Mass air conditioner load aggregator user balanced scheduling method and system based on learning optimization and differentiable game, program product and electronic equipment

Abstract

The invention provides a mass air conditioner load aggregator user balanced scheduling method and system based on learning optimization and differentiable game, a program product and electronic equipment. The method comprises the following steps: sensing and constructing environment information; constructing and training a deep learning model of the air conditioner load response of the lower-layer user; constructing an upper aggregator income optimization model; and solving aggregated commercial householder-slave game equilibrium. According to the method, the problems of improving the solving efficiency and the large-scale capability, realizing end-to-end differentiable optimization, ensuring the equilibrium solution quality and improving the model prediction precision and the physical rationality in the prior art are effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of power demand response and intelligent load regulation, and in particular to a method, system, program product and electronic equipment for balancing the dispatch of massive air-conditioning load aggregators based on learning optimization and differentiable game. Background Art

[0002] With urbanization and rising living standards, air conditioning loads have become the primary driver of summer peak loads on distribution networks. By issuing dynamic electricity prices and reducing incentives to thousands of air conditioning terminals, load aggregators can shave peak loads, participate in ancillary services, and generate demand response revenue while maintaining user comfort. However, when implementing demand response management for massive distributed air conditioning loads, existing technologies face the following technical challenges in solving the two-layer optimization model between aggregators and users: First, there is a bottleneck in scalability. Traditional solution strategies require invoking mixed integer programming or nonlinear programming on a household-by-household basis within the aggregator-user two-layer model. The computational complexity grows exponentially or with high-order polynomials with the number of terminals, making it difficult to meet the real-time or near-real-time decision-making requirements for large-scale device aggregation. Second, there is the difficulty of solving the two-layer optimization problem. Traditional two-layer optimization algorithms (such as KKT conditional transformation and iterative methods) often have slow convergence and poor stability for large-scale non-convex problems, and it is difficult to guarantee a global optimal or high-quality equilibrium solution. Third, there is the challenge of striking a balance between user model accuracy and solution efficiency. Furthermore, traditional optimization solvers are often "black boxes," making it difficult to obtain the derivatives of their outputs with respect to their inputs. This makes it difficult for upper-tier aggregators to effectively optimize their pricing and incentive strategies using gradient information. Therefore, there is an urgent need for innovative methods that can efficiently and accurately handle massive air conditioning loads and quickly converge to a reasonable Stackelberg equilibrium (master-slave game equilibrium).

[0003] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0004] In view of this, the present invention provides a method, system, program product and electronic device for balanced scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game, so as to solve the problems faced by the existing technology in solving the two-layer optimization model between the aggregator and the user when performing demand response management for massive distributed air-conditioning loads, such as high computational complexity, poor real-time performance, and difficulty in obtaining a stable and physically reasonable Stackelberg equilibrium (master-slave game equilibrium) solution.

[0005] The embodiment of the present invention provides a method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game, including the following steps:

[0006] S100. Perceive and construct environmental information:

[0007] S110. Collect system-side data, including weather forecast data within a preset time range, the day-ahead and real-time electricity prices of the power grid, and demand response subsidy prices issued by the system operator;

[0008] S120. Collect user-side data of at least one air-conditioning user, the user-side data including building envelope parameters, air-conditioning unit rated power, thermal inertia coefficient, indoor temperature initial value, upper and lower limits of comfort temperature, historical baseline load, and user sensitivity coefficient to comfort loss of at least one air-conditioning user;

[0009] S130. Integrate system-side data and user-side data to generate environmental status information;

[0010] S200. Build and train a deep learning model for lower-level user air conditioning load response:

[0011] S210. For each of the at least one air conditioning user, establish a lower-level user primitive optimization model. The lower-level user primitive optimization model uses the retail electricity price and curtailment incentive issued by the aggregator as input signals, minimizes the user's comprehensive cost taking comfort into account as the optimization objective, and imposes upper and lower constraints on air conditioning power, upper and lower constraints on indoor temperature, and a thermodynamic balance constraint.

[0012] S220. Offline generation of training scenario samples, the training scenario samples include the optimal air conditioning power sequence and the corresponding reduction amount of each air conditioning user obtained by solving the original optimization model of the lower user under different input signal combinations;

[0013] S230. Based on the training scenario samples, a deep neural network is trained, so that the deep neural network receives the retail electricity price and curtailment incentive signal issued by the aggregator and the environmental status information as input, and outputs the predicted air conditioning power and predicted curtailment amount for each air conditioning user, and the deep neural network has the characteristic that the output is differentiable with respect to the input;

[0014] S300. Build an upper-layer aggregator revenue optimization model:

[0015] S310. Set the decision variables of the aggregator, which include the time-of-use retail electricity price and unit load reduction incentive within the preset scheduling period;

[0016] S320. Constructing a revenue objective function for the aggregator, the revenue objective function comprises substituting the predicted total air conditioning power and predicted total reduction of the group of air conditioning users output by the deep neural network trained in step S230 into a revenue calculation formula that takes into account wholesale electricity prices and system demand response incentives;

[0017] S330. Set the decision variable constraints of the aggregator, where the decision variable constraints include the retail electricity price upper limit constraint and the incentive reduction upper limit constraint;

[0018] S400. Solve the equilibrium of the master-slave game between aggregator users:

[0019] S410. Embed the forward propagation process of the deep neural network trained in step S230 into the aggregator revenue objective function constructed in step S320;

[0020] S420. Based on the differentiability of the aggregator's profit objective function to the aggregator's decision variables, a gradient projection algorithm is used to iteratively update the aggregator's decision variables starting from an initial feasible decision variable until the preset convergence conditions are met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

[0021] In some optional embodiments, in step S230, the structure of the deep neural network includes:

[0022] An encoding module, used for extracting features from input time series data and static feature data;

[0023] An attention module, connected after the encoding module, is used to perform weighted processing on the extracted features;

[0024] A decoding module is connected to the attention module and is used to output the predicted air conditioning power and the predicted reduction amount.

[0025] In some optional embodiments, the encoding module uses a one-dimensional convolutional neural network to extract time series features of retail electricity prices, curtailment incentives and weather forecast data, and uses a multi-layer perceptron to encode static features such as building envelope parameters and air-conditioning unit rated power.

