A power system stochastic optimization scheduling method based on LSTM-t distribution

Abstract

This invention discloses a stochastic optimization scheduling method for power systems based on LSTM-t distribution, belonging to the field of power system scheduling technology. The method includes: 1) constructing a two-layer LSTM wind power prediction model, obtaining predicted wind power values ​​and residual sequences after data preprocessing and model training; 2) fitting the residual sequences using a t-distribution, determining the distribution parameters through maximum likelihood estimation, and verifying the fitting effect using Q-Q plots and K-S tests; 3) generating initial wind power scenarios based on the t-distribution parameters through Monte Carlo simulation, reducing them to typical scenarios through K-means clustering, constructing a two-stage chance-constrained stochastic programming model with constraints, and solving the scheduling scheme using the Gurobi optimizer. This method accurately characterizes the heavy-tailed nature of wind power prediction errors, achieves deep integration of LSTM prediction and probabilistic modeling, and synergistic optimization of energy storage and thermal power, significantly improving the economy and robustness of power system scheduling.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching technology, and specifically to a stochastic optimization dispatching method for power systems. Background Technology

[0002] As a crucial component of renewable energy, wind power has seen rapid and continuous growth in installed capacity and grid-connected scale. While large-scale wind power integration has increased the proportion of green energy in the power system, its intermittent, volatile, and uncontrollable output significantly increases dispatch complexity. Wind power output is highly dependent on four meteorological factors: wind speed, temperature, air pressure, and humidity. Its short-term forecast error rate is typically between 10% and 15%. When wind power penetration exceeds 15%, forecasting errors can easily lead to insufficient system reserve capacity, frequent start-ups and shutdowns of thermal power units, soaring regulation costs, and even wind curtailment, resulting in energy waste and economic losses. Especially against the backdrop of frequent extreme weather events (such as storms, cold waves, and thunderstorms), the sudden changes in wind power output are even more pronounced, further increasing the difficulty of grid dispatch.

[0003] Traditional deterministic dispatch methods typically use wind power forecasts as input, optimizing the start-up, shutdown, and output allocation of thermal power units to meet load demand and power balance constraints. While these methods are computationally efficient, they neglect the probabilistic distribution of forecast errors and cannot effectively address uncertainties in actual operation. For example, if actual wind power output is lower than the forecast, the system may be forced to utilize high-cost cold standby units due to insufficient reserve capacity; conversely, if actual output is higher than the forecast, the curtailment rate may increase due to limited peak-shaving capacity. This "one-size-fits-all" dispatch strategy is ill-suited to the complex operating environment under conditions of high-proportion renewable energy integration.

[0004] To improve the robustness of dispatching schemes, stochastic programming methods have been introduced into power system optimal dispatching. This method generates multiple possible wind power output scenarios and optimizes them with the goal of minimizing expected operating costs, achieving a balance between economy and reliability while considering uncertainty. However, existing research often assumes that prediction errors follow a normal distribution in scenario generation, while actual wind power prediction residuals often exhibit "fat-tailed" characteristics (i.e., the probability of extreme errors is much higher than the normal distribution assumption), leading to an underestimation of tail risks and affecting the effectiveness of dispatching strategies. At the prediction technology level, Long Short-Term Memory (LSTM) networks, due to their powerful temporal modeling capabilities, perform excellently in wind power point prediction, improving prediction accuracy. However, point prediction alone is insufficient to support dispatching decisions under uncertainty; how to effectively integrate the probabilistic information of prediction errors into the dispatching model remains a key problem to be solved. On the other hand, energy storage systems, as an important means of mitigating wind power fluctuations and improving system flexibility, still have significant shortcomings in economic modeling during dispatching. Most existing studies only consider the power constraints and charge / discharge efficiency of energy storage, ignoring the dynamic changes in state of charge (SOC) and failing to fully realize the synergistic optimization of energy storage and thermal power units, resulting in the overall economic efficiency of the system not reaching the optimal level. Summary of the Invention

[0005] Purpose of the invention: To address the aforementioned issues in the prior art, this invention proposes a stochastic optimization scheduling method for power systems based on the LSTM-t distribution. This method solves the problems of distorted wind power prediction error characterization, simplified energy storage modeling, and insufficient robustness of scheduling strategies in the prior art, thereby improving the reliability and economy of power system scheduling under high-proportion wind power integration.

[0006] Technical solution: A stochastic optimization scheduling method for power systems based on LSTM-t distribution, comprising the following steps:

[0007] Step 1: Build an LSTM wind power prediction model and complete its training.

[0008] 1.1 Data Preprocessing: Historical wind power data, meteorological data, and time-series feature data were collected. Z-score normalization was used to normalize the wind power and meteorological data, eliminating dimensional differences. Missing values ​​in the meteorological data were filled using linear interpolation between adjacent time points. Abnormal peaks in the wind power sequence were identified through 3... The rule is identified and replaced with the moving average of the previous 6 hours; the input sample is constructed using the sliding window technique with a window size of 24, and the power at the next moment is predicted using the data of the previous 24 hours, forming the input sequence and the target sequence.

[0009] 1.2 Network Structure Design: Construct a prediction model containing an input layer, a two-layer LSTM layer, a Dropout layer, a fully connected layer, and an output layer.

