A Transient Voltage Stability Analysis Method for DC Microgrids Based on Embedded Physical Constraints Deep Learning

Abstract

This invention belongs to the field of DC microgrid stability analysis technology, specifically a transient voltage stability analysis method for DC microgrids based on deep learning with embedded physical constraints. This method uses source-side, energy storage, and load power as input features. It constructs a deep learning model that integrates a one-dimensional convolutional neural network with embedded physical knowledge, a bidirectional long short-term memory network, and a multi-head attention mechanism to predict the short-time evolution of bus voltage changes. Furthermore, this method uses a data-driven approach to perform equivalent modeling of the DC microgrid system containing converters with complex control strategies, avoiding dependence on converter internal parameters and control details. Finally, a stable state machine decision logic is introduced to map the voltage change prediction results to a voltage evolution trajectory. Combined with voltage amplitude and duration threshold constraints, this enables rapid assessment of the transient instability trend of the DC microgrid. The effectiveness and engineering applicability of the proposed method are verified through numerical examples.

Description

Technical Field

[0001] This invention belongs to the field of DC microgrid stability analysis technology, specifically a DC microgrid transient voltage stability analysis method based on deep learning with embedded physical constraints. Background Technology

[0002] With the continuous increase in distributed power sources and various DC loads, DC microgrids have experienced rapid development due to their advantages such as simple system structure, high energy conversion efficiency, and ease of integration with distributed power sources. Compared with traditional AC microgrids, DC microgrids have a simpler system structure and do not require consideration of voltage phase and frequency synchronization issues. Therefore, they have been widely used in typical power application scenarios such as data centers, rail transit, electric vehicle charging systems, and new energy grid connection, which places higher demands on system operation and control performance. As the scale of DC microgrids continues to expand, more and more DC loads and distributed power sources are connected to the DC bus through different types of power electronic converters. The connection of a large number of power electronic devices reduces the equivalent damping level of the system, which can easily cause DC bus voltage oscillations and even system instability under certain conditions, thus posing potential risks to the safe and stable operation of DC microgrids.

[0003] The bus voltage of a DC microgrid is a crucial indicator of the system's operating status and stability. When the system is subjected to disturbances such as source-side power fluctuations or sudden load changes, the power imbalance between the source and load will quickly manifest as transient changes in the bus voltage. Unlike AC systems where frequency dynamics play a role in power balance regulation to some extent, in DC systems, power mismatch is almost directly mapped to changes in the amplitude and rate of change of the bus voltage. Therefore, the dynamic evolution of the bus voltage in the initial stage of a disturbance can directly reflect the system's transient recovery level and is an important basis for assessing the transient stability of a DC microgrid.

[0004] For transient voltage stability problems, existing research commonly uses time-domain simulation and energy function methods. Time-domain simulation can usually describe the dynamic characteristics of each component relatively accurately, but it involves significant computation, is time-consuming, and highly dependent on the detailed mathematical model of the system. The energy function method has advantages in computational efficiency and can provide visualized stability margin indices, but its applicability largely depends on the model structure and converter control parameters, making it difficult to directly extend to complex DC microgrids with diverse control strategies. In modern DC microgrids, converter types and control methods are increasingly diverse, and their internal parameters and control strategies are often set at the factory and vary significantly. Therefore, obtaining accurate parameters for all converters in practical engineering is quite difficult. Furthermore, current power electronic converters generally employ complex strategies such as adaptive control and nonlinear control, and their equivalent parameters exhibit significant time-varying characteristics with changing operating conditions, making them difficult to accurately describe using fixed-parameter models. Under conditions where the parameters and control strategies of power electronic converters are not fully known, the applicability of traditional transient voltage stability analysis methods in engineering applications remains limited.

