A power distribution network theoretical line loss dynamic prediction method considering distributed photovoltaic access

Abstract

The present application relates to the technical field of line loss prediction, and particularly relates to a power distribution network theoretical line loss dynamic prediction method considering distributed photovoltaic access, comprising obtaining historical section, switch state and meteorological data, constructing a multi-dimensional joint probability distribution model to generate a prediction scenario, mapping node injection power through a differentiable REF network, constructing a Laplace smoothing dynamic topology mask matrix and the like. The present application overcomes the defects of traditional pure data-driven models that are easy to output invalid results contrary to Kirchhoff's law, and pure physical mechanism models that have a calculation dimension explosion when dealing with frequent topology reconstruction of the power distribution network. Through explicit embedding of physical constraints in forward propagation and a gating second-order correction mechanism, while ensuring millisecond-level online calculation efficiency, the physical fidelity and accuracy of line loss prediction under extreme working conditions such as high penetration rate photovoltaic access and sunny-cloud alternation are greatly improved, providing highly reliable data support for subsequent power grid dispatching.

Description

Technical Field

[0001] This invention relates to the field of line loss prediction technology, and more specifically to a method for dynamic prediction of theoretical line loss in distribution networks that takes into account distributed photovoltaic access. Background Technology

[0002] With the deepening of the dual-carbon goals, the high proportion of distributed photovoltaic (PV) grid integration has become an inevitable trend in the development of new power systems. The strong randomness and volatility of distributed PV output, as well as the frequent topology reconfiguration of the distribution network to isolate faults or optimize operation, make the power flow distribution and line loss characteristics of the distribution network highly time-varying and highly nonlinear. Accurate theoretical dynamic prediction of line loss is an important foundation for distribution network loss reduction, energy saving, reactive power and voltage optimization control, and economic operation. In recent years, with the development of artificial intelligence technology, graph neural networks have been widely used in distribution network state estimation and line loss prediction due to their natural advantages in processing non-Euclidean space topology data.

[0003] However, existing methods for predicting and controlling line losses in distribution networks still suffer from several drawbacks in practical applications. Existing graph neural networks often suffer from gradient vanishing or feature aggregation distortion due to network edge disconnections caused by switching actions when dealing with frequent topology reconfigurations in distribution networks. Existing physical information neural networks often treat power flow equations merely as soft constraint penalties in the loss function, failing to explicitly guide hidden state updates in the intermediate layers of the network's forward propagation. This results in the output voltage prediction sequence frequently violating Kirchhoff's laws. Traditional methods often rely on steady-state power flow calculations or first-order Jacobian sensitivity analysis. When photovoltaic power output fluctuates drastically, causing the system to exhibit strong nonlinearity, the first-order approximation error becomes extremely large. Furthermore, globally calculating the second-order Hessian matrix leads to a computational dimensionality explosion, making it difficult to balance prediction. To address the requirements of accuracy and real-time online computation, existing probabilistic scenario generation models and graph neural network inputs suffer from a semantic gap, lacking an effective mapping mechanism that preserves the probabilistic topology. Furthermore, most prediction models are open-loop architectures, unable to adaptively update parameters based on actual measurement residuals, leading to a continuous decline in long-term prediction accuracy. Existing line loss predictions are often disconnected from downstream reactive power and voltage control, lacking a chance-constraint coordination mechanism based on prediction confidence intervals. When dealing with voltage over-limit risks, the reactive power support capacity of photovoltaic inverters and the operating life of on-load tap changers are not effectively coordinated, easily causing frequent mechanical wear of transformer taps. Moreover, control commands lack anti-maloperation verification safeguards for complex communication environments during issuance. Therefore, we propose a dynamic prediction method for theoretical line losses in distribution networks considering distributed photovoltaic access. Summary of the Invention

[0004] In view of the above-mentioned shortcomings of the existing technology, the first objective of the present invention is to provide a method for dynamic prediction of theoretical line loss of distribution network considering distributed photovoltaic access, so as to solve the problems in the background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for dynamic prediction of theoretical line losses in distribution networks considering distributed photovoltaic (PV) grid integration includes the following steps: S1. Acquire historical operating section data of the power distribution network, real-time switch status sequence, and multi-source meteorological monitoring data of distributed photovoltaic sites. The multi-source meteorological monitoring data includes solar irradiance, ambient temperature, wind speed, and cloud optical thickness. S2. Based on the multi-source meteorological monitoring data and historical power output sequence, construct a multi-dimensional joint probability distribution model that considers the spatiotemporal correlation of photovoltaic power output, and generate multiple photovoltaic power output prediction scenarios for future preset time periods; S3. The multiple photovoltaic power output prediction scenarios are converted into node feature initial vectors of a graph spatiotemporal neural network through a node injection power mapping function. The node injection power mapping function is a differentiable radial basis function network, which maps the active and reactive power injection values ​​of each node in the photovoltaic power output prediction scenario to the initial node embedding vector. In the mapping process, the relative probability distance between different scenarios is maintained by introducing a metric learning loss function. S4. Construct a dynamic topology mask matrix based on the real-time switch state sequence of the distribution network, and perform a Hadamard product operation on the dynamic topology mask matrix and the static physical topology adjacency matrix to generate a time-varying dynamic adjacency matrix. S5. Construct a graph spatiotemporal neural network model that includes a power flow direction perception attention mechanism. Input the node feature initial vector and the time-varying dynamic adjacency matrix into the graph spatiotemporal neural network model. Explicitly embed physical constraints into the forward propagation process using a differentiable Kirchhoff's current law residual calculation layer. The differentiable Kirchhoff's current law residual calculation layer is injected after each graph convolutional layer of the graph spatiotemporal neural network model in a residual connection manner. This explicitly guides the update direction of the hidden state from the intermediate layers of the network's forward propagation, so that the hidden state of the network explicitly satisfies the node power balance equation when updating layer by layer. Output the complex voltage prediction sequence of each node in the future preset time period. S6. Based on the complex voltage prediction sequence and the current operating section data, construct a branch line loss sensitivity dynamic correction model, calculate the higher-order changes in line loss caused by distributed photovoltaic power output fluctuations and topology switching, and superimpose the baseline line loss value with the higher-order changes in line loss to obtain the theoretical dynamic prediction value of line loss. S7. Extract the residual between the actual line loss measurement value and the theoretical dynamic line loss prediction value in the current prediction period. When the mean of the sliding window of the residual exceeds the preset statistical threshold, trigger the parameter update of the multidimensional joint probability distribution model to form a rolling correction closed loop.

