Source end data driven node voltage uncertainty quantification method and device

Abstract

The invention discloses a source end data driven node voltage uncertainty quantification method and device, and provides a quantification method for solving the problem that the voltage prediction deviation degree is large due to the fact that the phenomenon of right data deletion is neglected and the complex colinearity of source end data and user side data is generally existed in a low-voltage transformer area. Firstly, a source-load aggregation linear sensitivity model is derived based on a physical power flow equation; secondly, an inverse probability deletion weighting mechanism is introduced to improve a folding knife method model average ridge regression algorithm, and the voltage-power sensitivity is identified from biased truncation data under the condition of no topological parameters; meanwhile, a source end split-phase competition mechanism is used for jointly identifying phases to which nodes belong; and finally, establishing a linear mapping relation from the source end power uncertainty to the node voltage uncertainty, realizing the uncertainty quantification of the node voltage, and effectively solving the problems of low-voltage distribution network perception and risk assessment in a data limited and photovoltaic scene.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network operation and control technology, and more specifically, to a source-end data-driven method and apparatus for quantifying node voltage uncertainty. Background Technology

[0002] The penetration rate of new energy sources, represented by distributed photovoltaic (PV), in low-voltage distribution networks is continuously increasing. To date, distributed PV has become an important mode for power generation and clean energy consumption. However, the output of distributed PV is significantly affected by meteorological factors such as solar irradiance and temperature, exhibiting significant intermittency and volatility. When a high proportion of PV is connected to low-voltage distribution areas, it can easily lead to safety issues such as power flow backflow and node voltage exceeding limits. Therefore, accurately quantifying the uncertainty of node voltage is of great significance for improving the sensing capability and operational resilience of the distribution network.

[0003] Currently, methods for voltage analysis and prediction in distribution networks are mainly divided into two categories: the first category is based on physical models. These methods rely on accurate distribution network topology and line impedance parameters to solve for voltage distribution through power flow calculations. However, actual low-voltage distribution areas commonly suffer from problems such as missing data, outdated topology updates, and unknown line parameters, making it difficult to directly apply traditional physical model methods.

[0004] The second category is data-driven methods. In recent years, deep learning algorithms such as Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNN) have been widely used in voltage prediction. However, these methods are usually "black box" models with poor physical interpretability and extremely high requirements for data quality.

[0005] Despite some progress in voltage prediction, key technical challenges remain unresolved in practical low-voltage distribution scenarios.

[0006] First, the phenomenon of "right censoring" in data is overlooked. Most existing data-driven methods assume that historical data is complete and accurate. However, in actual operation, when the voltage at the photovoltaic grid connection point exceeds the safety threshold, the photovoltaic inverter automatically triggers overvoltage control (such as Volt-Watt control) to derating or trip the inverter. This results in the true values ​​of the high-voltage portion in the collected historical measurement data being truncated or hidden (statistically known as "right censoring"). If these biased truncated data are directly used for training, the model will severely underestimate the risk of voltage exceeding the limit, a point rarely addressed in existing literature.

[0007] Secondly, there is the issue of multicollinearity between source-side and user-side data. In low-voltage distribution areas, power fluctuations at the source (low-voltage side of the distribution transformer) are highly coupled with user-side load and photovoltaic output, and significant multicollinearity exists among multi-source data. Traditional methods such as least squares regression exhibit extremely large variance in parameter estimation under these circumstances, making it difficult to obtain stable sensitivity coefficients. Thirdly, low-voltage distribution areas commonly suffer from errors or missing user phase records. Most existing voltage analysis methods assume that the distribution area topology is known; if the topology information is incorrect, it will directly lead to the failure of voltage-power sensitivity calculations.

