Power distribution transformer overload prediction method based on phase separation level prediction and physical constraint

Abstract

This application relates to a distribution transformer overload prediction method based on phase-level prediction and physical constraints. The method involves preprocessing each load in the acquired distribution topology to obtain the corresponding load tensor; passing the input tensor of each load tensor through the distribution transformer phase-level load prediction model to output the baseline prediction for each corresponding phase; introducing a summary matrix determined by the distribution topology and performing hierarchical consistency prediction on each baseline prediction based on minimum trajectory error to obtain the corresponding coordinated load prediction; projecting all coordinated load predictions onto the physical domain to obtain the copper loss of each phase, and calculating the iron loss based on voltage; inputting the iron loss and the copper loss of each phase into the driving differentiable thermal circuit model; and using the output transformer top oil temperature and hot spot temperature, along with the baseline predictions for each phase, to optimize the distribution transformer phase-level load prediction model. Finally, after hierarchical consistency prediction, the method outputs the final load prediction for each phase, thereby determining the overload status of each phase and performing corresponding operation and maintenance.

Description

Technical Field

[0001] This application relates to the field of early warning technology for heavy overload operation status of distribution transformers, and in particular to a method for predicting overload of distribution transformers based on phase-level prediction and physical constraints. Background Technology

[0002] With the large-scale integration of new power sources and loads, the spatiotemporal characteristics of three-phase loads in distribution transformers have undergone profound changes, leading to a high incidence of three-phase imbalance conditions. This ultimately results in a mix of single-phase, two-phase, and three-phase heavy overload problems in distribution transformers, endangering power grid safety. Traditional transformer temperature rise models and most data-driven models treat the transformer as a whole, typically predicting only the top oil temperature or a representative hot spot temperature. However, in real-world scenarios, due to load imbalance, differences in internal structure, and uneven distribution of cooling oil flow, the operating temperature (especially the hot spot temperature) of each phase in a three-phase distribution transformer may vary significantly. Treating all three phases as a single entity results in the loss of crucial information, leading to a decrease in the accuracy of the final temperature rise prediction. Furthermore, traditional thermal circuit models are ill-suited to adapting to rapidly changing and highly random phase-specific loads. In addition, purely data-driven prediction models (such as deep learning) are "black boxes," learning patterns entirely from data. Under three-phase imbalance and extreme load conditions, they are prone to producing physically inconsistent predictions that violate physical laws, significantly reducing the reliability of the results. Simultaneously, existing technologies lack an end-to-end collaborative mechanism for "load prediction - physical model - joint optimization."

[0003] Therefore, in response to the problems of insufficient prediction accuracy and lack of physical consistency of distribution transformer temperature rise under distributed energy access and three-phase load imbalance conditions, there is an urgent need for an overload risk prediction method that can guarantee prediction accuracy and conform to the mechanism under the corresponding conditions. Summary of the Invention

[0004] Therefore, it is necessary to provide a method for predicting overload of distribution transformers based on phase-level prediction and physical constraints, including: S1: Obtain the user load, phase load, and total load in the distribution topology, and preprocess the user load, phase load, and total load to obtain the user load tensor, phase load tensor, and total load tensor; S2: The input tensors of user load tensor, phase load tensor and total load tensor are respectively processed by the distribution transformer phase load prediction model based on SwinMDGRU, and the bottom baseline prediction, phase baseline prediction and top baseline prediction are output respectively. S3: Introduce the summary matrix determined by the distribution topology and the coordination matrix constructed based on the summary matrix. Based on the minimum trajectory error, perform hierarchical consistency prediction on the bottom baseline prediction, phase baseline prediction and top baseline prediction respectively to obtain the corresponding coordinated load prediction. S4: Based on the electromagnetic-thermal mechanism, all coordinated load predictions are projected onto the physical domain to obtain the copper loss of each phase, and the iron loss is calculated based on the voltage. The iron loss and the copper loss of each phase are input into the drive differentiable thermal circuit model, and the top oil temperature and hot spot temperature of the transformer are output. S5: Based on the baseline predictions of each phase, the top oil temperature, and the hot spot temperature and their corresponding true values, a total optimization objective is constructed. The total optimization objective is used to optimize the network parameters of the distribution transformer phase load prediction model. The input tensors of the load tensors of each phase are processed by the optimized distribution transformer phase load prediction model and hierarchical consistency prediction to output the final load prediction of each phase. Based on the final load prediction of each phase and the hot spot temperature, the overload situation is determined, and corresponding operation and maintenance are carried out according to the overload situation.

[0005] Beneficial Effects: This method preprocesses each load in the acquired distribution topology to obtain the corresponding load tensor. The input tensors of each load are then processed by a distribution transformer phase-by-phase load prediction model based on SwinMDGRU, outputting baseline predictions for each corresponding phase. A summary matrix determined by the distribution topology is introduced, and based on minimum trajectory error, hierarchical consistency prediction is performed on each baseline prediction to obtain corresponding coordinated load predictions. All coordinated load predictions are projected onto the physical domain to obtain the copper loss for each phase, and iron loss is calculated based on voltage. The iron loss and copper loss for each phase are input into a driving differentiable thermal circuit model. The output transformer top oil temperature and hot spot temperature, along with the baseline predictions for each phase, are used to optimize the distribution transformer phase-by-phase load prediction model. After hierarchical consistency prediction, the final load prediction for each phase is output, thereby determining the overload situation of each phase and enabling corresponding operation and maintenance. This method, while ensuring prediction accuracy, outputs temperature rise curves and overload conditions that conform to the underlying mechanisms, providing interpretable technical support for distribution transformer operation evaluation and maintenance decisions. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a flowchart of the overload prediction method for distribution transformers based on phase-level prediction and physical constraints in the embodiments of this application.