[0006] The present invention is further configured such that: in step S2, a multidimensional joint probability distribution model considering the spatiotemporal correlation of photovoltaic power output is constructed, specifically including: An adaptive kernel density estimation method is used to fit the time-varying edge probability distribution function of each photovoltaic access node. The bandwidth parameter of the adaptive kernel density estimation is based on the basic bandwidth and is dynamically scaled and adjusted by an exponential function with the absolute value of the daily power ramp rate of photovoltaic power output and the vector magnitude of cloud movement speed as independent variables, so as to adaptively capture the peak and thick tail characteristics of photovoltaic power output. The Spearman rank correlation coefficient of the historical output sequence between different nodes is calculated. Based on the physical characteristics of the chain-like decay correlation of photovoltaic output of adjacent nodes under the radial topology of the distribution network, the D-Vine Copula structure is selected for dependency modeling. The first layer of the D-Vine Copula structure connects each photovoltaic node in sequence with the distribution network feeder path as the main chain, so that the dependency structure of the Copula explicitly matches the chain physical connection relationship of the radial topology of the distribution network. By coupling the time-varying edge probability distribution function of each node using the D-Vine Copula structure, a multidimensional joint probability density function describing the tail dependency of multi-node photovoltaic power output is generated, and the photovoltaic power output prediction scenario is generated using the Latin hypercube sampling algorithm.

[0007] The present invention is further configured such that, in step S6, the expression of the branch line loss sensitivity dynamic correction model is:

[0008] In the formula: Let be the dynamic change in line loss of branch ll at time tt; and Let be the time-varying first-order Jacobian sensitivity vectors of the active and reactive power injected into branch l at time t to line loss. and These are vectors representing the changes in active and reactive power injected by distributed photovoltaic systems relative to the reference section within a future preset time period; This is a conditionally triggered indicator function; The preset threshold value is determined adaptively based on the ratio of the total installed capacity of distributed photovoltaic power generation in the distribution network to the short-circuit capacity of the system. The higher the ratio, the smaller the preset threshold value. This is a state variable deviation vector containing the node voltage magnitude deviation and phase angle deviation; Let be the time-varying second-order Hessian matrix of the line loss of branch l at time t with respect to the state variable.

[0009] The present invention is further configured such that, in step S6, the method for obtaining the time-varying second-order Hessian matrix includes: The electrical distance between any two nodes is calculated based on the elements of the node impedance matrix. The electrical distance is defined as the sum of the self-impedances of the two nodes minus the absolute value of twice the mutual impedance, and then normalized by dividing by the impedance range of all nodes in the network. A dynamic threshold for electrical distance is set. The dynamic threshold is negatively correlated with the real-time penetration rate of distributed photovoltaic power in the current distribution network and is adaptively adjusted. When the dynamic threshold is lower than the preset minimum threshold, the preset minimum threshold is forcibly taken to ensure that the set of strongly coupled nodes at least includes the distributed photovoltaic access node itself and its first-level adjacent nodes. Nodes whose electrical distance from the distributed photovoltaic access node is less than the dynamic threshold are selected to form the strongly coupled node set, and the calculation of non-zero elements of the Hessian matrix and sparse storage are performed only within the set.

[0010] The present invention is further configured such that: in step S4, constructing a dynamic topology mask matrix specifically includes: The real-time opening and closing status of sectionalizing switches and tie switches in the distribution network is obtained and binarized to generate an initial switch status matrix. The initial switch state matrix is ​​smoothed using Laplace, and the mask elements corresponding to the open switch are assigned small positive numbers, while the mask elements corresponding to the closed switch are assigned 1, thus generating the dynamic topology mask matrix. The Laplacian smoothing process described herein differs fundamentally from the DropEdge regularization strategy of graph neural networks. While DropEdge randomly discards edges during the training phase to enhance generalization ability, it needs to restore the true topology afterward. In contrast, the Laplacian smoothing process described in this application maintains the small positive number of disconnected edges during the model inference phase, enabling a smooth transition of the receptive field of graph convolution when the switch state changes in real time. The small positive number is dynamically adjusted according to the historical closing frequency of the branch where the disconnected switch is located. The higher the historical closing frequency of the branch, the closer its corresponding small positive number is to the preset upper limit value.

[0011] The present invention is further configured such that, in step S5, the weight calculation strategy of the trend direction perception attention mechanism includes: Calculate the real-time active power flow per unit value of branches between adjacent nodes; Based on the real-time active power flow per unit value, the initial attention weight is directionally modulated. When the active power flow direction is consistent with the power transmission direction of the main feeder of the distribution network, the penalty term is not activated. When there is photovoltaic backfeeding or circulating current causing the power flow to reverse, the characteristic aggregation weight of the reverse power flow node is activated through the exponential decay term to suppress the characteristic aggregation weight of the reverse power flow node. When the active power flow direction of a branch reverses in an adjacent prediction cycle, the penalty intensity coefficient is temporarily increased to suppress the drastic jump in attention weights, so that the feature aggregation process of the graph spatiotemporal neural network model has an inertial smoothing characteristic for power flow reversal.

