High-precision power reconstruction method and system of electric energy meter under low-frequency sampling

Abstract

This invention discloses a high-precision power reconstruction method and system for low-frequency sampling of electricity meters, belonging to the field of electricity meter sampling. The method includes: acquiring low-frequency sampled current and voltage sequences; obtaining coarse-grained power baseline and residual data by performing two-dimensional phase point pairing and feature vector mining, and reconstructing using Gaussian process regression; importing the current and voltage sequences into a hybrid differential model, and calculating transient power increments through state transition equation propagation analysis; for the residual data, extracting harmonic amplitude, phase, and frequency parameters, and obtaining the power contribution of each harmonic through line impedance mapping inversion; and superimposing the coarse-grained power baseline, transient power increments, and the power contributions of each harmonic to obtain a full-band power sequence. This application solves the technical problem that existing low-frequency sampling electricity meters are unable to capture rapid transient processes, resulting in insufficient full-band power metering accuracy.

Description

Technical Field

[0001] This invention relates to the field of electricity meter sampling, and specifically to a high-precision power reconstruction method and system for low-frequency sampling of electricity meters. Background Technology

[0002] With the continuous advancement of smart grid construction, the demand for low power consumption and long battery life in smart meters is becoming increasingly urgent. Traditional meters generally adopt a high-frequency sampling mode of tens to hundreds of points per power frequency cycle to ensure power metering accuracy. This mode will significantly increase the hardware cost of the analog-to-digital conversion module, increase the computational load of the microprocessor, and significantly increase standby power consumption. On the other hand, if a low-frequency sampling scheme of 1 to 10 points per power frequency cycle is directly adopted, a large amount of voltage and current phasor information will be lost. The traditional instantaneous power integration method is not only difficult to capture fast transient processes such as load switching and power regulation, but also cannot effectively separate and quantify the power contribution of each harmonic, resulting in a serious decrease in power metering accuracy across the entire frequency band, which cannot meet the power metering error standards stipulated by the State Grid. Summary of the Invention

[0003] This application provides a high-precision power reconstruction method and system for low-frequency sampling of electricity meters, aiming to solve the technical problem that existing low-frequency sampling electricity meters are unable to capture fast transient processes, resulting in insufficient power measurement accuracy across the entire frequency band.

[0004] In view of the above problems, this application provides a high-precision power reconstruction method and system for low-frequency sampling of electricity meters.

[0005] The first aspect disclosed in this application provides a high-precision power reconstruction method for low-frequency sampling of an electricity meter, the method comprising:

[0006] Low-frequency sampled current and voltage sequences are acquired. Based on these sequences, two-dimensional phase point pairing and feature vector mining are performed, and reconstruction based on Gaussian process regression is adopted to obtain coarse-grained power baseline and residual data characterizing the main power sequence. The current and voltage sequences are imported into a hybrid differential model, and transient power increments are calculated by performing state transition equation propagation analysis based on unscented Kalman filtering. For the residual data, harmonic amplitude, phase, and frequency parameters are extracted by frequency division, and the power contribution of each harmonic is obtained by line impedance mapping inversion. The coarse-grained power baseline, transient power increment, and power contribution of each harmonic are superimposed to obtain the full-band power sequence.

[0007] Another aspect of this application discloses a high-precision power reconfiguration system for low-frequency sampling of an electricity meter, the system comprising: The system comprises the following modules: an acquisition module for acquiring low-frequency sampled current and voltage sequences; a mining module for obtaining coarse-grained power baseline and residual data characterizing the main power sequence by performing two-dimensional phase point pairing and feature vector mining, and using Gaussian process regression-based reconstruction based on the current and voltage sequences; an analysis module for importing the current and voltage sequences into a hybrid differential model and calculating transient power increments by performing state transition equation propagation analysis based on unscented Kalman filtering; an extraction module for extracting harmonic amplitude, phase, and frequency parameters from the residual data by frequency division, and obtaining the power contribution of each harmonic through line impedance mapping inversion; and a superposition module for superimposing the coarse-grained power baseline, transient power increments, and the power contributions of each harmonic to obtain a full-band power sequence.

[0008] One or more technical solutions provided in this application have at least the following technical effects or advantages: By transforming low-frequency sampled current and voltage sequences into two-dimensional phase points and mining their geometric features with clear physical meaning, and combining Gaussian process regression to reconstruct a coarse-grained power baseline with confidence intervals, a hybrid differential model integrating resistive inertia, inductive inertia, and physical constraints of electronic load response delay is used. Transient power increments are calculated through propagation analysis of the state transition equation using unscented Kalman filtering. Simultaneously, frequency division analysis and line impedance mapping inversion are performed on the residual data to obtain the power contribution of each harmonic. Finally, the full-band power sequence is obtained by superposition. While retaining the advantages of low power consumption and low cost of low-frequency sampling, the accuracy and reliability of power metering in complex load scenarios of low-voltage distribution networks are improved.

[0009] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0010] Figure 1 A flowchart illustrating a high-precision power reconstruction method for low-frequency sampling of an energy meter is provided for embodiments of this application. Figure 2 A schematic diagram of a high-precision power reconstruction system for low-frequency sampling of an electricity meter is provided for the embodiments of this application.

[0011] Explanation of reference numerals in the attached diagram: Acquisition module 11, Mining module 12, Analysis module 13, Extraction module 14, Overlay module 15. Detailed Implementation

[0012] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0013] The overall concept of the technical solution provided in this application is as follows: This application provides a high-precision power reconstruction method and system for low-frequency sampling of electricity meters. It reconstructs a coarse-grained power baseline with confidence intervals by combining two-dimensional phase point pairing and geometric feature vector mining with Gaussian process regression. A hybrid differential model integrating resistive inertia, inductive inertia, and physical constraints of electronic load response delay is constructed. Unscented Kalman filtering is used to calculate transient power increments through propagation analysis of the state transition equations. Based on the frequency characteristics of line impedance, the harmonic power contributions in the residual data are mapped and inverted. Finally, the entire frequency band power sequence is reconstructed by point-by-point superposition of the steady-state baseline, transient increments, and harmonic components on the time axis, improving the accuracy and reliability of electricity metering in complex load scenarios of low-voltage distribution networks.

[0014] After introducing the basic principles of this application, various non-limiting embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0015] Example 1, as Figure 1 As shown in the embodiment of this application, a high-precision power reconstruction method under low-frequency sampling of an energy meter is provided. The method includes: S100: Acquire low-frequency sampled current and voltage sequences.

[0016] Specifically, the AC current signal and AC voltage signal from the grid side are preprocessed by the signal conditioning circuit built into the electricity meter. The signal conditioning circuit mainly consists of a current transformer, a voltage transformer, an operational amplifier, and an anti-aliasing filter. The current transformer is used to linearly convert the large current of the grid into a weak current signal at the milliampere level, the voltage transformer is used to convert the high voltage of the grid into a weak voltage signal at the millivolt level, and the anti-aliasing filter is used to filter out high-frequency noise components in the signal that are higher than the Nyquist frequency.

[0017] Subsequently, the conditioned analog current signal and analog voltage signal are synchronously input to the analog-to-digital converter module of the energy meter for low-frequency sampling. Here, low-frequency sampling specifically refers to a low sampling rate mode of 1 to 10 points per power frequency cycle. This mode can reduce the hardware computing load and standby power consumption of the energy meter. At the same time, synchronous sampling means that the sampling time of the current signal and voltage signal is strictly consistent. After the analog-to-digital converter module completes the analog-to-digital conversion, it outputs discrete digital sample values. The system will perform preliminary outlier removal processing on the original digital sample values. The sliding window threshold method is used to identify and remove outlier sampling points caused by power grid peak interference and hardware electromagnetic interference. Then, the linear interpolation method is used to fill in the missing positions after removal.

