Complex power quality data classification method for loss reduction of distribution transformer

Abstract

This invention provides a method for classifying complex power quality data for loss reduction in distribution transformers, belonging to the field of power distribution technology. It constructs a mathematical representation model of the additional power quality loss in distribution transformers, calculating the additional power quality loss based on a reference loss; identifies a set of potential variables affecting the loss; samples from the prior distribution of these potential variables, generating a physically semantically interpretable loss data sample set through a nonlinear system mapping function; processes the loss data sample set to obtain a linear representation matrix; and uses blind source separation technology to analyze and decouple the coupling mechanism of the linear representation matrix, transforming the strongly coupled multivariate loss model into multiple independent single-variable models, thus decoupling the loss. The advantages are: by accurately separating the total loss into independent components such as reference loss, voltage loss, unbalanced loss, and harmonic loss, it avoids the cross-influence and redundant calculations of various factors in complex power quality scenarios.

Description

Technical Field

[0001] This invention belongs to the field of power distribution technology, specifically relating to a method for classifying complex power quality data to reduce losses in distribution transformers. Background Technology

[0003] Power grid losses account for a significant proportion of energy consumption, and reducing these losses is a crucial measure for achieving energy conservation and loss reduction. Distribution transformer (hereinafter referred to as "distribution transformer") losses account for more than 50% of the total losses in the distribution network. With the increase in distributed power sources and the integration of nonlinear loads in the power grid, power quality problems such as three-phase imbalance, harmonics, and voltage deviations in the distribution network are becoming increasingly serious, with the most direct impact being an increase in the system's active power loss. For example, three-phase load imbalance will generate unbalanced currents in the phase lines, and in a three-phase four-wire power supply system, it will also generate zero-sequence currents on the neutral line, thus increasing losses. Harmonic currents will cause skin and proximity effects in the transformer windings, increasing the impedance of the windings and conductors, and causing heating of the transformer's silicon steel sheets and casing. Voltage deviations not only affect the transformer's copper losses but also its no-load losses. Summary of the Invention

[0004] In view of this, the present invention addresses the shortcomings of the prior art by providing a complex power quality data classification method for reducing losses in distribution transformers. To solve the above-mentioned technical problems, the technical solution adopted by the present invention includes: based on the electromagnetic and loss physical mechanism of distribution transformers, decomposing the total loss into a fixed loss component and a variable loss component, wherein the fixed loss is determined by voltage and related power quality indicators, and the variable loss is determined by current and related power quality indicators. A mathematical characterization model for the additional power quality loss of distribution transformers is constructed, and the reference loss is defined as the ideal operating loss under the load condition without change. The additional power quality loss is calculated based on the reference loss. Identify a set of potential variables that affect additional losses in power quality, including the fundamental RMS values ​​of voltage / current, harmonic content, three-phase imbalance, harmonic equivalent resistance, and temperature. Samples are taken from the prior distribution of the latent variables, and a set of loss data samples that can be interpreted physically is generated through a nonlinear system mapping function. Each sample in the set corresponds to a set of coupled observations of latent variables. After standardizing the loss data sample set, the sample similarity matrix is ​​calculated using the radial basis kernel function. After double centering correction, kernel principal component analysis is performed to extract the main change direction and obtain the linear characterization matrix, so that the linear characterization matrix satisfies the linear mixture assumption. The linear characterization matrix is ​​subjected to coupling mechanism analysis and decoupling using blind source separation technology. The multivariate strongly coupled loss model is transformed into multiple independent single-variable models. The physical interpretable characterization factors of each variable of transformer loss are obtained. Loss decoupling is performed, and the influence of different variables on loss is quantitatively analyzed based on the physical interpretable characterization factors.

[0005] Furthermore, the fixed losses include eddy current losses and hysteresis losses, and the variable losses include winding losses, winding stray losses, and other stray losses. There is a coupling relationship between the fixed loss and the variable loss, and there is a coupling between harmonic loss and three-phase unbalance loss within the variable loss.

[0006] Furthermore, the mathematical representation model of the additional power quality loss is expressed as follows:

[0007] Where ΔP(t) is the power loss due to power quality, ΔW(t) is the power loss due to power quality during time interval T, P(u(t)) represents the fixed power loss, u(t) is the voltage function, and P(β,γ,α,i(t),R) is the voltage function. har ) represents winding power loss, β is three-phase current imbalance, α is current harmonic distortion rate, γ is power factor, and R har P represents the equivalent harmonic resistance of the distribution transformer; P0 represents other stray power losses; P ref (t) represents the reference loss power.

[0008] Furthermore, the ideal operating loss is the transformer base loss caused by the ideal voltage and current, where the transformer current / voltage is the three-phase fundamental positive sequence active current and the three-phase fundamental positive sequence rated voltage, respectively.

[0009] Furthermore, the method for sampling from the prior distribution of the latent variables and generating a physically semantically interpretable loss data sample set through a nonlinear system mapping function includes: sampling the latent variable values ​​z from the prior distribution p(z); sampling the distribution transformer separation loss observation value X from the conditional data generation distribution; where X is a series of physically semantically interpretable factors {v1, v2, ..., v...} n This is generated through the mutual coupling of the mapping function of the nonlinear system; that is:

[0010] Where, {v1,v2,...,v n Let {v1, v2, ..., v} represent the individual loss values ​​of the distribution transformer, and let the latent variable z be {v1, v2, ..., v}. n The conditional likelihood distribution p(x / z) is an approximation of the unknown function sim(.) from a probabilistic perspective. The latent variable is represented as z = {z1, z2, ..., z}. n},and Study the latent variable z k The corresponding generating factor v within the data k Effective characterization and control were used to derive the influence of power quality indicators on losses.

[0011] Furthermore, after standardizing the loss data sample set, the sample similarity matrix is ​​calculated using the radial basis function kernel. After double-centering correction, kernel principal component analysis is performed to extract the main directions of change and obtain the linear characterization matrix. The methods include: The original nonlinear feature data is standardized to eliminate the dimensional differences between different index parameters, so that the data meets the statistical characteristics of zero mean and unit variance. The similarity matrix between samples is calculated by radial basis kernel function. The original nonlinear features are implicitly mapped to a high-dimensional linear space by kernel trick, so that the originally nonlinear data presents linear separability in this space. Subsequently, the kernel matrix is ​​corrected by bicentering, and the main direction of change is extracted by kernel principal component analysis to reduce the dimensionality and obtain a low-dimensional linear representation matrix.

[0012] Furthermore, the model of the blind source separation technique satisfies ,in: It consists of observation vectors from N measuring points / channels. A is a vector composed of M source signals to be estimated, where the subscript t is the sample point index; A is an unknown N×M mixing matrix; the separation matrix W is used to make... For the estimation of the source signal, where D is a diagonal matrix, P is a permutation matrix, and W is an M×N solution mixing matrix.

[0013] Furthermore, blind source separation technology is used to couple and identify the linear characterization matrix, transforming the strongly coupled multivariate loss model into multiple independent univariate models, and obtaining the physical interpretable characterization factors of each variable of the transformer loss. The methods for loss decoupling include: A hierarchical identification algorithm is adopted to decompose the high-dimensional complex loss coupling problem into low-dimensional and easily identifiable subproblems. The coupling terms of fixed loss and variable loss, and the coupling terms within variable loss are identified respectively. The influence intensity of each coupling term on loss is quantified, and the decoupling priority is determined. Based on the physical mechanism of distribution transformer losses, losses are classified into separate losses such as reference losses, voltage losses, harmonic current losses, unbalanced current losses, power factor, reactive current losses, DC losses, and stray losses. The modeling process for separate losses includes: Let the high-precision sampling data of voltage and current be u(t) and i(t), respectively. Perform Fourier decomposition to obtain the DC component, fundamental component and harmonic components. Through integration, the total loss is decomposed into DC loss, fundamental loss and harmonic loss. Then, the three-phase unbalance loss and reactive power loss are separated from the fundamental loss. To improve the measurement methods of three-phase imbalance and harmonic distortion rate when the internal coupling of variable losses is separated, a power quality index system that is independent of each other and uniquely corresponds to the separated loss is constructed. To address the coupling between fixed and variable losses: establish the mathematical relationship between voltage and current through a load model, quantify the changes in variable losses caused by voltage fluctuations, and decouple strongly coupled terms based on coupling strength.

