A hybrid LSTM-transformer model for short-term urban electricity load forecasting: a two-city case study.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 11;16:16964. doi: 10.1038/s41598-026-47905-9 A hybrid LSTM-transformer model for short-term urban electricity load forecasting: a two-city case study Hongli Liu 1, 2 , Yang Wei 1, 2, ✉ , Han Zhang 1, 2 , Yang Wang 1, 2, 3 , Jie Zhang 1, 2 , Zhongqiang Luo 4 Author information Article notes Copyright and License information 1 Electric Power Science Research Institute, State Grid Corporation of Sichuan Province, Chengdu, 610095 China 2 Power System Security and Operation Key Laboratory of Sichuan Province, Chengdu, 610095 China 3 China Power Supply Company, Suining, China 4 School of Automation and Information Engineering, Sichuan University of Science & Engineering, Yibin, 644000 Sichuan China ✉ Corresponding author. Received 2025 Dec 16; Accepted 2026 Apr 3; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13230624  PMID: 41965471 Abstract Accurate short-term urban power load forecasting is crucial for power system dispatching, peak load management, and data-driven urban energy planning. To improve the forecasting performance of multivariate load time series under complex temporal dependencies and external influencing factors, this paper proposes a hybrid LSTM-Transformer model, combining the temporal representation capabilities of Long Short-Term Memory (LSTM) networks with the global dependency modeling capabilities of Transformer encoders. Based on multi-source 15-minute time series data from two representative cities, the proposed model is evaluated on a short-term power load forecasting task and compared with baseline models including traditional LSTM and DE-LSTM. Experimental results show that, under a given evaluation protocol, the hybrid model achieves lower prediction errors and higher fitting accuracy. These results demonstrate that the proposed structure can effectively capture the local temporal dynamics and long-distance feature interactions in urban load sequences. Subject terms: Energy science and technology, Engineering, Mathematics and computing Introduction Against the backdrop of increasingly severe global climate change, sustainable urban development faces growing pressure. The continuous rise in global average temperature and the frequent occurrence of extreme weather events have had a significant impact on socio-economic systems and natural ecosystems, making low-carbon development a recognized strategic response 1 . As the main carriers of economic and social activities, cities dominate global energy consumption and greenhouse gas emissions 2 , 3 . With the acceleration of urbanization and industrialization, urban energy demand continues to grow rigidly, while excessive reliance on fossil fuels further exacerbates carbon emissions 4 – 6 . In this context, the low-carbon transformation of cities should not be viewed merely as an energy issue, but rather as a complex systemic process involving the coordinated evolution of energy, economy, and environment 7 . Existing research mainly focuses on coupled measurement, policy design, and coordinated development analysis 8 – 12 , but these studies also highlight the urgent need for more effective data-driven tools to provide potential support for urban energy management. The rapid development of big data technology has created new opportunities to address this challenge. The massive amounts of multi-source data from the power grid, user-side electricity consumption, and environmental monitoring provide a richer empirical basis for analyzing the interactions between urban energy use, economic activities, environmental changes, and low-carbon goals 13 – 17 . Therefore, big data analytics and machine learning are increasingly being introduced into the energy field 18 . For example, the hybrid LSTM-Transformer framework has shown significant advantages in regional residential electricity forecasting 19 , providing potential support for urban energy management and serving as a reference for future. Among related tasks, short-term power load forecasting remains a particularly important and active research topic because load dynamics are influenced by a variety of factors, including environmental conditions, social behavior, economic activities, and weather-sensitive demand, resulting in strong periodicity, randomness, and uncertainty. Existing research shows that traditional forecasting methods are often limited by insufficient data preprocessing, limited nonlinear representation capabilities, and dependence on a single model structure. Reference 20 systematically reviews intelligent load forecasting methods and points out that ignoring data preprocessing is a common limitation of traditional models. To address this issue, Reference 21 proposes a comprehensive forecasting framework that integrates data preprocessing, GAN-based forecasting, and intelligent weighting mechanisms to improve the performance of nonlinear modeling. Reference 22 further enhances nonlinear feature extraction by improving the temporal convolutional structure in the IAVOA-EATCN model. For scenarios with high volatility and multi-factor coupling, Reference 22 develops a machine learning-based port energy demand forecasting model. Reference 23 provides a comparative review demonstrating that hybrid methods can generally provide more reliable and accurate industrial load