[0018] Finally, the system adds a timestamp to each completed sample value and arranges them in chronological order to form a structured current sequence and a voltage sequence. The current sequence consists of discrete instantaneous current values ​​sorted by timestamp, and the voltage sequence consists of discrete instantaneous voltage values ​​corresponding to the same time. The two sequences have the same length and the sampling points correspond one-to-one.

[0019] S200: Based on the current sequence and voltage sequence, by performing two-dimensional phase point pairing and feature vector mining, and using reconstruction based on Gaussian process regression, coarse-grained power baseline and residual data characterizing the main power sequence are obtained.

[0020] Specifically, the system first receives a current sequence and a voltage sequence that are strictly synchronized in time and have the same length. It then iterates through all the sampling points with corresponding timestamps in the two sequences and pairs the instantaneous current value at the same moment as the horizontal axis and the instantaneous voltage value as the vertical axis to generate several two-dimensional phase points. All two-dimensional phase points together constitute a sparse set of phase points. Sparseness specifically refers to the fact that the distribution density of phase points on the voltage-current plane is extremely low due to low-frequency sampling, making it impossible to obtain a continuous and accurate power sequence directly through the traditional instantaneous power integration method.

[0021] The system then performs geometric feature mining on the sparse point set of phase points, calculating and extracting four core geometric features in sequence: First, the horizontal and vertical coordinates of the centroid of the point set, whose values ​​directly reflect the phase difference between the fundamental voltage and the fundamental current; the closer the centroid is to the diagonal of the coordinate axis, the higher the power factor. Second, the area of ​​the bounding box of the point set, obtained by eigenvalue decomposition of the covariance matrix of the sparse point set of phase points, which is equal to the difference between the instantaneous values ​​of the maximum and minimum currents multiplied by the difference between the instantaneous values ​​of the maximum and minimum voltages. Third, the orientation angle of the principal inertial axis of the point set distribution, characterizing the overall rotational characteristics of the voltage and current phasors. Fourth, the average radial distance of the point set to the origin, reflecting the comprehensive impedance modulus of the load; the greater the distance, the higher the load impedance. The above four types of geometric features are concatenated in a fixed order to form a multidimensional feature vector, which serves as the input features for the subsequent regression model.

[0022] Next, the feature vector is input into a pre-trained Gaussian process regression model. This model is good at handling small-sample, nonlinear time series reconstruction problems. It preferably uses a combination of squared exponential covariance function and periodic covariance function as the function. The model learns the mapping relationship between the feature vector and the instantaneous power at the corresponding sampling time, and outputs a continuous coarse-grained power baseline and corresponding residual data. The coarse-grained power baseline represents the steady-state and quasi-steady-state principal components in the power sequence and has its own confidence interval for the model output, which can quantify the uncertainty of baseline reconstruction. The residual data is the difference between the original instantaneous power value at each sampling time and the corresponding value of the coarse-grained power baseline, which includes transient abrupt components and harmonic components that were not captured by the baseline.

[0023] S300: The current sequence and voltage sequence are imported into the hybrid differential model, and the transient power increment is calculated by performing state transition equation propagation analysis based on unscented Kalman filtering.

[0024] Specifically, a hybrid differential model is first constructed based on the physical characteristics of the power grid load. This model is a hybrid of a physical driving model that integrates the basic laws of circuits and a statistical model that describes the random changes of parameters. The state variables are the equivalent resistance and equivalent inductance of the load and their corresponding first-order time derivatives. At the same time, a state transition equation is constructed, which uses resistive inertia, inductive inertia and electronic load response delay as load parameters.

[0025] Subsequently, the output time-synchronized current sequence, voltage sequence, and coarse-grained power baseline are input into the hybrid differential model. The low-frequency sampled instantaneous current and voltage values ​​are mapped to power observations including equivalent resistance, equivalent inductance, and their time-varying rates through the observation equation. Next, an unscented Kalman filter is used to perform propagation analysis based on the state transition equation. The unscented Kalman filter is chosen over the traditional extended Kalman filter because it does not require calculating complex Jacobian matrices and offers higher accuracy in state estimation for nonlinear systems. Specifically, the process involves: first, generating a sigma point set covering the probability distribution of state variables through deterministic sampling, where each sigma point represents the equivalent resistance, equivalent inductance, and their time-varying rates. A probabilistic combination of equivalent inductance and its time derivative is used. All sigma points are substituted into the state transition equation and propagated to the next prediction time, calculating the mean and covariance matrix of the predicted state. The predicted state is then inversely mapped using the observation equation to obtain the predicted current and voltage observations at the corresponding time. The deviation between the predicted observations and the actual sampled current and voltage observations is measured, and a posterior recursive update is performed using Kalman gain. Finally, a sequence of hidden state variables in the continuous time domain is obtained, representing continuous estimates of the equivalent resistance, equivalent inductance, and their time derivatives that cannot be directly measured. Based on the derivative information of the hidden state variable sequence and the current sequence, the instantaneous power physical formula is used. ; Where p is power, R is resistance, i is current, L is inductance, and t is time. This refers to the Joule heat power consumed by the resistor, which is the active power. t is the rate of change of magnetic field energy stored / released by the inductor, i.e. reactive power. A complete power evolution curve is obtained. Subtracting this power evolution curve from the coarse-grained power baseline point by point on the time axis yields the transient power increment containing only the dynamic component of load mutation. This step can be activated only when a load power mutation is detected by a mutation detection algorithm, further reducing the system's computational load.

[0026] S400: For the residual data, after extracting the harmonic amplitude, phase and frequency parameters by frequency division, the power contribution of each harmonic is obtained by line impedance mapping inversion.

[0027] Specifically, the system first receives the output residual data, which is the signal component remaining after the original instantaneous power sequence has been subtracted sequentially from the coarse-grained power baseline, steady-state principal component, transient power increment, and dynamic mutation component. It only contains the harmonic components generated by the power grid and load. However, in practice, a small amount of fundamental steady-state wake and transient spikes that have not been completely filtered out may still remain. Therefore, the system first performs frequency division filtering on the residual data. Here, frequency division filtering specifically refers to a bandpass filter array constructed using a multi-order Butterworth digital filter bank. The fundamental steady-state component and transient mutation component are the precise filtering targets. By setting the passband interval corresponding to each harmonic frequency, the pure harmonic residual components are separated.

[0028] Subsequently, the harmonic residual components were analyzed in segmented frequency domains. Considering that low-frequency sampling resulted in insufficient Fourier transform frequency resolution for a single data segment, the system adopted a sliding window segmentation strategy to divide the harmonic residual components into multiple overlapping time segments. A windowed fast Fourier transform was performed on each segment, and spectral leakage was suppressed by using a window function. The analysis results of adjacent segments were then weighted and fused to extract the amplitude, phase, and frequency parameters of the main odd harmonics, such as the 3rd, 5th, and 7th harmonics. These parameters are the amplitude, phase, and frequency of each harmonic. The amplitude reflects the intensity of the harmonic, the phase reflects the phase relationship between the harmonic and the fundamental frequency, and the frequency is used to correct the harmonic frequency shift caused by power grid frequency fluctuations.

[0029] Next, an inversion calculation is performed based on the pre-calibrated line impedance mapping relationship. Here, the line impedance mapping relationship refers to the inherent characteristic of the impedance value of the power grid transmission line changing with frequency. Since the frequencies of different harmonics are different, the line impedance attenuation and phase shift they experience during transmission also have significant differences. The harmonic residual components measured by the energy meter are actually the result of the load-side harmonic source after transmission through the line impedance. Therefore, by establishing a mathematical model of load-side harmonic power - line impedance - energy meter-side harmonic voltage and current, the extracted harmonic amplitude, phase and frequency parameters of each harmonic are substituted into the model for inverse calculation, and finally the power contribution of each harmonic is restored. This contribution not only includes the magnitude of each harmonic power injected into the power grid by the load-side nonlinear equipment, but also decouples the harmonic distortion distribution state existing on the power grid side itself, realizing the accurate location and responsibility division of the harmonic source.

