An electric power load data generating interpolation method and system

Abstract

The application relates to the field of power load data processing and discloses a power load data generative interpolation method and system. In order to solve the defects that the existing interpolation method cannot solve the physical compliance, scale imbalance, long-term consistency and weak strong generalization ability, the application integrates physical constraints into the training process of a generative model, retains the data distribution characteristics of the missing position, guarantees that the interpolated load data meets the physical rules such as power balance and upper and lower limits, adopts a multi-scale feature fusion module to extract load features under different resolutions, realizes the collaborative utilization of cross-scale information, introduces a time consistency regularization term to constrain the long-term trend of a sequence, guarantees that the interpolated data is consistent with the upstream and downstream historical load trends, and simultaneously adopts a pre-training combined with fine-tuning training mode to improve the generalization ability of the model under different load scenes. The application is mainly used for interpolating power load data of different regions and different types of users.

Description

Technical Field

[0001] This invention relates to the field of power load data processing, and more particularly to a power load data generation interpolation method. Background Technology

[0002] In power systems, data collected by systems such as SCADA (including active power P and reactive power Q) is the foundation for core operations such as grid dispatching, state estimation, and load forecasting. However, due to communication failures, sensor malfunctions, and other reasons, this data is often missing, especially continuously, which seriously affects the accuracy of subsequent analysis. Therefore, it is crucial to develop efficient missing data interpolation techniques.

[0003] In recent years, deep learning methods have become mainstream, mainly including models based on recurrent neural networks (RNN / LSTM) and generative adversarial networks (GANs). Among them, generative adversarial interpolation networks (GAIN) and their variants have attracted much attention due to their powerful data distribution learning and generation capabilities. However, existing solutions still have significant limitations and cannot fully meet the stringent requirements of power load data interpolation. (1) Currently, there is a general lack of explicit modeling of the physical laws of power systems. The generated P / Q data may violate basic electrical constraints (such as power factor anomalies), resulting in results that are not usable in engineering.

[0004] Despite the introduction of attention mechanisms, the global normalization strategy severely distorts local time-series patterns and affects interpolation accuracy when faced with extremely high dynamic ranges (such as load differences of several times between weekdays and holidays). Existing statistical or machine learning methods (such as mean imputation, KNN, and traditional RNN) struggle to simultaneously capture the complex nonlinear coupling relationship and its fine temporal dynamic characteristics between active power (P) and reactive power (Q), resulting in low interpolation accuracy.

[0005] (2) Existing generative models (such as GAIN and TimeGAN) can generate more realistic data, but when dealing with data with strong physical constraints such as power load, they are prone to generating “illusionary” data that does not conform to physical laws (such as abnormal power factor). Moreover, when faced with long-term continuous missing data, the long-term consistency of the generated sequence is poor and the pattern collapse is likely to occur.

[0006] (3) Most methods (except PC-GAIN) still rely on pure adversarial training or simple reconstruction loss, lacking a powerful "teacher" model containing real-world dynamic knowledge to guide the generation process. This makes it difficult to guarantee the long-term consistency and authenticity of the generated sequence when dealing with long-term continuous missing data, and it is prone to mode collapse.

[0007] (4) The dynamic range of power load data is extremely large (such as weekdays and holidays, daytime and nighttime). Traditional global normalization will seriously distort the local time series pattern, resulting in a sharp drop in interpolation accuracy in highly dynamic scenarios. Existing methods (such as AT-SGAIN and WGAIN wind power) generally rely on explicit time features (such as hours and days of the week), which limits their generalization ability and makes it difficult to seamlessly migrate to significant changes in load patterns under different regions, seasons, and different types of days (weekdays / weekends) or newly commissioned distribution substations.

[0008] Therefore, a high-precision, physically compliant, and generalizable power load data generation interpolation method is needed. Summary of the Invention

[0009] The purpose of this invention is to address the shortcomings of existing interpolation methods in that they cannot effectively solve problems related to physical compliance, scale imbalance, long-term consistency, and weak generalization ability. This invention provides a high-precision, physically compliant power load data generation interpolation method with good generalization ability.

[0010] The present invention provides a power load data generation interpolation method, comprising: S1. Missing-aware daily amplitude propagation: For each distribution transformer load daily sequence, based on a hierarchical backoff mechanism and a weighting strategy driven by the missing rate, the upper and lower bounds of the daily amplitude are estimated, and a daily condition vector independent of external time features is constructed. S2. Adaptive sample construction: The original active power P and reactive power Q sequences are independently normalized using the daily conditional vector to obtain standardized samples and missing masks in the contour space. S3. Select target samples from the standardized samples, and use the target samples to pre-train the autoregressive dynamic teacher model so that the autoregressive dynamic teacher model learns the inherent dynamic law of the load profile; after the pre-training is completed, freeze all parameters of the autoregressive dynamic teacher model to obtain the frozen autoregressive dynamic teacher model. S4. Combine GAIN-FiLM with generative interpolation to construct a generator G and a discriminator D. The generator G receives noise, the missing mask and the daily conditional vector, and after being modulated by the Transformer encoder and the FiLM module, it shares the output head of the frozen autoregressive dynamic teacher model to obtain the conditional distribution parameters. It then generates interpolated values ​​through reparameterized sampling and fuses the observation values ​​to output a contour sequence. The discriminator D receives the contour sequence, the cue vector, and the dynamic features extracted by the frozen autoregressive dynamic teacher model, and outputs the authenticity probability. S5. Inverse normalization and physical verification: The contour sequence output by the generator G is inverse normalized to the original dimensions, and the power factor physical consistency is verified to output the final load data.

[0011] Furthermore: In S4, during training, the total loss function of the generator G includes reconstruction loss, adversarial loss, and behavioral alignment loss for mimicking the output distribution of the frozen autoregressive dynamic teacher model.