[0012] The present invention is further characterized in that: In step S5, the explicit embedding of physical constraints in the forward propagation process is implemented through a physical constraint graph spatiotemporal feature update formula, which is:

[0013] In the formula: Let be the hidden state feature vector of node i in the (k+1)th layer of the network at time t; It is a non-linear activation function; Let i be the set of neighboring nodes of node i, determined based on the time-varying dynamic adjacency matrix. The attention weight modulated by the direction of the current; Let be the trainable weight matrix of the k-th layer network; Let be the hidden state feature vector of adjacent node j; Let be the adaptive physical constraint strength coefficient for node i. Its value is configured hierarchically according to the region to which node i belongs: when the ratio of the electrical distance from node i to the root node of the distribution network to its electrical distance to the nearest distributed photovoltaic access node is less than 1, node i is determined to belong to the upstream region. A larger value is chosen to strengthen the constraints of Kirchhoff's current law; when the ratio is greater than or equal to 1, node i is determined to belong to the terminal region. Take the smaller value; For physical constraint mapping functions; The set of branches physically connected to node i; The time-varying complex admittance matrix considering the thermal stability effects of the line; and denoted as the complex voltage phasor prediction values ​​for node i and node l at time t, respectively.

[0014] The present invention is further configured such that, in step S5, the specific construction of the physical constraint mapping function includes: Calculate the residual vector between the theoretical injection current vector derived from the complex voltage phasor prediction and the dynamic complex admittance matrix and the predicted injection current vector output by the current layer of the graph-space-time neural network model; Before being input into the multilayer perceptron, the residual vector is first decomposed into multiple scales by discrete wavelet transform to extract the high-frequency transient residual components that characterize the rapid fluctuations of photovoltaics and the low-frequency steady-state residual components that characterize the slow changes in load, so that the physical violation penalty term can distinguish the sources of physical violations at different time scales. The residual components at multiple time scales are input into a multilayer perceptron containing a skip connection structure. The output layer of the multilayer perceptron uses a Softplus activation function to ensure that the physical violation penalty term of the output is strictly non-negative. Before the residual vector is input, it is weighted according to the electrical betweenness centrality index of each node in the distribution network topology.

[0015] The present invention is further configured such that: in step S5, the training of the graph spatiotemporal neural network model adopts a joint loss function for parameter optimization, the joint loss function including a data-driven prediction error term, a physical power flow equation violation penalty term, and a topology consistency regularization term; The weight ratio of the data-driven prediction error term and the physical flow equation violation penalty term is dynamically adjusted using a gradient norm balancing strategy. The gradient norm balancing strategy backtracks to the physical information graph convolutional layer. Since the data-driven term and the physical constraint term interact explicitly for the first time in the physical information graph convolutional layer, the gradient norm ratio of the two terms in the physical information graph convolutional layer is calculated and adaptively scaled to reflect the true degree of optimization conflict between the two types of losses in the current training stage. The topology consistency regularization term is used to penalize non-physical jumps in the complex voltage prediction sequence at the time of switch state switching, and its weighting coefficient is inversely proportional to the electrical distance between nodes involved in the topology switching.

[0016] The present invention is further configured such that, after obtaining the theoretical line loss dynamic prediction value in step S6, it further includes: Based on the theoretical dynamic prediction value of line loss and the prediction confidence interval output by the multidimensional joint probability distribution model, a multi-time-scale reactive voltage model prediction and control model for distribution networks with chance constraints is constructed. During the rolling solution process, the voltage over-limit probability constraint is transformed into a deterministic equivalent constraint based on the confidence interval, and a hard constraint on the maximum number of daily operations of the on-load tap-changing transformer is introduced. When the risk of voltage exceeding the limit is triggered during the predicted period and the remaining number of transformer operations is insufficient, the optimal reactive power output command sequence of the distributed photovoltaic inverter is issued first to provide rapid support; when the reactive power regulation margin of the distributed photovoltaic inverter is lower than the preset ratio and the risk of voltage exceeding the limit continues to rise during the predicted period, the daily maximum number of operations limit of the on-load tap-changing transformer is lifted and additional tap-changing operations are allowed. Before the optimal reactive power output command sequence is sent through the distribution network communication system, a timestamp check code and a command integrity check code are attached. The terminal execution device executes the command only if the verification is successful after receiving it; otherwise, it maintains the control command of the previous cycle to ensure the communication reliability of the control closed loop.

[0017] Beneficial effects Compared with known public technologies, the technical solution provided by this invention has the following beneficial effects: 1. This invention overcomes the shortcomings of traditional pure data-driven models, which are prone to outputting invalid results that violate Kirchhoff's laws, and pure physical mechanism models, which suffer from computational dimension explosion when dealing with frequent topology reconfiguration of distribution networks. By explicitly embedding physical constraints in forward propagation and using a gated second-order correction mechanism, it significantly improves the physical fidelity and accuracy of line loss prediction under extreme conditions such as high-penetration photovoltaic access and alternating sunny and cloudy conditions, while ensuring millisecond-level online computing efficiency. This provides highly reliable data support for subsequent power grid dispatching.

[0018] 2. This invention directly transforms the forward-looking line loss prediction results into control decisions, realizing a seamless closed loop of prediction and control. By prioritizing the use of the reactive power margin of the photovoltaic inverter and releasing the transformer operation restrictions when necessary, it not only effectively mitigates the risk of node voltage exceeding limits caused by drastic fluctuations in photovoltaic output and significantly reduces the actual line loss of the distribution network, but also fundamentally avoids the mechanical wear caused by frequent adjustments of transformer taps in traditional control strategies, extending the service life of the equipment. At the same time, the command verification mechanism ensures the extremely high reliability of the control closed loop in complex communication environments. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall steps of a dynamic prediction method for theoretical line loss in a distribution network that considers distributed photovoltaic access, according to the present invention. Figure 2 This is a schematic diagram of the overall system architecture of a distribution network theoretical line loss dynamic prediction method considering distributed photovoltaic access according to the present invention; Figure 3 This is a schematic diagram of the internal structure of the graph-temporal neural network and the physical constraint embedding of a dynamic prediction method for theoretical line loss in a distribution network considering distributed photovoltaic access, according to the present invention. Figure 4This is a schematic diagram of the line loss sensitivity gating correction and rolling closed-loop mechanism of a dynamic prediction method for theoretical line loss of distribution networks considering distributed photovoltaic access, according to the present invention. Detailed Implementation

