Cognitive uncertainty-driven energy storage planning method for topology-free low-voltage area

Abstract

The application relates to a cognitive uncertainty driven energy storage planning method for a low-voltage transformer area without topology. Historical PQV measurement data of a low-voltage transformer area is acquired; a data-driven pseudo-topology is constructed based on the historical PQV measurement data, and the pseudo-topology represents the statistical coupling relationship of power-voltage response between nodes; a DeepONet-GraphResidual voltage proxy model is constructed; the pseudo-topology, proxy error and scenario drift are used to respectively depict the cognitive uncertainty of the graph structure, proxy error and scenario drift; a candidate energy storage node set is determined according to the cognitive uncertainty and node voltage weakness; an energy storage capacity-operation collaborative optimization model is established on the candidate node set to obtain a candidate energy storage action; the candidate energy storage action is subjected to post-hoc safety checking, and the energy storage action meeting the safety acceptance rule is taken as the final scheme output. The method does not depend on real topology and line parameters, and can realize reliable energy storage planning in a low-voltage transformer area with missing data.

Description

Technical Field

[0001] This application relates to the field of power grid energy storage planning technology, and in particular to a cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas. Background Technology

[0002] Low-voltage distribution substations, as the basic units of the distribution network supplying power to end users, are crucial for the integration of distributed resources such as residential distributed photovoltaics, electric vehicles, flexible loads, and user-side energy storage. With the advancement of new power system construction, the number of source-load-storage resources on the distribution side is rapidly increasing, gradually breaking the traditional unidirectional power flow characteristics of low-voltage substations. Problems such as localized backflow, voltage exceeding limits at the end of the distribution line, and voltage fluctuations are becoming more prominent. Therefore, achieving scientific energy storage planning in low-voltage substations with incomplete topological information and limited measurement conditions is a critical issue for improving the voltage management capabilities and distributed resource carrying capacity of the distribution network.

[0003] Existing research mainly focuses on energy storage site selection and capacity determination, as well as distribution network voltage management, and is gradually recognizing energy storage systems as an important regulatory resource for improving the flexibility of low-voltage distribution networks. However, most methods still rely on relatively accurate network topology, line parameters, and power flow equations, which are easily limited in actual low-voltage distribution areas by factors such as missing ledger information, unclear line-customer relationships, and inaccurate line impedance.

[0004] To address the issue of missing information in distribution network models, some scholars have conducted research from the perspectives of state estimation, topology identification, and parameter estimation, providing an effective foundation for completing weakly observed distribution network models. However, their main objective remains topology or parameter identification. If the identification results are directly used for energy storage planning, the identification error may be further amplified in the subsequent optimization process.

[0005] With the continuous accumulation of data from smart meters, integrated distribution terminals, and distribution automation, data-driven power flow proxy models provide a new technical approach for voltage analysis under topology-less or weak topology conditions. However, existing research mostly focuses on voltage prediction or operation control, with less emphasis on further analyzing the impact of proxy model errors, pseudo-topology construction errors, and operation scenario drift on planning decisions in energy storage planning scenarios.

[0006] Furthermore, energy storage planning is not the same as ordinary voltage forecasting. A surrogate model with a small prediction error may not be able to provide the correct direction for energy storage regulation at low-voltage sensitive nodes and critical periods. Voltage surrogate models for energy storage planning not only need to have high prediction accuracy, but also need to be able to support candidate node selection, capacity operation optimization, and safety post-hoc verification.

[0007] While the aforementioned research has laid the foundation for energy storage planning in topologyless low-voltage distribution areas, the following shortcomings remain: First, traditional energy storage planning methods rely heavily on accurate topology and line parameters, making them unsuitable for low-voltage distribution areas with missing records, unclear line-customer relationships, and weak observation. Second, existing data-driven power flow agents primarily use prediction errors as the main evaluation indicator, lacking a reliable evaluation oriented towards the benefits of energy storage planning and the direction of regulation. Third, graph neural network methods typically assume that the true topology is available, while in topologyless scenarios, pseudo-topology can only reflect statistical coupling; how to characterize its cognitive uncertainty still requires further research. Fourth, existing energy storage planning research rarely forms a complete closed loop of "agent modeling—candidate screening—capacity operation optimization—post-hoc safety verification," making it difficult to guarantee the engineering acceptability of agent optimization actions. Summary of the Invention

[0008] Therefore, it is necessary to provide a cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas to address the aforementioned technical problems.

[0009] Firstly, this application provides a cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas. The method includes: Acquire historical active power measurements, historical reactive power measurements, and historical voltage amplitude measurements of the low-voltage distribution area to form historical PQV measurement data; A data-driven pseudo-topology is constructed based on the historical PQV measurement data. The pseudo-topology represents the statistical coupling relationship of power-voltage response between nodes and is different from the real physical line topology. A DeepONet-GraphResidual voltage proxy model is constructed. The voltage proxy model includes a DeepONet global mapping branch and a GraphResidual local residual compensation branch. The DeepONet global mapping branch is used to learn the operator mapping from global active power and reactive power to node voltage magnitude. The GraphResidual local residual compensation branch performs local residual compensation on the voltage prediction results output by the DeepONet branch based on the pseudo-topology to obtain the proxy voltage prediction value. Based on the pseudo-topology, the proxy error of the proxy voltage prediction value, and the scene feature distribution shift of the planned scene relative to the training samples, the cognitive uncertainty of graph structure, the cognitive uncertainty of proxy error, and the cognitive uncertainty of scene drift are respectively characterized. The candidate energy storage node set is determined based on the graph structure cognitive uncertainty, the proxy error cognitive uncertainty, the scene drift cognitive uncertainty, and the node voltage weakness. An energy storage capacity-operation collaborative optimization model is established on the candidate energy storage node set. The energy storage capacity-operation collaborative optimization model is solved to obtain candidate energy storage actions, which include energy storage access capacity, energy storage power limit and typical daily charging and discharging strategy. The candidate energy storage actions are subjected to a post-hoc safety verification, and the energy storage actions that meet the safety acceptance rules are output as the final energy storage planning scheme.

[0010] Optionally, in one embodiment of this application, constructing a data-driven pseudo-topology based on the historical PQV measurement data includes: Construct node feature vectors based on the historical active power sequence, historical reactive power sequence, and historical voltage amplitude sequence of each node; Calculate the Pearson correlation coefficient between the feature vectors of any two nodes, and determine the statistical distance between the nodes based on the absolute value of the Pearson correlation coefficient; For each node, a predetermined number of nodes with the smallest statistical distance are selected to form a neighborhood. The edge weights are defined according to the statistical distances. The edge weight matrix is ​​then symmetricized, self-loops are added, and degree normalization is performed to obtain the adjacency matrix of the pseudo-topology.

[0011] Optionally, in one embodiment of this application, the DeepONet global mapping branch includes a Branch network and a Trunk network. The Branch network takes the active and reactive power operating status of the entire distribution area as input and outputs global operating features. The Trunk network takes node location encoding and time period encoding as input and outputs the response pattern of the node to the global operating status in the corresponding time period. The output of the DeepONet branch is the sum of the inner product of the global operating features and the response pattern and the node bias term.

