Method and device for predicting traction load power of locomotive traction substation

Abstract

The invention discloses a traction load power prediction method and device for a locomotive traction substation, and relates to the technical field of power system load prediction. Extracting time sequence alternating characteristics of load operation in combination with train working diagram information; a training set and a test set are divided through a sampling technology, ARIMA and Holt-Winters prediction models are trained in parallel, in the sampling process, representative data can be extracted from the two aspects of space randomness and time alternation at the same time, data with the strong randomness, intermittency and space-time coupling characteristics in traction loads can be fully captured, and the accuracy and the reliability of the traction loads are improved. And then an optimal model is optimized according to performance indexes such as RMSE, and retraining is performed based on all historical data to generate a future time period power prediction result, so that the model trained by the captured data can greatly improve the accuracy of the traction load power during prediction.

Description

Technical Field

[0001] This invention relates to the field of power system load forecasting technology, and in particular to a method, device, equipment and medium for traction load power forecasting. Background Technology

[0002] my country boasts the world's largest rail transit network. The traction load of electrified railways refers to the electrical power or current supplied by the traction power supply system to meet the traction power demands of trains (including acceleration, constant speed operation, and climbing). Its value is the sum of the traction power and auxiliary power of each train, usually expressed as an instantaneous value or a time series, exhibiting strong random fluctuations, asymmetry, nonlinearity, impulsiveness, and typical spatiotemporal distribution characteristics. Currently, in the power supply structure of electric locomotives, traction substations step down the externally input 110 kV, 220 kV, or 330 kV high-voltage electricity to 25 kV or 2×25 kV via traction transformers, and then transmit it to the overhead contact line through feeders to power the electric locomotives. Since trains draw current sequentially and at intervals according to the timetable, the time difference mainly depends on the length of the power supply arm and the train's operating speed. Therefore, the load characteristics of the traction substation are essentially determined by the train load characteristics. The load distribution of multiple substations collectively characterizes the dynamic behavior of the electrified railway traction load in time and space.

[0003] Severe fluctuations in traction load can lead to power imbalances in the regional power grid and cause frequency deviations. Its nonlinear and impulsive characteristics can easily cause voltage fluctuations and harmonic pollution, which seriously affect power supply quality. Therefore, it is particularly important to predict the load data of train operation in advance to formulate operation strategies. Predicting dynamic traction load is an important basis for train operation and reducing energy consumption.

[0004] Current methods for predicting traction loads are mostly based on traditional time series or deterministic models. However, due to the complex characteristics of electric railway traction loads, such as asymmetry, nonlinearity, fluctuation, impact, and spatiotemporal dynamic movement, it is difficult to fully capture the strong randomness, intermittency, and spatiotemporal coupling characteristics of traction loads. In particular, there is a lack of deep integration of train timetables, electrical relationships of power supply arms, and load distribution probability characteristics, resulting in large prediction errors for traction load power. Summary of the Invention

[0005] This invention provides a method and apparatus for predicting traction load power in a locomotive traction substation, which can solve the problems existing in the prior art.

[0006] This invention provides a method for predicting the traction load power of a locomotive traction substation, comprising the following steps: Obtain historical traction load power data from multiple traction substations of the locomotive; Based on the kernel density estimation method, a traction load power uncertainty model is constructed that simultaneously characterizes spatial clustering characteristics and temporal dynamic changes. The traction load power uncertainty model includes: in the spatial dimension, clustering analysis is performed on the traction load power data of multiple traction substations to establish an aggregation probability model for the load power data of different traction substations or their power supply arms; in the temporal dimension, a day is divided into multiple time periods according to the locomotive operation diagram or load change pattern, and an independent kernel density estimation model is established for each time period. Based on the spatial dimension aggregation probability model and the temporal dimension kernel density estimation model, and using the nonparametric sampling method of kernel density estimation, a sample set of traction load power data representing the temporal alternation under load operation is extracted from historical traction load power data. Using a sample set of traction load power data, a medium-term probabilistic prediction of traction load power within a preset future time period is generated.

