Transformer series power equalization method based on winding parameter reconstruction

Abstract

This invention discloses a transformer series power balancing method based on winding parameter reconstruction, specifically relating to the field of transformers. First, voltage, current, and phase information of each series winding are collected, and an initial winding parameter set is constructed by combining this with winding structure parameters. Then, a winding difference mapping matrix is ​​established through disturbance response analysis, and the equivalent resistance parameters, leakage inductance parameters, and magnetic coupling coefficient parameters of each winding are inverted and reconstructed to obtain the winding parameter reconstruction matrix. Based on this, a series winding power coupling network model is constructed to identify the power transfer paths between windings and calculate the power offset factor for each series winding. Furthermore, an equivalent winding adjustment vector is generated based on the power offset factor, and this vector is fed back to the power coupling network model for iterative correction, thereby obtaining an updated power distribution result. This invention can identify hidden circulating current channels and achieve dynamic power balancing of series windings, improving the operational stability of transformers.

Description

Technical Field

[0001] This invention relates to the field of transformers, and more specifically to a transformer series power balancing method based on winding parameter reconstruction. Background Technology

[0002] In modular power electronic transformers, cascaded energy storage conversion systems, and high-voltage direct current flexible transmission devices, multiple transformer windings are often connected in series to achieve voltage superposition and power transmission. Due to factors such as winding manufacturing errors, insulation aging, and operating temperature variations, the leakage inductance, equivalent resistance, and magnetic coupling coefficient between the series windings will experience slight drifts. Under specific operating conditions (such as light load, harmonic power transmission, or high-frequency modulation operation scenarios), these subtle parameter differences can trigger a low-amplitude asymmetric power circulation phenomenon, where some winding branches generate implicit circulating currents and gradually form local power enrichment. This phenomenon is usually difficult to detect and suppress using conventional current balancing or passive compensation devices, and long-term operation may lead to local heat accumulation in the insulation of individual windings or even premature aging. Existing technologies mostly rely on external current sharing elements or simple power feedback regulation, but they cannot actively identify and dynamically reconstruct implicit power imbalances caused by internal winding parameter drifts. Therefore, there is an urgent need for a method that can achieve adaptive power balancing of series windings through winding parameter reconstruction. Summary of the Invention

[0003] The purpose of this invention is to provide a transformer series power balancing method based on winding parameter reconstruction to address the shortcomings in the prior art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a transformer series power balancing method based on winding parameter reconstruction, comprising: The instantaneous voltage, current and phase information of each series winding of the target transformer under operating conditions are collected, and the initial winding parameter set P is constructed by combining the winding structure parameters. Disturbance response analysis is performed on the initial winding parameter set P to extract the impedance response characteristics of each winding under micro-power fluctuation conditions and establish the winding difference mapping matrix D. Based on the winding difference mapping matrix D, the equivalent resistance, leakage inductance and coupling coefficient of each winding are inverted and reconstructed to obtain the winding parameter reconstruction matrix R. Based on the winding parameter reconstruction matrix R, a series winding power coupling network model W is constructed, and the implicit circulation channels and corresponding power transfer paths between each winding are calculated through the power coupling network model W. The power offset factor K of each series winding is determined according to the power transfer path, and the corresponding winding equivalent adjustment vector C is generated according to the power offset factor K. The equivalent adjustment vector C of the winding is fed back to the power coupling network model W for iterative correction to obtain the updated power allocation result.

[0005] Preferably, the step of performing disturbance response analysis on the initial winding parameter set P and extracting the impedance response characteristics of each winding under micro-power fluctuation conditions includes: Based on the instantaneous voltage parameters, current parameters, and power phase parameters in the initial winding parameter set P, an operating power sequence for each series winding is constructed, and a micro-power disturbance signal of a preset amplitude is superimposed on the operating power sequence to form a disturbance power sequence. Based on the disturbance power sequence, the instantaneous voltage change and current change corresponding to each series winding are recalculated, and the equivalent impedance response parameters of each series winding are obtained based on the changes to obtain the impedance response characteristic vector of each series winding.

[0006] Preferably, establishing the winding difference mapping matrix D specifically includes: normalizing the impedance response characteristic vector of each series winding and calculating the response difference degree between windings to generate difference correlation coefficients; and arranging the windings in a matrix according to the winding sequence number based on the difference correlation coefficients to construct the winding difference mapping matrix D.

[0007] Preferably, the step of inverting and reconstructing the equivalent resistance, leakage inductance, and coupling coefficient of each winding based on the winding difference mapping matrix D includes: Based on the difference correlation coefficients between each series winding in the winding difference mapping matrix D, a winding parameter offset weight matrix is ​​constructed, and the initial parameter offset of each series winding is determined according to the winding parameter offset weight matrix. Based on the initial parameter offset and the equivalent resistance parameter, leakage inductance parameter and magnetic coupling coefficient parameter of each series winding in the initial winding parameter set, a winding electromagnetic parameter inversion calculation model is established, and the parameter estimate value of each series winding is obtained through iterative calculation. The estimated parameter values ​​are substituted into the power response formula of the series winding for consistency verification. The estimated parameter values ​​are then corrected based on the verification results to obtain the target parameter reconstruction values ​​for each series winding. The target parameter reconstruction values ​​of each series winding are arranged in a matrix according to the winding number order to construct the winding parameter reconstruction matrix R.