[0008] Figure 2 This is a schematic diagram of the power distribution topology in an embodiment of this application.

[0009] Figure 3 This is a schematic diagram of the structure of the distribution transformer phase load prediction model based on SwinMDGRU in the embodiments of this application. Detailed Implementation

[0010] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0011] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0012] like Figure 1 As shown, this embodiment provides a method for predicting overload of distribution transformers based on phase-level prediction and physical constraints, including: S1: Obtain user load, phase load, and total load in the distribution topology based on AMI or SCADA, and preprocess the user load, phase load, and total load to obtain user load tensor, phase load tensor, and total load tensor.

[0013] Specifically, preprocessing includes: Perform horizontal anomaly detection on user load, phase load, or total load. If so, it is determined that the user load, phase load, or total load is abnormal, and then... Make corrections; otherwise, determine that the user load, phase load, or total load is normal; among which, This represents the user load, phase load, or total load at time t on day d. This represents the user load, phase load, or total load at time t-1 on day d. This represents the user load, phase load, or total load at time t+1 on day d. This represents the detection threshold at time t. This represents the user load, phase load, or total load at time t on day d after horizontal correction. Perform vertical anomaly detection on user load, phase load, or total load. Determine if the user load, phase load, or total load is abnormal, through... Make corrections; otherwise, determine that the user load, phase load, or total load is normal; among which, , Let represent the average load at time t among all similar days on day d, and n represent the number of similar days on day d. This represents the user load, phase load, or total load at time t on day k after horizontal correction. This represents the user load, phase load, or total load at time t on day d+1. This represents the user load, phase load, or total load at time t on day d-1. This represents the user load, phase load, or total load at time t on day d after vertical correction. Missing loads are detected for user load, phase load, or total load. When a missing load is found, it is filled based on the average load of adjacent times or similar days. The filling formula is as follows: ; in, This represents the user load, phase load, or total load at time t on day d after the fill is completed; Indicates the weighting coefficient; Normalize the user load, phase load, or total load after determining normal, horizontal correction, vertical correction, or filling to obtain the user load, phase load tensor, or total load tensor.

[0014] S2: The input tensors of user load tensor, phase load tensor and total load tensor are respectively processed by the distribution transformer phase load prediction model based on SwinMDGRU, and the bottom baseline prediction, phase baseline prediction and top baseline prediction are output respectively.

[0015] In this embodiment, as Figure 3 As shown, the transformer phase load prediction model based on SwinMDGRU includes an input layer, a flattening layer, a patch embedding layer, a first SwinMDGRU cell layer, a patch merging layer, a second SwinMDGRU cell layer, a patch expansion layer, a reconstruction layer, and an output layer.

[0016] The input layer is used to obtain the user load or phase load tensor or total load tensor at each time step.

[0017] The flattening layer is used to divide the user load, phase load tensor, or total load tensor at each time step into non-overlapping patches of size P×P, and flatten each patch as a feature. When the step size s=P, the flattening formula is: ; in, Represents the m-th feature, M represents the number of patches, at this time , Let L represent the input tensor, F represent the feature dimension, P represent the patch length, and vec(·) represent the flattening operation. When the step size s < P, the flattening formula is the same as above, but at this time... ; The patch embedding layer is used to obtain the corresponding flag features by linearly mapping and adding position encoding to the features of each time step. The flag features of each historical time step are combined in time step order to obtain the flag sequence corresponding to user load, phase load or total load.

[0018] Each feature is embedded using linear patches and positional encoding is added to obtain the corresponding marker features, calculated as follows: ; in, This represents the m-th characteristic. Indicates linear weights, This indicates a linear bias. This represents the sine or learnable position vector corresponding to the m-th feature.

[0019] The flag features of each time step are combined in time step order to obtain the flag sequence corresponding to user load, phase load, or total load. The flag sequence is denoted as... T represents transpose, and the flag sequence is the input to the transformer phase load prediction model based on SwinMDGRU. After being embedded with patches, it is sent to the transformer phase load prediction model for processing, ensuring effective representation of local spatial patterns and continuous modeling of temporal information.

[0020] The first SwinMDGRU cell layer is used to obtain the corresponding historical state by passing any flag sequence through the ReLU activation function, and to calculate the first reset gate, the first update gate, and the first candidate state of the current time step in sequence based on the flag sequence and the flag features of the corresponding current time step; and to obtain the first hidden state of the current time step by weighted summing of the historical state and the first candidate state of the current time step based on the first update gate.

[0021] The patch merging layer is used to merge the first hidden states of the current time step obtained from multiple first SwinMDGRU cell layers into the corresponding hidden state sequence.

[0022] The second SwinMDGRU cell layer is used to obtain the corresponding predicted state by passing the corresponding hidden state sequence through the ReLU activation function, and to calculate the second reset gate, the second update gate, and the second candidate state of the current time step in sequence based on the hidden state sequence and the corresponding current time step's flag features; and to obtain the second hidden state of the current time step by weighted summing of the predicted state and the second candidate state of the current time step based on the second update gate.

[0023] The patch extension layer is used to upsample the second hidden state at the current time step to obtain a feature map.

[0024] The reconstruction layer is used to linearly activate the feature map to obtain the corresponding baseline prediction.

[0025] The output layer is used to output the baseline prediction.

