Collaborative optimization operation method and device for power distribution system

Abstract

The invention discloses a power distribution system collaborative optimization operation method and device, and the method comprises the steps: constructing a generalized energy storage collaborative optimization model of a power distribution system according to the charging and discharging characteristics of an electric vehicle, the charging and discharging characteristics of a fixed energy storage device, and the load characteristics; constructing a context vector learning model containing a mapping relation between context vectors and optimization parameters by using historical operation data of the power distribution system and a generalized energy storage collaborative optimization model of the power distribution system and adopting a Gaussian process regression method; according to the mapping relation, a context vector of the current scene is extracted, initial distribution of parameters is predicted and optimized, and an initial mean vector and a covariance matrix of a CMA-ES algorithm are obtained; and executing a CMA-ES iterative optimization process by adopting the initial mean vector and the covariance matrix, and outputting a scheduling scheme of the electric vehicle and the fixed energy storage device containing the charging and discharging power of each time period. According to the scheme, hot start of the CMA-ES algorithm is realized through context vector learning, the optimization efficiency is improved, and falling into a local optimal solution is avoided.

Description

Technical Field

[0001] This application relates to the field of power system optimization and control technology, and in particular to a method and apparatus for collaborative optimization operation of a power distribution system. Background Technology

[0002] The power distribution system is a crucial component of the power system. With the widespread integration of electric vehicles and various energy storage devices, the operation and control of the power distribution system face new challenges. Electric vehicles, as mobile energy storage units, together with stationary energy storage devices, constitute a generalized energy storage system. How to coordinate and utilize these energy storage resources to achieve the economical and efficient operation of the power distribution system has become a hot research topic.

[0003] Currently, common methods for optimizing and scheduling power distribution systems mainly employ deterministic or stochastic programming. These methods typically use mathematical tools such as linear or nonlinear programming to find the optimal solution based on a predefined objective function and constraints. However, when dealing with complex power distribution systems containing a large number of electric vehicles and energy storage devices, these methods suffer from high computational complexity and struggle to meet the demands of real-time scheduling.

[0004] A more advanced method for power distribution system optimization employs the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) to handle complex nonlinear optimization problems. This method effectively addresses nonconvex optimization problems by adaptively adjusting the covariance matrix of the search distribution, demonstrating excellent performance in the field of power distribution system optimization. The CMA-ES algorithm can handle nonlinear optimization problems under complex constraints and is suitable for the coordinated scheduling optimization of generalized energy storage devices in power distribution systems.

[0005] However, existing CMA-ES methods have limitations when dealing with context-dependent optimization problems. Because they do not consider context vector information, each optimization requires a re-search, making it impossible to utilize historical optimization experience, reducing optimization efficiency, and making them prone to getting trapped in local optima. Especially in the daily operation of power distribution systems, although specific parameters may change, the contextual environment (such as load patterns and electricity pricing structures) often exhibits similarities. Utilizing this similarity to guide the optimization process would significantly improve optimization efficiency and result quality. Summary of the Invention

[0006] In view of this, this application provides a method and apparatus for collaborative optimization of power distribution system operation, which solves the problems of low optimization efficiency and easy trapping in local optima caused by the failure to consider context information in the existing CMA-ES optimization method.

[0007] This application provides a method for collaborative optimization of power distribution system operation, including:

[0008] Based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics, a generalized energy storage collaborative optimization model for power distribution systems is constructed.

[0009] Using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, a context vector learning model is constructed using the Gaussian process regression method. The context vector learning model includes the mapping relationship between the context vector and the optimization parameters. The context vector includes time features, load characteristics, electricity price information and environmental conditions.

[0010] Based on the mapping relationship between the context vector and the optimization parameters, the context vector of the current scene is extracted, and the initial distribution of the optimization parameters is predicted to obtain the initial mean vector and covariance matrix of the CMA-ES algorithm.

[0011] Using the initial mean vector and covariance matrix, the CMA-ES iterative optimization process is executed to output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0012] Optionally, a generalized energy storage collaborative optimization model for the power distribution system is constructed based on the charging and discharging characteristics of the electric vehicle, the charging and discharging characteristics of the stationary energy storage device, and the load characteristics, including:

[0013] Based on charging power limitations, state of charge change characteristics, and user driving needs, an electric vehicle charging and discharging model is constructed. This model is used to obtain the charging and discharging power constraints of the electric vehicle.

[0014] Using the electric vehicle charging and discharging power constraints, combined with the charging and discharging efficiency and capacity limitations of the stationary energy storage device, a stationary energy storage device model is constructed, and the charging and discharging power constraints of the stationary energy storage device are generated.

[0015] Using the electric vehicle charging and discharging power constraints and the fixed energy storage device charging and discharging power constraints, a power distribution network operation constraint model is constructed, forming node voltage constraints and line power constraints.

[0016] Based on the node voltage constraints and the line power constraints, an optimization objective function is constructed, and an optimization objective function and constraints are established that include minimizing operating costs and minimizing grid losses.

[0017] Optionally, it further includes: calculating weight coefficients using the analytic hierarchy process (AHP) based on the optimization objective functions of minimizing operating costs and minimizing grid losses, to form a weighted combined optimization objective function, wherein the operating costs include electricity purchase costs and energy storage device maintenance costs.

[0018] Optionally, the step of using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system to construct a context vector learning model using the Gaussian process regression method includes:

[0019] Data collection time characteristics, load characteristics, electricity price information, and environmental conditions are used, and data cleaning and normalization methods are employed to form preprocessed historical data.

[0020] Based on the preprocessed historical data, a combined kernel function containing a radial basis function kernel function and a classification kernel function is constructed to generate feature extraction results. The combined kernel function is a core component of the Gaussian process regression method.

[0021] Using the feature extraction results, the parameters of the combined kernel function are optimized by the maximum likelihood estimation method, and the mapping relationship between the context vector and the optimized parameters is obtained to complete the construction of the Gaussian process regression model.

[0022] Optionally, based on the mapping relationship between the context vector and the optimization parameters, the prediction accuracy index is calculated to obtain the root mean square error and the mean absolute error.

[0023] Based on the root mean square error and mean absolute error, determine whether the preset threshold is exceeded. If the preset threshold is exceeded, retrain the Gaussian process regression model.

[0024] Optionally, the step of extracting the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predicting the initial distribution of the optimization parameters, and obtaining the initial mean vector and covariance matrix of the CMA-ES algorithm includes:

[0025] Based on the current operational data, extract time features, operational status features, market features, and environmental features to form a context vector for the current scenario;

[0026] Using the context vector of the current scene, a learning model is used to predict parameters and generate an optimized parameter prediction distribution.

[0027] Based on the predicted distribution according to the optimization parameters, initialize the CMA-ES algorithm parameters and determine the initial mean vector and covariance matrix.

[0028] Optionally, the step of initializing the CMA-ES algorithm parameters based on the predicted distribution according to the optimized parameters includes:

[0029] The covariance matrix eigenvalues ​​of the predicted distribution are used with the optimized parameters to calculate the step size parameter and population size, and the initial configuration parameters of the CMA-ES algorithm are determined.

[0030] Based on the initial configuration parameters, the convergence performance of the optimization process is monitored. When the rate of change of the optimal fitness value for a consecutive specified number of generations is less than a preset threshold, the updated step size parameters and population size are generated.

[0031] Optionally, the CMA-ES iterative optimization process is performed using the initial mean vector and covariance matrix, including:

[0032] Based on the initial mean vector and covariance matrix, an initial population that satisfies the power limit and capacity boundary constraints is generated, forming a candidate solution set;

[0033] Using the candidate solution set, calculate the fitness values ​​of operating cost and grid loss, and obtain the fitness ranking results;

[0034] Based on the fitness ranking results, a log-normal weighted reorganization of individuals is performed to determine the mean vector of the new generation population.

[0035] When the iteration converges or reaches the maximum number of iterations, the solution corresponding to the optimal fitness is extracted to form a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0036] Optionally, it further includes: adjusting the optimization strategy based on the mean vector of the new generation population, including:

[0037] The mean vector of the new generation population is used to update the covariance matrix through evolutionary path accumulation and population distribution weighting methods to form an adaptively adjusted covariance matrix.

[0038] Based on the adaptively adjusted covariance matrix, the convergence status of the optimal fitness value is monitored. When the standard deviation of a consecutive specified number of algebras is less than a preset threshold, the covariance matrix after expanding the search range is determined.

[0039] This application also provides a power distribution system collaborative optimization operation device, including:

[0040] The optimization model building module is used to build a generalized energy storage collaborative optimization model for the power distribution system based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics.

[0041] The learning model construction module is used to construct a context vector learning model by using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, and adopting the Gaussian process regression method. The context vector learning model contains the mapping relationship between the context vector and the optimization parameters. The context vector contains time features, load characteristics, electricity price information and environmental conditions.

[0042] The hot start optimization module is used to extract the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predict the initial distribution of the optimization parameters, and obtain the initial mean vector and covariance matrix of the CMA-ES algorithm.

[0043] The scheduling optimization module is used to perform the CMA-ES iterative optimization process using the initial mean vector and covariance matrix, and output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0044] This application embodiment also provides a computer device, the computer device comprising:

[0045] At least one processor; and,

[0046] A memory communicatively connected to the at least one processor; wherein,

[0047] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the above-described method for coordinated optimization of the operation of the power distribution system.

[0048] This application also provides a computer-readable storage medium storing computer instructions for causing a computer to execute the above-described method for coordinated optimization of power distribution system operation.

[0049] This application also provides a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the above-described power distribution system collaborative optimization operation method.

[0050] This application has the following technical effects:

[0051] 1. By constructing a context vector learning model, a hot start of the CMA-ES algorithm based on historical optimization experience was achieved, which improved the convergence speed and optimization efficiency of the algorithm;

[0052] 2. A Gaussian process regression method is used to establish a mapping relationship between the context vector and the optimization parameters, enabling the optimization process to adapt to the characteristics of different scenarios and improving the adaptability of the optimization results;

[0053] 3. A model framework specifically designed for the generalized energy storage collaborative optimization of power distribution systems was developed, taking into account the mobility characteristics of electric vehicles and the characteristics of stationary energy storage devices, thereby maximizing the overall operational efficiency of the system;

[0054] 4. A CMA-ES initialization method based on the predicted distribution is proposed. By adaptively adjusting the covariance matrix and step size parameter, the problem of getting trapped in local optima during the optimization process is effectively avoided. Attached Figure Description

[0055] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. The following drawings only show some aspects of this application.

[0056] Figure 1 This is a flowchart illustrating a method for collaborative optimization of power distribution system operation according to an embodiment of this application;

[0057] Figure 2 This is a schematic diagram of the construction process of a generalized energy storage collaborative optimization model for a power distribution system provided in one embodiment of this application;

[0058] Figure 3 This is a schematic diagram of the context vector learning model structure provided in one embodiment of this application;

[0059] Figure 4 This is a schematic diagram of the CMA-ES-CWS hot start optimization process provided in one embodiment of this application;

[0060] Figure 5 This is a schematic diagram of the structure of a power distribution system collaborative optimization operation device provided in one embodiment of this application. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0062] like Figure 1 As shown in the figure, this application provides a method for collaborative optimization of power distribution system operation, including:

[0063] S1: Based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics, a generalized energy storage collaborative optimization model for the power distribution system is constructed.

[0064] S2: Using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, a context vector learning model is constructed using the Gaussian process regression method. The context vector learning model includes the mapping relationship between the context vector and the optimization parameters. The context vector includes time characteristics, load characteristics, electricity price information and environmental conditions.

[0065] S3: Based on the mapping relationship between the context vector and the optimization parameters, extract the context vector of the current scene, predict the initial distribution of the optimization parameters, and obtain the initial mean vector and covariance matrix of the CMA-ES algorithm.

[0066] S4: Using the initial mean vector and covariance matrix, perform the CMA-ES iterative optimization process to output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0067] Among them, the optimization parameters mainly refer to the key parameters of the CMA-ES algorithm (covariance matrix adaptive evolution strategy algorithm), specifically including:

[0068] The initial mean vector represents the central location of the algorithm's search, i.e., the location where the algorithm believes it is most likely to find the optimal solution. Each dimension of the mean vector corresponds to a decision variable, such as the charging and discharging power of electric vehicles at different times, or the scheduling strategy of fixed energy storage.

[0069] The covariance matrix determines the search scope and direction of the algorithm. The diagonal elements of the covariance matrix represent the search scope of each dimension, while the off-diagonal elements reflect the correlation between different dimensions.

[0070] The step size parameter σ controls the overall scale of the population distribution. A larger step size leads to a wider exploration, suitable for problems with high uncertainty or large scale; a smaller step size promotes fine-grained local search.

