultrasound propagates unimpeded, and the reflection multi-channel method is used to detect the parts that the windings and cores cannot penetrate.

[0094] One-way measurement uses two ultrasonic transducers as the transmitter and receiver respectively, working independently of each other. Since the measurement range of a group of ultrasonic transducers is limited, and multiple measurements of a single group will cause large random errors, in order to obtain as much temperature information as possible at the same time, multiple groups of ultrasonic transducers are combined into one-way multi-channels according to the actual volume structure of the transformer under test, and the area that the ultrasonic wave can penetrate is measured simultaneously. The principle is as follows: Figure 3As shown. The ultrasonic transducer on one side is responsible for transmission, and the other side is responsible for reception. The time difference method is used to obtain the flight time of the ultrasonic wave, that is, the time difference between the transducer transmission signal and the reception signal. The temperature distribution of the surrounding, bottom and top layers can be obtained on both sides of each face of the transformer by this method. In addition, since the outer wall and insulating oil of the transformer will attenuate the propagation energy of the ultrasonic wave, this paper selects a high-frequency ultrasonic transducer to transmit the signal, and applies an ultrasonic coupling agent between the box wall and the transducer to reduce the measurement error.

[0095] In reflection measurement, only one ultrasonic transducer is responsible for transmitting and receiving signals. When the transmitted signal encounters the winding or the core, it is reflected and the echo is received by the transducer. To solve the same random error problem as the one-way measurement method, multiple groups of ultrasonic transducers form a reflection multi-channel to simultaneously measure the parts that the winding core cannot penetrate, and obtain as much flight time of ultrasonic waves at different positions as possible, so as to obtain the oil temperature at each position more accurately. The principle is as follows: Figure 4 shown.

[0096] Step 2: The transformer oil tank is equivalent to a three-dimensional cuboid. The three-dimensional area inside the transformer under test is divided into M subspaces with uniform temperature. The average temperature is used as the center point temperature of the subspace. The geometric center point of each subspace is used as the center point of the radial basis function. The flight time of the N ultrasonic propagation paths is decomposed according to the subspace to obtain the time matrix t.

[0097] The core of the upper computer part of the transformer temperature field ultrasonic detection system is the transformer three-dimensional temperature field algorithm based on improved inverse multi-quadratic and Tikhonov regularization (IMQ-TR). The inverse multi-quadratic radial basis function in the algorithm is a global function that can realize the reconstruction of the global temperature field inside the transformer. Its formula is expressed as:

[0098]

[0099] Where: is the standard Euclidean norm of the inverse multi-quadratic function, which represents the distance from any point (x, y, z) in the three-dimensional measured space to the center point (x i ,y i ,z i ), that is, η is the shape parameter, which is usually determined by numerical methods. After the shape parameter is determined, the radial basis function only corresponds to the point (x, y, z) to the function center point (x i ,y i ,z i ) is related to the distance.

[0100] The three-dimensional internal area of ​​the transformer under test is divided into M 50mm×50mm×50mm subspaces with uniform temperature. The average temperature is taken as the center point temperature of the subspace. The temperature field distribution of the whole space is obtained by improving the inverse multi-quadratic interpolation of the center point temperature.

[0101] The inverse of the propagation speed of the ultrasonic wave in the three-dimensional space of the transformer oil tank is recorded as f(x, y, z), then along the path l k The propagation flight time t k for:

[0102]

[0103] Where: N is the number of effective propagation paths between ultrasonic transducers; f(x, y, z) is also expressed as the number of radial basis functions h on this path in three-dimensional coordinate form i (x i ,y i ,z i ), then:

[0104]

[0105] but:

[0106]

[0107] Where: ε i is the weight coefficient of the i-th basis function, which represents the distribution characteristics of f(x, y, z) in the i-th subspace.