[0007] Preferably, the construction of the aggregation probability model includes: In the spatial dimension, the kernel density estimation method is used to fit the nonparametric probability density of the spatial sample set; For one-dimensional Each sample feature space Let its true probability density function be... Obtained through KDE probability density estimation function for: ; in: Represents the kernel function; The scaling function representing smoothness is the bandwidth. This refers to the scaled kernel function; probability density estimation function This is the constructed aggregate probability model.

[0008] Preferably, the construction of the kernel density estimation model includes: In terms of time, the day is divided into multiple time periods based on the operation chart or load change pattern. For each time period, all load power values ​​belonging to that time period are extracted from historical traction load power data to form a time period-specific sample subset. For each subset, the kernel density estimation method is used to obtain its probability density estimation function. To obtain the kernel density estimation model.

[0009] Preferably, the extraction of the traction load power data sample set includes: For a predetermined time period that needs to be predicted in the future, select the aggregate probability model and kernel density estimation model constructed for that predetermined time period; Based on the pre-defined time period, an aggregation probability model and a kernel density estimation model are constructed. Then, an inverse transformation sampling or rejection sampling method is used to extract multiple load power values ​​representing the temporal alternation of load operation from historical traction load power data. These multiple load power values ​​constitute a traction load power data sample set.

[0010] Preferably, obtaining the intermediate probability prediction result includes: Using a traction load power data sample set, the ARIMA time series prediction model and the Holt-Winters three-parameter exponential smoothing model were trained in parallel, and the optimal model after training was selected based on the model performance index. Based on the trained optimal model, generate medium-term probabilistic prediction results of traction load power within a preset future time period; The standard form of the ARIMA time series forecasting model is ARIMA(p, d, q), where p is the autoregressive order, d is the difference order, and q is the moving average order. Its standard form, ARIMA(p, d, q), is expressed as: ; in: Indicates the trend of change in a time series; Indicates a constant; Represents a time series; Indicates the autoregressive fitting parameters; A noise sequence representing random fluctuations; Indicates the parameters of the moving average fit; The Holt-Winters three-parameter exponential smoothing model adopts an additive model, including a horizontal equation, a trend increment equation, and a seasonal equation; The horizontal equation is expressed as: ; The trend increment equation is expressed as: ; The seasonal equation is expressed as: ; The final prediction equation of the Holt-Winters three-parameter exponential smoothing model is then expressed as: ; in: This represents the decomposition of a time series; Indicates the smoothing parameter; It represents the long-term trend at time t; Represents the increment of the trend at time t; Indicates the seasonal variation at time t; c t-s Indicates the seasonal variation at time ts; a t-1 This represents the long-term trend at time t-1; b t-1 This represents the increment of the trend at time t-1; c t-s+h The value represents the seasonal variation at time t-s+h; h represents the prediction step size. The value range is [0,1]; Indicates the length of a season.

[0011] Preferably, after the historical traction load power data is acquired, it is preprocessed, including: Historical active and reactive power time series data of multiple traction substations in high-speed rail, conventional railway and hybrid traction systems were collected; Identify and correct recording errors and obvious noise points in time series data caused by sensor failures or transmission errors; Box plot analysis based on statistical distribution was used to identify and remove abnormal load values ​​that exceeded the reasonable range in time series data; Remove invalid data segments from traction substations that are operating under no-load or extremely low-load conditions to obtain effective load data; The effective load data is normalized to eliminate differences in capacity or dimensions between different substations.

[0012] This invention also provides a traction load power prediction device for a locomotive traction substation, comprising: The data module is used to acquire historical traction load power data from multiple traction substations of the locomotive; The nonparametric probabilistic model construction module is used to construct a traction load power uncertainty model that simultaneously characterizes spatial clustering characteristics and temporal dynamic changes based on the kernel density estimation method. The traction load power uncertainty model includes: in the spatial dimension, performing cluster analysis on the traction load power data of multiple traction substations to establish an aggregated probabilistic model for the load power data of different traction substations or their power supply arms; in the temporal dimension, dividing a day into multiple time periods according to the locomotive operation diagram or load change pattern, and establishing an independent kernel density estimation model for each time period. The prediction module is used to extract a sample set of traction load power data representing the temporal alternation of load operation from historical traction load power data based on the spatial dimension aggregation probability model and the temporal dimension kernel density estimation model, and using the nonparametric sampling method of kernel density estimation. Using a sample set of traction load power data, a medium-term probabilistic prediction of traction load power within a preset future time period is generated.

