A main and distribution integrated power flow calculation method and system considering missing data completion

Abstract

A main-distribution integrated power flow calculation method and system considering missing data completion. The spatiotemporal characteristics of the node power data at the time point where the data is missing in the actual operation of the distribution network are completed; the power injected into the distribution network by the boundary node is initialized, and the power flow calculation of the transmission network is performed; the transmission network at the boundary node is equivalent to the Thevenin equivalent circuit, and the equivalent parameters are calculated; the equivalent parameters are enhanced by historical data modeling, and the power injected into the transmission network by the boundary node is updated based on the completed data and the enhanced equivalent parameters; according to the power injected into the transmission network by the boundary node before and after the update, it is judged whether this iteration meets the convergence criterion; if so, the iteration is terminated, otherwise iterative feedback update is performed; the power injected into the transmission network by the boundary node after the update is used to update the equivalent parameters of the Thevenin equivalent circuit, and the equivalent circuit representation is returned. The present invention improves the accuracy and stability of the overall power flow calculation through the gradual convergence of the coupling relationship between the distribution network and the transmission network.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent operation and maintenance of power systems, and particularly relates to a main and distribution integrated power flow calculation method and system considering missing data completion. Background Art

[0002] In the context of the continued development of smart grids, the coordinated operation and analysis of main and distribution networks are crucial. As a core component of power system analysis, integrated main and distribution power flow calculations provide a key basis for grid planning and design, operation and dispatch, and security assessments.

[0003] In order to improve the accuracy of power flow calculations, many scholars have also conducted many in-depth studies. The patent application with publication number CN111181164A equates the distribution network to a constant power load in the transmission network, and equates the transmission network to a Thevenin model in the distribution network, effectively improving the convergence and calculation speed under heavy loads. This method reduces the spectral radius of the iterative matrix, has fast parameter calculation, and is less affected by power fluctuations. It is suitable for planning and online analysis under transmission and distribution coordination. The patent application with publication number CN112383063A uses the least squares method to fit and correct the iterative variables, which significantly improves the efficiency and robustness of the overall algorithm for transmission and distribution coordinated power flow calculation, especially when the distribution network has a large disturbance on the transmission network, and can solve the problem of divergence of the traditional master-slave splitting method.

[0004] However, in the actual process of power data collection and transmission, data missing from the distribution network frequently occurs due to irregularities in data collection and transmission at low-voltage distribution substations. The commonly used regression-based infill method completely ignores the spatiotemporal characteristics of power data when addressing missing data. Power data exhibits temporal correlations in time series, and data from different measurement points exhibit spatial correlations. The regression-based infill method fails to exploit these characteristics, resulting in the infilled data failing to accurately reflect the actual patterns of power data variation, severely impacting the accuracy of subsequent power flow calculations.

[0005] In summary, existing data completion methods and integrated power flow calculation methods have obvious shortcomings. To address these issues, a new method is urgently needed that can effectively complete various types of missing data and improve the convergence of integrated power flow calculations, providing stronger support for the reliable operation of power systems. Summary of the Invention

[0006] Purpose: To address the deficiencies in the prior art, the present application provides a main and distribution integrated power flow calculation method and system that considers missing data completion. First, based on spatiotemporal tensor modeling and deep convolutional autoencoder networks, input features of time and space dimensions are jointly constructed to complete the missing data of node power in the distribution network. Then, by introducing a symmetrically structured convolution-deconvolution network and a residual connection mechanism, combined with a customized missing mask loss function, the accuracy of missing point recovery is improved. Next, the main and distribution integrated power flow is iteratively calculated based on the completed data. During the iteration process, the boundary information between the main and distribution is dynamically interacted and the equivalent parameters are updated, and a time convolution network based on historical data modeling and an attention mechanism is introduced to enhance the estimation accuracy and robustness of the Thevenin equivalent voltage and impedance.

[0007] The first aspect of the present invention provides a main and distribution integrated power flow calculation method considering missing data completion, which adopts the following technical solutions:

[0008] Step 1: determine the missing time points in the actual operation data of the distribution network, and perform spatiotemporal feature completion on the missing values ​​of the node power data at the missing time points;

[0009] Step 2: Initialize the power injected into the distribution network by the boundary nodes and perform power flow calculation on the transmission network. Equate the transmission network at the boundary nodes to a Thevenin equivalent circuit and calculate the equivalent parameters, including equivalent voltage and equivalent impedance.

[0010] Step 3: Enhance the equivalent parameters using historical data modeling, and update the power injected into the transmission network by the boundary node based on the supplemented data and enhanced equivalent parameters in step 1;

[0011] Step 4: Determine whether this iteration satisfies the convergence criterion based on the power injected into the transmission network by the boundary nodes before and after the update; if so, terminate the iteration; if not, proceed to step 5;

[0012] Step 5: Update the equivalent parameters of the Thevenin equivalent circuit using the power injected into the transmission network by the updated boundary node, and return to step 3.