[0010] The number of neurons in the input layer is consistent with the dimension of the input features. The input features include 4-dimensional temporal features, 3-dimensional multi-altitude wind speed, 6-dimensional wind direction derived features, and 3-dimensional environmental features. Among them, the 4-dimensional temporal features are: hour, minute, weekday, and number of days in the year, all normalized to [0,1]. The 3-dimensional multi-altitude wind speed is: 10m, 30m, and 50m. The 6-dimensional wind direction derived features are: wind direction at each altitude is converted into two-dimensional orthogonal components by sine / cosine transformation. The 3-dimensional environmental features are: temperature, air pressure, and humidity. The total dimension D=16.

[0011] The system consists of two LSTM layers: the first LSTM layer contains 128 neurons with its OutputMode set to "last" to output the hidden state at the last time step; the second LSTM layer contains 64 neurons; to prevent overfitting, a Dropout layer with a 0.2 deactivation rate is set between the two LSTM layers to improve the model's generalization ability by randomly disabling some neuron connections; the fully connected layer expands the LSTM output feature vector into one dimension through the Flatten layer, and then passes it through a fully connected layer with 32 neurons and a ReLU activation function for nonlinear transformation. Finally, the wind power prediction value is generated through a single neuron output layer (linear activation), realizing the mapping from time-series features to continuous value prediction.

[0012] 1.3: Model Training Optimization: Using the mean absolute error (MAE) as the loss function, the Adam optimizer was selected, and an exponential decay strategy was adopted to dynamically adjust the learning rate. The learning rate was multiplied by 0.5 after every 10 training rounds. The dataset was divided into training, validation, and test sets in an 8:1:1 ratio. The MAE of the validation set was monitored in real time during training. If the validation loss did not decrease for 15 consecutive rounds, an early stopping mechanism was triggered, and the optimal model parameters were saved to prevent overfitting. After each training round, a loss curve was plotted to visually demonstrate the convergence trend. After training, the residuals of the test set were calculated, and the residual sequence was saved.

[0013] Step 2: Modeling the probability of wind power prediction error based on the t-distribution.

[0014] 2.1: t-distribution fitting: The residual sequence obtained in step 1.3 is fitted using Student's t-distribution. The degree of freedom parameter of the t-distribution is determined by maximum likelihood estimation (MLE). The degree of freedom parameter reflects the thickness of the tail of the distribution. The smaller the degree of freedom, the thicker the tail, and the more accurate the characterization of extreme errors.

[0015] 2.2: Fit Validation: The QQ plot and Kolmogorov-Smirnov (KS) test were used to verify the fit of the t-distribution. The QQ plot visually judges the goodness of fit by comparing the deviation of the residual quantiles from the theoretical t-distribution quantiles. The KS test calculates the maximum vertical distance between the sample distribution and the theoretical distribution to test whether to accept the null hypothesis that "the residuals follow a t-distribution" at a given significance level. The validated t-distribution fitting parameters (degrees of freedom, mean, standard deviation) were saved. The fitted and validated t-distribution parameters will be used to generate typical scenarios with probabilistic information, providing uncertainty input for subsequent stochastic programming models and ensuring the robustness of the scheduling strategy to wind power output fluctuations.

[0016] Step 3: Construct a stochastic planning and scheduling model for the power system based on t-distribution error.

[0017] 3.1: Wind power output scenario generation and reduction: Based on the LSTM wind power point prediction value obtained in step 1, and the t-distribution fitting parameters obtained in step 2, 1000 initial wind power output prediction error scenarios are generated through Monte Carlo simulation. The initial scenario set is reduced by K-means clustering algorithm to obtain 3 representative typical wind power output scenarios and their corresponding occurrence probabilities, which are used as uncertainty inputs for the stochastic programming model.

[0018] 3.2: Constructing a two-stage chance-constrained stochastic programming model: The objective function is to minimize the expected operating cost of the system. The objective function includes four parts: thermal power generation cost, thermal power unit start-up and shutdown cost, wind curtailment penalty cost, and energy storage dispatch cost. Six types of constraints are set: power balance constraint, wind curtailment rate constraint, thermal power unit start-up and shutdown logic constraint, thermal power unit output upper and lower limit constraint, thermal power unit ramp rate constraint, and energy storage system dynamic operation constraint. Among them, the energy storage system dynamic operation constraint includes charge and discharge mutual exclusion constraint, charge and discharge power upper and lower limit constraint, state of charge (SOC) time series change constraint, SOC upper and lower limit constraint, rated energy capacity constraint, and initial and final SOC constraints.

[0019] 3.3: Model Solution: The Gurobi optimizer is used to solve the two-stage chance-constrained stochastic programming model, which is a mixed integer quadratic programming (MIQP) problem with a quadratic objective function and integer constraints. This results in start-up and shutdown decisions for thermal power units applicable to all scenarios, as well as output allocation, energy storage charging and discharging strategies, and wind curtailment strategies for thermal power units in various typical scenarios, thus forming a stochastic optimal scheduling scheme for the power system.