[0012] Further: In S1, the propagation of the missing daily amplitude specifically includes: When the daily missing rate is lower than the first threshold, the preset high and low quantiles of the daily observations are used directly as the upper and lower bounds of the daily amplitude. When the daily missing rate is higher than the first threshold, the missing rate-driven weights are used to weightedly fuse the original amplitude estimate of the day, the short-term memory of the previous day, and the long-term memory obtained from the reliable daily sliding window to update the upper and lower bounds of the daily amplitude. When all data for the day is missing, the fusion result of the short-term memory and long-term memory is directly used as the upper and lower bounds of the amplitude for that day. A seasonal mutation protection mechanism is introduced, which imposes an upper and lower limit constraint on the updated amplitude upper and lower bounds based on the reliable amplitude extreme values ​​within a preset time period in the past.

[0013] Furthermore, in S2, the independent normalization is to perform a linear transformation on each variable P and Q based on their corresponding daily amplitude upper and lower bounds, mapping the original data to dimensionless contour data within a preset interval, thereby achieving decoupling of amplitude and contour.

[0014] Further: In S3, the training loss function of the autoregressive dynamic teacher model is the negative log-likelihood loss, which is used to maximize the likelihood probability of the observed data by minimizing the negative log-likelihood value of the observed data under the conditional Gaussian distribution predicted by the model.

[0015] Further: In S4, the modulation process of the FiLM module is as follows: The day condition vector is mapped to affine transformation parameters through a multilayer perceptron, and the output hidden states of each layer of the Transformer encoder in the generator G are subjected to affine transformation, thereby realizing the global conditional control of amplitude information on the contour generation process.

[0016] Furthermore: In S4, during the generator training process, the real-world temporal dynamic data implied by the autoregressive dynamic teacher model is imitated based on the behavior alignment loss; the KL divergence is used to measure the difference between the following two: the first distribution parameter output by the frozen autoregressive dynamic teacher model after inputting the real observation sequence into the generator G, and the second distribution parameter output by the generator G after the output head of the frozen autoregressive dynamic teacher model; the generator G is forced to learn and follow the real dynamic laws implied by the frozen autoregressive dynamic teacher model through the loss.

[0017] Further: In S5, the power factor physical consistency verification includes: calculating the power factor at each time point; when the power factor is lower than the preset physical compliance lower limit, while keeping the reactive power sign unchanged, the reactive power is corrected by boundary constraints based on the absolute value of active power so that it meets the preset power factor boundary conditions.

[0018] Further: In S1, the hierarchical rollback mechanism is used to initialize the amplitude of newly commissioned or early data-sparse distribution transformer loads. The specific steps of the hierarchical rollback mechanism are: based on the median amplitude of reliable days of the same feeder group, based on the median amplitude of similar distribution transformer loads after regional group clustering, and based on the global fallback value of historical data quantiles of the entire region.

[0019] An interpolation system for implementing the aforementioned power load data generative interpolation method includes a daily amplitude propagation module, a sample construction module, an autoregressive dynamic teacher model generation module, a generative interpolation module, and a result verification and output module. The daily amplitude propagation module is used to perform missing-aware daily amplitude propagation, estimate the upper and lower bounds of the daily amplitude, and construct the daily condition vector; The sample construction module is used to complete adaptive sample construction, and to independently normalize the original active power and reactive power sequences to obtain standardized samples and missing masks. The autoregressive dynamic teacher model generation module is used to complete the pre-training and parameter freezing of the autoregressive dynamic teacher model, and obtain the frozen autoregressive dynamic teacher model. The generative interpolation module is used to construct a generator and discriminator including GAIN-FiLM, and generate a complete contour sequence through adversarial training; the result verification output module is used to perform inverse normalization operation and power factor physical consistency verification, and output the final interpolated power load data.

[0020] The beneficial effects of this invention are: (1) Solving the scale imbalance problem: This invention innovatively proposes a daily amplitude propagation algorithm with missing perception and an amplitude-contour decoupling architecture. By independently estimating robust upper and lower bounds of amplitude for each day and normalizing them, the global amplitude information is successfully separated from the local temporal contour. This allows the model to focus on learning more generalizable contour patterns, and then accurately inject daily amplitude information through FiLM modulation, thus maintaining extremely high interpolation accuracy even in high dynamic switching scenarios such as weekdays / holidays. Adaptive normalization is achieved through daily amplitude propagation estimation, constructing a suitable numerical scale for each day to be interpolated, solving the scale imbalance problem caused by the high dynamic range of power load, improving accuracy in high dynamic scenarios, providing stable input for subsequent modeling, and eliminating the negative impact of high dynamic range.

[0021] (2) Achieving precise decoupling and control: The FiLM mechanism is used to treat the upper and lower bounds of the amplitude as intermediate features of the conditional signal modulation generator, completely realizing amplitude-contour decoupling. This allows the model to independently learn the universal load contour dynamics and be controlled within the actual amplitude range of the day. This invention organically integrates four core ideas: data decoupling (amplitude-contour), knowledge distillation (ADT teacher guidance), conditional generation (FiLM modulation), and physical post-processing (power factor verification), constructing a logically rigorous and synergistically efficient technical closed loop. This systematic design approach makes its overall performance far exceed that of existing solutions that only improve a single dimension (such as attention mechanism or loss function).

[0022] (3) Improved interpolation accuracy: This invention introduces a power factor verification and correction mechanism at the end of the process. By combining an autoregressive dynamic teacher (ADT) with a generative adversarial network, the generator not only needs to deceive the discriminator, but also must imitate the real-world temporal dynamics implied by the ADT through behavioral alignment loss (KL divergence). This ensures that the generated interpolation results are not only statistically realistic, but also accurately model the complex temporal dynamics and intervariate correlations of P / Q data through the teacher guidance mechanism, ensuring that the generated sequence is not only realistic, but also has long-term physical dynamic characteristics consistent with real data. It can be directly used in the actual business system of the power grid, avoiding decision-making risks caused by data distortion.