[0108] In determining the basis function h i (x i ,y i ,z i ), then ε i As the solution target in the temperature field reconstruction process. The center point of the basis function is the geometric center point of the subspace, then the i-th (x i ,y i ,z i ) coordinates are the center coordinates of the i-th subspace. After determining the center point of the basis function, the i-th inverse multiquadratic function is constructed as:

[0109]

[0110] make The integral of the inverse multi-quadratic radial basis function on the ultrasonic propagation path is expressed as h ki If t k This breaks down into:

[0111]

[0112] Then formula (10) can be rewritten in matrix form:

[0113] t=Hε (11)

[0114] Where: t=(t1,t2,...t k ) T ,ε=(ε1,ε2,...,ε i ) T , In practical applications, t is the ultrasonic flight time matrix, which is obtained by measuring the flight time of N ultrasonic propagation paths; ε is the coefficient matrix of M subspace basis functions; H is the reconstruction matrix, which is a constant matrix and the integral matrix of M subspace basis functions on N ultrasonic propagation paths.

[0115] Step 3: Determine the shape parameter η of the inverse multi-quadratic radial basis function, find the reconstruction matrix H based on the radial basis function of each subspace, and introduce singular value decomposition to find the generalized inverse matrix H + Solve the ill-posed matrix problem.

[0116] Because the number of ultrasonic propagation paths and the number of segmented subspaces are not equal, the number of conditions in equation (11) is different from the number of unknowns, and H is usually an ill-conditioned matrix with a large dimension and strong ill-posedness. To address this problem, this paper uses singular value decomposition to improve the algorithm, extracts the eigenvectors of the pseudo-inverse ill-conditioned matrix to simplify the calculation process, and obtains the optimal solution while satisfying the geometric constraints.

[0117] The reconstruction matrix H is expressed as:

[0118]

[0119] Where: Matrix U and Matrix Q are two orthogonal matrices, j is the rank of matrix H, σ j are the non-zero singular values ​​of the matrix H, and σ j >0.

[0120] The generalized inverse matrix of matrix H can be expressed as:

[0121]

[0122] Where:

[0123] The generalized inverse matrix of matrix H is:

[0124] H + =QS + U T (14)

[0125] Step 4: Determine the regularization parameter μ, obtain the coefficient matrix ε through the standard Tikhonov regularization method, obtain the inverse function f(x, y, z) of the ultrasonic velocity, and finally obtain the temperature field distribution T(x, y, z) of the transformer in the entire space.

[0126] The coefficient matrix ε is rewritten as:

[0127] ε=H + t=QS + U T t (15)

[0128] In actual measurement, the flight time obtained by the detection device is affected by the internal noise of the transformer. Assuming that the ultrasonic flight time t contains noise e, this paper uses the Tikhonov regularization method to improve the algorithm, reduce the influence of noise e on the reconstruction result, and solve the following minimization problem:

[0129]

[0130] Where: μ is the regularization parameter, A is the regularization matrix, and the standard Tikhonov regularization is taken as A unit matrix I. The solution of the above formula is:

[0131] ε=(H T H+μA T A) -1 H T t=(H T H+μI) -1 H T t (17)

[0132] Perform singular value decomposition on the reconstruction matrix H and regularization matrix I in the above formula, and the standard Tikhonov regularization solution is:

[0133]

[0134] Where: Matrix u and matrix q are the left and right singular value vectors of the reconstruction matrix H. γ j are the non-zero singular values ​​of the regularization matrix I, and γ j > 0. μ is a regularization parameter, which is generally selected based on experience.

[0135] Then the standard Tikhonov regularized filter function g is:

[0136]

[0137] The above formula corrects all singular values ​​in the reconstruction matrix H, solves the ill-conditioned matrix problem and suppresses the influence of noise on the solution, so as to obtain higher reconstruction accuracy.