[0008] Preferably, the step of constructing the series winding power coupling network model W based on the winding parameter reconstruction matrix R includes: Based on the reconstructed equivalent resistance parameters, reconstructed leakage inductance parameters, and reconstructed magnetic coupling coefficient parameters corresponding to each series winding in the reconstructed winding parameter matrix R, an electromagnetic coupling relationship expression between each series winding is established, and an initial winding coupling relationship network is constructed with each series winding as a node. The power coupling strength between any two series windings is calculated based on the electromagnetic coupling relationship expression, and the connection relationships in the initial winding coupling relationship network are weighted according to the power coupling strength to form a series winding power coupling network model W with a weighted connection structure.

[0009] Preferably, calculating the implicit circulation channels and corresponding power transfer paths between each winding using the power coupling network model W includes: solving for the power flow direction between each series winding according to the series winding power coupling network model W, and identifying the winding combinations that form closed power loops based on the power flow direction and power coupling strength to determine the implicit circulation channels; and calculating the power transfer paths and corresponding power transfer weights in each implicit circulation channel based on the connection sequence and corresponding power coupling strength between each series winding in the implicit circulation channel.

[0010] Preferably, the step of determining the power offset factor K of each series winding according to the power transfer path includes: A power propagation probability matrix is ​​constructed based on the power transfer path and the corresponding power transfer weight, wherein each series winding is regarded as a node, and the power transfer weight between adjacent series windings in the power transfer path is normalized to obtain the transfer probability value. A random walk power diffusion calculation sequence is established based on the power propagation probability matrix, and the initial power distribution value of each series winding is used as the initial state vector. The steady-state power distribution vector of each series winding during the power propagation process is obtained through iterative calculation. The degree of deviation of each series winding relative to the overall average power distribution is calculated based on the steady-state power distribution vector, and the power deviation weight corresponding to each series winding is determined based on the degree of deviation. The steady-state power distribution of each series winding is normalized and mapped according to the power offset weight to obtain the power offset factor K.

[0011] Preferably, the step of generating the corresponding winding equivalent adjustment vector C by the power offset factor K includes: A power offset mapping relationship is established based on the power offset factor K corresponding to each series winding and the steady-state power distribution value, and the power adjustment requirement of each series winding relative to the target balanced power is calculated. Based on the power regulation demand and the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter in the winding parameter reconstruction matrix, a winding power regulation mapping relationship is established, and the parameter adjustment amount corresponding to each series winding is calculated. Based on the parameter adjustment amount, a winding parameter adjustment vector is constructed, and the vectors are arranged according to the winding number order to form a winding adjustment vector; The adjustment amounts of each parameter are normalized proportionally constrained based on the winding adjustment vector to generate the equivalent winding adjustment vector C.

[0012] Preferably, the step of feeding back the equivalent adjustment vector C of the winding to the power coupling network model W for iterative correction includes: Based on the equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment of each series winding in the equivalent adjustment vector C, the corresponding parameters in the winding parameter reconstruction matrix are corrected to obtain the updated winding parameter matrix. The electromagnetic coupling relationship between each series winding is recalculated based on the updated winding parameter matrix, and the power coupling weights in the power coupling network model W are updated to form a corrected power coupling network structure. The power transfer paths between each series winding are recalculated based on the modified power coupling network structure, and a new power propagation probability distribution is calculated based on the updated power coupling weights. The power allocation value of each series winding is recalculated based on the new power propagation probability distribution, and the difference between the current power allocation value and the previous power allocation result is determined. When the difference is less than the preset convergence threshold, the updated power allocation result is output.

[0013] The technical effects and advantages provided by the present invention in the above technical solution are as follows: 1. This invention collects voltage, current, and phase information of each series winding under its operating state and constructs an initial winding parameter set by combining it with winding structural parameters. Based on this, a winding difference mapping matrix is ​​established through disturbance response analysis. Furthermore, the equivalent resistance parameters, leakage inductance parameters, and magnetic coupling coefficient parameters of the windings are inverted and reconstructed to obtain a winding parameter reconstruction matrix that truly reflects the electromagnetic characteristics of each series winding. Compared with existing technologies that rely solely on current balancing or external current sharing devices for adjustment, this invention can identify and reconstruct the differences between series windings at the level of winding electromagnetic parameters. It effectively reveals implicit parameter deviations caused by winding manufacturing discreteness, operational aging, or temperature changes, thereby providing a more accurate parameter basis for subsequent power balancing adjustment and improving the accuracy and reliability of series winding power analysis.

[0014] 2. This invention constructs a series winding power coupling network model and combines it with a random walk power diffusion algorithm to analyze the power transfer path, thereby identifying implicit circulating current channels between series windings and calculating the power offset factor. Based on this, an equivalent adjustment vector for the windings is generated, and the power coupling network model is iteratively corrected to obtain a stable power distribution result. Compared with traditional adjustment methods based on local power feedback or simple current sharing control, this invention can dynamically correct the power coupling relationship between series windings from the perspective of overall network power propagation. This not only effectively suppresses implicit circulating current phenomena but also improves the power balancing capability of the series structure under complex operating conditions, thereby reducing the risk of local winding heat accumulation and improving the long-term stability and safety of the transformer. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0016] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] For examples, please refer to Figure 1 As shown in this embodiment, the transformer series power balancing method based on winding parameter reconstruction includes: The instantaneous voltage, current and phase information of each series winding of the target transformer under operating conditions are collected, and the initial winding parameter set P is constructed by combining the winding structure parameters.

[0019] In this embodiment, firstly, under normal transformer operation, voltage sampling units and current sampling units are arranged at the input or output terminals of each series winding to synchronously acquire the instantaneous voltage and current signals of each winding branch. Simultaneously, a phase detection module measures the phase difference between the voltage and current signals to obtain the voltage amplitude, current amplitude, and corresponding phase information of each series winding at the current operating moment. To ensure data consistency, the voltage, current, and phase information are preferably sampled synchronously using a unified time reference.

