Data center frequency response capability modeling method based on data-driven inverse optimization

Abstract

A data center frequency response capability modeling method based on data-driven inverse optimization belongs to the technical field of power system scheduling and data center energy management, and comprises the following steps: carrying out mathematical modeling on a data center load response behavior, and constructing a comprehensive optimization objective function and constraint conditions including transferable loads, interruptible calculation loads and cooling equipment; based on an ALF adjustable load group concept, aggregating high-dimensional mixed integer constraints of the data center into a dimensionality-reduced low-order model; constructing a data-driven training framework based on inverse optimization, and learning ALF adjustable load group model parameters from historical operation data; and realizing dynamic scheduling and frequency response optimization decision of the data center based on the trained dimension reduction model. According to the method, the calculation complexity can be remarkably reduced while key physical constraints are kept, and the scheduling efficiency and modeling precision of the data center participating in the power grid auxiliary service are improved.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatching and data center energy management technology, and relates to a load modeling and optimized scheduling method for data centers participating in grid ancillary services, specifically a data center frequency response capability modeling method based on data-driven inverse optimization. Background Technology

[0002] With the rapid development of new power systems and the large-scale grid connection of renewable energy sources such as wind power and photovoltaics, the intermittency and volatility of their output pose challenges to the safe and stable operation of the power grid, putting immense pressure on the traditional "source follows load" dispatching model. Against this backdrop, tapping into demand-side flexibility resources to participate in grid regulation has become an important way to ensure the balance between power supply and demand.

[0003] As a core infrastructure of the information age, data centers consume 1%-2% of global electricity, and this figure continues to grow at a rate of 10%-15% annually. In-depth analysis of their operational characteristics reveals significant flexibility potential: First, the time-shifting nature of IT loads, with batch processing tasks (such as data backup and model training) accounting for 30%-50%, allows for flexible scheduling over a wide time window; second, the thermal inertia of cooling systems, with cooling loads accounting for approximately 30%-40% of total energy consumption, allows for earlier or later operation utilizing building thermal capacity; third, the energy storage characteristics of backup power supplies, with UPS battery banks and independent energy storage systems participating in grid peak shaving and frequency regulation; and fourth, geographically distributed load balancing, achieving cost optimization through the dynamic migration of workloads between different data centers. Based on these characteristics, data centers have been recognized as a potential flexible resource capable of participating in ancillary services such as frequency regulation.

[0004] Numerous studies have explored the potential for data centers to participate in the ancillary services market. Representative works have proposed frequency regulation optimization models that leverage IT load flexibility and integrate energy storage; mixed-integer programming models are widely used to capture workload migration and logical constraints; and two-level optimization models can collaboratively optimize flexible loads and equipment scheduling. However, these refined modeling methods require detailed equipment parameters within the data center, involving numerous integer variables and nonlinear constraints, leading to heavy computational burdens and limited scalability of real-time scheduling.