[0020] Beneficial effects: 1. Accurately characterizes the heavy-tailed characteristics of wind power prediction errors: Abandoning the traditional normal distribution assumption, the t-distribution is used to fit the LSTM prediction residuals. The degree of freedom parameters are determined by maximum likelihood estimation. The fitting effect is verified by combining the QQ plot and KS test. This accurately captures the heavy-tailed characteristics of wind power prediction errors, effectively covers the risk of extreme wind power fluctuations, and avoids scheduling decision deviations caused by underestimation of tail risks.

[0021] 2. Achieve deep integration of LSTM point prediction and probabilistic error modeling: Use the point prediction value output by LSTM as the benchmark for scene generation and the t-distribution parameter of LSTM residuals as the basis for scene fluctuations. This makes scene generation strictly dependent on prediction accuracy and residual distribution characteristics, reduces invalid fluctuations, and avoids "over-specification" or "insufficient backup" caused by scene distortion in the optimization model.

[0022] 3. Achieve deep synergistic optimization between energy storage and thermal power units: Establish a dynamic operation constraint model for the energy storage system across all dimensions, taking into account characteristics such as SOC time-series changes, charging and discharging efficiency, and charging and discharging mutual exclusion. Integrate energy storage constraints into the stochastic programming model to comprehensively optimize the operation strategies of thermal power, energy storage, and wind power, fully leverage the role of energy storage in mitigating wind power fluctuations, and enhance wind power absorption capacity.

[0023] 4. Balancing the accuracy and computational complexity of the scheduling model: A large number of initial scenarios are generated through Monte Carlo simulation to ensure the comprehensiveness of uncertainty capture. K-means clustering is used to reduce the number of scenarios to three typical scenarios, which significantly reduces the computational complexity while retaining the core uncertainty features. Combined with the interior point method and branch and bound algorithm of the Gurobi optimizer, the model can be solved efficiently and has engineering application value.

[0024] 5. Significantly improves the economy and robustness of dispatching: Compared with traditional deterministic dispatching methods, this invention reduces the total operating cost of the power system by 6.1%, the wind curtailment rate from 18.7% to 9.5%, a reduction of nearly 50%; the cost fluctuation coefficient from 0.0027 to 0.0016, a reduction of 40.7%; and the power deficit frequency from 15% to 0, effectively improving the system's stability in response to wind power fluctuations and eliminating the risk of power supply gaps. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method of the present invention;

[0026] Figure 2 This is a wind power prediction interval diagram of the LSTM model of this invention;

[0027] Figure 3 This is a probability distribution diagram of the wind power prediction error of the present invention;

[0028] Figure 4 This is a QQ plot for the normal distribution test of wind power prediction error in this invention;

[0029] Figure 5 This is a scheduling characteristic diagram of a typical scenario of the present invention;

[0030] Figure 6 This is a scheduling characteristic diagram for a typical scenario two of the present invention;

[0031] Figure 7 This is a scheduling characteristic diagram for a typical scenario three of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] This embodiment uses measured data from Xinjiang wind farms in 2019 (15-minute time resolution) as the basis for wind power prediction and uncertainty modeling. The data includes meteorological data such as wind speed, wind direction, temperature, and air pressure at heights of 10m / 30m / 50m, as well as the actual power generation during the corresponding time periods. Simultaneously, regional power grid load data is collected and time-aligned with the wind power data. The thermal power model uses 300MW coal-fired units as the model, setting up 5 thermal power units. The energy storage system adopts an energy storage device with a rated energy capacity of 200MWh. Specific parameters of the thermal power units and the energy storage system are provided in the appendix.

[0034] like Figure 1 The specific implementation steps are shown below:

[0035] Step 1: Build an LSTM wind power prediction model and complete its training.

[0036] 1.1 Data Preprocessing: Z-score normalization was used to normalize wind power and meteorological data, eliminating dimensional differences. The formula is: ,in , These represent the mean and standard deviation of each variable on the training set; missing values ​​in the meteorological data are filled using linear interpolation between adjacent time points; and abnormal peaks in the wind power sequence are identified using 3... The rule is identified and replaced with the moving average of the previous 6 hours; the input sample is constructed using a sliding window technique, with the window size... Set the time to 24, and use the data from the previous 24 hours to predict the power at the next moment, forming the input sequence. and target sequence , where N is the number of samples and D is the input feature dimension.

[0037] 1.2 Network Structure Design: Construct a prediction model containing an input layer, a two-layer LSTM layer, a Dropout layer, a fully connected layer, and an output layer.

[0038] The number of neurons in the input layer is consistent with the dimension of the input features. The input features include 4-dimensional temporal features, 3-dimensional multi-altitude wind speed, 6-dimensional wind direction derived features, and 3-dimensional environmental features. Among them, the 4-dimensional temporal features are: hour, minute, weekday, and number of days in the year, all normalized to [0,1]. The 3-dimensional multi-altitude wind speed is: 10m, 30m, and 50m. The 6-dimensional wind direction derived features are: wind direction at each altitude is converted into two-dimensional orthogonal components by sine / cosine transformation. The 3-dimensional environmental features are: temperature, air pressure, and humidity. The total dimension D=16.