[0005] In recent years, with the development of machine learning, data-driven methods have gradually gained attention in the field of power system stability assessment. These methods do not rely on precise physical models of the system, but rather achieve rapid assessment by learning from system operating data. As operating data accumulates, data-driven methods based on machine learning or deep learning are increasingly being introduced into the assessment of the operating status of DC microgrids. However, existing methods often directly use bus voltage or its absolute value as the prediction object, focusing on fitting voltage amplitude levels. Furthermore, due to the strong autocorrelation inherent in voltage time series, the model may learn more about the stationary characteristics of the series, while its ability to characterize the system's true dynamic response remains limited. Therefore, prediction methods based solely on absolute voltage values ​​struggle to reflect voltage change trends in a timely manner, easily leading to inflated prediction results.

[0006] Furthermore, most existing bus stability assessment methods focus on post-hoc analysis based on historical measurement data, making it difficult to effectively combine day-ahead dispatch results to predict future operating conditions and provide early warnings of risks. This fails to meet the needs of refined operation and proactive prevention and control in DC microgrids. Therefore, there is an urgent need for a bus stability determination method that can start from the dynamics of source and load power, take into account physical consistency, and support early prediction. Summary of the Invention

[0007] The purpose of this invention is to provide a transient voltage stability analysis method for DC microgrids based on deep learning with embedded physical constraints, so as to overcome the shortcomings of existing methods in terms of weak model interpretability and lag in stability assessment.

[0008] This invention is achieved using the following technical solution: a transient voltage stability analysis method for DC microgrids based on embedded physical constraint deep learning, comprising the following steps:

[0009] Step 1: Dataset Construction: Collect the source-side output power, energy storage output power, and load consumption power of the DC microgrid over a continuous period of time;

[0010] Step 2: Constructing the Deep Learning Model Architecture: Construct a deep learning model consisting of three layers. The first layer is a one-dimensional convolutional neural network (CNN), which extracts local temporal features from the collected data to obtain the power change sequence. The second layer is a bidirectional long short-term memory (LSTM) network, which models the forward and backward temporal dependencies of the power change sequence, explores the impact of power changes on the bus voltage evolution process, and obtains a temporal feature sequence covering different times and containing multi-dimensional features. The third layer is a multi-head attention mechanism, which adaptively weights the temporal feature sequence to obtain the predicted bus voltage change.

[0011] Step 3: Construction of Hybrid Loss Function: In the deep learning model training process, in addition to constructing a data-driven loss function based on the error between the voltage prediction value and the true value, a physical constraint loss function based on the DC bus capacitor power balance relationship and droop control characteristics is further constructed to constrain the predicted bus voltage change to meet the physical operation law of the DC microgrid. The data-driven loss function and the physical constraint loss function constitute a hybrid loss function.

[0012] Step 4: Constructing the steady state machine logic: ,in, for Predicted voltage value at time [time]. Voltage amplitude threshold, This is a voltage over-limit continuous accumulation time counter. The duration threshold is used as the input of the steady state machine, which takes the voltage prediction value reconstructed from the bus voltage change prediction result as the input. By simultaneously introducing the voltage amplitude threshold and the duration threshold, the operating state of the DC microgrid is determined. The output of the steady state machine is a three-value determination result, in which the stable state is recorded as 2, the early warning state is recorded as 1, and the unstable state is recorded as 0.

[0013] Step 5: Model Training and Stability Result Analysis: The predicted bus voltage change results after deep learning model training are fed into the steady state machine for judgment. The steady state machine uses the predicted bus voltage change results output by the deep learning model as a basis, reconstructs the corresponding voltage prediction value through time integration, and scans it time by time. According to the preset voltage amplitude threshold and duration threshold, the operating state of the DC microgrid is judged. When the voltage prediction value remains within the allowable operating range throughout the entire evaluation window, the DC microgrid is judged to be in a stable state. When the voltage prediction value shows continuous out-of-bounds behavior and meets the state machine criteria, the DC microgrid is considered to be in an unstable state.