[0008] In summary, there is an urgent need for a method that can accurately quantify voltage uncertainty even when topology parameters are unknown and measurement data suffers from right-hand censoring due to inverter control. Summary of the Invention

[0009] This invention overcomes the shortcomings of existing transformer area assessment methods, which ignore the "right censoring" phenomenon in data and suffer from large voltage prediction deviations due to the multicollinearity of source and user-side data. It provides a source-side data-driven node voltage uncertainty quantification method and apparatus, which can improve the neglect of the multicollinearity and "right censoring" phenomenon in source and user-side data, thereby predicting voltage more accurately and requiring less topology information and data accuracy.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0011] A source-side data-driven method for quantifying node voltage uncertainty includes the following steps: S1. Based on the disFlow power flow equation, construct a source-to-node two-factor linear observation model based on load and photovoltaic variations:

[0012] In the formula, and Let represent the squares of the voltage at node i and the source terminal, respectively. and The sensitivity of node i to net load fluctuations and photovoltaic back-transmission characteristics; For nodes Baseline sensitivity to net load fluctuations; For nodes Sensitivity to correction of photovoltaic back-feed characteristics; For nodes The combined error of higher-order nonlinear terms, user random behavior bias, and measurement noise. It is a fluctuation in the net load at the source; It is a typical photovoltaic power output; S2. Collect and preprocess data from the source and user sides of the low-voltage distribution area, and obtain the preliminary user phase based on the source phase competition mechanism; S3. Construct an inverse probabilistic censoring weighted (IPCW) matrix to correct data bias, combine it with weights constructed based on the Kaplan-Meier method, form and apply a weight diagonal matrix, and use the improved folding knife method model average ridge regression (JMAR) algorithm to estimate sensitivity and output the minimum statistical bisector phase. S4. Decompose the node voltage reconstruction error into background noise and photovoltaic noise, and quantize the voltage using an engineering approximation based on a given confidence range. Preferably, the data in step S2 is preprocessed using the Z-score method for normalization.

[0013] As a preferred option, the construction of the weighted ridge regression in step S3 also includes: Set multiple Candidate models are established, and leave-one-out cross-validation is used to evaluate them to obtain the average prediction error weight of each model. The final prediction value is obtained by weighted averaging based on the prediction results.

[0014] As a preferred approach, the projection matrix is ​​calculated based on the candidate model, the corresponding prediction error vector is calculated and represented in matrix form, the error matrix is ​​constructed, and the corresponding weights are obtained by solving the quadratic programming problem.

[0015] Preferably, step S2 further includes: utilizing the independent fluctuation characteristics of the three-phase voltage at the source end, constructing a phase competition model at the source end based on the data, and preliminarily determining the user phase by minimizing the signal reconstruction residual.

[0016] Preferably, the voltage quantization in step S5 includes: establishing a linear mapping from the uncertainty of source power to the uncertainty of node voltage, so as to achieve uncertainty quantization of node voltage.

[0017] As a preferred approach, the uncertainty of node voltage is analyzed by quantifying the root mean square error.

[0018] As a preferred approach, the engineering approximation voltage is a Gaussian distribution.

[0019] Preferably, step S3 further includes calculating the minimum cross-validation risk of the user belonging to the three electrical times based on the sensitivity to confirm the phase in which the user is located.

[0020] An apparatus for quantifying source-driven low-voltage substation node voltage uncertainty includes a processor and a memory, the processor being configured to read instructions from the memory to execute any of the methods described above.

[0021] Compared with the prior art, the beneficial effects of the present invention are: (1) No topology parameters required. It only relies on source and user side measurement data, without needing to know the specific network topology and line impedance, making it suitable for transformer substations with missing data.

[0022] (2) Resistance to data truncation interference. The IPCW mechanism effectively restores the true voltage fluctuation trend "hidden" by the inverter control, improving the voltage prediction accuracy under high photovoltaic penetration.

[0023] (3) Joint phase and parameter identification. It can identify voltage sensitivity while calibrating the user's phase assignment, thus improving the physical interpretability of the model.

[0024] (4) Accurate risk assessment. The heteroscedastic Gaussian model constructed in this invention fully considers the dynamic amplification effect of photovoltaic power output level on voltage prediction error. Compared with the traditional homoscedasticity assumption, the voltage confidence interval generated by this invention has better coverage (reliability) and narrower average interval width (sharpness) during peak photovoltaic power generation periods, which can more accurately capture the critical state of voltage exceeding the limit and avoid false alarms and missed alarms. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the present invention.

[0026] Figure 2 This is a typical user model training graph from an embodiment.

[0027] Figure 3 This is a node voltage uncertainty quantization diagram of an embodiment.