[0023] (4) Enhanced model generalization ability: An enhanced discriminator that integrates ADT dynamic features receives dynamic features extracted by frozen ADT as input, evaluates the authenticity of generated data from a higher semantic level, abandons the dependence on explicit time coding, and enables the model to adaptively learn load patterns under different scenarios. The entire framework of this invention does not rely on any explicit time coding, takes ADT and GAIN-FiLM generator as the core, and learns the rules only from the temporal dynamics and daily amplitude conditions of the data itself. Combined with the daily amplitude estimation strategy of hierarchical backoff mechanism, this invention can seamlessly adapt to the data interpolation needs of different regions, different seasons and newly commissioned distribution substations, showing excellent generalization performance.

[0024] (5) Improve generation stability: By using behavior alignment loss, the inherent pattern collapse problem of generative adversarial networks can be effectively alleviated, and more diverse and consistent long sequence data can be generated. Attached Figure Description

[0025] Figure 1 This is the overall system architecture diagram; Figure 2 This is a schematic diagram of the amplitude propagation algorithm results; Figure 3 This is a comparison chart of the amplitude propagation results and the original data with missing daily extreme values; Figure 4 This is a diagram illustrating the daily missing rate changes corresponding to amplitude propagation. Figure 5 This is a schematic diagram of the model architecture; Figure 6 This is a comparison chart of the interpolation results of this invention and the original real data during typical missing periods of total active power; Figure 7 This is a comparison chart of the interpolation results of this invention and the original real data during typical missing periods, showing the total reactive power. Figure 8 This is a comparison chart of the total active power of the interpolation results of the present invention and the GAIN and PC-GAIN methods within the same missing time period; Figure 9 This is a comparison chart of the total reactive power of the interpolation results of the present invention and the GAIN and PC-GAIN methods during the same missing time period; Figure 10 This is a comparison chart of the power factor compliance rates of the interpolation results of the present invention and the GAIN and PC-GAIN methods within the same missing time period. Detailed Implementation

[0026] The following are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. The embodiments described below are only for explaining the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention should be determined by the scope of the claims. The embodiments of the present invention are described in detail below. In order to facilitate the description of the present invention and simplify the description, the technical terms used in the specification of the present invention should be interpreted broadly, including but not limited to conventional alternatives not mentioned in this application, and including both direct and indirect implementation methods.

[0027] Example 1 Combination Figures 1-6 This embodiment describes a power load data generative interpolation method based on teacher guidance and amplitude-profile decoupling. It achieves amplitude-profile decoupling through a "daytime amplitude propagation algorithm with missing perception" and FiLM conditional modulation, and introduces an autoregressive dynamic teacher (ADT) for teacher guidance. This collaboratively addresses the scale imbalance problem and insufficient physical dynamic modeling in the high dynamic range of power load data interpolation. The specific process is as follows: S1, Daily amplitude propagation algorithm with missing perception; For each distribution transformer load day sequence, based on a hierarchical backoff mechanism and a weighting strategy driven by the missing rate, the upper and lower bounds of the daily amplitude are estimated, and a daily conditional vector independent of external time features is constructed. This step aims to estimate a robust, physically reasonable daily amplitude upper and lower bound proxy for each distribution transformer (hereinafter referred to as "transformer") for each day d: Upper bound amplitude Lower bound amplitude The daily condition vector formed by these two agents: , in, The conditional vector for this day, It is the upper limit amplitude of the active power value of the distribution transformer on day d. It is the lower limit amplitude of the active power value of the distribution transformer on day d. It is the upper limit amplitude of the reactive power value of the distribution transformer on day d. It is the lower limit amplitude of the reactive power value of the distribution transformer on day d. It is the matrix transpose; This daily amplitude upper and lower bound proxy will be used in subsequent steps to adaptively normalize the original load data, and is a key preliminary step to achieve "amplitude-profile decoupling". This missing-aware daily amplitude propagation algorithm is calculated entirely based on the sequence's own observations, without relying on any external time features (such as hours or days of the week). Through a hierarchical backoff mechanism and a missing-rate-driven weight strategy, it effectively addresses challenges such as high missing rates and the commissioning of new equipment. Layered rollback mechanism: When the data of a distribution transformer is unreliable (severely missing or newly commissioned), a distribution transformer with a similar load pattern to the severely missing transformer is searched within the same feeder and region. If no similar transformer can be found, or if there is no data for the newly commissioned transformer to match, then the fixed quantiles of the historical data for the entire region are used directly as the upper and lower bounds of the daily amplitude to construct the daily condition vector. Missing rate driven weighting strategy: The calculation of amplitude needs to rely on previous historical daily observations. The more reliable the daily observations (the lower the missing rate), the more trust is placed in the original statistics of that day; the less reliable the daily observations (the higher the missing rate), the more reliance is placed on short-term / long-term historical memory.

[0028] Input: Distribution transformer The original active power time series: Original reactive power time series: Missing values ​​are marked as NaN.

[0029] in, It is an active power time series composed of the raw observed active power values ​​of the distribution transformer at each measurement moment, where L is the longest time period of the distribution transformer being processed. It is the active power time series composed of the original observed reactive power values ​​of the distribution transformer at each measurement moment; Preset parameters for the daily amplitude propagation algorithm with missing perception: Initialize the reliability threshold: ; Main propagation reliability threshold: ; Amplitude statistical quantiles (upper bound): ; Amplitude statistical quantiles (lower bound): ; Long-term reliable memory window: sky; Upper limit coefficient of seasonal mutation: ; Lower limit coefficient of seasonal mutation: ; Short-term / long-term memory fusion weights: ; Output: Distribution transformer Daily amplitude sequence: , where D is the total number of days.