[0013] Furthermore, step 1 includes:

[0014] Arrange the power data of all nodes in the distribution network at the missing time point into a one-dimensional vector according to the spatial dimension;

[0015] Based on the one-dimensional vector, the continuous The node power data of the time window is recorded as the first time dimension data; before the introduction The historical node power data at the same time as the missing time point in the cycle is recorded as the second time dimension data;

[0016] The one-dimensional vector, the first time dimension data and the second time dimension data are fused to construct a space-time tensor; the size of the space-time tensor is: ,in, Represents the constructed space-time tensor; is the number of distribution network nodes; is the number of consecutive historical moments, is the number of periodic time points; represents the set of real numbers.

[0017] Furthermore, the spatiotemporal tensor is input into a deep convolutional autoencoder network for missing data completion, including:

[0018] The deep convolutional autoencoder network includes an encoder, a decoder and a residual connection module;

[0019] Inputting the spatiotemporal tensor into an encoder, extracting spatiotemporal joint features of node power data through multiple layers of one-dimensional convolution, wherein residual connections are introduced between multiple convolution layers within the encoder;

[0020] The decoder adopts a symmetrical structure with the encoder, and reconstructs the missing values ​​of the node power data through deconvolution to obtain the completed data tensor;

[0021] The output of the decoder is the non-missing part of the original data and the completed data tensor of the missing time points.

[0022] Furthermore, during the training of the deep convolutional autoencoder network, a binary mask is used to mark the data location of the missing time points and optimize the loss function. This step is expressed as:

[0023] ;

[0024] in, is the optimized loss function in the deep convolutional autoencoder network, and Missing time points The original power data tensor and the completed data tensor, Missing time point The corresponding binary mask, ” is the Hadamard product, ” denotes the Euclidean norm.

[0025] Furthermore, the process of obtaining the equivalent parameters in step 2 includes:

[0026] Initialize the power injected into the distribution network by the boundary node; based on the current boundary node power injection value, use the Newton-Raphson method to calculate the transmission network power flow to obtain the boundary node voltage and the transmission network node voltage;

[0027] Equivalently equating the transmission network to a Thevenin equivalent circuit, the equivalent voltage and equivalent impedance are calculated:

[0028] ;

[0029] in, and The transmission network The original values ​​of the equivalent voltage and equivalent impedance at the boundary nodes are: 、 and The transmission network The voltage, voltage increment and load current of each boundary node.

[0030] Furthermore, the enhancement process of the equivalent parameters includes:

[0031] Construct the original values ​​of the equivalent parameters of the mth boundary node at the past p moments as a time series:

[0032] ;

[0033] Where, Indicates the The boundary nodes at time The original value of the equivalent voltage; represents the corresponding equivalent impedance;

[0034] The time series Inputting the prediction result of the equivalent parameters at the current moment into the TCN-Attention network output; wherein, the TCN-Attention network parameters are optimized using the measured values ​​of the equivalent parameters at the historical moments;

[0035] The enhanced equivalent parameters are expressed as:

[0036] ;

[0037] Where, 、 For the The boundary nodes are The equivalent voltage and equivalent impedance after momentary enhancement are used for subsequent distribution network flow calculation; and They are the equivalent voltage prediction value and equivalent impedance prediction value output by the TCN-Attention network respectively; 、 、 and are the weight coefficients corresponding to each item in the formula.

[0038] Furthermore, the updating of the power injected into the transmission network by the boundary node includes:

[0039] The distribution network nodes are divided into PQ nodes, PV nodes, and balancing nodes, and the active power and reactive power of the PQ nodes, as well as the active power and voltage amplitude of the PV nodes, are obtained from the completed data in step 1.

[0040] The distribution network flow is calculated based on the enhanced equivalent parameters to obtain the boundary node voltage vector and the power vector injected into the distribution network by the boundary node in this round of iterative update. ;

[0041] in, That is, the power injected into the distribution network by the updated boundary node described in step 4 .

[0042] Furthermore, in step 4, the convergence criterion is expressed as:

[0043] ;

[0044] Where, and They represent the power injected into the transmission grid by the boundary nodes obtained in the previous and current iterations respectively; represents the norm calculation, which is used to quantify the power deviation between two iterations; is the preset convergence threshold.

[0045] Furthermore, in step 5, the current boundary node is injected with power Transfer to the transmission network. Recalculate the transmission network flow, expressed as:

[0046] ;

[0047] in, represents the power flow calculation function of the transmission network; is the transmission network node voltage vector to be recalculated, is the boundary node voltage vector to be recalculated, The power vector injected from the boundary node to the distribution network is the power vector of the transmission network, that is, the current boundary node injection power ;

[0048] Based on the results of the recalculation of the transmission network power flow, the actual voltage of the boundary nodes is calculated, the parameters of the Thevenin equivalent circuit are updated, and the equivalent model used in the next round of iteration is obtained;

[0049] Return to step 3 to perform the next round of distribution network power flow calculation.