[0020] To make the technical problems, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the described embodiments are only a part of the embodiments of this application, not all of them. The specific embodiments described herein are only used to explain the invention and are not intended to limit the invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] It should be further noted that the accompanying drawings and embodiments of the present invention mainly describe the concept of the present invention. Based on this concept, some specific forms and arrangements of connection relationships, positional relationships, power mechanisms, power supply systems, hydraulic systems and control systems may not be fully described. However, under the premise that those skilled in the art understand the concept of the present invention, they can implement the above-mentioned specific forms and arrangements in a well-known manner.

[0022] When a component is referred to as "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as "connected to" another component, it can be directly connected to or indirectly connected to that other component.

[0023] The directional terms "inner" and "outer" refer to the inner and outer contours of each component itself. The terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0024] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figure to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figure. For example, if the device in the figure is inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways, and the spatial relative descriptions used herein will be interpreted accordingly.

[0025] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, and "several" means one or more, unless otherwise explicitly specified.

[0026] The present invention will now describe a method for dynamic prediction of theoretical line losses in distribution networks that takes into account distributed photovoltaic access.

[0027] Example 1 like Figure 1 As shown in Figure 4, this invention provides a technical solution: a method for dynamic prediction of theoretical line losses in distribution networks considering distributed photovoltaic access, comprising the following steps: S1. Acquire historical operating section data of the power distribution network, real-time switch status sequence, and multi-source meteorological monitoring data of distributed photovoltaic sites. The multi-source meteorological monitoring data includes solar irradiance, ambient temperature, wind speed, and cloud optical thickness. S2. Based on the multi-source meteorological monitoring data and historical power output sequence, construct a multi-dimensional joint probability distribution model that considers the spatiotemporal correlation of photovoltaic power output, and generate multiple photovoltaic power output prediction scenarios for future preset time periods; S3. The multiple photovoltaic power output prediction scenarios are converted into node feature initial vectors of a graph spatiotemporal neural network through a node injection power mapping function. The node injection power mapping function is a differentiable radial basis function network, which maps the active and reactive power injection values ​​of each node in the photovoltaic power output prediction scenario to the initial node embedding vector. In the mapping process, the relative probability distance between different scenarios is maintained by introducing a metric learning loss function. S4. Construct a dynamic topology mask matrix based on the real-time switch state sequence of the distribution network, and perform a Hadamard product operation on the dynamic topology mask matrix and the static physical topology adjacency matrix to generate a time-varying dynamic adjacency matrix. S5. Construct a graph spatiotemporal neural network model that includes a power flow direction perception attention mechanism. Input the node feature initial vector and the time-varying dynamic adjacency matrix into the graph spatiotemporal neural network model. Explicitly embed physical constraints into the forward propagation process using a differentiable Kirchhoff's current law residual calculation layer. The differentiable Kirchhoff's current law residual calculation layer is injected after each graph convolutional layer of the graph spatiotemporal neural network model in a residual connection manner. This explicitly guides the update direction of the hidden state from the intermediate layers of the network's forward propagation, so that the hidden state of the network explicitly satisfies the node power balance equation when updating layer by layer. Output the complex voltage prediction sequence of each node in the future preset time period. S6. Based on the complex voltage prediction sequence and the current operating section data, construct a branch line loss sensitivity dynamic correction model, calculate the higher-order changes in line loss caused by distributed photovoltaic power output fluctuations and topology switching, and superimpose the baseline line loss value with the higher-order changes in line loss to obtain the theoretical dynamic prediction value of line loss. S7. Extract the residual between the actual line loss measurement value and the theoretical dynamic line loss prediction value in the current prediction period. When the mean of the sliding window of the residual exceeds the preset statistical threshold, trigger the parameter update of the multidimensional joint probability distribution model to form a rolling correction closed loop. In step S2, a multidimensional joint probability distribution model considering the spatiotemporal correlation of photovoltaic power output is constructed, specifically including: An adaptive kernel density estimation method is used to fit the time-varying edge probability distribution function of each photovoltaic access node. The bandwidth parameter of the adaptive kernel density estimation is based on the basic bandwidth and is dynamically scaled and adjusted by an exponential function with the absolute value of the daily power ramp rate of photovoltaic power output and the vector magnitude of cloud movement speed as independent variables, so as to adaptively capture the peak and thick tail characteristics of photovoltaic power output. The Spearman rank correlation coefficient of the historical output sequence between different nodes is calculated. Based on the physical characteristics of the chain-like decay correlation of photovoltaic output of adjacent nodes under the radial topology of the distribution network, the D-Vine Copula structure is selected for dependency modeling. The first layer of the D-Vine Copula structure connects each photovoltaic node in sequence with the distribution network feeder path as the main chain, so that the dependency structure of the Copula explicitly matches the chain physical connection relationship of the radial topology of the distribution network. By using the D-Vine Copula structure to couple the time-varying edge probability distribution function of each node, a multidimensional joint probability density function describing the tail dependency of multi-node photovoltaic power output is generated, and the photovoltaic power output prediction scenario is generated by using the Latin hypercube sampling algorithm. In step S6, the expression for the dynamic correction model of branch line loss sensitivity is:

[0028] In the formula: Let be the dynamic change in line loss of branch ll at time tt; and Let be the time-varying first-order Jacobian sensitivity vectors of the active and reactive power injected into branch l at time t to line loss. and These are vectors representing the changes in active and reactive power injected by distributed photovoltaic systems relative to the reference section within a future preset time period; This is a conditionally triggered indicator function; The preset threshold value is determined adaptively based on the ratio of the total installed capacity of distributed photovoltaic power generation in the distribution network to the short-circuit capacity of the system. The higher the ratio, the smaller the preset threshold value. This is a state variable deviation vector containing the node voltage magnitude deviation and phase angle deviation; Let be the time-varying second-order Hessian matrix of the line loss of branch l at time t with respect to the state variable; In step S6, the method for obtaining the time-varying second-order Hessian matrix includes: The electrical distance between any two nodes is calculated based on the elements of the node impedance matrix. The electrical distance is defined as the sum of the self-impedances of the two nodes minus the absolute value of twice the mutual impedance, and then normalized by dividing by the impedance range of all nodes in the network. A dynamic threshold for electrical distance is set. The dynamic threshold is negatively correlated with the real-time penetration rate of distributed photovoltaic power in the current distribution network and is adaptively adjusted. When the dynamic threshold is lower than the preset minimum threshold, the preset minimum threshold is forcibly taken to ensure that the set of strongly coupled nodes at least includes the distributed photovoltaic access node itself and its first-level adjacent nodes. Nodes whose electrical distance from the distributed photovoltaic access node is less than the dynamic threshold are selected to form the strongly coupled node set, and the calculation of non-zero elements of the Hessian matrix and sparse storage are performed only within the set. In step S4, constructing the dynamic topology mask matrix specifically includes: The real-time opening and closing status of sectionalizing switches and tie switches in the distribution network is obtained and binarized to generate an initial switch status matrix. The initial switch state matrix is ​​smoothed using Laplace, and the mask elements corresponding to the open switch are assigned small positive numbers, while the mask elements corresponding to the closed switch are assigned 1, thus generating the dynamic topology mask matrix. The Laplacian smoothing process described herein differs fundamentally from the DropEdge regularization strategy of graph neural networks. DropEdge randomly discards edges during the training phase to enhance generalization ability, but then needs to restore the true topology. In contrast, the Laplacian smoothing process described in this application maintains the small positive number of disconnected edges during the model inference phase, so that the receptive field of graph convolution transitions smoothly when the switch state changes in real time. The small positive number is dynamically adjusted according to the historical closing frequency of the branch where the disconnected switch is located. The higher the historical closing frequency of the branch, the closer its corresponding small positive number is to the preset upper limit value. In step S5, the weight calculation strategy of the trend direction perception attention mechanism includes: Calculate the real-time active power flow per unit value of branches between adjacent nodes; Based on the real-time active power flow per unit value, the initial attention weight is directionally modulated. When the active power flow direction is consistent with the power transmission direction of the main feeder of the distribution network, the penalty term is not activated. When there is photovoltaic backfeeding or circulating current causing the power flow to reverse, the characteristic aggregation weight of the reverse power flow node is activated through the exponential decay term to suppress the characteristic aggregation weight of the reverse power flow node. When the active power flow direction of a branch reverses in an adjacent prediction cycle, the penalty intensity coefficient is temporarily increased to suppress the drastic jump in attention weights, so that the feature aggregation process of the graph spatiotemporal neural network model has inertial smoothing characteristics for power flow reversal. Its features are, In step S5, the explicit embedding of physical constraints in the forward propagation process is implemented through a physical constraint graph spatiotemporal feature update formula, which is:

[0029] In the formula: Let be the hidden state feature vector of node i in the (k+1)th layer of the network at time t; It is a non-linear activation function; Let i be the set of neighboring nodes of node i, determined based on the time-varying dynamic adjacency matrix. The attention weight modulated by the direction of the current; Let be the trainable weight matrix of the k-th layer network; Let be the hidden state feature vector of adjacent node j; Let be the adaptive physical constraint strength coefficient for node i. Its value is configured hierarchically according to the region to which node i belongs: when the ratio of the electrical distance from node i to the root node of the distribution network to its electrical distance to the nearest distributed photovoltaic access node is less than 1, node i is determined to belong to the upstream region. A larger value is chosen to strengthen the constraints of Kirchhoff's current law; when the ratio is greater than or equal to 1, node i is determined to belong to the terminal region. Take the smaller value; For physical constraint mapping functions; The set of branches physically connected to node i; The time-varying complex admittance matrix considering the thermal stability effects of the line; and These are the predicted complex voltage phasors of nodes i and l at time t, respectively. In step S5, the specific construction of the physical constraint mapping function includes: Calculate the residual vector between the theoretical injection current vector derived from the complex voltage phasor prediction and the dynamic complex admittance matrix and the predicted injection current vector output by the current layer of the graph-temporal neural network model; Before being input into the multilayer perceptron, the residual vector is first decomposed into multiple scales by discrete wavelet transform to extract the high-frequency transient residual components that characterize the rapid fluctuations of photovoltaics and the low-frequency steady-state residual components that characterize the slow changes in load, so that the physical violation penalty term can distinguish the sources of physical violations at different time scales. The residual components at multiple time scales are input into a multilayer perceptron containing a skip connection structure. The output layer of the multilayer perceptron uses a Softplus activation function to ensure that the physical violation penalty term of the output is strictly non-negative. Before the residual vector is input, it is weighted according to the electrical betweenness centrality index of each node in the distribution network topology. In step S5, the training of the graph spatiotemporal neural network model uses a joint loss function for parameter optimization. The joint loss function includes a data-driven prediction error term, a physical power flow equation violation penalty term, and a topology consistency regularization term. The weight ratio of the data-driven prediction error term and the physical flow equation violation penalty term is dynamically adjusted using a gradient norm balancing strategy. The gradient norm balancing strategy backtracks to the physical information graph convolutional layer. Since the data-driven term and the physical constraint term interact explicitly for the first time in the physical information graph convolutional layer, the gradient norm ratio of the two terms in the physical information graph convolutional layer is calculated and adaptively scaled to reflect the true degree of optimization conflict between the two types of losses in the current training stage. The topology consistency regularization term is used to penalize non-physical jumps in the complex voltage prediction sequence at the time of switch state switching, and its weighting coefficient is inversely proportional to the electrical distance between nodes involved in the topology switching.

