Estimation and optimization fused energy storage optimal scheduling uncertainty set construction method

Abstract

The invention discloses a method for constructing an energy storage optimal scheduling uncertainty set fusing estimation and optimization, and the method comprises the following steps: constructing a risk-avoiding energy storage optimal scheduling model, constructing a robust optimization model based on an electricity price uncertainty error vector, and enabling an uncertainty set to cover the error distribution under a preset probability threshold; constructing a double-layer optimization model taking a decision as a center, and jointly optimizing related parameters and variables to form a nested structure; executing a statistical feasible size calibration method, determining a minimum feasible set radius based on mahalanobis distance sorting of historical samples, and ensuring that coverage probability constraints are met; and calculating an objective function gradient, solving the gradient by applying an implicit function theorem and a KKT condition, iteratively optimizing parameters by utilizing a gradient descent algorithm after synthesizing a total gradient, and obtaining an optimal uncertainty set in combination with an early stop mechanism. According to the method, the problem that a model and a strategy are disjointed in a traditional two-stage method of estimation first and optimization second is solved, and the robustness and the economical efficiency of energy storage scheduling can be effectively improved.

Description

Technical Field

[0001] The present invention relates to renewable energy scheduling technology, and in particular to a method for constructing an uncertainty set for energy storage optimal scheduling that integrates estimation and optimization. Background Art

[0002] Due to the volatility and uncertainty of intermittent renewable energy sources such as wind and solar power, the large-scale integration of these energy sources poses unprecedented challenges to the stability, security, and dispatch flexibility of power systems. Maintaining real-time power balance in power systems requires flexible and efficient regulation resources. Energy storage systems, with their advantages of fast response, high regulation accuracy, and flexible deployment, are playing an increasingly important role in modern power systems. A core dispatching strategy driving the deployment of energy storage systems is participation in the electricity market and coordinated with the grid for optimized dispatch. The effective implementation of this strategy relies heavily on accurate forecasts of future electricity prices. However, with increasing uncertainty in renewable energy output, intensified load fluctuations, and increasingly complex power market mechanisms, electricity price time series are exhibiting greater randomness and non-stationarity. This makes traditional energy storage operation strategies that rely on point forecasts difficult to adapt to the increasingly complex real-world operating environment. To ensure that energy storage systems can efficiently and reliably participate in grid optimization, it is imperative to fully consider the impact of electricity price uncertainty in dispatching decisions, thereby improving the robustness of dispatching strategies and the economic efficiency of the grid.

[0003] Existing optimal energy storage scheduling models that consider electricity price uncertainty primarily employ stochastic optimization, robust optimization, and distributed robust optimization. Stochastic optimization seeks to maximize the expected value of the scheduling objective and is a risk-neutral decision-making approach. Risk-neutral decision-making approaches can lead to suboptimal or even erroneous operational decisions for energy storage systems. In extreme cases, continuous forecast deviations can trigger continuous energy storage misoperations, resulting in suboptimal scheduling performance over multiple scheduling cycles. Therefore, robust optimization and distributed robust optimization are widely used as risk-averse decision-making methods. Robust optimization constructs a set of uncertainties to seek a feasible or optimal solution under the worst-case scenario, offering strong conservatism and safety. Distributed robust optimization considers a set of possible probability distributions (i.e., fuzzy sets) to strike a balance between computational complexity and risk controllability. Although these approaches have achieved widespread theoretical application, their commonly adopted two-stage "estimate first, optimize later" paradigm has inherent limitations. Specifically, the goal of the uncertainty modeling stage is typically to ensure that the model closely matches the characteristics of historical data, such as minimizing the distribution estimation error or constructing a set that covers the true uncertainty. However, this two-stage approach does not consider the actual demand for uncertainty structure in the subsequent optimization stage, resulting in the constructed model being difficult to truly serve the optimal scheduling decision.