[0026] In this embodiment, the workflow of the first SwinMDGRU cell layer and the second SwinMDGRU cell layer is the same. The workflow of the first SwinMDGRU cell layer can be expressed as follows: ; ; ; ; ; Among them, z t Let σ(·) denote the first update gate at time t, and let σ(·) denote the sigmoid function. Indicates the characteristic x t The corresponding first weight matrix, x t This represents the key feature at time step t. Represents the flag sequence H t-1 The corresponding first weight matrix, H t-1 Represents the flag sequence, b z Let represent the first bias vector, and represent the first reset gate at time t. Indicates the characteristic x t The corresponding second weight matrix, Represents the flag sequence H t-1 The corresponding second weight matrix, b r This represents the second bias vector. This represents the first candidate state at time step t. Indicates the characteristic x t The corresponding third weight matrix, Represents the flag sequence H t-1 The corresponding third weight matrix, Let represent the third bias vector, tanh(·) represent the hyperbolic tangent function, represent the first hidden state at time step t, represent the history state, and represent the ReLU activation function. Represents the flag sequence H t-1 The corresponding fourth weight matrix, b s This represents the fourth bias vector.

[0027] The core of both the first and second SwinMDGRU cell layers is the Swin-Transformer module. The operating mechanism of the Swin-Transformer module can be represented as follows: ; in, Z l Z l+1 They represent the first l Layer and first l Intermediate output features of layer +1 Z l and Z l+1 They represent the first l Layer and first l The output features of layer +1, LN represents layer normalization operation, W-MSA represents window-based multi-head self-attention mechanism, SW-MSA represents shift-window-based multi-head self-attention mechanism, and MLP is a multilayer perceptron. The Swin-Transformer module is a conventional module known in the art.

[0028] Furthermore, the double-weighted mixed loss DWH between the baseline prediction and the corresponding actual value output by the distribution transformer phase load prediction model is calculated, and the double-weighted mixed loss is minimized to optimize the distribution transformer phase load prediction model.

[0029] To meet the performance requirements of early warning missions at both light and heavy overload conditions, a dual-weighted hybrid (DWH) loss is designed as the training objective. The dual-weighted hybrid loss calculation formula is as follows: ; in, τ represents the weighting coefficient, τ1 represents the segmented threshold of the first function, and τ2 represents the segmented threshold of the second function.

[0030] Mean Absolute Percentage Error (MAPE) has become the most widely used evaluation metric in the field of time series forecasting. It is calculated as follows: ; Where N represents the total number of samples, A g F is the actual value of the g-th sample. g To be with A g The corresponding predicted value.

[0031] Based on the nonlinear sensitivity of MAPE (extremely sensitive to small errors when the load is close to zero, and the sensitivity decreases as the load increases), DWH divides the sample into three segments (threshold τ1<τ2) according to the load ratio r (actual load / rated capacity).

[0032] Heavy overload condition (r ≥ τ2): An adaptive weight that monotonically increases with r is superimposed on MAPE. The heavier the overload and the greater the loss, forcing the model to preferentially reduce the prediction error in the high-load area and improve the warning recall and accuracy.

[0033] Normal condition (τ1 < r < τ2): Directly use MAPE to ensure the overall robustness and comparability on the mainstream samples.

[0034] Light load condition (r ≤ τ1): Change to weighted mean square error to suppress noise amplification, and only impose a strong penalty on obvious deviations, thus avoiding overfitting under extremely low loads.

[0035] S3: Introduce a summary matrix determined by the distribution network topology and a coordination matrix constructed based on the summary matrix, and perform hierarchical consistency prediction on the underlying baseline prediction, phase-by-phase baseline prediction, and top-level baseline prediction respectively based on the minimum trajectory error, and obtain the corresponding coordinated load predictions for each phase.

[0036] Specifically, this step includes: Calculate the linear mapping relationship between all loads and user loads to obtain the summary matrix. The linear mapping relationship is expressed as: ; where represents all loads at the t-th moment, S represents the summary matrix, represents the user load at the t-th moment; if the distribution network topology is as Figure 2 shown, then , S, are respectively expressed as: ; ; ; where represents the total load at the t-th moment, represents the load of the i-th phase at the t-th moment, , represents the user load of the first user under the i-th phase at the t-th moment, represents the user load of the second user under the i-th phase at the t-th moment, represents the user load of the third user under the i-th phase at the t-th moment; Calculate the error between the underlying baseline prediction or phase-by-phase baseline prediction or top-level baseline prediction and the corresponding actual value to obtain the corresponding baseline error; For the baseline error corresponding to any baseline prediction, calculate the variance of the baseline errors corresponding to each time step, The calculation formula of ; where represents the variance of the baseline error at the h-th time step, and Var[·] represents the variance function, This represents the actual value of the baseline prediction at the h-th time step. Let L represent the baseline prediction at the h-th time step, and L represent the length of the corresponding baseline prediction.

[0037] As can be seen from the above, This is crucial for ensuring the consistency and numerical stability of MinT. This embodiment proposes two types of estimators, which are adapted to the scenarios of "small scale / sufficient sample" (sample covariance MinTSa) and "large scale / sparse sample" (shrinking covariance MinTSh), respectively.

[0038] MINTSa estimator: The covariance matrix obtained by the MinT estimator is an n×n matrix with no zero elements. For MinTSa, we set... W h =k h ,in k h >0, and is h The sample covariance estimator of the baseline prediction error when =1. This is because only the sample covariance estimator of the baseline prediction error is utilized. h For samples where = 1, MinTSa is simpler than MinTSh. m <T MinTSa performs best when the total number of observations is less than the amount of historical data used.

[0039] The MinTSa estimator calculates the coordinated load forecast using the following formula: ; in, This represents the coordinated load forecast corresponding to any baseline forecast at the h-th time step estimated by the MinTSa estimator. Let represent the weight matrix, which is the inverse of the covariance matrix at the h-th time step.

[0040] MINTSh estimator: The formula for calculating coordinated load forecasts using the MinTSh estimator is as follows: ; ; ; in, This represents the coordinated load forecast corresponding to any baseline forecast at the h-th time step estimated by the MinTSh estimator. The diagonal elements representing the contraction estimates Representation matrix diagonal elements of the matrix The off-diagonal elements decrease significantly and approach zero, but the diagonal elements (variance) remain unchanged. Var(·) represents the variance function. This represents the (i,j)th element in the corresponding matrix. This represents the shrinkage parameter.