[0050] A second aspect of the present application provides a main and distribution integrated power flow calculation system that considers missing data completion, and runs the main and distribution integrated power flow calculation method provided in the first aspect of the present application, the system comprising:

[0051] The data completion module is used to determine the time points at which data are missing in the actual operation data of the distribution network, and to complete the spatiotemporal characteristics of the missing values ​​of the node power data at the missing time points;

[0052] The equivalent modeling module is used to initialize the power injected into the distribution network at the boundary nodes and perform power flow calculations on the transmission network. It equates the transmission network at the boundary nodes to a Thevenin equivalent circuit and calculates equivalent parameters, including equivalent voltage and equivalent impedance.

[0053] an equivalent circuit characterization module, configured to enhance the equivalent parameters by using historical data modeling, and update the power injected into the transmission network by the boundary node based on the supplemented data and the enhanced equivalent parameters in the data supplementation module;

[0054] An iterative process judgment module is used to judge whether the current iteration meets the convergence criterion based on the power injected into the transmission network by the boundary nodes before and after the update; if so, the iteration is terminated; if not, the iterative feedback update module is executed;

[0055] The iterative feedback update module updates the power injected into the transmission network by the updated boundary nodes to update the equivalent parameters of the Thevenin equivalent circuit and returns to the equivalent circuit characterization module.

[0056] Technical solution: In order to solve the above technical problems, the technical solution adopted by the present invention is: a main-distribution integrated power flow calculation method that takes into account the completion of missing data, realizes the accurate completion of the missing power data of the distribution network, and performs efficient and accurate main-distribution integrated power flow calculation on this basis. First, the power data of the distribution network is converted into a one-dimensional convolutional space-time tensor suitable for deep learning processing, and the powerful feature extraction and data reconstruction capabilities of the deep convolutional autoencoder network are used to complete the missing data. Then, the transmission network is equivalently processed through the Thevenin equivalent circuit, and the distribution network power flow calculation and the transmission network power flow calculation are combined. Under the condition of considering the power interaction of the boundary nodes, multiple iterations are carried out until the convergence criterion is met to obtain a high-precision power flow calculation result.

[0057] Through the above technical solution, the present invention has at least one of the following beneficial effects, including:

[0058] 1. The present invention systematically solves the problem of missing power data at distribution network nodes by introducing a missing data completion process based on spatiotemporal tensor modeling and deep convolutional autoencoder networks. This method jointly models spatial and temporal features to construct a spatiotemporal input tensor to capture short-term changes and periodic laws of the data. Features are extracted and missing values ​​are reconstructed through a symmetrically structured convolution-deconvolution network, and the ability to transmit deep information is enhanced by combining residual links. The customized missing mask loss function further focuses on the accuracy of missing point completion to avoid overfitting. The final completed data is used for subsequent main and distribution integrated flow calculations, providing a high-quality data foundation for improving overall accuracy and stability.

[0059] 2. By introducing an iterative loop mechanism integrating the main and distribution networks, this method enables the distribution network and transmission network to continuously exchange boundary information in each round of calculations, dynamically updating equivalent parameters and achieving gradual convergence of the coupling relationship between the two. This method not only improves the stability and accuracy of power flow calculations but also addresses issues such as missing data and measurement errors in actual projects. It balances the model's computational efficiency with the fidelity of the system's characterization, demonstrating excellent engineering applicability and robustness.

[0060] 3. This invention uses historical data modeling to enhance the Thevenin equivalent parameters, effectively alleviating the instability issues caused by noise, measurement errors, or transient disturbances in single-time data. By introducing a temporal convolutional network with attention (TCN-Attention), it not only extracts the time series characteristics of equivalent voltage and impedance, but also adaptively focuses on historical moments that are more critical to the current prediction, thereby improving the accuracy and robustness of parameter estimation. This method enhances the credibility of equivalent parameters under multiple time periods and complex operating conditions, helping to improve the stability of distribution network flow calculations and the convergence efficiency of the overall main and distribution integrated flow iteration. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Implementation flow chart of the present invention. DETAILED DESCRIPTION

[0062] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0063] Example 1

[0064] This embodiment is used to describe in detail a specific implementation method of a main and distribution integrated power flow calculation method considering missing data completion, including steps 1 to 5, referring to Figure 1.

[0065] Step 1: Determine the missing time points in the actual operation data of the distribution network, and perform spatiotemporal feature completion on the missing values ​​of the node power data at the missing time points;

[0066] The time point at which the data needs to be supplemented is determined by the missing data in the actual operation data of the distribution network. As the target time of the completion process, the data completion process is started.

[0067] Step 1.1: Construct the power data of all nodes in the distribution network at that moment into a one-dimensional vector arranged in spatial dimensions. To fully explore the temporal and spatial correlation of power data, two additional time dimension information is introduced on the basis of the above one-dimensional spatial vector:

[0068] (1) Continuous before this moment time windows Data is used to depict short-term change trends;

[0069] (2) The moment is before At the same moment in the cycle Historical power data, where represents the period index, It is the number of time periods within a unit period, used to reflect periodic characteristics.

[0070] Finally, the data with spatial dimensions are stacked in time order to form an input tensor with spatiotemporal characteristics, whose size is:

[0071] ;

[0072] Where, Represents the constructed space-time tensor; is the number of distribution network nodes; is the number of consecutive historical moments, used to capture short-term fluctuations; is the number of periodic time points, used to capture periodic patterns; represents the set of real numbers, indicating the space-time tensor All elements in are real numbers.