[0013] This invention also provides an electronic device, including a memory and a processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the traction load power prediction method for a locomotive traction substation as described above.

[0014] This invention also provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of a locomotive traction substation traction power prediction method as described above.

[0015] This invention provides a method and apparatus for predicting traction load power in a locomotive traction substation. Compared with the prior art, its advantages are as follows: This invention, based on kernel density estimation, performs cluster analysis on traction load power data from multiple traction substations in the spatial dimension to construct an aggregation probability model. In the temporal dimension, a day is divided into multiple time periods, and an independent kernel density estimation model is established for each time period to construct a traction load power uncertainty model that simultaneously represents spatial clustering characteristics and temporal dynamic changes. Then, based on the aggregation probability model and the kernel density estimation model, where the aggregation probability model is used for spatial clustering and the kernel density estimation model is used for temporal modeling, historical traction load power data is sampled. During this sampling process, representative data can be extracted from both spatial randomness and temporal alternation, which can fully capture data with strong randomness, intermittency, and spatiotemporal coupling characteristics in traction load. In the capture process, the train operation diagram, the electrical relationship of the power supply arm, and the load distribution probability characteristics can be deeply integrated, thereby enabling the model trained by the captured data to significantly improve the accuracy of traction load power prediction.

[0016] Furthermore, this invention fully leverages the advantages of ARIMA and Holt-Winters time series models through a parallel model optimization mechanism, and comprehensively evaluates model performance based on multiple indicators, thereby using the optimal model to predict traction load power, thus achieving high-precision capture and prediction of complex load change patterns. Attached Figure Description

[0017] Figure 1 A schematic diagram of the overall process of a method for predicting the traction load power of a locomotive traction substation provided in an embodiment of the present invention; Figure 2A schematic diagram of the probability density function of active power in the left power supply arm of a traction substation, which is provided as an embodiment of the present invention for a method of predicting traction load power in a locomotive traction substation. Figure 3 A schematic diagram of the probability density function of active power in the right power supply arm of a traction substation, which is provided as an embodiment of the present invention for a method of predicting traction load power in a locomotive traction substation. Figure 4 A schematic diagram of the probability density function of reactive power in the left power supply arm of a traction substation, which is provided as an embodiment of the present invention for a method of predicting traction load power in a locomotive traction substation. Figure 5 A schematic diagram of the probability density function of reactive power in the right power supply arm of a traction substation, which is provided as an embodiment of the present invention for a method of predicting traction load power in a locomotive traction substation. Figure 6 A schematic diagram of the time-series probability model of a feeder traction load in a locomotive traction substation traction load power prediction method provided in an embodiment of the present invention. Figure 7 A schematic diagram illustrating the traction load prediction effect of a locomotive traction substation traction load prediction method provided in an embodiment of the present invention for a high-speed railway traction substation. Figure 8 A schematic diagram illustrating the traction load prediction effect of a conventional railway traction substation using a locomotive traction power prediction method provided in an embodiment of the present invention. Figure 9 This is a schematic diagram illustrating the traction load prediction method for a locomotive traction substation provided in an embodiment of the present invention, specifically for a mixed traction substation for high-speed and conventional railways. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0019] At present, in the power supply structure of electric locomotives, traction substations step down the externally input 110 kV, 220 kV or 330 kV high-voltage electricity to 25 kV or 2×25 kV through traction transformers, and then transmit it to the contact network through feeders to power the electric locomotives. Taking the measured data of a traction substation of a high-speed railway in Gansu as an example, the data collection intervals are 10 seconds and 10 minutes, respectively. The change in active power within 24 hours clearly reflects the dynamic characteristics of the traction load. Since the train takes power sequentially and at intervals according to the timetable, the time difference mainly depends on the length of the power supply arm and the train speed. Therefore, the load characteristics of the traction substation are essentially determined by the train load characteristics. The load distribution of multiple substations jointly depicts the dynamic behavior of the electrified railway traction load in time and space.