[0014] Furthermore, the method for decoupling losses and quantitatively analyzing the impact of different variables on losses based on physically interpretable characterization factors includes: the physically interpretable characterization factors obtained by decoupling satisfy the following physical constraint relationship; based on this constraint relationship, the percentage of the loss value corresponding to each characterization factor in the total loss of the distribution transformer is calculated, thereby quantifying the degree of impact of different variables on losses.

[0015] Physical constraints include:

[0016] Among them, W dc W is the DC loss, W1 is the fundamental frequency loss, W k For the kth harmonic loss, W ref For reference loss, W unb For unbalanced losses, W rea W represents reactive power loss, W0 represents other stray losses, and W... U For voltage loss, W har For harmonic loss, W δ This is the error value.

[0017] 10. The complex power quality data classification method for loss reduction of distribution transformers as described in claim 8, characterized in that it further includes instantiation verification of the decoupling principle, including: For three-phase unbalanced scenarios: Based on the winding structure of the Dyn11 connected transformer, the symmetrical component method is used to calculate the negative-sequence / zero-sequence unbalance, and the unbalance loss in the total loss is included. From fundamental frequency loss Separate from the middle, and quantify the imbalance by hierarchical identification. Impact weights, verification With harmonic loss Decoupling independence; For harmonic scenarios: Correcting harmonic resistance based on skin effect and proximity effect Construct the h-th harmonic loss The exponential fitting model was used to compare the loss calculation errors with the IEEE conventional model, the improved parameter method, and the experimental fitting method, thus verifying the model. and unbalanced loss The effectiveness of decoupling; For voltage deviation scenarios: Based on the decoupling principle, the total loss under voltage deviation is decomposed into a fixed loss component affected by voltage and a variable loss component affected by current, and the difference between the two is determined as the voltage loss; based on the voltage deviation percentage, the voltage loss is... From fixed losses Separate the middle part and verify the voltage deviation in the simulation model. Its independent variation characteristics.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The data-physical dual-drive decoupling method provided by this invention effectively solves the problems of strong coupling and multivariate interference in traditional distribution transformer loss models. By accurately separating the total loss into independent components such as reference loss, voltage variable control loss, unbalance variable control loss, harmonic variable control loss, three-phase unbalance variable control loss, reactive current conversion control loss, and temperature variable control loss, and obtaining the physically interpretable characterization factors of each variable, the cross-influence and redundant calculation of various factors in complex power quality scenarios are avoided.

[0019] By analyzing the magnitude of physically interpretable characterization factors, we can quantitatively analyze the impact of different variables on losses, thereby identifying the variables with the greatest impact on losses and focusing on managing these variables to reduce transformer losses with maximum efficiency.

[0020] This separation mechanism based on physical semantics enables complex nonlinear systems to be decomposed into multiple computational units of single variables, significantly reducing the difficulty of modeling and improving the model's adaptability to different operating conditions.

[0021] 2. This invention balances the physical interpretability and computational accuracy of the loss calculation model. Unlike black-box models that rely solely on data fitting, this invention defines the loss composition based on the physical mechanism of the electromagnetic transformation of the distribution transformer and uses blind source separation technology to decouple and characterize each loss component. This method not only retains the clear explanation of the causes of loss using physical analytical methods, but its combination with data-driven methods can absorb nonlinear frequency-varying characteristics (such as the skin effect) through the following logic, ensuring that the calculation results reflect the real physical process and adapt to complex and changing field operating environments. Attached Figure Description

[0022] The present invention will now be described in further detail with reference to the accompanying drawings.

[0023] Figure 1: A schematic diagram of the voltage and current waveforms of the distribution transformer in Embodiment 1 of the present invention; Figure 2 : A schematic diagram of the coupling relationship between the power quality and additional losses in the distribution transformer in Embodiment 1 of the present invention; Figure 3 : Overall technical roadmap of Embodiment 1 of the present invention; Figure 4 : A schematic diagram of the technical route in Embodiment 1 of the present invention; Figure 5 : A schematic diagram of the mutually independent indices characterizing loss in Embodiment 1 of the present invention; Figure 6 Schematic diagram of typical parameters of S11 series transformer in Embodiment 2 of the present invention; Figure 7 Example 2 of this invention includes a schematic diagram of the MATLAB parameter settings for the named values; Figure 8 : A schematic diagram of the MATLAB parameter settings for the unit value in Embodiment 2 of this invention; Figure 9 : Simulation diagram of the no-load experiment in Embodiment 2 of the present invention; Figure 10 : Simulation diagram of short-circuit experiment in Embodiment 2 of the present invention; Figure 11 : A schematic diagram of the simulation model of the 10kV distribution network system in Embodiment 2 of the present invention; Figure 12 Equivalent circuit diagram of a distribution transformer with a nonlinear load in Embodiment 3 of this invention; Figure 13 : A schematic diagram of the simulation model in Embodiment 3 of the present invention; Figure 14 Schematic diagram of the calculated and simulated values ​​of the additional loss of the third harmonic in Embodiment 3 of the present invention; Figure 15 Schematic diagram of the calculated and simulated values ​​of the additional loss of the 5th harmonic in Embodiment 3 of the present invention; Figure 16 Schematic diagram of the calculated and simulated values ​​of the additional loss of the 7th harmonic in Embodiment 3 of the present invention; Figure 17 Schematic diagram of the calculated and simulated values ​​of the additional loss of the 9th harmonic in Embodiment 3 of the present invention. Detailed Implementation

[0024] To better understand the present invention, the content of the invention is further clearly illustrated below with reference to embodiments and accompanying drawings. However, the scope of protection of the present invention is not limited to the embodiments described below. Numerous specific details are set forth in the following description to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the present invention can be practiced without one or more of these details.

[0025] Example 1: See Figure 1-5 This embodiment provides a method for classifying complex power quality data for loss reduction in distribution transformers, which includes:

[0026] 1. A method for generating and classifying complex power quality data samples to characterize distribution transformer losses 1.1 Method for Generating Physically Semantically Interpretable Data Samples Distribution transformer losses are divided into fixed losses and variable losses. Fixed losses include eddy current losses and hysteresis losses, while variable losses include winding losses, winding stray losses, and other stray losses. There are coupling characteristics between fixed and variable losses, and within variable losses themselves, exhibiting multivariable, strong coupling, and nonlinear features. A mathematical model is established based on physical characteristics to represent the losses in relation to voltage, current, and power quality indicators. Let ΔU be the voltage deviation coefficient, β be the three-phase unbalance coefficient, γ be the power factor coefficient, and α be the harmonic distortion coefficient. Then, the additional power quality loss of the distribution transformer can be expressed as:

[0027] Where ΔP(t) is the power loss due to power quality, ΔW(t) is the power loss due to power quality during time interval T, P(u(t)) represents the fixed power loss, u(t) is the voltage function, and P(β,γ,α,i(t),R) is the voltage function. har ) represents winding power loss, β is three-phase current imbalance, α is current harmonic distortion rate, γ is power factor, and R har This represents the equivalent harmonic resistance of the distribution transformer. P0 represents other stray power losses. ref (t) represents the reference loss power; The reference loss is a function of voltage, representing the change in voltage with load current. It refers to the transformer base loss caused by the ideal voltage and current without changing the load conditions, where the transformer current / voltage is the three-phase fundamental positive-sequence active current and the three-phase fundamental positive-sequence rated voltage, respectively. The reference loss serves as the benchmark for calculating additional power quality losses.