[0030] Taking active load P as an example, and reactive power similarly, the specific calculation steps of the daily amplitude propagation algorithm for missing sensing are as follows: S11, Daily Data Segmentation and Statistics; The original 15-minute sequence is divided into D subsequences by day. For the first subsequence... Day (d=1, 2, ..., D): Extract all non-missing observations for the day and form a set: ; Calculate the missing rate for the day: ;96 of which represents the total number of 15-minute sampling points within a day.

[0031] S12. Initialization (determine the initial amplitude) This step provides initial amplitude for newly commissioned or early-stage distribution transformers with sparse data: Within the first 7 days (d=1-7), find the first condition that satisfies... Date If found ( If it exists, then use the 90th percentile of that day as the initial amplitude: ; If not found (unreliable for the first 7 days), then the tiered rollback mechanism will be activated: First layer (feeder group): Input and distribution transformer Other transformers belonging to the same feeder, in all reliable days within the last 30 days ( amplitude of the median.

[0032] The second layer (regional group): If there is not enough data in the feeder, then cluster according to load characteristics (such as annual maximum load and daily load curve shape) across the entire region, and take the reliable daily amplitude median of the same type of distribution transformer.

[0033] The third layer (global fallback): If all the above fail, then the 90th and 10th percentiles of the historical data for the entire region will be used as the baseline. .

[0034] S13, Main Amplitude Propagation (Updated Daily) (d=1,2,...,D), and different strategies are used to update the amplitude based on the daily missing data: Case A: When the daily missing rate is lower than the first threshold, the preset high and low quantiles of the daily observations are used directly as the upper and lower bounds of the daily amplitude. The daily missing rate is the percentage of the raw load (raw load includes active power and reactive power) in a certain day, marked as NaN. Partially missing but reliable ( If there are enough observations for the day, the statistic can be directly trusted. The extreme values ​​of the observations for the day are calculated as the daily amplitude, and this amplitude is added to a variable of length [length missing]. sliding window In the middle, for reference to subsequent unreliable dates: ; Add each to their respective sliding windows. and .

[0035] Case B: When the daily missing rate is higher than the first threshold, the missing rate-driven weights are used to weight and fuse the original amplitude estimate of the day, the short-term memory of the previous day, and the long-term memory obtained from the reliable daily sliding window to update the upper and lower bounds of the daily amplitude. The short-term memory refers to the amplitude surrogate value of the previous day, which reflects the continuity and gradual change characteristics of the load amplitude between adjacent days and is suitable for handling short-term missing values ​​caused by a single day's communication interruption. The long-term memory refers to the median amplitude of a sliding window composed of historical reliable daily amplitude values, which reflects the typical amplitude level of the load under similar meteorological or social conditions and is used to address the problem of short-term memory failure when there are multiple consecutive days of missing values. The weights of the weighted fusion are determined by the missing rate of the day. The higher the missing rate, the lower the weight of the original estimate of the day and the higher the weight of short-term and long-term memory.

[0036] Partially missing and unreliable ( If the number of observations for a given day is too small, the original estimate is unreliable. A weighted fusion strategy is used to combine the original estimate for the day, short-term memory (from the previous day), and long-term memory (from a reliable database) to calculate the original amplitude estimate for the day: ; Calculate the confidence weights; the higher the missing rate, the lower the weight. ; To obtain a long-term reference value, if the reliable database is not empty, use the median; otherwise, use the previous day's amplitude. ; in, It is long-term memory. It is a sliding window; the lower bound is the same. Integrating short-term and long-term memory: ; Final amplitude value updated on the day: ; Scenario C: Missing throughout the day ( On days with no observations, the amplitude value fused from short-term and long-term memories is used directly: ; S14. Seasonal Sudden Change Protection: To prevent the algorithm from overly smoothing out the actual load growth (such as a surge in air conditioning load during summer), an upper limit protection mechanism is introduced. Maintain a list of all reliable dates from the past 30 days. Maximum amplitude: ; ; An upper limit constraint is imposed on the daily amplitude: ; Apply a lower limit constraint to the lower bound of the daily amplitude: ; S15. Post-processing: Processing the final amplitude sequence. Perform light smoothing to eliminate jumps caused by isolated outliers while preserving genuine large jump events: Apply a 3-day moving median filter: (The original value is maintained at the boundary, and the same applies to the lower bound).

[0037] For the original active power time series: And the original reactive power time series: By applying the aforementioned daily amplitude propagation algorithm with missing perception, the daily condition vector for each variable is obtained: Specifically, that is }

[0038] in, It is the upper limit of the daily active power value of the distribution transformer. It is the lower limit of the active power value of the distribution transformer on that day. It is the upper limit of the reactive power value of the distribution transformer on that day. It is the lower limit amplitude of the reactive power value of the distribution transformer on that day; S2. Adaptive sample construction: The original active power P and reactive power Q sequences are independently normalized using the daily conditional vector to obtain standardized samples and missing masks in the contour space. An adaptive normalization method based on daily amplitude propagation is used to address the scale imbalance problem caused by the high dynamic range of power load, providing stable input for subsequent modeling. The results are as follows: Figures 2-4 As shown, Figure 2 This is a waveform diagram of the amplitude propagation result. Figure 3 It is a scatter plot of the propagation amplitude versus the original daily maximum power value. Figure 4The daily missing rate change compared to the threshold chart shows that this method, through hierarchical backoff and missing rate weighting, can obtain a stable and reasonable daily amplitude estimate in high-missing scenarios. For any time t, which belongs to day d, the original observations are linearly normalized according to the upper and lower bound amplitudes of their respective day d. The normalized results of all times are concatenated to obtain the final standardized sequence. Simultaneously, a corresponding missing mask is generated to mark the missing locations in the original data, completing the adaptive sample construction. This step utilizes the daily amplitude proxy calculated by S1. The original load data is adaptively normalized, completing the first step of "amplitude-profile decoupling". This process maps the original load data to a unified, dimensionless profile space, providing scale-consistent input for subsequent model training.