[0071] Population size parameters, including λ (number of offspring per generation) and μ (number of parent generations used to update the distribution), affect the computational cost of each generation iteration and the diversity of the population.

[0072] These parameters are predicted through a context vector learning model, forming a predicted distribution of optimization parameters, including mean prediction and uncertainty estimation. This provides an initial configuration for a warm start of the CMA-ES algorithm, thereby improving optimization efficiency and avoiding getting trapped in local optima.

[0073] Figure 1The flowchart illustrates the collaborative optimization operation method for a power distribution system provided in this application. The method first constructs a generalized energy storage collaborative optimization model for the power distribution system, then builds a context vector learning model based on historical data, followed by CMA-ES-CWS hot-start optimization, and finally executes generalized energy storage collaborative scheduling optimization and outputs a scheduling scheme. This context vector-based optimization method can effectively utilize historical optimization experience and improve optimization efficiency.

[0074] like Figure 2 As shown, a generalized energy storage collaborative optimization model for the power distribution system is constructed based on the charging and discharging characteristics of the electric vehicle, the charging and discharging characteristics of the stationary energy storage device, and the load characteristics, including:

[0075] S1.1: Based on charging power limitations, state of charge change characteristics, and user driving needs, an electric vehicle charging and discharging model is constructed. The electric vehicle charging and discharging model is used to obtain the charging and discharging power constraints of the electric vehicle.

[0076] When constructing a charging and discharging model for electric vehicles, the physical characteristics of the electric vehicle must first be considered. As a mobile energy storage unit, the charging and discharging behavior of an electric vehicle exhibits significant randomness and uncertainty. To accurately describe this characteristic, the model needs to include various constraints.

[0077] First, the charging power constraint is the most fundamental physical limitation. It is usually expressed by a piecewise linear or quadratic function to represent the charging characteristic curve, reflecting the change in the battery's charging capacity under different states of charge. For example, when the battery is in a low state of charge, it can accept a larger charging power; while when it is close to a fully charged state, the charging power will gradually decrease, exhibiting obvious nonlinear characteristics.

[0078] Secondly, the dynamic change of the electric vehicle's State of Charge (SOC) is a core part of the model, requiring the establishment of an accurate SOC dynamic change equation. This equation comprehensively considers the impact of charge / discharge efficiency, self-discharge rate, and ambient temperature on battery performance. Specifically, the rate of change of SOC is directly related to charge / discharge power, battery capacity, and charge / discharge efficiency, and can be described by differential equations. The model also needs to set upper and lower limits for SOC, typically between 5% and 95%, to avoid damage caused by over-discharge and to prevent efficiency reduction and shortened lifespan caused by overcharging.

[0079] Most importantly, the electric vehicle charging and discharging model must consider the practical constraint of user travel demand. This requires the model to predict energy demand based on user travel plans, ensuring that the electric vehicle has sufficient charge when the user needs to use the vehicle. Statistical learning methods can be used to build a user travel pattern model, predicting travel time, distance, and energy consumption, thereby constraining the charging and discharging plan. Simultaneously, considering the uncertainty of user travel plans, the model also needs to include a safety margin to ensure sufficient energy response in emergency situations. By integrating these constraints, a complete electric vehicle charging and discharging model is formed, providing a foundation for subsequent optimization.

[0080] S1.2: Using the electric vehicle charging and discharging power constraints, combined with the charging and discharging efficiency and capacity limitations of the fixed energy storage device, construct a fixed energy storage device model and generate the fixed energy storage device charging and discharging power constraints.

[0081] The construction of stationary energy storage device models is more structurally defined than that of electric vehicle models, but special attention needs to be paid to the lifespan and efficiency characteristics of the energy storage devices.

[0082] First, the charge / discharge efficiency of stationary energy storage devices is a crucial component of the model, typically closely related to factors such as charge / discharge power and ambient temperature. The model needs to establish a mapping relationship between charge / discharge efficiency and power and temperature, usually achieved through table lookup or curve fitting. High-power charge / discharge generally leads to reduced efficiency, while extreme temperature conditions also adversely affect efficiency; these factors need to be accurately reflected in the model.

[0083] Capacity limitation is another key constraint in stationary energy storage device models. The usable capacity of an energy storage device is affected by various factors, including the cumulative number of cycles, deep discharge history, and degree of aging. The model needs to set dynamic upper and lower limits for the energy storage capacity and establish a relationship equation between the number of cycles and the deep discharge rate to assess the lifespan degradation of the energy storage device. For example, deep discharge accelerates battery capacity decay, an effect that can be quantified using rainflow counting combined with a battery life model.

[0084] To extend the lifespan of energy storage devices, the model also needs to include limits on the rate of change of charging and discharging power to avoid frequent high-power charging and discharging operations. These constraints are typically expressed as the maximum allowable power change between two adjacent time periods, effectively preventing accelerated aging of the energy storage device due to frequent and large power fluctuations. Furthermore, the model must consider the self-discharge characteristics of the energy storage device, especially energy loss during long-term storage. Finally, by combining the charging and discharging power constraints of electric vehicles, collaborative modeling of the generalized energy storage system can be achieved, laying the foundation for system-level optimization control. Integrating these characteristics and constraints, a complete model of a stationary energy storage device is formed.

[0085] S1.3: Using the charging and discharging power constraints of the electric vehicles and the charging and discharging power constraints of the fixed energy storage devices, a power distribution network operation constraint model is constructed to form node voltage constraints and line power constraints.

[0086] The distribution network operation constraint model is the foundation for ensuring the safe and stable operation of the system. It combines the operational constraints of electric vehicles and stationary energy storage devices with the physical characteristics of the distribution network.

[0087] First, power flow equations describe the fundamental relationships that define the power balance of a system. Depending on the application scenario and required computational accuracy, either a DC power flow model or an AC power flow model can be chosen. DC power flow models are computationally simple and suitable for preliminary planning and large-scale system analysis; while AC power flow models more accurately reflect the active and reactive power distribution of the system, making them suitable for refined optimization and control. When constructing power flow equations, the charging and discharging power of electric vehicles and stationary energy storage devices needs to be considered as controllable injected power, which, along with traditional loads and distributed generation, jointly influences the system's power balance.

[0088] Node voltage constraints are a key indicator for ensuring power quality. According to power system operation standards, the voltage at each node must be maintained within the allowable deviation range, typically ±5% or ±7% of the rated voltage, depending on the specific application scenario. The model needs to establish the sensitivity relationship between node voltage and system power injection, which is usually achieved through a Jacobian matrix or a simplified voltage sensitivity coefficient. For distribution networks containing a large number of electric vehicles and energy storage devices, their charging and discharging behavior directly affects the node voltage distribution; therefore, node voltage constraints are an important boundary condition for generalized energy storage co-optimization.

[0089] Line power constraints are set based on the rated capacity of the conductors to ensure that the lines do not operate under overload conditions. The model needs to establish a transmission distribution coefficient between line power and node-injected power to reflect the impact of power injection variations on line power flow. In particular, for urban distribution networks, concentrated charging of electric vehicles can lead to localized line overloads, making line power constraints especially important. The model also needs to consider the dynamic thermal capacity characteristics of the lines, i.e., dynamically adjusting the line's carrying capacity based on factors such as ambient temperature and wind speed to improve the system's operational flexibility.

[0090] Furthermore, the distribution network operation constraint model also includes constraints such as transformer capacity limitations, reactive power balance, and power factor requirements, which together constitute a complete distribution network operation safety domain. By integrating the charging and discharging power constraints of electric vehicles and stationary energy storage devices, a comprehensive distribution network operation constraint model is formed, providing clear boundary conditions for optimization decisions.

[0091] S1.4: Based on the node voltage constraints and the line power constraints, construct an optimization objective function, and establish an optimization objective function and constraints that include minimizing operating costs and minimizing grid losses.

[0092] Constructing a comprehensive optimization objective function is the final step in the generalized energy storage collaborative optimization model of the power distribution system, and it is also a key step in determining the optimization direction and effect. Considering the economic and reliability requirements of power distribution system operation, the objective function usually includes multiple sub-objectives, forming a multi-objective optimization problem.

[0093] First, minimizing operating costs is the most basic economic objective, encompassing multiple cost items such as electricity purchase cost, energy storage device maintenance cost, and battery cycle life depreciation cost. Electricity purchase cost is typically calculated based on time-of-use or real-time pricing, and can be reduced through peak-shaving and valley-filling charging / discharging strategies. Energy storage device maintenance cost is directly related to the number and depth of charge / discharge cycles and needs to be quantified in the model. Battery cycle life depreciation cost reflects the depreciation of battery value due to usage and is usually non-linearly related to cycle depth and number of cycles.

[0094] Minimizing grid losses is another important optimization objective, directly related to system operating efficiency. Distribution network losses primarily stem from heat loss due to line impedance, and are proportional to the square of the line current. By rationally coordinating the charging and discharging behaviors of electric vehicles and stationary energy storage devices, the load curve can be smoothed, peak current reduced, and system losses significantly decreased. In the objective function, grid losses are typically expressed as quadratic terms of line resistance and current, and can be directly calculated based on power flow calculations or approximated using the loss coefficient method.

[0095] In addition to the two basic objectives mentioned above, the optimization objective function may also include other sub-objectives, such as minimizing voltage deviation (improving power quality), maximizing load curve smoothness (improving system stability), and maximizing renewable energy absorption (improving system cleanliness). These sub-objectives may have certain conflicts and need to be balanced through reasonable weight settings.

[0096] In constructing the objective function, a weighted summation method is typically used to combine multiple sub-objectives into a comprehensive objective function. The weighting coefficients can be determined based on the decision-maker's preferences or calculated using scientific methods such as the analytic hierarchy process (AHP). Another approach is to employ the concept of Pareto optimality to generate a series of non-dominated solutions for the decision-maker to choose from based on actual needs.

[0097] The resulting objective function, together with the various constraints established in the preceding steps, constitutes a complete mathematical optimization problem. Solving this problem requires considering the high dimensionality of the variables, the nonlinearity of the constraints, and the complexity of the objective function; therefore, an efficient optimization algorithm such as the CMA-ES algorithm is needed. In this way, the generalized energy storage collaborative optimization model of the power distribution system is fully constructed, laying a solid foundation for subsequent optimization solutions.

[0098] In constructing the generalized energy storage collaborative optimization model for the power distribution system, the first step is to establish an accurate electric vehicle (EV) charging and discharging model. As mobile energy storage units, EVs exhibit strong randomness and uncertainty in their charging and discharging behavior. The model needs to consider the physical constraints of charging power, typically using piecewise linear or quadratic functions to describe the charging characteristic curve. Simultaneously, a dynamic equation for the EV's State of Charge (SOC) needs to be established, incorporating factors such as charging and discharging efficiency and self-discharge rate. Crucially, the model also needs to include user driving demand constraints to ensure that EVs have sufficient power when users require them.

[0099] Building a stationary energy storage device model is relatively simpler, but it requires a focus on the device's lifespan characteristics. The model should include the device's charge / discharge efficiency curves, which are typically related to factors such as charge / discharge power and ambient temperature. Furthermore, upper and lower limits on the energy storage capacity need to be set, and a relationship equation between the number of cycles and the deep discharge rate needs to be established to assess the device's lifespan degradation. To extend the device's lifespan, a limit on the rate of change of charge / discharge power should also be added to avoid frequent high-power charge / discharge operations.

[0100] The distribution network operation constraint model is fundamental to ensuring the safe and stable operation of the system. This part of the model mainly includes power flow equations, node voltage constraints, and line capacity limits. The power flow equations use DC or AC power flow models to describe the power balance relationship of the system. Node voltage constraints ensure that the voltage at each node is maintained within the allowable deviation range, typically ±5% or ±7% of the rated voltage. Line power limits are set according to the rated capacity of the conductors to ensure that the lines do not operate under overload.

[0101] Finally, a comprehensive optimization objective function needs to be constructed. Considering the economic and reliability requirements of power distribution system operation, the objective function typically includes multiple sub-objectives: the operating cost minimization objective considers electricity purchase costs, energy storage device maintenance costs, etc.; the grid loss minimization objective is used to improve system operating efficiency; in addition, it may also include sub-objectives such as voltage deviation minimization and load peak shaving and valley filling. These sub-objectives are weighted and combined using weighting coefficients to form the final optimization objective function.

[0102] According to one embodiment, the method further includes: calculating weight coefficients using the Analytic Hierarchy Process (AHP) based on the optimization objective functions of minimizing operating costs and minimizing grid losses, to form a weighted combined optimization objective function, wherein the operating costs include electricity purchase costs and energy storage device maintenance costs. The AHP can systematically determine the relative importance of multiple sub-objectives, thereby scientifically setting the weight coefficients so that the optimization results can better meet actual operational needs.

