A distributed super-gradient demand response regulation method, system, medium and device

Abstract

The application discloses a kind of distributed super-gradient demand response regulation methods, system, medium and equipment, belong to electric power system optimization technical field, the method is: obtaining the load data of demand side, and according to the load data, construct Stackelberg game model;According to the preset distributed super-gradient descent algorithm, iteratively solve the Stackelberg game model, output the load regulation strategy set of demand side;Wherein, the load regulation strategy set includes the load regulation strategy of each load resource;According to the load regulation strategy set, the terminal controller of each load resource corresponding to demand side is regulated, and load regulation is completed.Therefore, by implementing the present application, it can solve the problem of slow response speed and insufficient timeliness when the large-scale demand side resource demand response regulation of the existing technology is implemented.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization technology and relates to a distributed super-gradient demand response control method, system, medium and equipment. Background Technology

[0002] The continuously rising proportion of renewable energy generation has exacerbated the stochastic fluctuations in both the supply and demand sides of the power system, making the maintenance of dynamic grid balance a core challenge for the industry. Against this backdrop, demand response technology, with its flexible adjustment characteristics, has become a key regulatory tool for enhancing grid resilience. Load aggregators, as the main entities aggregating demand-side resources, need to incentivize resources such as electric vehicle clusters and adjustable industrial loads to participate in grid interaction through dynamic pricing mechanisms. The two-level game model, as the core framework describing the multiple game relationships between aggregators and distributed resource entities, has significant application value in system modeling.

[0003] Currently, solutions to two-level game problems generally employ two approaches: commercial mathematical solvers (such as CPLEX) or swarm intelligence algorithms (such as particle swarm optimization). The former requires relaxation of complementary constraints using the Big M method and introduces a large number of integer variables, leading to the curse of dimensionality and limiting its applicability to small-scale scenarios. The latter, while avoiding complex mathematical transformations, suffers from drawbacks such as large fluctuations in solution quality and uncontrollable convergence trajectories. Especially in scenarios involving large-scale demand-side resources, the frequency of individual game equilibrium interactions surges, causing traditional algorithms to take excessively long times per solution iteration. Both of these methods fail to meet the timeliness requirements of real-time regulation, becoming key bottlenecks restricting the large-scale application of demand response. Summary of the Invention

[0004] This application provides a distributed super-gradient demand response control method, system, medium, and device, which can solve the problems of slow response speed and insufficient timeliness in the existing technology when controlling large-scale demand-side resource demand response in power systems.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a distributed super-gradient demand response control method, comprising:

[0006] Obtain demand-side load data and construct a Stackelberg game model based on the load data;

[0007] The Stackelberg game model is iteratively solved using a pre-defined distributed super gradient descent algorithm, outputting a set of load control strategies for the demand side; wherein, the set of load control strategies includes load control strategies for each load resource.

[0008] Based on the load regulation strategy set, the terminal controllers of each load resource corresponding to the demand side are regulated to complete the load regulation.

[0009] Compared with existing technologies, the embodiments of this application have the following beneficial effects: by acquiring load data from the demand side and constructing a Stackelberg game model, a foundation is provided for solving the game theory problem of subsequent demand response regulation; by combining the Stackelberg game model with the distributed super gradient descent algorithm, and through hierarchical game modeling and distributed parallel computing, the computational efficiency of large-scale demand-side resource game equilibrium is significantly improved, solving the core problems of slow solution speed and inability to regulate in real time caused by the complexity of the model and the limitation of computing resources in traditional methods; at the same time, by outputting a set containing the regulation strategies of each load resource, the consistency optimization of individual resources and global objectives is achieved; finally, the theoretical strategy is transformed into actual control instructions, and the load regulation is completed by adjusting the terminal controller, which significantly improves the response speed and timeliness of demand response regulation.

[0010] In some embodiments of the first aspect of this application, the Stackelberg game model includes an upper-level model and a lower-level model;

[0011] The step of constructing a Stackelberg game model based on the load data includes:

[0012] Based on the load data, coefficient variables for the pricing strategy are set, and a linear expression for the pricing strategy is generated; wherein, the coefficient variables are configured with preset first constraints.

[0013] Based on the preset electricity consumption deviation penalty coefficient, a first objective function is constructed with the goal of minimizing negative electricity sales revenue;

[0014] The upper-level model is constructed based on the pricing strategy, the first constraint, and the first objective function;

[0015] The lower-level model is constructed based on the pricing strategy and the load data.

[0016] Compared to existing technologies, the above embodiments have the following advantages: By setting the coefficient variables of the pricing strategy and generating a linear expression, the pricing decisions of load aggregators are quantified, avoiding game imbalances caused by ambiguity in pricing strategies; further, the range of pricing parameters is limited by the first constraint condition to prevent the electricity price strategy from deviating from the actual supply and demand relationship; at the same time, an upper-level model is constructed with the goal of minimizing negative electricity sales revenue, directly linking economic benefits to the game objective function, avoiding overly subjective weight settings for multi-objective optimization, wherein the electricity consumption deviation penalty coefficient quantifies the cost of electricity consumption deviation, constraining the irrational game behavior of individual resources; finally, a lower-level model is constructed by using pricing strategies and load data to clarify the response mechanism of demand-side resources to pricing.

[0017] In some embodiments of the first aspect of this application, constructing the lower-level model based on the pricing strategy and the load data includes:

[0018] Based on the load data, the operating data of each load resource on the demand side are used to set operating constraints for each load resource.

[0019] Integrate and unify the operational constraints of various load resources to generate a second set of operational constraints;

[0020] Based on the second operating constraints and pricing strategy, a second objective function is constructed for each load resource with the goal of minimizing the operating cost of individual load resources; wherein, the second objective function includes the load regulation strategy of the corresponding load resource;

[0021] The lower-level model is constructed based on the second operational constraints and each of the second objective functions.

[0022] Compared with existing technologies, the above embodiments have the following beneficial effects: by setting operational constraints for each load resource and integrating them into a second operational constraint, the physical limitations of heterogeneous resources such as electric vehicles and industrial loads are unified, avoiding the complexity caused by the decentralized modeling of constraints for multiple types of resources; furthermore, by minimizing individual operating costs through a second objective function, the economic demands of individual resources are incorporated into the game framework, wherein the load regulation strategy incentivizes resources to actively participate in regulation through the coupling of dynamic electricity prices and individual cost functions; at the same time, when constructing the lower-level model, a linkage mechanism between operational constraints and objective functions is introduced to ensure that the game equilibrium solution simultaneously satisfies physical feasibility and economic optimality.