[0030] S500: By superimposing the coarse-grained power baseline, transient power increment, and power contribution of each harmonic, a full-band power sequence is obtained.

[0031] Specifically, the first step is to perform a time axis alignment operation. Since the coarse-grained power baseline is a continuous time series output by Gaussian process regression, the transient power increment is a high-resolution dynamic sequence that is activated only in the load mutation interval, and the power contribution of each harmonic is a quasi-continuous sequence obtained by piecewise analysis based on a sliding window with a window step size of one power frequency cycle, the transient power increment and the power contribution of each harmonic are resampled to a time grid that is completely consistent with the baseline using the continuous time axis of the coarse-grained power baseline as a reference and the linear interpolation method is used.

[0032] Subsequently, following the physical logic of steady-state basis - dynamic correction - harmonic compensation, point-by-point weighted superposition is performed. First, the coarse-grained power baseline is used as the power basis component for the entire time period. This component represents the average power level of the load in steady state and quasi-steady state, and comes with a confidence interval of Gaussian process regression output to quantify its estimation uncertainty. Next, transient power increments are superimposed. This component only has non-zero values ​​in dynamic intervals such as load switching and power adjustment identified by the mutation detection algorithm, and remains zero in other steady-state periods. When superimposing, the start and end times of mutations must be strictly matched to ensure that transient details are filled only in intervals where power changes rapidly. Finally, the harmonic power contributions are superimposed. This component is the algebraic sum of the power of the 3rd, 5th, 7th and other major odd harmonics, which exist throughout the entire time period and change slowly with time. When superimposing, the power of each harmonic must be vector synthesized according to its amplitude and phase at the corresponding time and then accumulated point by point.

[0033] After the superposition is completed, the system performs confidence interval synthesis and sampling point consistency verification. Confidence interval synthesis involves performing square root operations on the confidence interval of the coarse-grained power baseline, the transient power increment covariance of the unscented Kalman filter output, and the error variance of the harmonic frequency domain analysis to obtain the comprehensive confidence interval of each sampling point of the full-band power sequence, thus quantifying the uncertainty of the final reconstruction result. Sampling point consistency verification compares the values ​​of the reconstructed full-band power sequence at the original low-frequency sampling time with the instantaneous power values ​​calculated directly from the current and voltage sampling values. If the deviation exceeds a preset threshold, local reconstruction correction is triggered to ensure that the accuracy of the original sampling points is strictly preserved.

[0034] Finally, after slight edge smoothing, the final full-band power sequence is output only for the transition segments at the beginning and end of the abrupt change interval. This sequence covers all frequency components from DC to dozens of harmonics, with a time resolution consistent with the coarse-grained power baseline, and each sampling point is accompanied by a confidence level label.

[0035] Furthermore, in the method provided in the application embodiment, obtaining coarse-grained power baseline and residual data characterizing the main power sequence includes: traversing the current sequence and voltage sequence, obtaining two-dimensional phase points by pairing instantaneous current values ​​and instantaneous voltage values ​​to form a sparse set of phase points; based on the sparse set of phase points, splicing them into a feature vector by mining the geometric features of the point set; performing Gaussian process regression reconstruction on the feature vector to output coarse-grained power baseline and residual data, wherein the coarse-grained power baseline is identified with a confidence interval.

[0036] Specifically, the system first performs phase point pairing and point set construction. The system traverses all sampling points of the two sequences in the order of timestamps. The instantaneous current value at the same moment is used as the horizontal axis and the instantaneous voltage value is used as the vertical axis for one-to-one pairing, generating two-dimensional phase points equal to the number of sampling points. Each two-dimensional phase point is essentially a geometric projection of the electrical state of the power grid at that sampling moment onto the voltage-current plane. All two-dimensional phase points together constitute a sparse phase point set. The sparseness specifically refers to the low-frequency sampling mode of 1 to 10 points per power frequency cycle, which results in an extremely low distribution density of phase points on the voltage-current plane. It is impossible to directly obtain a continuous and accurate power sequence through the traditional instantaneous power integration method, and a large amount of steady-state and quasi-steady-state power details will be lost.

[0037] Subsequently, geometric feature mining was performed on the sparse point set of phase points. Four types of geometric features with clear physical meaning were calculated and extracted in sequence: First, the horizontal and vertical coordinates of the centroid of the point set, which are obtained by the arithmetic mean of the coordinates of all phase points. This directly reflects the phase difference between the fundamental voltage and the fundamental current. The closer the centroid is to the diagonal of the voltage-current plane, the higher the load power factor. Second, the area of ​​the bounding box of the point set, which is obtained by eigenvalue decomposition of the covariance matrix of the sparse point set of phase points. This area is equal to the difference between the instantaneous values ​​of the maximum and minimum currents multiplied by the difference between the instantaneous values ​​of the maximum and minimum voltages. Third, the orientation angle of the principal inertial axis of the point set distribution, which characterizes the overall rotational characteristics of the voltage and current phasors and is used to correct the phase shift caused by grid frequency fluctuations. Fourth, the average radial distance of the point set to the origin, which is obtained by averaging the Euclidean distances of all phase points to the origin. This reflects the comprehensive impedance modulus of the load. The larger the distance, the higher the load impedance and the lower the power consumption. The above four types of geometric features are then spliced ​​together in a preset fixed order to form a multidimensional feature vector.

[0038] Next, the instantaneous power label obtained by directly multiplying the feature vector by the current and voltage at the corresponding sampling time is input into the pre-trained Gaussian process regression model. This model is a non-parametric Bayesian regression method that does not require prior assumptions about the distribution of the data. It is good at handling small sample and nonlinear time series reconstruction problems. It preferably uses a combination of squared exponential covariance function and periodic covariance function as the function. The model learns the nonlinear mapping relationship between the feature vector and the instantaneous power and outputs a continuous coarse-grained power baseline and corresponding residual data covering the entire time interval. The coarse-grained power baseline represents the steady-state and quasi-steady-state principal components in the power sequence and has its own confidence interval output by the Gaussian process regression model, which can quantify the uncertainty in the baseline reconstruction process. The residual data is the difference between the original instantaneous power value at each sampling time and the corresponding value of the coarse-grained power baseline, which includes transient abrupt components and harmonic components that were not captured by the baseline.

[0039] Furthermore, in the method provided in the application embodiment, the geometric features of the point set include the horizontal and vertical coordinates of the centroid of the point set, the area of ​​the bounding box of the point set, the orientation angle of the principal inertial axis of the point set distribution, and the average radial distance of the point set from the origin; wherein, the horizontal and vertical coordinates of the centroid of the point set reflect the phase difference between the fundamental voltage and the current; the area of ​​the bounding box of the point set is obtained by eigenvalue decomposition of the covariance matrix of the sparse point set of phase points, which is the product of the difference between the maximum and minimum instantaneous current values ​​and the difference between the maximum and minimum instantaneous voltage values, and reflects the amplitude range of the apparent power; the average radial distance from the origin reflects the comprehensive impedance modulus of the load.

[0040] Specifically, first, the x and y coordinates of the centroid of the point set are calculated. The centroid of the point set is the geometric center of all phase points on the voltage-current plane. The system traverses N phase points, and for each phase point, the x-coordinate and the instantaneous current value i are calculated. k The vertical axis represents the instantaneous voltage value u. k Summing and dividing by the total number of phase points N, we obtain the centroid coordinates (C). i C u This coordinate value directly reflects the phase difference between the fundamental voltage and the current. When the voltage and current are in phase, the centroid is close to the diagonal of the voltage-current plane. The greater the phase difference, the more significant the centroid deviates from the diagonal.