[0020] Subsequently, the winding structure parameters corresponding to each series winding are obtained according to the transformer design data or structural parameter database. The winding structure parameters include at least one of the following: number of winding turns, conductor cross-sectional area, average winding length, interlayer distance, core magnetic circuit parameters, and winding design leakage inductance parameters.

[0021] After obtaining the operational measurement data and winding structure parameters, the voltage, current, and phase information corresponding to each series winding are organized and mapped with the corresponding winding structure parameters to form an initial winding parameter set P, which characterizes the electrical operating state and structural characteristics of each series winding. The initial winding parameter set P includes at least the instantaneous voltage parameters, current parameters, power phase parameters, and corresponding structural parameter identification information of each series winding, providing basic data for subsequent winding parameter identification and parameter reconstruction processes.

[0022] In this way, an initial data set reflecting the real-time operating status and structural differences of each series winding can be obtained without changing the original hardware structure of the transformer, thus providing a data foundation for subsequent winding parameter reconstruction and power balance analysis.

[0023] Disturbance response analysis is performed on the initial winding parameter set P to extract the impedance response characteristics of each winding under micro-power fluctuation conditions and establish the winding difference mapping matrix D.

[0024] In this embodiment, the operating power sequence of each series winding is constructed based on the instantaneous voltage parameters, current parameters, and power phase parameters in the initial winding parameter set P. A micro-power disturbance signal of preset amplitude is superimposed on the operating power sequence to form a disturbance power sequence. The specific implementation process is as follows: First, the data of each series winding in the initial winding parameter set P are sequentially arranged according to a uniform sampling period Δt, where Δt is one-twentieth of the fundamental period of the power grid. Let the instantaneous voltage of the i-th series winding at the k-th sampling time be Ui(k), the instantaneous current be Ii(k), and the power phase be φi(k). Then, the instantaneous operating power Pi(k) of the i-th series winding at that sampling time is obtained by the following formula: Subsequently, the continuously sampled Pi(k) are combined in the order of sampling time to form the operating power sequence of the i-th series winding: Pi={Pi(1), Pi(2), ..., Pi(k), ..., Pi(N)}, where N represents the number of consecutive sampling points.

[0025] After obtaining the operating power sequence, a micro-power perturbation signal δPi(k) is superimposed on each operating power sequence. The micro-power perturbation signal is generated by a sine function, and its expression is: , where α represents the disturbance amplitude coefficient, with a value between 0.01 and 0.03; δPi(k) represents the average power value of the operating power sequence; fd represents the disturbance frequency, which is 0.5 times the fundamental frequency of the power grid. The micro-power disturbance signal δPi(k) is superimposed onto the operating power sequence Pi(k) to obtain the disturbance power sequence P'i(k), whose expression is: The above process yields the disturbance power sequence corresponding to each series winding, which is used for subsequent impedance response characteristic analysis.

[0026] After obtaining the disturbance power sequence, the instantaneous voltage and current changes corresponding to each series winding are recalculated based on the disturbance power sequence. The equivalent impedance response parameters of each series winding are then obtained based on the changes to obtain the impedance response characteristic vector of each series winding. The specific process is as follows: First, under the influence of the disturbance power sequence, the instantaneous voltage U'i(k) and instantaneous current I'i(k) of the i-th series winding at each sampling time are re-acquired, and their changes relative to the original operating state are calculated respectively: ; Subsequently, the equivalent impedance response parameter Zi(k) at each sampling time is calculated based on the voltage and current changes. The calculation method is as follows: To improve parameter stability, Zi(k) is averaged over a continuous sampling interval to obtain the average impedance response value of the i-th series winding. i: k = 1 to N. Then, the average impedance response value i is combined with the corresponding voltage and current rate of change sequences to form the impedance response characteristic vector Fi of the i-th series winding, which is expressed as: Fi=[ [i, σUi, σIi], where σUi represents the standard deviation of the voltage change sequence ΔUi(k), and σIi represents the standard deviation of the current change sequence ΔIi(k). The impedance response characteristic vector of each series winding is obtained in the above manner.

[0027] After obtaining the impedance response characteristic vectors of each series winding, the impedance response characteristic vectors are normalized and the response difference between the windings is calculated to generate the difference correlation coefficient. The specific implementation process is as follows: First, the range normalization process is performed on each parameter in the impedance response eigenvector Fi. Let the maximum value of a certain characteristic parameter across all windings be Fmax, and the minimum value be Fmin. Then, the normalized characteristic parameter F'i is calculated as follows: After normalization, the standardized impedance response eigenvector F'i is obtained. Then, based on the standardized impedance response eigenvectors between the i-th and j-th series windings, the Euclidean distance Eij between them is calculated. Finally, a difference correlation coefficient Cij is constructed based on the Euclidean distance, calculated as: Cij = 1 / (1+Eij). The difference correlation coefficient Cij is used to characterize the degree of difference in impedance response between the i-th and j-th series windings.

[0028] After obtaining the difference correlation coefficients between each series winding, the windings are arranged in a matrix according to their winding numbers based on the difference correlation coefficients to construct the winding difference mapping matrix D. The specific implementation process is as follows: First, assuming the target transformer contains m series windings, an m×m dimensional matrix structure is established based on the difference correlation coefficient Cij calculated above, where the element in the i-th row and j-th column of the matrix is ​​Cij.

[0029] Subsequently, all the difference correlation coefficients are filled into the matrix according to the winding number order to form the winding difference mapping matrix D, the expression of which is: ; where the diagonal element Cii is defined as 1, which is used to indicate the complete consistency of the response characteristics of the same winding itself.