[0012] Optionally, in one embodiment of this application, the GraphResidual local residual compensation branch uses the pseudo-topology as a message carrier, splices the active power, reactive power, voltage amplitude, and node embedding of the nodes into initial node features, performs local information aggregation in the neighborhood of the pseudo-topology through multi-layer graph residual propagation, and outputs local residual voltage. The proxy voltage prediction value is the sum of the output of the DeepONet branch and the local residual voltage.

[0013] Optionally, in one embodiment of this application, the training objective of the voltage proxy model includes a low-voltage weighted voltage reconstruction loss, a voltage increment consistency loss, and a residual regularization term; the low-voltage weighted voltage reconstruction loss is used to increase the model's attention to samples near the low-voltage threshold, the voltage increment consistency loss is used to constrain the temporal change trend of the predicted voltage to be consistent with that of the true voltage, and the residual regularization term is used to constrain the residual magnitude of the GraphResidual branch output.

[0014] Optionally, in one embodiment of this application, the graph structure cognitive uncertainty is determined based on the standard deviation of the voltage prediction results of the voltage surrogate model for the planned scenario under various different graph construction methods; the surrogate error cognitive uncertainty is determined based on the prediction error of the voltage surrogate model in the low-voltage critical band of the validation set; and the scenario drift cognitive uncertainty is determined based on the Mahalanobis distance between the scenario features of the planned scenario and the scenario features of the training samples.

[0015] Optionally, in one embodiment of this application, the node voltage vulnerability is determined based on the continuous low-voltage gap and low-voltage frequency of the node when no energy storage is configured; before determining the candidate energy storage node set, the method further includes determining the comprehensive value of each node, which is composed of the node voltage vulnerability, soft observation response potential and node comprehensive cognitive uncertainty weighted together, the soft observation response potential representing the marginal improvement of the system low-voltage gap by a unit discharge disturbance of the node, and the node comprehensive cognitive uncertainty being composed of the graph structure cognitive uncertainty, the surrogate error cognitive uncertainty and the scene drift cognitive uncertainty weighted together.

[0016] Optionally, in one embodiment of this application, determining the candidate energy storage node set includes: A first number of voltage vulnerability priority nodes are determined based on voltage vulnerability ranking, and a second number of comprehensive value supplementary nodes are determined from the remaining nodes based on comprehensive value ranking. The first number is greater than the second number, and the union of the voltage vulnerability priority nodes and the comprehensive value supplementary nodes is taken as the candidate energy storage node set.

[0017] Optionally, in one embodiment of this application, the objective function of the energy storage capacity-operation co-optimization model takes the improvement of the low-voltage gap as the main objective, and also includes an overvoltage gap penalty term, an energy storage capacity cost penalty term, and a scheduling smoothness penalty term; the constraints of the energy storage capacity-operation co-optimization model include an upper limit constraint on energy storage capacity, an upper limit constraint on energy storage power, a mutual exclusion constraint on charging and discharging, a time-series recursive constraint on energy state, and an intraday cycle constraint; in the energy storage capacity-operation co-optimization model, the node power after the energy storage effect is obtained by subtracting the net energy storage discharge power from the node active power when no energy storage is configured, and the node voltage after the energy storage effect is predicted by the voltage proxy model based on the node power after the energy storage effect.

[0018] Optionally, in one embodiment of this application, the post-hoc safety verification of the candidate energy storage action includes: A set of action scales is constructed, and the candidate energy storage actions are scaled according to each scale. The node voltage after the execution of the energy storage action at each scale is calculated by a posterior evaluator. The posterior evaluator is independent of the voltage proxy model and does not participate in the training of the voltage proxy model or the solution of the energy storage capacity-operation co-optimization model. The safe acceptance rule is that the low-voltage gap does not worsen, the minimum voltage does not decrease, the number of low-voltage node time periods does not increase, and no overvoltage is introduced. The scaled energy storage action corresponding to the largest scale that satisfies the safe acceptance rule is selected as the final energy storage planning scheme output. If there is no non-zero scale that satisfies the safe acceptance rule, then zero action is output.

[0019] The aforementioned cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas has the following advantages compared to existing technologies: First, this invention does not rely on real topology and line parameters. It constructs a pseudo-topology using historical PQV measurements and establishes a DeepONet-GraphResidual voltage proxy model. This enables effective voltage response modeling in low-voltage distribution areas where records are missing or line-customer relationships are unclear, breaking through the dependence of traditional energy storage planning methods on complete physical models.

[0020] Second, this invention systematically characterizes cognitive uncertainty from three dimensions: graph structure, proxy error, and scene drift, and introduces it into the energy storage candidate node screening process. This makes up for the shortcomings of existing data-driven methods that only use prediction error as an evaluation indicator, and improves the credibility of energy storage planning decisions.

[0021] Third, the present invention adopts a candidate node selection strategy of "prioritizing voltage weakness and supplementing with cognitive value". While ensuring coverage of severely low-voltage areas, it introduces nodes with high marginal response or cognitive attention value, which can significantly improve the low-voltage governance effect of energy storage planning.

[0022] Fourth, this invention sets up a post-hoc safety verification step, which evaluates candidate energy storage actions in a unified manner through scale scanning and safety screening, avoiding the amplification of surrogate model errors in the optimization closed loop, improving the engineering acceptability and traceability of energy storage planning schemes, and forming a complete closed loop of "surrogate modeling - cognitive screening - capacity operation optimization - post-hoc safety verification".

[0023] Fifth, this invention jointly optimizes the energy storage access capacity, power limit, and typical daily charging and discharging strategy in the energy storage capacity-operation collaborative optimization, and makes multi-objective trade-offs for low-voltage gap improvement, overvoltage suppression, configuration scale, and scheduling smoothness, which can adapt to the actual planning needs of different low-voltage distribution areas. Attached Figure Description