[0039] The system consists of two LSTM layers: the first LSTM layer contains 128 neurons with its OutputMode set to "last" to output the hidden state at the last time step; the second LSTM layer contains 64 neurons; to prevent overfitting, a Dropout layer with a 0.2 deactivation rate is set between the two LSTM layers to improve the model's generalization ability by randomly disabling some neuron connections; the fully connected layer expands the LSTM output feature vector into one dimension through the Flatten layer, and then passes it through a fully connected layer with 32 neurons and a ReLU activation function for nonlinear transformation. Finally, the wind power prediction value is generated through a single neuron output layer (linear activation), realizing the mapping from time-series features to continuous value prediction.

[0040] 1.3: Model Training Optimization: Using Mean Absolute Error (MAE) as the loss function, the Adam optimizer was selected with an initial learning rate of 10. -3 The learning rate is dynamically adjusted using an exponential decay strategy, multiplied by 0.5 after every 10 training rounds. The dataset is divided into training, validation, and test sets in an 8:1:1 ratio. The MAE of the validation set is monitored in real time during training. If the validation loss does not decrease after 15 consecutive rounds, an early stopping mechanism is triggered and the optimal model parameters are saved to prevent overfitting. After each training round, a loss curve is plotted to visually demonstrate the convergence trend. After training, the residuals of the test set are calculated and the residual sequence is saved. The residual sequence is the difference between the actual wind power and the LSTM prediction value. The residual distribution histogram is plotted to verify whether it conforms to Student's t-distribution assumption, providing a probability distribution basis for the generation of scenarios for subsequent uncertainty modeling.

[0041] Step 2: Modeling the probability of wind power prediction error based on the t-distribution.

[0042] 2.1: t-distribution fitting: Since wind power prediction errors often exhibit "thick tail" characteristics, the traditional normal distribution is difficult to accurately characterize the tail risk. Therefore, Student's t-distribution is used to fit the residual sequence obtained in step 1.3. The degrees of freedom, mean, and standard deviation parameters of the t-distribution are determined by maximum likelihood estimation (MLE). The degree of freedom parameter reflects the thickness of the tail of the distribution. The smaller the degree of freedom, the thicker the tail, and the more accurate the characterization of extreme errors.

[0043] 2.2: Validation of Fit: Plot the Q-Q plot of the residuals and compare the deviation of the residual quantiles from the theoretical t-distribution quantiles; perform the KS test to calculate the maximum vertical distance between the sample distribution and the theoretical t-distribution, and verify the null hypothesis that the residuals follow the t-distribution at a given significance level. After successful validation, save the t-distribution fitting parameters.

[0044] Step 3: Wind power output scenario generation.

[0045] t-distribution fitting parameters based on LSTM prediction residuals, including degrees of freedom mean Standard deviation 1000 initial wind power output prediction error scenarios were generated through Monte Carlo simulation to fully capture the statistical characteristics of prediction uncertainty. The error values ​​were superimposed with the LSTM point prediction values ​​to obtain the actual wind power output of each initial scenario. To balance computational complexity and model accuracy, the 1000 initial scenarios were clustered and reduced using the K-means clustering algorithm to obtain three typical wind power output scenarios (low, medium, and high wind power output scenarios), and the occurrence probability of each typical scenario was calculated.

[0046] Figure 5 This is a scheduling characteristic diagram of a typical scenario of the present invention; it includes four sub-graphs: wind power and load comparison, energy storage charging and discharging, SOC change, and wind curtailment power. The horizontal axis represents time period, and the vertical axis represents power, power, SOC percentage, and power, respectively.

[0047] In Scenario 1, wind power rapidly climbs to a high level and remains stable in the initial period, which is consistent with the LSTM's prediction characteristics of wind power output in this scenario. The t-distribution also covers the potential extreme fluctuation risks, while the load exhibits irregular fluctuations, showing a significant difference between the two. Frequent and large-amplitude charging and discharging power reflects the optimization model's targeted adjustment strategy, combining the wind power characteristics predicted by LSTM with the fluctuation risks depicted by the t-distribution, to alleviate the high mismatch between wind power and load and ensure power balance. The State of Charge (SOC) fluctuates significantly, first rising rapidly, then falling, and then fluctuating again: the rising phase represents the energy storage's proactive response to the LSTM's prediction of "excess wind power," charging and storing a large amount of excess energy; subsequently, due to load fluctuations and continued over-demand of wind power, frequent discharging occurs, with the overall charging amount exceeding the discharging amount, demonstrating the optimization strategy's adaptation to the LSTM's predicted wind power characteristics. Large and frequent wind curtailment occurs; although energy storage actively adjusts, the actual wind power output still exceeds the adjustment range of the LSTM prediction and t-distribution error modeling. This represents an improvement over deterministic dispatch relying solely on point predictions, but the system's absorption capacity is currently limited by configuration, resulting in some energy waste.

[0048] Figure 6 This is a scheduling characteristic diagram of typical scenario two of the present invention; it includes four sub-graphs: wind power and load comparison, energy storage charging and discharging, SOC change, and wind curtailment power. The horizontal axis represents time period, and the vertical axis represents power, power, SOC percentage, and power, respectively.