[0030] The winding difference mapping matrix D is constructed in the above manner. The winding difference mapping matrix is ​​used to describe the difference relationship of impedance response characteristics between each series winding and serves as the input parameter for the subsequent winding parameter reconstruction process.

[0031] Based on the winding difference mapping matrix D, the equivalent resistance, leakage inductance and coupling coefficient of each winding are inverted and reconstructed to obtain the winding parameter reconstruction matrix R.

[0032] In this embodiment, a winding parameter offset weight matrix is ​​constructed based on the winding difference mapping matrix D, and the initial parameter offset of each series winding is determined based on the winding parameter offset weight matrix. The specific implementation process is as follows: First, assume the target transformer contains m series windings, and the winding difference mapping matrix D is an m×m dimensional matrix, with its element in the i-th row and j-th column denoted as Cij. Construct a winding parameter offset weight matrix W based on the difference correlation coefficients. The element Wij in the weight matrix W is calculated using the following formula: j=1 to m. The above calculations ensure that the sum of the weights of each row is 1, thus reflecting the degree of influence of the parameter offset of the i-th series winding relative to other windings.

[0033] Subsequently, weighted offset calculations are performed on the initial equivalent resistance parameter Ri0, leakage inductance parameter Li0, and magnetic coupling coefficient parameter Ki0 corresponding to each series winding based on the weight matrix W. The initial parameter offsets for the i-th series winding are determined as follows: ΔRi=∑Wij×(Rj0 Ri0); ΔLi=∑Wij×(Lj0 Li0); ΔKi=∑Wij×(Kj0 Ki0).

[0034] Where Ri0 represents the initial equivalent resistance parameter of the i-th series winding, Li0 represents the initial leakage inductance parameter of the i-th series winding, and Ki0 represents the initial magnetic coupling coefficient parameter of the i-th series winding. The initial offsets ΔRi (equivalent resistance), ΔLi (leakage inductance), and ΔKi (magnetic coupling coefficient) of each series winding are obtained through the above calculations, providing an initial correction basis for subsequent electromagnetic parameter inversion calculations.

[0035] After obtaining the initial parameter offsets of each series winding, an electromagnetic parameter inversion calculation model for the windings is established, and the parameter estimates of each series winding are obtained through iterative calculation. The specific process is as follows: First, an inversion calculation model for the winding electromagnetic parameters is constructed. Let Ri be the equivalent resistance parameter of the i-th series winding, Li be the leakage inductance parameter, and Ki be the magnetic coupling coefficient parameter. Then, based on the AC circuit impedance expression, the winding impedance calculation relationship is established: Zi = Ri + jωLi, where ω represents the angular frequency corresponding to the operating frequency. Subsequently, the impedance calculation relationship is compared with the average impedance response value in the aforementioned impedance response characteristic vector. i. Establish the error function F, whose expression is: Based on this, the parameters are updated by gradient iteration. The initial parameters are set as follows: Ri(0)=Ri0+ΔRi; Li(0) = Li0 + ΔLi; Ki(0) = Ki0 + ΔKi.

[0036] During the t-th iteration, the parameters are corrected using the following update formula: Ri(t+1)=Ri(t) β× F / Ri; Li(t+1)=Li(t) β× F / Li.

[0037] Where β represents the iteration step size, with a value between 0.001 and 0.01. The iteration ends when the error function F is less than a preset error threshold ε. The error threshold ε is defined as follows: .

[0038] After completing the iteration, the estimated equivalent resistance Ri and leakage inductance Li of the i-th series winding are obtained, and the parameter estimation results are formed by combining them with the initial magnetic coupling coefficient Ki(0).

[0039] After obtaining the parameter estimates, the estimates are substituted into the power response formula of the series winding for consistency verification. The parameter estimates are then corrected based on the verification results. The specific implementation process is as follows: First, we construct the power response equation for the series windings. Let the voltage of the i-th series winding be Ui and the current be Ii, then the theoretical power value... Calculated as follows: .

[0040] Subsequently, the theoretical current value is calculated based on the updated estimated equivalent resistance Ri and leakage inductance Li. : Substituting the theoretical current value Ii* into the power calculation formula yields the reconstructed power value Pri: Next, the power error ΔPi between the reconstructed power value Pri and the actual operating power Pi is calculated: If the power error ΔPi is greater than the power verification threshold θ, then the estimated equivalent resistance Ri and the estimated leakage inductance Li are proportionally corrected. The power verification threshold θ is defined as 2% of the average operating power. The correction method is as follows: ; .

[0041] After the correction is completed, the target parameter reconstruction value of the i-th series winding is obtained.

[0042] After obtaining the target parameter reconstruction values ​​for each series winding, the parameter reconstruction results of each series winding are arranged in matrix form according to the winding number order to construct the winding parameter reconstruction matrix R. The specific implementation process is as follows: Suppose the target transformer contains m series windings. Each series winding corresponds to a target equivalent resistance parameter Ri*, a target leakage inductance parameter Li, and a target magnetic coupling coefficient parameter Ki.

[0043] Arrange the parameters in a matrix according to the winding number order to form a three-column parameter matrix: The i-th row represents the electromagnetic parameter reconstruction result of the i-th series winding.

[0044] The winding parameter reconstruction matrix R is obtained in the above manner. This matrix is ​​used to characterize the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter of each series winding under the operating state, and serves as the basic parameter for subsequent power coupling relationship calculation.

[0045] Based on the winding parameter reconstruction matrix R, a series winding power coupling network model W is constructed, and the implicit circulation channels and corresponding power transfer paths between each winding are calculated through the power coupling network model W.