[0020] This complex load characteristic, especially its significant randomness, intermittency, and spatiotemporal migration, poses a severe challenge to the power balance, power quality, and safe and stable control of the power grid. Drastic fluctuations in traction load can lead to regional power imbalances and frequency deviations. Its nonlinear and impulsive characteristics easily cause voltage fluctuations and harmonic pollution, seriously affecting power quality. Therefore, predicting train load data in advance to formulate operational strategies is particularly important. Predicting dynamic traction load is a crucial foundation for train operation and reducing energy consumption, while simultaneously ensuring the safe and stable operation of the traction power supply system, thereby enabling rational planning of operational schemes to improve economic efficiency and reduce energy waste. However… Existing forecasting methods are mostly based on traditional time series or deterministic models, which make it difficult to fully capture the strong randomness and spatiotemporal coupling characteristics of traction loads. In particular, they lack deep integration of train timetables, electrical relationships of power supply arms, and load distribution probability characteristics, resulting in limited forecast accuracy and generally poor adaptability and large errors in medium-term power. Therefore, high-precision forecasting of traction load power is not only a key prerequisite for achieving lean grid dispatch and ensuring safe and stable operation, but also an important foundation for optimizing energy allocation and improving system economy. It has significant practical implications for supporting the reliable, efficient, and green transformation of new power systems under the background of high proportion of renewable energy access.

[0021] To address the shortcomings of existing traction load forecasting technologies, such as insufficient consideration of spatiotemporal coupling characteristics, limited ability to characterize non-stationarity and random fluctuations, and over-reliance on prior distribution assumptions, this invention proposes a medium-term traction load power forecasting method that comprehensively considers spatial randomness and temporal alternation; for example... Figure 1 As shown, this method effectively integrates multi-source monitoring data by establishing a time-series nonparametric probability model, generates representative samples by using sampling techniques such as kernel density estimation, and combines ARIMA and Holt-Winters multi-model parallel training and optimization mechanisms, which significantly improves the accuracy and robustness of medium-term traction load power prediction.

[0022] Specifically: Step 1: Systematically preprocess the measured power data from high-speed and conventional railway traction substations. This process includes data cleaning to eliminate recording errors and noise interference, using statistical methods (such as box plot analysis) to identify and remove outliers, removing invalid data under no-load or minimal load conditions, and normalizing the valid data to eliminate dimensional differences and improve data comparability. Based on this, representative load characteristics are extracted, and their statistical distribution patterns and spatiotemporal variation characteristics are analyzed to lay the data foundation for subsequent modeling.

[0023] Step Two: Introducing nonparametric probabilistic modeling methods to construct a traction load power uncertainty model that simultaneously reflects spatial clustering characteristics and temporal dynamic changes. Spatially, techniques such as kernel density estimation are used to perform cluster analysis on load data from multiple traction stations, establishing an aggregation probability model to characterize the randomness, variability, and spatial correlation between different stations. Temporally, combining historical load sequences, a nonparametric probabilistic model is constructed to accurately describe the dynamic characteristics and alternation patterns of load evolution over time. This step provides a rigorous statistical foundation for medium-term probabilistic forecasting.

[0024] Among them, kernel density estimator (KDE), as one of the most popular nonparametric estimation methods, is used for nonparametric probabilistic modeling of traction load power; it employs a smooth kernel function to fit sample points, thereby simulating the true probability density distribution; for one-dimensional... Each sample feature space Let its true probability density function be... Then it is obtained through KDE. The probability density function (PDF) estimate for: .

[0025] in: For kernel functions; A smooth scaling function is called bandwidth. This is the scaled kernel function.

[0026] The kernel functions that can be selected include Gauss, Epanechnikov, Biweight, Uniform, and Triangular functions. When the bandwidth is fixed, different kernel functions have little impact on the shape of the final probability density curve. For ease of description and analysis, this invention will denote the KDE using the Gaussian kernel function as GKDE (Gaussian Kernel Density Estimator).

[0027] Moreover, since the train models and quantities vary at different times, the probability distribution of traction load power exhibits significant temporal differences. To achieve high-precision fitting of the probability density for each time period, this paper proposes a segmented temporal nonparametric probability modeling strategy: first, the day is divided into multiple time periods based on the operation chart or load change pattern, and then a GKDE model is established for each time period to accurately capture the probability distribution characteristics of load power in different time periods.