[0041] Next, the area of ​​the bounding box of the point set is calculated using a robust calculation method based on the eigenvalue decomposition of the covariance matrix. First, a 2×2 covariance matrix of the sparse point set of phase points is constructed, where the diagonal elements are the variances of the current sequence and voltage sequence, respectively, and the off-diagonal elements are the covariances of current and voltage. Then, the covariance matrix is ​​decomposed to obtain two positive eigenvalues ​​λ1 and λ2, which correspond to the dispersion of the phase points in two orthogonal directions, respectively. Through calibration coefficients, √λ1×√λ2 is converted into an equivalent bounding box area with the same dimensions as the difference between the instantaneous values ​​of the maximum and minimum currents multiplied by the difference between the instantaneous values ​​of the maximum and minimum voltages. This area intuitively reflects the amplitude range of the apparent power; the larger the area, the wider the apparent power fluctuation range of the load.

[0042] Next, the orientation angle of the principal inertial axis of the point set distribution is calculated. The principal inertial axis refers to the direction with the greatest dispersion of the phase point distribution, corresponding to the direction of the eigenvector with the larger eigenvalue λ1 in the eigenvalue decomposition of the covariance matrix. The system calculates the angle between this eigenvector and the abscissa and current axis to obtain the orientation angle of the principal inertial axis, which is used to characterize the overall rotational characteristics of the voltage and current phasors and can correct the phase shift error caused by grid frequency fluctuations. Finally, the average radial distance from the point set to the origin is calculated. The radial distance refers to the Euclidean distance √(i) from a single phase point to the origin of the voltage-current plane coordinate system. k ²+u k ²), the system traverses all phase points to calculate the radial distance and then takes the arithmetic mean to obtain the average radial distance. This value reflects the comprehensive impedance modulus of the load. The larger the average radial distance, the higher the load impedance and the smaller the power consumed under the same voltage. After completing the calculation of the four types of features, the system splices the centroid coordinates, bounding box area, principal inertial axis direction angle, and average radial distance of the point set in a preset fixed order to form a four-dimensional feature vector, which is used as the input of the Gaussian process regression model.

[0043] Furthermore, in the method provided in the application embodiment, calculating the transient power increment includes: defining state variables, taking the load power as a flat output, constructing a hybrid differential model through training based on the state transition equation, wherein the equivalent resistance, equivalent inductance and the corresponding first-order time derivative are taken as state variables; inputting the current sequence, voltage sequence and coarse-grained power baseline into the hybrid differential model to obtain the transient power increment.

[0044] Specifically, the state variables are first defined based on the physical nature of the load's electrical characteristics. State variables refer to the smallest set of variables that can completely describe the dynamic behavior of the system. The equivalent resistance R, equivalent inductance L, and their corresponding first-order time derivatives dR / dt and dL / dt are selected as the four-dimensional state variables. At the same time, the model objective is set with load power as the flat output. Here, flat output specifically means that the obtained coarse-grained power baseline is used as a known steady-state smooth background. The model only needs to estimate the dynamic change of load power deviating from this baseline.

[0045] Subsequently, a hybrid differential model was constructed through training based on the state transition equation. This model incorporates fundamental physical laws of circuits, such as Kirchhoff's voltage law and Ohm's law, as hard constraints within its framework. Simultaneously, a statistical stochastic process is introduced to describe the uncertain changes in load parameters. The state transition equation is a mathematical equation describing the continuous evolution of state variables over time. It uses resistive inertia (the physical characteristic of resistive loads causing slow resistance drift due to heating), inductive inertia (the characteristic of inductive loads causing dynamic inductance changes due to core hysteresis and eddy current effects), and the inherent characteristic of millisecond-level lag in power regulation of power electronic loads such as switching power supplies and frequency converters as parameters to construct a state transition equation describing the random walk evolution of load parameters. The four-dimensional state vector is as follows: ; in: : Equivalent load resistance (Ω); : Equivalent inductance of load H; The first-order time derivative of resistance (Ω / s) characterizes the rate of change of resistance. H / s is the first-order time derivative of the inductance, which characterizes the rate of change of the inductance.

[0046] The continuous-time domain state transition equation is: ; in, For, the state vector The first derivative with respect to time, i.e., the instantaneous rate of change of the load state. It is a 4×4 continuous state matrix, representing the coupling relationship and evolution law between state variables. It is a 4-dimensional continuous process noise vector, representing random disturbances in the load parameters.

[0047] This equation simultaneously incorporates three major physical inertial constraints and the evolutionary law of random walk: State matrix Physical constraints: ; The first two lines establish the basic differential relationship between parameter values ​​and the rate of change of parameters; the third line embeds resistive inertia. The resistive thermal time constant describes the characteristic of a resistor slowly drifting due to heating. The larger the value, the smoother the resistance change. Fourth line: Embedded inductive inertia. The inductive magnetic time constant describes the characteristics of an inductor due to dynamic changes caused by hysteresis / eddy currents.

[0048] Process noise vector Random walk evolution: ; It follows a zero-mean Gaussian white noise distribution: It only applies to the rate of change of parameters, corresponding to the random walk of the load parameters as they slowly and randomly fluctuate around their nominal values ​​in steady state, resulting in electronic load response delay. Embedded in the noise covariance matrix of a continuous process In the middle section: By increasing the variance of the corresponding noise term, the hysteresis of power regulation in power electronic loads is simulated. It is the random noise term of the rate of change of resistance. Let be the random noise term of the inductance rate of change, and 0 represent the derivative term where the noise only acts on the state variable. Given a 4×4 continuous process noise covariance matrix, we quantify the intensity and correlation of each noise term. It is a diagonal matrix, only and Non-zero, respectively corresponding to and The variance.

[0049] Discrete-time domain state transition equations, due to the low-frequency discrete sampling used in the energy meter, the sampling intervals... For each power frequency cycle from 1 to 10 points, the continuous equation needs to be discretized using the Euler method to obtain the discrete form of the actual operation: ; in, This is the discrete time step index, i.e., the k-th sampling time. Let be the discrete state vector at the k-th sampling time, i.e., the load state at sampling time k. For the first The discrete state vector at each sampling time, i.e., the load state at the next sampling time. This is a 4-dimensional discrete process noise vector, representing the cumulative random disturbance within the sampling interval. It is a 4×4 discrete state transition matrix, describing the state from time k to... The evolution law, discrete state transition matrix From the continuous state matrix Discretization yields: ; in, The fourth-order identity matrix is ​​the discrete process noise vector. It follows a Gaussian distribution with zero mean: , Let the sampling interval be the time difference between two adjacent sampling times. The transformation relationship between the discrete covariance matrix and the continuous covariance matrix is ​​as follows: ; in, It is a 4×4 discrete process noise covariance matrix, which quantifies the intensity of random disturbances within a sampling interval. The formula is the covariance transformation formula under the Euler method, realizing the transformation from continuous noise to discrete noise.

[0050] The extended form of electronic load response delay, for loads with strong delay characteristics such as switching power supplies and frequency converters, can be directly applied... As parameters of the state matrix, construct the first-order delayed extended state transition equation: ; This form directly simulates the first-order inertial response of load parameters to a control signal, where, The electronic load response time constant, The resistive thermal time constant is is the inductive magnetic time constant.

[0051] Random walk evolution refers to the characteristic of load parameters slowly and randomly fluctuating around the nominal value under steady state. This is consistent with the variation law of load in the actual power grid due to factors such as temperature change, device aging, and operating condition adjustment. The training process of the model is to collect historical operating data of different types of typical loads and calibrate the variance and covariance matrix of the random noise term in the state transition equation so that the model can accurately simulate the transient response behavior of various loads.