[0026] In some optional embodiments, the attention module is a multi-head self-attention mechanism module.

[0027] In some optional embodiments, in step S230, the output of the deep neural network also includes a predicted indoor temperature sequence, and in step S210, the thermodynamic balance constraint of the lower-level user original optimization model is based on a resistance-capacitance (RC) model to characterize the relationship between indoor temperature and air conditioning cooling or heating capacity.

[0028] In some optional embodiments, when training the deep neural network in step S230, the loss function used includes:

[0029] The mean squared error between the predicted air conditioning power output by the deep neural network and the optimal air conditioning power in the training scene samples;

[0030] The mean squared error between the predicted load reduction output by the deep neural network and the corresponding load reduction in the training scenario samples.

[0031] In some optional embodiments, in step S210, the lower-layer user original optimization model further includes a linear constraint for describing whether the user participates in demand response and how much power is contributed. The linear constraint is implemented by introducing Boolean variables and large M parameters.

[0032] In some optional embodiments, in step S420, the gradient projection algorithm calculates the gradient of the aggregator profit objective function with respect to the aggregator decision variable by automatic differentiation technology at each iteration.

[0033] In some optional embodiments, the grid electricity price information collected in step S110 includes the day-ahead clearing electricity price and the real-time time-of-use electricity price; the upper and lower limits of user comfort collected in step S120 are used as hard constraints on indoor temperature in the lower-level user original optimization model of step S210 or as flexible penalty items in the optimization objective.

[0034] In some optional embodiments, in step S230, the deep neural network sets a gated thermal buffer unit between the output of the attention module and the input of the decoding module. The calculation formula of the gated thermal buffer unit is:

[0035]

[0036] where g t is the learnable gating vector; σ is the Sigmoid function; x t , x t-1 It is an intermediate variable in the neural network transmission process, and ⊙ is the element-by-element product, which is used to ensure the physical smoothness of the air conditioner power trajectory change.

[0037] In some optional embodiments, in step S320, the aggregator's profit objective function is specifically calculated as follows: (retail electricity price minus wholesale electricity price) multiplied by the group's predicted total air-conditioning power for each time period within the preset scheduling cycle, plus (system demand response subsidy minus unit load reduction incentive) multiplied by the group's predicted total reduction, and then accumulated.

[0038] In some optional embodiments, in step S420, the preset convergence condition is: the change in the vector norm of the aggregator decision variable in two adjacent iterations is less than a preset threshold.

[0039] The embodiment of the present invention further provides a massive air conditioning load aggregator user balanced scheduling system based on learning optimization and differentiable game, including:

[0040] Information perception and environment building modules, configured to:

[0041] Collect system-side data, including weather forecast data within a preset time range, the grid's day-ahead and real-time electricity prices, and demand response subsidy prices issued by the system operator;

[0042] Collecting user-side data of at least one air-conditioning user, the user-side data including building envelope parameters, air-conditioning unit rated power, thermal inertia coefficient, indoor temperature initial value, upper and lower limits of comfort temperature, historical baseline load, and user sensitivity coefficient to comfort loss of at least one air-conditioning user;

[0043] Integrate system-side data and user-side data to generate environmental status information;

[0044] The deep learning model module for lower-tier user air conditioning load response is configured to:

[0045] Storing and calling a pre-trained deep neural network, the deep neural network is obtained by: establishing a lower-level user original optimization model for each of at least one air conditioning user, the lower-level user original optimization model using the retail electricity price and curtailment incentive issued by the aggregator as input signals, minimizing the user's comprehensive cost taking comfort into account as the optimization goal, and imposing upper and lower constraints on air conditioning power, upper and lower constraints on indoor temperature, and thermodynamic balance constraints; generating training scenario samples offline, the training scenario samples including the optimal air conditioning power sequence and corresponding curtailment amount for each air conditioning user obtained by solving the lower-level user original optimization model under different input signal combinations; and performing training based on the training scenario samples;

[0046] The deep neural network receives retail electricity prices and curtailment incentive signals issued by aggregators, as well as environmental status information, as input during operation. It outputs the predicted air conditioning power and predicted curtailment amount for each air conditioning user, and has the characteristic of being differentiable with respect to the input.

[0047] The upper-layer aggregator revenue optimization model building module is configured to:

[0048] receiving aggregator decision variables set by a user, the decision variables including a time-of-use retail electricity price and a unit load reduction incentive within a preset dispatch period;

[0049] Constructing the aggregator's revenue objective function. This objective function is obtained by substituting the predicted total air conditioning power and predicted total curtailment of the group of air conditioning users, as output by the deep learning model module for the air conditioning load response of the lower-level users, into the revenue calculation formula that takes into account the wholesale electricity price and system demand response incentives.

[0050] receiving the aggregator decision variable constraints set by the user, where the decision variable constraints include a retail electricity price cap constraint and a curtailment incentive cap constraint;

[0051] The master-slave game equilibrium solving module is configured to:

[0052] The forward propagation process of the lower-level user air conditioning load response deep learning model module is embedded in the aggregator revenue objective function constructed by the upper-level aggregator revenue optimization model construction module;

[0053] Based on the differentiability of the aggregator's profit objective function to the aggregator's decision variables, a gradient projection algorithm is adopted. Starting from an initial feasible decision variable, the aggregator's decision variables are iteratively updated until the preset convergence conditions are met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

[0054] An embodiment of the present invention also provides a computer program product comprising computer executable instructions. When the instructions are executed by a processor, the processor executes the above-mentioned method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game.

[0055] An embodiment of the present invention further provides an electronic device, including:

[0056] a memory storing a computer program;

[0057] The processor is configured to implement the above method when executing the computer program.

[0058] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention.