[0023] In some embodiments of the first aspect of this application, the step of iteratively solving the Stackelberg game model according to a preset distributed supergradient descent algorithm and outputting a set of demand-side load regulation strategies includes:

[0024] Initialize the pricing strategy and load control strategy set, as well as the approximate Jacobian matrix of the distributed super gradient descent algorithm;

[0025] Based on the distributed supergradient descent algorithm, the current pricing strategy, load control strategy set, and approximate Jacobian matrix, the pricing strategy of the upper-level model is iteratively updated until the upper-level model converges, and the load control strategy set of the lower-level model after convergence is output. After each iteration, the lower-level model is iteratively updated according to the current pricing strategy until each load control strategy reaches a Nash equilibrium state, and the approximate Jacobian matrix is ​​iteratively updated according to the load control strategy set in the current Nash equilibrium state until convergence.

[0026] Compared to existing technologies, the above embodiments have the following advantages: by initializing the pricing strategy, load control strategy set, and approximate Jacobian matrix, feasible initial values ​​are provided for distributed iteration; furthermore, by iteratively updating the pricing strategy of the upper-level model and synchronously updating the lower-level model to the Nash equilibrium state, the temporal synchronization of the hierarchical solution of the game is achieved. In this case, the approximate Jacobian matrix is ​​used to replace the exact Jacobian calculation, transforming large-scale matrix inversion into low-dimensional approximate updates, reducing the computational load of a single iteration; setting the Nash equilibrium state can ensure the stability of the solution by dynamically adjusting the game termination conditions of individual strategies.

[0027] In some embodiments of the first aspect of this application, the step of iteratively updating the pricing strategy of the upper-level model based on the distributed supergradient descent algorithm, the current pricing strategy, the load control strategy set, and the approximate Jacobian matrix includes:

[0028] Based on the preset chain rule, and the current pricing strategy, load control strategy set, and approximate Jacobian matrix, the hypergradient of the first objective function is calculated; wherein, the algorithm for the hypergradient is as follows:

[0029] Where k represents the number of iterations. Let x represent the first objective function. k Indicates pricing strategy, u k Represents the set of load control strategies, (s k ) T Describing the approximate Jacobian matrix s k transpose, This represents gradient operation. This represents an approximate hypergradient;

[0030] The pricing strategy is iteratively updated based on the supergradient.

[0031] Compared with the prior art, the above embodiments have the following beneficial effects: by calculating the hypergradient of the first objective function through the chain rule, the complex game equilibrium sensitivity analysis is transformed into a computable gradient direction, which solves the error accumulation problem caused by the reliance on numerical difference in traditional methods. In particular, the transpose of the approximate Jacobian matrix gradually approximates the accurate value of the original Jacobian matrix through low-dimensional iterative updates, avoiding direct calculation of high-dimensional matrices and significantly improving the efficiency of solving the hypergradient.

[0032] In some embodiments of the first aspect of this application, the step of iteratively solving the Stackelberg game model according to a preset distributed super gradient descent algorithm and outputting a set of demand-side load regulation strategies further includes:

[0033] The average power of all load resources on the demand side is represented as the average effect of load resources. Based on the average effect, the linear expression of the pricing strategy and each second objective function are reconstructed to obtain the second pricing strategy and each third objective function. The third objective function includes the load regulation strategy of the corresponding load resources.

[0034] Initialize the second pricing strategy, the load control strategy set, and the average effect, as well as the approximate Jacobian matrix of the distributed supergradient descent algorithm;

[0035] Based on the distributed super gradient descent algorithm, the current second pricing strategy, load control strategy set, and approximate Jacobian matrix, the second pricing strategy is iteratively updated until the upper-level model converges, and the load control strategy set after the lower-level model converges is output.

[0036] Furthermore, after each iteration of the second pricing strategy, the load control strategy set of the lower-level model is iterated according to the current second pricing strategy until a preset number of iterations or the average effect converges. The approximate Jacobian matrix is ​​then iteratively updated according to the converged load control strategy set until convergence. After each iteration of the load control strategy set, the average effect is iteratively updated according to the preset Mann acceleration theory algorithm.

[0037] Compared to existing technologies, the above embodiments have the following beneficial effects: By representing the average power of all load resources on the demand side as the average effect of load resources, the large-scale individual game problem is transformed into mean field interaction, solving the dimensionality explosion problem caused by the large number of resources; further, the linear expression of the pricing strategy and the second objective function are reconstructed according to the average effect, simplifying the coupling complexity of the game model. The third objective function reduces the dimensionality of the objective function solution by binding individual strategies with the average effect; the second pricing strategy, the load control strategy set, and the approximate Jacobian matrix are initialized to provide stable initial values ​​for hierarchical iteration, avoiding convergence oscillations caused by initial value sensitivity; the second pricing strategy is iteratively updated through a distributed super gradient descent algorithm until the upper-level model converges, realizing real-time collaborative optimization of upper-level pricing and lower-level strategies. After each iteration, the load control strategy set of the lower-level model is updated until the average effect converges, and the average effect is updated through the Mann acceleration theory algorithm, significantly accelerating the global convergence speed of the game equilibrium.

[0038] In some embodiments of the first aspect of this application, the iterative update of the average effect according to a preset Mann acceleration theory algorithm includes:

[0039] The average effect is iteratively updated according to the Mann accelerated theoretical algorithm; wherein the update algorithm is expressed as follows:

[0040] a m =0.2 / m 0.98 Where m represents

[0041] The number of iterations, z represents the average effect, and u i N represents the power of load resource i, and N represents the total number of load resources.

[0042] Compared with the prior art, the above embodiments have the following beneficial effects: by iteratively updating the average effect through Mann acceleration theory, the traditional fixed step size optimization is improved into an adaptive step size mechanism, which solves the convergence instability problem of the average effect caused by individual policy fluctuations.

[0043] Secondly, the present invention also provides a distributed super-gradient demand response control system, comprising: a model building module, a model solving module, and a control module;

[0044] The model building module is used to acquire load data from the demand side and construct a Stackelberg game model based on the load data.

[0045] The model solving module is used to iteratively solve the Stackelberg game model according to a preset distributed super gradient descent algorithm and output a set of load control strategies on the demand side; wherein, the set of load control strategies includes load control strategies for each load resource.

[0046] The control module is used to control the terminal controllers of each load resource corresponding to the demand side according to the load control strategy set, so as to complete the load control.

[0047] Compared with existing technologies, the above embodiments of this application have the following beneficial effects: by acquiring load data from the demand side and constructing a Stackelberg game model, a foundation is provided for solving the game theory problem of subsequent demand response regulation; by combining the Stackelberg game model with the distributed super gradient descent algorithm, and through hierarchical game modeling and distributed parallel computing, the computational efficiency of large-scale demand-side resource game equilibrium is significantly improved, solving the core problems of slow solution speed and inability to real-time regulation caused by the complexity of the model and the limitation of computing resources in traditional methods; at the same time, by outputting a set containing the regulation strategies of each load resource, the consistency optimization of individual resources and global objectives is achieved; finally, the theoretical strategy is transformed into actual control instructions, and the load regulation is completed by adjusting the terminal controller, which significantly improves the response speed and timeliness of demand response regulation.