[0052] After model construction is completed, the system imports the strictly time-synchronized current and voltage sequences and coarse-grained power baseline output from the previous steps into the hybrid differential model. First, the directly measurable instantaneous current and voltage values ​​are mapped to power observations related to state variables using observation equations derived from Ohm's law. Then, an unscented Kalman filter algorithm is used to perform propagation analysis of the state transition equations. A sigma point set is generated through deterministic sampling and propagated to the next time step. A posteriori recursive update is performed based on the actual sampled values ​​to estimate the hidden state variable sequence in the continuous time domain. Finally, based on the instantaneous power decomposition formula: t; Where p is power, R is resistance, i is current, L is inductance, and t is time. This refers to the Joule heat power consumed by the resistor, which is the active power. t represents the rate of change of magnetic field energy stored / released by the inductor, i.e. reactive power. This yields a power evolution curve containing complete transient details. Finally, the power evolution curve is subtracted point by point from the coarse-grained power baseline on the time axis to obtain the transient power increment containing only the dynamic component of load abrupt changes. This step incorporates a sudden change detection trigger mechanism, which only activates model calculation when the rate of change of the coarse-grained power baseline exceeds a preset threshold. During other steady-state periods, the model remains dormant to reduce power consumption.

[0053] Furthermore, in the method provided in the application embodiment, the current sequence, voltage sequence, and coarse-grained power baseline are input into the hybrid differential model to obtain the transient power increment, including: mapping the low-frequency sampled instantaneous current and voltage values ​​to power observations through observation equations, wherein the power observations include equivalent resistance, equivalent inductance, and time rate of change; based on the power observations, using unscented Kalman filtering, performing propagation analysis based on the state transition equations to determine the hidden state variable sequence; obtaining the power evolution curve based on the hidden state variable sequence, and determining the transient power increment by performing integral calculation.

[0054] Specifically, firstly, the time-synchronized low-frequency sampled current and voltage sequences, along with the coarse-grained power baseline characterizing the steady-state principal component of power, are input into a pre-trained hybrid differential model. The first step is to perform an observation mapping operation, which transforms measurable signals into unmeasurable state parameters through observation equations. These observation equations are mathematical relationships derived from Ohm's law and Kirchhoff's voltage law, mapping the directly collectable instantaneous values ​​of low-frequency sampled current and voltage into power observations that contain internal load state information. The power observations include equivalent resistance, equivalent inductance, and their corresponding first-order time rates of change. These three parameters are core load state parameters that cannot be directly measured by sensors. The observation equations essentially build a bridge between measurable electrical signals and unmeasurable state parameters.

[0055] Subsequently, based on the obtained power observations, an unscented Kalman filter algorithm was used to perform propagation analysis based on the state transition equation. The reason for choosing the unscented Kalman filter instead of the traditional extended Kalman filter is that it does not require linearization approximation of the nonlinear model or calculation of complex Jacobian matrices. While ensuring higher accuracy in nonlinear state estimation, it is more suitable for the limited hardware computing resources of smart meters. The specific process is as follows: First, a sigma point set that can completely cover the probability distribution of state variables is generated through a deterministic sampling strategy. Each sigma point represents a probabilistic combination of equivalent resistance, equivalent inductance, and their time rate of change, and the weighted mean and covariance of all sigma points strictly match the current... The estimated range of the state is determined; then, all sigma points are substituted into the previously defined state transition equation and propagated to the next prediction time. The mean and covariance matrix of the predicted state are calculated as the prior result of the state estimation. Subsequently, the prior predicted state is inversely mapped through the observation equation to obtain the predicted observation value at the corresponding time. The deviation between this and the actual sampled current and voltage observation values ​​is measured, and the Kalman gain matrix is ​​used for posterior recursive update. Finally, the hidden state variable sequence in the continuous time domain is obtained. This hidden state variable sequence is the continuous high-precision estimate of the equivalent resistance, equivalent inductance and their first-order time rate of change, which makes up for the gap in state parameter measurement caused by low-frequency sampling.

[0056] Finally, based on the obtained sequence of hidden state variables and the numerical differential information of the current sequence, the instantaneous power decomposition formula is substituted into: t; The power evolution curve containing complete transient details is calculated. Then, by integrating the difference between the power evolution curve and the coarse-grained power baseline, the interference of steady-state components is eliminated. Finally, the transient power increment containing only the dynamic component of load change is determined. The purpose of the integration calculation is to accurately quantify the cumulative change of power during the transient process. At the same time, the system will perform interval verification on the integration results to avoid distortion of transient components due to numerical errors.

[0057] Furthermore, the method provided in the application embodiment employs unscented Kalman filtering to perform propagation analysis based on the state transition equation, including: using unscented Kalman filtering to generate a sigma point set of state variables through deterministic sampling, wherein each sigma point represents a probabilistic combination based on equivalent resistance, equivalent inductance, and the rate of change of time; propagating the sigma point set to the next prediction time through the state transition equation, calculating the prediction mean and covariance as the prediction state; performing an inverse mapping on the prediction state through the observation equation to obtain the prediction observation; and performing a posterior recursion through a deviation metric on the corresponding prediction observation and sampled observation to obtain a sequence of hidden state variables, wherein the sampled observation belongs to a current sequence or a voltage sequence.

[0058] Specifically, deterministic sampling is first used to generate a sigma point set for the state variables. This deterministic sampling generates a finite number of sampling points using fixed mathematical rules, ensuring that their weighted mean and covariance are strictly equal to the estimated mean and covariance of the current state variables. This allows for accurate representation of the complete probability distribution of the state variables with the fewest possible sampling points. The state variables are four-dimensional: equivalent resistance R, equivalent inductance L, the first-order time derivative of the equivalent resistance dR / dt, and the first-order time derivative of the equivalent inductance dL / dt. Therefore, 2×4+1=9 sigma points are generated according to the standard sampling rules of unscented Kalman filtering. Each sigma point represents a probabilistic combination of the equivalent resistance, equivalent inductance, and their time rate of change, and each point is assigned a corresponding mean weight and covariance weight for subsequent statistical calculations.

[0059] Subsequently, the nine generated sigma points are successively substituted into the pre-constructed state transition equation for time propagation. This state transition equation uses resistive inertia, inductive inertia, and electronic load response delay as core physical constraints to describe the random walk evolution of load parameters in the continuous time domain. After each sigma point is calculated by the state transition equation, its state value at the next prediction time is obtained, forming a propagated sigma point set. The propagated point set is then weighted and summed according to weights to obtain the mean of the predicted state. At the same time, the dispersion of the point set relative to the mean is calculated to obtain the prediction covariance matrix. The two together constitute the prior predicted state, where the prediction mean represents the most likely value of the state variable at the next time step, and the prediction covariance matrix quantifies the uncertainty of the prediction result.

[0060] Next, the prior predicted state is converted into a predicted observation that can be compared with the actual sampled value through the inverse mapping of the observation equation. Here, the inverse mapping refers to substituting the state variables that cannot be directly measured, R, L, dR / dt, and dL / dt, into the observation equation derived based on Ohm's law and Kirchhoff's voltage law, and calculating the predicted current value and predicted voltage value at the corresponding time, thus realizing the transformation from state space to observation space.

[0061] The deviation between the predicted observations and the actual current and voltage observations obtained at the corresponding times is then measured, and the residual vector and residual covariance matrix between the two are calculated. Then, the Kalman gain matrix is ​​calculated based on the residual covariance and the predicted covariance. The Kalman gain is used to balance the credibility of the prior prediction and the credibility of the actual observation. The larger the gain, the more reliable the actual observation, and vice versa.

[0062] Finally, based on the Kalman gain, the prior predicted state is updated posteriorly. The state correction is obtained by multiplying the residual vector by the Kalman gain and adding it to the prior prediction mean to obtain the posterior state mean. At the same time, the covariance matrix is ​​updated to obtain the posterior covariance. This posterior state is the optimal estimate of the hidden state variable at the current time. The system repeats the process of deterministic sampling, state propagation, observation mapping, and posterior update for each low-frequency sampling time, and finally obtains a continuous sequence of hidden state variables covering the entire time interval.