[0138] In summary, the three-dimensional temperature field detection of transformers based on improved inverse multi-quadratic and Tikhonov regularization (IMQ-TR) is based on the equivalent division of the three-dimensional rectangular space of the transformer oil tank into M subspaces. First, the geometric center point of each subspace is used as the center point of the radial basis function, and the flight time of the N ultrasonic propagation paths obtained by the detection system is decomposed according to the subspace to obtain the time matrix t. Determine the shape parameter η, and according to the radial basis function h of each subspace ki Find the reconstruction matrix H and introduce singular value decomposition to find H + Solve the ill-posed matrix problem. Determine the regularization parameter μ, use the standard Tikhonov regularization method to find the coefficient matrix ε, and then find the inverse function of the ultrasonic velocity f(x, y, z). Finally, get the temperature field distribution T(x, y, z) of the transformer in the whole space, which is expressed as:

[0139]

[0140] This paper takes the laboratory test transformer S11-400 / 10 as an example. Its size is 1400mm×700mm×1600mm, the outer diameter of the high-voltage winding is 380mm, and the outer diameter of the low-voltage winding is 200mm. The three-dimensional temperature field of the test transformer oil tank is reconstructed through the above system. Figure 5 As described in (a), due to its small capacity, the small effect of oil flow on temperature distribution is ignored. The temperature field in three-dimensional space is four-dimensional information. The xyz coordinate axis represents the position of each point in the three-dimensional space of the transformer, and the depth of the color represents the temperature. The specific stratification of the transformer is as follows: Figure 5 (b) as shown.

[0141] In order to more intuitively understand the temperature distribution inside the transformer tank, the detection system selects the characteristic layer for three-dimensional temperature field analysis. The bottom layer temperature analysis diagram ( Figure 6 a) shows the three-dimensional temperature of the horizontal layer temperature field at 200mm above the ground, and the middle layer temperature analysis diagram ( Figure 6 b) shows the three-dimensional temperature situation of the horizontal layer temperature field at a distance of 800 mm from the oil tank to the ground, and the highest temperature analysis diagram ( Figure 6 c) shows the three-dimensional temperature situation of the horizontal layer temperature field at 1200mm above the ground of the oil tank, and the top layer temperature analysis diagram ( Figure 6 d) Shows the three-dimensional temperature conditions of the horizontal layer temperature field at the oil tank 1500mm above the ground.

[0142] The visualization results of the temperature field of the detection system show that the temperature field near the winding and the core presents a "three-peak" distribution with high in the middle and low around. The oil tank temperature reaches the highest value of 81.2°C near the winding 1200mm above the ground, with the specific coordinates of (705,350,1210). The other two peaks are 80.9°C and 81.1°C, respectively, located at (295,352,1118) and (1108,348,1205) coordinates, and the height is about 3 / 4 of the oil tank. The peak values ​​of the middle layer oil temperature are 64.5°C, 64.7°C, and 64.6°C, respectively located at (294,353,800), (708,348,800), and (1108,352,800) coordinates. The bottom layer oil temperature is the lowest, with a peak value of 32.5°C.

[0143] The oil temperature of the top temperature field is slightly lower than the highest temperature, and there are no three peaks. Instead, based on the above-mentioned "three-peak" distribution, it presents a temperature distribution with high temperatures on the periphery and low temperatures in the middle. Because it resembles a crater, it is called the "three-crater" distribution. Due to the poor heat dissipation of the low-voltage winding, the temperature peak of the top oil temperature appears near the middle phase low-voltage winding.

[0144] In order to verify the effectiveness of the system reconstruction results, the three-dimensional temperature field of the transformer obtained by the ultrasonic detection system is compared with the results of the thermocouple test. In the vertical section at the midpoint of the wide side of the transformer oil tank, the inner wall of the oil tank, the outer diameter of the high-voltage winding, the outer diameter of the low-voltage winding and the center of the iron core are taken as characteristic points, and several thermocouples are placed to measure the temperature. The system reconstruction and thermocouple test results of the four characteristic layers of the bottom layer, middle layer, top layer and highest temperature layer are compared and analyzed. The temperature comparison is shown in Table 1. Since the thermocouple cannot directly measure the center of the iron core, the thermocouple and error data of the middle layer and the highest temperature field are empty.