[0014] The aforementioned method for analyzing transient voltage stability of DC microgrids based on embedded physical constraints uses RobustScaler to standardize the collected data before training the deep learning model, in order to ensure the consistency of different data in terms of numerical scale and statistical distribution.

[0015] The data-driven loss function in step 3 of the above-mentioned DC microgrid transient voltage stability analysis method based on embedded physical constraint deep learning is: ,in, Give the model an error threshold; This represents the error between the predicted and actual voltage values.

[0016] The power balance relationship of the DC bus capacitor is as follows: In the formula, The bus input power includes both source-side output power and energy storage output power. Power consumed by the load, Bus voltage The bus capacitor is used as the input; the collected source-side output power, energy storage output power, and load consumption power are substituted into the equation to construct the physical residual equation. ,in, for The physical residual at time, for Source-side output power at time , for Energy storage output power at any given time for Power consumption of the load at any given time. for Predicted voltage value at time [time]. for Predicted voltage value at time [time]. For the time interval, the first physical constraint loss function is... In the formula, This represents the total number of sampling times within the observation period.

[0017] The droop control characteristics are: In the formula, Bus voltage This is the bus reference voltage. The droop coefficient is... Energy storage output power; second physical constraint loss function ;

[0018] The overall mixture loss function is then defined as: In the formula, , This is the loss coefficient.

[0019] This invention focuses on assessing the transient voltage stability of DC microgrids. From the perspective of system power balance and dynamic response characteristics, it proposes a method for analyzing transient voltage stability of DC microgrids based on deep learning with embedded physical constraints, and implements transient stability assessment based on this method. This method uses source-side, energy storage, and load power information as input features. It constructs a deep learning model that integrates a one-dimensional convolutional neural network with embedded physical knowledge, a bidirectional long short-term memory network, and a multi-head attention mechanism to predict the short-time evolution of bus voltage changes, thus avoiding potential biases caused by time series autocorrelation in direct voltage prediction. Furthermore, this method models based on measurable external characteristic data at the system level, performing equivalent modeling of the DC microgrid system containing complex control strategy converters in a data-driven manner, avoiding dependence on converter internal parameters and control details. Finally, a steady-state machine decision logic is introduced to map the voltage change prediction results to voltage evolution trajectories. Combined with voltage amplitude and duration threshold constraints, it achieves rapid assessment of the transient instability trend of the DC microgrid. Finally, numerical examples verify the effectiveness and engineering applicability of this method. Attached Figure Description

[0020] Figure 1 The waveform diagram for predicting the bus voltage and voltage change of a DC microgrid.

[0021] Figure 2 This is a graph showing the voltage loss curve during the training process of the DC microgrid bus.

[0022] Figure 3 For model validation set Line graph.

[0023] Figure 4 This is a schematic diagram of the model confusion matrix. Detailed Implementation

[0024] A method for transient voltage stability analysis of DC microgrids based on embedded physical constraint deep learning includes the following steps:

[0025] Step 1: Dataset Construction

[0026] The system collects the source-side output power, energy storage output power, and load consumption power of a DC microgrid over a continuous time period. The load consumption power can be obtained from a real-time measurement system or from day-ahead or rolling dispatch results. Before training the deep learning model, the collected data undergoes uniform preprocessing to ensure consistency in numerical scale and statistical distribution across different data sets. This invention uses RobustScaler to standardize the collected data and divides the normalized data into training, validation, and test sets in a 6:2:2 ratio for deep learning model parameter learning and generalization performance verification.