[0024] Figure 1This is a schematic diagram of the overall framework of a cognitive uncertainty-driven energy storage planning method for topologyless low-voltage areas in one embodiment. Figure 2 This is a schematic diagram of the DeepONet-GraphResidual voltage proxy model in one embodiment; Figure 3 This is a schematic diagram of the energy storage capacity-operation collaborative optimization and post-test safety verification process in one embodiment; Figure 4 This is a comparison chart of posterior indices for energy storage planning under different graph structures in one embodiment. Figure 5 This is a diagram illustrating the mismatch between proxy prediction error and planning posterior benefit in one embodiment. Figure 6 This is a breakdown diagram of the voltage value, cognitive value, and overall value of the Top 10 nodes in one embodiment; Figure 7 This is a comparison chart of the energy storage planning effects under different site selection strategies in one embodiment; Figure 8 The diagram shows the effect of low-pressure treatment under a typical day and the most severe 24-hour scenario in one embodiment. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0026] In this embodiment, the cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas includes: acquiring historical active power measurements, historical reactive power measurements, and historical voltage amplitude measurements of the low-voltage distribution area to form historical PQV measurement data; constructing a data-driven pseudo-topology based on the historical PQV measurement data, wherein the pseudo-topology represents the statistical coupling relationship between power-voltage responses between nodes, and the pseudo-topology is distinct from the real physical line topology; and constructing a DeepONet-GraphResidual voltage proxy model, wherein the voltage proxy model includes a DeepONet global mapping branch and a GraphResidual local residual compensation branch, wherein the DeepONet global mapping branch is used to learn the operator mapping from global active power and reactive power to node voltage amplitude, and the GraphResidual local residual compensation branch is based on the pseudo-topology to learn the DeepONet-GraphResidual voltage amplitude. Local residual compensation is performed on the voltage prediction results output by the Net branch to obtain surrogate voltage prediction values. Based on the pseudo-topology, the surrogate error of the surrogate voltage prediction values, and the scene feature distribution offset of the planned scene relative to the training samples, the cognitive uncertainty of graph structure, the cognitive uncertainty of surrogate error, and the cognitive uncertainty of scene drift are characterized respectively. A set of candidate energy storage nodes is determined according to the cognitive uncertainty of graph structure, the cognitive uncertainty of surrogate error, the cognitive uncertainty of scene drift, and the weakness of node voltage. An energy storage capacity-operation co-optimization model is established on the set of candidate energy storage nodes, and the energy storage capacity-operation co-optimization model is solved to obtain candidate energy storage actions. The candidate energy storage actions include energy storage access capacity, energy storage power limit, and typical daily charging and discharging strategy. The candidate energy storage actions are subjected to posterior safety verification, and the energy storage actions that meet the safety acceptance rules are output as the final energy storage planning scheme.

[0027] In practice, low-voltage distribution substations typically face challenges such as a large number of users, limited measurement types, delayed record updates, and incomplete accuracy of line-user relationships. Complete line topology, line impedance, and phase connection relationships are difficult to obtain directly. Traditional energy storage planning methods usually rely on accurate power flow models, line parameters, and voltage constraints, determining energy storage access locations and capacities through sensitivity analysis, optimal power flow, or mixed-integer optimization. When low-voltage substation topology and line parameters are missing, these modeling prerequisites are difficult to meet. Directly applying accurate power flow models is susceptible to model mismatch and parameter errors, leading to a lack of reliable basis for energy storage site selection, capacity determination, and operation strategies.

[0028] To address this issue, the embodiments of this application do not aim to restore the complete physical topology. Instead, they learn the statistical mapping relationship between node power changes and voltage response based on historical active power, reactive power, and voltage amplitude measurements. It is important to emphasize that the pseudo-topology constructed in these embodiments does not represent actual line connections, but rather a statistical coupling structure of nodes extracted from historical measurement data. Its function is to provide local correlation information for the voltage proxy model, thereby enhancing the response expression capability of low-voltage sensitive areas. Therefore, the method in these embodiments differs from topology identification methods; its focus is not on determining whether lines are actually connected, but on constructing a voltage response proxy that can serve energy storage planning under topology-less conditions.

[0029] The overall framework for topology-free low-voltage distribution area energy storage planning proposed in this application is as follows: Figure 1 As shown, the framework follows the approach of "agent modeling - cognitive screening - capacity operation optimization - post-hoc safety verification", embedding the data-driven model into an interpretable and traceable planning process, rather than directly outputting the final energy storage solution from a black-box model.

[0030] First, a data-driven pseudo-topology is constructed using historical PQV measurements, and a DeepONet-GraphResidual voltage proxy model is established. DeepONet is used to learn the operator mapping from global active / reactive power to voltage amplitude, characterizing the main impact of power changes across the network on voltage distribution. GraphResidual, based on the pseudo-topology, performs local residual compensation to correct local response deviations between low-voltage sensitive nodes and statistically coupled nodes. This step addresses the problem of "how to obtain a voltage response model suitable for planning when a real topology is unavailable."

[0031] Secondly, the credibility of the surrogate model after its inclusion in energy storage planning is considered. In topology-free scenarios, the pseudo-topology construction method, surrogate model error, and the distribution differences between the planned scenario and the training samples can all affect the evaluation results of energy storage actions. To address this, this application's embodiments characterize cognitive uncertainty from three perspectives: graph structure uncertainty, surrogate error uncertainty, and scenario drift uncertainty, and combine voltage vulnerability and soft observation response potential to form a comprehensive node evaluation. Unlike simply ranking nodes according to the severity of low voltage, this application's embodiments adopt a candidate node selection strategy of "prioritizing voltage vulnerability and supplementing with cognitive value." While ensuring coverage of severely low-voltage areas, a small number of nodes with high response potential or model attention value are introduced to improve the planning benefits of the candidate set.

[0032] Furthermore, a capacity-operation co-optimization model is established on the candidate energy storage node set to jointly determine the energy storage access capacity, power ceiling, and typical daily charge-discharge strategy. This model primarily aims to improve the low-voltage gap while considering constraints such as energy storage capacity, power, SOC, intraday cycle time, and charging restrictions during low-voltage risk periods. This allows energy storage planning to go beyond node selection and further provide capacity configuration and operation strategies. The specific process is as follows: Figure 3 As shown.

[0033] Finally, to address the potential error amplification issue in the surrogate optimization results, this application embodiment includes a post-hoc safety verification step. The candidate energy storage actions obtained from the surrogate model are not directly used as the final planning scheme. Instead, they are subjected to scale scanning and safety screening through a unified post-hoc evaluator to determine whether they can improve the low-voltage gap while avoiding minimum voltage degradation and new voltage limits exceeding limits. This step enhances the engineering acceptability and traceability of the surrogate planning results and is a key difference between this application embodiment and ordinary data-driven voltage prediction methods.

[0034] In summary, the core of the framework proposed in this application is not simply to improve voltage prediction accuracy, but to establish a complete closed loop from topology-free voltage proxy to reliable energy storage planning. DeepONet-GraphResidual solves the problem of topology-free voltage response modeling; cognitive uncertainty and soft observation response potential solve the problem of candidate energy storage node selection; and capacity-operation co-optimization and posterior security verification solve the problem of secure implementation of proxy optimization results.

[0035] In one embodiment of this application, constructing a data-driven pseudo-topology based on the historical PQV measurement data includes: constructing node feature vectors based on the historical active power sequence, historical reactive power sequence, and historical voltage amplitude sequence of each node; calculating the Pearson correlation coefficient between any two node feature vectors, and determining the statistical distance between nodes based on the absolute value of the Pearson correlation coefficient; selecting a predetermined number of nodes with the smallest statistical distance for each node to form a neighborhood, defining edge weights based on the statistical distance, and performing symmetry processing, adding self-loops, and degree normalization on the edge weight matrix to obtain the adjacency matrix of the pseudo-topology.

[0036] Specifically, for nodes The node feature vector is constructed from the historical active power, reactive power, and voltage amplitude sequences. Define nodes based on the standardized node features. With nodes The statistical similarity and distance are as follows:

[0037]

[0038] in, This represents the Pearson correlation coefficient. Considering that both positive and negative correlations can reflect coupling relationships between nodes, this embodiment uses the correlation strength. Construct node distances.