[0059] The method, system, program product, and electronic device for balancing the scheduling of massive air-conditioning load aggregators based on learning optimization and differentiable game have the following beneficial effects:

[0060] The present invention provides a method for balancing the scheduling of massive air-conditioning load aggregators based on learning optimization and differentiable games. It replaces the complex optimization solution of massive users at the lower level with a deep learning model, thereby improving the solution efficiency and scalability. By utilizing the differentiable characteristics of the deep learning model, the optimization problem of the upper-level aggregator can be efficiently solved by the gradient method, and can quickly converge to a high-quality master-slave game equilibrium solution. The deep learning model embeds a differentiable physical model and a loss function design guided by physical constraints, ensuring that the air-conditioning load behavior and indoor temperature changes predicted by the model are more in line with actual physical laws and user comfort requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Other features, objects and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0062] Figure 1This is a flow chart of a method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to an embodiment of the present invention;

[0063] Figure 2 It is a structural diagram of a massive air-conditioning load aggregator-user balanced scheduling system based on learning optimization and differentiable game according to an embodiment of the present invention. DETAILED DESCRIPTION

[0064] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0065] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0066] The flowcharts shown in the accompanying drawings are merely exemplary and do not necessarily include all steps. For example, some steps may be decomposed, while some steps may be combined or partially combined. Therefore, the actual execution order may change according to actual circumstances.

[0067] In the context of electricity demand response, the optimal scheduling problem of massive air-conditioning loads can be modeled as a Stackelberg game between aggregators and users. As the leader, the aggregator guides follower users to adjust their air-conditioning energy consumption behavior by formulating strategies such as retail electricity prices and reducing incentives. Traditional solution methods face bottlenecks in computational complexity, making it difficult to achieve real-time scheduling. Learning optimization methods train deep neural networks to approximately replace the optimization solution process of lower-level users, thereby significantly reducing the computational burden. Differentiable programming technology ensures the differentiability of the objective function, allowing upper-level aggregators to efficiently optimize using gradient information and quickly converge to a high-quality Stackelberg equilibrium (master-slave game equilibrium) solution. At the same time, embedding the physical model into the deep neural network ensures that the model's prediction results conform to actual physical laws, thereby avoiding unreasonable scheduling results and improving user experience.

[0068] like Figure 1As shown, an embodiment of the present invention provides a method for balancing the scheduling of massive air conditioning loads for aggregators and users based on learning optimization and differentiable games. The method implements optimized scheduling for demand response management of massive distributed air conditioning loads, including the following steps:

[0069] S100. Perceive and construct environmental information, including:

[0070] S110. Collect system-side data, including weather forecast data within a preset time range, the day-ahead and real-time electricity prices of the power grid, and demand response subsidy prices issued by the system operator;

[0071] S120. Collect user-side data of at least one air-conditioning user, the user-side data including building envelope parameters, air-conditioning unit rated power, thermal inertia coefficient, indoor temperature initial value, upper and lower limits of comfort temperature, historical baseline load, and user sensitivity coefficient to comfort loss of at least one air-conditioning user;

[0072] S130. Integrate system-side data and user-side data to generate environmental status information;

[0073] In this embodiment of the present invention, environmental information is first perceived and constructed to provide comprehensive input for subsequent decision-making. This environmental information includes both acquired system-side data and user-side data. System-side data encompasses macro information such as weather forecasts, grid electricity prices, and demand response subsidies, while user-side data encompasses individual information such as building thermal parameters, air conditioning equipment parameters, and user comfort preferences. This heterogeneous data is integrated to form environmental state information, which provides input for lower-level models and upper-level optimization.

[0074] S200. Build and train a deep learning model for lower-level user air conditioning load response, including:

[0075] S210. For each of the at least one air conditioning user, establish a lower-level user primitive optimization model. The lower-level user primitive optimization model uses the retail electricity price and curtailment incentive issued by the aggregator as input signals, minimizes the user's comprehensive cost taking comfort into account as the optimization objective, and imposes upper and lower constraints on air conditioning power, upper and lower constraints on indoor temperature, and a thermodynamic balance constraint.

[0076] S220. Offline generation of training scenario samples, the training scenario samples include the optimal air conditioning power sequence and the corresponding reduction amount of each air conditioning user obtained by solving the original optimization model of the lower user under different input signal combinations;

[0077] S230. Based on the training scenario samples, a deep neural network is trained, so that the deep neural network receives the retail electricity price and curtailment incentive signal issued by the aggregator and the environmental status information as input, and outputs the predicted air conditioning power and predicted curtailment amount for each air conditioning user, and the deep neural network has the characteristic that the output is differentiable with respect to the input;

[0078] In an embodiment of the present invention, a deep learning model of the lower-level user air conditioning load response is constructed and trained, with the goal of quickly and accurately predicting the user's response under different aggregator signals. To this end, an original optimization model is established for each user, which aims to minimize the comprehensive cost taking comfort into account and imposes relevant constraints. The model is used to generate training samples offline, which contain the optimal air conditioning power sequence and reduction amount under different scenarios. Subsequently, a deep neural network is trained based on these samples, enabling it to receive aggregator signals and environmental state information as input and output predicted air conditioning power and reduction amount. Importantly, the deep neural network has the property that the output is differentiable with respect to the input, which provides gradient information for upper-level optimization.

[0079] S300. Build an upper-layer aggregator revenue optimization model:

[0080] S310. Set the decision variables of the aggregator, which include the time-of-use retail electricity price and unit load reduction incentive within the preset scheduling period;

[0081] S320. Constructing a revenue objective function for the aggregator, the revenue objective function comprises substituting the predicted total air conditioning power and predicted total reduction of the group of air conditioning users output by the deep neural network trained in step S230 into a revenue calculation formula that takes into account wholesale electricity prices and system demand response incentives;

[0082] S330. Set the decision variable constraints of the aggregator, where the decision variable constraints include the retail electricity price upper limit constraint and the incentive reduction upper limit constraint;

[0083] In this embodiment of the present invention, a revenue optimization model for the upper-layer aggregator is constructed in step S300. In this model, the aggregator's decision variables are the time-of-use retail electricity price and the unit load reduction incentive. The goal is to maximize its own revenue while meeting constraints such as the electricity price and the incentive cap.