[0041] S4: Based on the electromagnetic-thermal mechanism, all coordinated load predictions are projected onto the physical domain to obtain the copper loss of each phase. The iron loss is calculated based on the voltage. The iron loss and the copper loss of each phase are input into the drive differential thermal circuit model to output the transformer top oil temperature and hot spot temperature.

[0042] In this embodiment, all coordinated load predictions are projected onto the physical domain based on the electromagnetic-thermal mechanism to obtain the copper loss for each phase, and the iron loss is calculated based on the voltage, including: Based on the corresponding coordinated load predictions, the corresponding phase load currents are calculated using the following formula: ; in, I i ( t () represents the phase load current of the i-th phase at time t (unit: A). This represents the coordinated load forecast for the i-th phase at time t (unit: kW), and Un represents the rated line voltage on the low-voltage side of the transformer (unit: V). This represents the power factor, which can be calculated by taking the average value based on historical data or set to a typical value (such as 0.9-0.95). The copper loss of a transformer winding is proportional to the square of the load current. Based on Joule's law and the equivalent resistance referred to the transformer, the corresponding copper loss is calculated using the corresponding phase load current. The formula is as follows: ; in, q cu,i ( t The value represents the copper loss (in W) generated by the i-th phase winding at time t under a given load. r i This represents the total resistance (in Ω) of the i-th phase high and low voltage windings referred to the low voltage side. This copper loss calculation formula is equivalent to the copper loss calculation formula in the following drive differential thermal circuit model. The iron loss (no-load loss) of a transformer mainly consists of hysteresis loss and eddy current loss. When the operating voltage variation is small, it can be approximated as being proportional to the square of the voltage. Considering a base no-load loss value, the iron loss can be calculated based on the voltage using the following formula: ; in, q fe ( t() represents the iron loss at time t (unit: W). P 0 represents the no-load loss at rated voltage (unit: W), U(t) represents the transformer operating voltage at time t (unit: V), U N Indicates the rated voltage (unit: V). β This represents the relevant index of the core material (typically between 1.8 and 2.2, with 2 being the most common value). If we assume the operating voltage is stable near the rated value, the iron loss can be approximated as the no-load loss under the rated voltage. q fe ( t )≈ P 0.

[0043] Through the above mapping, the transformation from data-driven coordinated load prediction to physical-driven thermal analysis is completed. The calculated copper and iron losses will then be used as inputs to drive the differentiable thermal circuit model to solve for the transformer top oil temperature and hot spot temperature rise.

[0044] The above parameters r i , P 0, U N , β , belongs to physical parameters.

[0045] Furthermore, the driving differentiable thermal circuit model is expressed as: ; ; in, C i This represents the heat capacity of the i-th phase winding. i hs,i The temperature of the hot spot in the i-th phase winding is represented by , and t represents the time t. q cu,i This represents the copper loss generated by the i-th phase winding under a given load. R i It represents the thermal resistance between the i-th phase winding and the transformer oil, and is also used to calculate the equivalent resistance of the winding, including the conversion results between the high-voltage and low-voltage sides. i to Indicates the top oil temperature of the transformer. C oil Indicates the heat capacity of transformer oil. R oil This indicates the thermal resistance between the transformer oil and the environment. i amb Indicates ambient temperature. K i Represents the load factor of phase i, ( I N ) i This represents the phase rated current of the i-th phase.r i This indicates the sum of the high-voltage winding resistance value and the low-voltage winding resistance when referred to the low-voltage side. It is based on the ability to accurately capture the hot spot temperature and top oil temperature of the A, B, and C phase windings of the transformer, as well as the core, under given external conditions and considering three-phase unbalanced operating conditions.

[0046] S5: Based on the baseline predictions of each phase, the top oil temperature, and the hot spot temperature and their corresponding true values, a total optimization objective is constructed. The total optimization objective is used to optimize the network parameters of the distribution transformer phase load prediction model. The input tensors of the load tensors of each phase are processed by the optimized distribution transformer phase load prediction model and hierarchical consistency prediction to output the final load prediction of each phase. Based on the final load prediction of each phase and the hot spot temperature, the overload situation is determined, and corresponding operation and maintenance are carried out according to the overload situation.

[0047] In this implementation, the expression for the overall optimization objective is: ; ; ; ; in, L total Let Θ represent the total loss function, Θ represent the network parameters of the distribution transformer phase load prediction model, and Φ represent the physical parameters. l pred λ represents the load forecast loss weighting coefficient. mint λ represents the weighting coefficient for hierarchical consistency loss. phys λ represents the weighting coefficient for the physical consistency loss. reg Represents the regularization weight coefficient. L pred Indicates load forecasting error. L mint This indicates a loss of hierarchical consistency. L phys Let Λ represent the physical consistency loss, and let Λ represent the set of loss weight coefficients, Λ={ l pred , l mint , l phys , l reg}, Let N represent the L2 norm and N represent the sample size. This represents the total value of various baseline predictions at time j. This represents the actual total load at time j. Let T denote a vector consisting entirely of 1s, and let T denote the transpose. Let j represent the value of any baseline prediction at time j. This represents the value of the top-level baseline prediction at time j. This represents the predicted value of the transformer hotspot temperature at time j. This represents a temperature rise calculation model based on the thermal circuit differential equation. This represents any coordinated load forecast at time j (which is a physically more reasonable load forecast adjusted by MinT). The constraints include: Hierarchical consistency constraints: ; Physical consistency constraints: ; in, i hs,i ( t () represents the hot spot temperature of the i-th phase winding at time t, where t represents time t. q cu,i ( t () represents the copper loss generated by the i-th phase winding at time t under a given load. q fe ( t () represents the iron loss at time t. i to ( t () represents the transformer top oil temperature at time t. i amb ( t () represents the ambient temperature at time t; Parameter feasible region constraint: Φ min <Φ<Φ max Φ min Φ represents the minimum value of the corresponding physical parameter. max This indicates the maximum value of the corresponding physical parameter.