[0063] Furthermore, in the method provided in the application embodiments, the state transition equation uses resistive inertia, inductive inertia, and electronic load response delay as load parameters to describe the random walk evolution law of the load parameters in the continuous time domain.

[0064] Specifically, the state transition equation is first defined. It is a mathematical expression that describes the continuous change of the system's state variables over time. In the Kalman filter framework, it is responsible for propagating the state estimate at the current moment to the next moment. It is a bridge connecting state information at different time points. The state variable is a four-dimensional vector X=[R,L,dR / dt,dL / dt]^T, where R is the equivalent load resistance, L is the equivalent inductance, dR / dt is the first-order time derivative of the resistance, and dL / dt is the first-order time derivative of the inductance. It can completely characterize the dynamic electrical characteristics of resistive, inductive, and mixed resistive-inductive loads.

[0065] Subsequently, the physical characteristics of the three loads are transformed into mathematical constraints and incorporated into the state transition equation: First is resistive inertia, which refers to the physical characteristic of a resistive load whose resistance changes slowly with temperature due to heating caused by energization. Because temperature changes have thermal inertia, the resistance will not change abruptly, and its rate of change dR / dt remains approximately constant in a short time. Therefore, a differential relationship between R and dR / dt is established in the state transition equation: dR / dt = dR / dt, that is, the rate of change of resistance is determined by its own derivative. At the same time, the thermal time constant τ is introduced. R τ describes how quickly resistance changes. R A larger value indicates stronger and slower thermal inertia of the resistance. Secondly, there is inductive inertia, which refers to the physical characteristic of inductance changing with current due to the hysteresis and eddy current effects of the iron core. Changes in inductance also exhibit inertia and do not change instantaneously with sudden changes in current. Therefore, a differential relationship between L and dL / dt is established: dL / dt = dL / dt, and a magnetic time constant τ is introduced. L The first description describes the rate of change in inductance; then comes the response delay of the electronic load, which refers to the inherent millisecond-level lag in the power regulation of power electronic loads such as switching power supplies and frequency converters. The equivalent resistance and inductance of these loads do not immediately respond to changes in the control signal, but rather there is a delay time τ. d Therefore, a delay operator is introduced into the state transition equation, which modifies the rate of change of the state at the current moment with τ.d The state deviation before the time step is correlated to simulate the response hysteresis characteristics of the electronic load.

[0066] Building upon this, a random walk evolution law is introduced to describe the uncertain changes in load parameters. A random walk is a continuous-time stochastic process. It is assumed that the rate of change of the state variables follows zero-mean Gaussian white noise. This assumption aligns with the slow parameter drift characteristics of loads in real power grids caused by random factors such as temperature fluctuations, device aging, and fine-tuning of operating conditions. Therefore, the final form of the state transition equation is constructed as a hybrid form containing deterministic inertia terms and random noise terms. The deterministic term is jointly determined by resistive inertia, inductive inertia, and the electronic load response delay, describing the average evolution trend of the load parameters. The random noise term... The term is represented by the process noise vector w(t), which follows a zero-mean Gaussian distribution. Its covariance matrix Q is called the process noise covariance matrix, which is used to quantify the influence of random factors on the state evolution. Since the energy meter is a digital sampling system, the state transition equation in the continuous time domain needs to be discretized. The Euler method is used to convert the differential equation into a difference equation, and the state transition matrix Φ at the discrete time step Δt is obtained, so that the state X(k+1) at the next time step can be expressed as the product of the current state X(k) and the state transition matrix Φ plus the discretized process noise w(k).

[0067] Finally, key parameters in the state transition equation, including the thermal time constant τ, were determined through typical load calibration experiments. R Magnetic time constant τ L Electronic load response delay τ d The process noise covariance matrix Q is used to collect transient operating data of typical loads such as resistance furnaces, motors, and switching power supplies during the calibration process. The optimal parameter values ​​are obtained by fitting with the least squares method, so that the state transition equation can accurately simulate the transient response behavior of different types of loads.

[0068] Furthermore, in the method provided in the application embodiment, after extracting the harmonic amplitude, phase, and frequency parameters by frequency division, the power contribution of each harmonic is obtained through line impedance mapping inversion, including: performing frequency division filtering on the residual data, using the fundamental steady-state component and transient change component as filtering targets to obtain harmonic residual components; performing segmented frequency domain analysis on the harmonic residual components to extract each harmonic data, wherein each harmonic data includes corresponding amplitude, phase, and frequency characteristic parameters; and performing inversion calculation based on the harmonic data according to the line impedance mapping relationship to restore the power contribution of each harmonic, wherein each harmonic power contribution includes the magnitude of each harmonic injection on the load side and the distribution state of harmonic distortion in the power grid.

[0069] Specifically, the system first receives the residual data output from the previous step. This data is the signal component remaining after the original instantaneous power sequence has been subtracted sequentially from the coarse-grained power baseline, steady-state principal component, transient power increment, and dynamic mutation component. It only contains the harmonic components generated by the power grid and load. However, in reality, a small amount of fundamental steady-state wake and transient spike noise that have not been completely filtered out still remain. Therefore, the system first performs frequency division filtering on the residual data. Frequency division filtering specifically refers to a multi-channel parallel bandpass filter array constructed using an 8th-order Butterworth digital filter bank. The system targets the 50Hz fundamental steady-state component and transient mutation components below 1kHz for filtering. By setting passband intervals that correspond one-to-one with the main odd harmonic frequencies such as the 3rd, 5th, 7th, and 9th, and with a passband width of ±2Hz to adapt to power grid frequency fluctuations, a first-order high-pass filter is connected in series to filter out the DC component. Finally, a pure harmonic residual component without fundamental and transient interference is obtained.

[0070] Subsequently, the harmonic residual components were analyzed in the frequency domain by segmentation. A sliding window segmentation strategy was adopted to divide the harmonic residual components into multiple time segments with a length of 4 power frequency cycles and an overlap rate of 50%. The 50% overlap rate can effectively reduce the segmentation boundary effect and improve the time resolution. A Hanning window function was first applied to each segment to suppress spectral leakage. The window function can smooth the discontinuities at both ends of the signal and reduce the degree of energy diffusion to adjacent frequency points during the FFT process. Then, the FFT operation was performed to obtain the frequency domain amplitude spectrum and phase spectrum of each segment. The peak position of each harmonic was located by the peak detection algorithm, and the corresponding amplitude, phase and frequency parameters, i.e., the amplitude of each harmonic, were extracted, reflecting the harmonic intensity and phase, reflecting the phase relationship between the harmonic and the fundamental frequency and the actual frequency, and correcting the frequency fluctuation error within the ±0.2Hz range of the power grid. Finally, the analysis results of adjacent segments were weighted and fused using a Hanning window to obtain a time-continuous sequence of harmonic parameters.

[0071] Next, based on the pre-calibrated line impedance mapping relationship, inversion calculation is performed. The line impedance mapping relationship refers to the inherent characteristics of low-voltage distribution network transmission lines, where the impedance value increases with increasing frequency and the phase shift increases with increasing frequency due to the skin effect and proximity effect. The system has established a correspondence table of frequency-line resistance-line reactance through on-site calibration experiments. Since the harmonic residual components measured by the energy meter are the result of attenuation and phase shift of the load-side harmonic source after transmission through the line impedance, the system uses a π-type equivalent circuit to construct a transmission mathematical model of load-side harmonic voltage and current - line impedance - energy meter-side harmonic voltage and current. The extracted harmonic amplitude, phase, and frequency parameters are substituted into the model for inverse operation. First, the effective values ​​of harmonic voltage and harmonic current on the load side are calculated. Then, the active and reactive power of each harmonic is calculated using the instantaneous power formula. At the same time, the harmonic contribution of the decoupled load side and grid side is determined by the direction of harmonic power flow: if the harmonic power flows from the load to the grid, it is the harmonic injected by the nonlinear equipment on the load side; if it flows from the grid to the load, it is the harmonic distortion existing in the grid itself. Finally, the power contribution of each harmonic is restored. This contribution not only includes the magnitude and direction of each harmonic injection on the load side, but also quantifies the distortion distribution state of each harmonic on the grid side.