[0084] S400. Solve the equilibrium of the master-slave game between aggregator users:

[0085] S410. Embed the forward propagation process of the deep neural network trained in step S230 into the aggregator revenue objective function constructed in step S320;

[0086] S420. Based on the differentiability of the aggregator's profit objective function to the aggregator's decision variables, a gradient projection algorithm is used to iteratively update the aggregator's decision variables starting from an initial feasible decision variable until the preset convergence conditions are met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

[0087] In this embodiment of the present invention, step S400 solves the Stackelberg equilibrium for the aggregator and user. To achieve efficient solution, the forward propagation process of a deep neural network is embedded in the aggregator's revenue objective function, making the objective function differentiable with respect to the decision variables. Leveraging this differentiability, a gradient projection algorithm is used to iteratively update the decision variables until the preset convergence conditions are met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

[0088] In specific implementation, the meteorological forecast data in the system-side data can be obtained by combining numerical weather forecast models with machine learning correction. The power grid electricity price information can be received synchronously from the power trading center or independent system operator. The collection of user-side data can be carried out through secure encrypted channels such as smart gateways, smart thermostats or user apps. The original optimization model can be in the form of mixed integer programming (MIP) or nonlinear programming (NLP), and the solver can be commercial optimization software such as Gurobi or CPLEX. The deep neural network can adopt architectures such as convolutional neural network (CNN), recurrent neural network (RNN) or attention mechanism, and the training algorithm can use optimizers such as Adam or RMSProp. The step size in the gradient projection algorithm can be adaptively determined using the Armijo criterion or the Barzilai-Borwein method. The convergence condition can be set as the change in the vector norm of the decision variable between two adjacent iterations is less than a preset threshold.

[0089] Through the above steps, the present invention achieves rapid, accurate, and economical optimal scheduling and dynamic pricing of massive air conditioning loads, while satisfying multiple physical and market constraints. On the one hand, the use of deep learning models replaces the complex optimization solutions for each user at the lower level, significantly improving solution efficiency and scalability. On the other hand, differentiable programming ensures the solvability of the upper-level optimization problem and enables rapid convergence to a high-quality Stackelberg equilibrium solution. This method can improve the operational efficiency of load aggregators, enhance the flexibility and stability of the power grid, and ensure basic user comfort during the demand response process.

[0090] In some embodiments, the structure of the deep neural network in step S230 includes an encoding module, an attention module, and a decoding module. The encoding module is used to extract features from input data, which includes time series data and static feature data. Time series data includes retail electricity prices, curtailment incentives, and weather forecast data, and static feature data includes building envelope parameters and air conditioning unit rated power. The attention module is connected after the encoding module and is used to weight the extracted features, focusing on the information most important for the current decision, thereby improving the model's prediction accuracy. The decoding module is connected after the attention module and is used to output predicted air conditioning power and predicted curtailment amount. The encoding module can adopt, for example, a convolutional neural network (CNN), a recurrent neural network (RNN), or a Transformer architecture. The attention module can adopt, for example, a multi-head self-attention mechanism (Multi-Head Self-Attention) or a cross-attention mechanism. The decoding module can adopt, for example, a recurrent neural network (RNN) or a Transformer architecture. Different module combinations can adapt to different application scenarios and data characteristics, achieving flexible model design. By extracting the features of input data through the encoding module, focusing on important information with the attention module, and outputting the prediction results through the decoding module, the prediction accuracy and generalization ability of the deep neural network can be effectively improved, thereby providing a more accurate basis for subsequent optimization scheduling.

[0091] In some embodiments, the encoding module uses a one-dimensional convolutional neural network (1D CNN) to extract features from time-series data such as retail electricity prices, curtailment incentives, and weather forecast data, and a multi-layer perceptron (MLP) to encode static features such as building envelope parameters and air conditioning unit rated power. 1D CNN effectively captures temporal dependencies in time-series data, such as changing trends in electricity prices, cyclical fluctuations in incentives, and the impact of meteorological factors. Multi-layer perceptrons excel at processing static features, converting building parameters and equipment parameters into high-dimensional embedding vectors. This strategy of using different encoding methods for different data types can better extract effective information from the input data and improve the model's prediction accuracy. In specific implementations, 1D CNNs can use convolution kernels of varying sizes, numbers of convolution layers, and activation functions to adapt to different time-series data characteristics. Multi-layer perceptrons can use different numbers of hidden layers, neurons, and activation functions to adapt to different combinations of static features. By rationally designing the 1D CNN and MLP structures and conducting effective training, the encoding module can extract more representative features, thereby improving the predictive ability of the deep learning model of the lower-level user air conditioning load response and providing a more accurate basis for the optimized scheduling of the upper-level aggregators.

[0092] In some embodiments, the attention module utilizes a multi-head self-attention mechanism. The multi-head self-attention mechanism is an attention mechanism that can extract input sequence information from different representation subspaces in parallel. Specifically, the multi-head self-attention mechanism first maps the input sequence into different subspaces through multiple linear transformations, then calculates attention weights in each subspace. Finally, the attention results from each subspace are concatenated and linearly transformed to obtain the final attention output. Compared with the traditional single-head attention mechanism, the multi-head self-attention mechanism can capture richer input sequence information, thereby improving the model's expressiveness and prediction accuracy. In the present invention, the multi-head self-attention mechanism can be used to capture complex dependencies between different types of input data, such as retail electricity prices, curtailment incentives, weather forecast data, building parameters, and equipment parameters. Through the multi-head self-attention mechanism, the model can focus on the information most important for the current decision and ignore irrelevant information, thereby improving prediction accuracy and generalization. In specific implementations, the multi-head self-attention mechanism can use different numbers of attention heads, different subspace dimensions, and different linear transformation methods to adapt to different application scenarios and data characteristics. By rationally designing the structure of the multi-head self-attention mechanism and conducting effective training, the deep neural network can better understand the complex relationship between the input data, thereby improving the predictive ability of the deep learning model of the lower-level user air-conditioning load response.