[0027] Step 2: Building the Deep Learning Model Architecture

[0028] A deep learning model is constructed, consisting of three layers: The first layer is a one-dimensional convolutional neural network (CNN), which primarily extracts local temporal features from the collected data to obtain the power change sequence, capturing the short-term dynamic characteristics of source-load power changes. Its locality and translation invariance compensate for the shortcomings of the latter two layers in extracting local features from the original data. The second layer is a bidirectional long short-term memory network (Bi-LSTM), which models the forward and backward temporal dependencies of the power change sequence to fully explore the impact of power changes on the evolution of bus voltage, obtaining a temporal feature sequence covering different times and containing multi-dimensional features. The third layer is a multi-head attention mechanism (MHA), which adaptively weights the temporal feature sequence to obtain the predicted bus voltage change. The three layers complement each other and work together to effectively overcome the shortcomings of single models in processing complex sequence data with long-distance dependencies, enabling this deep learning model to have strong feature extraction and sequence modeling capabilities at the millisecond timescale.

[0029] Step 3: Constructing the model mixture loss function

[0030] In the deep learning model training process, in addition to constructing a data-driven loss function based on the error between the voltage prediction value and the true value, a physical constraint loss function based on the DC bus capacitor power balance relationship and droop control characteristics is further constructed to constrain the predicted bus voltage change to meet the basic physical operation law of the DC microgrid. This forms a hybrid loss function that combines data-driven loss and physical constraint loss to improve the physical consistency and engineering feasibility of the prediction results.

[0031] To balance the peak characteristics of voltage changes in the initial stage of disturbance identification with the near-zero distribution of voltage changes in the steady-state stage, this invention uses the Huber loss function as the data-driven loss function, the expression of which is:

[0032] ,

[0033] in, Give the model an error threshold; This represents the error between the predicted and actual voltage values.

[0034] Furthermore, addressing the issue of poor physical interpretability in purely data-driven deep learning models, this invention incorporates the DC bus capacitor power balance relationship and droop control characteristics into the model loss, thus constructing a hybrid loss function. The formula for the DC bus capacitor power balance relationship is as follows:

[0035] ,

[0036] In the formula, The bus input power includes both source-side output power and energy storage output power. Power consumed by the load, Bus voltage For bus capacitors;

[0037] Substitute the collected source-side output power, energy storage output power, and load consumption power into the equation to construct the physical residual equation.

[0038] ,

[0039] in, for The physical residual at time, for Source-side output power at time , for Energy storage output power at any given time for Power consumption of the load at any given time. for Predicted voltage value at time [time]. for The predicted voltage value at time -1 Let be the time interval. Then the first physical constraint loss function can be defined as:

[0040] ,

[0041] In the formula, This represents the total number of sampling times within the observation period.

[0042] The physical residual constraint forces the first derivative of the bus voltage change output by the deep learning model to conform to the physical laws of capacitor charging and discharging, thereby eliminating the possibility that a purely data-driven deep learning model might predict voltage jumps that violate physical common sense in sparse data regions.

[0043] The formula for droop control characteristics is as follows:

[0044] ,

[0045] In the formula, Bus voltage This is the bus reference voltage. The droop coefficient is... Let the energy storage output power be denoted as . Then the second physical constraint loss function can be defined as:

[0046] ,

[0047] The overall mixture loss function can then be defined as follows:

[0048] ,

[0049] In the formula, , This is the loss coefficient.

[0050] Step 4: Constructing the steady state machine logic

[0051] The steady-state machine takes the voltage prediction value reconstructed from the bus voltage change prediction as input and determines the operating state of the DC microgrid by simultaneously introducing a voltage amplitude threshold and a duration threshold. First, based on the operating requirements of the DC microgrid, an allowable operating range for the bus voltage is set, and a voltage amplitude threshold is set according to this range. When the voltage prediction value is greater than or equal to the voltage amplitude threshold, the DC microgrid is considered to be in a stable state. When the voltage prediction value is less than the voltage amplitude threshold, the steady-state machine does not immediately determine that the DC microgrid is unstable, but instead issues a warning and begins recording the duration of the voltage exceeding the voltage amplitude threshold. During this stage, the steady-state machine accumulates the voltage out-of-range state over time. Only when the voltage prediction value is lower than the voltage amplitude threshold for multiple consecutive sampling times, and the duration exceeds the duration threshold, is the DC microgrid's operating state determined to be unstable. The introduction of this duration threshold effectively reduces the impact of transient oscillations on the determination result. The output of the steady-state machine is a three-valued determination result, where a stable state is recorded as 2, a warning state as 1, and an unstable state as 0.