[0028] Fixed losses are functions of voltage and its power quality indices, while variable losses are functions of current and its power quality indices. This study investigates the mathematical relationships between fixed losses and voltage power quality indices, variable losses and current power quality indices, voltage and current, and other stray losses; it also investigates the mathematical relationships between additional power quality losses and various power quality indices.

[0029] This research investigates methods for generating physically semantically interpretable data samples, forms a representation learning network, and establishes a decoupled representation learning model driven by both physics and data. The specific technical framework is as follows: Figure 3 As shown.

[0030] The problem of power quality losses in distribution transformers is complex due to factors such as the skin effect, proximity effect, stray parameters, and coupling characteristics. From a physical perspective, these losses are caused by numerous individual factors; from a probabilistic perspective, one or more factors may contribute to the occurrence of these losses. This study investigates all potential variables that may affect losses, such as the fundamental RMS values ​​of voltage / current, harmonic content, three-phase imbalance, reactive current, and temperature, and establishes a comprehensive data sample.

[0031] The modeling process for the data samples is as follows: latent variable values ​​z are sampled from the prior distribution p(z); distribution transformer separation loss observations X are sampled from the conditional data generation distribution. X represents a series of physically semantically interpretable factors {v1, v2, ..., v...} n These are generated through the mutual coupling of the mapping function of the nonlinear system. That is:

[0032] Where, {v1,v2,...,v n Let {v1, v2, ..., v} represent the separation loss values ​​of the transformer loss, and let z be the physical interpretable factors {v1, v2, ..., v}. n The conditional likelihood distribution p(x / z) is an approximation of the unknown function sim(.) from a probabilistic perspective.

[0033] The latent variable is represented as z = {z1, z2, ..., z}. n},and Study the latent variable z k The corresponding generating factor v within the data k Effective characterization and control were used to derive the influence of power quality indicators on losses.

[0034] 1.2 Analysis of the Coupling Mechanism and Decoupling Principle of Additional Losses in Distribution Transformers 1.2.1 With the widespread integration of new energy sources and electric vehicles, the power quality problems of distribution networks are becoming increasingly severe and diverse, and harmonics exhibit broadband characteristics. The equivalent resistance in the loss model is exacerbated by factors such as the skin effect, and the coupling problems between fixed losses and variable losses, as well as within variable losses, cannot be ignored. Transforming the multivariate, strongly coupled model of distribution transformer losses into multiple independent single-variable models to achieve decoupling presents significant technical challenges.

[0035] This paper elucidates the coupling mechanism of losses caused by combined power quality issues, proposes a loss separation model for decoupling, improves power quality measurement methods such as three-phase imbalance and harmonic distortion rate, and forms an independent power quality index system that maps the distribution transformer's separation losses. It proposes that the decoupling principle for power quality-related additional losses is the foundation for constructing a decoupling characterization learning model for distribution transformer additional losses. The specific technical framework is as follows: Figure 4 As shown.

[0036] Blind source separation (BSS) is a novel research direction in the field of modern signal processing. It has a solid theoretical foundation and has been developed in many research areas, particularly in biomedical engineering, medical imaging, speech enhancement, remote sensing, communication systems, earthquake detection, geophysics, econometrics, and data mining.

[0037] The blind source separation problem can be described as: separating or estimating source signals from the output signal of a sensor array or converter when the transmission channel is unknown. The term "blind" here has two meanings: first, the source signal to be recovered cannot be directly observed; second, it is unknown how the received observation data vector is formed by mixing the source signals. Based on whether there is a time delay in the mixing of source signals, the mixing method can be divided into instantaneous mixing and convolutional mixing; based on the mapping relationship between the input and output of the mixing system, the mixing method can be divided into linear and nonlinear types; based on the number of source signals and observation signals, the mixing method can be divided into underdetermined (the number of source signals is greater than the number of observation signals), well-determined (the number of source signals equals the number of observation signals), and overdetermined (the number of source signals is less than the number of observation signals).

[0038] The core problem of BSS is the learning algorithm for separating (or demixing) matrices, which belongs to unsupervised learning. When the mixture model is nonlinear and there is no additional prior knowledge, it is usually difficult to uniquely recover the source signal from the mixture data. In this application, the nonlinear features are preprocessed or transformed into a linear representation form that can be handled by BSS before the physical semantic samples are input into the BSS module. First, the original nonlinear feature data is standardized to eliminate dimensional differences between different index parameters, ensuring the data meets the statistical characteristics of zero mean and unit variance. Then, a similarity matrix between samples is calculated using a radial basis function kernel. The kernel trick implicitly maps the original nonlinear features to a high-dimensional linear space, making the originally nonlinear data linearly separable in this space. Subsequently, the kernel matrix is ​​corrected by bicentering, and kernel principal component analysis is used to extract the main directions of change for dimensionality reduction, obtaining a low-dimensional linear representation matrix. Finally, this matrix is ​​input into the instantaneous linear mixture BSS algorithm. Nonlinear physical semantic sample data is considered to be X. The original nonlinear sample X is projected into a high-dimensional linear space to obtain a linear representation M, which satisfies the linear mixture hypothesis of blind source separation.

[0039] By expanding the original nonlinear sample X using nonlinear basis functions, the nonlinear relationship is transformed into a linear combination of basis functions, resulting in a linear representation M.

[0040]

[0041] The mathematical model of an instantaneous linear hybrid BSS can be expressed as:

[0042] In the formula: It consists of observation vectors from N measuring points / channels. A is a vector composed of M source signals; A is an unknown N×M mixing matrix, and the subscript t is the sample point index. When the source signals are statistically independent of each other, BSS is Independent Component Analysis (ICA).

[0043] The goal of BSS is to recover the original signal from the observed mixed data vector, based on the assumption that the source signals are statistically independent. To achieve this, a separation matrix W needs to be determined such that the transformed output is a copy or estimate of the source signals.

[0044]

[0045] Where W is the M×N solution mixing matrix, This is an estimate of the source signal. For simplicity, without loss of generality, we assume M=N. From the above equation, it can be seen that when the solution mixing matrix W is equal to or approximately equal to A... -1 hour, Equal to or approximately equal to the source signal Due to the mixing matrix A and the source signal Since both are unknown, the order and amplitude of the obtained source signals are uncertain. The BSS algorithm can only obtain a scalar transformation of the actual source signals. In this case, the demixing matrix W is expressed as:

[0046] Where D is a diagonal matrix, P is a permutation matrix, and W is an M×N solution mixing matrix.

[0047] Due to the independent components output by the blind source separation algorithm It only has statistical independence, but cannot determine the order of components and physical dimensions. Therefore, this invention introduces a physical anchor point calibration mechanism and uses a separation loss model to constrain the solution mixing matrix W. Amplitude calibration (resolving dimensions): based on the reference loss under three-phase balanced, rated sinusoidal operating conditions. Using the reference value, calculate the linear scaling factor between the separated components and the actual physical loss, and establish the diagonal matrix D; Arrangement calibration (solving sorting): Based on the order of coupling strength determined by hierarchical identification (e.g., fixed loss coupling is stronger than variable loss coupling), the output components are compared with those in the physical model. Once a one-to-one mapping is established, the permutation matrix P is determined.

[0048] Through the above calibration, the mathematical space is made... It accurately corresponds to the actual loss components in the physical space.

[0049] 1.2.2 Based on the blind source separation theory, a mapping function between loss measurement signals and potential influencing variables can be formed, thereby decoupling the additional losses of power quality.

[0050] 1) By adopting a hierarchical identification and coupling identification algorithm, the loss coupling problem with high dimension and complex structure is transformed into a low-dimensional and relatively easy identification problem to be solved. The coupling terms between fixed loss and variable loss, and between variable loss, are identified respectively. The coupling strength of each coupling term on the loss is studied, and the priority of decoupling is determined.