[0030] In this embodiment, a photovoltaic power output scenario is generated by constructing a multidimensional joint probability distribution model, feature mapping is performed using a differentiable radial basis function network, and a time-varying adjacency matrix is ​​constructed by combining a Laplace smoothing dynamic topology mask; then, a complex voltage prediction sequence is output through a graph spatiotemporal neural network containing power flow direction sensing attention and Kirchhoff current law residual calculation layer; finally, the theoretical line loss is calculated using a branch line loss sensitivity dynamic correction model containing a condition triggering mechanism.

[0031] Example 2 like Figure 1 As shown in Figure 4, after obtaining the theoretical line loss dynamic prediction value in step S6, the following steps are also included: Based on the theoretical dynamic prediction value of line loss and the prediction confidence interval output by the multidimensional joint probability distribution model, a multi-time-scale reactive voltage model prediction and control model for distribution networks with chance constraints is constructed. During the rolling solution process, the voltage over-limit probability constraint is transformed into a deterministic equivalent constraint based on the confidence interval, and a hard constraint on the maximum number of daily operations of the on-load tap-changing transformer is introduced. When the risk of voltage exceeding the limit is triggered during the predicted period and the remaining number of transformer operations is insufficient, the optimal reactive power output command sequence of the distributed photovoltaic inverter is issued first to provide rapid support; when the reactive power regulation margin of the distributed photovoltaic inverter is lower than the preset ratio and the risk of voltage exceeding the limit continues to rise during the predicted period, the daily maximum number of operations limit of the on-load tap-changing transformer is lifted and additional tap-changing operations are allowed. Before the optimal reactive power output command sequence is sent through the distribution network communication system, a timestamp check code and a command integrity check code are attached. The terminal execution device executes the command only if the verification is successful after receiving it; otherwise, it maintains the control command of the previous cycle to ensure the communication reliability of the control closed loop.

[0032] In this embodiment, based on the high-precision theoretical line loss dynamic prediction value and prediction confidence interval, a multi-time-scale reactive voltage model prediction control model with chance constraints is constructed. In the rolling solution, a hard constraint on the maximum number of daily operations of the on-load tap-changing transformer is introduced. Based on the reactive margin state, coordinated control instructions for the photovoltaic inverter and transformer are intelligently generated, and after adding a check code, they are sent to the terminal for execution.

[0033] Working principle: like Figure 1As shown in Figure 4, in actual use, the system first collects historical operating sections, switch status, and multi-source meteorological monitoring data including solar irradiance and cloud optical thickness in real time. Based on these data, a multi-dimensional joint probability distribution model is constructed to generate photovoltaic output prediction scenarios that fully consider spatiotemporal correlation. These scenarios are then mapped to node feature initial vectors that maintain relative probability distance through a differentiable radial basis function network. The system constructs a Laplace smoothed dynamic topology mask matrix based on the real-time switch status and combines it with the static physical topology to generate a time-varying dynamic adjacency matrix, providing a topology input for the subsequent graph neural network that conforms to both physical connectivity and gradient smoothing characteristics.

[0034] The system inputs the aforementioned node features and dynamic adjacency matrix into the graph spatiotemporal neural network model. During forward propagation, the network dynamically adjusts the feature aggregation weights using a power flow direction-aware attention mechanism. By injecting a Kirchhoff current law residual calculation layer after each graph convolutional layer, the hidden state update is explicitly guided in a hard-constraint manner, ensuring that the output complex voltage prediction sequence strictly satisfies the node power balance equation. Based on this complex voltage prediction sequence, the time-varying first-order Jacobian sensitivity vector is further calculated, and the time-varying second-order Hessian matrix correction is conditionally triggered based on whether the photovoltaic active power fluctuation exceeds a preset threshold value. This accurately captures the higher-order changes in nonlinear line loss, and outputs a high-fidelity theoretical line loss dynamic prediction value after superimposing the baseline line loss.

[0035] After outputting the prediction results, the system continuously extracts the residual between the actual line loss measurement and the predicted value. When the mean of the sliding window of the residual exceeds the statistical threshold, it automatically triggers the parameter update of the multidimensional joint probability distribution model to form an adaptive rolling correction closed loop. On this basis, it uses the theoretical dynamic prediction value of line loss and its confidence interval to construct a model prediction control model with chance constraints. In the rolling solution, it strictly enforces the hard constraint of the maximum number of daily operations of the on-load tap-changing transformer. When facing the risk of voltage exceeding the limit and the number of transformer operations is insufficient, the system prioritizes issuing the optimal reactive power output command of the distributed photovoltaic inverter for support. When the reactive power margin is exhausted, it intelligently releases the transformer operation restriction. Finally, it issues coordination commands through the communication gateway with additional check codes to achieve safe loss reduction and voltage stability control of the distribution network.

[0036] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0037] 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.