[0048] Thirdly, the present invention also provides a distributed super-gradient demand response control device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded onto the processor, implements the steps of any of the distributed super-gradient demand response control methods described above.

[0049] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the distributed hypergradient demand response control methods described in the present application. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating a distributed super-gradient demand response control method provided in some embodiments of the present invention.

[0051] Figure 2 : This is a schematic diagram of the structure of a distributed super-gradient demand response control system provided in some embodiments of the present invention.

[0052] Figure 3 : This is a structural diagram of a distributed super-gradient demand response control device provided in some embodiments of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1:

[0055] Please refer to Figure 1 To address the problems of slow response speed and insufficient timeliness in existing technologies for large-scale demand-side resource demand response regulation in power systems, an embodiment of the present invention provides a distributed super-gradient demand response regulation method, comprising steps S1 to S3:

[0056] Step S1: Obtain load data from the demand side and construct a Stackelberg game model based on the load data.

[0057] Furthermore, the Stackelberg game model includes an upper-level model and a lower-level model; step S1 can be implemented through the following preferred embodiments, including steps S11-S14, as follows:

[0058] S11: Based on the load data, set the coefficient variables of the pricing strategy and generate a linear expression for the pricing strategy; wherein the coefficient variables are configured with a preset first constraint condition;

[0059] S12: Based on the preset electricity consumption deviation penalty coefficient, construct the first objective function with the goal of minimizing negative electricity sales revenue;

[0060] S13: Construct the upper-level model based on the pricing strategy, the first constraint, and the first objective function;

[0061] S14: Construct the lower-level model based on the pricing strategy and the load data.

[0062] For example, when constructing the upper-level model, in order to incentivize demand-side resource response, a pricing strategy for demand response is set, as follows:

[0063] p(t) = qD(t) + b; (p, q, b) ∈ Ψ; where p(t) represents the retail electricity price corresponding to the total load D(t), q and b represent the pricing decision variables (i.e., coefficient variables, which are always positive), and Ψ represents the polyhedral region characterized by a set of linear constraints (i.e., the first constraint condition).

[0064] Furthermore, the total load consists of flexible loads and inflexible background loads from demand-side resources, as shown below:

[0065] D(t)=∑ i∈N u i (t)+D0(t); where, u i D0(t) represents the power of demand-side load resource i in time period t, D0(t) represents the background load, and N represents the total number of demand-side load resources.

[0066] Furthermore, the first objective function of the upper-level model is constructed as follows:

[0067] Where μ represents the penalty coefficient for the deviation of the electricity consumption of demand-side load resources from the original total electricity consumption y(t), and T represents the time variable.

[0068] Finally, based on the pricing strategy, the first constraint, and the first objective function described above, the upper-level model is constructed.

[0069] In this preferred embodiment, steps S11-S14 quantify the pricing decisions of load aggregators by setting coefficient variables for the pricing strategy and generating linear expressions, thus avoiding game imbalances caused by ambiguity in the pricing strategy. Furthermore, a first constraint condition limits the range of pricing parameters to prevent the electricity price strategy from deviating from the actual supply and demand relationship. Simultaneously, an upper-level model is constructed with the goal of minimizing negative electricity sales revenue, directly linking economic benefits to the game objective function, avoiding overly subjective weight settings in multi-objective optimization. The electricity consumption deviation penalty coefficient quantifies the cost of electricity consumption deviation, constraining irrational game behavior of individual resource providers. Finally, a lower-level model is constructed using the pricing strategy and load data to clarify the response mechanism of demand-side resources to pricing.

[0070] Furthermore, step S14 can be implemented through the following preferred embodiments, including steps S141-S144, as follows:

[0071] S141: Based on the operating data of each load resource on the demand side in the load data, set the operating constraints of each load resource;

[0072] S142: Integrate and unify the operational constraints of various load resources to generate a second operational constraint;

[0073] S143: Based on the second operating constraints and pricing strategy, construct a second objective function for each load resource with the goal of minimizing the operating cost of individual load resources; wherein, the second objective function includes the load regulation strategy of the corresponding load resource;

[0074] S144: Construct the lower-level model based on the second operational constraints and each of the second objective functions.

[0075] For example, in practical implementation, the operational constraints of each load resource can include the operational constraints of electric vehicles, industrial flexible loads, and temperature-controlled loads, which are expressed as follows:

[0076] Operating constraints of electric vehicles: E EV (t+1)=E EV (t)+u EV (t); where,

[0077]

[0078] Among them, E EV (t) and u EV (t) represents the electric vehicle's charge and power during time period t, respectively. E EV and These are the lower and upper limits of the battery capacity of electric vehicles, respectively. u EV and These represent the lower and upper limits of the power output of electric vehicles, respectively. ini and t ter These are the initial and final periods of the adjustment cycle, respectively. and T represents the electric vehicle's battery level at the beginning and end of the time period, respectively. EV This represents the set of time periods during which electric vehicles can participate in regulation.

[0079] Operating constraints of industrial flexible loads: E IFD (t+1)=E IFD (t)+u IFD (t); where,

[0080] t∈TIFD ;

[0081] Among them, E IFD (t) and u IFD (t) represent the total electricity consumed by the industrial flexible load up to time period t and the power consumed at time period t, respectively. u IFD and These are the lower and upper limits of the power capacity for industrial flexible loads, respectively. T represents the total electricity consumed by the industrial flexibility load until the end of the period. IFD This refers to the set of periods during which industrial flexible loads can participate in regulation.

[0082] Operating constraints of temperature-controlled loads:

[0083] in,

[0084]

[0085] t∈T TCL Among them, E TCL (t) and u TCL (t) represents the temperature and power of the temperature-controlled load during time period t, R and C represent the thermal resistance and heat capacity of the temperature-controlled load, respectively, and E... r (t) represents the deviation from the expected electrical quantity, and η represents the power-thermal coefficient. E TCL and These are the lower and upper limits of the acceptable temperature for the temperature-controlled load, respectively. This indicates the upper limit of the power of the temperature-controlled load. and T represents the temperature of the temperature-controlled load at the beginning and end of the adjustment cycle, respectively. TCL This represents the set of time periods during which temperature-controlled loads can participate in regulation.

[0086] By unifying and integrating the operational constraints of the above-mentioned various load resources, a second operational constraint is obtained, which is expressed as follows:

[0087] E i (t+1)=a i E i (t)+b i u i (t)+C i ;in,

[0088] Among them, E i (t) The electricity consumption of demand-side load resource i during time period t, a i b i and C i These represent the coefficients of the corresponding constraints on demand-side load resource i. E i and These represent the lower and upper limits of the electricity consumption for demand-side load resource i, respectively. u i and These represent the lower and upper limits of the power of demand-side load resource i, respectively. and These represent the electricity consumption of demand-side load resource i during the initial and final periods, respectively. and T represents the initial and final periods of the adjustment cycle for demand-side load resource i, respectively. i This represents the set of time periods during which demand-side load resource i can participate in the adjustment process.