[0145] Table 1 Comparison of characteristic layer temperatures

[0146]

[0147]

[0148] Note: The actual detection position may differ from the value in the table by 2-5mm.

[0149] As can be seen from Table 1, the deviation between the system reconstruction results of the characteristic layer and the thermocouple test results is within 3.6°C, and the minimum error is 0.8°C. For a more intuitive analysis, the temperature of each characteristic layer is compared, such as Figure 7As shown. It can be seen from the figure that the temperature distribution obtained from the thermocouple test is highly consistent with the temperature field reconstructed by the system. The temperature field near the winding and the core, that is, the bottom, middle and highest temperature layers, presents a "three-peak" distribution, and the top temperature field presents a "three-crater" distribution. The temperature rise from the edge to the peak value of the top and highest temperature layers is small, and the temperature rise of the bottom temperature layer closest to the ground is the largest. By comparison, it can be seen that the temperature of the thermocouple is slightly higher than the system detection temperature as a whole, the error of the top and highest temperature layers is small, and the bottom temperature error is the largest. In order to further study the error of the thermocouple and the system temperature field, the outer diameter of the side phase high-voltage winding is selected as the vertical height, that is, 350mm on the wide side and 100mm on the long side of the oil tank. The specific data of the temperature comparison analysis are shown in Table 2. The temperature field distribution comparison is Figure 8 shown.

[0150] Table 2 Comparison of temperature changes with altitude

[0151]

[0152] Depend on Figure 8 It is more intuitive to find that the temperature generally increases with the increase of height, reaches a peak at about 1200mm, and then decreases with the increase of height. The lowest temperature of the oil tank is close to the ambient temperature, and the error size shows a certain regularity with different temperatures, that is, the higher the temperature, the smaller the error, and the lower the temperature, the larger the error. The reason for this is that the transformer oil and its impurities have a certain attenuation effect on the propagation of ultrasonic waves, making the temperature field reconstructed by the system slightly lower than the actual temperature. The temperature field reconstructed by the system is obtained by obtaining data after ultrasonic waves propagate in the space between the winding core and the box wall, and is obtained through algorithm processing. The temperature data of the test is obtained by direct measurement of thermocouples placed in the winding coil, i.e., the heat source. Therefore, the error between the two is larger at the low temperature position, while the error is smaller at the high temperature position.

[0153] In summary, although the reconstruction accuracy of the system temperature field reconstruction method proposed in this paper is slightly lower, the reconstruction result of this method has certain accuracy and effectiveness for the temperature field reconstruction in the higher temperature area. The most important thing is that it realizes the non-destructive online detection of the transformer oil tank temperature field. When a turn-to-turn fault occurs in the winding, the oil temperature rises rapidly, and the system has a high accuracy in judging the occurrence of the fault. Therefore, this method can timely determine the risk of transformer failure, check the operating conditions at the potential risk position, find the fault and deal with it, and provide a temperature basis for the transformer operation status evaluation or fault diagnosis analysis.

Claims

1. A transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization, characterized in that: The steps include: Step 1: Place multiple groups of ultrasonic transducers outside the transformer oil tank, and use a multi-channel temperature detection method to measure the transformer temperature data. The multi-channel temperature detection method uses a unidirectional multi-channel method to detect the parts around the oil tank where ultrasonic wave propagation is unobstructed, and uses a reflection multi-channel method to detect the parts that the winding and the core cannot penetrate, and obtain the flight time of N ultrasonic wave propagation paths; Step 2: The transformer oil tank is equivalent to a three-dimensional cuboid, and the three-dimensional area inside the transformer under test is divided into M subspaces with uniform temperature. The average temperature is used as the center point temperature of the subspace, and the geometric center point of each subspace is used as the center point of the radial basis function. The flight time of the N ultrasonic propagation paths is decomposed according to the subspace to obtain the time matrix t; Step 3: Determine the shape parameter η of the inverse multi-quadratic radial basis function, find the reconstruction matrix H based on the radial basis function of each subspace, and introduce singular value decomposition to find the generalized inverse matrix H + Solve the ill-posed problem of ill-conditioned matrices; Step 4: Determine the regularization parameter μ, obtain the coefficient matrix ε through the standard Tikhonov regularization method, obtain the inverse function f(x, y, z) of the ultrasonic velocity, and finally obtain the temperature field distribution T(x, y, z) of the transformer in the entire space.