[0103] like Figure 3 As shown, the method of constructing a context vector learning model using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, employing the Gaussian process regression method, includes:

[0104] S2.1: Collect time characteristics, load characteristics, electricity price information and environmental conditions, and use data cleaning and normalization methods to form preprocessed historical data.

[0105] The first step in building a context vector learning model is to comprehensively collect and preprocess historical data. The quality of this step directly affects the prediction accuracy and reliability of the subsequent model.

[0106] First, it is necessary to collect multi-dimensional contextual information, including time characteristics, load characteristics, electricity price information, and environmental conditions. Time characteristics include time period identifiers (such as peak hours, normal hours, and off-peak hours), date types (weekdays, weekends, and holidays), and seasonal characteristics (spring, summer, autumn, and winter). These time characteristics reflect the periodic changes in the load and operating status of the power distribution system and are an important component of the context vector. In particular, for power systems, the load patterns on weekdays and weekends differ significantly, and the electricity consumption characteristics of different seasons also vary markedly; these all need to be captured through time characteristics.

[0107] Load characteristics are a core part of the contextual information, including historical load curves, peak-valley features, and load type composition (such as the proportion of industrial, commercial, and residential loads). Load characteristics directly reflect the distribution of electricity demand in the system and are a primary basis for optimization decisions. By analyzing the morphological characteristics of load curves, peak-valley differences, and load type composition, typical operating patterns of the system can be extracted, providing a foundation for subsequent pattern recognition and parameter prediction. For example, industrial-dominated load areas typically exhibit relatively stable load curves, while commercial and residential-dominated areas show a clear bimodal characteristic.

[0108] Electricity price information reflects economic signals in the energy market, including time-of-use pricing, real-time pricing, and ancillary service prices. The electricity price structure directly impacts the economic objectives of optimization decisions and is a crucial economic dimension characteristic of the context vector. Especially in market environments with fluctuating electricity prices, accurate capture of electricity price information is essential for achieving economic optimization. It is important to note that electricity price information may be lagging and uncertain, which needs to be considered during data processing.

[0109] Environmental conditions include meteorological factors such as temperature, humidity, wind speed, and irradiance. These factors not only affect load demand (such as air conditioning load) but also the performance of energy storage equipment and the load-bearing capacity of power lines. By integrating environmental condition information, the model's adaptability to changes in the operating environment can be improved. For example, in hot weather, battery performance may decline and line thermal capacity may decrease; these factors will affect optimization decisions.

[0110] After the raw data is collected, systematic data cleaning and preprocessing are required.

[0111] First, to address the issue of missing values, methods such as time series interpolation, similar day substitution, and machine learning prediction can be used for repair. For outliers, statistical tests and domain knowledge can be combined for identification and processing to avoid the negative impact of outlier data on model training.

[0112] Secondly, different types of feature data need to be normalized to ensure consistent dimensions, which facilitates subsequent model training. Commonly used normalization methods include min-max normalization and Z-score standardization; the specific choice depends on the distribution characteristics of the data and the requirements of the model.

[0113] In particular, for time-series data, such as load curves, techniques like sliding windows are needed to extract time-series features and capture the dynamic trends of load changes. Furthermore, signal processing methods such as wavelet transform and Fourier transform can be used to extract frequency domain features of the load curve, enriching the information dimensions of the context vector.

[0114] Through the aforementioned data collection and preprocessing steps, a high-quality, multi-dimensional historical dataset was generated, laying a solid foundation for the subsequent construction of the context vector learning model. The preprocessed data not only retains the core features of the original information but also enhances its expressive power through normalization and feature extraction, enabling it to more effectively support the model in learning the mapping relationship between context features and optimization parameters.

[0115] S2.2: Based on the preprocessed historical data, construct a combined kernel function containing a radial basis function kernel function and a classification kernel function to generate feature extraction results, wherein the combined kernel function is a core component of the Gaussian process regression method.

[0116] The selection and construction of the kernel function is a crucial step in Gaussian process regression models, directly determining the model's ability to capture data features and its generalization performance. Gaussian process regression is a nonparametric machine learning method based on Bayesian theory. Its core idea is the assumption that the joint distribution of any finite number of observation points follows a multivariate Gaussian distribution. Within this framework, the kernel function defines the covariance structure among observation points, reflecting a measure of similarity between points in the feature space. For power distribution system optimization problems, the context vector contains various heterogeneous features, such as continuous load values ​​and discrete time markers, requiring the design of kernel functions that can adapt to this complex feature structure.

[0117] Considering the heterogeneity of features across different dimensions of the context vector, this method employs a combined kernel function design. For continuous features, such as load values ​​and temperature, the radial basis function (RBF kernel, also known as the Gaussian kernel) is used as the basic kernel function. The RBF kernel has good smoothness and local correlation, effectively capturing the smooth changes in features. Its mathematical expression is k(x, x')=exp(-||x-x'||2 / (2σ 2 In this model, σ is the feature length parameter, which controls the rate of decay of the correlation. A larger σ value makes the model less sensitive to changes in the input, resulting in smoother predictions; a smaller σ value allows the model to capture more subtle changes, but may lead to overfitting. For different continuous features, independent σ parameters can be set to reflect the differences in the scale of change of each feature.

[0118] For discrete features, such as categorical variables like date type and weather type, a custom classification kernel function is used. The basic principle of classification kernel function design is that samples of the same class have high similarity, while samples of different classes have low similarity. A simple indicator function can be used, with a kernel value of 1 when two samples belong to the same class and 0 when they belong to different classes. More complex structures can also be used, such as designing a similarity matrix between classes to reflect the degree of correlation between different classes. For example, for the weather type feature, sunny and cloudy days may have high similarity, while sunny and rainy days may have low similarity. Through a carefully designed classification kernel function, the model can more accurately understand the semantic information of discrete features, improving predictive performance.

[0119] These basic kernel functions can be combined using addition or multiplication to form composite kernel functions capable of handling multiple feature types simultaneously. Additive combination (k(x, x') = k1(x, x') + k2(x, x')) is suitable for cases where features are independent, with each kernel function independently capturing patterns of different features. Multiplicative combination (k(x, x') = k1(x, x') × k2(x, x')) is suitable for cases where features interact, capturing the joint effects between features.

[0120] In practical applications, appropriate combinations can be selected based on domain knowledge and data characteristics, or empirical comparisons can be conducted through methods such as cross-validation.

[0121] Furthermore, periodic kernel functions can be introduced to capture periodic patterns in time features, such as daily, weekly, and yearly cycles; linear kernel functions can be introduced to capture linear trends in features; and Markov kernel functions can be introduced to capture local correlations in time series. Combining these specialized kernel functions with basic kernel functions further enhances the model's expressive power. The design of combined kernel functions requires a balance between model complexity and computational efficiency, avoiding over-design that leads to excessive computational burden. Simultaneously, the design of kernel functions must also consider the physical characteristics of the problem to ensure the model has good interpretability and practicality.

[0122] Through systematic kernel function design, Gaussian process regression models can effectively handle various features in complex context vectors, providing a powerful tool for subsequent parameter mapping relationship learning. These customized kernel functions directly affect the quality of feature extraction and the predictive ability of the model, and are key to the success of context vector learning models.

[0123] S2.3: Using the feature extraction results, the maximum likelihood estimation method is used to optimize the combined kernel function parameters, obtain the mapping relationship between the context vector and the optimized parameters, and complete the construction of the Gaussian process regression model.

[0124] After determining the structure of the combined kernel function, the next step is to optimize the hyperparameters within the kernel function to best adapt to the data characteristics and improve model performance. In Gaussian process regression models, hyperparameter optimization is a crucial step, directly impacting the model's fitting ability and generalization performance. Maximum Likelihood Estimation (MLE) is a commonly used hyperparameter optimization method; its basic idea is to select parameter values ​​that maximize the probability of observed data occurrences. In Gaussian process regression models, the log-likelihood function is expressed as:

[0125] L(θ) = -0.5log|Kθ| - 0.5y T Kθ -1 y-0.5nlog(2π)

[0126] Where Kθ is the covariance matrix determined by the kernel function and hyperparameter θ, y is the vector of observed data, and n is the number of observed data.

[0127] Maximum likelihood estimation is typically implemented using optimization algorithms such as gradient ascent or conjugate gradient, which iteratively adjust hyperparameters to maximize the log-likelihood function. This process requires calculating the partial derivatives of the log-likelihood function with respect to each hyperparameter and finding the optimal solution through iterative optimization.

[0128] In practice, since the log-likelihood function may have multiple local maxima, strategies such as multiple random initializations or grid search are typically used to select the best-performing parameter combination in order to avoid getting trapped in local optima. Furthermore, to prevent overfitting, regularization terms can be introduced, such as adding prior distribution constraints to the parameters to form the maximum a posteriori (MAP) estimate.

[0129] After hyperparameter optimization, the Gaussian process regression model can express the complex mapping relationship between the context vector and the optimized parameters. This mapping relationship is not only a point-to-point function mapping, but more importantly, it provides the probability distribution of the prediction results, including mean prediction and uncertainty estimation. For a new context vector x*, the distribution predicted by the Gaussian process regression model is p(f(x*)|D,x*)=N(μ*,σ*). 2 ), where μ*=k*TK -1 y is the predicted mean, σ* 2 = k(x*, x*) - k* T K -1 k* represents the prediction variance, and k* is the covariance vector between the new point x* and the training data. This prediction result with uncertainty estimation is particularly important for optimization problems because it not only provides the most probable parameter values ​​but also quantifies the reliability of the prediction, providing a risk assessment basis for subsequent decision-making.

[0130] It is worth noting that the computational complexity of Gaussian process regression increases rapidly with the increase of data size, with the main bottleneck being the matrix inversion operation (complexity O(n^2)). 3 (where n is the number of training samples).

[0131] To handle large-scale datasets, sparse approximation methods can be employed, such as selecting a representative set of induced points to reduce computational burden. Commonly used sparse Gaussian process methods include subset-based methods (such as FITC, PITC), local regression-based methods (such as local Gaussian processes), and methods based on stochastic features (such as stochastic Fourier features). These methods significantly reduce computational complexity while maintaining predictive performance, enabling the models to be applied to large-scale real-time optimization scenarios.

[0132] The model training phase employs a strategy combining batch learning and online learning. First, batch training is performed using historical datasets to establish a fundamental mapping between context vectors and optimized parameters. Then, as new data is acquired, an incremental learning mechanism is implemented to continuously update and optimize model parameters, maintaining the model's timeliness and adaptability. Incremental learning can be achieved through recursive Bayesian updates or sliding window techniques, considering both the long-term trends of historical data and assigning higher weights to the latest data, thus enabling dynamic adjustment of the model. This combination of batch and online learning allows the model to adapt to changes in the system's operating environment, maintaining predictive accuracy and timeliness.

[0133] Through the above steps, the Gaussian process regression model was constructed, realizing the mapping relationship between context vectors and optimization parameters. This mapping relationship provides a reliable predictive basis for subsequent hot-start optimization, enabling rapid prediction of suitable initial values ​​for optimization parameters based on the contextual characteristics of the current scenario, significantly improving optimization efficiency and result quality. In particular, the uncertainty information of the prediction provides an important reference for the optimization process, helping the system to rationally allocate computational resources during optimization search and achieve intelligent optimization control.

[0134] In constructing a context vector learning model, the first step is to conduct comprehensive historical data collection and preprocessing. Contextual information mainly includes time-dimensional features (such as time periods, date types, and seasonal characteristics), load characteristics (such as load curves, peak-valley characteristics, and load type composition), electricity price information (such as time-of-use pricing and real-time pricing), and environmental conditions (such as temperature and weather conditions). This raw data often contains noise, missing values, and outliers, requiring preprocessing methods such as data cleaning and normalization. In particular, for time-series data, techniques such as sliding windows are needed to extract temporal features to ensure that the temporal correlation of the data is fully expressed.

[0135] The selection and construction of the kernel function are crucial for Gaussian process regression models. Considering the heterogeneity of features across different dimensions of the context vector, this approach employs a combined kernel function design. For continuous features (such as load values ​​and temperature), a radial basis function (RBF kernel) is used to capture the smooth changes in these features; for discrete features (such as date type and weather type), a custom classification kernel function is used. These basic kernel functions are combined through addition or multiplication to form a composite kernel function capable of handling multiple feature types simultaneously. The hyperparameters of the kernel function are optimized using maximum likelihood estimation to adapt to the actual distribution characteristics of the data.

[0136] According to one embodiment, the method further includes:

[0137] S2.4: Based on the mapping relationship between the context vector and the optimization parameters, calculate the prediction accuracy index and obtain the root mean square error and the mean absolute error.