[0049] In Scenario 2, wind power initially increases gradually and then stabilizes, consistent with the LSTM's predicted wind power output trend for this scenario. The t-distribution accurately depicts the potential for small fluctuations in wind power, resulting in relatively mild load fluctuations. The matching degree between the two is higher than in Scenario 1. Charging and discharging are relatively stable, reflecting the targeted scheduling strategy developed by the optimized model, which combines the LSTM's predicted wind power trend with the fluctuation characteristics depicted by the t-distribution: charging according to the strategy during periods of abundant wind power and discharging in an orderly manner during peak load periods, fully demonstrating the effective mitigation effect of energy storage on wind power and load fluctuations. SOC initially decreases and then gradually increases with fluctuations: initially, because the LSTM predicts that wind power is not yet at a sufficient level, energy storage prioritizes discharging to supplement load demand. As wind power gradually increases according to the predicted trend, energy storage then continuously charges to accumulate energy. The entire process clearly demonstrates the dynamic adaptation of the optimized strategy to changes in wind power predictions. Only a few periods experience wind curtailment with small amplitudes, indicating that relying on the accurate predictions of LSTM and the effective error coverage of the t-distribution, the system, through energy storage regulation and optimized scheduling strategies, pre-adapts to the dynamic relationship between wind power and load, achieving effective wind power absorption and reducing energy waste.

[0050] Figure 7 This is a scheduling characteristic diagram of typical scenario three of the present invention; it includes four sub-graphs: wind power and load comparison, wind curtailment power, energy storage charging and discharging, and SOC change. The horizontal axis represents time period, and the vertical axis represents power, power, power, and SOC percentage, respectively.

[0051] In Scenario 3, wind power output is low and stable, consistent with the LSTM prediction characteristics for this scenario. The t-distribution also covers the risk of small fluctuations. Load fluctuates at a relatively high level, indicating limited support from wind power. Charging and discharging are almost zero, reflecting the optimized model's combination of prediction and error modeling. This model determines that when wind power is insufficient, frequent adjustments by energy storage are unnecessary, and the system primarily relies on thermal power to meet load demands. The State of Charge (SOC) initially decreases and then stabilizes, as energy storage participates minimally in regulation, resulting in slow energy consumption. There is almost no wind curtailment, as wind power output remains low as predicted and can be fully absorbed by the system.

[0052] Scenario 1 shows significant wind curtailment, impacting overall economic efficiency; Scenario 2 demonstrates efficient wind power allocation and effective cost control due to reasonable scheduling; Scenario 3, with limited wind power, results in minimal energy storage usage and no wind curtailment, but may lead to reliance on high-cost thermal power. By comparing these three scenarios, it's evident that the system flexibly schedules energy storage based on the dynamic relationship between wind power and load, optimizing unit operating status and balancing wind power absorption, energy storage utilization, and cost control across different scenarios to achieve overall optimization goals.

[0053] Compared to traditional stochastic programming, which generates scenarios directly based on empirical assumptions, this method's scenario generation strictly relies on the prediction accuracy and residual distribution characteristics of LSTM: if the prediction accuracy of LSTM is improved, the fluctuation range of the residuals will be reduced, and the proportion of invalid fluctuations (fluctuations that deviate from the actual wind power characteristics) in the generated scenarios will be reduced, avoiding the optimization model from being "over-specified" or "under-specified" due to scenario distortion; at the same time, the t-distribution characterizes the heavy-tailed characteristics of the residuals, ensuring that the scenarios cover extreme wind power fluctuations, providing data support for the optimization model to cope with tail risks.

[0054] Step 4: Construction and solution of stochastic programming scheduling model.

[0055] 4.1 Objective Function Construction: The objective function is to minimize the expected operating cost C of the system. The objective function includes the cost of thermal power generation. Start-up and shutdown costs of thermal power units Cost of wind curtailment and energy storage dispatch costs Four parts. Specifically, the objective function is expressed as:

[0056]

[0057] in, This refers to the number of thermal power units. This refers to the number of scheduling periods in the previous day; Number of scenes; Let be the probability of the s-th scene occurring; Let g be the fuel cost function coefficient of the g-th thermal power unit; The power output of the g-th thermal power unit at time t in the s-th scenario; Costs for starting and stopping thermal power units; For the start-up and shutdown actions of the g-th thermal power unit at time t in the s-th scenario; Let be the cost of wind curtailment at time t for the wind farm in the s-th scenario; Let be the wind curtailment power of the wind farm at time t in the s-th scenario; This is the energy storage operating cost coefficient; The charging power in the s-th scenario at time t; Let be the discharge power in the s-th scenario at time t.

[0058] 4.2 Constraint Settings:

[0059] (1) Power balance constraint:

[0060] ;

[0061] in, The load in the s-th scenario at time t; The power output of the g-th thermal power unit at time t in the s-th scenario; The actual power output of the wind farm at time t in the s-th scenario; Let be the wind curtailment power of the wind farm at time t in the s-th scenario; The charging power in the s-th scenario at time t; Let be the discharge power in the s-th scenario at time t.