[0052] ,

[0053] in, This is a voltage over-limit continuous accumulation time counter. For duration threshold, This is the voltage amplitude threshold.

[0054] Step 5: Model Training and Stabilization Result Analysis

[0055] During the deep learning model training phase, a three-layer convolutional structure of a one-dimensional convolutional neural network sequentially extracts local variation features of the collected data at different time scales. Subsequently, a bidirectional long short-term memory network performs time-series modeling of the power change sequence, characterizing the evolution of the system's operating state from both forward and reverse time dimensions. Finally, a multi-head attention mechanism is introduced to weighted reconstruct the time-series features at different times, enabling the model to pay more attention to key time segments during the initial disturbance and voltage recovery phases during training. The predicted bus voltage change results after deep learning model training are fed into a steady-state machine for judgment. The steady-state machine uses the predicted bus voltage change results output by the deep learning model as a basis, reconstructs the corresponding voltage prediction value through time integration, and scans it time-by-time. Based on pre-set voltage amplitude and duration thresholds, the operating state of the DC microgrid is determined. When the voltage prediction value remains within the allowable operating range throughout the entire evaluation window, the DC microgrid is determined to be in a stable state; when the voltage prediction value exhibits continuous out-of-bounds behavior and meets the state machine criteria, the DC microgrid is considered to have shown a significant instability trend.

[0056] This invention, by using bus voltage variation rather than absolute voltage value as the prediction object, can more directly characterize the impact of dynamic imbalance of source and load power on the bus voltage evolution process, improving the modeling ability for transient processes and sudden changes in operating conditions. Simultaneously, by introducing the DC bus capacitor power balance relationship and droop control characteristics during the deep learning model training process, this invention effectively avoids the problem of physically infeasible predictions under strong disturbance conditions, improving the physical consistency and engineering interpretability of the prediction results. Furthermore, by constructing a steady-state machine and combining it with the predicted bus voltage, this invention achieves automated identification of the bus operating state, reducing reliance on manual experience and threshold selection. This invention can also achieve advance prediction of the future operating state of the DC microgrid bus by introducing day-ahead or rolling dispatch power information as model input, providing effective support for operation dispatching decisions, risk warning, and safety control.

[0057] To verify the reliability and effectiveness of this invention, a deep learning model with embedded physics knowledge was built on the PyCharm platform. The model was trained and validated using data, and the results are as follows:

[0058] from Figure 1The voltage prediction comparison results show that the model-predicted voltage trajectory and the actual voltage trajectory maintain good consistency in overall trend. Whether in the relatively stable voltage operating range or in the rapid voltage drop phase caused by load disturbance, the predicted voltage can continuously track the actual voltage evolution process without significant amplitude deviation or trend lag.

[0059] from Figure 1 The comparison of voltage changes in model b further reveals that the actual voltage changes exhibit significant high-frequency fluctuations, reflecting the dynamic characteristics of the DC microgrid under the combined influence of multi-source disturbances and control effects during transient processes. Under these conditions, the voltage change prediction results output by the model can effectively reflect the overall voltage fluctuation range and main change patterns.

[0060] The above results show that deep learning models can not only depict the main evolution trend of bus voltage at the level of voltage change prediction, but also retain the rapid change characteristics in the transient process to a certain extent, providing a relatively sufficient dynamic information basis for subsequent stability determination based on time characteristics.