[0039] For each node Select the closest A neighborhood is formed by nodes. The edge weight is defined as:

[0040] in, This is the kernel width parameter. To ensure the numerical stability of graph propagation, the edge weight matrix... After symmetrization, adding self-loops, and degree normalization, a pseudo-topological matrix is ​​obtained:

[0041]

[0042]

[0043] income It is a statistical coupling graph, not a physical topology identification result. Its function is to provide a local information aggregation channel for GraphResidual, enabling the surrogate model to utilize the node association information contained in historical measurements even without a real topology.

[0044] It should be noted that the pseudo-topology does not represent the actual line connections, but rather the statistical coupling structure of power-voltage responses between nodes. The goal of constructing the surrogate model in this application is not to recover the true topology, but to learn voltage response relationships that can be used for energy storage planning comparisons under topology-free conditions.

[0045] In one embodiment of this application, the DeepONet global mapping branch includes a Branch network and a Trunk network. The Branch network takes the active and reactive power operating status of the entire distribution area as input and outputs global operating features. The Trunk network takes node location encoding and time period encoding as input and outputs the response pattern of the node to the global operating status in the corresponding time period. The output of the DeepONet branch is the sum of the inner product of the global operating features and the response pattern and the node bias term.

[0046] like Figure 2 As shown, DeepONet consists of a Branch network and a Trunk network. For the task in this embodiment, the Branch network encodes the overall PQ operating state of the entire distribution area, and the Trunk network encodes the node-time period location. The two networks form the base voltage response through their inner product. Its output can be written as:

[0047] In the formula: For Branch networks; For trunk networks; The node embedding vector can be obtained by dimensionality reduction from historical voltage curves, or it can be used as a trainable embedding. Time period encoding; This is the node bias term, used to characterize the difference in average voltage levels between different nodes.

[0048] From an electrical perspective, This represents the global operating characteristics induced by the power state of the entire distribution area. Represents a node During the period The DeepONet branch primarily handles the global PQ-V mapping learning task, reflecting its response pattern to the global runtime state.

[0049] In one embodiment of this application, the GraphResidual local residual compensation branch uses the pseudo-topology as a message carrier, concatenates the node's active power, reactive power, voltage amplitude, and node embedding into initial node features, and performs local information aggregation within the neighborhood of the pseudo-topology through multi-layer graph residual propagation, outputting a local residual voltage. The surrogate voltage prediction value is the sum of the output of the DeepONet branch and the local residual voltage. This branch structure is similar to... Figure 2 As shown.

[0050] Let the first Each sample in the time period The initial node features are derived from , , The result is obtained by concatenating and embedding nodes, denoted as . No. Layer diagram residual propagation is as follows:

[0051] In the formula: Weights for neighboring messages; Transform the weights of the nodes; For bias terms; This is a non-linear activation function. After... After layer graph propagation, the GraphResidual output voltage residual The final agent voltage is:

[0052]

[0053] This formula is the core expression of the DeepONet-GraphResidual proxy model in the embodiments of this application. Its meaning is: DeepONet provides a global voltage response base, while GraphResidual only learns the local residuals that DeepONet fails to fully represent, rather than directly replacing the complete power flow model. This structure, on the one hand, avoids over-reliance on GNNs for full voltage mapping in the absence of a real topology, and on the other hand, allows the pseudo-topology to primarily serve local response compensation, which is more in line with its positioning as a "statistical coupled graph".

[0054] In one embodiment of this application, the training objective of the voltage proxy model includes a low-voltage weighted voltage reconstruction loss, a voltage increment consistency loss, and a residual regularization term; the low-voltage weighted voltage reconstruction loss is used to increase the model's attention to samples near the low-voltage threshold, the voltage increment consistency loss is used to constrain the temporal variation trend of the predicted voltage to be consistent with that of the true voltage, and the residual regularization term is used to constrain the residual magnitude of the GraphResidual branch output.

[0055] Since the proxy model in this application ultimately serves energy storage planning, model training should not only focus on the global average error, but also enhance the fitting ability in the low-pressure critical region. Let the training sample set be... Introducing low-voltage weighted voltage reconstruction loss:

[0056]

[0057]

[0058]

[0059] In the formula: Low-pressure weighting coefficient; This represents the critical band width at low pressure. This is the indicator function. This loss is used to increase the model's attention to samples near the low-voltage threshold, preventing the model from only achieving a small average error in the normal voltage range.

[0060] Considering the continuous nature of intraday voltage variations, a voltage increment consistency loss is further introduced:

[0061] This constraint ensures that the predicted voltage time-varying trend is consistent with the actual voltage trend, reducing unreasonable time-series oscillations generated by the surrogate model.

[0062] Integrating voltage reconstruction, timing consistency, and residual regularization, the training objective of DeepONet-GraphResidual is:

[0063] In the formula, and The weights are used to determine the loss. The low-voltage weighting term improves the fitting ability to the low-voltage critical region, the incremental consistency term constrains the intraday voltage change trend, and the residual regularization term preserves the local correction properties of GraphResidual. It should be noted that this training objective only guarantees the voltage reconstruction capability of the surrogate model on historical samples; after the surrogate model is incorporated into energy storage planning, the safety of its action recommendations still needs to be verified through posterior validation.

[0064] In one embodiment of this application, the graph structure cognitive uncertainty is determined based on the standard deviation of the voltage prediction results of the voltage surrogate model for the planned scenario under various different graph construction methods; the surrogate error cognitive uncertainty is determined based on the prediction error of the voltage surrogate model in the low-voltage critical band of the validation set; and the scenario drift cognitive uncertainty is determined based on the Mahalanobis distance between the scenario features of the planned scenario and the scenario features of the training samples.

[0065] The embodiments of this application characterize the cognitive uncertainty at the node level from three aspects: pseudo-topology construction differences, proxy local errors, and planning scenario drift.

[0066] Regarding the uncertainty in graph structure perception: In topologyless low-voltage distribution areas, the pseudo-topology is constructed from historical PQV measurements and is not equivalent to the actual line connections. Different graphing parameters, historical windows, or similarity metrics may alter the surrogate model's judgment of node voltage responses. Let's assume... The pseudo-topological set obtained by this graph construction method is In planning scenarios Next, the The predicted voltage corresponding to each pseudo-topology is: .node The cognitive uncertainty of graph structures is defined as:

[0067]

[0068] In the formula, for The mean value under different pseudo-topologies. This index reflects the sensitivity of node voltage prediction to pseudo-topology assumptions. If The large value indicates that the node's voltage response is highly sensitive to the graph structure assumption, and subsequent planning should not rely solely on the judgment given by a single pseudo-topology.

[0069] Regarding the uncertainty of proxy error perception: Energy storage planning focuses more on the reliability of predictions near the low-pressure threshold. Let the validation set error be... The low-pressure critical zone indicator function is Then the node The cognitive uncertainty of agent error is defined as:

[0070] In the formula, To prevent extremely small positive numbers with a denominator of zero, this definition focuses more on the exposure of local errors within the low-pressure critical zone compared to global RMSE, and can reflect the credibility of the surrogate model in key areas of energy storage planning.