[0048] Furthermore, based on the overall optimization objective and constraints, the AdamW algorithm is used to optimize the network parameters of the distribution transformer phase load prediction model, and the particle swarm optimization algorithm is used to optimize the physical parameters and the set of loss weight coefficients. Specifically: A two-layer framework is adopted, consisting of an outer PSO (global optimization Φ,Λ) layer and an inner AdamW (gradient update Θ).

[0049] Step 1: Setting the feasible region and initializing parameters; ① Define the feasible region: Φ∈[Φmin,Φmax], Λ ≥0; ② Initialization: Θ0, Φ0, Λ0, learning rate η and weight decay λw; outer layer PSO hyperparameters: number of particles K, inertia δ, learning factors c1, c2, iteration limit Gmax; inner layer termination threshold ε, iteration limit Emax; ③ Selection error covariance estimation W; Step 2: Optimize the global search for the outer PSO layer; Particle position: Z = [Φ,Λ], velocity v; population size N, iteration G.

[0050] Constraint mapping: Φ = Softplus(·); Λ ≥ 0.

[0051] Step 3: Inner layer (AdamW, conditional training); Given a fixed outer layer [Φ,Λ], train Θ using AdamW and perform consistent forward-backward operations in each batch.

[0052] ① Network prediction: ← SwinMDGRU Θ(X) ; ②MinT-Conformity: ; ③ Load → Heat Source Mapping: ; ④ Thermal integral: ,get Trajectory; ⑤ Calculate the total target loss: ; ⑥ Reverse transmission and update Θ (AdamW); ⑦ Update: Residuals and variances are re-estimated every M epochs, and the MinT mapping is refreshed. The total target is used as the particle fitness, and the outer PSO updates the position and velocity based on the fitness. Step 4: Repeat steps 2 and 3 until the outer / inner loop meets the convergence condition; Step 5: Output the optimal combination parameters (Θ,Φ,Λ).

[0053] Furthermore, the determination of overload conditions based on the final load forecast of each phase and the hot spot temperature includes: For any phase, obtain the average and maximum values ​​of the final load forecast over a certain period of time, and calculate the corresponding load factor based on the average and maximum values ​​of the final load forecast. load factor K i Hotspot temperature i hs,i The overload condition is determined by comparing it with the corresponding threshold: when K i ≤ K' and i hs,i ≤ I will At that time, the overload condition is judged as normal; K' The first load factor threshold (e.g., 80%). I will The first hot spot temperature threshold (e.g., 105℃); when K' < K i ≤ K'' or I will < i hs,i ≤ I'' When the overload condition is determined to be a heavy load, K'' This is the second load factor threshold (e.g., 100%). I'' The second hot spot temperature threshold (e.g., 115℃); when K'' < K i ≤ K''' or I'' < i hs,i ≤ I''' When an overload condition is detected, it is determined to be an overload. K''' The third load factor threshold (e.g., 120%). I''' The third hot spot temperature threshold (e.g., 125℃); when K i > K''' or i hs,i > I''' When the overload condition is determined to be a severe overload, the situation is considered to be an overload.

[0054] This embodiment also provides early warning strategies and risk level assessments: Distribution transformers are highly susceptible to short-term or long-term heavy overloads due to factors such as load rate changes, ambient temperature fluctuations, and heat dissipation conditions during long-term operation. Relying solely on fixed threshold criteria may lead to false alarms or missed alarms, reducing the effectiveness of the early warning system. Therefore, this study proposes an early warning strategy that integrates physical information and data-driven prediction, and constructs a hierarchical risk assessment system to achieve accurate identification and graded response to distribution transformer heavy overload risks. Referring to IEC60076 and relevant State Grid standards, the early warning strategy and risk level assessment classification are shown in Table 1.

[0055] Table 1 Early Warning Strategies and Risk Level Assessment Classification

[0056] The simulation analysis in this embodiment was completed on the MATLAB platform to verify the proposed overload prediction method for distribution transformers based on SwinMDGRU+MinT+physical information.

[0057] Table 2. Parameters of the research model and physical property parameters

[0058] To comprehensively evaluate the performance of the distribution transformer phase-level prediction model that integrates data-driven and physical constraints, MAPE, root mean square error (RMSE), and early warning accuracy are used as evaluation indicators.

[0059] ; ; In the formula, TP, FP, and FN represent the number of correct warnings, the number of false alarms, and the number of missed warnings, respectively.

[0060] To verify the performance of the proposed prediction method, this paper sets up six methods for comparison: Method 1 (hereinafter referred to as M1): Only considering load timing, LSTM.

[0061] Method 2 (hereinafter referred to as M2): Taking into account load timing and interphase load correlation, CNN-LSTM.

[0062] Method 3 (hereinafter referred to as M3): Taking into account load timing, multi-periodicity and inter-phase load correlation, SwinLSTM.

[0063] Method 4 (hereinafter referred to as M4): SwingLSTM+DWH.

[0064] Method 5 (hereinafter referred to as M5): SwinLSTM+DWH+MinT.

[0065] Method 6 (hereinafter referred to as M6): SwingLSTM+DWH+MinT+Physical Information Constraints (the method in this paper).