[0073] Step 1.2: Arrange the power data of all nodes in the distribution network at the missing time point into a one-dimensional vector according to the spatial dimension;

[0074] Based on the one-dimensional vector, the continuous The node power data of the time window is recorded as the first time dimension data; before the introduction The historical node power data at the same time as the missing time point in the cycle is recorded as the second time dimension data;

[0075] The one-dimensional vector, the first time dimension data and the second time dimension data are fused to construct a space-time tensor;

[0076] The dimensions of the spacetime tensor are: ,in, Represents the constructed space-time tensor; is the number of distribution network nodes; is the number of consecutive historical moments, is the number of periodic time points; represents the set of real numbers.

[0077] Step 1.3: Convert the space-time tensor Input into the improved deep convolutional autoencoder network to complete the missing data and output the complete data completion result.

[0078] The improved deep convolutional autoencoder network includes an encoder, a decoder, and a residual connection module. Assume that the encoder has Layer, decoder corresponds to Layer, encoder layer( ) and the decoder For example, the output feature map of the first layer of the encoder is used as the output feature map of the first layer of the decoder. The input of the layer, the second layer of the encoder corresponds to the first layer of the decoder layer, and so on.

[0079] The encoder consists of multiple layers of one-dimensional convolutional layers to extract the spatiotemporal joint features of node power data; layer( ), whose output feature map is defined as:

[0080] ;

[0081] Where, For encoder The input feature map of the layer (initial input is the space-time tensor); For the The weight parameters of the layer convolution kernel; For the The bias term of the layer; " is a one-dimensional convolution operation; is an activation function used to introduce nonlinear transformation.

[0082] The decoder and encoder have an inverse symmetric structure. layer( ) is:

[0083] ;

[0084] Where, For decoder The input feature map of the layer (initial input is the output of the last layer of the encoder), is the power data after filling in the missing values; For decoder The independent weight parameters of the layer deconvolution kernel are the same as the encoder weights There is no shared relationship, only structural symmetry; For the The independent bias term of the layer, and the encoder bias No shared relationships, only structural symmetry;" ” is a one-dimensional deconvolution operation; is the activation function, which is consistent with the encoder.

[0085] To improve the network's expressiveness and training stability in deep structures, residual connections are introduced. These connections are set between multiple convolutional layers within the encoder. They are used to introduce an identity mapping path within the convolutional module, allowing the network to learn nonlinear changes while retaining the original input information. This structure uses skip connections to allow error signals to propagate directly from deep layers to shallow layers, effectively alleviating the vanishing gradient problem.

[0086] Assume that the encoder The input of the layer is the spatiotemporal feature map ,in is the number of distribution network nodes, is the fused time dimension (including short-term and periodic time windows).

[0087] The mapping function of the residual structure is expressed as:

[0088] ;

[0089] Where, is the nonlinear transformation function to be learned; Indicates the The nonlinear transformation of the layer convolution operation, is the output of the residual unit (original data or the output of the previous layer), which is directly used as the first The input of the layer; For the The weight parameters of the convolution kernel of the layer; the weight parameters of the last layer of the encoder Output to the decoder for data reconstruction.

[0090] The key mathematical property of this structure is that its derivative is of the form:

[0091] ;

[0092] This shows that even the deep network Approaching zero, the identity mapping term It can still ensure that the gradient is effectively transmitted to the shallow layer, avoiding the gradient disappearance during the training process.

[0093] In step 1, the space-time tensor After being processed layer by layer by the encoder, the first layer input is , the last layer output The data is then passed to the decoder for data reconstruction. Residual connections are implemented throughout all convolutional layers of the encoder to ensure that deep features always contain both local and global information of the original spatiotemporal tensor.

[0094] During the training of a deep convolutional autoencoder network, a custom loss function based on a missingness mask is used to focus the model on the reconstruction accuracy of missing locations. Masking is a common technique in machine learning and deep learning, especially in tasks that deal with missing data or require attention to specific regions. Here, the mask is a binary tensor that indicates the missing locations, with values ​​corresponding to 1 for these missing locations and 0 for non-missing locations. This mask, which has the same shape as the data, is used to identify which data points require optimization during training.

[0095] This loss function marks the missing position through a binary mask, optimizes the prediction error of the missing point only, suppresses overfitting of the non-missing area, and improves the effectiveness of the completed data. It is defined as follows:

[0096] ;

[0097] Where, is the loss function of the deep convolutional autoencoder network; Indicates the index of the time point sample, specifically the location of the missing data to be filled time; For the The raw power data tensor at each time point (including missing values, dimension ); For the model The output power data tensor after completion at each time point; For the The binary mask corresponding to each time point has the same dimension as same;" " is the Hadamard product (element-wise multiplication);" " represents the Euclidean norm, which is used to measure the error between the predicted value and the true value in the missing position.

[0098] Step 1.4: The output of the model consists of the non-missing parts retained in the original data and the missing parts filled in by the model, expressed as:

[0099] ;

[0100] In the formula, the subscript Indicates the index of the time point sample; For the The final completed power data at each time point; For the The non-missing part of the original data at each time point; For the model The missing part is completed at a certain time point.