[0004] Existing energy storage systems generally rely on accurate predictions of future electricity prices when participating in power system optimization and scheduling. However, with the increasing penetration of renewable energy and increasing market complexity, electricity prices are highly uncertain. While existing technologies, such as stochastic optimization, robust optimization, and distributionally robust optimization, can address electricity price uncertainty to a certain extent, their commonly adopted "two-stage" modeling process—first building an uncertainty model based on historical data and then making optimization decisions—does not fully consider the actual requirements of uncertainty modeling for final decision-making performance. This leads to a disconnect between the constructed model and the optimization strategy, thus affecting the economic efficiency and robustness of the energy storage system.

[0005] In addition, as electricity market price volatility intensifies, energy storage systems face a series of problems when participating in grid optimization and scheduling, including incorrect decisions on energy storage operations caused by electricity price forecast errors, overly conservative or insufficient risk control in existing uncertainty modeling methods, disconnection between uncertainty set construction and actual decision-making needs, lack of a customized modeling framework for energy storage operation characteristics, high computational complexity affecting actual application efficiency, and poor adaptability to market fluctuations. These problems seriously affect the economic feasibility and operational robustness of energy storage systems in participating in grid scheduling.

[0006] Therefore, there is an urgent need to propose an integrated modeling method that closely combines uncertainty modeling with optimization decision-making and is guided by decision-making performance. This method can ensure that the energy storage system can achieve effective and risk-controlled operation in the optimized scheduling of the power grid even when electricity price forecast errors are inevitable.

[0007] It should be noted that the information disclosed in the above background technology section is only used to understand the background of this application, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0008] The main purpose of the present invention is to overcome the defects existing in the above-mentioned background technology and provide a method for constructing an uncertainty set of energy storage optimal scheduling that integrates estimation and optimization.

[0009] To achieve the above object, the present invention adopts the following technical solutions: A method for constructing an uncertainty set for optimal energy storage scheduling by integrating estimation and optimization includes the following steps: S1. Construct a risk-averse energy storage optimization scheduling model: Based on the electricity price uncertainty error vector, a robust optimization model is constructed to minimize the worst-case task loss. The uncertainty set must cover the error distribution under a preset probability threshold. S2. Construct a decision-centered two-level optimization model: Guided by minimizing the scheduling objective function, jointly optimize the uncertainty set parameters and energy storage decision variables to form a nested decision structure; S3. Execute a statistically feasible size calibration method: dynamically determine the minimum feasible set radius based on the Mahalanobis distance sorting of historical samples to ensure that the uncertainty set meets the preset coverage probability constraint; S4. Calculate the objective function gradient: Apply the implicit function theorem and KKT conditions to analytically solve the gradient of the decision variable with respect to the set parameters, combine the radius gradient to synthesize the total gradient of the objective function, and use the gradient descent algorithm to iteratively optimize the set parameters. Combined with the early stopping mechanism, the optimal uncertainty set is obtained.

[0010] Furthermore, step S1 specifically includes: The energy storage scheduling model is transformed into a robust optimization form, and an ellipsoidal uncertainty set is defined to characterize the statistical characteristics and correlation of electricity price errors. By taking the dual transformation of the inner maximization problem, the robust optimization model is transformed into an equivalent convex optimization form that can be solved analytically. The uncertainty set must meet a preset confidence requirement for covering the true distribution of the error vector.

[0011] Furthermore, step S2 specifically includes: Establish an explicit association between the objective function and the uncertainty set parameters, and determine the optimal set parameters by minimizing the target value of the scheduling decision; The two-layer model includes a nested structure of outer layer collective parameter optimization and inner layer energy storage decision optimization, and is subject to coverage probability constraints.

[0012] Furthermore, step S3 specifically includes: Calculate the Mahalanobis distance of historical samples relative to the center of the set and arrange them in ascending order to generate a scalar sequence; Based on the statistical characteristics of the binomial distribution and the preset confidence level, the minimum radius threshold that satisfies the coverage probability is selected from the scalar sequence; The radius parameter is expressed as a function of the center of the set and the shape parameter.

[0013] Furthermore, the Mahalanobis distance is calculated as follows: The inverse matrix of the covariance matrix based on the ellipsoid set measures the degree of sample deviation, and its scalarization transformation retains the correlation characteristics between error vectors.