[0093] In some embodiments, the output of the deep neural network in step S230 includes not only the predicted air conditioning power and predicted reduction amount, but also a predicted indoor temperature sequence. Furthermore, the thermodynamic balance constraints of the lower-level user's original optimization model in step S210 are based on a resistor-capacitor (RC) model to characterize the relationship between indoor temperature and air conditioning cooling or heating capacity. The RC model is a commonly used simplified thermodynamic model that equates the room's thermal resistance and thermal capacitance to the resistance and capacitance in a circuit, respectively, thereby establishing a dynamic relationship between indoor temperature and air conditioning power. Specifically, the RC model can be first-order or second-order. The first-order RC model has a simple structure and low computational complexity, making it suitable for scenarios with high real-time requirements. The second-order RC model can more accurately describe the dynamic changes in indoor temperature and is suitable for scenarios with high model accuracy requirements. The output of the predicted indoor temperature sequence by the deep neural network, combined with the thermodynamic balance constraints of the RC model, allows the deep neural network's learning process to be constrained by physical laws, improving the physical rationality of the model's predictions and avoiding the unreasonable scheduling results that may be generated by purely data-driven models. In specific implementations, the parameters of the RC model (such as thermal resistance and thermal capacitance) can be provided by the user, identified from historical data, or estimated based on a building type database. During the training process of the deep neural network, a physical consistency loss function can be used to penalize the deviation between the predicted indoor temperature and the indoor temperature calculated by the RC model, thereby further improving the physical rationality of the model prediction.

[0094] In some embodiments, when training the deep neural network in step S230, the loss function used consists of two parts: one is the mean squared error (MSE) between the predicted air conditioning power output by the deep neural network and the optimal air conditioning power in the training scenario samples, which measures the deviation between the model-predicted air conditioning power and the actual optimal power; the other is the mean squared error (MSE) between the predicted load reduction output by the deep neural network and the corresponding load reduction in the training scenario samples, which measures the deviation between the model-predicted indoor temperature and the actual indoor temperature. MSE is a commonly used loss function with the advantages of being simple to calculate, easy to optimize, and able to effectively guide the model to learn accurate prediction results. In addition to MSE, other loss functions can also be used, such as mean absolute error (MAE) and Huber loss. By simultaneously optimizing the predicted air conditioning power and predicted indoor temperature, and incorporating the thermodynamic equilibrium constraints of the RC model, the deep neural network learning process can be made more stable, improving the accuracy and physical rationality of the model predictions, thereby providing a more reliable basis for subsequent optimization scheduling. In practical applications, the weights of predicted air conditioning power and predicted indoor temperature in the loss function can be adjusted according to different needs and scenarios to achieve optimal prediction results.

[0095] In some embodiments, the lower-level user original optimization model in step S210 also includes linearized constraints describing whether the user participates in demand response and how much power they contribute. These linearized constraints are implemented by introducing Boolean variables and large-M parameters. In actual demand response scenarios, whether a user participates in demand response and how much power they contribute is typically a discrete decision problem. To accurately describe this behavior in the optimization model and ensure the solvability of the model, the present invention implements linearized constraints by introducing Boolean variables and large-M parameters. Specifically, a Boolean variable is introduced to indicate whether the user participates in demand response. If the user participates in demand response, the variable takes the value of 1, otherwise it takes the value of 0. The large-M parameter is a sufficiently large constant that links the Boolean variable to the user's demand response contribution. By properly setting the expression of the linearized constraints, accurate modeling of the user's demand response behavior can be achieved and the solvability of the model can be ensured. This method not only effectively describes the user's discrete decision-making behavior but also transforms complex mixed-integer programming problems into linear programming problems, thereby reducing the solution difficulty and improving the solution efficiency. In specific implementations, the value of the large-M parameter needs to be adjusted according to actual conditions to ensure the effectiveness of the constraints and the accuracy of the model. Furthermore, the specific form of the linearization constraint can be adjusted to suit different demand response scenarios, adapting to varying user behavior patterns and incentive mechanisms. By introducing linearization constraints, users' demand response behaviors can be more accurately described, allowing the underlying user optimization model to more realistically reflect their energy decisions, providing a more accurate basis for the optimized scheduling of higher-level aggregators.

[0096] In some embodiments, in step S420, the gradient projection algorithm calculates the gradient of the aggregator revenue objective function with respect to the aggregator decision variables at each iteration using automatic differentiation techniques. Automatic differentiation (AD) is a general method for calculating function derivatives. It uses the chain rule to differentiate each basic operation in a numerical computation process and then combines these derivatives to obtain the derivative of the entire function. Compared with traditional numerical differentiation methods, automatic differentiation has higher accuracy and efficiency and can handle complex function forms. In the present invention, due to the differentiable nature of deep neural networks, the forward propagation process of the deep neural network can be embedded in the aggregator revenue objective function, making the objective function differentiable with respect to the aggregator decision variables. Automatic differentiation techniques can conveniently calculate the gradient of the objective function with respect to the decision variables without manually deriving complex Jacobian matrices. In specific implementations, existing automatic differentiation frameworks, such as TensorFlow and PyTorch, can be used to implement gradient calculation. These frameworks provide a wealth of automatic differentiation tools and interfaces that facilitate the construction and training of deep neural networks and the calculation of the gradient of the objective function. Through automatic differentiation technology, the gradient information of the aggregator's profit objective function with respect to the decision variables can be efficiently obtained, providing accurate guidance for the iterative update of the gradient projection algorithm, thereby improving the solution efficiency and the quality of the equilibrium solution.

[0097] In some embodiments, the grid electricity price information collected in step S110 includes day-ahead clearing prices and real-time time-of-use prices. Day-ahead clearing prices refer to the electricity prices for various future time periods determined by the electricity market the day before, while real-time time-of-use prices refer to the electricity prices for various time periods published in real time by the electricity market. These two types of price information can reflect electricity supply and demand and market price fluctuations, providing a basis for aggregators to formulate reasonable retail electricity prices and incentive strategies. Furthermore, the user comfort upper and lower bounds collected in step S120 can be used as hard constraints on indoor temperature in the lower-level user's original optimization model in step S210, or as flexible penalty terms in the optimization objective. When used as hard constraints, indoor temperature must be strictly within the user-defined comfort range; when used as flexible penalty terms, indoor temperature can deviate from the comfort range to a certain extent, but with a penalty. This approach balances user comfort needs with the economic benefits of the aggregator, making the demand response process more flexible and sustainable. In implementation, the appropriate approach can be selected based on user preferences and actual circumstances. When users have high comfort requirements, hard constraints can be used to ensure a good energy experience. When users are price-sensitive, flexible penalties can be used to improve the economic efficiency of demand response. Furthermore, the strictness of comfort constraints can be dynamically adjusted based on time periods and demand response events, enabling more refined demand response management. By comprehensively considering grid electricity price information and user comfort preferences, aggregators can formulate more reasonable retail electricity prices and incentive strategies, thereby achieving the multiple goals of grid peak load shifting, improving energy efficiency, and ensuring user comfort.