[0051] 2) Based on the physical mechanism of transformer losses, losses are classified into separate losses such as reference losses, voltage losses, harmonic current losses, unbalanced current losses, reactive current losses, DC losses, and stray losses. The modeling process for separate losses is as follows: Let the high-precision sampling data of voltage and current be u(t) and i(t), respectively, the power be p(t), and the loss within the time period T be W. T :

[0052] After Fourier decomposition, we can obtain:

[0053]

[0054] Among them, U dc and I dc Let u1(t) and i1(t) represent the DC components of the voltage and current, respectively, and let u1(t) and i1(t) represent the fundamental components of the voltage and current, respectively. k (t) and i k (t) represent the kth harmonic voltage and harmonic current, respectively, W dc W1 and W k This represents DC loss, fundamental loss, and k-th harmonic loss. Losses such as three-phase imbalance and reactive power can be separated from the fundamental loss. Therefore, based on the above equation, the loss separation model can be expressed as:

[0055] Among them, W dc For DC losses, W ref For reference loss, W unb For unbalanced losses, W rea W represents reactive power loss, W0 represents other stray losses, and W... U For voltage loss, Whar For harmonic loss, W δ The value represents the error. The reference loss is the transformer loss when there are theoretically no power quality issues, while the additional power quality loss is mainly due to waveform non-ideality. Starting from all potential variables affecting transformer loss, this study investigates a loss separation model that covers all variables, laying the physical foundation for establishing a decoupled representation learning model.

[0056] Using the separation loss model as a constraint for blind source separation, the output components need to satisfy the following conditions during BSS decoupling: This is used as one of the criteria for algorithm convergence. To ensure the independent components output by the blind source separation algorithm... Given that the system possesses statistical independence and the ability to determine the order and physical dimensions of its components, this invention introduces a physical anchor point calibration mechanism, utilizing a separation loss model to constrain the solution mixing matrix W. Amplitude calibration: based on the reference loss under three-phase balanced, rated sinusoidal operating conditions. Using the reference value, calculate the linear scaling factor between the separated components and the actual physical loss, and establish the diagonal matrix D; Alignment and calibration: Based on the hierarchical identification of coupling strength (e.g., fixed loss coupling is stronger than variable loss coupling), the output components are aligned with those in the physical model. Once a one-to-one mapping is established, the permutation matrix P is determined.

[0057] Through the above calibration, the mathematical space is made... It accurately corresponds to the actual loss components in the physical space.

[0058] 3) Establish decoupling principles. Specifically, starting from the physical mechanism of loss generation, by improving power quality measurement methods and identifying the strength of coupling, the multivariable system is systematized into multiple independent single-variable systems. Different isolated losses are controlled by different input quantities, and strong coupling is decoupled first. For the internal coupling of variable losses, the different definitions of power quality indicators in national standards, IEC, and IEEE are summarized. Improvements to power quality measurement methods such as unbalance and harmonic distortion rate are studied for distribution transformer losses. A new index system (IIS) for characterizing losses is constructed, with each index uniquely corresponding to the isolated losses of the distribution transformer. For the coupling between fixed and variable losses, the mathematical relationship between voltage and current is established through a load model. The quantitative relationship of variable losses caused by voltage fluctuations is studied. Based on the identification of the strength of coupling, strong coupling terms are decoupled first. This provides physical mechanism support for the data-driven distribution transformer loss model, reduces system coupling terms, and increases the physical interpretability of the model.

[0059] Technical effects of this embodiment: 1. The data-physical dual-drive decoupling method provided by this invention effectively solves the problems of strong coupling and multivariate interference in traditional distribution transformer loss models. By accurately separating the total loss into independent components such as reference loss, voltage loss, imbalance loss, and harmonic loss, it avoids the cross-influence and redundant calculation of various factors under complex power quality scenarios. This separation mechanism based on physical semantics enables the originally complex nonlinear system to be decomposed into multiple single-variable calculation units, significantly reducing the modeling difficulty and improving the model's adaptability to different operating conditions.

[0060] 2. The physical model provides the physical semantics of the loss components (e.g., Corresponding harmonic loss, Corresponding to unbalanced loss), data-driven methods (such as hierarchical identification and sample generation) learn nonlinear mappings through a large amount of measured data, transforming complex nonlinear coupling relationships into linear hybrid forms that can be handled by BSS. At this time, BSS is responsible for decoupling the linear hybrid signals that have been stripped of nonlinear characteristics, while data-driven methods have already absorbed the influence of nonlinear frequency-varying characteristics in advance.

[0061] Example 2: See Figure 6-11 A complex power quality data classification method for distribution transformer loss reduction is proposed, based on the complex power quality data classification method for distribution transformer loss reduction as described in Example 1. It includes: 1.3 Analysis of Additional Losses in Distribution Transformers under Three-Phase Unbalance 1.3.1 Classification of Three-Phase Imbalance Characterization Indicators The integration of rooftop photovoltaic systems and high-power single-phase loads has exacerbated the problem of three-phase imbalance. Three-phase imbalance in power systems leads to reduced motor efficiency, increased line losses, and affects the accuracy of measuring and metering instruments. Imbalance measurement is fundamental to the analysis and management of three-phase imbalance, and numerous studies have been conducted by scholars and institutions both domestically and internationally. The following is a summary and classification of these studies. 1) International Electrotechnical Commission / National Standards Given the magnitude and phase angle of the three-phase currents, the International Electrotechnical Commission (IEC) / National Standards use the symmetrical component method to calculate the sequence current components from the three-phase current phasors, and accurately calculate the negative-sequence and zero-sequence current imbalance:

[0062]

[0063] The negative-sequence three-phase imbalance rate and the zero-sequence three-phase imbalance rate defined in the above formula make the measurement of the three-phase imbalance rate not unique, which affects subsequent analysis.

[0064] 2) IEEE IEEE Standard 936-1987 uses the maximum and minimum effective values ​​of the voltages in phases a, b, and c, as well as their three-phase average value, to calculate the current imbalance, as shown in the following formula.

[0065] IEEE Standard 112-2004 uses the effective values ​​of phases a, b, and c, and their three-phase average value to calculate voltage unbalance, as shown in the following formula.

[0066]

[0067] 3) National Electrical Manufacturers Association

[0068] This formula is an estimate, an estimate with small deviations in amplitude and phase angle, and cannot guarantee that it falls within the interval 0, 1.

[0069] 4) International Commission on Large Electric Systems

[0070]

[0071] Suitable for three-phase systems without zero-sequence components, it provides accurate calculations. The algorithm itself is simple, but it requires the amplitude of the line voltage, while most electrical testing equipment measures phase voltage and also requires measuring the phase angle, which is not easy to obtain. Moreover, it cannot provide the phase sequence decomposition results.

[0072] A comparison of different three-phase imbalance measurement methods is shown in Table 2-1. Table 2-1 Comparison of Three-Phase Imbalance Measurement Methods

[0073] 1.3.2 Comparative Study on Calculation Models of Additional Losses of Distribution Transformers under Three-Phase Unbalance The additional losses in a distribution transformer due to three-phase imbalance can be divided into additional copper losses and additional iron losses, where the additional copper loss is the increase in losses ∆P. R The additional iron loss is the eddy current loss generated by the zero-sequence current in the structural components. Zero-sequence current can flow in both windings of the Dyn11 connected transformer, so the currents in each phase on both sides are proportional, and the zero-sequence impedance can be considered approximately equal to the positive or negative sequence impedance. In three-phase imbalance, only a small amount of leakage flux is generated by the secondary side zero-sequence current, resulting in very small eddy current losses, which can be ignored. Therefore, the additional loss due to three-phase imbalance in the Dyn11 transformer is mainly the additional copper loss. This paper takes the Dyn11 connected transformer as an example to compare and analyze the calculation models of additional losses in distribution transformers under three-phase imbalance both domestically and internationally.

[0074] The representation of three-phase imbalance using IEEE std 112-1991 The three-phase unbalance is expressed as follows:

[0075] The additional losses of distribution transformers in low-voltage distribution networks are:

[0076] in .