[0014] Furthermore, step S4 specifically includes: The inner optimization problem is expressed as a differentiable system that satisfies the KKT condition, and the gradient of the decision variable with respect to the set parameter is analyzed by the implicit function theorem. Combine the gradient of the objective function with respect to the decision variable, the gradient with respect to the radius parameter, and the gradient of the radius with respect to the set parameter to synthesize the total gradient; The gradient calculation includes a piecewise derivation process on the Mahalanobis distance sorting result.

[0015] Furthermore, step S4 specifically includes: Adaptive gradient descent algorithm is used to update the set center parameters; Each iteration performs size calibration based on the current parameters to calculate the feasible radius; When the objective function value does not improve for consecutive preset rounds, the iteration is terminated and the optimal parameters are output.

[0016] Furthermore, the gradient descent algorithm is specifically as follows: An adaptive moment estimation algorithm is used to adjust the parameter update step size, and a greedy early stopping mechanism is used to avoid overfitting.

[0017] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the method for constructing an uncertainty set for optimal energy storage scheduling by integrating estimation and optimization.

[0018] A computer program product includes a computer program, which, when executed by a processor, implements the method for constructing an uncertainty set for optimal energy storage scheduling by integrating estimation and optimization.

[0019] The present invention has the following beneficial effects: The present invention proposes a method for constructing an uncertainty set for optimal energy storage scheduling that integrates estimation and optimization. It is a risk-averse, decision-centered uncertainty set construction method. Through a decision-oriented gradient descent method designed based on the implicit function theorem and combined with a statistically feasible size calibration method, uncertainty estimation and optimization decision-making are organically integrated, thereby improving the operational robustness and economy of the energy storage system participating in grid scheduling under an uncertain electricity price environment. This method constructs an integrated modeling framework that can closely combine uncertainty modeling with optimization decision-making and is guided by the final decision performance. By deeply integrating electricity price uncertainty modeling with the optimization decision-making process, it solves the problem of disconnection between model and strategy in the traditional "estimate first, then optimize" two-stage method. This integrated modeling method guided by decision performance can ensure that the energy storage system can achieve risk-controlled and effective operation in the optimized scheduling of the power grid when electricity price forecast errors are inevitable, thereby effectively dealing with the operational risks brought about by electricity price forecast errors and improving the operational robustness and grid economy of the optimized scheduling of the energy storage system in a complex market environment. At the same time, this method is based on statistically effective size calibration technology, and combines a differentiable optimization framework and gradient analysis methods to dynamically adjust the uncertainty set parameters, so that it can directly serve to improve the operating economy and robustness of the energy storage system. In practical applications, it can effectively reduce the risk of erroneous operations caused by prediction errors while ensuring the preset safety probability, enhance the system's adaptability to market fluctuations, and have good computing efficiency and online deployment potential. The present invention not only helps to improve the effective utilization of energy storage assets in the power grid system, but also provides key technical support for promoting the safe and stable operation of high-proportion renewable energy systems, and provides a more intelligent and robust technical path for energy storage to participate in power grid scheduling under the background of high-proportion renewable energy.

[0020] Other beneficial effects of the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Flowchart of the method for constructing an uncertainty set for optimal energy storage scheduling that integrates estimation and optimization of the present invention. DETAILED DESCRIPTION

[0022] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0024] See Figure 1 , an embodiment of the present invention provides a method for constructing an uncertainty set for energy storage optimal scheduling by integrating estimation and optimization, comprising the following steps: Step S1: Construct a risk-averse energy storage optimization scheduling model: Based on the electricity price uncertainty error vector, construct a robust optimization model with the goal of minimizing the worst-case task loss, where the uncertainty set must cover the error distribution under a preset probability threshold.

[0025] In some embodiments, step S1 specifically includes: converting the energy storage scheduling model into a robust optimization form, defining an ellipsoidal uncertainty set to characterize the statistical characteristics and correlation of electricity price errors; converting the robust optimization model into an equivalent convex optimization form that can be solved analytically by taking a dual transformation of the inner layer maximization problem; the uncertainty set must meet the preset confidence requirements of covering the true distribution of the error vector.