[0028] Figure 4 This is a training diagram of a photovoltaic node model in an embodiment.

[0029] Figure 5 This is a quantification diagram of the voltage uncertainty of photovoltaic nodes in the embodiment. Detailed Implementation

[0030] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0031] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0032] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0033] like Figure 1 As shown, a source-side data-driven method for quantifying node voltage uncertainty includes the following steps: S1. Based on the disFlow power flow equation, construct a source-to-node two-factor linear observation model based on load and photovoltaic variations:

[0034] In the formula, and Let represent the squares of the voltage at node i and the source terminal, respectively. and The sensitivity of node i to net load fluctuations and photovoltaic back-transmission characteristics; For noise error, It is a fluctuation in the net load at the source; It is a typical photovoltaic power output; S2. Collect and preprocess data from the source and user sides of the low-voltage distribution area, and obtain the preliminary user phase based on the source phase competition mechanism; S3. Construct an inverse probabilistic censoring weighted (IPCW) matrix to correct data bias, combine it with weights constructed based on the Kaplan-Meier method to form a weight diagonal matrix, and use the improved folding knife method model average ridge regression (JMAR) algorithm to estimate sensitivity and output the minimum statistical bisector phase. S4. Decompose the node voltage reconstruction error into background noise and photovoltaic noise, and quantize the voltage using an engineering approximation voltage based on a given confidence range.

[0035] Linear sensitivity derivation based on DistFlow: For any branch in a radial low-voltage distribution network, assuming it connects upstream node i and downstream node j, the classic DistFlow equations describe the nonlinear relationship between node voltage and branch power, consisting of power balance equations and voltage drop equations:

[0036] In the formula, Let i and j represent the voltage magnitudes at nodes i and j, respectively. It is the set of nodes downstream of node j; , Let them represent the active power flow and reactive power flow of node ij, respectively; These represent the resistance and reactance between nodes i and j, respectively. These are the active power and reactive power of nodes i and j, respectively.

[0037] To simplify the derivation, the voltage drop equation is rewritten as follows:

[0038] In the formula, Let i and j represent the squares of the voltage amplitudes at nodes i and j, respectively.

[0039] For ease of derivation, we define: , (The square of the voltage amplitude); (The square of the line impedance modulus); (The square of the apparent power of the branch) get:

[0040] The above equation can be linearized by setting the following conditions: To calculate the voltage-to-power sensitivity, we perform: When building the model, set the nodes. Injection power It is an independent variable, and does not change with the power of other nodes, that is...

[0041] For low-voltage distribution networks, neglecting the minute increment of losses, the power flowing through the branches... It equals the sum of the injected power of all nodes downstream of that branch. If the node Power is injected downstream of the branch. Changes in will be fully reflected in ; otherwise, they will be 0.

[0042]

[0043] In the formula, For nodes The set of downstream nodes.

[0044] Step S3: When constructing the model, it is assumed that changes in active power have minimal impact on reactive power flow.

[0045]

[0046] We can conclude that on low-voltage lines, voltage drop and power loss are very small, and second-order terms can be ignored.

[0047]

[0048] set up The expression is:

[0049] right Differentiation yields:

[0050] right Differentiation yields:

[0051] We can obtain:

[0052] because

[0053] The voltage drop on the line is much smaller than the nominal voltage and can often be ignored. Based on this,

[0054] visible, The impact is minimal, compared and

[0055]

[0056] It can be seen that this can be ignored. .

[0057] Based on this, the linearized expression for active power and reactive power is as follows:

[0058] The above derivation shows that the second-order nonlinear term caused by branch losses is numerically much smaller than the dominant linear term determined by line impedance. This also means that within the operating range of a low-voltage distribution network, the derivative of the node voltage with respect to the injected power can be considered a constant. Based on this conclusion, to construct an explicit expression of the overall network voltage state, combining the previous formula and performing a multivariate first-order Taylor series expansion of the node voltage function at the system's no-load operating point, the linear sensitivity model can be obtained as follows:

[0059] Due to the unclear topology of low-voltage distribution areas, the matrix formed by the obtained data has low-rank characteristics. Starting from the statistical characteristics of high-dimensional data, we demonstrate the sparse expression of the node injection power vector on the low-dimensional manifold, and derive the macroscopic mapping model by combining the physical sensitivity equation.