[0101] Step 2: Initialize the main and distribution integrated power flow calculation and transmission network modeling.

[0102] Step 2.1: System Division: Divide the main and distribution integrated system into the transmission network, the distribution network, and boundary nodes, denoted as TN (Transmission Network), DN (Distribution Network), and Boundary Node (B). Boundary nodes are defined as the interface nodes connecting the transmission and distribution networks, i.e., the root nodes of the distribution network. Topologically, they mark the end point of the transmission network and the beginning point of the distribution network.

[0103] Step 2.2: Initialize the power of the boundary nodes; Based on the empirical value, initialize the power injected into the distribution network by the boundary nodes to form the initial power vector. The power injected into the distribution network at any moment constitutes the vector . Subscript Indicates the number of iterations, at this time .

[0104] Step 2.3: Calculate the power flow of the transmission network. Based on the current power injection value of the boundary node, the Newton-Raphson method is used to calculate the power flow of the transmission network, which is expressed as:

[0105] ;

[0106] Where, represents the power flow calculation function of the transmission network; is the quantity to be determined, which represents the voltage vector of the transmission network node; is the quantity to be determined, representing the voltage vector of the boundary node; is a known quantity, which represents the power vector injected from the transmission network to the distribution network from the boundary node, and its value is Through the calculation of transmission network flow, we can get 、 .

[0107] Step 2.4: Thevenin equivalent modeling; equate the transmission network to a Thevenin equivalent circuit and calculate the equivalent voltage and equivalent impedance of the Thevenin equivalent circuit. Thevenin equivalent circuit is a classic method for simplifying complex power systems. Its basic idea is that the electrical behavior of any two-terminal network outside its port can be equivalent to a voltage source and a series impedance. Among them, the Thevenin equivalent voltage is the voltage measured when the port is open-circuited, and the Thevenin equivalent impedance is the equivalent impedance seen from the port after all independent power sources are set to zero. Specifically:

[0108] The transmission network is equivalent to a voltage source and series impedance at each boundary node. Equivalent to the Thevenin equivalent circuit, in essence, the entire transmission network is represented by a voltage source and series impedance at the boundary node. There are boundary nodes The voltage source and series impedance are combined to simplify the computational complexity of the distribution network power flow calculation and improve the convergence and efficiency of the main and distribution integrated power flow calculation.

[0109] 2.4.1: Equivalent voltage calculation; for the transmission network nodes, , this node is a boundary node, and the equivalent voltage can be expressed as:

[0110] ;

[0111] Where, For the transmission grid The original value of the equivalent voltage of the Thevenin equivalent circuit at each boundary node; For the transmission grid The actual voltage of each boundary node is known through power flow calculation; For the transmission grid The voltage increment at each boundary node.

[0112] Voltage increment The calculation can be performed by injecting the load current in reverse to simulate the open circuit state. Its essence is to achieve the effect of open circuit by applying a current in the opposite direction of the original load current while keeping the network structure unchanged. The specific calculation is done by the following formula:

[0113] ;

[0114] In the formula, the left matrix is the node admittance matrix; is the number of transmission network nodes; For the transmission grid The load current of a boundary node can be calculated by the following formula:

[0115] ;

[0116] Where, is the power injected into the distribution network from the boundary node, Part of a vector, represents a complex conjugate number.

[0117] 2.4.2: Equivalent impedance calculation; for the transmission network For each boundary node, the equivalent impedance can be expressed as:

[0118] ;

[0119] Where, For the transmission grid The original value of the equivalent impedance of the Thevenin equivalent circuit at each boundary node.

[0120] Step 3: The entire transmission network is characterized by a Thevenin equivalent circuit at the boundary nodes;

[0121] In step 2, the reverse injection method was used to obtain Moment The original values ​​of the equivalent voltage and equivalent impedance of the boundary nodes.

[0122] Step 3.1: Enhance the Thevenin equivalent parameters using historical data modeling;

[0123] Since the operation of the power system has obvious time series correlation, the equivalent parameters at a single moment are often easily affected by noise interference, measurement errors or transient disturbances, resulting in unstable calculation results. Therefore, it is necessary to introduce historical data for smoothing to improve the robustness and credibility of the equivalent parameters.

[0124] Pick The equivalent voltage and equivalent impedance of a total of p moments before the moment are obtained based on the time convolutional network with attention mechanism (TCN-Attention) technology. The equivalent voltage and equivalent impedance used in the distribution network power flow calculation at all times. Specifically:

[0125] Step 3.1.1: Time series construction; suppose The equivalent voltage and equivalent impedance of the boundary nodes at the past p moments are:

[0126] ;

[0127] Where, Indicates the The boundary nodes at time The original value of the equivalent voltage; Indicates the corresponding original value of equivalent impedance.

[0128] Step 3.1.2: Time Series Modeling; the input sequence It is input into the TCN-Attention network to capture the dynamic characteristics of the time series.