[0038] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

Claims

1. A method for dynamic prediction of theoretical line losses in distribution networks considering distributed photovoltaic (PV) grid integration, characterized in that, Includes the following steps: S1. Acquire historical operating section data of the power distribution network, real-time switch status sequence, and multi-source meteorological monitoring data of distributed photovoltaic sites. The multi-source meteorological monitoring data includes solar irradiance, ambient temperature, wind speed, and cloud optical thickness. S2. Based on the multi-source meteorological monitoring data and historical power output sequence, construct a multi-dimensional joint probability distribution model that considers the spatiotemporal correlation of photovoltaic power output, and generate multiple photovoltaic power output prediction scenarios for future preset time periods; S3. The multiple photovoltaic power output prediction scenarios are converted into node feature initial vectors of a graph spatiotemporal neural network through a node injection power mapping function. The node injection power mapping function is a differentiable radial basis function network, which maps the active and reactive power injection values ​​of each node in the photovoltaic power output prediction scenario to the initial node embedding vector. In the mapping process, the relative probability distance between different scenarios is maintained by introducing a metric learning loss function. S4. Construct a dynamic topology mask matrix based on the real-time switch state sequence of the distribution network, and perform a Hadamard product operation on the dynamic topology mask matrix and the static physical topology adjacency matrix to generate a time-varying dynamic adjacency matrix. S5. Construct a graph spatiotemporal neural network model that includes a power flow direction perception attention mechanism. Input the node feature initial vector and the time-varying dynamic adjacency matrix into the graph spatiotemporal neural network model. Explicitly embed physical constraints into the forward propagation process using a differentiable Kirchhoff's current law residual calculation layer. The differentiable Kirchhoff's current law residual calculation layer is injected after each graph convolutional layer of the graph spatiotemporal neural network model in a residual connection manner. This explicitly guides the update direction of the hidden state from the intermediate layers of the network's forward propagation, so that the hidden state of the network explicitly satisfies the node power balance equation when updating layer by layer. Output the complex voltage prediction sequence of each node in the future preset time period. S6. Based on the complex voltage prediction sequence and the current operating section data, construct a branch line loss sensitivity dynamic correction model, calculate the higher-order changes in line loss caused by distributed photovoltaic power output fluctuations and topology switching, and superimpose the baseline line loss value with the higher-order changes in line loss to obtain the theoretical dynamic prediction value of line loss. S7. Extract the residual between the actual line loss measurement value and the theoretical dynamic line loss prediction value in the current prediction period. When the mean of the sliding window of the residual exceeds the preset statistical threshold, trigger the parameter update of the multidimensional joint probability distribution model to form a rolling correction closed loop.

2. The method for dynamic prediction of theoretical line loss in a distribution network considering distributed photovoltaic access as described in claim 1, characterized in that: In step S2, a multidimensional joint probability distribution model considering the spatiotemporal correlation of photovoltaic power output is constructed, specifically including: An adaptive kernel density estimation method is used to fit the time-varying edge probability distribution function of each photovoltaic access node. The bandwidth parameter of the adaptive kernel density estimation is based on the basic bandwidth and is dynamically scaled and adjusted by an exponential function with the absolute value of the daily power ramp rate of photovoltaic power output and the vector magnitude of cloud movement speed as independent variables, so as to adaptively capture the peak and thick tail characteristics of photovoltaic power output. The Spearman rank correlation coefficient of the historical output sequence between different nodes is calculated. Based on the physical characteristics of the chain-like decay correlation of photovoltaic output of adjacent nodes under the radial topology of the distribution network, the D-Vine Copula structure is selected for dependency modeling. The first layer of the D-Vine Copula structure connects each photovoltaic node in sequence with the distribution network feeder path as the main chain, so that the dependency structure of the Copula explicitly matches the chain physical connection relationship of the radial topology of the distribution network. By coupling the time-varying edge probability distribution function of each node using the D-Vine Copula structure, a multidimensional joint probability density function describing the tail dependency of multi-node photovoltaic power output is generated, and the photovoltaic power output prediction scenario is generated using the Latin hypercube sampling algorithm.

3. The method for dynamic prediction of theoretical line loss in a distribution network considering distributed photovoltaic access, as described in claim 1, is characterized in that: In step S6, the expression for the dynamic correction model of branch line loss sensitivity is:

4. In the formula: Let be the dynamic change in line loss of branch ll at time tt; and Let be the time-varying first-order Jacobian sensitivity vectors of the active and reactive power injected into branch l at time t to line loss. and These are vectors representing the changes in active and reactive power injected by distributed photovoltaic systems relative to the reference section within a future preset time period; This is a conditionally triggered indicator function; The preset threshold value is determined adaptively based on the ratio of the total installed capacity of distributed photovoltaic power generation in the distribution network to the short-circuit capacity of the system. The higher the ratio, the smaller the preset threshold value. This is a state variable deviation vector containing the node voltage magnitude deviation and phase angle deviation; Let be the time-varying second-order Hessian matrix of the line loss of branch l at time t with respect to the state variable.

5. The method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 3, is characterized in that: In step S6, the method for obtaining the time-varying second-order Hessian matrix includes: The electrical distance between any two nodes is calculated based on the elements of the node impedance matrix. The electrical distance is defined as the sum of the self-impedances of the two nodes minus the absolute value of twice the mutual impedance, and then normalized by dividing by the impedance range of all nodes in the network. A dynamic threshold for electrical distance is set. The dynamic threshold is negatively correlated with the real-time penetration rate of distributed photovoltaic power in the current distribution network and is adaptively adjusted. When the dynamic threshold is lower than the preset minimum threshold, the preset minimum threshold is forcibly taken to ensure that the set of strongly coupled nodes at least includes the distributed photovoltaic access node itself and its first-level adjacent nodes. Nodes whose electrical distance from the distributed photovoltaic access node is less than the dynamic threshold are selected to form the strongly coupled node set, and the calculation of non-zero elements of the Hessian matrix and sparse storage are performed only within the set.

6. The method for dynamic prediction of theoretical line loss in a distribution network considering distributed photovoltaic access according to claim 1, characterized in that: In step S4, constructing the dynamic topology mask matrix specifically includes: The real-time opening and closing status of sectionalizing switches and tie switches in the distribution network is obtained and binarized to generate an initial switch status matrix. The initial switch state matrix is ​​smoothed using Laplace, and the mask elements corresponding to the open switch are assigned small positive numbers, while the mask elements corresponding to the closed switch are assigned 1, thus generating the dynamic topology mask matrix. The Laplacian smoothing process described herein differs fundamentally from the DropEdge regularization strategy of graph neural networks. While DropEdge randomly discards edges during the training phase to enhance generalization ability, it needs to restore the true topology afterward. In contrast, the Laplacian smoothing process described in this application maintains the small positive number of disconnected edges during the model inference phase, enabling a smooth transition of the receptive field of graph convolution when the switch state changes in real time. The small positive number is dynamically adjusted according to the historical closing frequency of the branch where the disconnected switch is located. The higher the historical closing frequency of the branch, the closer its corresponding small positive number is to the preset upper limit value.