[0071] Regarding the uncertainty of scenario drift perception: The operating status of low-voltage distribution areas is also affected by seasonality, photovoltaic output, user behavior, and load structure changes, causing the planned scenarios to deviate from the training sample distribution. To characterize the distribution shift of the planned scenarios relative to the training samples, node scenario features are constructed. and using the mean of the training set Covariance Based on this, we define scene drift cognitive uncertainty:

[0072] In the formula, For planning nodes in the scenario Scene characteristics, This is the covariance matrix regularization term. The definition uses the Mahalanobis distance to characterize the deviation of the planning scenario from the training distribution. This distance can take into account the correlation between different feature dimensions and is often used for anomaly and out-of-distribution sample detection.

[0073] To unify the dimensions of different indicators, the min-max normalization operator is adopted. Considering the three factors of graph structure, proxy error, and scene drift, the overall cognitive uncertainty of nodes is defined as follows:

[0074] It should be noted that high cognitive uncertainty does not necessarily mean that the node is suitable for energy storage configuration, but rather that the node is more sensitive in topology-less planning, and further judgment needs to be made in combination with voltage weakness and marginal response of energy storage.

[0075] In one embodiment of this application, the node voltage vulnerability is determined based on the continuous low-voltage gap and low-voltage frequency of the node when no energy storage is configured; before determining the candidate energy storage node set, the method further includes determining the comprehensive value of each node, which is composed of the node voltage vulnerability, soft observation response potential and node comprehensive cognitive uncertainty weighted together. The soft observation response potential represents the marginal improvement of the system low-voltage gap by a unit discharge disturbance of the node, and the node comprehensive cognitive uncertainty is composed of the graph structure cognitive uncertainty, the surrogate error cognitive uncertainty and the scene drift cognitive uncertainty weighted together.

[0076] Voltage vulnerability is used to characterize the current low-voltage management needs of a node and is the basis for selecting candidate energy storage nodes. Let the voltage of the planned scenario without energy storage be... ,node The continuous low-pressure gaps and low-pressure frequencies are as follows:

[0077]

[0078] In the formula A series of low-voltage gaps reflects the depth of low-voltage overshoot, while the frequency of low-voltage gaps reflects the duration of overshoot. Node voltage vulnerability is defined as:

[0079] Ranking nodes solely based on voltage vulnerability may concentrate candidate nodes in low-voltage end regions, neglecting certain nodes with strong marginal improvement capabilities for the global low-voltage gap. Therefore, embodiments of this application define soft observation response potential to characterize the marginal impact of small-disturbance energy storage actions at nodes on the overall network's low-voltage gap.

[0080] According to the sign convention of positive load and positive energy storage discharge, at the node Apply a small discharge disturbance , equivalent to Become ,in For nodes The unit perturbation matrix. Nodes The improvement in low-pressure gap is:

[0081] The soft observation response potential is defined as:

[0082] This definition represents a node. The marginal improvement in low-voltage gap that can be achieved by a unit discharge disturbance. This indicator is calculated offline using only a surrogate model and does not require physical disturbance to be applied in the actual transformer area.

[0083] To illustrate the mathematical meaning of the soft observation response potential, we will discuss the composite function. about Perform a first-order Taylor expansion:

[0084] Further, by the chain rule, we have:

[0085] The above derivation shows that the soft observation response potential is essentially the directional derivative of the low-pressure gap with respect to nodal load disturbances. If the node An increase in load will cause a drop in voltage at low-voltage nodes. ,at this time This indicates that an increase in load at a node will widen the low-voltage gap; conversely, energy storage discharge at that node effectively reduces the load, thus decreasing the low-voltage gap. This indicator explains why the node with the lowest initial voltage is not necessarily the optimal energy storage node: energy storage site selection depends not only on the severity of the low voltage but also on the marginal improvement capability of a node's unit discharge on the global low-voltage gap.

[0086] Taking into account voltage vulnerability, soft observation response potential, and cognitive uncertainty, the comprehensive value of a node is defined as follows:

[0087]

[0088] In the formula, This indicates the need for low-voltage governance at the node. This indicates the marginal improvement capability of node energy storage operations. This indicates the cognitive sensitivity of nodes in topology-free proxy planning. It is important to emphasize that the embodiments of this application do not directly equate cognitive uncertainty with the value of energy storage configuration, but rather use it as supplementary information for sensitive areas of the proxy model.

[0089] In one embodiment of this application, determining the candidate energy storage node set includes: determining a first number of voltage vulnerability priority nodes according to voltage vulnerability ranking, determining a second number of comprehensive value supplementary nodes from the remaining nodes according to comprehensive value ranking, wherein the first number is greater than the second number, and taking the union of the voltage vulnerability priority nodes and the comprehensive value supplementary nodes as the candidate energy storage node set.

[0090] If only based on comprehensive value Performing a global Top-K ordering may result in insufficient coverage of low-voltage nodes or over-selection of nodes with high uncertainty. Therefore, this application adopts an engineering-constrained hybrid screening strategy that prioritizes voltage weaknesses and supplements them with cognitive value.

[0091] Let the set of nodes that satisfy the installation conditions be . The total number of energy storage candidate nodes is ,in Each node is determined primarily based on its voltage vulnerability. Each node is determined by its comprehensive value, and the candidate node set is constructed as follows:

[0092]

[0093]

[0094] In the formula, This is the set of nodes with priority for voltage vulnerability. To supplement the set of nodes for comprehensive value, This forms the final set of candidate energy storage nodes. This strategy first ensures coverage of severely low-pressure areas, and then supplements the list with nodes that have high marginal response or cognitive interest value. This avoids over-concentration of candidate nodes due to simple low-pressure ranking, and also avoids insufficient coverage of severely low-pressure nodes due to simple comprehensive ranking.

[0095] It should be noted that determining the candidate node set only identifies the set of candidate nodes that may be integrated into the energy storage system; it does not directly provide the final energy storage planning scheme. The energy storage capacity, power limit, and intraday charging / discharging strategy still need to be determined within the candidate set. Further optimizations were made, and the acceptability of the proxy optimization results was verified through post-hoc security checks.

[0096] In one embodiment of this application, the objective function of the energy storage capacity-operation co-optimization model takes the improvement of the low-voltage gap as the main objective, and also includes an overvoltage gap penalty term, an energy storage capacity cost penalty term, and a scheduling smoothness penalty term; the constraints of the energy storage capacity-operation co-optimization model include an upper limit constraint on energy storage capacity, an upper limit constraint on energy storage power, a mutual exclusion constraint between charging and discharging, a time-series recursive constraint on energy state, and an intraday cycle constraint; in the energy storage capacity-operation co-optimization model, the node power after the energy storage effect is obtained by subtracting the net energy storage discharge power from the node active power when no energy storage is configured, and the node voltage after the energy storage effect is predicted by the voltage proxy model based on the node power after the energy storage effect.

[0097] From the candidate node set After obtaining the data, it is still necessary to further determine the energy storage capacity, power limit, and typical daily charging and discharging strategy of each candidate node. Unlike planning models that rely on explicit network constraints, this embodiment replaces the explicit power flow equations with a voltage surrogate model under topology-free conditions, and ensures the safety and acceptability of the output scheme through posterior verification. The specific process is as follows: Figure 3 As shown.