[0026] Step S2: Construct a decision-centered two-layer optimization model: guided by minimizing the scheduling objective function, jointly optimize the uncertainty set parameters and energy storage decision variables to form a nested decision structure.

[0027] In some embodiments, step S2 specifically includes: establishing an explicit association between the objective function and the uncertainty set parameters, and determining the optimal set parameters by minimizing the target value of the scheduling decision; the two-layer model includes a nested structure of outer layer set parameter optimization and inner layer energy storage decision optimization, and is subject to coverage probability constraints.

[0028] Step S3, executing a statistically feasible size calibration method: dynamically determining the minimum feasible set radius based on the Mahalanobis distance sorting of historical samples to ensure that the uncertainty set meets the preset coverage probability constraint.

[0029] In some embodiments, step S3 specifically includes: calculating the Mahalanobis distance of historical samples relative to the center of the set and arranging them in ascending order to generate a scalar sequence; based on the statistical characteristics of the binomial distribution and a preset confidence level, selecting a minimum radius threshold that meets the coverage probability from the scalar sequence; the radius parameter is expressed as a function of the center of the set and the shape parameter.

[0030] In some embodiments, the Mahalanobis distance calculation is specifically as follows: measuring the degree of sample deviation based on the inverse matrix of the covariance matrix of the ellipsoid set, and its scalarization conversion retains the correlation characteristics between error vectors.

[0031] Step S4, calculate the objective function gradient: apply the implicit function theorem and KKT condition to analytically solve the gradient of the decision variable with respect to the set parameters, combine the radius gradient to synthesize the total gradient of the objective function, and use the gradient descent algorithm to iteratively optimize the set parameters, and combine the early stopping mechanism to obtain the optimal uncertainty set.

[0032] In some embodiments, step S4 specifically includes: expressing the inner optimization problem as a differentiable system that satisfies the KKT condition, and analyzing the gradient of the decision variable with respect to the set parameter through implicit function definition; combining the gradient of the objective function with respect to the decision variable, the gradient with respect to the radius parameter, and the gradient of the radius with respect to the set parameter to synthesize the total gradient; the gradient calculation includes piecewise derivation processing of the Mahalanobis distance sorting result.

[0033] In some embodiments, step S4 specifically also includes: using an adaptive gradient descent algorithm to update the set center parameters; performing size calibration to calculate the feasible radius based on the current parameters in each iteration; terminating the iteration and outputting the optimal parameters when the objective function value has not improved for consecutive preset rounds.

[0034] In a further embodiment, the gradient descent algorithm specifically adopts an adaptive moment estimation algorithm to adjust the parameter update step size, and avoids overfitting through a greedy early stopping mechanism.

[0035] The main technical advantage of the present invention lies in that it deeply integrates electricity price uncertainty modeling and optimization decision-making processes, and innovatively proposes a decision-centered uncertainty set construction method, which effectively overcomes the problem of disconnection between model and strategy caused by the traditional two-stage paradigm of "estimation first, then optimization"; based on statistically feasible size calibration technology, the minimum set radius is dynamically determined to ensure error coverage capability under a preset safety probability, and at the same time combines the differentiable optimization framework and implicit function gradient analysis means to achieve adaptive adjustment of uncertainty set parameters, significantly improving the dispatch economy and operational robustness of the energy storage system in a highly random electricity price environment; this method reduces the risk of misoperation caused by prediction errors and enhances the ability to adapt to market fluctuations, while having both computational efficiency and online deployment potential, providing key technical support for the intelligent dispatch of energy storage assets in power grids with a high proportion of renewable energy.

[0036] The following further describes specific embodiments of the present invention and examples of algorithm implementation thereof.