forecasts. To better address weather-driven abrupt changes, Reference 24 proposes a weather-aware multi-scale fusion bidirectional nonlinear spiking neural network model, while Reference 25 introduces a deep learning method based on adaptive mode decomposition to achieve more refined short-term regional load forecasts. To support reliable short-term load forecasting in urban power systems, it is necessary to focus on a more clearly defined technological research gap. Existing research shows that single recurrent neural network models can capture local time dependencies well, but they still have shortcomings in modeling long-range dependencies and complex cross-feature interactions in multivariate load sequences 27 . In recent years, hybrid deep learning models have improved prediction accuracy to some extent, but many studies either rely on load data from a single source or lack a systematic discussion on how “sequence feature extraction” and “attention-based dependency modeling” work synergistically for urban load forecasting. Against this backdrop, this paper develops and evaluates a hybrid forecasting architecture for short-term urban power load forecasting, oriented towards multi-source time series inputs. This framework is essentially an empirical model for forecasting tasks, providing a methodological foundation for future broader urban energy and low-carbon research. The main contributions of this paper can be summarized as follows: Hybrid Forecasting Architecture Design: A hybrid LSTM-Transformer model for short-term urban power load forecasting is proposed. The LSTM module is used to extract time-series dynamic features, while the Transformer encoder is used to model long-range dependencies and cross-feature interactions. Multi-Source Input Setting for Load Forecasting: This paper employs multi-source time-series inputs, including historical load observations and relevant exogenous features, to evaluate whether richer input representations can improve urban load forecasting performance. Empirical Comparison under a Unified Evaluation Protocol: Under the same preprocessing procedures and evaluation metrics, the proposed model is compared with baseline models, and its predictive performance is evaluated from the perspective of standard error. The remainder of this paper is structured as follows. Section  2 provides a detailed explanation of the LSTM and Transformer models. Section  3 elaborates on the specifics of model construction. This includes LSTM formulas, Transformer position encoding, multi-head attention operations, and hyperparameter optimization methods. Section  4 compares the performance of the three models using typical regional data. Their advantages are validated through MAPE plots and time-series curves. Finally, Sect.  5 summarizes the value of the models and identifies future directions. Section  6 describes the limitations of existing research and future research directions. Preliminaries LSTM model Recurrent Neural Networks (RNNs) are a class of artificial neural networks whose core function is processing sequential data. The LSTM model is a significant variant of RNNs, with its most advantage being the ability to retain information over extended periods and effectively capture long-term dependencies within data. The fundamental building block of an LSTM is called a “cell” (as shown in Fig. 1 ). At each time step, this cell receives three types of inputs: the cell state from the previous time step (representing long-term memory), the hidden state from the previous time step (representing short-term memory), and the input data for the current time step. Ultimately, it outputs two results: the updated cell state (new long-term memory) and the updated hidden state (new short-term memory). Fig. 1. Open in a new tab The basic unit of LSTM. LSTM consists of three gates: the input gate, the forget gate, and the output gate. Its state propagates between units, each capable of performing information addition or subtraction operations. These operations enable information to selectively influence the state through the “gate” structure at each time step. The gate structure includes sigmoid layer operations and vector dot product calculations. Within the LSTM architecture, the first step involves determining which information within the cell state should be discarded—a function performed by the “forget gate.” The forget gate combines the current input with the previous time step’s output to decide which portions of the previous cell state’s information should be forgotten. The forget gate formula is as follows: 1 Here, denotes the connection weights of the S-shaped layer of the forgetting gate, and denotes the threshold value of the S-shaped layer. After the LSTM “forgets” some of the previous state information, the current cell state must learn new information from the current input. This process is accomplished by the “input gate.” The “input gate” consists of a tanh layer and a sigmoid layer. The tanh layer generates a new candidate value vector, while the sigmoid layer controls which information from the tanh layer is added to the current cell state. The formula is as follows: 2 3 After calculating the updated cell states, the final step of the LSTM is to determine the output value for the current time step using the “output gate.” Its calculation formula is as follows: 4 Within the LSTM module architecture, multiple LSTM layers are