[0138] Establishing a model validation mechanism is crucial for ensuring the practicality and reliability of context vector learning models. After training a Gaussian process regression model, it's necessary to systematically evaluate its prediction accuracy to verify its ability to effectively capture the complex relationship between context vectors and optimization parameters. Prediction accuracy evaluation first requires designing a reasonable validation strategy. Common methods include hold-out, cross-validation, and bootstrapping. Among these, K-fold cross-validation is an effective method balancing computational cost and evaluation reliability; typically, K is set to 5 or 10. This method randomly divides the dataset into K subsets. Each iteration uses K-1 subsets as the training set and the remaining subset as the test set, repeating this process K times and taking the average performance as the final evaluation result. This method fully utilizes limited data resources while reducing the variance of the evaluation results, thus improving the reliability of the evaluation.

[0139] Root Mean Square Error (RMSE) is one of the most commonly used metrics for evaluating prediction accuracy. It calculates the square root of the average of the sum of squares of the differences between predicted and actual values, with higher penalty weights for larger error terms. Since the dimensions and importance of different parameters in distribution system optimization problems may vary, it is usually necessary to calculate RMSE separately for each parameter to ensure a comprehensive evaluation of prediction performance. For example, the prediction accuracy should be evaluated separately for different components of the CMA-ES algorithm, such as the mean vector, step size parameter, and covariance matrix. Furthermore, to facilitate comparisons between different scenarios, a standardized RMSE can be calculated by dividing the RMSE by the range or standard deviation of the actual values, yielding a dimensionless relative error index.

[0140] Mean Absolute Error (MAE) is another important evaluation metric, calculating the average of the absolute differences between predicted and actual values. Compared to RMSE, MAE assigns equal weight to all error terms, avoiding excessive emphasis on large error terms, thus providing a balanced assessment of overall forecasting performance. The physical meaning of MAE is more intuitive, representing the average degree to which predicted values ​​deviate from actual values, facilitating interpretation and decision-making in practical applications. Similarly, MAE needs to be calculated separately for different optimization parameters and then comprehensively evaluated. In addition to RMSE and MAE, the coefficient of determination (R²) can also be introduced. 2 The model's goodness of fit is evaluated, the mean absolute percentage error (MAPE) is used to evaluate relative prediction accuracy, and the maximum absolute error is used to evaluate prediction performance in the worst case.

[0141] Predictive accuracy assessment requires particular attention to the model's performance under different operating conditions. The operating environment of power distribution systems is complex and variable, encompassing various scenarios such as typical load days, extreme weather conditions, and periods of special events. A comprehensive predictive accuracy assessment should cover these different scenarios, analyzing the model's adaptability and reliability under various conditions. For example, during periods of severe load fluctuations or under special weather conditions, the model's predictive performance may degrade, necessitating specific assessments and potentially different handling strategies for these situations. Therefore, a tiered assessment system based on operating conditions can be constructed, calculating error indices and setting differentiated threshold standards for different types of operating conditions.

[0142] Furthermore, prediction accuracy evaluation also needs to consider the timeliness factor. As the system operating environment changes, the correlation between historical data and the current state may gradually decrease, leading to a decline in model prediction accuracy. Therefore, a time-based weighting evaluation mechanism can be introduced, giving higher weight to prediction errors of recent data to more accurately reflect the model's current applicability. Simultaneously, a prediction accuracy trend monitoring mechanism can be designed to track changes in error indicators, promptly detect signs of model performance degradation, and trigger subsequent model updates. Through these systematic prediction accuracy evaluation mechanisms, it can be ensured that the context vector learning model maintains a consistently high level of predictive capability, providing reliable support for warm-start optimization.

[0143] S2.5: Based on the root mean square error and mean absolute error, determine whether the preset threshold is exceeded. If the preset threshold is exceeded, retrain the Gaussian process regression model.

[0144] Model maintenance and update mechanisms are crucial for ensuring the long-term effectiveness of context vector learning models. In practical applications, the predictive performance of a model may change with variations in the operating environment and the accumulation of new data. Therefore, it is necessary to establish scientific judgment criteria and adaptive update strategies to ensure that the model maintains good predictive capabilities. First, reasonable preset thresholds need to be set as standards for evaluating model performance. These thresholds should be set based on the actual needs of system operation and acceptable risk levels; they should not be too strict, leading to frequent and unnecessary model updates, nor too lenient, allowing poorly performing models to continue to be used. Typical threshold setting methods include statistical analysis based on historical performance (e.g., the average of historical errors plus twice the standard deviation), fixed thresholds based on expert experience, and sensitivity analysis results based on the impact of optimization performance. Thresholds can be fixed values ​​or dynamic values ​​that change with operating conditions to adapt to the accuracy requirements of different scenarios.

[0145] When the calculated root mean square error (RMSE) or mean absolute error (MAE) exceeds a preset threshold, the system triggers a model retraining process. Retraining can be performed using either full retraining or incremental updates. Full retraining involves retraining the model using all the latest historical data. This method thoroughly updates the model parameters and can adapt to significant changes in the system environment, but it is computationally expensive. Incremental updates, on the other hand, adjust the parameters using only the newly added data on the existing model. This method is more computationally efficient and suitable for situations where system changes are relatively slow. The choice of update method depends on the degree to which the error exceeds the threshold, the availability of computing resources, and timeliness requirements. Typically, a tiered update strategy can be designed: incremental updates are used when the error slightly exceeds the threshold, and full retraining is initiated only when the error significantly exceeds the threshold or when performance remains unsatisfactory after incremental updates.

[0146] Furthermore, model updates are not simply about retraining; they may also involve adjusting and optimizing the model structure. When it is found that the current model structure cannot adapt to new data characteristics, it is necessary to re-evaluate the choice of kernel function, the setting of hyperparameters, and the methods of feature engineering.

[0147] For example, one could try adding new feature dimensions, adjusting the complexity of the kernel function, or modifying the feature preprocessing method to improve the model's adaptability to new environments. Such structural adjustments typically require systematic comparative analysis using methods such as cross-validation to select the optimal model configuration.

[0148] Model updates also need to consider data aging and forgetting mechanisms. Over time, outdated historical data may no longer reflect the current system's operational characteristics, and retaining this data may actually degrade model performance. To address this, a time-window-based data management strategy can be designed, retaining only data from the most recent period (e.g., the last few months) for model training; or a data weighting mechanism can be designed to assign higher weights to newer data, achieving "soft forgetting." These strategies help ensure that the model primarily captures the current system's operational characteristics, improving the timeliness and accuracy of predictions.

[0149] Finally, the timing and method of model updates also need to be considered. To avoid impacting normal system operation, model updates are typically scheduled during periods of low system load or when redundant computing resources are available. Simultaneously, a canary release strategy is adopted, first validating the performance of the new model in a test environment, and then gradually replacing the old model in the production environment once stability is confirmed. During the update process, it is also necessary to save the model's version history and performance evaluation records for rollback or issue tracing when necessary. This systematic model maintenance and update mechanism ensures that the context vector learning model maintains a consistently high level of predictive performance, providing reliable intelligent support for the collaborative optimization of power distribution systems.

[0150] This step establishes a model validation mechanism to ensure prediction reliability. Cross-validation is used to evaluate the model's generalization performance, and prediction accuracy is quantified using metrics such as root mean square error (RMSE) and mean absolute error (MAE). Special attention is paid to the model's prediction performance under different operating conditions, such as accuracy during periods of severe load fluctuations or under special weather conditions. When prediction accuracy fails to meet requirements, a model retraining mechanism is triggered to ensure the model's usability and reliability.

[0151] like Figure 4 As shown, the step of extracting the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predicting the initial distribution of the optimization parameters, and obtaining the initial mean vector and covariance matrix of the CMA-ES algorithm includes:

[0152] S3.1: Based on the current operational data, extract time features, operational status features, market features, and environmental features to form the context vector of the current scenario.

[0153] The first step in achieving CMA-ES-CWS hot start optimization is to accurately extract and construct the context vector of the current scene. The context vector serves as a bridge connecting historical experience with current decisions, and its quality directly affects the accuracy of predictions and the efficiency of optimization.

[0154] First, the system needs to collect multi-dimensional feature information in real time to ensure the comprehensiveness and timeliness of the features. Time features are the fundamental dimensions of the context vector, including the current time period (e.g., morning, afternoon, evening), weekday type (weekday, weekend), holiday markers, and seasonal information. These time features are crucial for capturing the periodic patterns of load changes. For example, load patterns differ significantly between weekends and weekdays, and electricity consumption behavior during holidays also has unique characteristics; these differences need to be distinguished through refined time features. Extracting time features also requires consideration of special date markers, such as before and after major holidays, and seasonal transitions. These special periods typically exhibit unique load characteristics and require specialized processing.

[0155] Operational status characteristics reflect the real-time operating status of the current power distribution system and are a core component of the context vector. These characteristics include current load levels, load composition (industrial, commercial, and residential proportions), load change trends (increasing, decreasing, or stable), electric vehicle access status (number of connected vehicles, distribution location, average remaining capacity), and the status of stationary energy storage devices (current state of charge, cumulative cycle count). Operational status characteristics need to be collected in real-time by the power distribution system's monitoring system to ensure data accuracy and completeness. Timely and accurate perception of the access status is particularly crucial for highly mobile energy storage units such as electric vehicles. Furthermore, techniques such as sliding windows are needed to extract recent historical data trends, such as load growth rate and peak-to-valley differences. This trend information can help predict system behavior in the near future.

[0156] Market characteristics primarily include economic signals from the energy market, such as real-time electricity price information, day-ahead price forecasts, ancillary service prices, and changes in energy market policies. Market characteristics directly impact optimized economic objectives and are crucial considerations in the decision-making process. In environments with multi-tiered electricity markets, it is necessary to comprehensively consider price signals from different market levels, such as price differences between wholesale, retail, and ancillary service markets. Simultaneously, attention must be paid to the timeliness and accuracy of price information to ensure decisions are based on the latest market conditions. For scenarios with anticipated price changes, such as the approaching peak electricity price period, this forward-looking information should also be incorporated into the context vector to support predictive optimization decisions.

[0157] Environmental characteristics reflect the impact of external environmental conditions on system operation, including meteorological factors such as temperature, humidity, wind speed, and solar radiation intensity. These environmental conditions not only affect load demand (e.g., air conditioning load varies with temperature), but also the performance of energy storage devices (e.g., battery efficiency is affected by temperature) and the carrying capacity of power grid equipment (e.g., line capacity is affected by temperature). The extraction of environmental characteristics typically relies on meteorological monitoring systems or weather forecasting services, requiring assurance of data accuracy and coverage. Especially for extreme weather conditions, such as high temperatures, cold waves, and torrential rain, specific labels are needed so that the model can identify these special situations and make corresponding adjustments.

[0158] These multi-dimensional features are standardized and normalized through a preprocessing workflow consistent with the training phase, ensuring the consistency and comparability of feature representations. The preprocessing includes steps such as missing value handling, outlier detection and correction, data smoothing, and feature transformation, aiming to improve data quality and enhance the expressive power of the features. After processing, the features of each dimension are organized into a unified context vector according to a predefined structure, forming a comprehensive description of the current scene. This context vector includes both static environmental features and captures dynamic system states, providing a rich information foundation for subsequent parameter prediction.

[0159] S3.2: Using the context vector of the current scene, perform parameter prediction through the context vector learning model to generate an optimized parameter prediction distribution.

[0160] Based on the constructed context vector, the system calls the trained Gaussian process regression model to predict optimization parameters, which is the core step of warm-start optimization. The prediction process not only outputs the expected optimization parameter values, but more importantly, it also provides an estimate of the prediction uncertainty, forming a complete prediction distribution.

[0161] Specifically, for key parameters of the CMA-ES algorithm, such as the initial mean vector, step size parameter σ, and covariance matrix, the model provides corresponding predicted distributions, including mean prediction and variance estimation. This prediction result with uncertainty quantification is a unique advantage of the Gaussian process regression model, providing an important basis for subsequent optimization strategy adjustments.

[0162] The prediction process first requires ensuring that the format of the context vector is consistent with that of the training phase, including the feature order, normalization method, and data type. Any inconsistency can lead to prediction bias. Before inputting the context vector into the model, the system performs a final validity check to ensure that all necessary features are included and of acceptable quality. For special cases, such as missing or abnormal features, the system employs backup strategies such as feature imputation or feature substitution to ensure the robustness of the prediction process. In particular, for time series features, it is necessary to ensure that the window size and feature extraction method are consistent with those used in the training phase to avoid mismatches in time series features.