[0098] In some embodiments, in step S230, the deep neural network sets a gated thermal buffer unit between the output of the attention module and the input of the decoding module. The calculation formula of the gated thermal buffer unit is:

[0099]

[0100] where g t is the learnable gating vector; σ is the Sigmoid function; x t , x t-1 It is an intermediate variable in the neural network transmission process, which is used to ensure the physical smoothness of the air conditioner power trajectory change. Since the air conditioner has a certain inertia during operation, frequent switching actions will not only affect the service life of the air conditioner, but also reduce the user's comfort. In order to better simulate the inertia of the air conditioner start and stop and avoid too frequent switching actions, the present invention introduces a gated thermal buffer unit in the deep neural network. This unit uses a learnable gate vector g tTo control the unit output at the current moment, it can retain the output information of the attention module and inherit the unit output information of the previous moment. Among them, the Sigmoid function σ can limit the value of the gate vector to between 0 and 1, and ⊙ is the element-by-element product, which is used to achieve weighted fusion of different information. The gated thermal buffer unit can effectively smooth the power output of the deep neural network, making it more consistent with the physical laws of actual operation and avoiding the overly frequent switching actions that may be generated by purely data-driven models. In specific implementations, the gate vector can be learned through a multi-layer perceptron (MLP) or other neural network structures, and the specific implementation of the gated thermal buffer unit can be adjusted according to different application scenarios and data characteristics. By introducing the gated thermal buffer unit, the physical rationality of the air-conditioning load behavior predicted by the deep neural network can be effectively improved, thereby providing a more reliable basis for the optimized scheduling of upper-level aggregators and improving user comfort.

[0101] In some embodiments, the aggregator's revenue objective function in step S320 is specifically calculated as follows: (retail electricity price minus wholesale electricity price) multiplied by the group's predicted total air conditioning power for each time period within the preset scheduling cycle, plus (system demand response subsidy minus unit load reduction incentive) multiplied by the group's predicted total reduction, and then summed. This calculation formula accurately describes the aggregator's revenue sources during the demand response process. (Retail electricity price minus wholesale electricity price) multiplied by the group's predicted total air conditioning power represents the aggregator's profit from the retail electricity price difference; (system demand response subsidy minus unit load reduction incentive) multiplied by the group's predicted total reduction represents the subsidy revenue the aggregator receives from demand response. Adding these two revenue components yields the aggregator's total revenue. This objective function can guide aggregators to fully consider market prices, subsidy policies, and user response behavior when formulating retail electricity prices and reduction incentive strategies, thereby maximizing their operating revenue. To more accurately reflect actual operating conditions, this revenue objective function can also further consider the aggregator's other operating costs, such as communication costs and maintenance costs, and deduct them from the calculation process. This profit function provides an accurate optimization target for the upper-level optimization, so that the final Stackelberg equilibrium solution can better balance the aggregator's profit and the user's comfort.

[0102] In some embodiments, the preset convergence condition in step S420 is: the change in the vector norm of the aggregator's decision variables between two consecutive iterations is less than a preset threshold. During the iterative process of the gradient projection algorithm, the aggregator's decision variables (including the time-of-use retail electricity price and the unit load reduction incentive) are continuously updated, gradually approaching the Stackelberg equilibrium solution. To determine whether the iterative process has converged to the equilibrium solution, the present invention uses the vector norm as a convergence criterion. The vector norm measures the magnitude of a vector. When the change in the vector norm of the decision variables between two consecutive iterations is less than a preset threshold, the iterative process is considered to have converged. The obtained decision variables are the optimal pricing and incentive strategy for the aggregator under the approximate Stackelberg equilibrium. The vector norm can take different forms, such as the 1-norm, the 2-norm, or the infinity norm. Different norm forms have different sensitivities to the components of the vector and can be selected based on actual conditions. In addition to the vector norm, other convergence criteria can also be used, such as the improvement in the objective function value being less than a certain threshold or reaching the maximum number of iterations. By setting reasonable convergence conditions, the gradient projection algorithm can be guaranteed to converge to a high-quality Stackelberg equilibrium solution within a limited number of iterations, thereby providing a reliable decision-making basis for aggregators.

[0103] like Figure 2 As shown, an embodiment of the present invention also provides a massive air-conditioning load aggregator-user balanced scheduling system based on learning optimization and differentiable game. The system consists of an information perception and environment construction module M100, a lower-level user air-conditioning load response deep learning model module M200, an upper-level aggregator revenue optimization model construction module M300, and a Stackelberg equilibrium solution module M400, which work together to achieve efficient scheduling and optimization of massive air-conditioning loads.

[0104] The Information Perception and Environment Construction Module (M100) collects and integrates system-side and user-side data to construct environmental status information. System-side data includes weather forecasts, grid electricity prices, and demand response subsidy prices, reflecting changes in the external environment. User-side data, including building envelope parameters, air conditioning unit rated power, thermal inertia coefficients, initial indoor temperature values, upper and lower comfort temperature limits, historical baseline loads, and user sensitivity to comfort loss, describes individual user characteristics. By collecting and integrating this multi-dimensional data, the module provides a comprehensive and accurate information foundation for subsequent optimized scheduling.

[0105] The core function of the lower-tier user air conditioning load response deep learning model module M200 is to store and call a pre-trained deep neural network. This deep neural network is obtained through offline training. Its training data comes from the optimal air conditioning power sequence and corresponding curtailment amount for each air conditioning user, obtained by solving the original optimization model of the lower-tier users. During operation, this deep neural network receives the retail electricity price and curtailment incentive signal issued by the aggregator as input, as well as environmental status information. It outputs the predicted air conditioning power and predicted curtailment amount for each air conditioning user. The deep neural network has the characteristic of differentiability of the output with respect to the input, providing a basis for the optimization decision of the upper-tier aggregator.