[0005] Another research direction focuses on energy consumption modeling, describing the coupling relationship between IT equipment, cooling systems, and the environment. Modular simulation frameworks, rack-level airflow and cooling models, and polynomial IT power formulas considering temperature and humidity have all shown value, but they heavily rely on device-level data. Data center operators are often unwilling to disclose internal parameters due to trade secrets and data security considerations, creating obstacles for system operators. To improve processability, dimensionality reduction and proxy models are widely used. Virtual battery (VB) models approximate flexibility by pre-setting a prototype feasible region, including external approximation of temperature-controlled load flexibility and multi-battery approximation of electric vehicle fleets. These methods reduce complexity, but may oversimplify operational constraints and weaken interpretability, limiting their direct application in system-level scheduling. The shortcomings of existing technical solutions are mainly reflected in the following aspects: High complexity of refined modeling: Traditional methods require obtaining detailed parameters such as server start-stop sequences, task dependencies, and network bandwidth constraints, which are often difficult to obtain and involve data privacy issues. At the same time, high-dimensional mixed integer constraints significantly increase the difficulty of solving scheduling problems, making it difficult to meet the timeliness requirements of real-time scheduling. Insufficient accuracy of proxy models: The prototype feasible domain preset by proxy models such as virtual batteries may oversimplify the actual operational constraints of data centers. The flexibility boundary of a data center is coupled with multiple factors such as task type, service level agreement, and equipment capacity, resulting in a complex shape in its true feasible domain, which deviates significantly from the preset shape, leading to scheduling decisions that deviate from the actual optimum. Lack of data-driven learning capability: Existing methods mostly rely on expert experience or simple statistical analysis to determine model parameters, failing to fully utilize historical operational data for parameter learning. Due to the lack of an effective parameter learning mechanism, existing models struggle to adapt to the differentiated characteristics of different types of data centers and cannot track characteristic drift caused by equipment updates and business changes. How to construct a data center load model that can maintain key physical constraints while significantly reducing computational complexity, and simultaneously possess the ability to automatically learn parameters from operational data, has become a critical issue that urgently needs to be addressed for data centers to participate in grid ancillary services. Summary of the Invention

[0006] This invention aims to aggregate the high-dimensional mixed integer constraints of data centers into a lower-dimensional form by introducing an adjustable load group (ALF) model, and to automatically learn model parameters from historical operating data using a data-driven method based on inverse optimization. This significantly reduces computational complexity while maintaining key physical constraints, thereby improving the scheduling efficiency and modeling accuracy of data centers participating in grid ancillary services.

[0007] The technical solution adopted in this invention is: a data center frequency response capability modeling method based on data-driven inverse optimization, comprising: Step 1: Perform mathematical modeling of the data center load response behavior, and construct a comprehensive optimization objective function and constraints that include transferable load, interruptible computing load, and cooling equipment; Step 2: Based on the ALF adjustable load group concept, aggregate the high-dimensional mixed integer constraints of the data center into a low-order model with reduced dimensionality; Step 3: Construct a data-driven training framework based on inverse optimization to learn the parameters of the ALF adjustable load swarm model from historical operating data; Step 4: Implement dynamic scheduling and frequency response optimization decisions for the data center based on the trained dimensionality reduction model.

[0008] The beneficial effects of this invention are as follows: Reduced computational complexity: By introducing an Adjustable Load Group (ALF) model, the high-dimensional mixed integer constraints of the data center are aggregated into a low-order linear constraint model containing only 12 continuous parameters. For example, in this embodiment, the three data centers originally involved a large number of 0-1 integer variables and nonlinear constraints such as server start-up and shutdown, task migration, and cooling adjustment. After dimensionality reduction, only 12 parameters, namely the power upper and lower limits and energy upper and lower limits of each AL unit, need to be determined. The constraint complexity is significantly reduced, and the optimization problem is transformed from an NP-hard mixed integer programming problem into a linear programming problem that can be solved quickly, meeting the computational timeliness requirements of real-time scheduling. Improved modeling accuracy: By adopting a data-driven method based on inverse optimization to learn model parameters from actual operating data, it can more accurately describe the adjustment capability boundary of the data center compared to traditional surrogate models with preset feasible regions. As shown in simulation verification, the AL modeling loss is reduced from approximately 6.5 × 10⁻⁶. 4 It rapidly decreases to a stable value, and the convergence index drops from 10. 0 The magnitude dropped to 10 -6 The magnitude of the learned parameters indicates a high degree of consistency with the actual operating characteristics of the data center, achieving higher modeling accuracy while maintaining near-optimal performance. Improved scheduling efficiency: Based on the dimensionality-reduced ALF model, the data center scheduling problem is transformed into a standard linear programming problem, which can be solved in milliseconds using the simplex method or interior-point method. Compared to the exponential solution complexity of the refined mixed-integer programming model, this method significantly improves scheduling efficiency, enabling data centers to quickly respond to power grid frequency regulation signals and meet the stringent response speed requirements of ancillary services. Enhanced generalization ability: No detailed equipment parameters within the data center are required; model training can be completed using only historical operating data, avoiding data privacy and trade secret issues. Furthermore, the inverse optimization framework supports continuous iterative updates of the model. When data center characteristics drift due to equipment expansion, business changes, etc., the model can be retrained based on new data, ensuring that the strategy adapts to the actual scenario in the long term, exhibiting strong generalization ability and environmental adaptability. Attached Figure Description