[0089] Furthermore, the objective of each demand-side load resource is to minimize its individual operating cost within the second operational constraint. The corresponding second objective function is expressed as follows:

[0090]

[0091] Among them, u ；i χ represents the power of all demand-side load resources except demand-side load resource i. i and ξ i The deviation of load resource i from the expected power and deviation from expected power The penalty factor.

[0092] Based on the second operational constraint and the second objective function mentioned above, the lower-level model is constructed.

[0093] In this preferred embodiment, steps S141-S144 unify the physical constraints of heterogeneous resources such as electric vehicles and industrial loads by setting operational constraints for each load resource and integrating them into a second operational constraint, thus avoiding the complexity caused by the decentralized modeling of constraints for multiple types of resources. Furthermore, by minimizing the individual operating cost through the second objective function, the economic demands of individual resources are incorporated into the game framework. The load regulation strategy incentivizes resources to actively participate in regulation through the coupling of dynamic electricity prices and individual cost functions. At the same time, when constructing the lower-level model, a linkage mechanism between operational constraints and objective functions is introduced to ensure that the game equilibrium solution simultaneously satisfies physical feasibility and economic optimality.

[0094] Step S2: Iteratively solve the Stackelberg game model according to the preset distributed super gradient descent algorithm, and output the load regulation strategy set on the demand side; wherein, the load regulation strategy set includes the load regulation strategy for each load resource.

[0095] Furthermore, step S2 can be implemented through the following preferred embodiments, including steps S21-S22, as detailed below:

[0096] S21: Initialize the pricing strategy and load control strategy set, as well as the approximate Jacobian matrix of the distributed super gradient descent algorithm;

[0097] S22: Based on the distributed super gradient descent algorithm, the current pricing strategy, load control strategy set, and approximate Jacobian matrix, iteratively update the pricing strategy of the upper-level model until the upper-level model converges, and output the load control strategy set of the lower-level model after convergence; and after each iteration, iteratively update the lower-level model according to the current pricing strategy until each load control strategy reaches a Nash equilibrium state, and iteratively update the approximate Jacobian matrix according to the load control strategy set in the current Nash equilibrium state until convergence.

[0098] In this preferred embodiment, steps S21-S22 provide feasible initial values ​​for distributed iteration by initializing the pricing strategy, load control strategy set, and approximate Jacobian matrix; further, by iteratively updating the pricing strategy of the upper-level model and synchronously updating the lower-level model to the Nash equilibrium state, the temporal synchronization of the game-playing hierarchical solution is achieved. Here, the approximate Jacobian matrix is ​​used to replace the exact Jacobian calculation, transforming large-scale matrix inversion into low-dimensional approximate updates, reducing the computational load of a single iteration; setting the Nash equilibrium state can ensure the stability of the solution by dynamically adjusting the game termination conditions of individual strategies.

[0099] Furthermore, when iteratively updating the pricing strategy of the upper-level model in step S22, it can be implemented through the following preferred implementation method, including steps S221-S222, as follows:

[0100] S221: Based on the preset chain rule, and the current pricing strategy, load control strategy set, and approximate Jacobian matrix, calculate the hypergradient of the first objective function; wherein, the algorithm for the hypergradient is as follows:

[0101] Where k represents the number of iterations. Let x represent the first objective function. k Indicates pricing strategy, u k Represents the set of load control strategies, (s k ) T Describing the approximate Jacobian matrix s k transpose, This represents gradient operation. This represents an approximate hypergradient;

[0102] S222: Iteratively update the pricing strategy based on the supergradient.

[0103] In practical implementation, the demand response regulation problem based on Stackelberg game theory is NP-hard. As the problem size increases, the direct solution time grows exponentially, making it difficult to solve when dealing with large amounts of demand-side resources. To achieve efficient solution, a distributed hypergradient descent algorithm is employed. For ease of description, the problem is abstractly described as follows: in,

[0104] Where x represents the pricing strategy, and X represents the set of feasible pricing strategies. The load regulation strategy for demand-side load resource i when it reaches Nash equilibrium, where U is the set of feasible load regulation strategies for demand-side load resource f. i () represents the individual operating cost function for load resources.

[0105] The core of the algorithm is to calculate the objective function of the upper-level model. The hypergradient is obtained, and hypergradient descent is used to solve the problem described above abstractly. The expression for the hypergradient can be derived using the chain rule as follows:

[0106] Among them, u * (x) represents the Nash equilibrium solution, i.e., the load control strategy when the load resources reach the Nash equilibrium state. * (x) represents u * Jacobian matrix of (x).

[0107] When solving the model in steps S21-S22, the specific steps can be as follows:

[0108] First, the iteration step size α in the distributed supergradient descent algorithm is preset. k β k and γ, as well as the error tolerance σ, the maximum number of iterations L and M;

[0109] Initialize the number of iterations k = 1, and the initial pricing strategy x. k ∈X, load regulation strategy set (i.e., the initial Nash equilibrium solution) u k ∈U and Jacobian matrix s k ;

[0110] In the upper-level model, the hypergradient is calculated and the upper-level pricing strategy is updated. The algorithms are expressed as follows:

[0111] Hypergradient update:

[0112] Pricing strategy update: in,

[0113]

[0114] After each pricing strategy update, the lower-level model is iterated using the current pricing strategy. During iteration, the Nash equilibrium solution of the load control strategy set is first calculated through a two-layer loop. The number of iterations in the outer loop is controlled by the maximum number of iterations M, and the number of iterations in the inner loop is controlled by the total number of load resources N. The process is as follows:

[0115] Initialize the current iteration count m = 1 of the outer loop, and the Nash equilibrium solution.

[0116] Initiate a double-loop iteration. In each inner loop, calculate an approximate value of the Nash equilibrium solution using the following algorithm:

[0117] Where u represents the power of the load resource, This represents the power of load resource i in the m-th iteration.

[0118] In the inner loop, after each iteration to obtain an approximate value of the Nash equilibrium solution, a preset error tolerance σ is used to determine whether the entire iterative process for calculating the Nash equilibrium solution needs to be terminated prematurely, as shown below:

[0119] If satisfied but And terminate the iterative cycle of the entire Nash equilibrium solution.

[0120] After stopping the loop iteration, the Jacobian matrix s is then calculated and updated based on the current Nash equilibrium solution. k The method is as follows:

[0121] The same two-level loop iterative calculation is used, with the outer loop controlled by the maximum number of iterations L and the inner loop controlled by the total number of load resources N:

[0122] Initialization: the current iteration count of the outer loop is l = 1, approximating the Jacobian matrix.