[0066] Table 3 Comparison of Prediction Accuracy of Different Methods

[0067] As shown in Table 3, the model performance shows a continuous improvement trend with the gradual enhancement of feature modeling and structural design: from M1, which only considers temporal sequence, to M5, which introduces spatial attention and heavy overload perception mechanisms, the MAE and RMSE of each phase and the overall load all decrease significantly. Specifically, the MAE of the three phases A / B / C decreased from 12.99 / 12.67 / 13.15 to 7.45 / 7.18 / 7.64, respectively, and the overall MAE decreased from 38.15 to 22.27, with an average decrease of more than 40%; the overall RMSE decreased from 44.38 to 28.49, a decrease of about 36%. This effectively illustrates that the accuracy of phase load prediction is affected by spatiotemporal characteristics, and also shows that the SwinMDGRU+MinT model accurately captures the periodic changes of load and the differences in load between phases through spatiotemporal feature fusion, thereby significantly improving the prediction accuracy.

[0068] Table 4 Comparative Analysis of Overload Prediction Accuracy of Different Methods

[0069] Table 5. Overload / overload time intervals for different methods

[0070] As shown in Tables 4 and 5, traditional time-series models perform poorly in load anomaly early warning, with an overall accuracy of only 38%–61%, especially exhibiting significant response lag under high dynamic load and heavy overload scenarios. By introducing more complex spatiotemporal feature modeling, the early warning performance is significantly improved. The proposed SwinMDGRU+MinT model, which integrates spatial interactive attention, periodic memory mechanism, and hierarchical consistency calibration, improves the overall early warning accuracy to 95%, almost covering all actual heavy overload periods. At the phase level, the heavy load / overload recognition rate of phase A is significantly improved from 38% to 95%, effectively solving the perception blind spot problem of traditional models under high-risk conditions. This verifies the key role of multi-scale spatiotemporal feature fusion and hierarchical coordination mechanism in low-voltage distribution transformer heavy overload early warning.

[0071] To address the heterogeneity and non-stationarity of three-phase loads in low-voltage distribution transformers, a SwinMDGRU+MinT prediction and early warning model was constructed. Simulation analysis yielded the following conclusions: 1) By combining the local spatial perception capability of the Swin-Transformer with the cross-cycle memory mechanism of MDGRU, a more comprehensive characterization of non-stationary, multi-scale load characteristics is achieved. Experimental results show that the model's comprehensive error MAE_Σ from M1 to M6 decreased from 38.15 to 22.27, and RMSE_Σ decreased from 44.38 to 28.49, representing reductions of 41.6% and 35.8%, respectively. This verifies the significant advantages of this spatiotemporal fusion strategy in predicting complex phase loads.

[0072] 2) By introducing the MinT hierarchical consistency strategy, the model can ensure the consistency of physical constraints between the three phases and the total load while maintaining prediction accuracy, thereby effectively improving risk identification capabilities. Experiments show that the overall early warning accuracy has increased from 42% to 95%, and M6 can completely identify all three-phase heavy load and overload times, with the heavy / overload time intervals consistent with the true values, significantly reducing the risk of missed and false alarms.

[0073] The overload prediction method for distribution transformers based on phase-level prediction and physical constraints provided in this embodiment has the following beneficial effects: 1. Using a "differentiable physical model" as a bridge, a backpropagating causal constraint closed loop is constructed from load prediction to temperature prediction: This method designs the thermal path model based on differential equations as a "differentiable physical operator" and seamlessly embeds it into the training graph of the entire model. In this way, the gradient generated by the inconsistency of the physical model (the deviation between predicted temperature and measured temperature) can be backpropagated to the front-end load prediction neural network.

[0074] 2. The "hierarchical consistency constraint determined by the power grid topology (MinT)" and the "physical mechanism constraint" are used together as regularization terms in the joint loss function to achieve dual correction: the MinT consistency requirement (the sum of user loads equals the phase load, and the sum of phase loads equals the total load) is transformed into a hierarchical consistency loss L. mint This directly impacts the training process of the distribution transformer phase load forecasting model, ensuring it "knows" the topological aggregation relationship of the power grid from the outset, and correlates with the load forecasting error L. pred Physical consistency loss L phys The weighted combination forms the overall optimization objective, which is used to optimize the network parameters of the distribution transformer phase load prediction model.

[0075] 3. A nested collaborative optimization strategy for "high-dimensional neural network parameters" and "low-dimensional physical model parameters" was designed: a two-layer (Bilevel) optimization framework was adopted, with an outer layer of PSO optimizing physical parameters and an inner layer of AdamW optimizing network parameters. The inner layer: fixed physical parameters and efficiently trained the large neural network using gradient descent. The outer layer: used global optimization algorithms such as particle swarm optimization to search for the set of physical parameters that minimized the final loss of the entire system (neural network + physical model).

[0076] In summary, a deep spatiotemporal prediction network (SwinMDGRU), a grid topology-based hierarchical statistical coordination (MinT), and a differentiable electromagnetic-thermal physical model are deeply coupled through a backpropagating joint loss function. An end-to-end prediction framework is then implemented using a two-layer optimization algorithm to achieve collaborative learning of network and physical parameters. This framework ensures that the final overload prediction results simultaneously guarantee the accuracy of time-series predictions, the structural constraints of grid operation, and the credibility of thermodynamic mechanisms. Therefore, it provides a solution with both data intelligence and physical interpretability for accurate early warning of three-phase unbalanced transformers.