[0037] A method for constructing an uncertainty set for optimal energy storage scheduling that integrates estimation and optimization is proposed. Aiming at risk aversion, it implements a decision-centered uncertainty set construction. It uses a decision-oriented gradient descent method based on implicit function theorem and combines it with a statistically feasible sizing method to organically integrate uncertainty estimation and optimization decision-making, thereby improving the operational robustness and economic efficiency of energy storage systems participating in grid scheduling under uncertain electricity prices. Figure 1 , the method specifically comprises the following steps: 1) Establishing a risk-averse optimal scheduling model for energy storage This method focuses on the operation mechanism of energy storage systems participating in day-ahead grid dispatch. Energy storage owners, as price takers, participate in grid dispatch by only declaring power consumption without specifying a transaction price. t is the index of the market clearing period, T Represents the total number of time periods within the optimization cycle. The optimal scheduling problem of energy storage can be modeled as follows:

[0038] Where, represents the market electricity price; Represents the interaction power between energy storage and the grid; Indicates the charging power of the energy storage, Indicates the discharge power of energy storage; Indicates the charging rated power of the energy storage, Indicates the discharge rated power of energy storage; Indicates the state of charge of the energy storage; represents the charging efficiency of energy storage, Indicates the discharge efficiency of energy storage; and Indicates the upper and lower limits of energy storage.

[0039] The inherent uncertainty in market price forecasts creates economic risks, prompting risk-averse decision makers to seek robust bidding strategies. These forecast uncertainties are represented by the error vector In order to effectively manage the uncertainty in the optimal scheduling, the model defined by (1)-(5) is reformulated as a robust optimization problem. The charging decision goal is to achieve the error vector The true distribution of Minimize the worst-case task loss within the confidence region: Where, represents the feasible domain of charging decisions defined by constraints (2)-(5), x represents the error vector in the uncertainty set, λ is the regularization coefficient, represents the uncertainty set established,p Represents decision variables. The uncertainty set needs to be guaranteed to cover The error vector above The true distribution of: , e Indicates the error tolerance.

[0040] In actual scenarios, the error vector The exact distribution of is unknown, and the uncertainty set Based on a set of historical data samples The proposed method adopts the ellipsoidal uncertainty set as shown in (7) because it has the dual advantages of computational tractability and inherent ability to model correlations between uncertain variables. The proposed method is also applicable to other convex and differentiable uncertainty sets, such as box-shaped and polyhedral sets.

[0041]

[0042] In the formula, the parameter tuple Determines the shape and size of the ellipsoid, where L is a lower triangular matrix, is the error vector x The mean of r is a scalar.

[0043] By taking the duality of the inner maximization problem and exploiting the strong duality, the robust optimization problem (6) can be transformed into an equivalent tractable form:

[0044] When the uncertainty set Ideally, the uncertainty coverage condition is satisfied, i.e. , then the objective function value of model (8) is equal to the following conditional risk probability value: In the formula represents the objective function in formula (6).

[0045] 2) Establish a decision-centered uncertainty set As shown in Equation (8), energy storage scheduling decisions are affected by uncertainty set parameters. However, the "two-stage" modeling process adopted by existing methods—first building an uncertainty model based on historical data and then making optimization decisions—does not fully consider the actual requirements of uncertainty modeling for the final decision performance. This leads to a disconnect between the constructed model and the optimization strategy, thus affecting the economic efficiency and robustness of the energy storage system. To address this problem, this paper proposes a decision-centric uncertainty set (DCUS). This method combines parameter estimation with bidding profitability, enhancing the match between uncertainty modeling and economic performance.

[0046] The goal of the proposed method is to determine the parameters of DCUS to minimize the objective function while ensuring the coverage of the uncertainty set for the uncertainty variables. Its mathematical model is expressed as follows: The double-layer nested structure of the above model and the coverage probability constraint (12) make it difficult to solve the model. In order to effectively solve the model, the present invention first adopts a statistically feasible size calibration method to ensure that the coverage probability constraint (12) is met. According to formula (7), once and L OK, parameters r Determines the size of the uncertainty set. r A value of allows DCUS to cover more sample points, but at the expense of increased conservatism. Conversely, a smaller r The value leads to a less conservative solution, but may not satisfy Equation (12). Therefore, the proposed size calibration method aims to find the minimum feasible solution that satisfies Equation (12). r To achieve this, the Mahalanobis distance is defined MD ( x )as follows: . Each sample vector Convert to a scalar using the Mahalanobis distance , and arrange them in ascending order into a new set Required parameters r Estimated by the following formula: Where, Indicates the confidence level; Indicates the index corresponding to the optimal value.