incorporated, each composed of a series of LSTM units. These units are connected in a chain-like structure, where the output of one unit feeds into the next, as illustrated in Fig. 2 . As data flows through these layers, each subsequent layer receives input from the preceding layer. It is important to note that the operations within each unit of a specific layer employ identical weights and biases. The output from the final LSTM layer is fed into a fully connected layer (FCL), where the output from each activation function in the preceding layer is input into all activation functions of the FCL. The FCL maps the LSTM output to the desired output dimension T, thereby generating the embedding vector Y. This design ensures consistent feature extraction for time series data, with the LSTM module’s final output serving as the input data’s vector representation. Fig. 2. Open in a new tab The LSTM module utilized in this paper. Transformer model The core of the Transformer model is an encoder-decoder architecture. Both components incorporate residual connections and “Add & Norm” layers, crucial for enhancing training stability. The encoder transforms the input sequence into a series of representations based on attention mechanisms within this structure. The decoder handles the generation task, utilizing the encoder’s output representations and self-attention mechanism to produce the target sequence. This mechanism enables the model to selectively focus on specific parts of the input sequence, which is essential for power load forecasting. Specifically, the self-attention mechanism is implemented through the scaled dot-product attention defined in 9 , formally described as a function mapping queries and a set of key-value pairs to an output. Queries, keys, values, and the generated output are all represented as vectors. Let represent the dimension shared by both Query and Query vectors. The attention mechanism hinges on three primary matrices: the Query matrix ( ), the Key matrix ( ), and the Value matrix ( ). The attention mechanism can be expressed as a matrix computation described in Eq. ( 5 ) as defined in 9 . 5 In the power load forecasting scenario, the encoder feeds the output of its LSTM component back as its own input. It is important to note that positional encoding was introduced initially because Transformers cannot inherently recognize the order or position of input elements. Positional encodings based on sine and cosine functions are added to the input embeddings to convey positional information to the model. In this research, we adopt the positional encoding implementation consistent with 26 . The dimension of these positional encodings matches that of the embeddings, uniformly denoted as T. As shown in Fig. 3 , the encoder architecture consists of multiple parallel self-attention layers that collectively form a complex multi-head attention mechanism. Following the multi-head attention layer, the encoder includes a feedforward fully-connected network with residual connections. The outputs from both components are jointly fed into a normalization layer (i.e., Add and Norm operations). Starting from the input sequence ( ), the matrices ( , , ) are generated and successively processed through both the Multi-Head Attention and the Feed-Forward Network. The final output represents the predicted electricity load for the next time instance. In classification tasks, such predictions typically require the Softmax activation function to map input data to discrete categories. However, in electricity load forecasting task—a regression problem—the linear layer’s output directly provides continuous value predictions without the use of Softmax. Fig. 3. Open in a new tab Transformer encoder architecture. When generating the output sequence, the decoder employs an element-wise generation approach, simultaneously considering both the encoder’s output and previously generated elements in the sequence. Each layer of the decoder comprises three fundamental building blocks: the first is a masked multi-head attention mechanism, which operates similarly to the encoder’s multi-head attention but incorporates an additional masking operation. This ensures each position can only focus on earlier positions within the output sequence. The second building block is the encoder-decoder attention, which consists of another multi-head attention mechanism enabling the decoder to focus on the encoder’s output. The final building block is a feedforward network, structurally similar to the encoder’s FFN, which processes each position individually. Additionally, each sublayer of the decoder employs residual connections and layer normalization. Due to the more complex structure of Transformer models, training them typically requires more time than training LSTM models. A hybrid LSTM-transformer-based prediction model This section details the methodology underlying the hybrid LSTM-Transformer model for electricity load forecasting. The proposed hybrid model integrates the strengths of both LSTM and Transformer architectures. This hybrid framework efficiently captures and leverages temporal dependencies within multivariate time series data, thereby enhancing the performance of electricity load forecasting. At its core, the hybrid model employs a sequence structure capable of effectively processing input multivariate time series data. It primarily consists of two components, with its main structure