[0009] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0011] This invention proposes a data-driven inverse optimization-based method for modeling the frequency response capability of data centers, comprising: Step 1: mathematically modeling the load response behavior of the data center, constructing a comprehensive optimization objective function and constraints including transferable loads, interruptible computing loads, and cooling equipment; Step 2: based on the concept of Adjustable Load Group (ALF), aggregating the high-dimensional mixed integer constraints of the data center into a dimensionality-reduced low-order model; Step 3: constructing a data-driven training framework based on inverse optimization, learning ALF model parameters from historical operating data; Step 4: realizing dynamic scheduling and frequency response optimization decisions of the data center based on the trained dimensionality-reduced model.

[0012] Furthermore, one possible implementation of step 1 includes: step 1.1: constructing a comprehensive optimization objective function for the data center; step 1.2: modeling transferable loads; step 1.3: modeling interruptible computing loads; and step 1.4: modeling cooling equipment.

[0013] In step 1.1, considering that data center optimization not only requires minimizing energy consumption but also needs to take into account potential market adjustments and demand response measures during scheduling, demand response costs and incentive costs are incorporated into the objective function. The objective function is expressed as: Among them, C inv The cost of equipment investment, including servers, cooling equipment, etc., is expressed in yuan; C op Operation and maintenance costs, including labor, equipment maintenance, etc., are expressed in yuan; C energy Operation and maintenance costs, and energy procurement costs, including electricity, cooling, and other energy sources, are expressed in yuan. The carbon emission cost is expressed in yuan; λ is the carbon emission coefficient, C. DR The demand response revenue is expressed in yuan (C). Inc The incentive revenue is expressed in yuan. This objective function aims to minimize total operating costs while considering the benefits of participating in demand response and incentive mechanisms.

[0014] In step 1.2, transferable workload refers to task workloads that can be transferred between different time periods, mainly including batch processing tasks such as data backup, model training, and batch computation. A binary decision variable x is introduced. n,t To represent task scheduling decisions, a linear programming model for transferable loads is established: Among them, P n,t x represents the power of task n during time period t, in kilowatts; n,t For a binary decision variable, x n,t =1 indicates that task n is executed during time period t, x n,t =0 indicates that task n will not be executed during time period t; T is the set of time periods within the scheduling cycle; N is the set of tasks to be scheduled.

[0015] The constraint is that each task must be executed one and only once within the scheduling cycle: In step 1.3, interruptible computing load refers to a load that can be interrupted during computation and resumed after a certain period of time. Unlike transferable load, interruptible load requires additional recovery costs upon resumption, including overhead such as reloading data and restoring the computation state. A recovery decision variable y is introduced. n,t Establish an interruptible computational load model: Where, μ n,t Let y be the recovery cost of task n in time period t, in yuan; n,t Let y be a binary decision variable for whether the task should be resumed. n,t =1. Task n resumes execution in time period t, y n,t =0 indicates no recovery.