[0028] Step 3: Based on the cleaned and reconstructed load data, advanced resampling techniques such as kernel sampling are used to generate a representative probability sample set to simulate possible load states under real operating scenarios. The sample set is divided into a training set and a test set according to a scientific ratio (7:3) to ensure that the model has good generalization ability and robustness during training and validation.

[0029] Based on the established nonparametric time-series probabilistic model of traction load, advanced nonparametric sampling techniques (such as kernel-based sampling) can be used to predict the power of each traction substation at different time periods. (kW); furthermore, by combining the train timetable to obtain the duration of the traction load, the power consumption of the traction substation can be accurately predicted. W (kWh), the calculation formula is expressed as: .

[0030] in: P j Indicates the first j Average power over a time interval; ΔT j This indicates the time length corresponding to the interval; in summary, the analysis and prediction of traction load must systematically integrate its time-series characteristics and external uncertainties (such as weather changes) to support accurate power grid analysis, optimized scheduling, and efficient consumption of new energy sources.

[0031] Specifically, modern probabilistic sampling methods such as kernel density estimation (KDE) are employed to generate a representative sample set from the preprocessed traction load data. This better captures the probability distribution characteristics and spatiotemporal variation patterns of the original data. Based on this, and following general standards for machine learning model validation, the samples are scientifically divided into training and test sets. The training set is used for model parameter training and structure learning, while the test set is used to objectively evaluate the model's predictive performance and generalization ability. This division process must balance the principle of temporal consistency with random sampling requirements, ensuring that the model can both fully learn historical patterns and possess effective predictive capabilities for future unknown data, thereby comprehensively improving the robustness and reliability of the prediction results.

[0032] Step 4: Construct time series prediction models including ARIMA and Holt-Winters exponential smoothing, and adopt a parallel training strategy to improve modeling efficiency; use cross-validation to prevent overfitting, and combine grid search algorithm to systematically optimize the hyperparameters of various models; comprehensively calculate performance indicators such as root mean square error (RMSE) and mean absolute error (MAE) on the test set to quantitatively evaluate the prediction accuracy and robustness of each model, and finally select the model with the lowest error and the best fitting effect as the basic model for medium-term load power prediction.

[0033] The ARIMA model is a comprehensive method that integrates autoregression (AR) and moving average (MA), suitable for handling non-stationary time series, and overcomes the limitations of AR and MA models in such data. This model has a clear structure, efficient modeling, and wide applicability, and is widely used in prediction and evaluation. Its standard form is ARIMA(p, d, q), where: p is the autoregressive order, reflecting the degree of dependence on historical data; d is the differencing order, used to make the series stationary; and q is the moving average order, representing the sensitivity to random disturbances. Its form is as follows: .

[0034] in: Indicates the trend of change in a time series; Indicates a constant; Represents a time series; Indicates the autoregressive fitting parameters; A noise sequence representing random fluctuations; This represents the parameters fitted to the moving average.

[0035] Autoregressive models are used to describe the linear relationship between current and past values ​​of a time series. Assuming the time series is... , Let represent the lag order, then The model can be represented as: .

[0036] in: Represents the autoregressive coefficient; This represents the white noise error term; it means the value at the current time. It's the past The weighted sum of the values ​​at each time point plus a random error; the integrated part is mainly used to handle the non-stationarity of the time series; if the statistical properties of a time series, such as the mean, variance, or autocovariance, change over time, then it is non-stationary; [The text then abruptly shifts to a different topic:] ...the weighted sum of the values ​​at each time point plus a random error; the integrated part is mainly used to handle the non-stationary nature of the time series; if the statistical properties of a time series, such as the mean, variance, or autocovariance, change over time, then it is non-stationary; [The text then abruptly shifts again:] ...to process non-stationary series... order difference, By representing the degree of difference, it can be transformed into a stationary sequence. For example: First-order difference: .

[0037] Second-order difference: .

[0038] Seasonal differences: .

[0039] Among them The period is indicated; the moving average part describes the linear relationship between the current error term and past error terms. Then... The model can be represented as: .