[0129] Compared to the traditional TCN network structure, the TCN-Attention network, with its introduction of the attention mechanism, has a stronger ability to identify key moments in the temporal dimension. Traditional TCN networks assign equal weights to features output at different historical moments, making it impossible to distinguish key moments that have a greater impact on the current prediction. The attention mechanism, however, adaptively assigns weights to different time steps, enabling the model to focus on historical features that are more representative of the current prediction.

[0130] Step 3.1.3: Loss optimization; To train the TCN-Attention neural network, use the actual measurement values ​​at historical moments as supervision labels and optimize the network parameters by minimizing the mean squared error loss function:

[0131] ;

[0132] Where, is the total number of boundary nodes; is the weighting coefficient of impedance error, which is used to balance the weights of voltage and impedance in the loss function; 、 Respectively The boundary nodes at the current moment The predicted values ​​of equivalent voltage and equivalent impedance.

[0133] The output of the TCN-Attention network represents the prediction result of the equivalent parameters at the current moment:

[0134] ;

[0135] Where, Represents the trained TCN-Attention network function; parameters Contains the weights and biases of the network.

[0136] Step 3.1.4: Predict output; The equivalent voltage and equivalent impedance used in the distribution network flow calculation at each moment are obtained by weighting two parts, one of which is the predicted value after the TCN-Attention network. , the other part is the original value , expressed as:

[0137] ;

[0138] ;

[0139] Where, 、 For the The boundary nodes are The enhanced equivalent voltage and equivalent impedance used in the distribution network power flow calculation at all times; 、 、 、 is the weight coefficient.

[0140] Step 3.2: Based on the completed data in step 1, the weighted equivalent voltage and equivalent impedance, the power flow calculation of the distribution network is performed again;

[0141] 3.2.1: Node Classification and Input Preparation: Classify distribution network nodes into PQ nodes, PV nodes, and balancing nodes. PQ nodes require their active and reactive power, PV nodes require known active power and voltage amplitude, and balancing nodes, as voltage references, require fixed voltage amplitudes and phase angles. The required data is obtained based on the completed data from step 1.

[0142] Due to the irregularities in data collection and transmission at low-voltage distribution substations, power data loss in distribution networks frequently occurs. In step 1, the missing power data for all nodes has been supplemented. For the The raw power data tensor of each time point (including missing values), For the If the completion process is missing, the power of the PQ node and PV node cannot be known, making it difficult to directly perform power flow calculations.

[0143] 3.2.2: Distribution network flow calculation: The Newton-Raphson method is used to calculate the distribution network flow, which is expressed as:

[0144] ;

[0145] Where, represents the distribution network power flow calculation function; is the voltage vector of the distribution network node; is the boundary node voltage vector, which is a value to be calculated, although the transmission network flow calculation in step 2 has already obtained a value of the boundary node voltage vector ,Here, it is necessary to perform distribution network flow calculation and recalculate the boundary node voltage vector, so the symbols are different. The superscript DN is the abbreviation of distribution network, which means the boundary node voltage vector obtained in the distribution network flow calculation; The power vector injected from the boundary node of the transmission network into the distribution network is a value to be evaluated, although the same meaning variable is used in the transmission network power flow calculation in step 2. ,Here, it is necessary to perform distribution network flow calculation and recalculate the boundary node injection power, so the symbols are different. The superscript DN is the abbreviation of distribution network, which means the boundary node injection power obtained in the distribution network flow calculation; is the enhanced boundary node equivalent voltage vector; is the enhanced boundary node equivalent impedance vector.

[0146] Through the distribution network flow calculation, we can get 、 as well as ,at this time After iteration .

[0147] Step 4: The power injected into the transmission network by the boundary nodes obtained in the previous iteration , and the current iteration , calculate whether the deviation between the two is less than or equal to the preset convergence threshold;

[0148] If so, the convergence criterion is met and the iteration is terminated; if not, the next iteration is entered (step 5);

[0149] The convergence criterion is expressed as:

[0150] ;

[0151] Where, represents the norm calculation, which is used to quantify the power deviation between two iterations; is the preset convergence threshold.

[0152] Step 5: Feedback updates the equivalent model used in the next iteration;

[0153] Step 5.1: Inject power into the current boundary node Transfer to the transmission network. Recalculate the transmission network flow, expressed as:

[0154] ;

[0155] Where, represents the power flow calculation function of the transmission network; is the voltage vector of the transmission network node, which is an unresolved value and needs to be recalculated; is the boundary node voltage vector, which is an unresolved value and needs to be recalculated; The power vector injected from the boundary node of the transmission network into the distribution network is the last obtained in step 3. Known value, value is .

[0156] Through the transmission network flow calculation, the updated 、 .

[0157] Similar to step 3, before using the Newton-Raphson method to calculate the power flow of the transmission network, the missing power data of all nodes have been supplemented in step 1. Otherwise, the active power and reactive power of the PQ nodes and PV nodes cannot be known, making it difficult to directly calculate the power flow.

[0158] Step 5.2: Based on the recalculated results of the transmission network, calculate the actual voltage of the boundary node, recalculate the Thevenin equivalent voltage and equivalent impedance, and use this to update the Thevenin equivalent circuit parameters to obtain the equivalent model used in the next iteration.