[0123] Initiate a double-loop iteration. In each inner loop, iteratively calculate the approximate Jacobian matrix according to the following algorithm:

[0124] in,

[0125]

[0126]

[0127] Where J1 and J2 represent the partial Jacobian matrices of the function f. f i About u i The partial gradient of , where I represents the identity matrix.

[0128] Similarly, in the inner loop, after each round of calculating the approximate Jacobian matrix, a preset error tolerance σ is used to determine whether the entire iterative calculation of the approximate Jacobian matrix needs to be terminated. The update method for the Jacobian matrix is ​​as follows:

[0129] If satisfied but Then terminate the entire iteration loop and return to the upper-level model for the next iteration.

[0130] In the iteration of the upper-level model, if the pricing strategy is updated while satisfying: ||s k:1 -s k If ||≤σ, then the iterative solution of the entire Stackelberg game model is terminated, and the set of load control strategies that the lower-level model converges at this point is output.

[0131] In this preferred embodiment, the hypergradient of the first objective function is calculated by the chain rule, which transforms the complex game equilibrium sensitivity analysis into a computable gradient direction. This solves the error accumulation problem caused by the reliance on numerical difference in traditional methods. The transpose of the approximate Jacobian matrix gradually approximates the accurate value of the original Jacobian matrix through low-dimensional iterative updates, avoiding direct calculation of high-dimensional matrices and significantly improving the efficiency of solving the hypergradient.

[0132] When the number of individuals with demand-side resources is large, steps S21-S22 above are prone to numerical oscillations during the Nash equilibrium solution process, resulting in a slow solution speed. To improve the algorithm's solution speed for large-scale demand response regulation problems, the average effect of the overall behavior of demand-side resources can be used to approximate the individual game behavior, representing the complex game between large-scale individuals. Mann's acceleration theory can then be used to solve the problem, enabling rapid computation of large-scale game equilibrium issues and improving overall solution efficiency.

[0133] Therefore, step S2 can also be implemented through another preferred embodiment, including steps S23-S25, as follows:

[0134] S23: The average power of all load resources on the demand side is represented as the average effect of load resources, and the linear expression of the pricing strategy and each second objective function are reconstructed based on the average effect to obtain the second pricing strategy and each third objective function; wherein, the third objective function includes the load regulation strategy of the corresponding load resources;

[0135] S24: Initialize the second pricing strategy, the load control strategy set and the average effect, as well as the approximate Jacobian matrix of the distributed supergradient descent algorithm;

[0136] S25: Based on the distributed super gradient descent algorithm, the current second pricing strategy, load control strategy set, and approximate Jacobian matrix, iteratively update the second pricing strategy until the upper-level model converges, and output the load control strategy set after the lower-level model converges.

[0137] Furthermore, after each iteration of the second pricing strategy, the load control strategy set of the lower-level model is iterated according to the current second pricing strategy until a preset number of iterations or the average effect converges. The approximate Jacobian matrix is ​​then iteratively updated according to the converged load control strategy set until convergence. After each iteration of the load control strategy set, the average effect is iteratively updated according to the preset Mann acceleration theory algorithm.

[0138] In this preferred embodiment, steps S23-S25 transform the large-scale individual game problem into mean field interaction by representing the average power of all load resources on the demand side as the average effect of load resources, thus solving the dimensionality explosion problem caused by the large number of resources. Furthermore, the linear expression of the pricing strategy and the second objective function are reconstructed based on the average effect, simplifying the coupling complexity of the game model. The third objective function reduces the dimensionality of the objective function by binding individual strategies to the average effect. The second pricing strategy, the load control strategy set, and the approximate Jacobian matrix are initialized to provide stable initial values ​​for hierarchical iteration, avoiding convergence oscillations caused by initial value sensitivity. The second pricing strategy is iteratively updated using a distributed supergradient descent algorithm until the upper-level model converges, achieving real-time collaborative optimization between the upper-level pricing and lower-level strategies. After each iteration, the load control strategy set of the lower-level model is updated until the average effect converges, and the average effect is updated using the Mann acceleration theory algorithm, significantly accelerating the global convergence speed of the game equilibrium.

[0139] Furthermore, when iteratively updating the average effect using the Mann accelerated theoretical algorithm, step S25 can be implemented through the following preferred embodiment, as follows:

[0140] The average effect is iteratively updated according to the Mann accelerated theoretical algorithm; wherein the update algorithm is expressed as follows:

[0141] Where m represents the number of iterations, z represents the average effect, and u i N represents the power of load resource i, and N represents the total number of load resources.

[0142] In the specific implementation steps S23-S25, the average effect of the overall behavior of demand-side load resources is first defined as:

[0143]

[0144] The second pricing strategy is obtained by restating the pricing strategy:

[0145] p(t) = q ′ z(t)+b ′ ; where q ′ =qN, b ′ =qD0(t)+b;

[0146] Furthermore, the function for the individual operating cost of reconstructing demand-side load resources is:

[0147]

[0148] Furthermore, the optimal load regulation strategy for reconfiguring demand-side load resource i relative to the average effect z(t) is expressed as:

[0149] During model iteration, by iterating over z(t) and... To update the individual optimal control strategy for average effect and load resources, and to iterate the average effect using Mann acceleration theory, the complete iterative solution process of the model is as follows:

[0150] First, the iteration step size α in the distributed supergradient descent algorithm is preset. k β k and γ, as well as the error tolerance σ, the maximum number of iterations L and M;

[0151] Initialize the number of iterations k = 1, and set the initial second pricing strategy x. k ∈X, load regulation strategy set (i.e., the initial Nash equilibrium solution) u k ∈U and Jacobian matrix s k ;

[0152] In the upper-level model, the supergradient is calculated and the second pricing strategy of the upper level is updated. The algorithms are expressed as follows:

[0153] Hypergradient update:

[0154] Update the second pricing strategy using a commercial solver: in,

[0155]

[0156] After each update of the second pricing strategy, the lower-level model is iterated using the current second pricing strategy. First, the Nash equilibrium solution of the load control strategy set is calculated iteratively through a two-layer loop. The number of iterations in the outer loop is controlled by the maximum number of iterations M, and the number of iterations in the inner loop is controlled by the total number of load resources N. The process is as follows:

[0157] Initialize the outer loop's current iteration count m = 1, and the Nash equilibrium solution.

[0158] Initiate a double-loop iteration; in each inner loop, solve the formula. To iteratively update the optimal load control strategy for each individual load resource.

[0159] In the inner loop, after each iteration of the load control strategy set, the average effect is updated using the following formula:

[0160] a m =0.2 / m 0.98 Where m represents the number of iterations, z represents the average effect, and u i N represents the power of load resource i, and N represents the total number of load resources.

[0161] When updating the average effect, if ||z m:1 -z m If ||≤σ, then update the load control strategy set: And terminate the entire iteration loop.