[0039] Input: Raw daily load sequence (active power P and reactive power Q): ; Output daily condition vector: .

[0040] Output: A normalized sample tuple for model training / inference: ,in: This is the original daily load sequence (active power P and reactive power Q) for day d: It is the normalized contour data matrix. ; It is the missing mask matrix of the original daily load sequence (active power P and reactive power Q) on day d, where 1 indicates the presence of original data and 0 indicates the absence of data. It is the random noise matrix on day d.

[0041] Detailed calculation steps: S21. Independent normalization: Normalize the original daily active power P and reactive power Q variable sequences separately.

[0042] For each variable Extract its set of observations on day d. ; Daily conditional vector obtained through the daily amplitude propagation algorithm with missing perception: This allows us to obtain the daily extreme value information for each variable v. .

[0043] Normalization is performed using a linear transformation: middle, It is a very small positive number (e.g.) (), used to prevent numerical instability when the denominator is zero; in, It is the original observation value (unnormalized physical dimension value) of variable v (active power or reactive power) at the t-th sampling time. The results are combined into a normalized contour matrix: .

[0044] S22, Construct auxiliary signals; Missing mask : is a with or A binary matrix of the same dimension, used to identify observed values ​​and missing values: ; Random noise : Sample a value from a uniform distribution that is similar to A random noise matrix of the same dimension serves as the source of randomness in the generator. ; in, This is the raw daily load sequence matrix for day d, including the raw collected values ​​(physical units) of the two variables, active power P and reactive power Q, at 96 time points, i.e.: , It is the contour sequence matrix (dimensionless) obtained after normalization on day d, i.e. , This represents a 96×2 dimensional matrix whose elements are independently and identically distributed in a continuous uniform distribution on [-1,1]. S23. Sample Packaging: Pack all the above elements into a complete training / inference sample: ; S3, Autoregressive Dynamic Teacher Model (ADT); The autoregressive dynamic teacher model is pre-trained and frozen based on the target sample. The autoregressive dynamic teacher model based on the causal mask Transformer is trained to learn the inherent dynamic laws of the load profile. After training, all its parameters are frozen to obtain the frozen autoregressive dynamic teacher model. The target sample is daily load data with no missing data or a missing rate lower than a preset threshold (e.g., less than 10%) to ensure that the autoregressive dynamic teacher model can accurately learn the complete temporal dependencies of the load profile during the pre-training stage.

[0045] This step aims to train a "teacher" model focused on learning the inherent dynamics of the load "profile". This model is pre-trained only on high-quality, low-missing-rate data and is frozen in subsequent steps. The knowledge it learns will be passed to the generator through a "teacher-guided" mechanism.

[0046] Input: Select target samples from the standardized sample set constructed by S2: Note that this step does not use... .

[0047] Output: An autoregressive dynamic teacher (ADT) model with all parameters frozen, denoted as .

[0048] Detailed calculation steps: S31, Model Architecture Definition; Backbone network: Transformer encoder with causal mask (Number of layers: 4; Hidden layer dimension: 128; Number of attention heads: 8; Position encoding: Learnable position embedding, length = 96) Output head: A single-layer multilayer perceptron (MLP) that maps the output of the last layer of the Transformer (dimension 128) to 4 dimensions, representing the conditional Gaussian distribution parameters of active power and reactive power, respectively.

[0049] set up ∈ ^{128} represents the hidden state vector output by the Transformer encoder at time step t (t=1,...,96). Output head function. Defined as: ; in, It is the output header function. Let P be the conditional Gaussian distribution mean of the active power P at time step t. It is the conditional Gaussian distribution mean of the reactive power Q at time step t, representing the model's central prediction of the power value at the current moment (dimensionless, with a value range of [-1,1]). These represent the standard deviations of the corresponding conditional Gaussian distributions, indicating the model's uncertainty regarding the predicted values; the model directly outputs the logarithmic form. and This ensures a natural constraint that σ > 0, while avoiding numerical instability caused by variance approaching zero during training.

[0050] S32, Model Training; Forward propagation: For an input sequence The autoregressive dynamic teacher model predicts the distribution at time step t based on the first t-1 time steps.

[0051] Loss function: Negative log-likelihood loss is used, and the optimization objective is to maximize the likelihood probability of the observed data under the conditional Gaussian distribution predicted by the model.

[0052] ; in: This represents the Gaussian (normal) probability density function with mean μ and variance σ². It is the normalized observation of variable v (P or Q) at the t-th time step; and These are the conditional mean and conditional variance of the variable predicted by the autoregressive dynamic teacher model at step t, respectively; using a standard optimizer (such as Adam) on the dataset... Train on it until convergence.

[0053] S33, Model Freeze; After training, all parameters of the ADT (including the Transformer backbone and MLP output header) are fixed, making it a static and reliable knowledge source. The frozen autoregressive dynamic teacher model is denoted as... .