[0046] In this embodiment, an electromagnetic coupling relationship expression between each series winding is established based on the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter corresponding to each series winding in the winding parameter reconstruction matrix R. An initial winding coupling relationship network is then constructed with each series winding as a node. The specific implementation process is as follows: First, assume the target transformer contains m series windings. The i-th row of the winding parameter reconstruction matrix R corresponds to the parameter reconstruction result of the i-th series winding, where the reconstructed equivalent resistance parameter is denoted as... The reconstructed leakage inductance parameter is denoted as The reconstructed magnetic coupling coefficient parameter is denoted as .

[0047] Subsequently, the complex impedance Zi of the i-th series winding is calculated based on the AC circuit impedance relationship, and its expression is: , where ω represents the angular frequency corresponding to the operating frequency.

[0048] Based on this, the coupling impedance relationship is established according to the magnetic coupling coefficient between the two series windings. Let Kij be the magnetic coupling coefficient between the i-th series winding and the j-th series winding, then the coupling inductance Mij between them is calculated as follows: Subsequently, the coupling impedance Zij is calculated based on the coupling inductance, and its expression is: Zij = jωMij.

[0049] Each series winding is considered as a node, and the coupling impedance Zij is considered as the connection relationship between the nodes. Thus, an initial winding coupling relationship network containing m nodes is constructed, where each node corresponds to a series winding, and each connection edge corresponds to the electromagnetic coupling relationship between two series windings.

[0050] The above method yields an initial winding coupling relationship network describing the electromagnetic coupling relationship of each series winding, providing a basic structure for subsequent power coupling calculations.

[0051] After obtaining the initial winding coupling relationship network, the power coupling strength between any two series windings is calculated according to the electromagnetic coupling relationship expression. Then, the connection relationship is weighted according to the power coupling strength to form a series winding power coupling network model W with a weighted connection structure. The specific implementation process is as follows: First, the coupling current Iij transmitted from the i-th series winding to the j-th series winding is calculated based on the coupling impedance Zij. The calculation formula is as follows: Where Ui represents the voltage amplitude of the i-th series winding, and Uj represents the voltage amplitude of the j-th series winding. Then, the power coupling strength Pij between the two series windings is calculated based on the coupling current, and its expression is: φij represents the phase difference between the coupling current and the voltage of the i-th series winding. The power coupling strength Pij is used as the weight of the connecting edge and filled into the power coupling matrix according to the node number order, where the matrix element Wij is defined as the power coupling strength between the i-th and j-th series windings. This constructs the series winding power coupling network model W, which characterizes the degree of power coupling between each series winding.

[0052] After obtaining the series winding power coupling network model W, the power flow direction between each series winding is solved based on the power coupling strength. Then, the winding combinations forming closed power loops are identified based on the power flow direction and power coupling strength to determine the implicit circulation channels. The specific implementation process is as follows: First, the power flow direction is determined based on the sign of each element in the power coupling matrix W. When Wij is positive, it indicates that power flows from the i-th series winding to the j-th series winding; when Wij is negative, it indicates that power flows from the j-th series winding to the i-th series winding.

[0053] Subsequently, a directed connectivity graph is constructed based on the power flow direction, and closed paths are searched one by one according to the node connectivity.

[0054] The condition for determining a closed path is: starting from a certain series winding node, passing through multiple nodes in sequence along the power flow direction, and then returning to the original node.

[0055] During the search process, if the absolute value of the power coupling strength corresponding to all connecting edges in the path is greater than the power identification threshold λ, then the path is determined to be a hidden circulation channel.

[0056] The power identification threshold λ is defined as 5% of the average absolute value of all power coupling strengths.

[0057] All hidden circulation channels were identified through the above process.

[0058] After determining the implicit circulating current channels, the power transfer path and corresponding power transfer weight in each channel are calculated based on the connection sequence and corresponding power coupling strength between the series windings in each implicit circulating current channel. The specific implementation process is as follows: First, record the node sequence for each implicit circulation channel according to the power flow direction. For example, if an implicit circulation channel contains the a-th series winding, the b-th series winding, and the c-th series winding, its power transfer path is represented as: a→b→c→a. Then, calculate the absolute value of the power coupling strength corresponding to each connecting edge in the channel, and obtain the total power coupling value Ptotal for the channel: Ptotal = |Pab| + |Pbc| + |Pca|. Next, determine the power transfer weight based on the proportion of the power coupling strength of each connecting edge in the total power coupling value. For example, the power transfer weight Wab between the a-th series winding and the b-th series winding is calculated as follows: Wab = |Pab| / Ptotal.

[0059] The above calculations can be used to obtain the power transfer weights corresponding to each power transfer path in each implicit circulation channel, thereby providing a path basis for subsequent power balance adjustment.

[0060] The power offset factor K of each series winding is determined according to the power transfer path, and the corresponding winding equivalent adjustment vector C is generated based on the power offset factor K.

[0061] In this embodiment, a power propagation probability matrix is ​​constructed based on the power transfer path and the corresponding power transfer weights. The specific implementation process is as follows: First, assume the target transformer contains m series windings, each corresponding to a network node. Based on the power transfer path obtained above, record the power transfer weight between any two adjacent series windings, denoted as . ,in This represents the weight value by which power is transferred from the i-th series winding to the j-th series winding.

[0062] Subsequently, the power transfer weights of all power transmitted outward from the same series winding are normalized. Suppose there are n power transfer paths between the i-th series winding and other series windings, then the corresponding normalized power propagation probability... Calculate as follows: ;in This represents the probability that power propagates from the i-th series winding to the j-th series winding.