[0062] (2) Wind curtailment rate constraint:

[0063] ;

[0064] in, The actual power output of the wind farm at time t in the s-th scenario; Let be the wind curtailment power of the wind farm at time t in the s-th scenario;

[0065] (3) Start-up and shutdown logic constraints for thermal power units:

[0066] ;

[0067] in, These represent the start-up and shutdown states of the g-th thermal power unit in the s-th scenario at time t and (t-1), respectively. A value of 1 indicates that the unit is in the start-up state, and a value of 0 indicates that the unit is in the shutdown state. Let t represent the start-up and shutdown actions of the g-th thermal power unit in the s-th scenario at time t; where A value of 1 indicates that a power-on operation has been performed, while a value of 0 indicates that no power-on operation has been performed. A value of 1 indicates that a shutdown operation has been performed, while a value of 0 indicates that no shutdown operation has been performed.

[0068] (4) Upper and lower limits of thermal power unit output:

[0069] ;

[0070] in, These are the minimum and maximum output power of the g-th thermal power unit, respectively.

[0071] (5) Curb rate constraint for thermal power units:

[0072] ;

[0073] in The power output of the g-th thermal power unit at time t in the s-th scenario. The power output of the g-th thermal power unit at time (t-1) in the s-th scenario; The power limit for the g-th thermal power unit to climb the slope.

[0074] (6) Constraints of energy storage systems:

[0075] ;

[0076] in, These represent whether the s-th energy storage unit is "charging" at time t, with 1 indicating charging and 0 indicating not charging; Whether the s-th energy storage unit is "discharging" at time t, 1 indicates charging and 0 indicates not charging; The actual charging power in the s-th scenario at time t; This represents the actual discharge power in the s-th scenario at time t; The maximum charging power at time t in the s-th scenario; The maximum discharge power at time t in the s-th scenario; Let the state of charge of the energy storage at time t be the s-th scenario. The state of charge of the energy storage at time t-1 in the s-th scenario; For charging efficiency, For discharge efficiency; , These are the minimum and maximum allowed percentages of charge, respectively; This refers to the rated energy capacity of the energy storage device. For the SOC in the s-th scene at the last moment (out of a total of NTDs), This is the initial state of charge.

[0077] 4.3: Model Solving: Typical scenarios, objective functions, and constraints are imported into the Gurobi optimizer. The mixed integer quadratic programming (MIQP) problem is solved by combining the interior point method and the branch and bound algorithm. The relaxation problem is solved iteratively and the cutting plane is added to tighten the feasible region. Finally, it converges to the global optimum and obtains the start-up and shutdown decision of thermal power units and the output allocation, energy storage charging and discharging, and wind curtailment optimization strategies under various typical scenarios.

[0078] Gurobi directly addresses quadratic terms in the objective function through a combination of interior-point methods and branch-and-bound algorithms. It also simplifies the model structure using preprocessing techniques and gradually narrows the feasible region by iteratively solving relaxation problems and adding cutting planes, ultimately converging to the global optimum. Its built-in heuristics and parallel computing capabilities enhance the efficiency of solving stochastic programming problems across various scenarios.

[0079] Implementation effect verification:

[0080] This invention compares the system's adaptability to wind power fluctuations under different scheduling strategies. Deterministic scheduling methods, by ignoring the distribution characteristics of prediction errors, require frequent adjustments to thermal power units when wind power output deviates from the predicted value, leading to increased operating costs and higher wind curtailment rates. In contrast, the stochastic programming method proposed in this invention generates typical scenarios through t-distribution error modeling, and the optimization results demonstrate better adaptability and stability in all scenarios.

[0081] Figure 2 This is a wind power prediction interval diagram of the LSTM model of this invention; the horizontal axis represents time points, the vertical axis represents power, the blue curve represents the actual value, the red curve represents the predicted value, and the green area represents the 95% confidence interval. The predicted value and the actual value have a high degree of agreement, and the 95% confidence interval covers most of the data points, indicating that the LSTM model has good prediction accuracy and uncertainty quantification ability. This further shows that the model can not only accurately track the overall trend of wind power, but also provide a reliable uncertainty range for grid dispatch, which helps to effectively manage risks in subsequent optimization.

[0082] Figure 3 This is a probability distribution diagram of the wind power prediction error of this invention; the blue histogram represents the sample error distribution, the red curve represents the normal distribution fit, and the green curve represents the t-distribution fit. Compared with the commonly used normal distribution, the t-distribution fits the sample error more accurately in the heavy-tailed region. This conclusion can also be verified in the QQ plot. Figure 3 The QQ plot is used to test the normal distribution of the wind power prediction error of this invention, which verifies the superiority of the t-distribution fitting.

[0083] The above analysis not only confirms the superior performance of the LSTM model in short-term wind power forecasting but also reveals the t-distribution characteristics of the prediction residuals. This distribution characteristic provides solid data support for constructing stochastic programming scheduling models based on chance constraints or scenario generation, enabling more accurate quantification and control of wind power uncertainties in actual scheduling. This, in turn, maximizes the economic utilization of renewable energy while ensuring the safe operation of the system.

[0084] Based on the constructed two-stage stochastic programming model, the Gurobi solver was used to obtain the globally optimal scheduling scheme. This scheme includes a set of start-up and shutdown decisions for thermal power units applicable to all scenarios, as well as detailed power allocation, energy storage scheduling, and wind curtailment strategies corresponding to low, medium, and high wind power output scenarios. The following analysis details the operation of the optimized scheme for each scenario.