[0106] The upper-level aggregator revenue optimization model construction module, M300, receives user-defined aggregator decision variables (including time-of-use retail electricity prices and unit load reduction incentives), constructs the aggregator's revenue objective function, and sets constraints on the aggregator's decision variables (including upper limits on retail electricity prices and incentive reduction). This module provides the optimization objective and constraint boundaries for the Stackelberg equilibrium solver module, M400.

[0107] The core function of the Stackelberg equilibrium solution module M400 is to embed the forward propagation process of the lower-level user air-conditioning load response deep learning model module M200 into the aggregator profit objective function constructed by the upper-level aggregator profit optimization model construction module M300. Based on the differentiability of the objective function with respect to the aggregator's decision variables, the gradient projection algorithm is used to iteratively update the aggregator's decision variables until the preset convergence conditions are met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

[0108] During specific implementation, each module can adopt different hardware and software implementation methods. For example, the information perception and environment construction module M100 can adopt sensor networks, data acquisition systems and databases; the lower-level user air-conditioning load response deep learning model module M200 can adopt GPUs, CPUs and deep learning frameworks; the upper-level aggregator revenue optimization model construction module M300 and the Stackelberg equilibrium solution module M400 can adopt optimization algorithm libraries and high-performance computing platforms.

[0109] Through the collaborative work of the above modules, the system can achieve efficient scheduling and optimization of massive air-conditioning loads, improve the operational efficiency of load aggregators, enhance the flexibility and stability of the power grid, and ensure the basic comfort of users when participating in the demand response process.

[0110] An embodiment of the present invention also provides a computer program product comprising computer-executable instructions. When executed by a processor, these instructions cause the processor to perform the aforementioned method for balanced scheduling of massive air conditioning load aggregators and users based on learning optimization and differentiable games. A computer program product refers to a combination of computer software, firmware, and hardware that can implement a specific function. In the present invention, a computer program product refers to a storage medium containing computer-executable instructions that can be read and executed by a processor, thereby implementing the method for balanced scheduling of massive air conditioning load aggregators and users proposed in the present invention. The computer program product can utilize various forms of storage media, such as read-only memory (ROM), random access memory (RAM), hard disk, optical disk, flash drive, etc. When the processor executes the instructions in the computer program product, it can implement the aforementioned scheduling method, including steps such as information perception and environment construction, construction of a deep learning model for lower-level user air conditioning load responses, construction of an upper-level aggregator revenue optimization model, and solving the Stackelberg equilibrium. Through the computer program product, the scheduling method of the present invention can be conveniently deployed on various computing platforms and smart terminals, enabling intelligent management and optimized scheduling of massive air conditioning loads.

[0111] An embodiment of the present invention further provides an electronic device, which may be a dedicated energy management server, a computing node in a cloud platform, or an embedded controller. The electronic device includes:

[0112] Processor: For example, a central processing unit (CPU), graphics processing unit (GPU), application-specific integrated circuit (ASIC), field-programmable gate array (FPGA), or digital signal processor (DSP). A processor is the control center of an electronic device, used to execute computer program instructions stored in memory.

[0113] Memory: For example, random access memory (RAM), read-only memory (ROM), solid-state drive (SSD), or hard disk drive (HDD). Memory is used to store an operating system, application programs, and the computer programs and related data required to execute the methods of the present invention. Specifically, the memory stores the computer program that implements the methods described above.

[0114] In some embodiments, the electronic device further comprises:

[0115] Communication interface: For example, Ethernet interface, Wi-Fi module, cellular network module (such as 4G / 5G), etc. Communication interface is used to exchange data with external devices or networks. For example, it can receive demand response subsidy prices and meteorological data from system operators, receive air conditioning user data from user-side smart terminals, and send scheduling results to the aggregator management platform.

[0116] Input / output interface: such as display interface, keyboard interface, mouse interface, etc., used for human-computer interaction or connecting peripheral devices.

[0117] In a specific working scenario, when the electronic device executes a computer program stored in the memory, the processor operates in the following manner to implement the above method:

[0118] Data Acquisition and Environmental Information Generation: The processor receives system-side data (such as weather forecasts, grid electricity prices, and DR subsidies) and user-side data from multiple air conditioning users (such as building parameters, air conditioning parameters, comfort preferences, and historical loads) through a communication interface. The received data is temporarily stored in memory. The processor then executes data integration and preprocessing procedures to integrate this heterogeneous data into a unified format for environmental status information to be used by subsequent models.

[0119] Lower-level deep learning model construction and training:

[0120] The processor executes a pre-set training procedure. This procedure first constructs a primitive optimization model for each air conditioner user, such as a mixed integer programming model that considers comfort and electricity costs. This model definition is also stored in memory. Then, by simulating different aggregator signals, including retail electricity prices and curtailment incentives, the processor's computing power is used to solve these primitive optimization models, generating a large number of training scenario samples, including optimal air conditioner power sequences and curtailment amounts. These samples are also stored in memory.

[0121] Based on these samples, the processor loads and trains a deep learning model, such as a neural network with an encoder-attention-decoder architecture implemented in the TensorFlow or PyTorch framework. The trained model parameters are stored in memory. This deep learning model is designed to be differentiable with respect to input aggregator signals and environmental state information.

[0122] Construction of the upper-level aggregator revenue optimization model: The processor builds the upper-level optimization model in the memory based on the preset aggregator revenue objective function, taking into account the power purchase cost, power sales revenue, DR incentive benefits, and decision variables, including time-of-use retail electricity prices, unit load reduction incentives and their constraints.

[0123] Master-Slave Game Equilibrium Solution: The processor executes an equilibrium solution algorithm (such as the gradient projection algorithm). During this process, it embeds the forward propagation of the trained lower-level deep learning model into the upper-level aggregator revenue optimization model. Leveraging the differentiable nature of the deep learning model, the processor efficiently calculates the gradient of the revenue objective function with respect to the aggregator's decision variables and iteratively updates the decision variables until convergence. Ultimately, the optimal time-of-use retail electricity price and the optimal unit load reduction incentive are determined in the equilibrium state. These results are transmitted to the aggregator via a communication interface.