[0159] Step 5.3: Return to step 3 and perform the next round of distribution network flow calculation to achieve alternating coupling iteration between the main and distribution networks.

[0160] The core idea of ​​the integrated power flow calculation for the main and distribution systems in this application is to use an alternating iterative method to perform power flow calculations on the distribution network and the transmission network separately in each iteration. Specifically, in the distribution network power flow calculation stage, the Thevenin equivalent circuit of the transmission network (i.e., equivalent voltage source and series impedance) is used to replace the real transmission network to construct the electrical conditions of the boundary nodes; in the transmission network power flow calculation stage, the distribution network is equivalent to a constant power load injected into the boundary nodes, thereby simplifying its impact on the transmission network. Through continuous iteration, the dynamic coupling and convergence solution between the main and distribution systems are achieved, and the intermediate variables of the alternating iteration are the power injected into the distribution network at the boundary nodes, and the Thevenin equivalent circuit parameters of the transmission network, including equivalent voltage and equivalent impedance.

[0161] The transmission network used in this example is the IEEE 30 system, and the radial distribution network is the 69-node system of the PG&E distribution network. Table 1 shows the error of the data completed by the deep convolutional autoencoder network under different data missing rates. It can be seen that the proposed method can achieve small errors even at higher data missing rates, verifying the effectiveness of the data completion method used in this invention. Table 2 shows the number of iterations and errors of the power flow calculation under different load conditions of the radial distribution network. The data in the table show that when the radial distribution network is overloaded, the proposed method has fewer iterations, better convergence performance, and higher calculation accuracy, verifying the effectiveness of the proposed method.

[0162] Table 1. Errors of data completed by deep convolutional autoencoder network under different data missing rates

[0163]

[0164] Table 2. The number of iterations and errors of power flow calculation under different load conditions in radial distribution network

[0165]

[0166] Example 2

[0167] This embodiment is used to describe in detail a main and distribution integrated power flow calculation system that considers missing data completion. The system adopts a main and distribution integrated power flow calculation method as described in Example 1. The system includes:

[0168] The data completion module is used to determine the time points at which data are missing in the actual operation data of the distribution network, and to complete the spatiotemporal characteristics of the missing values ​​of the node power data at the missing time points;

[0169] The equivalent modeling module is used to initialize the power injected into the distribution network at the boundary nodes and perform power flow calculations on the transmission network. It equates the transmission network at the boundary nodes to a Thevenin equivalent circuit and calculates equivalent parameters, including equivalent voltage and equivalent impedance.

[0170] An equivalent circuit characterization module is configured to enhance the equivalent parameters by using historical data modeling, and update the power injected into the transmission network by the boundary node based on the supplemented data and the enhanced equivalent parameters in step 1;

[0171] An iterative process judgment module is used to judge whether the current iteration meets the convergence criterion based on the power injected into the transmission network by the boundary nodes before and after the update; if so, the iteration is terminated; if not, step 5 is executed;

[0172] The iterative feedback update module updates the power injected into the transmission network by the updated boundary node to update the equivalent parameters of the Thevenin equivalent circuit, and then returns to step 3.

[0173] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A main and distribution integrated power flow calculation method considering missing data completion, characterized in that: The method comprises the following steps: Step 1: Determine the missing time points in the actual operation data of the distribution network, and perform spatiotemporal feature completion on the missing values ​​of the node power data at the missing time points; arrange the power data of all nodes in the distribution network at the missing time points into a one-dimensional vector according to the spatial dimension; Based on the one-dimensional vector, the continuous The node power data of the time window is recorded as the first time dimension data; before the introduction The historical node power data at the same time as the missing time point in the cycle is recorded as the second time dimension data; The one-dimensional vector, the first time dimension data and the second time dimension data are fused to construct a space-time tensor; the size of the space-time tensor is: ,in, Represents the constructed space-time tensor; is the number of distribution network nodes; is the number of consecutive historical moments, is the number of periodic time points; represents the set of real numbers; The spatiotemporal tensor is input into a deep convolutional autoencoder network for missing data completion, including: The deep convolutional autoencoder network includes an encoder, a decoder and a residual connection module; Inputting the spatiotemporal tensor into an encoder, extracting spatiotemporal joint features of node power data through multiple layers of one-dimensional convolution, wherein residual connections are introduced between multiple convolution layers within the encoder; The decoder adopts a symmetrical structure with the encoder, and reconstructs the missing values ​​of the node power data through deconvolution to obtain the completed data tensor; The output of the decoder is the non-missing part of the original data and the completed data tensor of the missing time points; During the training of the deep convolutional autoencoder network, a binary mask is used to mark the data location of the missing time point and optimize the loss function. This step is expressed as: ； in, is the optimized loss function in the deep convolutional autoencoder network, and Missing time points The original power data tensor and the completed data tensor, Missing time point The corresponding binary mask, "is the Hadamard product," ” denotes the Euclidean norm; Step 2: Initialize the power injected into the distribution network by the boundary node and perform the power flow calculation of the transmission network; the transmission network at the boundary node is equivalent to the Thevenin equivalent circuit and the equivalent parameters are calculated, including the equivalent voltage and equivalent impedance. Step 3: Enhance the equivalent parameters using historical data modeling, and update the power injected into the transmission network by the boundary node based on the supplemented data and enhanced equivalent parameters in step 1. The enhancement process of the equivalent parameters includes: Construct the original values ​​of the equivalent parameters of the mth boundary node at the past p moments as a time series: ； Where, Indicates the The boundary nodes at time The original value of the equivalent voltage; represents the corresponding equivalent impedance; The time series Inputting the prediction result of the equivalent parameters at the current moment into the TCN-Attention network output; wherein, the TCN-Attention network parameters are optimized using the measured values ​​of the equivalent parameters at the historical moments; The enhanced equivalent parameters are expressed as: ； Where, 、 For the The boundary nodes are The equivalent voltage and equivalent impedance after momentary enhancement are used for subsequent distribution network flow calculation; and They are the equivalent voltage prediction value and equivalent impedance prediction value output by the TCN-Attention network respectively; 、 、 and are the weight coefficients corresponding to each item in the formula; Step 4: Determine whether this iteration satisfies the convergence criterion based on the power injected into the transmission network by the boundary nodes before and after the update; if so, terminate the iteration; if not, proceed to step 5; Step 5: Update the equivalent parameters of the Thevenin equivalent circuit using the power injected into the transmission network by the updated boundary node, and return to step 3.