7. The method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 1, is characterized in that... In step S5, the weight calculation strategy of the trend direction perception attention mechanism includes: Calculate the real-time active power flow per unit value of branches between adjacent nodes; Based on the real-time active power flow per unit value, the initial attention weight is directionally modulated. When the active power flow direction is consistent with the power transmission direction of the main feeder of the distribution network, the penalty term is not activated. When there is photovoltaic backfeeding or circulating current causing the power flow to reverse, the characteristic aggregation weight of the reverse power flow node is activated through the exponential decay term to suppress the characteristic aggregation weight of the reverse power flow node. When the active power flow direction of a branch reverses in an adjacent prediction cycle, the penalty intensity coefficient is temporarily increased to suppress the drastic jump in attention weights, so that the feature aggregation process of the graph spatiotemporal neural network model has an inertial smoothing characteristic for power flow reversal.

8. The method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 1, is characterized in that... In step S5, the explicit embedding of physical constraints in the forward propagation process is implemented through a physical constraint graph spatiotemporal feature update formula, which is:

9. In the formula: Let be the hidden state feature vector of node i in the (k+1)th layer of the network at time t; It is a non-linear activation function; Let i be the set of neighboring nodes of node i, determined based on the time-varying dynamic adjacency matrix. The attention weight modulated by the direction of the current; Let be the trainable weight matrix of the k-th layer network; Let be the hidden state feature vector of adjacent node j; Let be the adaptive physical constraint strength coefficient for node i. Its value is configured hierarchically according to the region to which node i belongs: when the ratio of the electrical distance from node i to the root node of the distribution network to its electrical distance to the nearest distributed photovoltaic access node is less than 1, node i is determined to belong to the upstream region. A larger value is chosen to strengthen the constraints of Kirchhoff's current law; when the ratio is greater than or equal to 1, node i is determined to belong to the terminal region. Take the smaller value; For physical constraint mapping functions; The set of branches physically connected to node i; The time-varying complex admittance matrix considering the thermal stability effects of the line; and denoted as the complex voltage phasor prediction values ​​for node i and node l at time t, respectively.

10. A method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 7, is characterized in that... In step S5, the specific construction of the physical constraint mapping function includes: Calculate the residual vector between the theoretical injection current vector derived from the complex voltage phasor prediction and the dynamic complex admittance matrix and the predicted injection current vector output by the current layer of the graph-space-time neural network model; Before being input into the multilayer perceptron, the residual vector is first decomposed into multiple scales by discrete wavelet transform to extract the high-frequency transient residual components that characterize the rapid fluctuations of photovoltaics and the low-frequency steady-state residual components that characterize the slow changes in load, so that the physical violation penalty term can distinguish the sources of physical violations at different time scales. The residual components at multiple time scales are input into a multilayer perceptron containing a skip connection structure. The output layer of the multilayer perceptron uses a Softplus activation function to ensure that the physical violation penalty term of the output is strictly non-negative. Before the residual vector is input, it is weighted according to the electrical betweenness centrality index of each node in the distribution network topology.

11. The method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 1, is characterized in that, In step S5, the training of the graph spatiotemporal neural network model uses a joint loss function for parameter optimization. The joint loss function includes a data-driven prediction error term, a physical power flow equation violation penalty term, and a topology consistency regularization term. The weight ratio of the data-driven prediction error term and the physical flow equation violation penalty term is dynamically adjusted using a gradient norm balancing strategy. The gradient norm balancing strategy backtracks to the physical information graph convolutional layer. Since the data-driven term and the physical constraint term interact explicitly for the first time in the physical information graph convolutional layer, the gradient norm ratio of the two terms in the physical information graph convolutional layer is calculated and adaptively scaled to reflect the true degree of optimization conflict between the two types of losses in the current training stage. The topology consistency regularization term is used to penalize non-physical jumps in the complex voltage prediction sequence at the time of switch state switching, and its weighting coefficient is inversely proportional to the electrical distance between nodes involved in the topology switching.

12. The method for dynamic prediction of theoretical line losses in a distribution network considering distributed photovoltaic access, as described in claim 1, is characterized in that, After obtaining the theoretical line loss dynamic prediction value in step S6, the method further includes: Based on the theoretical dynamic prediction value of line loss and the prediction confidence interval output by the multidimensional joint probability distribution model, a multi-time-scale reactive voltage model prediction and control model for distribution networks with chance constraints is constructed. During the rolling solution process, the voltage over-limit probability constraint is transformed into a deterministic equivalent constraint based on the confidence interval, and a hard constraint on the maximum number of daily operations of the on-load tap-changing transformer is introduced. When the risk of voltage exceeding the limit is triggered during the predicted period and the remaining number of transformer operations is insufficient, the optimal reactive power output command sequence of the distributed photovoltaic inverter is issued first to provide rapid support; when the reactive power regulation margin of the distributed photovoltaic inverter is lower than the preset ratio and the risk of voltage exceeding the limit continues to rise during the predicted period, the daily maximum number of operations limit of the on-load tap-changing transformer is lifted and additional tap-changing operations are allowed. Before the optimal reactive power output command sequence is sent through the distribution network communication system, a timestamp check code and a command integrity check code are attached. The terminal execution device executes the command only if the verification is successful after receiving it; otherwise, it maintains the control command of the previous cycle to ensure the communication reliability of the control closed loop.

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