[0162] After stopping the above double-loop iteration, the updated Jacobian matrix s is calculated based on the current Nash equilibrium solution. k The method is as follows:

[0163] The same two-level loop iterative calculation is used, with the outer loop controlled by the maximum number of iterations L and the inner loop controlled by the total number of load resources N:

[0164] Initialization: the current iteration count of the outer loop is l = 1, approximating the Jacobian matrix.

[0165] Initiate a double-loop iteration. In each inner loop, iteratively calculate the approximate Jacobian matrix according to the following algorithm:

[0166] in,

[0167]

[0168]

[0169] Where J1 and J2 represent the partial Jacobian matrices of the function f. f i About u i The partial gradient of , where I represents the identity matrix.

[0170] Similarly, after each calculation of the approximate Jacobian matrix, a preset error tolerance σ can be used to determine whether the entire iterative calculation of the approximate Jacobian matrix needs to be terminated early, as shown below:

[0171] If satisfied but Then terminate the entire iteration loop and return to the upper-level model for the next iteration.

[0172] In the iteration of the upper-level model, if the second pricing strategy satisfies the following during iterative update: ||s k:1 -s k If ||≤σ, then the iterative solution of the entire Stackelberg game model is terminated, and the set of load control strategies that the lower-level model converges at this point is output.

[0173] In this preferred embodiment, the average effect is iteratively updated using Mann acceleration theory, and the traditional fixed step size optimization is improved into an adaptive step size mechanism, which solves the convergence instability problem of the average effect caused by individual policy fluctuations.

[0174] Step S3: According to the load control strategy set, control the terminal controllers of each load resource corresponding to the demand side to complete the load control.

[0175] In practical implementation, the load control strategy includes the power parameters of the corresponding resource load, such as power parameters. After obtaining the load control strategy set, the power parameters in the strategy are extracted and converted into corresponding control signals to realize the control of the terminal controller of the corresponding load resource on the demand side.

[0176] In summary, compared with the prior art, the above embodiments of this application have the following beneficial effects: by acquiring load data on the demand side and constructing a Stackelberg game model, a foundation is provided for solving the game theory problem of subsequent demand response regulation; by combining the Stackelberg game model with the distributed super gradient descent algorithm, through hierarchical game modeling and distributed parallel computing, the computational efficiency of large-scale demand-side resource game equilibrium is significantly improved, solving the core problems of slow solution speed and inability to real-time regulation caused by the complexity of the model and the limitation of computing resources in traditional methods; at the same time, by outputting a set containing the regulation strategies of each load resource, the consistency optimization of individual resources and global objectives is achieved; finally, the theoretical strategy is transformed into actual control instructions, and the load regulation is completed by adjusting the terminal controller, which significantly improves the response speed and timeliness of demand response regulation.

[0177] Example 2:

[0178] Please refer to Figure 2Based on the same inventive concept, the present invention discloses a distributed super-gradient demand response control system, comprising: a model building module M1, a model solving module M2, and a control module M3;

[0179] The model building module M1 is used to acquire load data from the demand side and construct a Stackelberg game model based on the load data.

[0180] The Stackelberg game model includes an upper-level model and a lower-level model; the model construction module M1 includes: a pricing strategy generation unit, a first objective function construction unit, an upper-level model construction unit, and a lower-level model construction unit.

[0181] The pricing strategy generation unit is used to set the coefficient variables of the pricing strategy based on the load data and generate a linear expression of the pricing strategy; wherein the coefficient variables are configured with preset first constraints.

[0182] The first objective function construction unit is used to construct a first objective function based on a preset electricity consumption deviation penalty coefficient, with the goal of minimizing negative electricity sales revenue;

[0183] The upper-level model construction unit is used to construct the upper-level model based on the pricing strategy, the first constraint condition, and the first objective function.

[0184] The lower-level model building unit is used to build the lower-level model based on the pricing strategy and the load data.

[0185] In this preferred embodiment, by setting coefficient variables for the pricing strategy and generating a linear expression, the pricing decisions of load aggregators are quantified, avoiding game imbalances caused by ambiguity in pricing strategies. Furthermore, a first constraint condition limits the range of pricing parameters to prevent the electricity price strategy from deviating from the actual supply and demand relationship. Simultaneously, an upper-level model is constructed with the goal of minimizing negative electricity sales revenue, directly linking economic benefits to the game objective function, avoiding overly subjective weight settings in multi-objective optimization. The electricity consumption deviation penalty coefficient quantifies the cost of electricity consumption deviation, constraining irrational game behavior of individual resource providers. Finally, a lower-level model is constructed using pricing strategies and load data to clarify the response mechanism of demand-side resources to pricing.

[0186] Furthermore, the lower-level model construction unit includes: a constraint setting subunit, a constraint integration subunit, a second objective function construction subunit, and a lower-level model generation subunit;

[0187] The operation constraint setting subunit is used to set operation constraints for each load resource based on the operation data of each load resource on the demand side in the load data.

[0188] The constraint integration subunit is used to integrate and unify the operational constraints of each load resource to generate a second operational constraint.

[0189] The second objective function construction subunit is used to construct a second objective function for each load resource based on the second operating constraints and pricing strategy, with the goal of minimizing the operating cost of individual load resources; wherein, the second objective function includes the load regulation strategy of the corresponding load resource;

[0190] The lower-level model generation subunit is used to construct the lower-level model based on the second running constraints and each of the second objective functions.

[0191] In this preferred embodiment, by setting operational constraints for each load resource and integrating them into a second operational constraint, the physical limitations of heterogeneous resources such as electric vehicles and industrial loads are unified, avoiding the complexity caused by the decentralized modeling of constraints for multiple types of resources. Furthermore, by minimizing individual operating costs through a second objective function, the economic demands of individual resources are incorporated into the game framework. The load regulation strategy incentivizes resources to actively participate in regulation through the coupling of dynamic electricity prices and individual cost functions. At the same time, when constructing the lower-level model, a linkage mechanism between operational constraints and objective functions is introduced to ensure that the game equilibrium solution simultaneously satisfies physical feasibility and economic optimality.

[0192] The model solving module M2 is used to iteratively solve the Stackelberg game model according to a preset distributed super gradient descent algorithm and output a set of load control strategies on the demand side; wherein, the set of load control strategies includes load control strategies for each load resource.

[0193] Furthermore, the model solving module M2 includes: a first initialization unit and a first iteration unit;

[0194] The first initialization unit is used to initialize the pricing strategy and load control strategy set, as well as the approximate Jacobian matrix of the distributed super gradient descent algorithm.

[0195] The first iterative unit is used to iteratively update the pricing strategy of the upper-level model according to the distributed super gradient descent algorithm, the current pricing strategy, the load control strategy set, and the approximate Jacobian matrix, until the upper-level model converges, and output the load control strategy set of the lower-level model after convergence; and after each iteration, iteratively update the lower-level model according to the current pricing strategy until each load control strategy reaches a Nash equilibrium state, and iteratively update the approximate Jacobian matrix according to the load control strategy set in the current Nash equilibrium state until convergence.