illustrated in the Fig. 4 . Fig. 4. Open in a new tab Hybrid LSTM-Transformer Model. The proposed model adopts a hybrid design that combines LSTM with an encoder-only Transformer. This design is intended for regression-based short-term load forecasting rather than sequence generation. The LSTM module is used to extract short-term sequential patterns from historical observations, while the encoder-only Transformer further captures longer-range dependencies and cross-feature interactions within the multivariate input sequence. Compared with a full encoder-decoder design, this implementation provides a lighter and more task-matched architecture for point forecasting. In this architecture, the LSTM component occupies a central position and is responsible for processing complex temporal relationships within the input data. Unlike traditional standalone LSTM models typically employed for regression tasks, the LSTM module proposed in this section generates effective embedding vectors of dimension T representing the input data through a series of iterative operations. This approach captures key features and patterns within multivariate time series data. The formula for the LSTM feature extraction layer is as follows: 6 The LSTM model is designed with K layers containing L LSTM cells. The outputs of these cells are fed into a fully connected layer to generate an embedding vector of dimension T. T, K, and L values were empirically optimized through a systematic trial-and-error process to achieve optimal performance in the load forecasting task. The LSTM model demonstrates strong capabilities in understanding and learning complex temporal dynamics within sequential data. Incorporating LSTM as the initial component enables the model to effectively capture key sequential features before passing processed information to the Transformer component. This architecture reduces system complexity, shortens training time, and minimizes computational overhead when handling long sequences by eliminating the decoder. The second component of this architecture is the Transformer encoder, which generates load consumption predictions based on the vector embeddings obtained from the LSTM. The encoder is a core component of the original Transformer architecture, but does not include a decoder module. First, the encoder adds positional encoding to the embedding vectors to preserve the sequential order of the input data. Subsequently, these augmented embedding vectors are fed into the main encoder body. The main encoder body consists of P identical stacked layers. Within each layer, the encoder employs a multi-head attention mechanism to perform parallel self-attention operations, namely:: 7 Among them, Specifically, each attention layer employs R attention heads to capture distinct features within the input data effectively. The keys, values, and queries required for these attention heads derive from the previous layer’s output, ensuring continuous context propagation. Additionally, each layer incorporates a fully connected feedforward network that processes each position in the input sequence individually, facilitating the generation of richer feature representations. Experimental results Accurate short-term electricity load forecasting is essential for urban energy management and can provide data support for energy system planning and may be indirectly relevant to broader energy-environment research. As a key operating variable in urban energy systems, electricity load reflects the combined influence of socioeconomic activity, environmental conditions, and policy-related factors. Accordingly, this study focuses on short-term urban electricity load forecasting using real multi-source time-series data from two representative urban areas (Area 1 and Area 2). The dataset spans from January 1, 2012 to January 10, 2015, with a sampling interval of 15 min, resulting in 105,984 samples for each area. It includes five input features: electricity load (MW), average temperature (temp_avg, °C), relative humidity (humidity, %), rainfall (rain, mm), and a quarter-hour code (0–95) to capture intraday periodicity. Missing values were handled by complete case deletion, and all features were standardized using Z-score normalization. To avoid time-series data leakage, the data were divided chronologically into a training set (70%, 74,188 samples, January 2012 to February 2014), a validation set (15%, 15,897 samples, February 2014 to July 2014), and a test set (15%, 15,899 samples, July 2014 to January 2015). A sliding window of 96 time steps (24 h) was used to construct historical input sequences for predicting the load value in the next 15-minute interval. Based on this dataset, a hybrid deep forecasting model integrating LSTM and Transformer architectures was developed, and its performance was compared with that of a conventional LSTM model and a differential evolution-optimized DE-LSTM model. The experiment was quantitatively evaluated based on metrics including root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and Mean Absolute Percentage Error (MAPE), defined as: 8 9 10 11 Among these, parameter meanings: n: Total number of sample data points. represents the true value of the i th sample. is the predicted value output by the model for the i –th sample. is the difference between the true value and the predicted value of the i –th sample. is the absolute value of the residual for the i th sample. is