[0060] Consider a low-voltage distribution area with N users. Define the active and reactive power injection vectors of all nodes in the network at time t as follows: , Since photovoltaic (PV) power and user load exhibit significantly different behaviors, the net injection at any node k is decomposed into two orthogonal components: load and PV power, expressed as:

[0061] In the formula Let be the active power injection vector for node k at time t, representing the load consumption. It is the active and reactive power vector of the photovoltaic output at node k at time t.

[0062] The active and reactive power injection vectors are , The performance exhibits volatility, but at the same regional scale, user behavior and photovoltaic processing show significant low-rank characteristics. We will analyze the system-level load modes across the entire region. and photovoltaic mode Based on spectral clustering theory, the node power vector can be approximated as a two-dimensional linear manifold spanned by these two latent factors, as expressed below:

[0063] In the formula, This is the load distribution characteristic vector, characterizing the response strength of each node's load as the total system load changes; correspondingly, The photovoltaic distribution feature vector characterizes the synchronicity of photovoltaic output at each node with changes in irradiance.

[0064] Ignoring reactive power directly will lead to model bias. Since household appliances such as refrigerators or air conditioners have relatively stable power factors, they can be regarded as linear dependent variables of active power load, and the expression is:

[0065] For photovoltaics, the photovoltaic inverters in the actual distribution area are operating in unity power factor mode, which can be considered... .

[0066] Substituting the above formulas, the summarized expression is:

[0067] In the formula, , Due to the total system load Since it cannot be directly measured, the net power is measured using a distribution transformer gate meter. Variable elimination was performed, and the measured photovoltaic power of a typical user was introduced. As a coherent proxy for the total photovoltaic mode of the system, the following expression can be obtained:

[0068] In the formula, For typical measured photovoltaic power, the system-level photovoltaic power is obtained through a coefficient K. The total system load is obtained by subtracting the photovoltaic power from the system's net load, i.e. .

[0069] The final form is:

[0070] After obtaining the two-factor linear observation model, data on the voltage of the transformer substations that need to be monitored are collected: Considering the significant order-of-magnitude difference between the source-end net power and the photovoltaic reference signal, and the potential inclusion of occasional measurement outliers in the measured data, the data is processed using the Z-score method for standardization, expressed as:

[0071] In the formula, , These are the mean and variance, respectively, which improves the comparability of the data.

[0072] Perform preliminary phase identification: Phase identification based on source-side phase competition. This method utilizes the independent fluctuation characteristics of the three-phase voltages at the source. For any user, the reconstructed residuals are calculated by substituting the three-phase voltages. Based on the principle of minimum statistical risk, the phase with the smallest residual is the true phase.

[0073] Phase identification and initial value acquisition are performed based on a source-end phase competition mechanism. A source-end phase competition model is constructed using the independent fluctuation characteristics of the three-phase voltage at the source. This model determines the phase by minimizing the signal reconstruction residual. For the user to be identified, it is assumed that they belong to... Given {A,B,C}, calculate the following objective function.

[0074]

[0075] In the formula, Belongs to The root node voltage value during phase; , Assuming the node belongs to The load reference sensitivity and photovoltaic correction sensitivity to be identified at different phase times; These are the root node power and the reference photovoltaic power, respectively, after Z-Score standardization.

[0076] The results obtained in this way align with engineers' physical intuition, and compared to subsequent methods, it requires less computation, allowing for pre-screening of massive datasets.

[0077] Phase discrimination and sensitivity estimation are performed on the obtained data: The user's load is always applied to a specific phase of the three-phase electricity. By utilizing the independent fluctuation characteristics of the three phase voltages at the source, any user is brought into the two-factor linear observation model to reconstruct the residuals. According to the principle of minimum statistical risk, the phase with the smallest residual is the true phase.