[0098] Let the first The discharge power and charging power of the energy stored at each candidate node are respectively and The net discharge power is .make Under the sign convention of "load is positive, energy storage discharge is positive", the equivalent active power after energy storage is connected is:

[0099]

[0100] In the formula: For the first time without energy storage Active power at nodes during a given time period; An embedding matrix is ​​used to embed energy storage nodes, mapping candidate energy storage actions to corresponding low-voltage nodes. If the stored energy is discharged, then... The equivalent load of the corresponding node decreases; if energy storage is charged, then... The equivalent load of the corresponding node increases.

[0101] For the first Let there be an energy storage device with an energy capacity of [value missing]. The upper limit of power is The energy state is Energy storage capacity, power, charge / discharge mutual exclusion, and energy state constraints are uniformly expressed as:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] In the formula: and The first The maximum energy storage capacity and maximum access power that can be configured for each candidate node; and This is a charge / discharge state variable used to avoid simultaneous charging and discharging within the same time period; and These are charging efficiency and discharging efficiency, respectively. For time intervals. Intraday cycle constraint. This is used to avoid situations where the energy storage is artificially depleted or fully replenished during typical daily optimization.

[0108] Based on the equivalent power after energy storage, the surrogate model predicts the voltage after energy storage as follows:

[0109] In the formula, To plan the node reactive power matrix in the scenario.

[0110] To characterize the effectiveness of energy storage planning, a low-voltage gap is defined. Overvoltage gap and scheduling smoothing items Among them, the low-voltage gap is used to characterize the depth of low-voltage over-limit, the overvoltage gap is used to suppress the overvoltage risk caused by energy storage discharge, and the scheduling smoothing term is used to reduce frequent fluctuations in energy storage power. Based on this, the capacity-operation co-optimization objective is:

[0111] In the formula, , , , , All coefficients are non-negative weights. The primary objective is to improve the low-voltage gap, while simultaneously mitigating overvoltage risks, energy storage deployment scale, and drastic dispatch fluctuations. Since the voltage response is provided by the surrogate model rather than directly calculated from the actual power flow equations, the obtained energy storage actions are only candidate planning results and still need to undergo posterior safety verification before being used as the final scheme output.

[0112] In one embodiment of this application, the posterior safety verification of the candidate energy storage actions includes: constructing a set of action scales, scaling the candidate energy storage actions according to each scale, calculating the node voltage after the execution of the energy storage action at each scale using a posterior evaluator, wherein the posterior evaluator is independent of the voltage proxy model and does not participate in the training of the voltage proxy model or the solution of the energy storage capacity-operation co-optimization model; taking the non-deterioration of the low-voltage gap, the non-decrease of the minimum voltage, the non-increase of the number of low-voltage node time periods, and the non-introduction of overvoltage as the safety acceptance rules, selecting the scaled energy storage action corresponding to the largest scale that satisfies the safety acceptance rules as the final energy storage planning scheme output; if there is no non-zero scale that satisfies the safety acceptance rules, then zero action is output.

[0113] Since the voltage surrogate model is trained on historical samples, its output may be affected by model errors, pseudo-topology errors, and planning scenario drift. When the surrogate model enters the capacity-operation optimization closed loop, these errors may be amplified by the optimization process, leading to situations where candidate energy storage actions, although performing well under the surrogate model, exhibit insufficient low-voltage improvement, minimum voltage deterioration, or new overvoltages in the posterior evaluation. Therefore, this application does not directly use the surrogate optimization results as the final planning scheme, but instead sets a posterior safety verification step before output. The relationship between this step and capacity-operation co-optimization is as follows: Figure 3 As shown.

[0114] Let the net discharge power of the candidate energy storage obtained by the solution be... To avoid over-excitation caused by proxy errors, a set of action scales is constructed. And perform a scale scan on the candidate actions:

[0115] For any scale Its corresponding equivalent active power is The voltage after the candidate action is executed is calculated using a unified posterior evaluator.

[0116] In the formula, This serves as a posterior evaluator, which can be a real power flow model, a high-precision simulation model, or a uniformly calibrated evaluation model. It is important to emphasize that... It does not participate in the training of the proxy model, nor in the capacity-run optimization solution, and is only used for safety verification before the final solution output.

[0117] set up For scale Improvement in the low-pressure gap below, This is the minimum voltage improvement amount. and These are the number of low-voltage nodes and the number of overvoltage nodes and the number of time periods, respectively. To optimize the number of low-voltage nodes-time periods, this application defines the safety acceptance rule as follows: the low-voltage gap does not worsen, the minimum voltage does not decrease, the number of low-voltage nodes-time periods does not increase, and no overvoltage is introduced. The corresponding maximum safety action threshold is:

[0118] The final safe energy storage action is as follows:

[0119] If no non-zero scale satisfies the safety acceptance rule, then let This means reverting to a zero-action state. The purpose of this mechanism is not to retrain the surrogate model, nor to replace the capacity-operation optimization model, but rather to perform a unified safety screening before candidate actions are output, thereby preventing the surrogate optimization results from directly entering the final planning scheme. Through this post-hoc verification step, the method proposed in this application can balance surrogate planning efficiency and result security under topology-free conditions, improving the engineering acceptability and traceability of energy storage planning schemes.

[0120] To verify the effectiveness of the method in this application, the IEEE 33-node low-voltage distribution system is selected as the case study. After removing the slack node, the system contains 32 observable low-voltage nodes. The historical samples consist of node active power, reactive power, and voltage amplitude measurements, totaling 2000 PQV samples, which are used to train the DeepONet-GraphResidual topologyless voltage proxy model and construct a data-driven PQV pseudo-topology. In the planning phase, a typical 24-hour daily P / Q curve is used as the input scenario, the number of energy storage access nodes is set to 4, and the voltage safety lower limit is set to 0.95 pu.

[0121] To ensure comparability between different methods, all comparative experiments in this application use the same training / testing partition, the same typical daily planning scenario, the same energy storage capacity-operation constraints, and a unified posterior evaluator. Specifically, the voltage surrogate model is used to quickly evaluate the node voltage response under different energy storage actions; the posterior evaluator is only used for safety verification after the candidate planning action output and does not participate in surrogate model training or capacity-operation optimization. These settings avoid result deviations caused by inconsistencies in scenarios, constraints, or evaluation criteria between different methods.

[0122] This application evaluates the performance of the proposed method from two aspects: the prediction layer and the planning layer. The prediction layer metrics include root mean square error (RMSE), mean absolute error (MAE), and the low-voltage identification F1 value, used to evaluate the surrogate model's ability to characterize node voltage amplitude and low-voltage conditions. The planning layer metrics include posterior low-voltage reduction, voltage gap improvement, minimum voltage improvement, and posterior verification status, used to evaluate the actual governance effect of the energy storage planning scheme under a unified posterior evaluator.

[0123] Among them, the posterior low-voltage reduction reflects the effect of energy storage actions on reducing the number of low-voltage nodes and time periods; the voltage gap improvement characterizes the overall improvement in the depth and duration of low-voltage exceedances; and the minimum voltage improvement measures the effectiveness of mitigation measures for the most severe low-voltage nodes. Compared to a simple voltage prediction problem, energy storage planning focuses more on the posterior benefits and safety acceptability of the proxy model after it enters the optimization closed loop.