[0016] The constraints also require that each task must be allocated a time period for completion: In step 1.4, cooling equipment is a significant energy-consuming component of the data center, and its power consumption is closely related to ambient temperature and IT load. Based on optimization using liquid cooling and heat recovery technologies, a regression model for the power consumption of the cooling equipment is established: P cooling =α·T env +β·L, Among them, P cooling The power of the cooling equipment is expressed in kilowatts (kW); T env α represents ambient temperature in degrees Celsius; L represents IT load in kilowatts; α is the temperature influence coefficient, characterizing the impact of a 1-degree increase in ambient temperature on cooling power; β is the load influence coefficient, characterizing the impact of a 1-kilowatt increase in IT load on cooling power. This regression model can be obtained by fitting historical operating data using the least squares method.

[0017] Furthermore, one possible implementation of step 2 includes: step 2.1: constructing the basic architecture of Adjustable Load Group (ALF); step 2.2: establishing ALF power balance constraints; step 2.3: establishing ALF device power constraints; step 2.4: establishing ALF daily cumulative energy constraints; step 2.5: setting differentiated constraints for different types of data centers.

[0018] In step 2.1, the Adjustable Load Fleet (ALF) concept groups a large number of servers into small "Adjustable Load Units" (ALs) based on their functions. Each AL unit... c,i It consists of several servers, which are adjusted at 15-minute intervals. Unlike traditional methods where servers run continuously, the ALF method uses linear constraints to adjust each unit at a defined minimum power. and maximum power This ensures that load distribution remains within system operating limits. The ALF model constructed in this embodiment contains three AL units {AL1, AL2, AL3}, corresponding to three data centers with different characteristics.

[0019] In step 2.2, the total system power consumption must be equal to the sum of the power consumption of each AL unit. The power balance constraint is expressed as: In the formula, x t p represents the total power consumption of the system at time t, in kilowatt-hours; t,i The average power of AL unit i at time t is expressed in kilowatts; Δt = 0.25 is the time interval in hours (corresponding to 15 minutes); T is the total number of time periods in a day, taken as T = 96 (96 15-minute time periods per day).

[0020] In step 2.3, the power of each AL unit in each time period is constrained by a lower limit and an upper limit to ensure that the power consumption does not exceed the hardware limit or is lower than the minimum operating power level: In the formula, This represents the lower limit of the power of AL unit i, in kilowatts; This represents the upper power limit for AL unit i, in kilowatts. The upper and lower power limits are determined based on historical data or equipment specifications, reflecting the equipment's maximum load capacity and minimum operating requirements.

[0021] In step 2.4, the total energy consumption of each AL unit throughout the day is constrained by the Service Level Agreement (SLA) or daily workload: in, Let be the minimum daily energy consumption of AL unit i, in kilowatt-hours; This represents the maximum daily energy consumption of AL unit i, expressed in kilowatt-hours. Energy constraints ensure that the data center regulates power while meeting business needs.

[0022] In step 2.5, differentiated constraint parameters are set according to the operating characteristics and adjustment capabilities of different types of data centers: AL1 (DC1) corresponds to the core business data center, which mainly handles sensitive core business operations, has the characteristic of "non-migratory", has strict task execution order, power consumption closely follows the task intensity, and has a small power adjustment range.

[0023] AL2 (DC2) corresponds to the cloud computing platform data center, which supports extended processing tasks and elastic computing services. It has the feature of "flexible migration over time", and tasks can be migrated within a 4-hour window for load balancing, with a large power adjustment capability.

[0024] AL3 (DC3) corresponds to edge data centers, which are located near the network edge. They need to meet the low latency requirements of local users and have the feature of "remote flexible migration". They allow power adjustment without interfering with critical services.

[0025] Using the above constraint set, the ALF model reduces the dimensionality of the high-dimensional mixed-integer data center regulation problem to include only 12 continuous parameters (3 AL units × 4 parameters). (a low-order linear constraint problem).

[0026] Furthermore, one possible implementation of step 3 includes: step 3.1: constructing a training dataset; step 3.2: establishing an inverse optimization objective function; step 3.3: designing a rule-based hybrid optimization algorithm; and step 3.4: adopting a batch training and parameter update strategy.