[0085] The present invention method is compared with traditional deterministic scheduling methods, and the comparison of economic efficiency and robustness indicators is shown in Table 1 and Table 2:

[0086] Table 1. Economic Comparison of Different Scheduling Methods

[0087]

[0088] Simulation results show that, compared with traditional deterministic scheduling methods, the stochastic programming method based on LSTM prediction and t-distribution error modeling proposed in this invention exhibits significant advantages in terms of economic efficiency and renewable energy consumption: the total operating cost is reduced from RMB 81,254.83 to RMB 76,307.27, a decrease of 6.1%. The core reason for this cost reduction lies in the deep synergy between LSTM prediction and the optimization model: on the one hand, the high-precision prediction of wind power by the LSTM model reduces redundant fluctuations in the stochastic programming scenario; on the other hand, the accurate modeling of the LSTM residuals by the t-distribution avoids the problem of underestimating extreme errors in the traditional normal distribution. For example, in scenario one (high wind power scenario), the extreme high-output scenario generated based on the t-distribution prompts the optimization model to arrange energy storage charging in advance during off-peak hours, rather than the wind curtailment rate as high as 18.7% caused by the failure to consider extreme high output, as is the case with deterministic scheduling.

[0089] In contrast, deterministic dispatch relies solely on LSTM point predictions as input for wind power output. Assuming stable wind power output, when actual output deviates from the prediction (e.g., in scenario one, actual output is 15% higher than the prediction), the system, lacking pre-optimized energy storage and thermal power strategies, can only respond through wind curtailment or emergency shutdown of thermal power plants, resulting in persistently high wind curtailment rates. Our proposed method, however, uses stochastic optimization to probabilistically model LSTM prediction errors, transforming "uncertainty" into "quantifiable multi-scenario inputs." This allows for adaptation to different deviation scenarios during the optimization phase, thus achieving a dual improvement in economic efficiency and wind power absorption capacity. This provides an effective technical path for the optimized dispatch of future new power systems.

[0090] Table 2. Comparison of robustness of different scheduling methods

[0091]

[0092] As can be seen from the comparison of robustness indices of different scheduling methods in Table 2, stochastic programming (t-distribution) performs better in dealing with wind power uncertainty: the cost fluctuation coefficient decreased from 0.0027 in deterministic scheduling to 0.0016, a reduction of 40.7%. This is because it relies on the accurate prediction of LSTM and the characterization of the fat tail of error by the t-distribution, allowing the optimization scheme to adapt to the cost structure of different wind power scenarios in advance, avoiding the drastic cost fluctuations caused by a single prediction in deterministic scheduling; the power deficit frequency decreased from 15% to 0, because stochastic programming covers extreme wind power scenarios through the t-distribution, pre-configures thermal power reserves and energy storage regulation capabilities, and eliminates the risk of power supply gaps; the wind curtailment rate fluctuation also decreased from 12% to 11%, thanks to the accurate prediction of high wind power scenarios by LSTM combined with the error expansion of the t-distribution, which allows energy storage to charge and absorb wind power in advance during high wind power periods, while coordinating the output of thermal power and energy storage in low wind power scenarios, reducing the absorption differences between different scenarios. In summary, the technical approach of "LSTM prediction + t-distribution error modeling + stochastic optimization" effectively improves the system's robustness to wind power fluctuations.

[0093] Appendix A:

[0094] To clarify the calculation logic of robustness quantitative indicators, the definitions, formulas, and variable meanings of each indicator are supplemented here.

[0095] 1. Cost fluctuation coefficient

[0096] Definition: This measures the stability of system operating costs under different wind power fluctuation scenarios. The smaller the coefficient, the weaker the impact of scenario fluctuations on costs and the stronger the system robustness.

[0097] Calculation formula: ,in The standard deviation of system operating costs under different wind power scenarios reflects the degree of cost dispersion. This represents the arithmetic mean of system operating costs under different wind power scenarios.

[0098] 2. Power deficit frequency

[0099] Definition: Measures the probability that "the power supply cannot meet the load demand" within a scheduling cycle. The lower the frequency, the higher the reliability and robustness of the system power supply.

[0100] Calculation formula: ,in This indicates the number of time periods during which power deficit occurs within the scheduling cycle; Total number of time periods in the scheduling cycle.

[0101] 3. Fluctuation range of wind curtailment rate

[0102] Definition: Measures the range of wind curtailment rate variation under different wind power scenarios. The smaller the range, the stronger the stability and robustness of the system's wind power absorption capacity.

[0103] Calculation formula: ,in This represents the maximum value of the wind curtailment rate across all wind power scenarios; This represents the minimum wind curtailment rate across all wind power scenarios.