[0047] After ensuring the probability constraint (12) using the statistically feasible size calibration method mentioned above, the parameter r It can be expressed as The function of .Then The gradient of can be used to optimize the objective function in equation (10) to solve the model. The gradient is calculated as follows: Where, represents the objective function in (10); and The gradient represented by can be obtained directly through mathematical analysis. The main challenge in calculating the gradient shown in (15) is to calculate and .

[0048] This method proposes to use a differentiable optimization layer to compute , the gradient calculation is realized by applying the KKT conditions (Karush-Kuhn-Tucker Conditions, KKT conditions) and implicit functions. For the clarity of subsequent derivation, Equation (11) is expressed in the following general form: h ( p ) represents an equality constraint, g ( p ) represents an inequality constraint.

[0049] The KKT condition of model (16) can be expressed in the following matrix form: Where, represents the original and dual variables of the model, p represents the decision variable, v Representation and inequality constraints g ( p ) related dual variables, m Representation and equality constraints h ( p ) related dual variables; A diagonal matrix of vectors.

[0050] According to the implicit function theorem, for a continuously differentiable function , which has the following derivative relationship: Where, express F The Jacobian matrix of .

[0051] According to the implicit function theorem shown in formula (18), solving it can be obtained : In calculation After that, the next step is to calculate . The expression is as follows: The second equation is valid because In the collection Chinese style only, so when hour Otherwise it is 0.

[0052] By taking the above steps, the gradient of the objective function (10) can be calculated under the premise of satisfying the constraint (12), and then the uncertainty set parameters of the decision center can be obtained by sampling the algorithm 1 shown in Table 1 below: Table 1

[0053] In summary, the present invention proposes a method for constructing an uncertainty set for optimal energy storage scheduling that integrates estimation and optimization. This method constructs an uncertainty set with decision-making as the center for risk avoidance. Uncertainty estimation and optimization decision-making are organically integrated through a decision-oriented gradient descent method designed based on the implicit function theorem and combined with a statistically feasible sizing calibration method. This decision-centric modeling method solves the problem of disconnection between model and strategy in the traditional "estimate first, optimize later" two-stage method by deeply integrating electricity price uncertainty modeling with the optimization decision-making process. Furthermore, based on statistically effective sizing calibration technology, combined with a differentiable optimization framework and gradient analysis methods, the uncertainty set parameters are dynamically adjusted, directly serving to improve the operational robustness and economic efficiency of energy storage systems participating in grid scheduling under electricity price uncertainty. In practical applications, this method can effectively reduce the risk of erroneous operations caused by prediction errors while ensuring a preset safety probability, enhance the system's adaptability to market fluctuations, and at the same time possess good computational efficiency and online deployment potential, providing a more intelligent and robust technical path for energy storage to participate in grid scheduling in the context of a high proportion of renewable energy.

[0054] An embodiment of the present invention further provides a storage medium for storing a computer program, which at least performs the above method when executed.

[0055] An embodiment of the present invention further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is configured to execute at least the method described above when executing the computer program.

[0056] An embodiment of the present invention further provides a processor, which executes a computer program and at least performs the method described above.

[0057] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, the non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic random access memory (FRAM), a flash memory (Flash Memory), a magnetic surface memory, an optical disc or a read-only optical disc (CD-ROM); the magnetic surface memory can be a magnetic disk memory or a magnetic tape memory. The storage medium described in the embodiments of the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0058] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0059] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0060] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0061] Those skilled in the art will appreciate that all or part of the steps of the above-mentioned method embodiments may be implemented by hardware associated with program instructions, and the aforementioned program may be stored in a computer-readable storage medium. When the program is executed, the program executes the steps of the above-mentioned method embodiments. The aforementioned storage medium includes various media that can store program codes, such as mobile storage devices, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0062] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