the mean of all true values, calculated as . is the sum of squared errors (SSE), representing the variation unexplained by the model. is the total sum of squares (SST), representing the total variation in the true data. The model architecture parameters and training hyperparameters used in this study are listed in Tables 1 and 2 , respectively. All hyperparameters were selected using a grid search method based on validation set performance to achieve the best balance between mean absolute error (MAE) and root mean square error (RMSE). Table 1. Model architecture parameters. Component Parameter LSTM-Transformer LSTM DE-LSTM Input Layer Input feature dimension 5 5 5 Sequence length 96 96 96 LSTM Encoder Hidden dimension 128 128 16 Number of layers 2 2 1 Dropout rate 0.1 0.1 0.0 Transformer Encoder Number of layers 4 - - Embedding dimension 32 - - Number of attention heads 8 - - Feedforward dimension 128 - - Dropout rate 0.1 - - Output Layer Fully connected layers 32→16→1 128→64→1 16→1 Output dimension 1 1 1 Open in a new tab Table 2. Training hyperparameters. Category Parameter Configuration Optimizer Algorithm Adam Initial learning rate 0.001 Weight decay 1 × 10⁻⁵ Learning Rate Scheduler Strategy ReduceLROnPlateau Monitor metric Validation loss Patience 5 epochs Reduction factor 0.5 Training Strategy Batch size 32 Maximum epochs 100 Early stopping patience 15 epochs Loss function MSE Data Processing Normalization method Z-score standardization Random seed 42 Open in a new tab Table 3 summarizes the overall prediction results of each model on the test set. From the overall metrics, the proposed LSTM-Transformer model achieved the best performance under the current experimental settings, demonstrating lower prediction errors in RMSE and MAE metrics, and a higher goodness of fit in R². Compared to the traditional LSTM model, the hybrid architecture further reduces the overall error level while maintaining high fitting ability; and compared to DE-LSTM, the proposed model shows more significant performance advantages across all metrics. These results indicate that, under current data conditions, combining the local time-series modeling capabilities of LSTM with the long-range dependency characterization capabilities of Transformer helps improve the prediction accuracy of multivariate urban load sequences. Table 3. Comparison of predictive performance across models. Model RMSE MAE R ² LSTM-Transformer 61.83 39.26 0.9991 DE-LSTM 205.96 167.88 0.9889 LSTM 82.28 60.52 0.9981 Open in a new tab To provide a more intuitive comparison of model error levels, a bar chart of MAPE for the three models is plotted, as shown in Fig. 5 . This metric measures the relative error between the model’s predicted values and the actual values. Fig. 5. Open in a new tab Comparison of MAPE across different models. Figure 5 shows the comparison results of the three models on the mean absolute percentage error (MAPE) metric. It can be seen that the proposed LSTM-Transformer model also maintains the best performance in terms of relative error, with its MAPE significantly lower than that of LSTM and DE-LSTM. This phenomenon is consistent with the conclusions in Table 1 based on absolute error and goodness of fit, indicating that the performance improvement of the proposed model is not limited to a single metric, but exhibits good stability across different evaluation dimensions. Figure 6 shows a time-series comparison of the actual load and the predicted results of each model in City 1. Overall, the proposed LSTM-Transformer model more closely matches the actual load curve, demonstrating better trend-following ability in most time periods. Especially in areas with rapid load changes and near peak transitions, the proposed model responds more promptly to local fluctuations, and the consistency between the predicted trajectory and the actual curve is higher. In contrast, the traditional LSTM model exhibits a certain degree of smoothing effect in some sections and is insufficient in responding to rapidly changing load patterns; DE-LSTM shows relatively more significant deviations in some local periods. These phenomena indicate that, in the City 1 scenario, the proposed hybrid structure can better balance short-term fluctuation information with the overall time-series evolution trend, thereby improving the fitting ability for complex load dynamics. Fig. 6. Open in a new tab Typical City 1 electricity load forecast time series comparison chart. It can be observed that the LSTM-Transformer model demonstrates greater predictive accuracy during midday and evening peak periods, particularly in periods of significant energy fluctuations within the city, where it effectively fits the actual trends. This characteristic holds potential relevance for energy planning and system operation. Figure 7 further illustrates the Absolute Percentage Error (APE) characteristics of the three models over time in City 1. As can be seen from the figure, the LSTM-Transformer model maintains a smaller error amplitude for most periods, and its overall fluctuations are relatively stable. This indicates that the proposed model not only has higher prediction accuracy overall, but also exhibits more consistent prediction stability at the time-by-time level. Although error peaks can still be observed at a few times, the magnitude of these peaks is generally lower than that of the two baseline models. Combined with the prediction