[0077] Representation of three-phase imbalance using the national standard method The three-phase unbalance is expressed as follows:

[0078]

[0079] When the three phases are in balance, the eddy current losses caused by the small leakage magnetic field are negligible. Therefore, the losses are only related to the DC resistance loss of the windings, and the calculation formula is as follows:

[0080] In the Dyn11 connection mode, the primary winding of a 10kV distribution transformer is delta connected. Under delta conditions, the high-order harmonic current, which is mainly composed of the third harmonic, can form a circulating current on the primary side and will not flow into the high-voltage power grid. Therefore, additional core losses are generated in structural components such as the tank and clamps.

[0081] In the Dyn11 connection configuration, positive-sequence, negative-sequence, and zero-sequence currents all have closed loops on both the primary and secondary sides of the transformer. Therefore, the load currents on the primary and secondary sides are proportional, and the ratio of the currents is the reciprocal of the turns ratio. Furthermore, the excitation current on the low-voltage side is relatively small, resulting in a small leakage flux. Therefore, the slight difference in excitation loss caused by the difference between the magnetic circuit of the zero-sequence flux and the magnetic circuits of the positive-sequence and negative-sequence fluxes can be ignored. In this case, the zero-sequence impedance flowing through the zero-sequence current injected from the low-voltage side of the distribution transformer is exactly equal to the positive-sequence impedance flowing through its positive (negative) sequence current.

[0082] When the three phases are unbalanced, the DC resistance loss of the primary winding of the Dyn11 type distribution transformer is:

[0083] In the formula: k is the transformer turns ratio; R eq This is the equivalent resistance of the first section of the transformer. ;R t1 This refers to the resistive component of the positive sequence impedance on the secondary side of the transformer. ;R t0 This refers to the resistive component in the zero-sequence impedance of the secondary side of the transformer. .

[0084] The load loss in the secondary winding is

[0085] In the formula: R eq This is the equivalent resistance of the first section of the transformer. ;R t1 This refers to the resistive component of the positive sequence impedance on the secondary side of the transformer. ;R t0 This refers to the resistive component in the zero-sequence impedance of the secondary side of the transformer. .

[0086] Therefore, the increase in distribution transformer losses caused by three-phase imbalance The calculation formula is

[0087] According to the unbalance formula, the formula for calculating the additional losses caused by three-phase unbalance to the distribution transformer under the Dyn11 type connection method is as follows:

[0088] 1.3.3 Simulation Analysis of Additional Transformer Losses under Three-Phase Unbalance Transformer original parameters are as follows Figure 6 As shown;

[0089]

[0090]

[0091]

[0092] In the formula ∆P S The unit of ∆P0 is kW; S N The unit is kVA; U N The unit is kV.

[0093] The above four formulas are used in the parameter calculation of two-winding transformers in power systems. Expressions and The expression is determined based on the reciprocals of the transformer's conductance and susceptance. Substituting the original data and calculating back to the high-voltage side, we obtain R. T =3.86Ω, X T =12.70Ω, R m =208333.33Ω, X m =35273.37Ω.

[0094]

[0095] L can be obtained from the above formula. T =0.04H, L m =112.28H, in actual engineering, half is usually taken from the primary side and half from the secondary side. In the actual MATLAB model, it was found that under a delta connection, the resistance should be three times the calculated value, i.e., the high-voltage side R... T =1.93*3=5.79Ω, L T =0.02*3=0.06H. In the MATLAB model, the excitation parameters are also calculated for the high-voltage side, i.e., R. m =208333.33*3=624999.99Ω, L m =112.28*3=336.84H. When setting low-voltage side parameters, the calculation must first be transferred from the high-voltage side to the low-voltage side. High-voltage side R... T =1.93 / 625=0.003088Ω, L T =0.02 / 625=0.000032H. Parameter settings are shown in Figure 7. This setup is based on named values. In this case, switch the Units setting in the MATLAB window to per-unit values, such as... Figure 8 As shown, the per-unit values ​​set on the primary and secondary sides are equal at this time, which proves that the calculated values ​​must be multiplied by 3 when setting parameters for a transformer in a delta connection. (Because if the calculated values ​​are not multiplied by 3, the calculated values ​​are evenly distributed on the primary and secondary sides, and the per-unit values ​​on the primary and secondary sides should also be equal, but in fact they are not equal. They are only equal when the calculated values ​​are multiplied by 3). This is related to the MATLAB transformer delta connection model. If the high and low voltage sides are all Y-connected, there will be no problem.

[0096] The accuracy of the following parameters will be verified by conducting no-load and short-circuit tests. (1) No-load test The experiment is conducted on the high-voltage side, with the rated voltage applied to the primary side and the secondary side switched off to simulate an open-circuit condition. For example... Figure 9 As shown, the simulation parameters were set to an unloaded loss of 480W, and the simulation showed a primary-side power of 480W, consistent with the set value. The unloaded current percentage was set to 0.9%, and the rated current was [missing value]. A. The simulation shows a current of 0.166A, and the calculated no-load current percentage is 0.9%, which is consistent with the simulation value.

[0097] (2) Short circuit test An adjustable voltage is applied to the primary side to bring the short-circuit current to the rated current of 18.18A. A three-phase fault template (consistent with the three-phase short-circuit wiring configuration) is used on the secondary side to simulate a short circuit. Figure 10The simulation parameters were set to a short-circuit loss of 3830W, and the simulated power was 3825W, which is basically consistent with the set value. The short-circuit voltage percentage was set to 4%, and the simulated short-circuit percentage was 4.152%, which is basically consistent with the simulated value.

[0098] From a simulation perspective, the calculated values ​​are not multiplied by three when setting up a delta connection. Taking a short-circuit test as an example, the short-circuit voltage percentage is selected as 4%. At this time, the current is 26.23A, which is not equal to the rated current of 18.18A. At this time, the power is 5308W, which is also not equal to the short-circuit power of 3830W. The above analysis shows that the transformer parameters are set correctly.

[0099] To quantify and analyze the impact of power quality disturbances on the additional losses of 10kV and distribution transformers, a simulation model of the 10kV distribution network was established in the Matlab / Simulink simulation software, such as... Figure 11 In the simulation model of the 10kV distribution network system shown, the rated capacity of the power source is 100MVA, the rated voltage is 10kV, and X / R=10; the impedance values ​​of the three phases of the distribution lines are equal; the load consists of three single-phase loads with a rated voltage of 220V, and the rated capacity of each distribution transformer is 100kVA; the transformer simulation parameters are set as shown in Table 2-2. Table 2-2 Transformer Simulation Parameters

[0100] While ensuring that the total load on each transformer remains constant, the degree of three-phase imbalance in the system is adjusted by changing the load weight of each phase. Table 2-3 shows different degrees of imbalance in the load distribution, simulating power quality disturbances in many typical scenarios that far exceed the standard limits for various indicators. The three-phase imbalance data under different operating conditions are shown in Table 2-4.

[0101] Table 2-3 Specific distribution of loads for each phase

[0102] Table 2-4 Three-phase imbalance under different operating conditions

[0103] Table 25 shows the additional transformer losses under different conditions. Comparative analysis of the numerical values ​​revealed that the imbalance became increasingly severe, with transformer losses gradually increasing. The losses were minimized when all three phases were balanced. The table shows that the calculated and simulated values ​​obtained using the additional loss model method one were within 1% of each other, demonstrating higher accuracy than method two.

[0104] Table 2-5 Additional Transformer Losses under Different Conditions numerical value

[0105] Example 3: A method for analyzing the additional losses of distribution transformers under harmonic conditions, based on the complex power quality data classification method for loss reduction in distribution transformers as described in Example 1, includes: 1.4 Analysis of Additional Losses in Distribution Transformers under Harmonic Effects Transformers are designed based on power frequency conditions. The presence of harmonics in the system affects transformer performance; transformer losses are lowest at the fundamental frequency. When harmonics are present, the additional losses in distribution transformers cause a significant temperature rise, severely impacting operating efficiency and accelerating insulation aging. When the load current contains harmonics, the harmonic current increases the root-mean-square current, leading to increased losses as the current flows through the transformer conductors. Simultaneously, at high frequencies, transformers are affected by proximity and skin effects, causing significant changes in the conductor parameters surrounding the magnetic field, further increasing additional losses.