[0078] The solution is based on the parameters of IPCW-JMAR. An IPCW matrix is ​​constructed to identify the moments when the voltage exceeds the inverter threshold. The Kaplan-Meier estimator was used to calculate the uncensored probability. Construct weights This method can assign greater weight to untruncated high-voltage samples to compensate for truncation loss. Then, to overcome the arbitrariness of choosing a single regularization parameter, a method is constructed that includes... A set of candidate ridge parameters For each phase assumption Construct the input feature matrix and voltage drop vector For each element in the set The corresponding candidate component estimator is calculated using the following expression:

[0079] We obtain the following by weighting and combining all candidate models:

[0080] In the formula, The model weight vector is determined by minimizing the leave-one-out cross-validation criterion.

[0081] Specifically, to simplify the calculation, the projection matrix of the m-th candidate model is defined as follows:

[0082] Then construct a diagonal magnification matrix:

[0083] in, for The diagonal elements then transform the model's average cross-validation criterion into:

[0084] In the formula, ,in, Let the fast one-to-one error of the m-th model be given by the following constraints:

[0085] This method can reduce the computational complexity from O(n³M) to O(n²M), thereby improving efficiency.

[0086] This estimator automatically balances bias and variance: high-performing models (small LOO-CV error) receive larger weights, while low-performing models receive smaller weights. Through averaging, it effectively smooths out the variance. Estimated fluctuations caused by improper selection.

[0087] Based on the optimal weighted model calculated by JMAR, the minimum cross-validation risk is calculated when user i belongs to phases A, B, and C respectively.

[0088]

[0089] In summary, the final true physical phase and the final sensitivity parameter estimates are as follows:

[0090] In the formula, To identify the phase of user i,

[0091] Voltage uncertainty quantification: Given the significant intermittency and volatility of photovoltaic (PV) output in low-voltage distribution networks, the node voltage prediction error is not constant but exhibits heteroscedasticity strongly correlated with the source-side PV injection power. To achieve risk assessment under topology-free and parameter-limited conditions, a probabilistic modeling method is proposed, expressed as:

[0092] The voltage reconstruction error at node i is decomposed into background noise and photovoltaic-induced noise. Furthermore, after reconstruction using JMAR, the error is primarily composed of the superposition of multi-source random noise. Based on the central limit theorem, a Gaussian distribution can be used to provide a reasonable engineering approximation of the error. The following variance model is constructed.

[0093]

[0094] In the formula, standard deviation Defined as a function of the photovoltaic reference signal, its expression is:

[0095] In the formula, The background noise level, which is the voltage fluctuation noise caused by random switching of user loads, can be obtained through the JMAR reconstruction error statistics at night. The photovoltaic fluctuation transmission coefficient represents the amplification effect of photovoltaic power output uncertainty on voltage fluctuations. This coefficient can be obtained by fitting a linear relationship between the absolute value of historical residuals and photovoltaic power output.

[0096] For a given confidence level Its upper and lower boundaries are shown below:

[0097] In addition, there is an apparatus for quantifying the voltage uncertainty of low-voltage substation nodes driven by source data, including a processor and a memory, wherein the processor is configured to read instructions from the memory to execute the method described in any of the preceding descriptions.

[0098] Example: The low-voltage distribution area of ​​Huishan Village, Zhejiang Province, was selected for verification. The data includes measurement data from the source end, some users, and the photovoltaic side, with a resolution of 15 minutes. The ratio of training set to validation set was set to 3:2. Data from June 1st to June 9th was used for phase identification and sensitivity parameter training. Data from June 10th was used to verify the effectiveness of voltage uncertainty quantification.

[0099] The root mean square error (RMSE) is introduced to analyze the accuracy of deterministic predictions. The calculation formula is as follows.

[0100]

[0101] In the formula, These are the actual value and the predicted result of the test sample at sampling point t, respectively. This represents the number of test samples.

[0102] The test results are as follows: like Figures 2 to 5 As shown in the figure below, and in the table below:

[0103] This embodiment proposes a method for estimating node voltages and quantifying risks using source-end data without relying on distribution network topology files and line parameters. Based on actual data testing in the Huishan Village transformer substation in Zhejiang Province, the following conclusions are drawn.

[0104] (1) In complex scenarios involving residential, agricultural, industrial and commercial, and photovoltaic users, the average error of the method in estimating node voltage is 0.0053. This accuracy indicates that even without the assistance of power grid physical model parameters, the real-time voltage change trajectory can be accurately reconstructed by relying solely on source-side measurement data.