[0063] All Arranged in order of winding numbering, forming an m×m matrix structure, we obtain the power propagation probability matrix A, where the element in the i-th row and j-th column is... The power propagation probability matrix A is used to describe the probabilistic relationship of power propagation between the series windings and serves as the basic input data for random walk power diffusion calculation.

[0064] After obtaining the power propagation probability matrix A, a random walk power diffusion calculation sequence is established based on the power propagation probability matrix. The initial power distribution value of each series winding is used as the initial state vector, and the steady-state power distribution vector is obtained through iterative calculation. The specific implementation process is as follows: First, the actual operating power of each series winding is calculated based on the operational measurement data. Let the voltage of the i-th series winding be Ui, the current be Ii, and the power phase be φi. Then, the initial power value Pi of the i-th series winding is calculated using the following formula: Pi = Ui × Ii × cosφi. Subsequently, the initial power values ​​of all series windings are arranged in order of winding number to form the initial state vector S(0): S(0) = [P1, P2, ..., Pm]; then, the random walk power diffusion iterative relation is constructed: S(t+1) = S(t) × A; where S(t) represents the power distribution vector at the t-th iteration.

[0065] After each iteration, the error difference between two adjacent iterations is calculated: The iterative calculation terminates when the error E is less than the preset convergence threshold η. The convergence threshold η is defined as one-thousandth of the norm of the initial power vector. After completing the iteration, the steady-state power distribution vector is obtained.

[0066] After obtaining the steady-state power distribution vector, the offset of each series winding relative to the overall average power distribution is calculated based on the steady-state power distribution vector. The specific implementation process is as follows: First, calculate the average steady-state power value of all series windings. Let the power of the i-th series winding in the steady-state power distribution vector be... Then the overall average power value Calculate as follows: Then calculate the power offset ΔPi of the i-th series winding: Then, the power offset weight Gi is calculated based on the power offset, and its expression is: The power offset weight Gi is used to characterize the degree of offset of the i-th series winding relative to the overall power distribution.

[0067] After obtaining the power offset weights of each series winding, the steady-state power distribution is normalized and mapped to obtain the power offset factor K of each series winding. The specific implementation process is as follows: First, the steady-state power value is proportionally mapped based on the power offset weight Gi, and the corrected power value is calculated. : Then, all corrected power values ​​are normalized. Let the sum of all corrected power values ​​be... : Then the power offset factor of the i-th series winding. Calculate as follows: Power offset factor It is used to characterize the degree of offset of the i-th series winding in the overall power distribution and serves as an input parameter for the subsequent power equalization adjustment process.

[0068] In this embodiment, a power offset mapping relationship is established based on the power offset factor K corresponding to each series winding and the steady-state power distribution value, and the power adjustment requirement of each series winding relative to the target balanced power is calculated. The specific implementation process is as follows: First, assume the target transformer contains m series windings, and the power offset factor corresponding to each series winding is denoted as . The steady-state power distribution value is denoted as Calculate the overall average power value based on the steady-state power distribution value. The calculation method is as follows: ;in This represents the target balanced power value. Subsequently, a power offset mapping relationship is constructed based on the power offset factor, and the target power value of the i-th series winding is calculated. The calculation method is as follows: Then calculate the power regulation requirement of the i-th series winding. Its expression is: Power regulation requirements It is used to characterize the adjustment magnitude of the i-th series winding relative to the target equalization power, and serves as the input for subsequent parameter adjustment calculations.

[0069] After obtaining the power regulation requirement, a winding power regulation mapping relationship is established based on the power regulation requirement and the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter in the winding parameter reconstruction matrix. The parameter adjustment amount corresponding to each series winding is then calculated. The specific process is as follows: First, the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter of the i-th series winding are obtained based on the winding parameter reconstruction matrix. Then, the comprehensive impedance amplitude of this series winding is determined according to the AC circuit impedance relationship.

[0070] Subsequently, a power regulation mapping model is constructed based on the power regulation demand to convert the power change demand into an impedance change demand. The impedance change is determined according to the following calculation expression: ;in: This represents the overall impedance change of the i-th series winding; Indicates the power regulation requirement; This represents the steady-state power distribution value; Indicates the magnitude of the combined impedance; This represents the adjustment ratio coefficient, with a value ranging from 0.1 to 0.3.

[0071] Subsequently, the changes in comprehensive impedance are proportionally allocated to the changes in equivalent resistance and leakage inductance parameters, and the adjustment of the magnetic coupling coefficient is determined based on the proportional relationship between the power adjustment demand and the target balanced power.

[0072] The equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment of each series winding are obtained through the above steps.

[0073] After obtaining the parameter adjustment values ​​for each series winding, a winding parameter adjustment vector is constructed based on these values ​​and arranged in vectorized order according to the winding number. For the i-th series winding, an adjustment vector containing three parameters is established: equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment. This adjustment vector describes the electromagnetic parameter adjustment requirements of this series winding during power balancing. All series winding parameter adjustment vectors are arranged sequentially according to their winding numbers to form a complete set of parameter adjustment vectors. This vector set describes the overall parameter changes of the entire series winding structure during power balancing. After obtaining the parameter adjustment vector set, each parameter adjustment value is normalized proportionally to generate the equivalent winding adjustment vector. The absolute values ​​of the equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment values ​​for all series windings are summed to obtain the overall adjustment reference value. Using this overall adjustment reference value as the normalization reference, the parameter adjustment value for each series winding is scaled proportionally to keep all adjustment values ​​within a uniform proportional range.

[0074] The normalized adjustment values ​​of each series winding parameter are arranged in a matrix according to the winding number order to obtain the equivalent adjustment vector C of the winding. This equivalent adjustment vector is used to characterize the comprehensive adjustment requirements of each series winding during the power balancing process and serves as the input parameter for subsequent power balancing control calculations.