[0106] 1.4.1 Analysis of the superposition principle under harmonic action In a distribution network system with a nonlinear load, the grid supplies fundamental energy to the load side. Since the nonlinear load introduces complex harmonic currents, the harmonic currents on the transformer secondary side can be considered as independent harmonic current sources. Each independent harmonic current source is transmitted to the primary side through the transformer secondary side and flows to the grid. Because power system harmonics exhibit half-wave symmetry, their characteristics are as follows: Therefore, even-order harmonics in the power system are usually ignored. Based on the above principles, the equivalent circuit of the distribution transformer with a nonlinear load is obtained as follows: Figure 12 Show.

[0107] Figure 12 In the middle, R h(1) R h(2) --The resistance values ​​of the primary and secondary windings of the transformer corresponding to each harmonic component; jX h(1) jX h(2) --The transformer primary and secondary winding reactances corresponding to each harmonic component; R h(m) --Transformer excitation resistance corresponding to each harmonic component; jX h(m) --Transformer magnetizing reactance corresponding to each harmonic component.

[0108] When a transformer is subjected to a nonlinear load, the h-th harmonic current source (h=1, 3, 5, 7, 9, 11...) can be expressed as:

[0109] The load-side harmonic current is:

[0110] Under the influence of the h-th harmonic impedance of the transformer, the h-th harmonic voltage of the secondary winding is:

[0111] Based on the above analysis, when each harmonic current source acts on the secondary side of the transformer, the harmonic voltages generated on the primary and secondary sides of the transformer are as follows:

[0112] Since the fundamental current originates from the power supply side, and the harmonic currents are mainly caused by nonlinear loads, the fundamental current and harmonic currents flow in opposite directions. Using the superposition principle, the voltages at the primary and secondary winding terminals of the transformer are obtained as follows:

[0113] 1.4.2 Comparative Study on Calculation Models for Additional Losses of Distribution Transformers under Harmonic Effects Transformer losses under harmonic conditions mainly include core losses, winding losses, and stray losses. Stray losses typically account for 15% to 20% of core losses and are difficult to measure, so they are generally ignored. Core losses, also known as iron losses or fixed losses, are mainly calculated by considering hysteresis losses and eddy current losses. Under ideal operating conditions with constant voltage, their magnitude is independent of the load. Winding losses, also known as load losses or copper losses, mainly consist of DC losses and eddy current losses in the windings.

[0114] (1) Harmonic Iron Loss Analysis of Distribution Transformers Hysteresis loss occurs when an external magnetic field repeatedly magnetizes an iron core. After the external magnetic field is removed, some magnetic domains return to their original positions, while others retain their original magnetization direction. The heat generated by friction between adjacent domains during repeated magnetization is the hysteresis loss. In one magnetization cycle, the heat generated by this friction is called hysteresis loss. This represents the hysteresis loss per unit volume of iron core per magnetization cycle:

[0115] In the formula, f is the magnetization frequency of the iron core, and V is the volume of the iron core material.

[0116] Introducing the Steinmetz formula:

[0117] in, --Stametz coefficient; B m --Maximum magnetic flux density; s--Steinmetz index, usually 1.6, the value of which is determined by the properties of the core material; U--Induced voltage; A--Effective cross-sectional area of ​​the core.

[0118] The above Substituting the expression into the above The expression can be derived as follows:

[0119] When multiple harmonics are introduced into the iron core, the magnetic saturation effect is ignored, that is, the magnetic circuit is considered to be linear and satisfies the superposition theorem. Therefore, the formula for calculating magnetic hysteresis loss is as follows:

[0120] Among them, U h --RMS values ​​of each harmonic voltage component; f h -- The core magnetization frequency corresponding to each harmonic; M -- The maximum harmonic order.

[0121] When alternating magnetic field lines pass through a transformer conductor, an induced electromotive force is generated, which in turn produces an induced current. The loss caused by this induced current is called eddy current loss. The eddy current loss of the iron core is calculated as follows:

[0122] In the formula, - Resistance parameters of core loss; ρ - resistivity of silicon steel sheet; w - thickness of silicon steel sheet; T - period of magnetic flux density.

[0123] The above analysis shows that harmonic voltage is the main factor affecting transformer iron loss. In actual distribution networks, the system's harmonic voltage will not exceed 5% due to the use of filtering devices and reactive power compensation equipment. Compared with the fundamental frequency, the voltage harmonic component usually accounts for only 2%-3% or less, so this part of the loss can be ignored.

[0124] (2) Harmonic Copper Loss Analysis of Distribution Transformers The load loss of a transformer is calculated from its current and resistance. Fourier series decomposition of the current under harmonic influence yields the harmonic currents. However, the resistance changes due to the skin effect and proximity effect caused by harmonics. Therefore, this paper analyzes the representation of transformer impedance under harmonic conditions, focusing primarily on the impact of the skin effect on transformer impedance parameters. Based on this, the following three winding harmonic resistance models are proposed: 1) IEEE Conventional Transformer Model The harmonic current content is:

[0125] The additional losses of the distribution transformer under harmonic disturbances are:

[0126] 2) Improved parameter method Taking a single-phase transformer as an example, the IEEE Std C57.110 standard proposes a method that combines the harmonic loss factor with actual measurement data to calculate the load loss under harmonic effects:

[0127] In the formula: P R-O P EC-O P OSL-O These represent the DC, eddy current, and other stray losses in the load loss under measured power frequency current, in W and F, respectively. HL-EC F HL-OSL P respectively EC and P OSL The harmonic loss factor.

[0128] For P EC and P OSL The harmonic loss factor is defined as follows:

[0129]

[0130] In the formula: h is the harmonic order; , Let A and B be the effective values ​​of the fundamental current and the h-th harmonic current, respectively. The load loss under the measured power frequency current is calculated by multiplying the loss values ​​of each component under rated conditions by a correction parameter (I / I). R ) 2 Based on the obtained engineering measurement data, the correction parameters are transformed as follows:

[0131] The load loss of the transformer under rated conditions is:

[0132] P under actual rated conditions EC-R and P OSL-R Determining these values ​​is relatively difficult, as both are generally 20% to 30% of the rated load loss. Therefore, the rated DC loss is usually multiplied by a coefficient c to represent the rated load loss of a single-phase transformer, with c typically taken as 1.25. The load loss of a single-phase transformer under actual power frequency measurement can be expressed as follows:

[0133] Some scholars, taking into account the effects of skin and proximity effects of harmonics, have made the following improvements to the DC resistance parameters of the winding:

[0134] In the formula: R1 is the AC fundamental frequency resistance, Ω; c0, c1, c2, and b are coefficients, and their value ranges are shown in Table 2-6. Generally, they have... .

[0135] Table 2-6 Range of values ​​for each parameter

[0136] 3) Experimental data fitting method Makram EB et al. proposed a method for determining winding harmonic impedance using experimental data fitting. Ignoring core magnetic saturation and other nonlinear factors, they established an equivalent model of the transformer under various harmonic effects. Based on the superposition theorem, the harmonic source was equivalently represented as independent harmonic components acting separately on the transformer's equivalent model. Numerical fitting was performed on transformer parameter values ​​measured under no-load and short-circuit tests with numerous harmonic effects to obtain a fitting expression for the transformer harmonic resistance index:

[0137] In the formula: R is the resistance value obtained by exponential fitting calculation, in Ω; , These are the coefficients in the fitted expression.

[0138] The exponential fitting expression for the harmonic resistance parameters of the windings on both sides is obtained from the short-circuit test:

[0139] Compared to theoretically derived winding harmonic resistance, the experimental data fitting method can more accurately reflect the influence of harmonics on winding resistance, resulting in a more accurate harmonic resistance, specifically the h-th winding harmonic resistance referred to the secondary side. :

[0140] The harmonic-induced copper loss of the transformer is:

[0141] In the formula: , , and , , The effective values ​​of the fundamental and h-th harmonic currents of each phase on the secondary side, in A; , , The h-th harmonic current content of each phase on the secondary side, %.