[0196] In this preferred embodiment, feasible initial values ​​are provided for distributed iteration by initializing the pricing strategy, load control strategy set, and approximate Jacobian matrix. Furthermore, the pricing strategy of the upper-level model is updated iteratively and the lower-level model is updated synchronously to the Nash equilibrium state, thereby achieving temporal synchronization of the game-playing hierarchical solution. Here, the approximate Jacobian matrix is ​​used to replace the exact Jacobian calculation, transforming large-scale matrix inversion into low-dimensional approximate updates, reducing the computational load of a single iteration. Setting the Nash equilibrium state can ensure the stability of the solution by dynamically adjusting the game termination conditions of individual strategies.

[0197] Furthermore, the first iteration unit includes: a supergradient calculation subunit and a pricing strategy update subunit;

[0198] The supergradient calculation subunit is used to calculate the supergradient of the first objective function according to a preset chain rule, the current pricing strategy, the load control strategy set, and the approximate Jacobian matrix; wherein, the algorithm for the supergradient is as follows:

[0199] Where k represents the number of iterations. Let x represent the first objective function. k Indicates pricing strategy, u k Represents the set of load control strategies, (s k ) T Describing the approximate Jacobian matrix s k transpose, This represents gradient operation. This represents an approximate hypergradient;

[0200] The pricing strategy update subunit is used to iteratively update the pricing strategy based on the super gradient.

[0201] In this preferred embodiment, the hypergradient of the first objective function is calculated by the chain rule, which transforms the complex game equilibrium sensitivity analysis into a computable gradient direction. This solves the error accumulation problem caused by the reliance on numerical difference in traditional methods. The transpose of the approximate Jacobian matrix gradually approximates the accurate value of the original Jacobian matrix through low-dimensional iterative updates, avoiding direct calculation of high-dimensional matrices and significantly improving the efficiency of solving the hypergradient.

[0202] Furthermore, the model solving module M2 also includes: a reconstruction unit, a second initialization unit, and a second iteration unit;

[0203] The reconfiguration unit is used to characterize the average power of all load resources on the demand side as the average effect of load resources, and reconfigure the linear expression of the pricing strategy and each second objective function according to the average effect to obtain the second pricing strategy and each third objective function; wherein, the third objective function includes the load regulation strategy of the corresponding load resources;

[0204] The second initialization unit is used to initialize the second pricing strategy, the load control strategy set and the average effect, as well as the approximate Jacobian matrix of the distributed supergradient descent algorithm;

[0205] The second iteration unit is used to iteratively update the second pricing strategy according to the distributed super gradient descent algorithm, the current second pricing strategy, the load control strategy set, and the approximate Jacobian matrix, until the upper-level model converges, and output the load control strategy set after the lower-level model converges.

[0206] Furthermore, after each iteration of the second pricing strategy, the load control strategy set of the lower-level model is iterated according to the current second pricing strategy until a preset number of iterations or the average effect converges. The approximate Jacobian matrix is ​​then iteratively updated according to the converged load control strategy set until convergence. After each iteration of the load control strategy set, the average effect is iteratively updated according to the preset Mann acceleration theory algorithm.

[0207] In this preferred embodiment, by representing the average power of all load resources on the demand side as the average effect of load resources, the large-scale individual game problem is transformed into mean field interaction, solving the dimensionality explosion problem caused by the large number of resources. Furthermore, the linear expression of the pricing strategy and the second objective function are reconstructed based on the average effect, simplifying the coupling complexity of the game model. The third objective function reduces the dimensionality of the objective function solution by binding individual strategies with the average effect. The second pricing strategy, the load control strategy set, and the approximate Jacobian matrix are initialized to provide stable initial values ​​for hierarchical iteration, avoiding convergence oscillations caused by initial value sensitivity. The second pricing strategy is iteratively updated through a distributed super gradient descent algorithm until the upper-level model converges, realizing real-time collaborative optimization between the upper-level pricing and the lower-level strategy. After each iteration, the load control strategy set of the lower-level model is updated until the average effect converges, and the average effect is updated through the Mann acceleration theory algorithm, significantly accelerating the global convergence speed of the game equilibrium.

[0208] Furthermore, in the second iteration unit, the average effect is iteratively updated according to a preset Mann acceleration theory algorithm, which can be implemented through the following preferred embodiment, specifically:

[0209] The average effect is iteratively updated according to the Mann accelerated theoretical algorithm; wherein the update algorithm is expressed as follows:

[0210] a m =0.2 / m 0.98 Where m represents

[0211] The number of iterations, z represents the average effect, and ui N represents the power of load resource i, and N represents the total number of load resources.

[0212] In this preferred embodiment, the average effect is iteratively updated using Mann acceleration theory, and the traditional fixed step size optimization is improved into an adaptive step size mechanism, which solves the convergence instability problem of the average effect caused by individual policy fluctuations.

[0213] The control module M3 is used to control the terminal controllers of each load resource corresponding to the demand side according to the load control strategy set, so as to complete the load control.

[0214] In summary, compared with existing technologies, the embodiments of this application have the following beneficial effects: by acquiring load data from the demand side and constructing a Stackelberg game model, a foundation is provided for solving the game theory problem of subsequent demand response regulation; by combining the Stackelberg game model with the distributed super gradient descent algorithm, and through hierarchical game modeling and distributed parallel computing, the computational efficiency of large-scale demand-side resource game equilibrium is significantly improved, solving the core problems of slow solution speed and inability to real-time regulation caused by the complexity of the model and the limitation of computing resources in traditional methods; at the same time, by outputting a set containing the regulation strategies of each load resource, the consistency optimization of individual resources and global objectives is achieved; finally, the theoretical strategies are transformed into actual control instructions, and the load regulation is completed by adjusting the terminal controller, which significantly improves the response speed and timeliness of demand response regulation.

[0215] Example 3:

[0216] Figure 3 A structural diagram of a distributed hypergradient demand response control device according to this application is shown. Figure 3 As shown, the distributed super-gradient demand response control device may include: processor N1, memory N2, data interface N3, and communication bus N4.

[0217] Wherein: processor N1, memory N2, and data interface N3 communicate with each other through communication bus N4; data interface N3 is used for data communication with other devices such as input devices or output devices; processor N1 is used to execute program N5, specifically to execute the relevant steps in any of the above embodiments of a distributed super-gradient demand response control method.

[0218] Specifically, program N5 may include program code, which includes computer-executable instructions.

[0219] The processor N1 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application. The distributed hypergradient demand response control device includes one or more processors, which may be processors of the same type, such as one or more CPUs, or processors of different types, such as one or more CPUs and one or more ASICs.

[0220] Memory N2 is used to store program N5. Memory N2 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage.

[0221] The algorithms or displays provided herein are not inherently related to any particular computer, virtual system, or other device. Furthermore, the embodiments in this application are not directed to any particular programming language.