[0040] in: Indicates the moving average coefficient; This represents the white noise error term; This indicates the lag order of the error.

[0041] Therefore, the autoregressive part captures long-term trends, the differencing part stabilizes the sequence, and the moving average part handles short-term fluctuations and errors. These three parts work together to form a complete ARIMA model. Specifically, it uses historical observations of the time series to predict the current value. For a p-order autoregressive model AR(p), it assumes a linear relationship between the current observation and the observations at the past p times. The autoregressive coefficients in this linear relationship reflect the degree of influence of observations at different historical times on the current value. By estimating these autoregressive coefficients, the AR part can effectively capture long-term trends and periodic patterns in the time series. The sequence stabilization process addresses the issues of the original non-stationary sequence. y t Perform d-order differencing, repeating this process until the resulting new sequence is determined to be a stationary sequence through a unit root test (such as the ADF test). The number of differencing operations at this point is the value of parameter d. The moving average part uses past prediction errors to improve the current prediction. For a q-order moving average model MA(q), it assumes a linear relationship between the prediction error at the current time and the prediction errors at the past q times. The moving average coefficient in the linear relationship reflects the degree of influence of prediction errors at different historical times on the current value. By predicting the moving average coefficient, short-term fluctuations and random errors in the time series can be effectively captured. By weighted averaging of past prediction errors, the current prediction value can be adjusted to be closer to the true value. By organically combining the three parts of autoregression (AR), differencing (I), and moving average (MA), a comprehensive time series prediction model is formed, expressed as: .

[0042] The Holt-Winters method is used for time series analysis and is suitable for non-stationary series with linear trends and fixed periods. The fitting of the time series considers both new and old information by "mixing" them, and the weights of the relevant new and old information are controlled by an adjustable smoothing parameter. The basic idea is to decompose the time series. Three smoothing parameters are introduced. For long-term trends Incremental trend and seasonal changes To make estimates and thus predictions, the Holt-Winters model includes additive and multiplicative models. In this prediction model, the additive model is used, expressed as: Horizontal equation: .

[0043] Trend Increment Equation: .

[0044] Seasonal equation: .

[0045] Prediction equation: .

[0046] in: The value range is [0,1]; This represents the length of the season. A prediction equation is used when you want to predict values ​​h moments in the future.

[0047] In addition, the Holt-Winters method decomposes the data into three components: horizontal, seasonal, and trend data.

[0048] The formula for updating the level components is: .

[0049] in: Indicates time t Level components; It represents the smoothing constant, which controls the model's sensitivity to new data; Indicates the horizontal component at the previous moment; It indicates the seasonal component of the previous seasonal cycle.

[0050] The trend component update formula is: .

[0051] in: Indicates time t Trend components; Indicates the horizontal component at the previous moment; Indicates the trend component of the previous moment; This represents the trend smoothing constant, which controls the speed at which the trend is updated.

[0052] The formula for updating seasonal components is: .

[0053] in: Indicates time Seasonal components; Indicates the observed value; This represents the seasonal smoothing coefficient, which controls the weighting of seasonal component updates; It indicates the seasonal component of the previous seasonal cycle.

[0054] Step 5: Based on the selected optimal model, retrain it using all available historical data to fully absorb historical information, enhance the model's expressive power, and generate medium-term probabilistic prediction results of traction load power in a specific future period, providing a reliable basis for power grid dispatch and energy management.

[0055] After the optimal model is trained, the traction load power prediction results for the next 7 months are generated accordingly. The historical data changes, the fitting of the test and validation segments, and the future prediction trends are displayed through multi-curve visualization, which enhances the interpretability of the results and the ability to support decision-making.

[0056] Step Six: In actual deployment, continuously monitor the system's operation and evaluate its performance to promptly identify prediction deviations or model degradation issues. Through dynamic adjustment of algorithm parameters and optimization of control strategies, continuously improve model capabilities and enhance system stability.