[0072] Furthermore, in the method provided in the application embodiment, the power baseline is used as the steady-state component, the transient power increment is used to fill the abrupt change interval, and the power contribution of each harmonic is superimposed on the entire time period, and point-by-point superposition on the time axis is performed to obtain the full-band power sequence.

[0073] Specifically, the first step is to perform a time axis alignment operation. Since the coarse-grained power baseline is a continuous time series output by Gaussian process regression, the time resolution is usually 1ms, which is much higher than the 2~20ms interval of the original low-frequency sampling. The transient power increment is a high-resolution dynamic sequence that is activated only in the load mutation interval. The time resolution in the mutation interval can reach 0.5ms to capture the peak characteristics. The power contribution of each harmonic is a quasi-continuous sequence obtained by piecewise analysis based on a sliding window. The window step size is usually one power frequency cycle, i.e., 20ms. Using the continuous time axis of the coarse-grained power baseline as a unified benchmark, the transient power increment and the power contribution of each harmonic are resampled to a time grid that is completely consistent with the baseline using linear interpolation, ensuring that the sampling points of the three components at any time strictly correspond one-to-one.

[0074] Subsequently, following the physical logic of steady-state basis - dynamic correction - harmonic compensation, point-by-point vector superposition is performed. First, the coarse-grained power baseline is used as the power basis component for the entire time period. This component represents the average power level of the load in steady state and quasi-steady state, and comes with a confidence interval from the Gaussian process regression output to quantify its estimation uncertainty. During superposition, it is directly used as the initial power value at each time point. Next, transient power increments are superimposed. This component only has non-zero values ​​in the dynamic range of load switching, power regulation, etc., identified and marked by the pre-amplified mutation detection algorithm, and remains zero in other steady-state periods. During superposition, the start and end times of mutations must be strictly matched. Finally, the power contributions of each harmonic are superimposed. This component is the vector sum of the active power of the 3rd, 5th, 7th, and other major odd harmonics. Vector superposition is necessary because the harmonic active power is the product of the in-phase components of harmonic voltage and harmonic current. Phase matching must be performed according to the phase parameters of each harmonic before point-by-point accumulation. Otherwise, the calculated harmonic power value will be too large. After superposition, a preliminary reconstructed power sequence is obtained.

[0075] Next, the system performs sampling point consistency verification and comprehensive confidence interval synthesis. Sampling point consistency verification compares the values ​​of the initially reconstructed power sequence at the original low-frequency sampling time with the true instantaneous power values ​​obtained by multiplying the current and voltage sampling values ​​at the corresponding time. If the deviation exceeds a preset threshold of 0.1%, local reconstruction correction is triggered to ensure that the accuracy of the most reliable physical measurement data, the original sampling point, is strictly preserved. Comprehensive confidence interval synthesis performs square root operations on the confidence interval of the coarse-grained power baseline, the transient power increment covariance of the unscented Kalman filter output, and the error variance of the harmonic frequency domain analysis to obtain the comprehensive confidence interval of each sampling point of the full-band power sequence, quantifying the uncertainty of the final reconstruction result.

[0076] Finally, a slight edge smoothing process is applied to the reconstructed sequence. Three-point moving average smoothing is performed only on the transition segments at the beginning and end of the abrupt change interval. At the same time, the core peak characteristics of the transient process are strictly preserved to ensure the accuracy of transient power measurement. The final output is a full-band power sequence covering all frequency components from DC to the 50th harmonic, with a time resolution of 1ms and a confidence level label for each sampling point.

[0077] In summary, the high-precision power reconstruction method for low-frequency sampling of electricity meters provided in this application has the following technical effects: By transforming low-frequency sampled current and voltage sequences into two-dimensional phase points and mining their geometric features with clear physical meaning, and combining Gaussian process regression to reconstruct a coarse-grained power baseline with confidence intervals, a hybrid differential model integrating resistive inertia, inductive inertia, and physical constraints of electronic load response delay is used. Transient power increments are calculated through propagation analysis of the state transition equation using unscented Kalman filtering. Simultaneously, frequency division analysis and line impedance mapping inversion are performed on the residual data to obtain the power contribution of each harmonic. Finally, the full-band power sequence is obtained by superposition. While retaining the advantages of low power consumption and low cost of low-frequency sampling, the accuracy and reliability of power metering in complex load scenarios of low-voltage distribution networks are improved.

[0078] Example 2, based on the same inventive concept as the high-precision power reconstruction method under low-frequency sampling of the electricity meter in the foregoing examples, such as... Figure 2 As shown in the figure, this application provides a high-precision power reconstruction system for low-frequency sampling of electricity meters. The system includes: The acquisition module 11 is used to acquire low-frequency sampled current and voltage sequences; the mining module 12 is used to obtain coarse-grained power baseline and residual data characterizing the main power sequence by performing two-dimensional phase point pairing and feature vector mining and reconstructing based on Gaussian process regression based on the current and voltage sequences; the analysis module 13 is used to import the current and voltage sequences into a hybrid differential model and calculate the transient power increment by performing state transition equation propagation analysis based on unscented Kalman filtering; the extraction module 14 is used to extract harmonic amplitude, phase and frequency parameters from the residual data by frequency division and obtain the power contribution of each harmonic by line impedance mapping inversion; the superposition module 15 is used to superimpose the coarse-grained power baseline, transient power increment and the power contribution of each harmonic to obtain the full-band power sequence.

[0079] Furthermore, the mining module 12 is also used to perform the following steps: traversing the current sequence and voltage sequence, obtaining two-dimensional phase points by pairing instantaneous current values ​​and instantaneous voltage values, and forming a sparse point set of phase points; according to the sparse point set of phase points, splicing it into a feature vector by mining the geometric features of the point set; performing Gaussian process regression reconstruction on the feature vector, and outputting coarse-grained power baseline and residual data, wherein the coarse-grained power baseline is identified with a confidence interval.

[0080] Furthermore, the mining module 12 is also used to perform the following steps: the geometric features of the point set include the horizontal and vertical coordinates of the centroid of the point set, the area of ​​the bounding box of the point set, the orientation angle of the principal inertial axis of the point set distribution, and the average radial distance of the point set from the origin; wherein, the horizontal and vertical coordinates of the centroid of the point set reflect the phase difference between the fundamental voltage and the current; the area of ​​the bounding box of the point set is the product of the difference between the maximum instantaneous current value and the minimum instantaneous current value, and the difference between the maximum instantaneous voltage value and the minimum instantaneous voltage value, obtained by eigenvalue decomposition of the covariance matrix of the sparse point set of phase points, reflecting the amplitude range of the apparent power; the average radial distance of the origin reflects the comprehensive impedance modulus of the load.

[0081] Furthermore, the analysis module 13 is also used to perform the following steps: defining state variables, with load power as the flat output, and constructing a hybrid differential model through training based on the state transition equation, wherein the equivalent resistance, equivalent inductance and the corresponding first-order time derivative are used as state variables; inputting the current sequence, voltage sequence and coarse-grained power baseline into the hybrid differential model to obtain transient power increments.

[0082] Furthermore, the analysis module 13 is also used to perform the following steps: mapping the instantaneous current and voltage values ​​sampled at low frequencies to power observations through observation equations, wherein the power observations include equivalent resistance, equivalent inductance, and time rate of change; based on the power observations, performing propagation analysis based on the state transition equations using unscented Kalman filtering to determine the hidden state variable sequence; obtaining the power evolution curve based on the hidden state variable sequence, and determining the transient power increment by performing integral calculations.