2. A transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 1, characterized in that: In step 1, the unidirectional multi-channel method is specifically as follows: Two ultrasonic transducers are used as the transmitting end and the receiving end respectively, working independently of each other. According to the actual volume structure of the transformer under test, multiple groups of ultrasonic transducers are composed of unidirectional multi-channel to simultaneously measure the area penetrated by ultrasonic waves. The ultrasonic transducer on one side is responsible for transmission and the other side is responsible for reception. The time difference method is used to obtain the flight time of the ultrasonic wave, that is, the time difference between the transducer transmitting signal and the receiving signal. The temperature distribution of the surroundings, bottom layer and top layer is obtained on both sides of each surface of the transformer.

3. The transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 1 is characterized in that: In step 1, the reflection multi-channel method is specifically as follows: An ultrasonic transducer is responsible for transmitting and receiving signals. When the transmitted signal encounters the winding or the core, it is reflected and the echo is received by the ultrasonic transducer. Multiple groups of ultrasonic transducers form a reflective multi-channel to simultaneously measure the parts that the winding core cannot penetrate.

4. A transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to any one of claims 1 to 3, characterized in that: Select a high-frequency ultrasonic transducer to transmit the signal, and apply ultrasonic coupling agent between the box wall and the transducer to reduce the measurement error.

5. The transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 1 is characterized in that: The step 1 also includes sorting out the specific coordinates according to the location of the ultrasonic transducer, clarifying the ultrasonic flight path, calculating the ultrasonic flight time of each subspace according to the flight time corresponding to each collected flight path, and calculating the geometric center coordinates of each subspace when determining the geometric center point in step 2.

6. The transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 1 is characterized in that: In step 2, the flight time of the N ultrasonic propagation paths is decomposed according to the subspace to obtain the time matrix t. The specific process is: The inverse multi-quadratic radial basis function is used to reconstruct the global temperature field inside the transformer, and its formula is expressed as: Where: is the standard Euclidean norm of the inverse multi-quadratic function, which represents the distance from any point (x, y, z) in the three-dimensional measured space to the center point (x i ,y i ,z i ), that is, η is the shape parameter. After the shape parameter is determined, the radial basis function only connects the point (x, y, z) to the function center point (x i ,y i ,z i ) is related to the distance; The inverse of the propagation speed of the ultrasonic wave in the three-dimensional space of the transformer oil tank is recorded as f(x, y, z), then along the path l k The propagation flight time t k for: Where: N is the number of effective propagation paths between ultrasonic transducers; f(x, y, z) is also expressed as the number of radial basis functions h on this path in three-dimensional coordinate form i (x i ,y i ,z i ), then: but: Where: ε i is the weight coefficient of the i-th basis function, which represents the distribution characteristics of f(x, y, z) in the i-th subspace; In determining the basis function h i (x i ,y i ,z i ), the center point of the basis function is the geometric center point of the subspace, then the i-th (x i ,y i ,z i ) coordinates are the center coordinates of the i-th subspace. After determining the center point of the basis function, the i-th inverse multi-quadratic function is constructed as follows: make The integral of the inverse multi-quadratic radial basis function on the ultrasonic propagation path is expressed as h ki If t k This breaks down into: Rewritten in matrix form: t=Hε (7) Where: t=(t1,t2,...t k ) T ,ε=(ε1,ε2,...,ε i ) T , t is the ultrasonic flight time matrix, which is obtained by measuring the flight time of N ultrasonic propagation paths; ε is the coefficient matrix of M subspace basis functions, and the coefficient matrix ε is a number of weight coefficients ε i A set of; H is the reconstruction matrix, is a constant matrix, and is the integral matrix of M subspace basis functions on N ultrasonic propagation paths.