[0057] This invention first collects raw power data from traction substations using high-precision measurement tools, and then preprocesses the data through cleaning, denoising, and normalization to extract its inherent time-series characteristics and statistical regularities. Based on this, a time-series-based nonparametric probabilistic modeling framework is constructed. This framework can establish high-precision probability density models for different time periods and accurately calculate the traction load for each period. Furthermore, advanced nonparametric sampling techniques such as kernel density estimation are used to generate a representative sample set from the preprocessed data, and this set is rationally divided into training and test sets. Subsequently, ARIMA is built in parallel. The time series model and the Holt-Winters three-parameter exponential smoothing model were trained and their structures optimized using cross-validation and grid search strategies. Multiple performance metrics, including root mean square error (RMSE), were calculated based on the test set to objectively evaluate their prediction accuracy and robustness, thus selecting the optimal model. Finally, the selected optimal model was retrained using all 17 months of measured data to generate traction load power predictions for the next 7 months. A multi-curve overlay visualization method was used to comprehensively display historical data trends, test-segment validation results, and future prediction ranges, thereby supporting scientific decision-making in power grid dispatching and energy management.

[0058] This invention is based on the spatiotemporal randomness and temporal alternation of traction loads. It overcomes the limitations of traditional parametric methods in terms of distribution assumptions by constructing a nonparametric probabilistic model, and combines a parallel modeling strategy to achieve high-precision capture and prediction of complex load change patterns, providing reliable data support for power system dispatching and energy management.

[0059] This invention effectively characterizes the randomness and time-varying nature of traction loads by introducing time-series nonparametric probabilistic modeling and advanced sampling techniques (such as kernel density estimation sampling), overcoming the dependence of traditional parametric models on prior distribution assumptions and significantly improving prediction accuracy and robustness. Its parallel modeling and model optimization mechanism fully leverages the advantages of various time series models such as ARIMA and Holt-Winters, achieves automatic hyperparameter optimization through cross-validation and grid search, and comprehensively evaluates model performance based on multiple indicators such as RMSE, thus providing a systematic, reliable, and adaptive solution for complex load forecasting problems.

[0060] This invention addresses the complex characteristics of electric railway traction loads, such as asymmetry, nonlinearity, volatility, impulsiveness, and spatiotemporal dynamic movement. By systematically collecting and preprocessing power data from traction substations, it constructs a load uncertainty model based on nonparametric probability theory, effectively integrating spatiotemporal variation patterns. This model can effectively address the prediction challenges brought about by the large-scale development of uncertain loads in new power systems, significantly improving the accuracy and robustness of traction load prediction.

[0061] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for predicting the traction load power of a locomotive traction substation, characterized in that, Includes the following steps: Obtain historical traction load power data from multiple traction substations of the locomotive; Based on the kernel density estimation method, a traction load power uncertainty model is constructed that simultaneously characterizes spatial clustering characteristics and temporal dynamic changes. The traction load power uncertainty model includes: in the spatial dimension, clustering analysis is performed on the traction load power data of multiple traction substations to establish an aggregation probability model for the load power data of different traction substations or their power supply arms; in the temporal dimension, a day is divided into multiple time periods according to the locomotive operation diagram or load change pattern, and an independent kernel density estimation model is established for each time period. Based on the spatial dimension aggregation probability model and the temporal dimension kernel density estimation model, and using the nonparametric sampling method of kernel density estimation, a sample set of traction load power data representing the temporal alternation under load operation is extracted from historical traction load power data. Using a sample set of traction load power data, a medium-term probabilistic prediction of traction load power within a preset future time period is generated.

2. The method for predicting traction load power in a locomotive traction substation according to claim 1, characterized in that, The construction of the aggregation probability model includes: In the spatial dimension, the kernel density estimation method is used to fit the nonparametric probability density of the spatial sample set; For one-dimensional Each sample feature space Let its true probability density function be... Obtained through KDE probability density estimation function for: ； in: Represents the kernel function; The scaling function representing smoothness is the bandwidth. This refers to the scaled kernel function; probability density estimation function This is the constructed aggregate probability model.

3. The method for predicting traction load power in a locomotive traction substation according to claim 2, characterized in that, The construction of the kernel density estimation model includes: In terms of time, the day is divided into multiple time periods based on the operation chart or load change pattern. For each time period, all load power values ​​belonging to that time period are extracted from historical traction load power data to form a time period-specific sample subset. For each subset, the kernel density estimation method is used to obtain its probability density estimation function. To obtain the kernel density estimation model.