[0063] The methods disclosed in the several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0064] The features disclosed in several product embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0065] The features disclosed in several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0066] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that, without departing from the scope of the present invention, several equivalent substitutions or obvious variations can be made, and the performance or use of the same should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for constructing an uncertainty set for optimal energy storage scheduling that integrates estimation and optimization, characterized by: The following steps are involved: S1. Construct a risk-averse energy storage optimization scheduling model: Based on the electricity price uncertainty error vector, a robust optimization model is constructed to minimize the worst-case task loss. The uncertainty set must cover the error distribution under a preset probability threshold. S2. Construct a decision-centered two-level optimization model: Guided by minimizing the scheduling objective function, jointly optimize the uncertainty set parameters and energy storage decision variables to form a nested decision structure; S3. Execute a statistically feasible size calibration method: dynamically determine the minimum feasible set radius based on the Mahalanobis distance sorting of historical samples to ensure that the uncertainty set meets the preset coverage probability constraint; S4. Calculate the objective function gradient: Apply the implicit function theorem and KKT conditions to analytically solve the gradient of the decision variable with respect to the set parameters, combine the radius gradient to synthesize the total gradient of the objective function, and use the gradient descent algorithm to iteratively optimize the set parameters. Combined with the early stopping mechanism, the optimal uncertainty set is obtained.

2. The method according to claim 1, characterized in that Step S1 specifically includes: The energy storage scheduling model is transformed into a robust optimization form, and an ellipsoidal uncertainty set is defined to characterize the statistical characteristics and correlation of electricity price errors. By taking the dual transformation of the inner maximization problem, the robust optimization model is transformed into an equivalent convex optimization form that can be solved analytically. The uncertainty set must meet a preset confidence requirement for covering the true distribution of the error vector.

3. The method according to claim 1 or 2, characterized in that Step S2 specifically includes: Establish an explicit association between the objective function and the uncertainty set parameters, and determine the optimal set parameters by minimizing the target value of the scheduling decision; The two-layer optimization model includes a nested structure of outer layer set parameter optimization and inner layer energy storage decision optimization, and is subject to coverage probability constraints.

4. The method according to any one of claims 1 to 2, characterized in that Step S3 specifically includes: Calculate the Mahalanobis distance of historical samples relative to the center of the set and arrange them in ascending order to generate a scalar sequence; Based on the statistical characteristics of the binomial distribution and the preset confidence level, the minimum radius threshold that satisfies the coverage probability is selected from the scalar sequence; The radius parameter is expressed as a function of the center of the set and the shape parameter.

5. The method according to claim 4, characterized in that The Mahalanobis distance calculation is specifically as follows: The inverse matrix of the covariance matrix based on the ellipsoid set measures the degree of sample deviation, and its scalarization transformation retains the correlation characteristics between error vectors.

6. The method according to any one of claims 1 to 2, characterized in that Step S4 specifically includes: The inner optimization problem is expressed as a differentiable system that satisfies the KKT condition, and the gradient of the decision variable with respect to the set parameter is analyzed by the implicit function theorem. Combine the gradient of the objective function with respect to the decision variable, the gradient with respect to the radius parameter, and the gradient of the radius with respect to the set parameter to synthesize the total gradient; Gradient calculation includes piecewise derivation of the Mahalanobis distance sorting results.

7. The method according to any one of claims 1 to 2, characterized in that Step S4 specifically includes: Adaptive gradient descent algorithm is used to update the set center parameters; Each iteration performs size calibration based on the current parameters to calculate the feasible radius; When the objective function value does not improve for consecutive preset rounds, the iteration is terminated and the optimal parameters are output.

8. The method according to claim 7, characterized in that The gradient descent algorithm is specifically: An adaptive moment estimation algorithm is used to adjust the parameter update step size, and a greedy early stopping mechanism is used to avoid overfitting.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for constructing an uncertainty set of energy storage optimal scheduling by integrating estimation and optimization as described in any one of claims 1 to 8 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for constructing an uncertainty set of energy storage optimal scheduling by integrating estimation and optimization as described in any one of claims 1 to 8 is implemented.

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