[0061] like Figure 2 As shown, in the initial training phase, the loss value decreases rapidly within the first 10 epochs, then gradually stabilizes, indicating that the deep learning model can learn the main features in a relatively small number of iterations. Throughout the training process, the loss curves of the training set and the validation set show consistent trends, with their values ​​remaining close and no significant separation occurring with increasing training epochs. This result demonstrates that the deep learning model's fit to the training set is largely consistent with its response to the test and validation sets.

[0062] Coefficient of determination of deep learning models on the validation set (The closer the value is to 1, the better the model's prediction results.) The changes with training epochs are as follows: Figure 3 As shown in the figure. It can be seen from the graph that the coefficient of determination... The training loss improved rapidly in the early stages and remained stable at approximately 0.96 in subsequent iterations without significant decline. This result indicates that the deep learning model's fitting performance to the validation set reached a stable state early during training and remained consistent in subsequent iterations, suggesting that the model parameter update process did not introduce additional fluctuations to the test and validation sets. Combining the trends of the training and validation set losses, the deep learning model can be considered to have good convergence consistency under the current training configuration. The training process ended at the 66th iteration due to an early stopping mechanism, indicating that further iterations at this stage were unlikely to bring significant performance improvements. These phenomena demonstrate that the deep learning model achieved relatively stable convergence behavior while maintaining prediction accuracy.

[0063] Table 1 Model Evaluation Indicators

[0064]

[0065] To differentiate the influence between model prediction performance and the inherent inertia of the voltage time series, this invention introduces an inertial benchmark as a control. The inertial benchmark for voltage change is defined as predicting no change at the next time step, i.e., predicting a voltage change of 0 at that time step; while the inertial benchmark for restoring the voltage value is defined as directly reusing the true value from the previous time step.

[0066] As can be seen from Table 1, the inertial reference can achieve a higher coefficient of determination in absolute voltage prediction. In the prediction of voltage change, the inertial reference determination coefficient The value approaches zero. This phenomenon indicates that in bus voltage sequences with significant time correlation, performance indicators based solely on voltage values ​​are easily affected by time continuity, making it difficult to reflect the model's ability to characterize transient dynamics. In contrast, voltage change prediction can effectively mitigate the interference of time continuity and is more conducive to evaluating the model's ability to characterize the dynamic evolution of voltage under source load power disturbances.

[0067] Table 2. Results of Steady State Machine Judgment

[0068]

[0069] The data in the table shows that during this state transition, the model predictions remained consistent with the actual system at key time points. Within the instability range, at time step 1687, the actual bus voltage dropped to 759.85V, while the model predicted 759.86V; both triggered the over-limit warning at the same time step. Subsequently, at time step 1703, the DC microgrid entered an unstable state, and the corresponding predictions did not show any premature or delayed changes in timing.

[0070] During the voltage recovery phase, the model predictions remained synchronized with the actual system evolution. When the time step was 3242, the predicted voltage and the actual voltage showed consistency in both numerical values ​​and state determination, indicating that the model did not introduce any additional time offset during the state recovery process.

[0071] The comparison results above show that the steady-state determination logic built based on the predicted voltage sequence can maintain good time consistency at critical state transition nodes, realize a continuous mapping from predicted values ​​to steady-state determination, and provide a quantifiable basis for stability assessment.

[0072] Normalized confusion matrix as follows Figure 4As shown in the figure, the deep learning model achieves a recognition accuracy of 97.37% under steady-state conditions, with only 2.63% of steady-state samples being classified as warning states. This result indicates that in the boundary region between steady-state and critical states, the deep learning model tends to make relatively conservative judgments, thereby avoiding the neglect of potential risk states.

[0073] For unstable conditions, the deep learning model did not misclassify unstable samples as stable states, with a misclassification probability of 0.00%. This indicates that the constructed state determination logic has strong consistency in identifying unstable states, effectively avoiding the risk accumulation problem that may be caused by missed classifications. Meanwhile, the deep learning model achieved a weighted F1 score of 0.9787 on the test set. This metric, while comprehensively considering the differences in the number of samples of different categories, reflects the overall balance achieved by the deep learning model between precision and recall, indicating that the deep learning model can maintain relatively stable classification performance in multi-state determination tasks.