[0027] In step 3.1, operational data from each data center over the past N days is collected to form a training dataset: Among them, Pr (n) ∈R T This represents the actual power consumption vector for each time period on day n; x (n) ∈R T×3 This is the power adjustment matrix for each AL unit on day n; Task (n) ∈R T×3 This represents the task intensity matrix for each AL unit on day n. T = 96 indicates the number of time slots per day (each time slot is 15 minutes long).

[0028] In step 3.2, the core idea of ​​inverse optimization is to deduce the model parameters from the observed decision results. The set of parameters to be learned is... The inverse optimization objective function is to minimize the error between the ALF model predictions and the observed data. In the formula, ||·|| F Let x be the Frobenius norm. n (θ) represents the optimal solution of the ALF model under parameter θ on day n. In the formula, VEC(·) represents the vectorization operation; Ω(θ) represents the feasible region of the ALF constraint defined by the parameter θ.

[0029] In step 3.3, since the objective function of the inverse optimization problem is not differentiable with respect to the parameter θ (the solution to the inner optimization problem has a complex dependency on the parameter), a derivative-free optimization method is used to solve it. A hybrid rule-based search optimization algorithm is designed, integrating three complementary search strategies:

[0030] Pattern Search: A systematic exploration along the standard coordinate axis, searching for improvement directions in the neighborhood of the current point according to a fixed pattern, ensuring local optima along each parameter dimension.

[0031] Grid Search: Divides the parameter space into a grid, evaluates the grid nodes, provides comprehensive local search capabilities, and avoids missing potential good solution regions.

[0032] Intelligent direction search: Based on historical iteration information, it predicts promising search directions and uses the parameter change trends of previous iterations to accelerate convergence.

[0033] The algorithm employs an adaptive step size adjustment mechanism: when no improved solution is found after multiple consecutive searches, the search step size is reduced for a more refined search; when an improved solution is found, the step size is appropriately increased to accelerate the exploration. Simultaneously, a multi-criteria early stopping mechanism is implemented: when the improvement in the objective function after K consecutive iterations is less than a threshold ò, convergence is determined and iteration stops.

[0034] In step 3.4, a batch training strategy is adopted to improve training efficiency and avoid local minima. B samples are randomly selected for training in each generation (B=1 in this embodiment). This mini-batch strategy can reduce the computational burden of each optimization step, increase the training iteration frequency to escape local optima, and improve the model's generalization ability. θ (k+1) =(1-α)θ (k) +αθ * , Where, θ (k) θ is the parameter of the kth generation; * α represents the optimal parameters for the current generation; α is the learning rate, which is set to 0.1 to ensure the stability of parameter updates and avoid drastic parameter fluctuations.

[0035] Furthermore, one possible implementation of step 4 includes: step 4.1: deployment of the model application environment; step 4.2: collaborative decision execution; step 4.3: iterative optimization of the model; and step 4.4: output of the decision optimization results.

[0036] In step 4.1, the trained ALF model is deployed to the data center scheduling system. Environmental parameters are acquired in real time through the data interface, including: the current power status of each data center, task queue length and urgency, real-time electricity price signals, and grid frequency regulation demand signals. These parameters serve as inputs to the ALF model, providing a basis for optimization decisions.

[0037] In step 4.2, based on the real-time acquired status information, each data center generates power adjustment decisions using the ALF model. Specifically, the following optimization problem is solved: Where, x t Let be the electricity price for time period t, expressed in yuan / kWh. This optimization problem is a linear programming problem, which can be solved quickly using the simplex method or interior-point method. If multiple data centers compete for the same regulating resource, the system coordinates decisions based on task urgency and power status through preset priority rules to avoid resource conflicts.

[0038] In step 4.3, real-time scheduling data is collected periodically to evaluate model performance, including metrics such as task completion rate, actual adjustment cost, and frequency response accuracy. When significant changes occur in the environment (such as data center expansion, electricity price policy adjustments, or changes in business type), the model retraining process is triggered to update the ALF model parameters based on the new data, ensuring that the strategy continues to adapt to the actual scenario.