[0163] When making parameter predictions, the Gaussian process regression model considers not only the similarity between the current context vector and historical data, but also the internal structure of the historical data, i.e., the data distribution patterns in the feature space captured by the kernel function. This prediction mechanism based on a probabilistic model can handle adaptive inference for new scenarios while preserving historical experience. For completely unseen context scenarios, i.e., when the context vector is far removed from the training data, the model will give a large prediction uncertainty, suggesting that the system may need to adopt a more conservative strategy or additional verification mechanisms. Conversely, for scenarios highly similar to historical data, the model will give predictions with higher confidence, allowing the system to utilize the prediction results more actively.

[0164] The reliability of the prediction results is quantified by the prediction variance. One advantage of Gaussian process regression is its ability to naturally provide estimates of prediction uncertainty, rather than just point predictions. Prediction variance reflects the model's confidence in the current prediction and is influenced by two main factors: first, the similarity between the current context vector and the training data (greater similarity indicates a more reliable prediction); and second, the density of the training data in the corresponding region (richer training data indicates a more reliable prediction). When the prediction variance exceeds a preset threshold, the system triggers a risk assessment mechanism, which may employ strategies such as adjusting prediction weights, triggering a backup prediction model, or reducing reliance on the prediction results and increasing the proportion of exploratory search.

[0165] Simultaneously, the prediction results must consider the rationality of physical constraints. For example, the charging and discharging power of electric vehicles must be within a physically feasible range, and the step size parameter must be positive. The system performs a rationality check on the prediction results to ensure that all parameters meet basic physical and mathematical constraints. When the prediction results do not meet these basic constraints, the system will make necessary adjustments or remappings to ensure that the final parameter values ​​used fall within a reasonable range. This post-processing mechanism guarantees the practicality of the prediction results and avoids the non-physical interpretations that may arise from purely statistical models.

[0166] Through the above process, the system ultimately generates a complete predicted distribution of the optimization parameters, including the mean vector as the optimal estimation point and the covariance matrix expressing the uncertainty structure of the prediction. These prediction results will be directly used for the subsequent initialization of the CMA-ES algorithm, providing a good starting point for the optimization process.

[0167] S3.3: Based on the predicted distribution according to the optimization parameters, initialize the CMA-ES algorithm parameters and determine the initial mean vector and covariance matrix.

[0168] Transforming the prediction results into initialization parameters for the CMA-ES algorithm is a crucial step in warm-start optimization. As an efficient evolutionary optimization strategy, the performance of the CMA-ES algorithm largely depends on the setting of its initial parameters. The core idea of ​​the warm-start mechanism is to leverage historical optimization experience and, through the mapping relationship of context vectors, find the most suitable initial parameter settings for the current scenario, thereby accelerating the optimization process and improving the quality of the final result.

[0169] First, the system uses the mean of the predicted distribution as the initial mean vector for the CMA-ES algorithm, representing the location where the algorithm believes it is most likely to find the optimal solution. Each dimension of the mean vector corresponds to a decision variable, such as the charging and discharging power of electric vehicles at different times or the scheduling strategy of fixed energy storage. An accurate initial mean vector can significantly reduce the number of iterations of the optimization algorithm because the search process begins at a position closer to the optimal solution.

[0170] The uncertainty information from the prediction is used to construct the initial covariance matrix, which determines the search range and direction of the algorithm. The diagonal elements of the covariance matrix represent the search range of each dimension, while the off-diagonal elements reflect the correlation between different dimensions. Larger prediction uncertainty leads to a larger initial search range, ensuring that the algorithm can fully explore the solution space; while smaller prediction uncertainty means a more focused search, which helps to quickly converge to a local optimum. In this way, the system can automatically adjust the balance between exploration and utilization based on the prediction reliability of the current situation, achieving intelligent optimization control.

[0171] The step size parameter σ is set by comprehensively considering the uncertainty of the prediction and the size of the problem, controlling the overall scale of the population distribution. A larger step size leads to a wider exploration, suitable for high uncertainty or large-scale problems; a smaller step size promotes a finer local search, suitable for low uncertainty or situations requiring an exact solution. In the warm-start framework, the step size parameter can be adaptively set based on the standard deviation of the prediction distribution, ensuring that the search strategy matches the difficulty and uncertainty of the problem.

[0172] Specifically, the system dynamically adjusts the population size and other algorithm parameters based on the reliability of the prediction. When the prediction is relatively reliable, a smaller population size can be used to reduce computational overhead; while when the prediction uncertainty is high, the population size is increased to improve the stability and coverage of the search. Similarly, parameters such as selection pressure and recombination weights can also be adjusted according to the prediction reliability, forming a complete parameter configuration scheme. This adaptive parameter setting strategy ensures that the algorithm can both efficiently utilize reliable prediction information and cope with the challenges brought by uncertainty.

[0173] Furthermore, the system fine-tunes the initial parameters by incorporating problem-specific knowledge. For example, it considers factors such as the physical constraints of electric vehicles and energy storage systems, and the safety boundaries of the distribution network, ensuring that the initial parameters are set within the feasible region and have practical operational significance. This integration of domain knowledge means that parameter initialization is not only based on statistical learning but also considers the physical nature of the problem, further improving the efficiency of optimization and the quality of results.

[0174] The first step in implementing CMA-ES-CWS hot start optimization is to extract and construct the context vector of the current scenario. The system first needs to collect various feature information in real time, including time features (such as current time period, weekday type, and holiday identifiers), operational status features (such as current load level and electric vehicle access status), market features (such as real-time electricity price information), and environmental features (such as weather conditions and temperature). These features are standardized through a preprocessing procedure consistent with the training phase to ensure consistency in feature representation.

[0175] Based on the constructed context vector, the system invokes a trained Gaussian process regression model for prediction. The prediction process not only outputs the desired optimized parameter values ​​but also includes estimates of the prediction uncertainty. Specifically, for key parameters of the CMA-ES algorithm, such as the initial mean vector and step size parameter σ, the model provides corresponding prediction distributions. The reliability of the prediction results is quantified by the prediction variance. When the prediction variance exceeds a preset threshold, the system automatically adjusts the prediction weights or triggers a backup prediction strategy.

[0176] Converting the prediction results into initialization parameters for the CMA-ES algorithm is the core step in warm-start optimization.

[0177] First, the search center of CMA-ES is initialized using the predicted mean vector, representing the location where the algorithm believes the optimal solution is most likely to be found. The uncertainty information of the prediction is used to construct the initial covariance matrix; larger prediction uncertainty leads to a larger initial search range. The step size parameter σ is set to comprehensively consider the prediction uncertainty and the problem size, achieving a balance between exploration and exploitation.

[0178] According to one embodiment, initializing the CMA-ES algorithm parameters based on the predicted distribution of the optimized parameters includes:

[0179] S3.3.1: Using the eigenvalues ​​of the covariance matrix of the predicted distribution with the optimized parameters, calculate the step size parameter and population size, and determine the initial configuration parameters of the CMA-ES algorithm.

[0180] Based on the optimized parameter prediction distribution, the system needs to further calculate and determine the specific configuration parameters of the CMA-ES algorithm. This process requires comprehensive consideration of the statistical characteristics of the prediction distribution and the structural characteristics of the optimization problem.

[0181] First, the step size parameter σ is a key parameter in the CMA-ES algorithm that controls the search range, directly affecting the dispersion of the population and the algorithm's exploration ability. Traditional CMA-ES algorithms typically require manual setting of the initial step size, which is often based on experience or repeated trials. However, in the warm-start framework, the step size parameter can be intelligently set based on the statistical characteristics of the predicted distribution.

[0182] Specifically, the appropriate step size can be calculated using the eigenvalues ​​of the predicted distribution covariance matrix. The eigenvalues ​​reflect the dispersion of the distribution along each principal component direction, and their square roots can be considered as the standard deviation in the corresponding direction. The system can take the geometric mean or weighted average of these eigenvalues ​​as the basis for the step size parameter, and then adjust it appropriately according to the scale and accuracy requirements of the problem. This method ensures that the step size parameter matches the uncertainty of the predicted distribution, avoiding premature convergence due to an excessively small step size, and preventing inefficient search due to an excessively large step size.

[0183] Population size is another crucial parameter that needs to be determined, as it affects the computational cost of each iteration and the diversity of the population. In the CMA-ES algorithm, population size typically includes two parameters: λ represents the number of offspring generated per generation, and μ represents the number of parent generations used to update the distribution. The traditional CMA-ES algorithm recommends λ = 4 + 3ln(n), where n is the dimension of the problem, and μ = λ / 2. However, in the warm-start framework, the population size can be adaptively adjusted based on the reliability of the predicted distribution. When the uncertainty of the predicted distribution is low, it indicates that the system has high confidence in the optimal solution region, and a smaller population size can be used to accelerate convergence. Conversely, when the uncertainty of the predicted distribution is high, the population size should be increased to improve the search coverage and stability. Specifically, a mapping function based on the condition number or average eigenvalue of the covariance matrix can be designed to dynamically determine the population size parameter. This adaptive population size setting ensures the algorithm's exploration capability while avoiding unnecessary waste of computational resources.

[0184] Besides step size and population size, the CMA-ES algorithm requires setting other configuration parameters, such as recombination weights and accumulation factors. These parameters can also be intelligently configured based on the characteristics of the predicted distribution and historical optimization experience. For example, recombination weights can be adjusted according to the reliability of the prediction, increasing the weight of elite individuals in high-reliability scenarios to accelerate convergence to the predicted optimal region; while accumulation factors can be adjusted according to the uncertainty structure of the prediction, increasing the accumulation rate in directions of high uncertainty to enhance adaptability to these directions. Through this systematic parameter configuration strategy, the CMA-ES algorithm can better adapt to the characteristics of the current optimization problem, improving optimization efficiency and result quality.

[0185] Determining the initial configuration parameters also requires consideration of the problem's physical constraints and unique structure. For example, for variables with boundary constraints, the step size parameter needs to be adjusted to ensure the initial population does not excessively violate the constraints; for objective functions with multimodal characteristics, it may be necessary to increase population diversity to avoid prematurely falling into local optima. These problem-specific considerations need to be rationally set by combining domain knowledge and historical optimization experience to ensure that the parameter configuration possesses both the intelligence of statistical learning and respects the physical nature and structural characteristics of the problem. Overall, by using a parameter configuration strategy driven by the eigenvalues ​​of the predicted distribution covariance matrix, the system can provide a tailor-made initial configuration for the CMA-ES algorithm, significantly improving the algorithm's starting point and overall performance.

[0186] S3.3.2: Based on the initial configuration parameters, monitor the convergence performance of the optimization process. When the rate of change of the optimal fitness value for a consecutive specified number of generations is less than a preset threshold, generate updated step size parameters and population size.

[0187] Dynamic monitoring and parameter adjustment during the optimization process are crucial mechanisms for ensuring the stable and efficient operation of the CMA-ES algorithm. Although the initial configuration parameters are set based on the predicted distribution and historical experience, they may need to be dynamically adjusted during the optimization process according to the actual convergence situation to cope with various challenges that may arise.

[0188] The system first establishes a convergence performance monitoring mechanism to continuously track key indicators during the optimization process. The most basic indicator is the change in the optimal fitness value, including absolute improvement and relative improvement rate. The system records the optimal fitness value for multiple consecutive generations and calculates its trend and rate of change. In addition, it monitors the evolutionary characteristics of the population distribution, such as the standard deviation of the distribution and population diversity, which reflect the balance between exploration and utilization in the search process. Convergence monitoring not only focuses on the improvement of the optimal solution but also on the quality and stability of the solution. For example, it comprehensively judges the health of the optimization process by evaluating whether the optimal solution satisfies the constraints and has sufficient robustness.

[0189] When the system detects that the rate of change of the optimal fitness value is less than a preset threshold for a specified number of generations (e.g., 10 or 20 generations), it indicates that the current optimization process may have entered a stagnant state or is close to convergence. At this point, the system needs to assess the nature of this state: whether it is normal convergence, trapped in a local optimum, or encountering search difficulties. This judgment is usually based on multiple factors, including the quality assessment of the current optimal solution, the characteristic analysis of the population distribution, and a comparison with historical optimization experience. Based on the assessment results, the system will adopt different adjustment strategies. If it is judged to be normal convergence but has not yet reached sufficient accuracy, the step size parameter can be reduced for a more refined local search; if it is judged to be trapped in a local optimum, the step size parameter may need to be increased or the covariance matrix reset to expand the search range; and if it is judged to be encountering special difficulties in the search, such as the objective function being nearly flat in certain regions or exhibiting high nonlinearity, the population size or recombination strategy may need to be adjusted to enhance the algorithm's exploration ability and adaptability.