[0142] 1.4.3 Simulation Analysis of Additional Losses of Distribution Transformer under Harmonic Disturbance Low-voltage distribution networks mostly use a three-phase four-wire system. A simulation model of a three-phase four-wire low-voltage network was built in Matlab / Simulink. The schematic diagram of the simulation model is shown below. Figure 13As shown in Table 2-7. Table 2-7 Transformer Simulation Parameters

[0143] To incorporate harmonic disturbances into the simulation model, a harmonic current source is used to simulate the harmonic power quality disturbances caused by the photovoltaic system connected to the 10kV system via a transformer. First, the three-phase load distribution of the system is assumed to be in a balanced state, with three single-phase loads, each with a power factor of 0.9. Then, a three-phase harmonic current source with adjustable amplitude and frequency is injected into the system. By changing the amplitude of the three-phase current source, the harmonic content is adjusted. The harmonic current amplitude is changed sequentially, increasing the harmonic content from 5% to 30%, thus obtaining the simulated value of the transformer's additional losses. Figures 14-17 The calculated and simulated values ​​of the additional losses of the 3rd, 5th, 7th, and 9th harmonic distribution transformers are presented.

[0144] Taking the third harmonic as an example, the additional harmonic loss increases rapidly and exponentially with the increase of harmonic content. Further comprehensive analysis of the loss changes at various frequencies reveals that different calculation models have varying accuracy at different harmonic orders. At the third and fifth harmonic frequencies, Method 2 provides more accurate loss predictions; at the seventh harmonic frequency, Method 3 shows higher calculation accuracy; and at the ninth harmonic frequency, Method 1 performs best in this frequency range.

[0145] Example 3: A method for analyzing additional losses in distribution transformers under voltage deviation, based on the complex power quality data classification method for loss reduction in distribution transformers as described in Example 1, includes: 1.5.1 Mechanism Analysis of the Influence of Voltage Deviation on Additional Losses of Distribution Transformers (1) Voltage deviation characterization index Under normal operating conditions, power systems may experience imbalances between the reactive power required by the load and the reactive power provided by the distribution system due to changes in the operating status and characteristics of the total or partial load, transformer tap adjustments, and capacitor switching. This imbalance can cause the supply voltage to continuously deviate from the rated nominal voltage. Voltage deviation measures the degree to which the steady-state voltage at the power supply point deviates from the system's nominal value under normal operating conditions. Generally, the power grid needs to transmit and distribute electrical energy to end-users. For medium- and low-voltage distribution networks, it is essential to design and select appropriate supply radii to ensure adequate power supply levels.

[0146] Typically, the percentage difference between the actual voltage and the nominal voltage relative to the system's nominal voltage is defined as voltage deviation, denoted by letters, and its expression is as follows:

[0147] (2) The impact of voltage deviation on additional losses in distribution network When voltage deviation exceeds the allowable limit, it poses a significant threat to the safety and economy of electrical equipment and the power grid. Generally, all electrical equipment is designed and manufactured based on its rated voltage. When the voltage deviation is large, the operating performance of the equipment will deteriorate, its service life will be shortened, its operating efficiency will be reduced, and it may even be damaged due to overvoltage or overcurrent.

[0148] 1.5.2 Comparative Study on Calculation Models for Additional Losses of Distribution Transformers under Voltage Deviation Research on calculation models for additional losses under voltage deviation, both domestically and internationally, mainly falls into two categories: 1) Overall consideration of three-phase transformers When voltage deviation is not considered, the losses of a distribution transformer mainly consist of no-load losses and load losses, calculated as follows:

[0149] Where P and Q represent the total three-phase active / reactive power (in W / Var), and U... N The effective value of the line voltage (V) is given by (P). 2 +Q 2 ) / U_N 2 = 3I 2 The load loss term is ((P) 2 +Q 2 ) / U_N 2 )·R T / 3 or simply 3I 2 R T ; When considering voltage deviation, the no-load loss of a distribution transformer increases with voltage rise, while during peak load periods when voltage is low, the no-load loss decreases significantly, and the main loss becomes load loss. Experimental data from relevant literature indicates that the relationship between actual operating voltage and transformer no-load loss is as follows:

[0150] In the formula, --No-load loss of distribution transformer; --Voltage deviation correlation coefficient. Specific values ​​are as follows:

[0151] When disturbances exist under voltage deviation, the losses of the distribution transformer are:

[0152] According to the above The expression and the above The expression yields the following additional losses of the distribution transformer under voltage deviation disturbance:

[0153] 2) Consider it as three three-phase transformers For transformers operating under load, the no-load loss accounts for a very small proportion of the total loss. Generally, the no-load loss is considered a fixed value. However, in actual operation, the no-load loss is proportional to the square of the actual operating voltage, as shown in the following formula:

[0154] In the formula: , These are the actual operating voltage and tap voltage of the transformer, respectively, in V; The percentage of voltage deviation on the primary side, % W represents the rated no-load loss.

[0155] Taking phase A of the distribution transformer as an example, the loss of a single phase considering voltage deviation is:

[0156] In the formula: The actual operating voltage of phase A on the primary side, in V; , Let W and Var be the active and reactive power of phase a on the secondary side. , The percentages of voltage deviation between the primary side phase A and the secondary side phase a, respectively, are %. Let be the apparent power of phase a on the secondary side, in VA; , V represents the actual operating voltage and rated voltage of the secondary side.

[0157] The single-phase loss of a distribution transformer, neglecting the effect of voltage deviation, is:

[0158] The additional loss due to voltage deviation of a single phase of a distribution transformer is:

[0159] Based on the additional loss due to single-phase voltage deviation of the distribution transformer, the additional loss due to three-phase voltage deviation is obtained as follows:

[0160] In the formula: , The voltage deviation percentage between phases B and C on the primary side, in % , The voltage deviation percentage between phases b and c on the secondary side, % , ΔP represents the apparent power (VA) of phases b and c on the secondary side, respectively. When the voltage is lower than the rated value, ΔP can be negative, indicating that the loss is lower than the reference value.

[0161] 1.5.3 Simulation Analysis of Additional Losses of Distribution Transformers under Voltage Deviation In the simulation model of the power distribution system, the transformer simulation parameters are set as shown in Table 2-8. The three single-phase loads are set to 100kVA to ensure that the system is in a three-phase balanced state. Adjusting the harmonic current injection in the harmonic current source to zero ensures that there are no harmonic disturbances in the system. The voltage deviation of the low-voltage power distribution system generally does not exceed +7% to 10% of the rated voltage. To conduct simulation analysis of the additional losses of the distribution transformer under different voltage deviation percentages, the voltage at the beginning of the distribution network is gradually increased from 9kV to 11kV in the simulation model, so that the voltage deviation percentage varies between -10% and +10%. The simulated values ​​and theoretical calculated values ​​of the additional losses of the transformer under different voltage deviations are shown in Table 2-9.