[0075] The equivalent adjustment vector C of the winding is fed back to the power coupling network model W for iterative correction to obtain the updated power allocation result.

[0076] In this embodiment, the corresponding parameters in the winding parameter reconstruction matrix are corrected according to the equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment of each series winding in the winding equivalent adjustment vector C, so as to obtain the updated winding parameter matrix.

[0077] First, the equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment for the i-th series winding are read from the winding equivalent adjustment vector C. Based on the reconstructed equivalent resistance, leakage inductance, and magnetic coupling coefficient parameters of the i-th series winding recorded in the winding parameter reconstruction matrix, the corresponding parameter adjustments are superimposed onto the original parameter values ​​to obtain the updated equivalent resistance, leakage inductance, and magnetic coupling coefficient parameters for the i-th series winding. The updated equivalent resistance, leakage inductance, and magnetic coupling coefficient parameters for all series windings are then rearranged according to their winding numbers to form the updated winding parameter matrix. This winding parameter matrix reflects the electromagnetic parameter state of each series winding under the current power regulation conditions.

[0078] After obtaining the updated winding parameter matrix, the electromagnetic coupling relationship between each series winding is recalculated based on the updated winding parameter matrix, and the power coupling weights in the power coupling network model are updated.

[0079] The updated equivalent resistance and leakage inductance parameters of each series winding are obtained based on the updated winding parameter matrix, and the updated complex impedance of the series winding is calculated accordingly. The complex impedance is composed of the equivalent resistance and the inductive reactance corresponding to the leakage inductance, where the inductive reactance is determined by the operating angular frequency and the leakage inductance parameter. The coupling inductance between the two series windings is calculated based on the updated magnetic coupling coefficient parameters and the leakage inductance parameters of the two series windings. The coupling inductance is calculated using the geometric mean of the magnetic coupling coefficient and the leakage inductance of the two windings. The coupling impedance between the two series windings is calculated based on the coupling inductance, and the power transfer is calculated based on the coupling impedance and the voltage difference between the two windings. The recalculated power transfer is used as the connection weight to update the power coupling network model, thus obtaining the corrected power coupling network structure.

[0080] After obtaining the corrected power coupling network structure, the power transfer path between each series winding is recalculated based on the updated power coupling weights, and a new power propagation probability distribution is calculated based on the updated power coupling weights.

[0081] Each series winding in the power-coupled network is treated as a network node, and the power coupling weight between two series windings is used as the connection weight between nodes. All power coupling weights for each series winding node's outward connections are normalized so that the sum of the probabilities of that node propagating outwards is 1, thus obtaining the power propagation probability. The power propagation probabilities between all nodes are arranged in winding number order to form a new power propagation probability matrix. Based on this, a random walk power diffusion model is established according to the probability matrix, and the power propagation process is calculated through continuous iteration. The power propagation state vector is updated according to the following calculation relationship: S(t+1) = S(t) × A; where S(t) represents the power distribution vector at the t-th iteration, and A represents the new power propagation probability matrix.

[0082] After obtaining the new power propagation probability distribution, the power allocation values ​​of each series winding are re-solved according to the random walk power diffusion model, and the final power allocation result is obtained through convergence determination.

[0083] The power distribution vector for the current iteration is obtained through random walk power diffusion iteration calculation.

[0084] The difference between the power distribution vector of the current iteration and the power distribution vector obtained in the previous iteration is calculated to obtain the change in power distribution. A convergence criterion is then calculated based on this change in power distribution. The convergence criterion is obtained by calculating the vector norm of the power distribution change and is used to characterize the overall difference between the results of the two iterations.

[0085] When the convergence criterion is less than the preset convergence threshold, the power allocation result is considered to have reached a stable state. The convergence threshold is defined as one-thousandth of the norm of the initial power distribution vector.

[0086] Finally, the power distribution vector of the current iteration is output as the updated power allocation result, which is used to characterize the final power distribution of each series winding under power balance.

[0087] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A transformer series power equalization method based on winding parameter reconstruction, characterized in that: include: The instantaneous voltage, current and phase information of each series winding of the target transformer under operating conditions are collected, and the initial winding parameter set P is constructed by combining the winding structure parameters. Disturbance response analysis is performed on the initial winding parameter set P to extract the impedance response characteristics of each winding under micro-power fluctuation conditions and establish the winding difference mapping matrix D. Based on the winding difference mapping matrix D, the equivalent resistance, leakage inductance and coupling coefficient of each winding are inverted and reconstructed to obtain the winding parameter reconstruction matrix R. Based on the winding parameter reconstruction matrix R, a series winding power coupling network model W is constructed, and the implicit circulation channels and corresponding power transfer paths between each winding are calculated through the power coupling network model W. The power offset factor K of each series winding is determined according to the power transfer path, and the corresponding winding equivalent adjustment vector C is generated according to the power offset factor K. The equivalent adjustment vector C of the winding is fed back to the power coupling network model W for iterative correction to obtain the updated power allocation result.

2. The transformer series power balancing method based on winding parameter reconstruction according to claim 1, characterized in that: The steps for performing disturbance response analysis on the initial winding parameter set P and extracting the impedance response characteristics of each winding under micro-power fluctuation conditions include: Based on the instantaneous voltage parameters, current parameters, and power phase parameters in the initial winding parameter set P, an operating power sequence for each series winding is constructed, and a micro-power disturbance signal of a preset amplitude is superimposed on the operating power sequence to form a disturbance power sequence. Based on the disturbance power sequence, the instantaneous voltage change and current change corresponding to each series winding are recalculated, and the equivalent impedance response parameters of each series winding are obtained based on the changes to obtain the impedance response characteristic vector of each series winding.