[0190] Dynamic adjustment of the step size parameter is the most common intervention measure. When the system determines that a more focused search is needed, it generates a smaller step size parameter, usually halving the current step size or reducing it by a specific ratio; conversely, when the search range needs to be expanded, the step size parameter is increased, possibly several times the current step size or a new value calculated based on special rules. Step size adjustments are usually gradual to avoid search instability caused by drastic changes. Meanwhile, adjusting the population size is also an important strategy. When the search enters a refined stage, the population size can be appropriately reduced to improve computational efficiency; while in stages requiring enhanced exploration, the population size may be increased to improve coverage and diversity. Adjusting the population size requires considering both μ and λ parameters simultaneously to maintain appropriate selection pressure and parent ratios.

[0191] Besides step size and population size, the system may also adjust other optimization strategy parameters, such as the weight distribution for recombination, weight updates in the covariance matrix, and evolutionary path accumulation parameters. These adjustments aim to change the algorithm's behavior to address optimization challenges at different stages. For example, in the early exploration phase, a more uniform recombination weight might be used to encourage diversity; while in the later convergence phase, the weight of elite individuals might be increased to accelerate the convergence to the optimal solution. These adjustments to strategy parameters are usually based on pre-defined rules and historical optimization experience, and may also utilize methods such as reinforcement learning for adaptive optimization.

[0192] The system also incorporates a restart mechanism as a last resort to address search difficulties. When optimization performance remains unsatisfactory after multiple adjustments, the system may trigger a full or partial restart. A full restart means reinitializing all parameters, while a partial restart may only reset the step size or covariance matrix, retaining the current optimal solution as the new search center. Restart strategies typically combine randomness and directionality, introducing new exploration space while utilizing existing optimization experience. Through this multi-layered dynamic monitoring and adjustment mechanism, the system can effectively address various challenges during the optimization process, maintaining the stability and efficiency of the algorithm, and ultimately achieving high-quality optimization results.

[0193] A key component of the hot-start optimization framework is the construction of a dynamic adjustment mechanism. The system continuously monitors the convergence progress during the optimization process and can promptly adjust the search strategy when unsatisfactory search results are detected. This includes dynamically updating the step size parameter, adjusting the update weights of the covariance matrix, and changing the population selection pressure. Simultaneously, the system maintains an optimization experience pool, recording optimization trajectory information under different contextual conditions. This information can be used for online adjustment of the optimization strategy and experience learning. To handle special situations that may arise during optimization, such as getting stuck in local optima or slow convergence, the system is designed with multi-layered contingency strategies, including a restart mechanism and adaptive mutation, to ensure the stability and efficiency of the optimization process.

[0194] The CMA-ES iterative optimization process is performed using the initial mean vector and covariance matrix, including:

[0195] S4.1: Based on the initial mean vector and covariance matrix, generate an initial population that satisfies the power limit and capacity boundary constraints, forming a candidate solution set.

[0196] In the execution phase of generalized energy storage collaborative scheduling optimization, the initial population for the CMA-ES algorithm needs to be constructed based on the hot start results. Population initialization is the starting point of the optimization process, and its quality directly affects the efficiency of subsequent iterations and the final result. The system uses the initial distribution parameters (including the mean vector and covariance matrix) obtained from the hot start to generate the first generation of population individuals. Specifically, the system uses the initial distribution parameters (including the mean vector and covariance matrix) obtained from the multivariate normal distribution N(m, σ) to generate the first generation of population individuals. 2Sampling is performed in step C), where m is the initial mean vector, σ is the step size parameter, and C is the covariance matrix, generating a set of candidate solutions. Each candidate solution represents a potential scheduling scheme, containing the charging and discharging power values ​​of electric vehicles and stationary energy storage devices at various time periods. The population size setting needs to balance computational efficiency and optimization performance, and it is generally recommended to set it to 4-10 times the problem dimension. For large-scale optimization problems, such as long-term scheduling schemes, the population size may reach several hundred individuals; while for small-scale problems, a few dozen individuals may be sufficient.

[0197] The initial population generation process needs to take into account the physical constraints of the problem to ensure that the generated individuals meet the basic constraints as much as possible, thereby improving the effectiveness of the population.

[0198] First, there are power constraints: the charging and discharging power of electric vehicles and stationary energy storage devices must be within the rated range of the equipment. For electric vehicles, the charging power is typically limited by the charging pile capacity and on-board charger, while the discharging power is controlled by the battery management system. For stationary energy storage devices, the charging and discharging power is similarly limited by the power converter capacity and battery characteristics. The system employs constraint handling strategies, such as boundary reflection or resampling, to ensure that the generated values ​​meet these power constraints. When a sampled value exceeds the boundary, it can be mapped back to the boundary value or resampled until a value that satisfies the constraints is obtained.

[0199] Capacity boundary constraints are another crucial consideration, ensuring that the state of charge (SOC) of energy storage devices remains within a safe range. For electric vehicles, user driving demand must be taken into account to ensure sufficient charge at the time of vehicle use. For stationary energy storage devices, the SOC must not exceed the upper limit or fall below the lower limit, typically within the range of 5%-95%. This type of constraint involves the correlation between charging and discharging power over multiple time periods, representing a dynamic cumulative constraint. The system constructs an SOC evolution equation, converting the charging and discharging power sequence into an SOC sequence, and then checks whether the capacity constraints are met. For individuals that do not meet the constraints, constraint repair strategies, such as proportional adjustment or priority pruning, can be employed to bring them to compliance.

[0200] In addition to the basic constraints mentioned above, initial population generation also needs to consider other system-level constraints, such as distribution network node voltage limits and line power limits. These constraints are usually difficult to satisfy directly during the initial population generation stage, but can be reflected in subsequent fitness evaluations through penalty functions. Another strategy is to use heuristic rules to guide initial population generation, such as charging and discharging patterns based on load peak-valley characteristics and economic dispatch principles based on electricity price structures. These rules help generate initial individuals that are closer to a feasible solution.

[0201] By comprehensively considering the above constraints and strategies, the system ultimately generates an initial population with appropriate diversity and high constraint satisfaction. These individuals collectively constitute the candidate solution set, providing a good starting point for subsequent iterative optimization. The quality of the initial population directly affects the convergence speed and result quality of the algorithm; therefore, careful design of this step is crucial to the entire optimization process. In particular, the warm-start mechanism significantly improves the quality of the initial population by providing an initial mean vector closer to the optimal solution and a more reasonable covariance structure, laying a solid foundation for subsequent optimization.

[0202] S4.2: Using the candidate solution set, calculate the fitness values ​​of operating cost and power grid loss, and obtain the fitness ranking results.

[0203] In each generation of the CMA-ES iterative optimization, the system needs to evaluate the fitness of all individuals in the current population to identify high-quality solutions and guide subsequent evolutionary directions. Fitness evaluation is the core step in the optimization process, transforming abstract mathematical solutions into evaluation indicators with practical physical meaning. For the generalized energy storage co-optimization problem of power distribution systems, the fitness function typically considers multiple optimization objectives, mainly including two categories of indicators: operating costs and grid losses. Operating costs reflect the system's economics, including electricity purchase costs and energy storage device maintenance costs; while grid losses reflect the system's operating efficiency, usually manifested as line heat losses. These indicators together constitute a multi-objective optimization problem, requiring comprehensive evaluation through reasonable weight settings or multi-objective processing strategies.

[0204] The first step in fitness calculation is operating cost assessment. Electricity purchase costs are typically calculated based on time-of-use (TOU) or real-time (RTU) pricing. The system calculates the total electricity expenditure over the entire scheduling cycle based on the charging and discharging schemes in the candidate solutions and the electricity price information. Specifically, the electricity purchase cost for each time period equals the net load for that period (original load minus energy storage discharge power or plus energy storage charging power) multiplied by the corresponding electricity price. The total electricity expenditure is obtained by summing the costs for all time periods. The maintenance cost of the energy storage device is related to the energy throughput and cycle depth during charging and discharging, and is usually calculated as the product of the equivalent number of cycles and the unit cycle cost. For electric vehicles, user convenience costs also need to be considered, such as penalties for deviating from the user's expected charging curve. These cost items are combined according to preset weights to form the total operating cost index.

[0205] Grid loss assessment is the second crucial component of fitness calculation. Grid losses primarily arise from heat loss due to line resistance, and are proportional to the square of the line current. The system calculates the network power flow distribution for each time period based on the charging and discharging schemes in candidate solutions, combined with the distribution network topology and parameters. This typically involves solving power flow equations, which can be done using DC power flow approximations or complete AC power flow calculations, depending on the required accuracy and computational resources. Based on the power flow calculation results, the system obtains the current or power flow of each line and then calculates the line losses. The losses for all time periods and all lines are summed to obtain the total grid loss index. To facilitate integration with operating costs, the loss index is usually converted into an equivalent economic cost, which is the amount of electricity lost multiplied by the corresponding electricity price or loss cost coefficient.

[0206] In multi-objective optimization problems, fitness evaluation also needs to consider the satisfaction of various constraints. Key constraints include node voltage limits, line capacity limits, and energy storage device state of charge (SOC) range limits. For solutions that violate constraints, the system typically employs a penalty function method, converting the degree of constraint violation into an additional penalty term added to the fitness value. The penalty strength needs to be appropriately set; it should not be too lenient, leading to a large number of infeasible solutions, nor too strict, causing excessive shrinkage of the search space. A common strategy is to use an adaptive penalty mechanism, dynamically adjusting the penalty strength based on the statistical distribution of constraint violations in the population, gradually increasing the enforcement of constraints during the optimization process.

[0207] After fitness calculation, the system sorts all individuals in the population according to their fitness values, obtaining a fitness ranking. In minimization problems, individuals with smaller fitness values ​​rank higher. This ranking is the basis for subsequent selection and recombination operations, determining which individuals will pass on their characteristics to the next generation as parents. The ranking process may also consider the diversity and robustness of solutions, for example, through techniques such as crowding distance sorting or hegemony-based sorting, ensuring that selection considers not only the quality of solutions but also the coverage of the solution space. Through this systematic fitness evaluation and ranking mechanism, the CMA-ES algorithm can effectively identify high-quality solutions and guide the population to evolve towards more promising regions, gradually approaching the global optimum.

[0208] S4.3: Based on the fitness ranking results, use log-normal distribution weights to perform individual weighted recombination to determine the mean vector of the new generation population.

[0209] After completing population evaluation and ranking, the CMA-ES algorithm enters the recombination phase. The core task of this phase is to generate the mean vector of the next generation population by selecting high-quality individuals and rationally combining their features. Traditional evolutionary algorithms typically use random crossover and mutation operations to generate new individuals, while CMA-ES employs a more systematic weighted recombination strategy. This strategy retains the swarm intelligence characteristics of evolutionary algorithms while introducing a deterministic convergence mechanism. First, based on the fitness ranking results, the system selects the top μ high-quality individuals as parents to participate in recombination. The value of μ is usually set to half the population size λ, but it can be dynamically adjusted according to the problem characteristics and optimization stage. Choosing a larger μ value is beneficial for maintaining population diversity and search stability, while a smaller μ value increases selection pressure and accelerates convergence to a local optimum.

[0210] Log-normal weight distribution is one of the key features of the CMA-ES algorithm. It assigns different influence weights to each parent individual, allowing individuals with better fitness to contribute more. Specifically, the weight values ​​are designed according to the principle of log-normal distribution. The weight of the i-th individual is usually set to wi∝ln(μ+1)-ln(i), and then normalized so that the sum of all weights is 1. This weight allocation strategy ensures that top-ranked individuals receive significantly higher weights, while lower-ranked individuals retain some influence. This guarantees the directionality of convergence towards a high-quality solution and avoids premature loss of valuable genetic information. Compared to truncated selection (selecting only the top individuals) or linear weights, log-normal weight distribution provides a better balance between selection pressure and diversity, making it particularly suitable for handling complex nonlinear optimization problems.

[0211] During the weighted recombination process, the system uses selected μ parent individuals and calculates their weighted average according to their corresponding weights to form the mean vector of the new generation. The mean vector represents the central position of the new generation population and is one of the most important evolutionary information in the CMA-ES algorithm. Through this weighted averaging mechanism, the central position of the population gradually moves towards the high-quality solution region, realizing the directed evolution of swarm intelligence.

[0212] In practical implementation, weighted recombining requires consideration of several important technical details. First, it necessitates handling boundary constraints. When certain dimensions of the recombined mean vector exceed the variable boundaries, boundary correction is needed to ensure the mean vector remains within the feasible region. Second, an elite retention mechanism is required, comparing historical best solutions with current best solutions and retaining the globally optimal solution as the elite. Elite retention ensures the algorithm doesn't lose previously discovered best solutions during evolution, improving the robustness of the optimization. Furthermore, in multi-objective optimization scenarios, weighted recombining may require incorporating the concept of the Pareto front to find a suitable balance point for different objectives.