[0162] Table 2-8 Transformer Simulation Parameters

[0163] Table 2-9 Simulated and calculated values ​​of transformer additional losses under different voltage deviations

[0164] Additional losses are defined in the table as follows: The reference voltage is taken as the rated voltage and the three-phase balanced operating condition, therefore when U N A negative time difference value indicates a loss below the baseline. Table 2-9 shows that the additional loss of the transformer increases with the percentage increase in voltage deviation. When the load at the end of the distribution network is constant, the higher the voltage at the beginning of the distribution network, the greater the voltage drop across the distribution transformer, and consequently, the greater the transformer loss. The relative error between Method 1 for calculating the additional transformer loss and the simulation data is guaranteed to be within 5%. The overall accuracy of the data obtained by Method 1 is higher than that of Method 2.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.​

Claims

1. A method for classifying complex power quality data for loss reduction in distribution transformers, characterized in that, include: Based on the electromagnetic and physical mechanisms of distribution transformer losses, the total loss is decomposed into fixed loss components and variable loss components. The fixed loss is determined by voltage and related power quality indicators, while the variable loss is determined by current and related power quality indicators. A mathematical characterization model for the additional power quality loss of distribution transformers is constructed, and the reference loss is defined as the ideal operating loss under the load condition without change. The additional power quality loss is calculated based on the reference loss. Identify a set of potential variables that affect additional losses in power quality, including the fundamental RMS values ​​of voltage / current, harmonic content, three-phase imbalance, harmonic equivalent resistance, and temperature. Samples are taken from the prior distribution of the latent variables, and a set of loss data samples that can be interpreted physically is generated through a nonlinear system mapping function. Each sample in the set corresponds to a set of coupled observations of latent variables. After standardizing the loss data sample set, the sample similarity matrix is ​​calculated using the radial basis kernel function. After double centering correction, kernel principal component analysis is performed to extract the main change direction and obtain the linear characterization matrix, so that the linear characterization matrix satisfies the linear mixture assumption. The linear characterization matrix is ​​subjected to coupling mechanism analysis and decoupling using blind source separation technology. The multivariate strongly coupled loss model is transformed into multiple independent single-variable models. The physical interpretable characterization factors of each variable of transformer loss are obtained. Loss decoupling is performed, and the influence of different variables on loss is quantitatively analyzed based on the physical interpretable characterization factors.

2. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, The fixed losses include eddy current losses and hysteresis losses, and the variable losses include winding losses, winding stray losses, and other stray losses. There is a coupling relationship between the fixed loss and the variable loss, and there is a coupling between harmonic loss and three-phase unbalance loss within the variable loss.

3. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, The mathematical representation model of the additional power quality loss is as follows: Where ΔP(t) is the power loss due to power quality, ΔW(t) is the power loss due to power quality during time interval T, P(u(t)) represents the fixed power loss, u(t) is the voltage function, and P(β,γ,α,i(t),R) is the voltage function. har ) represents winding power loss, β is three-phase current imbalance, α is current harmonic distortion rate, γ is power factor, and R har P represents the equivalent harmonic resistance of the distribution transformer; P0 represents other stray power losses; P ref (t) represents the reference loss power.

4. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, The ideal operating loss is the transformer base loss caused by the ideal voltage and current, where the transformer current / voltage is the three-phase fundamental positive sequence active current and the three-phase fundamental positive sequence rated voltage, respectively.

5. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, The method for generating a physically semantically interpretable loss data sample set by sampling from the prior distribution of the latent variables and using a nonlinear system mapping function includes: sampling the latent variable values ​​z from the prior distribution p(z); sampling the transformer separation loss observation values ​​X from the conditional data generation distribution; where X is a series of physically semantically interpretable factors {v1, v2, ..., v...} n This is generated through the mutual coupling of the mapping function of the nonlinear system; that is: Where, {v1,v2,...,v n Let {v1, v2, ..., v} represent the individual loss values ​​of the distribution transformer, and let the latent variable z be {v1, v2, ..., v}. n The conditional likelihood distribution p(x / z) is an approximation of the unknown function sim(.) from a probabilistic perspective. The latent variable is represented as z = {z1, z2, ..., z}. n },and Study the latent variable z k The corresponding generating factor v within the data k Effective characterization and control were used to derive the influence of power quality indicators on losses.

6. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, After standardizing the loss data sample set, the sample similarity matrix is ​​calculated using the radial basis function kernel. After double-centering correction, kernel principal component analysis is performed to extract the main directions of change and obtain the linear characterization matrix. Methods include: The original nonlinear feature data is standardized to eliminate the dimensional differences between different index parameters, so that the data meets the statistical characteristics of zero mean and unit variance. The similarity matrix between samples is calculated by radial basis kernel function. The original nonlinear features are implicitly mapped to a high-dimensional linear space by kernel trick, so that the originally nonlinear data presents linear separability in this space. Subsequently, the kernel matrix is ​​corrected by bicentering, and the main direction of change is extracted by kernel principal component analysis to reduce the dimensionality and obtain a low-dimensional linear representation matrix.

7. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1, characterized in that, The model of the blind source separation technology satisfies ,in: It consists of observation vectors from N measuring points / channels. A is a vector composed of M source signals to be estimated, where the subscript t is the sample point index; A is an unknown N×M mixing matrix; the separation matrix W is used to make... For the estimation of the source signal, where D is a diagonal matrix, P is a permutation matrix, and W is an M×N solution mixing matrix.

8. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 7, characterized in that, The linear characterization matrix is ​​coupled and identified using blind source separation technology, transforming the strongly coupled multivariate loss model into multiple independent univariate models. This yields the physically interpretable characterization factors for each variable of the transformer loss. The methods for loss decoupling include: A hierarchical identification algorithm is adopted to decompose the high-dimensional complex loss coupling problem into low-dimensional and easily identifiable subproblems. The coupling terms of fixed loss and variable loss, and the coupling terms within variable loss are identified respectively. The influence intensity of each coupling term on loss is quantified, and the decoupling priority is determined. Based on the physical mechanism of distribution transformer losses, losses are classified into separate losses such as reference losses, voltage losses, harmonic current losses, unbalanced current losses, power factor, reactive current losses, DC losses, and stray losses. The modeling process for separate losses includes: Let the high-precision sampling data of voltage and current be u(t) and i(t), respectively. Perform Fourier decomposition to obtain the DC component, fundamental component and harmonic components. Through integration, the total loss is decomposed into DC loss, fundamental loss and harmonic loss. Then, the three-phase unbalance loss and reactive power loss are separated from the fundamental loss. To improve the measurement methods of three-phase imbalance and harmonic distortion rate when the internal coupling of variable losses is separated, a power quality index system that is independent of each other and uniquely corresponds to the separated loss is constructed. To address the coupling between fixed and variable losses: establish the mathematical relationship between voltage and current through a load model, quantify the changes in variable losses caused by voltage fluctuations, and decouple strongly coupled terms based on coupling strength.

9. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 1 or 8, characterized in that, The method for decoupling losses and quantitatively analyzing the impact of different variables on losses based on physically interpretable characterization factors includes: the physically interpretable characterization factors obtained by decoupling satisfy the following physical constraint relationship; based on the constraint relationship, the percentage of the loss value corresponding to each characterization factor in the total loss of the distribution transformer is calculated, thereby quantifying the degree of impact of different variables on losses. Physical constraints include: Among them, W dc W is the DC loss, W1 is the fundamental frequency loss, W k For the kth harmonic loss, W ref For reference loss, W unb For unbalanced losses, W rea W represents reactive power loss, W0 represents other stray losses, and W... U For voltage loss, W har For harmonic loss, W δ This is the error value.

10. The method for classifying complex power quality data for loss reduction in distribution transformers as described in claim 8, characterized in that, It also includes the instantiation and verification of the decoupling principle, including: For three-phase unbalanced scenarios: Based on the winding structure of the Dyn11 connected transformer, the symmetrical component method is used to calculate the negative-sequence / zero-sequence unbalance, and the unbalance loss in the total loss is included. From fundamental frequency loss Separate from the middle, and quantify the imbalance by hierarchical identification. Impact weights, verification With harmonic loss Decoupling independence; For harmonic scenarios: Correcting harmonic resistance based on skin effect and proximity effect Construct the h-th harmonic loss The exponential fitting model was used to compare the loss calculation errors with the IEEE conventional model, the improved parameter method, and the experimental fitting method, thus verifying the model. and unbalanced loss The effectiveness of decoupling; For voltage deviation scenarios: Based on the decoupling principle, the total loss under voltage deviation is decomposed into a fixed loss component affected by voltage and a variable loss component affected by current, and the difference between the two is determined as the voltage loss; based on the voltage deviation percentage, the voltage loss is... From fixed losses Separate the middle part and verify the voltage deviation in the simulation model. Its independent variation characteristics.

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