[0077] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0078] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for predicting overload of distribution transformers based on phase-level prediction and physical constraints, characterized in that, include: S1: Obtain the user load, phase load, and total load in the distribution topology, and preprocess the user load, phase load, and total load to obtain the user load tensor, phase load tensor, and total load tensor; S2: The input tensors of user load tensor, phase load tensor and total load tensor are respectively processed by the distribution transformer phase load prediction model based on SwinMDGRU, and the bottom baseline prediction, phase baseline prediction and top baseline prediction are output respectively. S3: Introduce the summary matrix determined by the distribution topology and the coordination matrix constructed based on the summary matrix. Based on the minimum trajectory error, perform hierarchical consistency prediction on the bottom baseline prediction, phase baseline prediction and top baseline prediction respectively to obtain the corresponding coordinated load prediction. S4: Based on the electromagnetic-thermal mechanism, all coordinated load predictions are projected onto the physical domain to obtain the copper loss of each phase. The iron loss is calculated based on the voltage. The iron loss and the copper loss of each phase are input into the drive differentiable thermal circuit model to output the transformer top oil temperature and hot spot temperature. S5: Based on the baseline predictions of each phase, the top oil temperature, and the hot spot temperature and their corresponding true values, a total optimization objective is constructed. The total optimization objective is used to optimize the network parameters of the distribution transformer phase load prediction model. The input tensors of the load tensors of each phase are processed by the optimized distribution transformer phase load prediction model and hierarchical consistency prediction to output the final load prediction of each phase. Based on the final load prediction of each phase and the hot spot temperature, the overload situation is determined, and corresponding operation and maintenance are carried out according to the overload situation.

2. The overload prediction method for distribution transformers according to claim 1, characterized in that, Obtain user loads, phase loads, and total loads in the distribution topology based on AMI or SCADA.

3. The overload prediction method for distribution transformers according to claim 1, characterized in that, Preprocessing includes: Perform horizontal anomaly detection on user load, phase load, or total load. If so, it is determined that the user load, phase load, or total load is abnormal, and then... Make corrections; otherwise, determine that the user load, phase load, or total load is normal; among which, This represents the user load, phase load, or total load at time t on day d. This represents the user load, phase load, or total load at time t-1 on day d. This represents the user load, phase load, or total load at time t+1 on day d. This represents the detection threshold at time t. This represents the user load, phase load, or total load at time t on day d after horizontal correction. Perform vertical anomaly detection on user load, phase load, or total load. Determine if the user load, phase load, or total load is abnormal, through... Make corrections; otherwise, determine that the user load, phase load, or total load is normal; among which, , Let represent the average load at time t among all similar days on day d, and n represent the number of similar days on day d. This represents the user load, phase load, or total load at time t on day k after horizontal correction. This represents the user load, phase load, or total load at time t on day d+1. This represents the user load, phase load, or total load at time t on day d-1. This represents the user load, phase load, or total load at time t on day d after vertical correction. Missing loads are detected for user load, phase load, or total load. When a missing load is found, it is filled based on the average load of adjacent times or similar days. The filling formula is as follows: ； in, This represents the user load, phase load, or total load at time t on day d after the fill is completed; Indicates the weighting coefficient; Normalize the user load, phase load, or total load after determining normal, horizontal correction, vertical correction, or filling to obtain the user load, phase load tensor, or total load tensor.

4. The overload prediction method for distribution transformers according to claim 1, characterized in that, The phase load prediction model for distribution transformers based on SwinMDGRU includes an input layer, a flattening layer, a patch embedding layer, a first SwinMDGRU cell layer, a patch merging layer, a second SwinMDGRU cell layer, a patch expansion layer, a reconstruction layer, and an output layer. The input layer is used to obtain the user load or phase load tensor or total load tensor at each time step; The flattening layer is used to divide the user load or phase load tensor or total load tensor at each time step into non-overlapping patches of size P×P, and flatten each patch into a feature. The patch embedding layer is used to obtain the corresponding flag features by linearly mapping and adding position encoding to the features of each time step. The flag features of each historical time step are combined in the order of time steps to obtain the flag sequence corresponding to user load, phase load or total load. The first SwinMDGRU cell layer is used to obtain the corresponding historical state by passing any flag sequence through the ReLU activation function, and to calculate the first reset gate, the first update gate, and the first candidate state of the current time step in sequence based on the flag sequence and the flag features of the corresponding current time step; and to obtain the first hidden state of the current time step by weighted summing of the historical state and the first candidate state of the current time step based on the first update gate. The patch merging layer is used to merge the first hidden states of the current time step obtained from multiple first SwinMDGRU cell layers into a corresponding hidden state sequence; The second SwinMDGRU cell layer is used to obtain the corresponding predicted state by passing the corresponding hidden state sequence through the ReLU activation function, and to calculate the second reset gate, the second update gate, and the second candidate state of the current time step in sequence based on the hidden state sequence and the corresponding current time step's flag features; and to obtain the second hidden state of the current time step by weighted summing of the predicted state and the second candidate state of the current time step based on the second update gate. The patch extension layer is used to upsample the second hidden state at the current time step to obtain a feature map; The reconstruction layer is used to perform linear activation on the feature map to obtain the corresponding baseline prediction; The output layer is used to output the baseline prediction.

5. The overload prediction method for distribution transformers according to claim 4, characterized in that, Calculate the double-weighted mixed loss between the baseline prediction and the corresponding actual value output by the distribution transformer phase load prediction model, and optimize the distribution transformer phase load prediction model by minimizing the double-weighted mixed loss.