2. A main and distribution integrated power flow calculation method considering missing data completion according to claim 1, characterized in that: The process of obtaining equivalent parameters in step 2 includes: Initialize the power injected into the distribution network by the boundary node; based on the current boundary node power injection value, use the Newton-Raphson method to calculate the transmission network power flow to obtain the boundary node voltage and the transmission network node voltage; Equivalently equating the transmission network to a Thevenin equivalent circuit, the equivalent voltage and equivalent impedance are calculated: ； in, and The transmission network The original values ​​of the equivalent voltage and equivalent impedance at the boundary nodes are: 、 and The transmission network The voltage, voltage increment and load current of each boundary node.

3. A main and distribution integrated power flow calculation method considering missing data completion according to claim 1, characterized in that: The updating of the power injected into the transmission grid by the boundary node comprises: The distribution network nodes are divided into PQ nodes, PV nodes, and balancing nodes, and the active power and reactive power of the PQ nodes, as well as the active power and voltage amplitude of the PV nodes, are obtained from the completed data in step 1. The distribution network flow is calculated based on the enhanced equivalent parameters to obtain the boundary node voltage vector and the power vector injected into the distribution network by the boundary node in this round of iterative update. ; in, That is, the power injected into the distribution network by the updated boundary node described in step 4 .

4. A main and distribution integrated power flow calculation method considering missing data completion according to claim 1, characterized in that: In step 4, the convergence criterion is expressed as: ； Where, and They represent the power injected into the transmission grid by the boundary nodes obtained in the previous and current iterations respectively; represents the norm calculation, which is used to quantify the power deviation between two iterations; is the preset convergence threshold.

5. The main and distribution integrated power flow calculation method considering missing data completion according to claim 1 is characterized in that: Step 5: Inject power into the current boundary node It is transferred to the transmission network and the transmission network power flow calculation is re-performed, which is expressed as: ； in, represents the power flow calculation function of the transmission network; is the transmission network node voltage vector to be recalculated, is the boundary node voltage vector to be recalculated, The power vector injected from the boundary node to the distribution network is the power vector of the transmission network, that is, the current boundary node injection power ; Based on the results of the recalculation of the transmission network power flow, the actual voltage of the boundary nodes is calculated, the parameters of the Thevenin equivalent circuit are updated, and the equivalent model used in the next round of iteration is obtained; Return to step 3 to perform the next round of distribution network power flow calculation.

6. A main and distribution integrated power flow calculation system considering missing data completion, running the main and distribution integrated power flow calculation method according to any one of claims 1 to 5, characterized in that: The system comprises: The data completion module is used to determine the time points at which data are missing in the actual operation data of the distribution network, and to complete the spatiotemporal characteristics of the missing values ​​of the node power data at the missing time points; The equivalent modeling module is used to initialize the power injected into the distribution network at the boundary nodes and perform power flow calculations on the transmission network. It equates the transmission network at the boundary nodes to a Thevenin equivalent circuit and calculates equivalent parameters, including equivalent voltage and equivalent impedance. an equivalent circuit characterization module, configured to enhance the equivalent parameters by using historical data modeling, and update the power injected into the transmission network by the boundary node based on the supplemented data and the enhanced equivalent parameters in the data supplementation module; An iterative process judgment module is used to judge whether the current iteration meets the convergence criterion based on the power injected into the transmission network by the boundary nodes before and after the update; if so, the iteration is terminated; if not, the iterative feedback update module is executed; The iterative feedback update module updates the power injected into the transmission network by the updated boundary nodes to update the equivalent parameters of the Thevenin equivalent circuit and returns to the equivalent circuit characterization module.

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