[0124] Ablation analysis of voltage surrogate models: To verify the effectiveness of the proposed DeepONet-GraphResidual voltage surrogate model, this application's embodiments compare and ablate MLP, GNN-only, DeepONet-only, DeepONet+GNN, and DeepONet+GraphResidual models. The results are shown in Table 1.

[0125] Table 1. Voltage prediction and low-voltage identification results of different surrogate models

[0126] The results show that DeepONet-only achieves lower RMSE and MAE, indicating that the operator learning structure can effectively characterize the global mapping relationship between active / reactive power and voltage amplitude across multiple nodes. GNN-only exhibits significantly higher errors than other models, suggesting that without a realistic topology and stable physical edge weights, relying solely on graph message passing is insufficient to handle the complete voltage proxy task. The global RMSE of DeepONet+GraphResidual is on the same order of magnitude as DeepONet-only, but its F1 score for low-voltage identification is slightly improved; further addition of low-voltage constraint-related training terms further improves the F1 score to 0.986626. These results demonstrate that the role of the GraphResidual branch is not simply to pursue the lowest average prediction error, but rather to compensate for local correlation residuals at nodes based on the DeepONet global operator mapping, thereby enhancing the model's ability to characterize low-voltage sensitive regions.

[0127] Regarding the effectiveness analysis of the PQV pseudo-topology: To verify the effectiveness of the constructed PQV pseudo-topology in topology-free energy storage planning, this application's embodiments compare different graph structures under the same surrogate model, the same typical daily scenario, the same energy storage constraints, and a unified posterior evaluator. The results are as follows: Figure 4 As shown in Table 2, the comparison objects include physically connected adjacency graphs, PQV pseudo-topologies, self-loop graphs, and random graphs.

[0128] Table 2. Posterior results of surrogate models and energy storage planning under different graph structures.

[0129] The results show that the RMSE of the physical connection adjacency graph baseline is slightly lower than that of the PQV pseudo-topology, indicating that the actual line connection relationships have a certain effect on average voltage prediction. However, from the posterior planning results, the posterior low voltage reduction of the PQV pseudo-topology reaches 36, which is higher than the 23 of the physical connection adjacency graph and the self-loop graph, and also significantly higher than the mean of the random graph; at the same time, the minimum voltage improvement of the PQV pseudo-topology is 0.001365 pu, while the corresponding value of the physical connection adjacency graph baseline is negative. The above results indicate that in topology-free energy storage planning tasks, the value of the graph structure does not entirely depend on whether it is close to the actual line connections, but on whether it can express the power-voltage response coupling related to energy storage regulation. The PQV pseudo-topology is not used to recover the actual physical topology, but to extract planning-related statistical coupling relationships from historical power and voltage measurements.

[0130] Regarding the mismatch analysis between prediction error and planning benefits: To further analyze the relationship between the prediction accuracy of the surrogate model and the effectiveness of energy storage planning, this application compares the prediction errors of different surrogate methods and their posterior benefits after entering the planning closed loop. The results are as follows: Figure 5 As shown in Table 3.

[0131] Table 3. Prediction error and posterior planning benefits of different proxy methods

[0132] The results show that DeepONet-only has the lowest RMSE (0.002368), but its posterior low-voltage reduction is only 3, and its minimum voltage improvement is negative. Conversely, GR-PQV's RMSE is not optimal at 0.002832, but its posterior low-voltage reduction reaches 36, 12 times that of DeepONet-only; simultaneously, its minimum voltage improvement is 0.001365 pu, and its total capacity is 35.773 MWh, lower than DeepONet-only's 37.483 MWh. These results indicate that higher planning benefits are not obtained by increasing the scale of energy storage configuration, but rather from more efficient node coupling expression and more rational adjustment direction. For topologyless energy storage planning problems, the global prediction error of the surrogate model is only a necessary condition, not a sufficient condition, for entering the optimization link.

[0133] Regarding the effectiveness of cognitive value-driven candidate energy storage node selection: To analyze the impact of cognitive uncertainty on the selection of candidate energy storage nodes, embodiments of this application calculate the voltage value, cognitive value, and comprehensive value of each node, as shown in the following figures. Figure 6As shown in the figure. The results indicate that nodes with high voltage value are mainly concentrated in the low-voltage region at the end; while some nodes that are not the most severely low-voltage also have high cognitive value. This result shows that selecting a site solely based on voltage weakness easily leads to the concentration of candidate nodes in the low-voltage region at the end; by introducing cognitive value, non-obvious nodes that have a potential impact on the planning results can be identified. To further verify the effectiveness of the "voltage weakness priority, cognitive value supplement" strategy, embodiments of this application compare the posterior results of energy storage planning under different site selection strategies, such as... Figure 7 The figure shows the voltage gap improvement and minimum voltage improvement for different strategies, and Table 4 lists the corresponding posterior results.

[0134] Table 4. Posterior Structures of Different Strategies

[0135] S1, which selects low-voltage nodes solely based on voltage vulnerability, passes the posterior safety check, but its voltage gap improvement is only 0.116279. S2, with its simple comprehensive ranking, introduces nodes with high cognitive value but fails the posterior safety check, indicating that cognitive value cannot be used independently of voltage coverage constraints. In contrast, S3, employing a voltage Top-3 + cognitive Top-1 strategy, achieves a voltage gap improvement of 0.617091, approximately 5.31 times that of S1; its minimum voltage improvement reaches 0.003838 pu, about 4.31 times that of S1. Furthermore, S3's total capacity of 43.697 MWh is roughly equivalent to S1's 43.728 MWh, suggesting that the increased returns do not stem from stacked energy storage capacity but rather from optimized candidate node structure.

[0136] Regarding the post-hoc safety verification results: To verify the effectiveness of capacity-operation collaborative optimization and post-hoc safety verification, this application's embodiments further compare the planning results under typical daily and most severe 24-hour scenarios, such as... Figure 8 As shown in Table 5.

[0137] Table 5. Low-pressure system control effectiveness under typical daytime and most severe 24-hour scenarios.

[0138] In a typical daily scenario, the optimized low-voltage node-time period count decreased by 3, the voltage gap improvement was 0.243660, and the minimum voltage improvement was 0.001562 pu, with post-hoc safety verification passing. In the most severe 24-hour scenario, the initial low-voltage range was wider and deeper. The optimized low-voltage point count decreased by only 1, but the voltage gap improvement reached 0.297617, and the minimum voltage improvement was 0.000432 pu, also passing post-hoc safety verification. These results indicate that in severe low-voltage scenarios, due to energy storage capacity and power constraints, energy storage operations may struggle to enable a large number of nodes to cross the 0.95 pu threshold, but can still compress the low-voltage gap area and reduce the low-voltage depth. Therefore, it is necessary to report both the low-voltage reduction and the voltage gap improvement; the former reflects changes in the over-limit range, while the latter reflects changes in the over-limit depth and duration.