[0039] In step 4.4, the decision optimization results are output, including: the power scheduling scheme for each data center in each time period {p t,i The frequency response capability curve (the change of adjustable power range over time), expected cost savings and adjustment benefit assessment, etc., provide decision-making basis and effect evaluation for data centers to participate in grid ancillary services.

[0040] The present invention also proposes an embodiment of an apparatus for implementing the above-described data center frequency response capability modeling method based on data-driven inverse optimization, comprising:

[0041] Data Center Load Response Modeling Module: Used for mathematical modeling of data center load response behavior, constructing a comprehensive optimization objective function and constraints that include transferable load, interruptible computing load, and cooling equipment;

[0042] Adjustable load group dimensionality reduction module: Based on the concept of adjustable load group, it aggregates high-dimensional mixed integer constraints of data centers into a low-order model with reduced dimensionality, and outputs an ALF model structure that includes power constraints and energy constraints;

[0043] Inverse optimization training module: used to build a data-driven training framework based on inverse optimization, learning the 12 continuous parameters of the ALF model from historical running data;

[0044] Dynamic scheduling and optimization decision module: Based on the trained dimensionality reduction model, it acquires environmental parameters in real time, solves linear programming problems, and outputs dynamic scheduling schemes and frequency response optimization decisions for the data center.

[0045] The present invention also proposes an embodiment of an electronic device, including a processor and a memory, wherein the processor is used to execute a computer program stored in the memory to implement the above-described data center frequency response capability modeling method based on data-driven inverse optimization.

[0046] The present invention also proposes an embodiment of a computer-readable storage medium for storing a computer program that, when executed by a processor, implements the above-described data center frequency response capability modeling method based on data-driven inverse optimization.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data center frequency response capability modeling method based on data-driven inverse optimization, characterized in that, include: Step 1: Perform mathematical modeling of the data center load response behavior, and construct a comprehensive optimization objective function and constraints that include transferable load, interruptible computing load, and cooling equipment; Step 2: Based on the ALF adjustable load group concept, aggregate the high-dimensional mixed integer constraints of the data center into a low-order model with reduced dimensionality; Step 3: Construct a data-driven training framework based on inverse optimization to learn the parameters of the ALF adjustable load swarm model from historical operating data; Step 4: Implement dynamic scheduling and frequency response optimization decisions for the data center based on the trained dimensionality reduction model.

2. The data center frequency response capability modeling method according to claim 1, characterized in that, Step 1 includes: Step 1.1: Construct the comprehensive optimization objective function for the data center; Step 1.2: Transferable load modeling; Step 1.3: Interruptible load modeling; Step 1.4: Modeling the cooling equipment.

3. The modeling method according to claim 2, characterized in that, In step 1.1, the comprehensive optimization objective function is: Among them, C inv For equipment investment costs, C op For maintenance costs, C energy For energy procurement costs, Let C be the carbon emission cost, λ be the carbon emission coefficient, and C be the carbon emission cost. DR For demand response revenue, C Inc To incentivize earnings; In step 1.2, the transferable load is modeled using a linear programming model: Among them, P n,t Let x be the power of task n in time period t. n,t For binary decision variables, it represents whether task n can be executed in time period t; The constraints are: That is, each task can only be executed within one time period; In step 1.3, the model for the interruptible computing load is represented as follows: Where, μ n,t Let y be the recovery cost of task n in time period t. n,t For the binary decision variable of whether the task should be resumed; in step 1.4, the power of the cooling equipment is represented by a regression model as follows: P cooling =α·T env +β·L, Among them, T env Let L be the ambient temperature, L be the load, and α and β be the regression coefficients, representing the impact of ambient temperature and load on the power consumption of the cooling equipment.