[0213] After weighted reorganization, the new mean vector serves as the center of the next generation population, guiding subsequent covariance matrix updates and new individual generation. This swarm intelligence-based evolutionary mechanism enables the CMA-ES algorithm to effectively handle complex nonlinear optimization problems, possessing both strong global search capabilities and rapid convergence to high-quality solutions. In particular, when combined with a warm-start mechanism, the initial mean vector is already located in a promising region, allowing weighted reorganization to more efficiently guide the population towards the optimal solution, significantly improving optimization efficiency and result quality.

[0214] S4.4: When the iteration converges or the maximum number of iterations is reached, extract the solution corresponding to the optimal fitness to form a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0215] The CMA-ES algorithm iterates continuously, gradually converging the population towards a high-quality solution region. When the algorithm reaches the termination condition, the final result needs to be extracted from the optimization process and transformed into a practically executable scheduling scheme. Termination conditions typically fall into two categories: first, convergence criteria, such as the change in optimal fitness over multiple generations being less than a preset threshold, the step size parameter σ being less than a minimum threshold, or the condition number of the covariance matrix exceeding a maximum threshold; second, resource constraints, such as reaching the maximum number of iterations or computation time limits. Regardless of which condition triggers termination, the system needs to extract the optimal solution from the optimization history as the final scheduling scheme. Generally, the optimal solution refers to the individual with the smallest fitness value (for minimization problems) throughout the entire optimization process. This is because the evolutionary process of CMA-ES may experience slight fluctuations in the later stages, and the optimal individual in the last generation may not necessarily be the global optimum.

[0216] After extracting the optimal solution, the system needs to perform detailed feasibility verification to ensure that all physical and operational constraints are met. This includes multi-level verification such as power limit checks, SOC boundary checks, node voltage checks, and line capacity checks. For any minor constraint violations, the system will make necessary corrections, such as through proportional adjustments or local optimization methods, to ensure that the solution strictly satisfies all constraints. This step ensures the practical operability of the final solution and avoids a disconnect between the theoretical optimal solution and actual operating conditions.

[0217] The core of the scheduling scheme is the arrangement of charging and discharging power in each time period. For electric vehicles, the scheduling scheme includes the charging or discharging power for each time period, as well as the corresponding SOC evolution curve. The scheme design needs to fully consider user travel needs to ensure sufficient power at the time of vehicle use. For electric vehicles with V2G (vehicle-to-grid) functionality, it is also necessary to specify the discharging time and power, as well as the corresponding compensation mechanism. For stationary energy storage devices, the scheduling scheme also includes the charging and discharging power and SOC change trajectory for each time period. Unlike electric vehicles, stationary energy storage usually emphasizes system-level economics and efficiency, such as peak-valley price arbitrage and load smoothing.

[0218] To improve the practicality and robustness of the scheduling scheme, the system also generates a set of alternative solutions. These alternative solutions may come from non-dominated solutions on the Pareto front discovered during the optimization process, or from approximate optimal solutions obtained by slightly modifying the optimal solution. The alternative solutions provide strategies for dealing with uncertainties that may arise during actual operation, enhancing the system's adaptability. For example, when some electric vehicles fail to connect or disconnect as expected, the alternative solutions can guide the system to quickly adjust the operating plans of other energy storage resources, maintaining the overall optimization objective.

[0219] The dispatching scheme outputs a hierarchical structure to adapt to decision-making needs at different time scales. Short-term (hourly) dispatching instructions are directly issued to relevant equipment for execution, including precise power setpoints and operation times. Medium-term (daily) dispatching recommendations serve as a reference for operators' decision-making, typically including more uncertainty handling strategies and adjustment margins. Long-term (weekly / monthly) trend analysis is used to guide the planning and management of energy storage resources, such as strategic decisions regarding electric vehicle charging infrastructure deployment and fixed energy storage capacity configuration.

[0220] Finally, the system generates a diagnostic report on the optimization process, including convergence analysis, constraint satisfaction assessment, and sensitivity analysis. This information helps operators understand the reliability and robustness of the optimization results and provides a basis for subsequent model improvements and optimization strategy adjustments. Through this systematic result extraction and solution generation process, the mathematical solution of the CMA-ES optimization algorithm is transformed into practically executable scheduling instructions, achieving a seamless transition from theoretical optimization to actual operation.

[0221] In the execution phase of the generalized energy storage collaborative scheduling optimization, the initial population of the CMA-ES algorithm needs to be constructed based on the hot-start results. The system uses the initial distribution parameters (including the mean vector and covariance matrix) obtained during the hot start to generate the first generation of individuals. The population size needs to be set in a balance between computational efficiency and optimization performance, and it is generally recommended to set it to 4-10 times the problem dimension. Each individual represents a potential scheduling scheme, containing the charging and discharging power values ​​of electric vehicles and stationary energy storage devices in various time periods. The initial population generation process adopts a sampling strategy that considers constraints to ensure that individuals meet basic physical constraints, such as power limits and capacity boundaries, which can improve the effectiveness of the population.

[0222] The iterative optimization process is the core of the CMA-ES algorithm. In each iteration, the fitness of all individuals in the current population is first evaluated. The fitness function comprehensively considers multiple optimization objectives such as operating cost, loss, and voltage deviation. Then, individuals are ranked based on their fitness values, and the top μ high-quality individuals are selected as parents. In particular, to improve the stability of the optimization, a weighted recombination strategy is used to generate the mean vector of the new generation. The weights are designed according to the log-normal distribution principle, so that individuals with better fitness have greater influence. An elite retention mechanism is also introduced in the selection process to ensure that the historical optimal solution is not lost during the evolution.

[0223] According to one embodiment, the method further includes: adjusting an optimization strategy based on the mean vector of the new generation population, including:

[0224] S4.5: Using the mean vector of the new generation population, update the covariance matrix through evolutionary path accumulation and population distribution weighting methods to form an adaptively adjusted covariance matrix.

[0225] In each iteration of the CMA-ES algorithm, after updating the mean vector, the next crucial step is the adaptive adjustment of the covariance matrix. The covariance matrix determines the shape and direction of the algorithm's search distribution, and its adaptive update is one of the core characteristics of the CMA-ES algorithm. Unlike the simple mutation operation of traditional evolutionary algorithms, CMA-ES can learn the structural features of the problem and adaptively adjust the search distribution, greatly improving optimization efficiency. The update of the covariance matrix employs a two-pronged mechanism: one is an update based on the evolutionary path, capturing long-term trend information of population evolution; the other is an update based on the current population distribution, utilizing the distribution information of the latest generation of high-quality individuals.

[0226] Evolutionary path accumulation is the first key mechanism for covariance matrix updating. The evolutionary path (also known as the search path or cumulative path) records the movement trajectory of the mean vector over multiple generations, capturing long-term trends and directional information in the optimization search. The accumulation mechanism of the evolutionary path strengthens movements in similar directions over multiple generations while weakening movements in inconsistent directions, which helps the algorithm identify and utilize the long-term trends of the problem.

[0227] The first part of the covariance matrix update is based on the outer product of the evolutionary paths, and is expressed as:

[0228] c1*pc*pc T

[0229] Here, c1 is the corresponding learning rate parameter. This update mechanism allows the covariance matrix to adapt to the global structure of the problem, strengthening the search effort in promising directions. Specifically, when the evolutionary path moves consistently in a certain direction for multiple generations, the eigenvalues ​​of the covariance matrix in that direction increase, expanding the search range in that direction; while in dimensions where the evolutionary direction changes frequently, the eigenvalues ​​are relatively small, focusing the search on a smaller region. This adaptive mechanism allows the algorithm to use different search scales in different dimensions, making it well-suited for handling complex anisotropic optimization problems.

[0230] The population distribution weighted method is the second important mechanism for covariance matrix updates. It is based on the deviation distribution of the selected μ parents in the current generation relative to the mean vector. This mechanism allows the covariance matrix to quickly adapt to the local characteristics of the current population distribution, capturing the spatial structure of the distribution of high-quality solutions. Unlike evolutionary paths, which focus on long-term trends, population distribution updates reflect the immediate state of the current population. The two complement each other, ensuring a balance between global trends and local adaptation in the algorithm.

[0231] After the covariance matrix is ​​updated, the system needs to perform necessary stability processing, such as eigenvalue constraints and matrix renormalization. When the condition number of the covariance matrix is ​​too large, it may lead to numerical instability, which needs to be avoided by limiting the ratio of the largest and smallest eigenvalues. Furthermore, to improve computational efficiency, the covariance matrix can be updated using a low-rank update technique to avoid performing a complete matrix operation in each generation. Through this systematic adaptive adjustment mechanism of the covariance matrix, the CMA-ES algorithm can effectively learn and utilize the structural characteristics of the problem, gradually forming an optimal distribution shape that matches the characteristics of the problem during the search process, significantly improving search efficiency and result quality.

[0232] S4.6: Based on the adaptively adjusted covariance matrix, monitor the convergence status of the optimal fitness value. When the standard deviation of a consecutive specified algebra is less than a preset threshold, determine the covariance matrix after expanding the search range.

[0233] After adaptive adjustment of the covariance matrix, the system needs to further monitor the convergence status of the optimization process and implement necessary intervention measures as needed to prevent premature convergence or getting trapped in local optima. The convergence trend of the optimal fitness value is an important indicator for judging the optimization status. The system continuously records the optimal fitness value for multiple consecutive generations and calculates its standard deviation or rate of change to reflect the degree of optimization progress in a recent period. When the standard deviation of the optimal fitness value for a specified number of consecutive generations (such as 10 or 20 generations) is less than a preset threshold, it indicates that the optimization process may have entered a stagnant state. This stagnation may have two situations: one is that the algorithm has successfully converged to the optimal solution or a region close to the optimal solution, in which case small changes in the fitness value are normal; the other is that the algorithm is trapped in a local optimum and finds it difficult to escape the current region to explore a wider solution space. Distinguishing between these two situations is crucial because they require completely different processing strategies.

[0234] To determine the nature of the stagnation, the system comprehensively analyzes multiple indicators, such as the quality assessment of the current optimal solution (compared to historical optimal solutions or theoretical lower bounds), the characteristics of the search distribution (e.g., the eigenvalue distribution of the step size parameter and covariance matrix), and recent evolutionary trends (e.g., the length and direction of the evolutionary path). If it is determined to be normal convergence, the system may further refine the search, such as reducing the step size parameter or increasing the population size, to obtain a more accurate solution; if it is determined to be trapped in a local optimum, intervention measures are needed to expand the search range and help the algorithm escape the current trap.

[0235] Expanding the search range hinges on adjusting the covariance matrix to enhance the algorithm's exploratory capabilities. A direct approach is to uniformly expand all eigenvalues ​​of the covariance matrix, effectively increasing the search range across all dimensions. This method is simple and effective, but it may waste computational resources in directions that have already been thoroughly explored.

[0236] A more targeted approach is to increase the search range only in specific directions. For example, the search range can be increased along the eigenvector directions corresponding to smaller eigenvalues ​​in the covariance matrix, as these directions may have been insufficiently explored previously. Alternatively, the exploration intensity can be increased in directions orthogonal to the current evolutionary path, as these directions may contain unexplored solution spaces. In this way, the system enhances its ability to explore new directions while maintaining exploration of known promising regions.

[0237] Another strategy is to introduce random perturbations, adding random components to the covariance matrix to disrupt the current search pattern. For example, the covariance matrix can be mixed with a randomly generated positive definite matrix in a certain proportion, or random fluctuations can be added to the eigenvalues ​​of the covariance matrix. This randomization strategy helps the algorithm escape local attraction basins and discover new promising regions. Compared to a complete restart, this method retains some of the learned problem structure information, achieving a better balance between exploration and exploitation.

[0238] In extreme cases, if multiple attempts to expand the search scope fail to yield significant improvement, the system may trigger a full restart. A full restart means resetting all algorithm parameters, including the mean vector, step size, and covariance matrix, but typically retains previously found optimal solutions as a reference. Parameter settings after a restart can vary, such as using different initialization strategies or adjusting key parameters, to increase diversity and avoid repeating previous search paths. A common strategy is to restart CMA-ES multiple times, each time with different initial parameter configurations, and then combine the results of all runs to select the globally optimal solution.