curves in Fig. 6 , it can be inferred that the proposed model has relatively better robustness in City 1 to load increases, decreases, and local fluctuations. Fig. 7. Open in a new tab Typical absolute percentage error (APE) variation curve for city one. Figure 8 shows the prediction results for City 2. As the second test scenario, City 2 differs from City 1 in its load change pattern, thus this figure can be used to examine the model’s generalization performance under different city load characteristics. Consistent with the results for City 1, the proposed LSTM-Transformer model maintains a higher consistency with the actual load curve in City 2, and can track the overall trend and some local fluctuations well. In contrast, the LSTM model shows some lag in several rapidly changing intervals, while the DE-LSTM shows significant prediction deviations in some segments. The results in Fig. 8 illustrate that although different city load sequences have different temporal characteristics, the proposed hybrid model still shows good adaptability and stability under the current dual-city test framework. This indicates that the performance improvement of the model is not limited to a single data scenario, but has a certain degree of cross-scenario consistency. Fig. 8. Open in a new tab Typical City 2 electricity load forecast time series comparison chart. Figure 9 shows the APE changes of the three models in City 2. Overall, the LSTM-Transformer model maintains a lower error amplitude and more stable error fluctuations, which is consistent with the better curve fitting performance shown in Fig. 8 . In contrast, LSTM and DE-LSTM show more significant error increases in some time periods, especially during periods of rapid load transitions, where error fluctuations are more pronounced. This indicates that the baseline model has relatively limited adaptability to abrupt changes when the system load changes drastically in a short period. Although the proposed model may still produce some errors in such high-dynamic sections, its overall error control level is still better than the comparative methods. Therefore, in the more variable test scenario of City 2, the proposed model also demonstrates good time stability and robustness. Fig. 9. Open in a new tab Variation curve of absolute percentage error (APE) for typical urban area 2. The experimental results presented in Table 1 ; Figs. 5 , 6 , 7 , 8 and 9 demonstrate that the proposed LSTM-Transformer model outperforms the baseline LSTM and DE-LSTM models in both overall error metrics and local time-series performance. Overall, the proposed model exhibits superior predictive capabilities in RMSE, MAE, R², and MAPE metrics. Graph-by-graph analysis shows that it more accurately tracks the actual load curves in both city test scenarios and maintains smaller and more stable error fluctuations over most time periods. These results indicate that this hybrid architecture effectively combines the advantages of LSTM in local time-series dependency modeling with the capabilities of Transformer in long-range dependency learning, thereby enhancing the model’s ability to characterize complex urban load dynamics. Conclusion This study develops a hybrid LSTM-Transformer model for short-term urban electricity load forecasting and evaluates its performance using multi-source time-series data from two representative cities. The experimental results indicate that, under the adopted evaluation protocol, the proposed model outperforms the compared baseline models in terms of RMSE, MAE, and R². These findings suggest that combining LSTM-based sequential feature extraction with Transformer-based dependency modeling is effective for multivariate urban load forecasting. Limitations and future work This paper still has certain limitations. First, this study only evaluated short-term electricity load forecasting tasks and did not explicitly include carbon emission variables. Second, the dataset is limited to two representative cities. Third, this study focuses on point forecasts and does not provide uncertainty intervals. Finally, it used multi-source input data but did not analyze individual data. Future research will expand this framework by incorporating explicit carbon-related indicators, broader cross-city datasets, stronger forecasting benchmarks, and forecasting methods that consider uncertainty. Author contributions Conceptualization: Hongli Liu, Yang Wei; Methodology: Han Zhang; Software: Yang Wang; Validation: Jie Zhang； Investigation: Hongli Liu, Yang Wei, Zhongqiang Luo; Writing-Original Draft: Hongli Liu, Yang Wei; Writing-Review & Editing: All of the authors. All authors have read and agreed to the published version of the manuscript. Funding This research was funded by Science &Technology Project of Sichuan Province Electric Power Company, grant number 52199723002T. Data availability The datasets generated during and/or analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request. Declarations Competing interests The authors declare no competing interests. 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Data Availability Statement The datasets generated during and/or analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request. Articles from Scientific Reports are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (2.0 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

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