4. The data center frequency response capability modeling method according to claim 1, characterized in that, In step 2, the adjustable load group model includes multiple adjustable load units (ALs), each AL unit consisting of several servers grouped by function. The basic constraints of the model include: Power balance constraints: Equipment power constraint: P i min ≤p t,i ≤P i max ; Daily accumulated energy constraint: Where, x t Let p be the total power consumption of the system at time t. t,i Let P be the power of AL element i at time t, where Δt is the time interval. i min and P i max These are the upper and lower limits of power. These are the upper and lower limits of energy.

5. The data center frequency response capability modeling method according to claim 4, characterized in that, The adjustable load group model sets differentiated constraints for different types of data centers: AL1 corresponds to the core business data center, which is non-portable, has a strict task execution order, and its power consumption closely follows the task intensity. AL2 corresponds to the cloud computing platform data center, which has the characteristic of flexible migration time. Tasks can be migrated within a 4-hour window for load balancing. AL3 corresponds to edge data centers, featuring flexible remote migration capabilities and allowing power adjustments while ensuring service quality.

6. The modeling method according to claim 1, characterized in that, Step 3 includes: Step 3.1: Dataset Construction - Collect data from each data center over the past N days to form a dataset. Among them, Pr (n) Let x be the power consumption on day n. (n) For power adjustment, Task (n) Task intensity; Step 3.2: Construct the inverse optimization objective function: Among them, ||·|| F Let x be the Frobenius norm. n This represents the optimal solution for the ALF model under the condition of day n. Step 3.3: Solve the problem using a rule-based hybrid optimization algorithm that integrates three strategies: pattern search, grid search, and intelligent direction search. Step 3.4: Employ a batch training strategy, randomly selecting B data points for training in each generation, and updating the parameters using an exponentially weighted moving average: θ (k+1) =(1-α)θ (k) +αθ * , where θ * α represents the optimal parameters for the current generation, and α is the learning rate.

7. The data center frequency response capability modeling method according to claim 6, characterized in that, In step 3.3, the rule-based hybrid optimization algorithm belongs to the derivative-free optimization method, specifically including: Pattern search is used for systematic exploration along the standard axis; Grid search is used for fine-grained local searches; Intelligent directional search predicts promising search directions based on historical information; Adaptive step size adjustment and multi-criteria early stopping mechanism are adopted to ensure search efficiency and convergence stability.

8. The data center frequency response capability modeling method according to claim 1, characterized in that, Step 4 includes: Step 4.1: Deploy the model application environment. Deploy the trained model to the data center scheduling system to obtain environmental parameters such as load, electricity price, and task intensity in real time. Step 4.2: Collaborative decision execution, each data center generates power adjustment decisions based on real-time status using the ALF model; Step 4.3: Iterative optimization of the model, periodically collect real-time scheduling data to evaluate model performance, and retrain the model based on new data when the environment changes significantly; Step 4.4: Output of decision optimization results and participation of frequency response service.

9. The modeling method according to claim 1, characterized in that, The ALF model reduces the high-dimensional mixed integer constraints to a low-order linear constraint model containing 12 continuous parameters, including the power lower limit, power upper limit, energy lower limit, and energy upper limit of each of the three AL units.

10. A data center frequency response capability modeling device based on data-driven inverse optimization, characterized in that, include: Data Center Load Response Modeling Module: Used for mathematical modeling of data center load response behavior, constructing a comprehensive optimization objective function and constraints that include transferable load, interruptible computing load, and cooling equipment; Adjustable load group dimensionality reduction module: used to aggregate high-dimensional mixed integer constraints of data centers into a low-order model with reduced dimensionality based on the concept of adjustable load groups; Inverse optimization training module: used to build a data-driven training framework based on inverse optimization, learning ALF model parameters from historical running data; Dynamic scheduling and optimization decision module: used to realize dynamic scheduling and frequency response optimization decisions for data centers based on the trained dimensionality reduction model.

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