7. A transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 6, characterized in that: The specific process of step 3 is: Singular value decomposition is used for improvement, and the eigenvectors of the pseudo-inverse ill-conditioned matrix are extracted to simplify the calculation process, specifically: The reconstruction matrix H is expressed as: Where: Matrix U and Matrix Q are two orthogonal matrices, j is the rank of matrix H, σ j are the non-zero singular values ​​of the matrix H, and σ j >0; The generalized inverse matrix of matrix H can be expressed as: Where: The generalized inverse matrix of matrix H is: H + =QS + U T (10)。 8. The transformer three-dimensional temperature field detection method based on improved inverse multi-quadratic and Tikhonov regularization according to claim 7 is characterized in that: The specific process in step 4 is: The coefficient matrix ε is rewritten as: ε=H + t=QS + U T t (11) Assume that the ultrasonic flight time t contains noise e. The Tikhonov regularization method is used to improve it, reduce the influence of noise e on the reconstruction result, and solve the following minimization problem: Where: μ is the regularization parameter, A is the regularization matrix, the standard Tikhonov regularization is taken as A unit matrix I, the solution of the above formula is: ε=(H T H+μA T A) -1 H T t=(H T H+μI) -1 H T t (13) Perform singular value decomposition on the reconstruction matrix H and the regularization matrix I, and the standard Tikhonov regularization solution is: Where: Matrix u and Matrix q are the left and right singular value vectors of the reconstruction matrix H, γ j are the non-zero singular values ​​of the regularization matrix I, and γ j >0. Then the standard Tikhonov regularized filter function g is: After determining the coefficient matrix ε, the inverse function of the ultrasonic velocity f(x, y, z) is obtained by formula (3), and finally the temperature field distribution T(x, y, z) of the transformer in the whole space is obtained, which is expressed as: Among them, B is the ideal gas constant, G is the molecular mass, and λ is the adiabatic compressibility coefficient of the liquid, which is the ratio of the specific heat capacity of ultrasound under equal pressure conditions and equal volume conditions in the liquid medium.

9. A transformer temperature field ultrasonic detection system, characterized in that: It includes hardware equipment, ultrasonic transducer and host computer, wherein the hardware equipment includes main control module, ultrasonic transmitting module, ultrasonic receiving module, data acquisition module and power supply module, the main control module includes FPGA chip and transceiver control circuit; ultrasonic transmitting module includes high voltage driving circuit; ultrasonic receiving module includes signal processing circuit; The transceiver control circuit pre-sets the working modes of multiple groups of ultrasonic transducers, namely, only transmit, only receive, transmit first and then receive, and receive first and then transmit. The FPGA chip transmits a 3.3V 400kHz square wave pulse signal to the ultrasonic transmitting module, and the high-voltage drive circuit converts it into a pulse high voltage to stimulate the ultrasonic transducer to generate a 400kHz signal. At the moment of ultrasonic transmission, the internal timer of the FPGA chip is started, the ultrasonic receiving module receives the signal, the timing stops, and the flight time of the ultrasonic wave in each propagation path is obtained. The signal processing circuit filters, amplifies, and integrates the echo signal. The data acquisition module transmits the detected data information to the host computer, and the hardware device, ultrasonic transducer and host computer implement the transformer three-dimensional temperature field detection method based on improved inverse multi-secondary and Tikhonov regularization as described in any one of claims 1 to 8 above, thereby realizing online non-destructive detection of the temperature field of the oil-immersed transformer.

10. The transformer temperature field ultrasonic detection system according to claim 9, characterized in that: The host computer also performs visual display through MATLAB GUI software to perform online non-destructive detection of the oil tank temperature of the oil-immersed transformer.

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