4. The method for predicting traction load power in a locomotive traction substation according to claim 1, characterized in that, The extraction of the traction load power data sample set includes: For a predetermined time period that needs to be predicted in the future, select the aggregate probability model and kernel density estimation model constructed for that predetermined time period; Based on the pre-defined time period, an aggregation probability model and a kernel density estimation model are constructed. Then, an inverse transformation sampling or rejection sampling method is used to extract multiple load power values ​​representing the temporal alternation of load operation from historical traction load power data. These multiple load power values ​​constitute a traction load power data sample set.

5. The method for predicting traction load power in a locomotive traction substation according to claim 1, characterized in that, The acquisition of the intermediate probability prediction results includes: Using a traction load power data sample set, the ARIMA time series prediction model and the Holt-Winters three-parameter exponential smoothing model were trained in parallel, and the optimal model after training was selected based on the model performance index. Based on the trained optimal model, generate medium-term probabilistic prediction results of traction load power within a preset future time period; The standard form of the ARIMA time series forecasting model is ARIMA(p, d, q), where p is the autoregressive order, d is the difference order, and q is the moving average order. Its standard form, ARIMA(p, d, q), is expressed as: ； in: Indicates the trend of change in a time series; Indicates a constant; Represents a time series; Indicates the autoregressive fitting parameters; A noise sequence representing random fluctuations; Indicates the parameters of the moving average fit; The Holt-Winters three-parameter exponential smoothing model adopts an additive model, including a horizontal equation, a trend increment equation, and a seasonal equation; The horizontal equation is expressed as: ； The trend increment equation is expressed as: ； The seasonal equation is expressed as: ； The final prediction equation of the Holt-Winters three-parameter exponential smoothing model is then expressed as: ； in: This represents the decomposition of a time series; Indicates the smoothing parameter; It represents the long-term trend at time t; Represents the increment of the trend at time t; Indicates the seasonal variation at time t; c t-s Indicates the seasonal variation at time ts; a t-1 This represents the long-term trend at time t-1; b t-1 This represents the increment of the trend at time t-1; c t-s+h The value represents the seasonal variation at time t-s+h; h represents the prediction step size. The value range is [0,1]; Indicates the length of a season.

6. The method for predicting traction load power in a locomotive traction substation according to claim 1, characterized in that, After the historical traction load power data is acquired, it is preprocessed, including: Historical active and reactive power time series data of multiple traction substations in high-speed rail, conventional railway and hybrid traction systems were collected; Identify and correct recording errors and obvious noise points in time series data caused by sensor failures or transmission errors; Box plot analysis based on statistical distribution was used to identify and remove abnormal load values ​​that exceeded the reasonable range in time series data; Remove invalid data segments from traction substations that are operating under no-load or extremely low-load conditions to obtain effective load data; The effective load data is normalized to eliminate differences in capacity or dimensions between different substations.

7. A traction load power prediction device for a locomotive traction substation, characterized in that, include: The data module is used to acquire historical traction load power data from multiple traction substations of the locomotive; The nonparametric probabilistic model construction module is used to construct a traction load power uncertainty model that simultaneously characterizes spatial clustering characteristics and temporal dynamic changes based on the kernel density estimation method. The traction load power uncertainty model includes: in the spatial dimension, performing cluster analysis on the traction load power data of multiple traction substations to establish an aggregated probabilistic model for the load power data of different traction substations or their power supply arms; in the temporal dimension, dividing a day into multiple time periods according to the locomotive operation diagram or load change pattern, and establishing an independent kernel density estimation model for each time period. The prediction module is used to extract a sample set of traction load power data representing the temporal alternation of load operation from historical traction load power data based on the spatial dimension aggregation probability model and the temporal dimension kernel density estimation model, and using the nonparametric sampling method of kernel density estimation. Using a sample set of traction load power data, a medium-term probabilistic prediction of traction load power within a preset future time period is generated.

8. An electronic device, characterized in that, include: Memory and processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the traction load power prediction method for a locomotive traction substation as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the steps of a method for predicting the traction load power of a locomotive traction substation as described in any one of claims 1 to 6.

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