[0083] Furthermore, the analysis module 13 is also used to perform the following steps: using unscented Kalman filtering, a sigma point set of state variables is generated through deterministic sampling, wherein each sigma point represents a probabilistic combination based on equivalent resistance, equivalent inductance, and the rate of change of time; the sigma point set is propagated to the next prediction time through a state transition equation, and the prediction mean and covariance are calculated as the prediction state; the prediction state is inversely mapped through an observation equation to obtain the prediction observation; for the corresponding prediction observation and sampled observation, a posterior recursion is performed through a deviation metric to obtain the hidden state variable sequence, wherein the sampled observation belongs to a current sequence or a voltage sequence.

[0084] Furthermore, the analysis module 13 is also used to perform the following steps: the state transition equation is defined using resistive inertia, inductive inertia and electronic load response delay as load parameters, and describes the random walk evolution law of the load parameters in the continuous time domain.

[0085] Furthermore, the extraction module 14 is also used to perform the following steps: performing frequency division filtering on the residual data, using the fundamental steady-state component and transient change component as filtering targets to obtain harmonic residual components; performing segmented frequency domain analysis on the harmonic residual components to extract each harmonic data, wherein each harmonic data includes corresponding amplitude, phase and frequency characteristic parameters; relying on the line impedance mapping relationship, performing inversion calculation based on each harmonic data to restore the power contribution of each harmonic, wherein the power contribution of each harmonic includes the magnitude of each harmonic injection on the load side and the distribution state of harmonic distortion in the power grid.

[0086] Furthermore, the mining module 12 is also used to perform the following steps: using the power baseline as the steady-state component, filling the abrupt change interval with the transient power increment, and superimposing the power contributions of each harmonic on the entire time period, performing point-by-point superposition on the time axis to obtain the full-band power sequence.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A high-precision power reconstruction method for low-frequency sampling of electricity meters, characterized in that, The method includes: Obtain low-frequency sampled current and voltage sequences; Based on the current and voltage sequences, by performing two-dimensional phase point pairing and feature vector mining, and using reconstruction based on Gaussian process regression, coarse-grained power baseline and residual data characterizing the main power sequence are obtained. The current and voltage sequences are imported into a hybrid differential model, and the transient power increment is calculated by performing a propagation analysis of the state transition equation based on unscented Kalman filtering. For the residual data, after extracting the harmonic amplitude, phase and frequency parameters by frequency division, the power contribution of each harmonic is obtained by line impedance mapping inversion. By superimposing the coarse-grained power baseline, transient power increment, and power contribution of each harmonic, a full-band power sequence is obtained.

2. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 1, characterized in that, We obtained coarse-grained power baseline and residual data characterizing the main power sequence, including: By traversing the current sequence and voltage sequence, two-dimensional phase points are obtained by pairing instantaneous current values ​​with instantaneous voltage values, thus forming a sparse set of phase points; Based on the sparse point set of phase points, geometric features of the point set are extracted and concatenated into a feature vector; The feature vector is reconstructed using Gaussian process regression, and coarse-grained power baseline and residual data are output, wherein the coarse-grained power baseline is identified with a confidence interval.

3. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 2, characterized in that, The geometric features of the point set include the x and y coordinates of the centroid of the point set, the area of ​​the bounding box of the point set, the orientation angle of the principal inertial axis of the point set distribution, and the average radial distance of the point set from the origin. The horizontal and vertical coordinates of the centroid of the point set reflect the phase difference between the fundamental voltage and the current. The area of ​​the bounding box of the point set is the product of the difference between the maximum instantaneous current value and the minimum instantaneous current value, and the difference between the maximum instantaneous voltage value and the minimum instantaneous voltage value. This is obtained by eigenvalue decomposition of the covariance matrix of the sparse point set of phase points, and reflects the amplitude range of the apparent power. The average radial distance from the origin reflects the overall impedance modulus of the load.

4. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 1, characterized in that, Calculating transient power increments includes: Define state variables, with load power as the flat output, and construct a hybrid differential model through training based on the state transition equation, where the equivalent resistance, equivalent inductance and the corresponding first-order time derivative are the state variables; The current sequence, voltage sequence, and coarse-grained power baseline are input into the hybrid differential model to obtain the transient power increment.

5. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 4, characterized in that, The current sequence, voltage sequence, and coarse-grained power baseline are input into the hybrid differential model to obtain transient power increments, including: By using the observation equation, the instantaneous values ​​of current and voltage sampled at low frequency are mapped to power observations, wherein the power observations include equivalent resistance, equivalent inductance and time rate of change. Based on the power observations, an unscented Kalman filter is used to perform propagation analysis based on the state transition equations to determine the sequence of hidden state variables. The power evolution curve is obtained from the hidden state variable sequence, and the transient power increment is determined by integral calculation.

6. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 5, characterized in that, Using unscented Kalman filtering, propagation analysis based on the stated state transition equation is performed, including: An unscented Kalman filter is used to generate a set of sigma points for the state variables through deterministic sampling. Each sigma point represents a probabilistic combination based on the equivalent resistance, equivalent inductance and the rate of change of time. The sigma point set is propagated to the next prediction time through the state transition equation, and the prediction mean and covariance are calculated as the prediction state. By inversely mapping the predicted state through the observation equation, the predicted observation value is obtained; For the corresponding predicted and sampled observations, a posterior recursion is performed using a deviation metric to obtain a sequence of hidden state variables, wherein the sampled observations are current or voltage sequences.

7. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 4, characterized in that, The state transition equations use resistive inertia, inductive inertia, and electronic load response delay as load parameters to describe the random walk evolution of load parameters in the continuous time domain.

8. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 1, characterized in that, After extracting the harmonic amplitude, phase, and frequency parameters by frequency division, the power contribution of each harmonic is obtained through line impedance mapping inversion, including: The residual data is subjected to frequency division filtering, with the fundamental steady-state component and transient abrupt component as the filtering targets, to obtain the harmonic residual components; The harmonic residual components are subjected to segmented frequency domain analysis to extract the harmonic data of each order, wherein each harmonic data includes the corresponding amplitude, phase and frequency characteristic parameters. Based on the line impedance mapping relationship, an inversion calculation based on the harmonic data is performed to restore the power contribution of each harmonic. The power contribution of each harmonic includes the magnitude of each harmonic injection on the load side and the distribution state of harmonic distortion in the power grid.

9. The high-precision power reconstruction method for low-frequency sampling of an energy meter as described in claim 1, characterized in that, Using the power baseline as the steady-state component, the transient power increment fills the abrupt change interval, and the power contribution of each harmonic is superimposed on the entire time period, point-by-point superposition on the time axis is performed to obtain the full-band power sequence.

10. A high-precision power reconstruction system for low-frequency sampling of an electricity meter, characterized in that, The system is used for implementing the high-precision power reconstruction method for low-frequency sampling of an energy meter according to any one of claims 1 to 9, wherein the system comprises: The acquisition module is used to acquire low-frequency sampled current and voltage sequences; The mining module is used to obtain coarse-grained power baseline and residual data characterizing the main power sequence by performing two-dimensional phase point pairing and feature vector mining based on the current sequence and voltage sequence, and by using reconstruction based on Gaussian process regression. The analysis module is used to import the current sequence and voltage sequence into a hybrid differential model, and calculate the transient power increment by performing a propagation analysis of the state transition equation based on unscented Kalman filtering. The extraction module is used to extract harmonic amplitude, phase and frequency parameters from the residual data by frequency division, and then obtain the power contribution of each harmonic by line impedance mapping inversion. The overlay module is used to overlay the coarse-grained power baseline, transient power increment, and power contribution of each harmonic to obtain a full-band power sequence.

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