[0139] Furthermore, this application embodiment rigorously paired ablation verification of the static and dynamic graphs. Both modes employed the same typical day, the same surrogate model, the same set of candidate energy storage nodes, the same energy storage constraints, and the same posterior evaluator. Results showed that both modes passed posterior verification, with a safety scaling factor of 0.8, and formed the same non-zero safety schedule. The dynamic graph generated 15 unique graph structures within 24 hours, indicating that the dynamic graph branches indeed entered the surrogate forward and optimization objectives. Considering that the final planning benefits of the two modes are the same under the current fixed candidate set, this application embodiment does not use the dynamic graph as the primary source of performance gain, but rather as supplementary evidence for time-varying statistical correlation expression and graph structure cognitive uncertainty analysis.

[0140] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0141] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0142] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0143] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0144] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0145] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0146] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0147] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas, characterized in that, The method includes: Acquire historical active power measurements, historical reactive power measurements, and historical voltage amplitude measurements of the low-voltage distribution area to form historical PQV measurement data; A data-driven pseudo-topology is constructed based on the historical PQV measurement data. The pseudo-topology represents the statistical coupling relationship of power-voltage response between nodes and is different from the real physical line topology. A DeepONet-GraphResidual voltage proxy model is constructed. The voltage proxy model includes a DeepONet global mapping branch and a GraphResidual local residual compensation branch. The DeepONet global mapping branch is used to learn the operator mapping from global active power and reactive power to node voltage magnitude. The GraphResidual local residual compensation branch performs local residual compensation on the voltage prediction results output by the DeepONet branch based on the pseudo-topology to obtain the proxy voltage prediction value. Based on the pseudo-topology, the proxy error of the proxy voltage prediction value, and the scene feature distribution shift of the planned scene relative to the training samples, the cognitive uncertainty of graph structure, the cognitive uncertainty of proxy error, and the cognitive uncertainty of scene drift are respectively characterized. The candidate energy storage node set is determined based on the graph structure cognitive uncertainty, the proxy error cognitive uncertainty, the scene drift cognitive uncertainty, and the node voltage weakness. An energy storage capacity-operation collaborative optimization model is established on the candidate energy storage node set. The energy storage capacity-operation collaborative optimization model is solved to obtain candidate energy storage actions, which include energy storage access capacity, energy storage power limit and typical daily charging and discharging strategy. The candidate energy storage actions are subjected to a post-hoc safety verification, and the energy storage actions that meet the safety acceptance rules are output as the final energy storage planning scheme.

2. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The construction of the data-driven pseudo-topology based on the historical PQV measurement data includes: Construct node feature vectors based on the historical active power sequence, historical reactive power sequence, and historical voltage amplitude sequence of each node; Calculate the Pearson correlation coefficient between the feature vectors of any two nodes, and determine the statistical distance between the nodes based on the absolute value of the Pearson correlation coefficient; For each node, a predetermined number of nodes with the smallest statistical distance are selected to form a neighborhood. The edge weights are defined according to the statistical distances. The edge weight matrix is ​​then symmetricized, self-loops are added, and degree normalization is performed to obtain the adjacency matrix of the pseudo-topology.

3. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The DeepONet global mapping branch includes a Branch network and a Trunk network. The Branch network takes the active and reactive power operating status of the entire distribution area as input and outputs global operating features. The Trunk network takes node location encoding and time period encoding as input and outputs the node's response pattern to the global operating status in the corresponding time period. The output of the DeepONet branch is the sum of the inner product of the global operating features and the response pattern and the node bias term.

4. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The GraphResidual local residual compensation branch uses the pseudo-topology as a message carrier, and concatenates the active power, reactive power, voltage amplitude, and node embedding of the nodes into initial node features. It performs local information aggregation in the neighborhood of the pseudo-topology through multi-layer graph residual propagation, and outputs local residual voltage. The proxy voltage prediction value is the sum of the output of the DeepONet branch and the local residual voltage.

5. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The training objectives of the voltage proxy model include low-voltage weighted voltage reconstruction loss, voltage increment consistency loss, and residual regularization term. The low-voltage weighted voltage reconstruction loss is used to increase the model's attention to samples near the low-voltage threshold. The voltage increment consistency loss is used to constrain the temporal variation trend of the predicted voltage to be consistent with that of the true voltage. The residual regularization term is used to constrain the residual magnitude of the GraphResidual branch output.

6. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The cognitive uncertainty of the graph structure is determined based on the standard deviation of the voltage prediction results of the voltage surrogate model for the planned scenario under various different graph construction methods; the cognitive uncertainty of the surrogate error is determined based on the prediction error of the voltage surrogate model in the low-voltage critical band of the validation set; and the cognitive uncertainty of the scenario drift is determined based on the Mahalanobis distance between the scenario features of the planned scenario and the scenario features of the training samples.

7. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The node voltage vulnerability is determined based on the continuous low-voltage gap and low-voltage frequency of the node when no energy storage is configured. Before determining the candidate energy storage node set, the comprehensive value of each node is also determined. The comprehensive value is composed of the node voltage vulnerability, soft observation response potential and node comprehensive cognitive uncertainty weighted. The soft observation response potential represents the marginal improvement of the system low-voltage gap by a unit discharge disturbance of the node. The node comprehensive cognitive uncertainty is composed of the graph structure cognitive uncertainty, the surrogate error cognitive uncertainty and the scene drift cognitive uncertainty weighted.

8. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 7, characterized in that, The set of candidate energy storage nodes includes: A first number of voltage vulnerability priority nodes are determined based on voltage vulnerability ranking, and a second number of comprehensive value supplementary nodes are determined from the remaining nodes based on comprehensive value ranking. The first number is greater than the second number, and the union of the voltage vulnerability priority nodes and the comprehensive value supplementary nodes is taken as the candidate energy storage node set.

9. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The objective function of the energy storage capacity-operation co-optimization model is primarily aimed at improving the low-voltage gap, while also including overvoltage gap penalty terms, energy storage capacity cost penalty terms, and scheduling smoothness penalty terms. The constraints of the energy storage capacity-operation co-optimization model include upper limit constraints on energy storage capacity, upper limit constraints on energy storage power, mutual exclusion constraints on charging and discharging, time-series recursive constraints on energy state, and intraday cycle constraints. In the energy storage capacity-operation co-optimization model, the node power after energy storage is applied is obtained by subtracting the net discharge power of energy storage from the active power of the node when no energy storage is configured, and the node voltage after energy storage is applied is predicted by the voltage proxy model based on the node power after energy storage.

10. The cognitive uncertainty-driven energy storage planning method for topologyless low-voltage distribution areas according to claim 1, characterized in that, The post-hoc safety verification of the candidate energy storage action includes: A set of action scales is constructed, and the candidate energy storage actions are scaled according to each scale. The node voltage after the execution of the energy storage action at each scale is calculated by a posterior evaluator. The posterior evaluator is independent of the voltage proxy model and does not participate in the training of the voltage proxy model or the solution of the energy storage capacity-operation co-optimization model. The safe acceptance rule is that the low-voltage gap does not worsen, the minimum voltage does not decrease, the number of low-voltage node time periods does not increase, and no overvoltage is introduced. The scaled energy storage action corresponding to the largest scale that satisfies the safe acceptance rule is selected as the final energy storage planning scheme output. If there is no non-zero scale that satisfies the safe acceptance rule, a zero action is output.

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