[0105] (2) The model demonstrates good adaptability to users with varying load characteristics. For residential and agricultural users, whose load behavior is relatively random, the model can effectively capture their fluctuation patterns, with the estimation error for some typical users as low as 0.0021 to 0.0035. For industrial and commercial users facing impact loads, the model can still control the error to around 0.0023, proving the algorithm's ability to track large power fluctuations.

[0106] (3) Statistical data shows that the average error of the model on the training set (0.0052) is highly consistent with that on the test set (0.0053), and the standard deviation of the two is only 0.0018. This indicates that the algorithm effectively overcomes the multicollinearity problem among multi-source data, does not exhibit overfitting, and has the ability to work stably under different time periods and different operating conditions.

[0107] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Other variations and modifications may be made without departing from the technical solutions described in the claims.

Claims

1. A source-side data-driven method for quantifying node voltage uncertainty, characterized in that, The steps include: S1. Based on the disFlow power flow equation, construct a source-to-node two-factor linear observation model based on load and photovoltaic variations: In the formula, and Let represent the squares of the voltage at node i and the source terminal, respectively. and The sensitivity of node i to net load fluctuations and photovoltaic back-transmission characteristics; For noise error, It is a fluctuation in the net load at the source; It is a typical photovoltaic power output; S2. Collect and preprocess data from the source and user sides of the low-voltage distribution area, and obtain the preliminary user phase based on the source phase competition mechanism; S3. Construct an inverse probabilistic censoring weighted (IPCW) matrix to correct data bias, combine it with weights constructed based on the Kaplan-Meier method, form and apply a weight diagonal matrix, use the folding knife method model average ridge regression (JMAR) algorithm to estimate sensitivity and output the minimum statistical bisector phase. S4. Decompose the node voltage reconstruction error into background noise and photovoltaic noise, and quantize the voltage using an engineering approximation based on a given confidence range. Preferably, the data in step S2 is preprocessed using the Z-score method for normalization.

2. The source-side data-driven node voltage uncertainty quantification method according to claim 1, characterized in that, The data in step S2 is preprocessed using the Z-score method for standardization.

3. The source-side data-driven node voltage uncertainty quantification method according to claim 1, characterized in that, The JMAR (Junior Ridge Regression) algorithm for the folding knife method model in step S3 includes: setting multiple... Candidate models are established, and leave-one-out cross-validation is used to evaluate them to obtain the average prediction error weight of each model. The final prediction value is obtained by weighted averaging based on the prediction results.

4. The source-side data-driven node voltage uncertainty quantification method according to claim 3, characterized in that, The projection matrix is ​​calculated based on the candidate model, the corresponding prediction error vector is calculated and represented in matrix form, the error matrix is ​​constructed, and the corresponding weights are obtained by solving the quadratic programming problem.

5. The source-side data-driven node voltage uncertainty quantification method according to claim 1, characterized in that, Step S2 also includes: utilizing the independent fluctuation characteristics of the three-phase voltage at the source end, constructing a phase competition model at the source end based on the data, and preliminarily determining the user phase by minimizing the signal reconstruction residual.

6. The source-side data-driven node voltage uncertainty quantification method according to claim 5, characterized in that, Step S3 further includes calculating the minimum cross-validation risk of the user belonging to the three electrical times based on the sensitivity to confirm the phase in which the user is located.

7. The source-side data-driven node voltage uncertainty quantification method according to claim 1, characterized in that, The voltage quantization in step S5 includes: establishing a linear mapping from the uncertainty of source power to the uncertainty of node voltage, so as to realize the uncertainty quantization of node voltage.

8. The source-side data-driven node voltage uncertainty quantification method according to claim 1, characterized in that, Analysis of the uncertainty of node voltage through root mean square error quantification results.

9. A source-side data-driven node voltage uncertainty quantification method according to claim 8, characterized in that, The engineering approximation of voltage is based on a Gaussian distribution.

10. An apparatus for quantifying source-driven low-voltage substation node voltage uncertainty, comprising a processor and a memory, characterized in that, The processor is configured to read instructions from the memory to execute the method according to any one of claims 1 to 9.

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