6. The overload prediction method for distribution transformers according to claim 1, characterized in that, S3 includes: Calculate the linear mapping relationship between all loads and user loads to obtain a summary matrix. The linear mapping relationship is expressed as follows: ;in, Let S represent the total load at time t, and let S be the summary matrix. This represents the user load at time t; Calculate the error between the bottom-level baseline prediction, phase-by-phase baseline prediction, or top-level baseline prediction and the corresponding actual value to obtain the corresponding baseline error; for any baseline prediction, calculate the variance of the baseline error at each time step, using the following formula: ;in, Var[·] represents the variance of the baseline error at the h-th time step, and Var[·] represents the variance function. This represents the actual value of the baseline prediction at the h-th time step. This represents the baseline prediction at the h-th time step, and L represents the length of the corresponding baseline prediction. The coordination matrix is ​​constructed based on the summary matrix and the covariance matrix, and is represented as follows: Where G represents the coordination matrix and T represents the transpose; Based on the minimum trajectory error, hierarchical consistency prediction is performed on the bottom-level baseline prediction, phase-specific baseline prediction, or top-level baseline prediction using the summary matrix and coordination matrix to obtain the corresponding coordinated load prediction. The calculation formula is as follows: , This represents the coordinated load forecast corresponding to any baseline forecast at the h-th time step.

7. The overload prediction method for distribution transformers according to claim 1, characterized in that, Based on the electromagnetic-thermal mechanism, all coordinated load predictions are projected onto the physical domain to obtain the copper loss for each phase, and the iron loss is calculated based on the voltage, including: Based on the corresponding coordinated load predictions, the corresponding phase load currents are calculated using the following formula: ； in, I i ( t () represents the phase load current of the i-th phase at time t. This represents the coordinated load forecast for the i-th phase at time t, where Un represents the rated line voltage on the low-voltage side of the transformer. Indicates the power factor; The copper loss is calculated based on the corresponding phase load current, using the following formula: ； in, q cu,i ( t () represents the copper loss generated by the i-th phase winding at time t under a given load. r i This represents the total resistance of the i-th phase high-voltage and low-voltage windings referred to the low-voltage side; Iron loss is calculated based on voltage; the formula is as follows: ； in, q fe ( t () represents the iron loss at time t. P 0 represents the no-load loss at rated voltage, and U(t) represents the transformer operating voltage at time t. N Indicates the rated voltage. β This indicates the relevant index of the iron core material.

8. The overload prediction method for distribution transformers according to claim 1, characterized in that, The driving differentiable thermal circuit model is represented as: ； ； in, C i This represents the heat capacity of the i-th phase winding. θ hs,i The temperature of the hot spot in the i-th phase winding is represented by , and t represents the time t. q cu,i This represents the copper loss generated by the i-th phase winding under a given load. R i This represents the thermal resistance between the i-th phase winding and the transformer oil. θ to Indicates the top oil temperature of the transformer. C oil Indicates the heat capacity of transformer oil. R oil This indicates the thermal resistance between the transformer oil and the environment. θ amb Indicates ambient temperature. K i Represents the load factor of phase i, ( I N ) i This represents the phase rated current of the i-th phase. r i This indicates that the resistance value of the high-voltage winding is referred to the low-voltage side and is the sum of the resistance of the low-voltage winding.

9. The overload prediction method for distribution transformers according to claim 8, characterized in that, The expression for the overall optimization objective is: ； ； ； ； in, L total Let Θ represent the total loss function, Θ represent the network parameters of the distribution transformer phase load prediction model, and Φ represent the physical parameters. λ pred Load forecasting loss weighting factor, λ mint Hierarchical consistency loss weighting coefficient, λ phys Physical consistency loss weighting coefficient, λ reg Regularization weight coefficients, L pred Load forecasting error L mint Hierarchical consistency loss L phys Physical consistency loss, where Λ represents the set of loss weight coefficients, Λ={ λ pred , λ mint , λ phys , λ reg }, Let N represent the L2 norm and N represent the sample size. This represents the total value of various baseline predictions at time j. This represents the actual total load at time j. Let T denote a vector consisting entirely of 1s, and let T denote the transpose. Let j represent the value of any baseline prediction at time j. This represents the value of the top-level baseline prediction at time j. This represents the predicted value of the transformer hotspot temperature at time j. This represents a temperature rise calculation model based on the thermal circuit differential equation. This represents any coordinated load forecast at time j; The constraints include: Hierarchical consistency constraints: ; Physical consistency constraints: ； in, θ hs,i ( t () represents the hot spot temperature of the i-th phase winding at time t, where t represents time t. q cu,i ( t () represents the copper loss generated by the i-th phase winding at time t under a given load. q fe ( t () represents the iron loss at time t. θ to ( t () represents the transformer top oil temperature at time t. θ amb ( t () represents the ambient temperature at time t; Parameter feasible region constraint: Φ min <Φ<Φ max Φ min Φ represents the minimum value of the corresponding physical parameter. max This represents the maximum value of the corresponding physical parameter; Based on the overall optimization objective and constraints, the AdamW algorithm is used to optimize the network parameters of the distribution transformer phase load prediction model, and the particle swarm optimization algorithm is used to optimize the physical parameters and the set of loss weight coefficients.

10. The overload prediction method for distribution transformers according to claim 9, characterized in that, In S5, the determination of overload conditions based on the final load prediction of each phase and the hot spot temperature includes: For any phase, obtain the average and maximum values ​​of the final load forecast over a certain period of time, and calculate the corresponding load factor based on the average and maximum values ​​of the final load forecast. load factor K i Hotspot temperature θ hs,i The overload condition is determined by comparing it with the corresponding threshold: when K i ≤ K' and θ hs,i ≤ θ' At that time, the overload condition is judged as normal; K' The first load factor threshold, θ' The first hotspot temperature threshold; when K' < K i ≤ K'' or θ' < θ hs,i ≤ θ'' When the overload condition is determined to be a heavy load, K'' The second load factor threshold, θ'' The second hotspot temperature threshold; when K'' < K i ≤ K''' or θ'' < θ hs,i ≤ θ''' When an overload condition is detected, it is determined to be an overload. K''' The third load factor threshold, θ''' The third hotspot temperature threshold; when K i > K''' or θ hs,i > θ''' When the overload condition is determined to be a severe overload, the situation is considered to be under severe overload.

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