Claims

1. A method for transient voltage stability analysis of DC microgrids based on embedded physical constraint deep learning, characterized in that: Includes the following steps: Step 1: Dataset Construction: Collect the source-side output power, energy storage output power, and load consumption power of the DC microgrid over a continuous period of time; Step 2: Constructing the Deep Learning Model Architecture: Construct a deep learning model consisting of three layers. The first layer is a one-dimensional convolutional neural network (CNN), which extracts local temporal features from the collected data to obtain the power change sequence. The second layer is a bidirectional long short-term memory (LSTM) network, which models the forward and backward temporal dependencies of the power change sequence, explores the impact of power changes on the bus voltage evolution process, and obtains a temporal feature sequence covering different times and containing multi-dimensional features. The third layer is a multi-head attention mechanism, which adaptively weights the temporal feature sequence to obtain the predicted bus voltage change. Step 3: Construction of Hybrid Loss Function: In the deep learning model training process, in addition to constructing a data-driven loss function based on the error between the voltage prediction value and the true value, a physical constraint loss function based on the DC bus capacitor power balance relationship and droop control characteristics is further constructed to constrain the predicted bus voltage change to meet the physical operation law of the DC microgrid. The data-driven loss function and the physical constraint loss function constitute a hybrid loss function. Step 4: Constructing the steady state machine logic: ,in, for Predicted voltage value at time [time]. For voltage amplitude threshold, This is a voltage over-limit continuous accumulation time counter. The duration threshold is used as the input of the steady state machine, which takes the voltage prediction value reconstructed from the bus voltage change prediction result as the input. By simultaneously introducing the voltage amplitude threshold and the duration threshold, the operating state of the DC microgrid is determined. The output of the steady state machine is a three-value determination result, in which the stable state is recorded as 2, the early warning state is recorded as 1, and the unstable state is recorded as 0. Step 5: Model Training and Stability Result Analysis: The predicted bus voltage change results after deep learning model training are fed into the steady state machine for judgment. The steady state machine uses the predicted bus voltage change results output by the deep learning model as a basis, reconstructs the corresponding voltage prediction value through time integration, and scans it time by time. According to the pre-set voltage amplitude threshold and duration threshold, the operating state of the DC microgrid is judged. When the voltage prediction value remains within the allowable operating range throughout the entire evaluation window, the DC microgrid is judged to be in a stable state. When the voltage prediction value shows continuous out-of-bounds behavior and meets the state machine criteria, the DC microgrid is considered to be in an unstable state. The data-driven loss function mentioned in step 3 is: ,in, Give the model an error threshold; This represents the error between the predicted and actual voltage values. The power balance relationship of the DC bus capacitor is as follows: In the formula, The bus input power includes both source-side output power and energy storage output power. Power consumed by the load, Bus voltage The bus capacitor is used as the input; the collected source-side output power, energy storage output power, and load consumption power are substituted into the equation to construct the physical residual equation. ,in, for The physical residual at time, for Source-side output power at time , for Energy storage output power at any given time for Power consumption of the load at any given time. for Predicted voltage value at time [time]. for Predicted voltage value at time [time]. For the time interval, the first physical constraint loss function is... In the formula, This represents the total number of sampling times within the observation period. The droop control characteristics are: In the formula, Bus voltage This is the bus reference voltage. The droop coefficient is... Energy storage output power; second physical constraint loss function ; The overall mixture loss function is then defined as: In the formula, , This is the loss coefficient.

2. The method for transient voltage stability analysis of DC microgrids based on embedded physical constraint deep learning according to claim 1, characterized in that: Before training the deep learning model, the collected data is standardized using RobustScaler to ensure consistency in numerical scale and statistical distribution among different data.

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