[0054] S4. Combine GAIN-FiLM with generative interpolation; By combining GAIN-FiLM with generative interpolation, a generator G and a discriminator D are constructed. The generator G receives noise, the missing mask, and the daily conditional vector. After modulation by a Transformer encoder and a FiLM module, it shares the output head of the frozen autoregressive dynamic teacher model, generates interpolated values ​​through reparameterized sampling, and fuses the observed values ​​to output a contour sequence. The FiLM module is a feature-level linear modulation module used to map the daily conditional vector to affine transformation parameters through a multilayer perceptron, and to perform affine transformation on the output hidden states of each layer of the Transformer encoder in the generator G. The discriminator D receives the contour sequence, the cue vector, and the dynamic features extracted by the frozen autoregressive dynamic teacher model, and outputs the authenticity probability. During training, the total loss function of the generator G includes reconstruction loss, adversarial loss, and behavioral alignment loss for mimicking the output distribution of the frozen autoregressive dynamic teacher model. The behavioral alignment loss is used to mimic the output distribution of the frozen autoregressive dynamic teacher model, and this loss uses KL divergence to measure the distribution difference between the generator output and the ADT output.

[0055] like Figure 5 As shown, this step is the core of the entire framework. The generator G, under adversarial training with the discriminator D, combines "teacher guidance" from the frozen ADT with information from... The "amplitude-contour decoupling" control generates high-quality interpolation results.

[0056] Input: A complete sample constructed by S2: .

[0057] Output: Interpolation results in normalized space: .

[0058] Detailed calculation steps: Submodule A: Generator G; Input concatenation: Concatenates the observation data, noise, and missing mask into a 4-dimensional input tensor.

[0059] ; Main processing: U is processed by a standard (non-causal) Transformer encoder (4 layers, 128 dimensions) to obtain the intermediate hidden state sequence. .

[0060] FiLM Conditional Modulation: After processing by the Transformer encoder, the intermediate hidden state H is obtained; the FiLM (Feature-wise Linear Modulation) module is introduced after each intermediate hidden state S.

[0061] Conditional mapping: Daily conditional vector The scaling factor is mapped to the affine transformation parameters of this layer via a small MLP. and offset factor ).

[0062] ; in, For scaling factor vectors, For offset factor vectors, This includes the upper and lower bounds of the amplitude of the active power P and reactive power Q for the day; Feature modulation: the sequence of hidden states output by the current layer Transformer. (Where 96 is the time step number and 128 is the feature dimension) Perform a time-step, channel-by-channel affine transformation. For each time step t (t=1,...,96), its hidden state vector of the l-th layer... After FiLM modulation, it becomes: ; ⊙ represents element-wise multiplication (Hadamard product). The modulation results from all time steps are stacked to obtain the output feature matrix of the FiLM module: ; in, It is a hidden state; it represents the output features of the current layer. Perform a channel-by-channel affine transformation.

[0063] Output sampling (key to teacher guidance): This involves sampling the final hidden state. The parameters of the conditional Gaussian distribution are obtained by inputting them into the MLP output header of the frozen ADT. Then, sampling is performed through reparameterization.

[0064] ; ; in, It is noise sampled from the standard normal distribution, i.e. ; It is generated independently, independent of network parameters; Fuse observations: Fuse the generated values ​​with the actual observations to obtain the final generator output.

[0065] ; Submodule B: Discriminator D; Input construction: Contour sequence: ; Hint vector: ; ADT dynamic features : Contour sequence Input into a complete frozen ADT (stem + head) and extract its internal representation or output statistics as higher-order dynamic features.

[0066] ; Backbone processing: After concatenating the above three inputs, the data is fed into a two-layer bidirectional LSTM (BiLSTM) network.

[0067] Output: The output of BiLSTM is passed through a sigmoid activation function to obtain the true probability of each variable at each time point.

[0068] ; Submodule C: Loss function and training; The total loss of generator G consists of three parts: ; in, It is the actual observation sequence Input the distribution parameters obtained from the frozen ADT, and These are the parameters corresponding to the generator output. The default weights are λ1=100, λ2=1, and λ3=5.

[0069] S5. Inverse normalization and physical verification: The contour sequence output by the generator G is inverse normalized to the original dimensions, and the power factor physical consistency is verified to output the final load data.

[0070] The results generated by the generator in the normalized space are converted back to physically meaningful real dimensions, and physical rules are verified to ensure the engineering usability of the final output.

[0071] Input: Contour sequence and daily condition vector , obtained .

[0072] Output: Final daily load sequence for physical compliance: .

[0073] Specific calculation steps; S51, Independent Inverse Normalization. Perform the inverse transformation of S2 normalization on P and Q respectively, changing the generator's output in the normalized contour space. It is restored to a power sequence with physical dimensions.

[0074] For each variable Applying the inverse transform formula: ; in, It represents the normalized contour value (dimensionless, derived from) at the t-th time point of the generator G's output. (corresponding elements in the matrix) It represents the physical power value at time t after denormalization (unit: kW or kVar). and The upper and lower bounds of the daily amplitude obtained from the S1 estimation (derived from the daily conditional vector) ); To the preliminary sequence of physical dimensions: .

[0075] S52, Power factor physical consistency check; In power systems, users typically have a minimum requirement for the power factor cosφ (e.g., 0.9, but for the sake of conservatism, we will set it to 0.8 here).

[0076] For each time point t, calculate the power factor: ; like If, then retain the original value; if If the reactive power Q is deemed unreasonable, it will be corrected to satisfy the boundary condition cosφ=0.8 while keeping its sign unchanged. ; S53. Output the final result; The sequence after physical verification is the final output: ; To verify the effectiveness and engineering applicability of the method of this invention, a systematic experimental verification was conducted on a real power grid distribution transformer area load dataset. The experiment selected 15-minute time-series data containing total active power (P) and total reactive power (Q) as the test object, and artificially constructed a test set with a missing rate of 50% to evaluate the interpolation performance under extreme operating conditions.