[0124] Through the above configuration and operation, the electronic device can efficiently and accurately execute the method for balancing the scheduling of aggregators and users of massive air-conditioning loads. The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for balancing the scheduling of massive air-conditioning load aggregators based on learning optimization and differentiable game, characterized by: The following steps are involved: Collecting system-side data and user-side data of at least one air-conditioning user and integrating the system-side data and the user-side data to generate environmental status information; Constructing and training a deep learning model for the lower-level user air conditioning load response, wherein the deep learning model predicts the user air conditioning load response based on the environmental state information and the signal released by the aggregator, and has the characteristic that the output is differentiable with respect to the input; Constructing an upper-layer aggregator revenue optimization model, wherein the upper-layer aggregator revenue optimization model takes the aggregator revenue as a target, and its decision variables include signals issued by the aggregator that affect the user's air conditioning load response; The differentiable characteristics of the deep learning model are utilized to optimize the decision variables of the upper-layer aggregator revenue optimization model to obtain an equilibrium solution.

2. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 1 is characterized in that: The system-side data includes weather forecast data within a preset time range, the day-ahead electricity price and real-time electricity price of the power grid, and the demand response subsidy price issued by the system operator; the user-side data includes the building envelope parameters of the at least one air-conditioning user, the rated power of the air-conditioning unit, the cooling and heating inertia coefficients, the initial value of the indoor temperature, the upper and lower limits of the comfort temperature, the historical baseline load, and the user's sensitivity coefficient to comfort loss.

3. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 1 is characterized in that: The construction and training of the deep learning model for the lower-level user air conditioning load response includes: For each of the at least one air conditioning user, establishing a lower-level user original optimization model, wherein the lower-level user original optimization model uses the retail electricity price and curtailment incentive issued by the aggregator as input signals, minimizes the user's comprehensive cost taking comfort into account as an optimization objective, and imposes upper and lower constraints on air conditioning power, upper and lower constraints on indoor temperature, and a thermodynamic balance constraint; Offline generation of training scenario samples, wherein the training scenario samples include the optimal air conditioning power sequence and corresponding reduction amount of each air conditioning user obtained by solving the original optimization model of the lower-layer user under different input signal combinations; Based on the training scenario samples, the deep learning model is trained so that the deep learning model receives the retail electricity price and reduction incentive signal issued by the aggregator and the environmental status information as input, and outputs the predicted air conditioning power and predicted reduction amount of each air conditioning user.

4. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 3 is characterized in that: The construction of the upper-layer aggregator revenue optimization model includes: The decision variables of the aggregator are set as the time-of-use retail electricity price and the unit load reduction incentive within a preset dispatch period; Constructing a revenue objective function for the aggregator, the revenue objective function comprising substituting the predicted total air conditioning power and predicted total curtailment of the group of air conditioning users output by the deep learning model into a revenue calculation formula that takes into account wholesale electricity prices and system demand response incentives; Decision variable constraints of the aggregator are set, where the decision variable constraints include a retail electricity price upper limit constraint and a curtailment incentive upper limit constraint.

5. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 4 is characterized in that: Solving the master-slave game equilibrium of aggregator users includes: Embedding the forward propagation process of the deep learning model into the aggregator revenue objective function; Based on the differentiability of the aggregator's profit objective function with respect to the aggregator's decision variables, a gradient projection algorithm is adopted, starting from an initial feasible decision variable, to iteratively update the aggregator's decision variables until a preset convergence condition is met, thereby obtaining the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state as the equilibrium solution.

6. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 3 is characterized in that: The structure of the deep learning model includes: An encoding module, used for extracting features from input time series data and static feature data; an attention module, connected to the encoding module, for performing weighted processing on the extracted features; A decoding module is connected to the attention module and is used to output the predicted air conditioning power and the predicted reduction amount.

7. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 6 is characterized in that: The deep learning model includes training a deep neural network, wherein the deep neural network sets a gated thermal buffer unit between the output of the attention module and the input of the decoding module. The calculation formula of the gated thermal buffer unit is Used to ensure the physical smoothness of changes in air conditioning power trajectory.

8. The method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game according to claim 3 is characterized in that: When training the deep learning model, the loss functions used include: The mean square error between the predicted air conditioning power output by the deep learning model and the optimal air conditioning power in the training scenario sample; The mean square error between the predicted load reduction output by the deep learning model and the corresponding load reduction in the training scenario samples.

9. A massive air conditioning load aggregator user balanced scheduling system based on learning optimization and differentiable game, characterized by: The steps for implementing the method for balancing the scheduling of massive air-conditioning load aggregators and users based on learning optimization and differentiable game as described in any one of claims 1 to 8 include: An information perception and environment construction module is configured to collect system-side data and user-side data and generate environmental status information; a lower-level user air conditioning load response deep learning model module, configured to store and call a pre-trained deep neural network, wherein the deep neural network receives as input the retail electricity price and curtailment incentive signal issued by the aggregator and environmental status information, and outputs the predicted air conditioning power and predicted curtailment amount of each air conditioning user, with the output being differentiable with respect to the input; an upper-layer aggregator revenue optimization model construction module, configured to receive aggregator decision variables set by a user and construct a revenue objective function for the aggregator; The master-slave game equilibrium solving module is configured to embed the forward propagation process of the lower-level user air-conditioning load response deep learning model module into the aggregator profit objective function constructed by the upper-level aggregator profit optimization model construction module, and based on the differentiability of the aggregator profit objective function with respect to the aggregator decision variables, adopt a gradient projection algorithm to obtain the optimal time-of-use retail electricity price and the optimal unit load reduction incentive in the equilibrium state.

10. A computer program product, characterized in that The method comprises computer executable instructions, which, when executed by a processor, enable the processor to execute the massive air-conditioning load aggregator-user balanced scheduling method based on learning optimization and differentiable game as described in any one of claims 1 to 8.

11. An electronic device, characterized in that: include: a memory storing a computer program; A processor, configured to implement the method according to any one of claims 1 to 8 when executing the computer program.

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