3. The transformer series power balancing method based on winding parameter reconstruction according to claim 2, characterized in that: The winding difference mapping matrix D is established by: normalizing the impedance response characteristic vectors of each series winding and calculating the response difference between windings to generate difference correlation coefficients; and arranging the windings in a matrix according to the winding numbers based on the difference correlation coefficients to construct the winding difference mapping matrix D.

4. The transformer series power balancing method based on winding parameter reconstruction according to claim 1, characterized in that: The steps for inverting and reconstructing the equivalent resistance, leakage inductance, and coupling coefficient of each winding based on the winding difference mapping matrix D include: Based on the difference correlation coefficients between each series winding in the winding difference mapping matrix D, a winding parameter offset weight matrix is ​​constructed, and the initial parameter offset of each series winding is determined according to the winding parameter offset weight matrix. Based on the initial parameter offset and the equivalent resistance parameter, leakage inductance parameter and magnetic coupling coefficient parameter of each series winding in the initial winding parameter set, a winding electromagnetic parameter inversion calculation model is established, and the parameter estimate value of each series winding is obtained through iterative calculation. The estimated parameter values ​​are substituted into the power response formula of the series winding for consistency verification. The estimated parameter values ​​are then corrected based on the verification results to obtain the target parameter reconstruction values ​​for each series winding. The target parameter reconstruction values ​​of each series winding are arranged in a matrix according to the winding number order to construct the winding parameter reconstruction matrix R.

5. The transformer series power balancing method based on winding parameter reconstruction according to claim 1, characterized in that: The steps for constructing a series winding power coupling network model W based on the winding parameter reconstruction matrix R include: Based on the reconstructed equivalent resistance parameters, reconstructed leakage inductance parameters, and reconstructed magnetic coupling coefficient parameters corresponding to each series winding in the reconstructed winding parameter matrix R, an electromagnetic coupling relationship expression between each series winding is established, and an initial winding coupling relationship network is constructed with each series winding as a node. The power coupling strength between any two series windings is calculated based on the electromagnetic coupling relationship expression, and the connection relationships in the initial winding coupling relationship network are weighted according to the power coupling strength to form a series winding power coupling network model W with a weighted connection structure.

6. The transformer series power balancing method based on winding parameter reconstruction according to claim 5, characterized in that: The implicit circulation channels and corresponding power transfer paths between windings are calculated using the power coupling network model W, including: solving for the power flow direction between series windings based on the series winding power coupling network model W, and identifying winding combinations that form closed power loops based on the power flow direction and power coupling strength to determine the implicit circulation channels; and calculating the power transfer paths and corresponding power transfer weights in each implicit circulation channel based on the connection sequence and corresponding power coupling strength between the series windings in the implicit circulation channels.

7. The transformer series power balancing method based on winding parameter reconstruction according to claim 1, characterized in that: The steps for determining the power offset factor K of each series winding based on the power transfer path include: A power propagation probability matrix is ​​constructed based on the power transfer path and the corresponding power transfer weight, wherein each series winding is regarded as a node, and the power transfer weight between adjacent series windings in the power transfer path is normalized to obtain the transfer probability value. A random walk power diffusion calculation sequence is established based on the power propagation probability matrix, and the initial power distribution value of each series winding is used as the initial state vector. The steady-state power distribution vector of each series winding during the power propagation process is obtained through iterative calculation. The degree of deviation of each series winding relative to the overall average power distribution is calculated based on the steady-state power distribution vector, and the power deviation weight corresponding to each series winding is determined based on the degree of deviation. The steady-state power distribution of each series winding is normalized and mapped according to the power offset weight to obtain the power offset factor K.

8. The transformer series power balancing method based on winding parameter reconstruction according to claim 7, characterized in that: The step of generating the corresponding winding equivalent adjustment vector C by the power offset factor K includes: A power offset mapping relationship is established based on the power offset factor K corresponding to each series winding and the steady-state power distribution value, and the power adjustment requirement of each series winding relative to the target balanced power is calculated. Based on the power regulation demand and the reconstructed equivalent resistance parameter, reconstructed leakage inductance parameter, and reconstructed magnetic coupling coefficient parameter in the winding parameter reconstruction matrix, a winding power regulation mapping relationship is established, and the parameter adjustment amount corresponding to each series winding is calculated. Based on the parameter adjustment amount, a winding parameter adjustment vector is constructed, and the vectors are arranged according to the winding number order to form a winding adjustment vector; The adjustment amounts of each parameter are normalized proportionally constrained based on the winding adjustment vector to generate the equivalent winding adjustment vector C.

9. The transformer series power balancing method based on winding parameter reconstruction according to claim 1, characterized in that: The steps of feeding back the equivalent winding adjustment vector C to the power coupling network model W for iterative correction include: Based on the equivalent resistance adjustment, leakage inductance adjustment, and magnetic coupling coefficient adjustment of each series winding in the equivalent adjustment vector C, the corresponding parameters in the winding parameter reconstruction matrix are corrected to obtain the updated winding parameter matrix. The electromagnetic coupling relationship between each series winding is recalculated based on the updated winding parameter matrix, and the power coupling weights in the power coupling network model W are updated to form a corrected power coupling network structure. The power transfer paths between each series winding are recalculated based on the modified power coupling network structure, and a new power propagation probability distribution is calculated based on the updated power coupling weights. The power allocation value of each series winding is recalculated based on the new power propagation probability distribution, and the difference between the current power allocation value and the previous power allocation result is determined. When the difference is less than the preset convergence threshold, the updated power allocation result is output.

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