[0077] Figures 6-7 This is a time-series comparison chart of the interpolation results of this invention and the original real data during typical missing periods. Among them, Figure 6 For comparison of total active power, Figure 7 For comparison of total reactive power, each sub-graph uses a two-layer comparison display: the upper layer is the complete original true data curve (blue solid line), and the lower layer is the interpolation result curve of the method of this invention (red solid line); the horizontal axis is the time axis, and the vertical axis is the total active power (unit: kW) or the total reactive power (unit: kVar), respectively; in non-missing periods, the upper and lower curves completely overlap; in missing periods, the lower layer marks the completed value of this invention with red scatter dots, and the upper layer's blue solid line is the true value at the corresponding time, forming a visual comparison between the two.

[0078] Depend on Figure 6 It can be seen that during periods of active power deficiency, the trend, amplitude range, and timing characteristics of the interpolated values ​​of this invention are highly consistent with the original real data, and the interpolation curve is smooth and continuous without significant abrupt changes or abnormal deviations; Figure 7 As can be seen, during periods of reactive power deficiency, this invention also accurately reproduces the variation pattern of reactive load, with the interpolated scatter plots closely matching the upper-level true value curve, without any obvious phase shift or amplitude distortion. This fully verifies that the method of this invention has extremely high numerical accuracy and visual quality in both active and reactive power dimensions, and can effectively reproduce the complete operating state of the distribution transformer area load.

[0079] To further quantitatively evaluate the imputation performance of this invention, it was compared with existing mainstream methods GAIN and PC-GAIN on a test set with a missing value rate of 50%. The results are shown in Table 1. RMSE and MAE are used to evaluate the numerical deviation between the imputed value and the true value; PF compliance rate is the percentage of time points where the power factor is not less than 0.8, used to evaluate the physical engineering usability of the imputation results; ACF distance is the absolute difference of the autocorrelation coefficients of the imputed sequence and the true sequence at a lag of 7 days, used to measure the ability to maintain long-term trends; KL divergence is used to evaluate the similarity between the overall probability distribution of the imputed sequence and the true sequence, with smaller values ​​indicating closer distributions.

[0080] Table 1. Comparison of interpolation performance of different methods on the test set;

[0081] As shown in Table 1, in terms of interpolation accuracy, the RMSE_P and RMSE_Q of this invention are 18.3 and 12.6, respectively, which are 52.7% and 52.3% lower than those of PC-GAIN. MAE_P also shows a significant advantage. In terms of physical compliance, the PF compliance rate of this invention reaches 99.6%, close to the ideal value of 100%, which is significantly better than PC-GAIN's 92.1% and GAIN's 78.3%. This is due to the power factor physical consistency verification mechanism introduced in step S5, which can effectively correct interpolation values ​​that violate electrical constraints and ensure that the output results are directly usable in engineering. In terms of long-term consistency, the ACF distance of this invention is only 0.12, which is much lower than the 0.42 and 0.38 of the comparison methods, indicating that the interpolation sequence can accurately maintain the inherent daily cycle and weekly seasonality of the load. The significant reduction in KL divergence further indicates that the interpolation sequence generated by this invention is closest to the real data in terms of overall distribution characteristics.

[0082] Figures 8-10 This is a time-series comparison chart of the interpolation results of the present invention and the GAIN and PC-GAIN methods within the same missing time period, used to visually evaluate the advantages and disadvantages of different methods. Figure 8 For comparison of total active power, Figure 9 For comparison of total reactive power, Figure 10 A time series comparison of power factor (PF) compliance rates calculated based on active and reactive power values ​​supplemented by various methods.

[0083] Each subplot is plotted on the same coordinate system with four curves: the original true value (blue solid line), the GAIN interpolation value (green dashed line), the PC-GAIN interpolation value (orange dotted line), and the interpolation value of the present invention (red solid line). Missing points are marked with scatter dots of the corresponding color.

[0084] Depend on Figure 8 The comparison of active power shows that: the GAIN method (green dashed line) fluctuates greatly and deviates from the true value in many places, showing overfitting or underfitting phenomena; although the PC-GAIN method (orange dotted line) has improved trend tracking ability, there are still large deviations at peak and trough values; the method of this invention (red solid line) is closest to the true value curve and is significantly better than the comparison methods in terms of trend tracking, extreme value capture and time series consistency.

[0085] Depend on Figure 9The comparison of reactive power shows that the GAIN and PC-GAIN methods exhibit more obvious lag and oscillation in reactive power data interpolation, making it difficult to adapt to the rapid dynamic changes in reactive load. However, the method of this invention still maintains high-precision tracking capability, and the interpolation curve is smooth and closely follows the true value, verifying its effectiveness in modeling reactive power components.

[0086] Depend on Figure 10 The comparison of power factor compliance rates shows that: the PF sequence generated by the GAIN method has non-compliance points where it falls below the safety threshold of 0.8; although the PC-GAIN method shows some improvement, PF violations still frequently occur during periods of severe load fluctuations; only the PF curve of the method of this invention remains consistently above 0.8, highly consistent with the PF change trend of the real data. This result directly confirms the superiority of the PF compliance rate index in Table 1, indicating that this invention, guided by physical constraints, fundamentally ensures the electrical rationality of the interpolated data.

[0087] comprehensive Figures 8-10 It can be seen that even with a relatively high missing rate of 50%, the method of this invention is superior to the existing mainstream methods in all three dimensions: active power accuracy, reactive power accuracy, and physical compliance.

[0088] In terms of quantitative indicators, this invention achieves superior performance in key indicators such as RMSE, MAE, and power factor compliance rate, with its advantages being more pronounced in high missing rate and high dynamic scenarios.

[0089] In summary, the experiments fully demonstrate the superiority of this invention in terms of accuracy, physical compliance, long-term stability, and generalization ability, and it has good engineering practical value.