[0104] Appendix B: Parameters of Thermal Power Units and Energy Storage Systems

[0105] Table B.1 Parameters of Thermal Power Units

[0106]

[0107] Table B.2 Energy Storage System Parameters

[0108]

[0109] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A stochastic optimal scheduling method for power systems based on LSTM-t distribution, characterized in that, Includes the following steps: Step 1: Construct and train an LSTM wind power prediction model: Collect historical wind power data, meteorological data and time series feature data, and construct input samples and target sequences after preprocessing; construct a two-layer LSTM prediction model, and obtain wind power prediction values ​​and prediction residual sequences after training and optimization. Step 2: Wind power prediction error probability modeling based on t-distribution: The residual sequence obtained in Step 1 is fitted with Student's t-distribution, the degree of freedom parameters of t-distribution are determined by maximum likelihood estimation, the fitting effect is verified by QQ plot and KS test, and the verified t-distribution fitting parameters are saved. Step 3: Construct a stochastic programming and scheduling model for the power system based on t-distribution error: Using the LSTM wind power point prediction value obtained in Step 1 as a benchmark, and based on the t-distribution fitting parameters in Step 2, generate an initial wind power output prediction error scenario through Monte Carlo simulation, and reduce it to a typical wind power output scenario through K-means clustering; construct a two-stage chance-constrained stochastic programming model, set constraints, and solve it using the Gurobi optimizer to obtain a stochastic optimal scheduling scheme for the power system.

2. The method according to claim 1, characterized in that, The data preprocessing described in step 1 specifically includes: normalizing wind power and meteorological data using the Z-score normalization method; filling missing values ​​in the meteorological data using linear interpolation between adjacent time points; and identifying abnormal peaks in the wind power sequence using a 3D interpolation method. The rule is identified and replaced with the moving average of the previous 6 hours; the input sample is constructed using the sliding window technique with a window size of 24, and the power at the next moment is predicted using the data of the previous 24 hours, forming the input sequence and the target sequence.

3. The method according to claim 1, characterized in that, The structure of the dual-layer LSTM prediction model described in step 1 is as follows: it includes an input layer, a dual-layer LSTM layer, a Dropout layer, a fully connected layer, and an output layer. The number of neurons in the input layer is consistent with the dimension of the input features, which include 4-dimensional temporal features, 3-dimensional multi-height wind speed, 6-dimensional wind direction derived features, and 3-dimensional environmental features. The first LSTM layer contains 128 neurons with OutputMode set to "last", and the second LSTM layer contains 64 neurons. A Dropout layer with a deactivation rate of 0.2 is set between the two LSTM layers. The fully connected layer expands the LSTM output feature vector through a Flatten layer, connects it to a fully connected layer with 32 neurons and a ReLU activation function, and finally generates the wind power prediction value through linear activation of a single neuron output layer.

4. The method according to claim 1, characterized in that, The model training optimization described in step 1 is as follows: using the mean absolute error (MAE) as the loss function, the Adam optimizer is selected and the learning rate is dynamically adjusted using an exponential decay strategy, with the learning rate multiplied by 0.5 after every 10 training rounds; the dataset is divided into training, validation, and test sets in an 8:1:1 ratio; the MAE of the validation set is monitored in real time during training; if the validation loss does not decrease after 15 consecutive rounds, an early stopping mechanism is triggered and the optimal model parameters are saved; after training is completed, the residuals of the test set are calculated and the residual sequence is saved.

5. The method according to claim 1, characterized in that, The degrees of freedom parameter for fitting the t-distribution in step 2 is determined by maximum likelihood estimation. The degrees of freedom parameter reflects the thickness of the tail of the distribution; the smaller the degrees of freedom, the thicker the tail. The QQ plot intuitively judges the goodness of fit by comparing the deviation of the residual quantiles from the theoretical t-distribution quantiles. The KS test tests whether the residuals follow the t-distribution by calculating the maximum vertical distance between the sample distribution and the theoretical distribution.

6. The method according to claim 1, characterized in that, The wind power output scenario generation and reduction in step 3 are as follows: Based on the t-distribution fitting parameters, 1000 initial wind power output prediction error scenarios are generated through Monte Carlo simulation. The error values ​​are superimposed with the LSTM point prediction values ​​to obtain the actual wind power output of each initial scenario. The 1000 initial scenarios are clustered and reduced using the K-means clustering algorithm to obtain 3 representative typical wind power output scenarios and their corresponding occurrence probabilities.

7. The method according to claim 1, characterized in that, The two-stage chance-constrained stochastic programming model described in step 3 takes minimizing the expected operating cost of the system as its objective function. The objective function includes four parts: thermal power generation cost, thermal power unit start-up and shutdown cost, wind curtailment penalty cost, and energy storage dispatch cost.

8. The method according to claim 1, characterized in that, The constraints mentioned in step 3 specifically include: power balance constraints, wind curtailment rate constraints, start-stop logic constraints for thermal power units, upper and lower limits of output constraints for thermal power units, ramp-up rate constraints for thermal power units, and dynamic operation constraints for energy storage systems; wherein the dynamic operation constraints for energy storage systems cover charging and discharging mutual exclusion constraints, upper and lower limits of charging and discharging power constraints, time-series changes in state of charge constraints, upper and lower limits of state of charge constraints, rated energy capacity constraints, and initial and final state of charge constraints.

9. The method according to claim 1, characterized in that, The specific solution of the model in step 3 is as follows: the Gurobi optimizer is used to solve the two-stage chance-constrained stochastic programming model, which is a mixed integer quadratic programming problem with a quadratic objective function and integer constraints. This results in start-up and shutdown decisions for thermal power units applicable to all scenarios, as well as output allocation, energy storage charging and discharging strategies, and wind curtailment strategies for thermal power units in various typical scenarios.

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