[0239] Through this multi-layered monitoring and intervention mechanism, the system can effectively address various challenges during the optimization process, prevent the algorithm from getting trapped in local optima, maintain a balance between exploration and utilization, and ultimately obtain high-quality optimization results. In particular, when combined with a warm-start mechanism, the system can more intelligently determine the convergence state and select intervention strategies because it already possesses prior knowledge of the problem structure. For example, if the warm-start prediction distribution shows high uncertainty in certain regions, the system may prioritize expanding the search range in these directions when encountering convergence problems; while for regions with higher certainty in the prediction distribution, the system may prefer a more refined search strategy. This intelligent decision-making mechanism, combining historical knowledge and the current optimization state, greatly improves the algorithm's ability to handle complex nonlinear optimization problems, especially demonstrating significant advantages when facing multi-peak, non-convex, or high-dimensional problems.

[0240] Furthermore, the system also performs self-evaluation and learning based on the effects of expanding the search scope. If a certain intervention strategy performs well under specific circumstances, the system will increase the selection weight of that strategy in similar situations in the future; conversely, it will decrease its weight. This strategy adaptive mechanism enables the system to continuously improve its intervention decisions as optimization experience accumulates, forming a meta-optimization process. Through continuous monitoring, intervention, and learning, the system ultimately forms a complete optimization control framework, capable of efficiently solving complex practical engineering problems such as the generalized energy storage coordinated dispatch of power distribution systems.

[0241] In summary, the covariance matrix, after expanding the search range, is not merely a simple mathematical object, but a core component of the system's intelligent optimization control, reflecting the learning outcomes of the problem structure and the algorithm's adaptive capabilities. Through dynamic adjustment of the covariance matrix, the CMA-ES algorithm achieves an optimal balance between precise convergence and extensive exploration, providing strong algorithmic support for the collaborative optimization of power distribution systems.

[0242] Adaptive adjustment of the covariance matrix is ​​crucial for ensuring the algorithm's convergence efficiency. The system employs a two-path update mechanism: one based on the evolutionary path, capturing long-term trends in population evolution; and the other based on population distribution, utilizing the distribution information of current high-performing individuals. The evolutionary path update uses an accumulation mechanism, controlling the degree of historical information retention through the learning rate parameter. Simultaneously, the step size parameter σ is adjusted using a similar path accumulation mechanism, but with a different learning rate, allowing for dynamic adjustment of the search step size while maintaining the search direction. To prevent premature convergence, the system also incorporates an adaptive restart mechanism. When the search is found to be trapped in a local optimum, the search range is expanded by increasing the step size or adjusting the eigenvalues ​​of the covariance matrix.

[0243] The final optimization output includes not only the generation of the optimal scheduling scheme but also feasibility verification and implementation recommendations. The system first performs detailed constraint checks on the obtained optimal solution to ensure all physical and operational limitations are met. Then, it generates a detailed scheduling plan containing the charging and discharging power of electric vehicles and stationary energy storage devices for each time period. To improve the practicality of the scheme, the system also generates a set of alternative schemes to address uncertainties that may arise during actual operation. The output of the scheduling scheme adopts a hierarchical structure: short-term (hourly) scheduling instructions are directly issued to relevant equipment for execution; medium-term (daily) scheduling suggestions serve as a reference for operators' decision-making; and long-term (weekly / monthly) trend analysis guides the planning and management of energy storage resources. Simultaneously, the system generates a diagnostic report on the optimization process, including convergence analysis and constraint satisfaction assessment, providing a basis for improving subsequent optimization strategies.

[0244] like Figure 5 As shown in the figure, an embodiment of this application provides a power distribution system collaborative optimization operation device, comprising:

[0245] The optimization model building module is used to build a generalized energy storage collaborative optimization model for the power distribution system based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics.

[0246] The learning model construction module is used to construct a context vector learning model by using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, and adopting the Gaussian process regression method. The context vector learning model contains the mapping relationship between the context vector and the optimization parameters. The context vector contains time features, load characteristics, electricity price information and environmental conditions.

[0247] The hot start optimization module is used to extract the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predict the initial distribution of the optimization parameters, and obtain the initial mean vector and covariance matrix of the CMA-ES algorithm.

[0248] The scheduling optimization module is used to perform the CMA-ES iterative optimization process using the initial mean vector and covariance matrix, and output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

[0249] The functions of each module of this device correspond to the steps in the aforementioned method embodiments, and the specific implementation can be found in the detailed description of the aforementioned method embodiments. By implementing the method as an integrated device, automated power distribution system collaborative optimization operation can be achieved, improving system operating efficiency and stability.

[0250] The optimization model building module is responsible for constructing a generalized energy storage collaborative optimization model for the power distribution system. This model comprehensively considers the characteristics of electric vehicles and stationary energy storage devices, as well as the operational constraints of the power distribution network, forming the basic framework for optimization. The learning model building module constructs a context vector learning model based on historical data, realizing the mapping relationship between context vectors and optimization parameters, providing crucial support for hot-start optimization. The hot-start optimization module utilizes the prediction results of the learning model to achieve intelligent initialization of the CMA-ES algorithm, significantly improving the starting point level of optimization. The scheduling optimization module is responsible for executing the CMA-ES iterative optimization process and ultimately outputting a practically executable scheduling scheme.

[0251] It should be noted that the various devices, apparatuses, and modules in this application can be implemented by software, hardware, or any combination of both. These modules can be integrated together to form a single system, or they can be distributed and deployed in multiple systems or devices. The separation or integration of these modules may vary in different examples; they can be integrated into a single processing unit, or each module can be a separate unit, or two or more modules can be integrated into a single unit. Such integrated units can be implemented as hardware or as software functional units.

[0252] Furthermore, embodiments of this application also provide a computer device, including:

[0253] At least one processor; and,

[0254] A memory communicatively connected to the at least one processor; wherein,

[0255] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the above-described method for coordinated optimization of the operation of the power distribution system.

[0256] This computer device, as a hardware implementation, provides a platform for executing the methods of this application. The processor may be a central processing unit (CPU), a network processor (NP), or a combination of both, capable of controlling and processing various data processing, computation, and control tasks related to the methods of this application. The memory may include random access memory (RAM) and read-only memory (ROM), as well as other types of storage devices, for storing program code and data.

[0257] This application also provides a computer-readable storage medium storing computer instructions for causing a computer to execute the above-described method for coordinated optimization of power distribution system operation.

[0258] This application also provides a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the above-described power distribution system collaborative optimization operation method.

[0259] Through the detailed description of the above embodiments, those skilled in the art will clearly understand that this application provides a method and apparatus for collaborative optimization of power distribution systems based on context vectors. This method, by constructing a context vector learning model, achieves hot-start optimization of the CMA-ES algorithm, significantly improving the optimization efficiency and result quality of generalized energy storage collaborative scheduling in power distribution systems. This method is applicable to modern power distribution systems containing a large number of electric vehicles and stationary energy storage devices, providing strong support for achieving economical and efficient system operation.

[0260] The above description is merely a preferred embodiment of this application and does not limit the patent scope of this application. Any equivalent structural transformations made based on the inventive concept of this application and the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for collaborative optimization of power distribution system operation, characterized in that, include: Based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics, a generalized energy storage collaborative optimization model for power distribution systems is constructed. Using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, a context vector learning model is constructed using the Gaussian process regression method. The context vector learning model includes the mapping relationship between the context vector and the optimization parameters. The context vector includes time features, load characteristics, electricity price information and environmental conditions. Based on the mapping relationship between the context vector and the optimization parameters, the context vector of the current scene is extracted, and the initial distribution of the optimization parameters is predicted to obtain the initial mean vector and covariance matrix of the CMA-ES algorithm. Using the initial mean vector and covariance matrix, the CMA-ES iterative optimization process is executed to output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

2. The method according to claim 1, characterized in that, Based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics, a generalized energy storage collaborative optimization model for the power distribution system is constructed, including: Based on charging power limitations, state of charge change characteristics, and user driving needs, an electric vehicle charging and discharging model is constructed. This model is used to obtain the charging and discharging power constraints of the electric vehicle. Using the electric vehicle charging and discharging power constraints, combined with the charging and discharging efficiency and capacity limitations of the stationary energy storage device, a stationary energy storage device model is constructed, and the charging and discharging power constraints of the stationary energy storage device are generated. Using the electric vehicle charging and discharging power constraints and the fixed energy storage device charging and discharging power constraints, a power distribution network operation constraint model is constructed, forming node voltage constraints and line power constraints. Based on the node voltage constraints and the line power constraints, an optimization objective function is constructed, and an optimization objective function and constraints are established that include minimizing operating costs and minimizing grid losses.

3. The method according to claim 2, characterized in that, Also includes: Based on the optimization objective functions of minimizing operating costs and minimizing grid losses, the weight coefficients are calculated using the analytic hierarchy process (AHP) to form a weighted combined optimization objective function. The operating costs include electricity purchase costs and energy storage device maintenance costs.

4. The method according to claim 1, characterized in that, The method of constructing a context vector learning model using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, employing Gaussian process regression, includes: Data collection time characteristics, load characteristics, electricity price information, and environmental conditions are used, and data cleaning and normalization methods are employed to form preprocessed historical data. Based on the preprocessed historical data, a combined kernel function containing a radial basis function kernel function and a classification kernel function is constructed to generate feature extraction results. The combined kernel function is a core component of the Gaussian process regression method. Using the feature extraction results, the parameters of the combined kernel function are optimized by the maximum likelihood estimation method, and the mapping relationship between the context vector and the optimized parameters is obtained to complete the construction of the Gaussian process regression model.

5. The method according to claim 4, characterized in that, Based on the mapping relationship between the context vector and the optimization parameters, the prediction accuracy index is calculated, and the root mean square error and mean absolute error are obtained. Based on the root mean square error and mean absolute error, determine whether the preset threshold is exceeded. If the preset threshold is exceeded, retrain the Gaussian process regression model.

6. The method according to claim 1, characterized in that, The step of extracting the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predicting the initial distribution of the optimization parameters, and obtaining the initial mean vector and covariance matrix of the CMA-ES algorithm includes: Based on the current operational data, extract time features, operational status features, market features, and environmental features to form a context vector for the current scenario; Using the context vector of the current scene, parameter prediction is performed through the context vector learning model to generate an optimized parameter prediction distribution; Based on the predicted distribution according to the optimization parameters, initialize the CMA-ES algorithm parameters and determine the initial mean vector and covariance matrix.

7. The method according to claim 6, characterized in that, The step of predicting the distribution based on the optimized parameters and initializing the CMA-ES algorithm parameters includes: The covariance matrix eigenvalues ​​of the predicted distribution are used with the optimized parameters to calculate the step size parameter and population size, and the initial configuration parameters of the CMA-ES algorithm are determined. Based on the initial configuration parameters, the convergence performance of the optimization process is monitored. When the rate of change of the optimal fitness value for a consecutive specified number of generations is less than a preset threshold, the updated step size parameters and population size are generated.

8. The method according to claim 1, characterized in that, The CMA-ES iterative optimization process is performed using the initial mean vector and covariance matrix, including: Based on the initial mean vector and covariance matrix, an initial population that satisfies the power limit and capacity boundary constraints is generated, forming a candidate solution set; Using the candidate solution set, calculate the fitness values ​​of operating cost and grid loss, and obtain the fitness ranking results; Based on the fitness ranking results, a log-normal weighted reorganization of individuals is performed to determine the mean vector of the new generation population. When the iteration converges or reaches the maximum number of iterations, the solution corresponding to the optimal fitness is extracted to form a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

9. The method according to claim 8, characterized in that, Also includes: Based on the mean vector of the new generation population, the optimization strategy is adjusted, including: The mean vector of the new generation population is used to update the covariance matrix through evolutionary path accumulation and population distribution weighting methods to form an adaptively adjusted covariance matrix. Based on the adaptively adjusted covariance matrix, the convergence status of the optimal fitness value is monitored. When the standard deviation of a consecutive specified number of algebras is less than a preset threshold, the covariance matrix after expanding the search range is determined.

10. A power distribution system collaborative optimization operation device, characterized in that, include: The optimization model building module is used to build a generalized energy storage collaborative optimization model for the power distribution system based on the charging and discharging characteristics of electric vehicles, the charging and discharging characteristics of stationary energy storage devices, and load characteristics. The learning model construction module is used to construct a context vector learning model by using historical operating data of the power distribution system and the generalized energy storage collaborative optimization model of the power distribution system, and adopting the Gaussian process regression method. The context vector learning model contains the mapping relationship between the context vector and the optimization parameters. The context vector contains time features, load characteristics, electricity price information and environmental conditions. The hot start optimization module is used to extract the context vector of the current scene based on the mapping relationship between the context vector and the optimization parameters, predict the initial distribution of the optimization parameters, and obtain the initial mean vector and covariance matrix of the CMA-ES algorithm. The scheduling optimization module is used to perform the CMA-ES iterative optimization process using the initial mean vector and covariance matrix, and output a scheduling scheme for electric vehicles and stationary energy storage devices that includes the charging and discharging power of each time period.

Images