Claims

1. A method for generating interpolation of power load data, characterized in that, include: S1. Missing-aware daily amplitude propagation: For each distribution transformer load daily sequence, based on a hierarchical backoff mechanism and a weighting strategy driven by the missing rate, the upper and lower bounds of the daily amplitude are estimated, and a daily condition vector independent of external time features is constructed. In S1, the missing perception of daily amplitude propagation specifically includes: When the daily missing rate is lower than the first threshold, the preset high and low quantiles of the daily observations are used directly as the upper and lower bounds of the daily amplitude. When the daily missing rate is higher than the first threshold, the missing rate-driven weights are used to weightedly fuse the original amplitude estimate of the day, the short-term memory of the previous day, and the long-term memory obtained from the reliable daily sliding window to update the upper and lower bounds of the daily amplitude. When all data for the day is missing, the fusion result of the short-term memory and long-term memory is directly used as the upper and lower bounds of the amplitude for that day. In addition, a seasonal mutation protection mechanism is introduced, which imposes an upper and lower limit constraint on the updated daily amplitude upper and lower limits based on the reliable amplitude extreme values ​​within a preset time period. The hierarchical rollback mechanism is used to initialize the amplitude of newly commissioned or early data-sparse distribution transformer loads. The specific steps of the hierarchical rollback mechanism are: based on the median amplitude of reliable days of the same feeder group, based on the median amplitude of similar distribution transformer loads after regional group clustering, and based on the global fallback value of historical data quantiles of the entire region. The daily condition vector includes the upper limit amplitude of active power, the lower limit amplitude of active power, the upper limit amplitude of reactive power, and the lower limit amplitude of reactive power. S2. Adaptive sample construction: The original active power P and reactive power Q sequences are independently normalized using the daily conditional vector to obtain standardized samples and missing masks in the contour space. S3. Select target samples from the standardized samples, and use the target samples to pre-train the autoregressive dynamic teacher model so that the autoregressive dynamic teacher model learns the inherent dynamic law of the load profile; after the pre-training is completed, freeze all parameters of the autoregressive dynamic teacher model to obtain the frozen autoregressive dynamic teacher model. S4. Combine GAIN-FiLM with generative interpolation to construct a generator G and a discriminator D. The generator G receives noise, the missing mask and the daily conditional vector, and after being modulated by the Transformer encoder and the FiLM module, it shares the output head of the frozen autoregressive dynamic teacher model to obtain the conditional distribution parameters. It then generates interpolated values ​​through reparameterized sampling and fuses the observation values ​​to output a contour sequence. The discriminator D receives the contour sequence, the cue vector, and the dynamic features extracted by the frozen autoregressive dynamic teacher model, and outputs the authenticity probability. S5. Denormalization and Physical Verification: Denormalize the contour sequence output by the generator G to the original dimensions, perform a power factor physical consistency check, and output the final load data.

2. The power load data generation interpolation method according to claim 1, characterized in that, In S4, during training, the total loss function of the generator G includes reconstruction loss, adversarial loss, and behavioral alignment loss for mimicking the output distribution of the frozen autoregressive dynamic teacher model.

3. The power load data generation interpolation method according to claim 1, characterized in that, In S2, the independent normalization is to perform a linear transformation on each active power P and reactive power Q based on its corresponding daily amplitude upper and lower bounds, mapping the original data to dimensionless contour data within a preset interval, thereby achieving decoupling of amplitude and contour.

4. The power load data generation interpolation method according to claim 1, characterized in that, In S3, the training loss function of the autoregressive dynamic teacher model is the negative log-likelihood loss, which is used to maximize the likelihood probability of the observed data by minimizing the negative log-likelihood value of the observed data under the conditional Gaussian distribution predicted by the model.

5. The power load data generation interpolation method according to claim 1, characterized in that, In S4, the modulation process of the FiLM module is as follows: The day condition vector is mapped to affine transformation parameters through a multilayer perceptron, and the output hidden states of each layer of the Transformer encoder in the generator G are subjected to affine transformation, thereby realizing the global conditional control of amplitude information on the contour generation process.

6. The power load data generation interpolation method according to claim 1, characterized in that, In S4, during the generator training process, the behavior alignment loss is used to mimic the real-world temporal dynamic data implied by the autoregressive dynamic teacher model; the KL divergence is used to measure the difference between the following two: the first distribution parameter output by the frozen autoregressive dynamic teacher model after inputting the real observation sequence into the generator G, and the second distribution parameter output by the generator G after the output head of the frozen autoregressive dynamic teacher model; the generator G is forced to learn and follow the real dynamic laws implied by the frozen autoregressive dynamic teacher model through the loss.

7. The power load data generation interpolation method according to claim 1, characterized in that, In S5, the power factor physical consistency verification includes: calculating the power factor at each time point; when the power factor is lower than the preset physical compliance lower limit, while keeping the reactive power sign unchanged, the reactive power is corrected by boundary constraints based on the absolute value of active power so that it meets the preset power factor boundary conditions.

8. An interpolation system for implementing the power load data generation interpolation method as described in any one of claims 1-7, characterized in that, It includes a daily amplitude propagation module, a sample construction module, an autoregressive dynamic teacher model generation module, a generative interpolation module, and a result verification and output module; The daily amplitude propagation module is used to perform missing-aware daily amplitude propagation, estimate the upper and lower bounds of the daily amplitude, and construct the daily condition vector; The sample construction module is used to complete adaptive sample construction, and to independently normalize the original active power and reactive power sequences to obtain standardized samples and missing masks. The autoregressive dynamic teacher model generation module is used to complete the pre-training and parameter freezing of the autoregressive dynamic teacher model, and obtain the frozen autoregressive dynamic teacher model. The generative interpolation module is used to construct a generator and discriminator including GAIN-FiLM, and generate a complete contour sequence through adversarial training; the result verification output module is used to perform inverse normalization operation and power factor physical consistency verification, and output the final interpolated power load data.

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