[0222] Example 4:

[0223] This invention also provides a computer-readable storage medium storing at least one executable instruction that, when executed on a distributed super-gradient demand response control device / system, causes the distributed super-gradient demand response control device / system to perform one of the distributed super-gradient demand response control methods described in any of the above method embodiments.

[0224] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of this application may be practiced without these specific details. Similarly, for the purpose of simplification and aiding understanding of one or more aspects of the invention, in the above description of exemplary embodiments of this application, various features of the embodiments are sometimes grouped together in a single embodiment, figure, or description thereof. The claims, which follow the detailed description, are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of this application.

[0225] Those skilled in the art will understand that the modules in the device of the embodiment can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or components in the embodiment can be combined into a single module, unit, or component, and further, they can be divided into multiple sub-modules, sub-units, or sub-components, except that at least some of such features and / or processes or units are mutually exclusive.

Claims

1. A distributed super-gradient demand response control method, characterized in that, include: Obtain demand-side load data and construct a Stackelberg game model based on the load data; The Stackelberg game model is iteratively solved using a pre-defined distributed super gradient descent algorithm, outputting a set of load control strategies for the demand side; wherein, the set of load control strategies includes load control strategies for each load resource. According to the load regulation strategy set, the terminal controllers of each load resource corresponding to the demand side are regulated to complete the load regulation; The Stackelberg game model includes an upper-level model and a lower-level model. The step of constructing a Stackelberg game model based on the load data includes: Based on the load data, coefficient variables for the pricing strategy are set, and a linear expression for the pricing strategy is generated; wherein, the coefficient variables are configured with preset first constraints. Based on the preset electricity consumption deviation penalty coefficient, a first objective function is constructed with the goal of minimizing negative electricity sales revenue; The upper-level model is constructed based on the pricing strategy, the first constraint, and the first objective function; The lower-level model is constructed based on the pricing strategy and the load data; The step of constructing the lower-level model based on the pricing strategy and the load data includes: Based on the load data, the operating data of each load resource on the demand side are used to set operating constraints for each load resource. Integrate and unify the operational constraints of various load resources to generate a second set of operational constraints; Based on the second operating constraints and pricing strategy, a second objective function is constructed for each load resource with the goal of minimizing the operating cost of individual load resources; wherein, the second objective function includes the load regulation strategy of the corresponding load resource; The lower-level model is constructed based on the second operational constraints and each of the second objective functions; The step of iteratively solving the Stackelberg game model using a preset distributed supergradient descent algorithm to output a set of demand-side load regulation strategies includes: The average power of all load resources on the demand side is represented as the average effect of load resources. Based on the average effect, the linear expression of the pricing strategy and each second objective function are reconstructed to obtain the second pricing strategy and each third objective function. The third objective function includes the load regulation strategy of the corresponding load resources. Initialize the second pricing strategy, the load control strategy set, and the average effect, as well as the approximate Jacobian matrix of the distributed supergradient descent algorithm; Based on the distributed super gradient descent algorithm, the current second pricing strategy, load control strategy set, and approximate Jacobian matrix, the second pricing strategy is iteratively updated until the upper-level model converges, and the load control strategy set after the lower-level model converges is output. Furthermore, after each iteration of the second pricing strategy, the load control strategy set of the lower-level model is iterated according to the current second pricing strategy until a preset number of iterations or the average effect converges. The approximate Jacobian matrix is ​​then iteratively updated according to the converged load control strategy set until convergence. After each iteration of the load control strategy set, the average effect is iteratively updated according to the preset Mann acceleration theory algorithm.

2. The distributed super-gradient demand response control method as described in claim 1, characterized in that, The process involves iteratively solving the Stackelberg game model using a pre-defined distributed supergradient descent algorithm to output a set of demand-side load regulation strategies, including: Initialize the pricing strategy and load control strategy set, as well as the approximate Jacobian matrix of the distributed super gradient descent algorithm; Based on the distributed supergradient descent algorithm, the current pricing strategy, load control strategy set, and approximate Jacobian matrix, the pricing strategy of the upper-level model is iteratively updated until the upper-level model converges, and the load control strategy set of the lower-level model after convergence is output. After each iteration, the lower-level model is iteratively updated according to the current pricing strategy until each load control strategy reaches a Nash equilibrium state, and the approximate Jacobian matrix is ​​iteratively updated according to the load control strategy set in the current Nash equilibrium state until convergence.

3. The distributed super-gradient demand response control method as described in claim 2, characterized in that, The step of iteratively updating the pricing strategy of the upper-level model based on the distributed supergradient descent algorithm, the current pricing strategy, the load control strategy set, and the approximate Jacobian matrix includes: Based on the preset chain rule, and the current pricing strategy, load control strategy set, and approximate Jacobian matrix, the hypergradient of the first objective function is calculated; wherein, the algorithm for the hypergradient is as follows: Where k represents the number of iterations, Denotes the first objective function. Indicates pricing strategy, This represents a set of load control strategies. Represents an approximate Jacobian matrix transpose, This represents gradient operation. This represents an approximate hypergradient; The pricing strategy is iteratively updated based on the supergradient.

4. The distributed super-gradient demand response control method as described in claim 1, characterized in that, The iterative update of the average effect according to the preset Mann acceleration theory algorithm includes: The average effect is iteratively updated according to the Mann accelerated theoretical algorithm; wherein the update algorithm is expressed as follows: ; Where m represents the number of iterations and z represents the average effect. Let N represent the power of load resource i, and let N represent the total number of load resources.

5. A distributed super-gradient demand response control system, characterized in that, include: Model building module, model solving module, and control module; The model building module is used to acquire load data from the demand side and construct a Stackelberg game model based on the load data. The model solving module is used to iteratively solve the Stackelberg game model according to a preset distributed super gradient descent algorithm and output a set of load control strategies on the demand side; wherein, the set of load control strategies includes load control strategies for each load resource. The control module is used to control the terminal controllers of each load resource corresponding to the demand side according to the load control strategy set, so as to complete the load control. The Stackelberg game model includes an upper-level model and a lower-level model; the model construction module includes: a pricing strategy generation unit, a first objective function construction unit, an upper-level model construction unit, and a lower-level model construction unit. The pricing strategy generation unit is used to set the coefficient variables of the pricing strategy based on the load data and generate a linear expression of the pricing strategy; wherein the coefficient variables are configured with preset first constraints. The first objective function construction unit is used to construct a first objective function based on a preset electricity consumption deviation penalty coefficient, with the goal of minimizing negative electricity sales revenue; The upper-level model construction unit is used to construct the upper-level model based on the pricing strategy, the first constraint condition, and the first objective function. The lower-level model building unit is used to build the lower-level model based on the pricing strategy and the load data; The lower-level model construction unit includes: a constraint setting subunit, a constraint integration subunit, a second objective function construction subunit, and a lower-level model generation subunit; The operation constraint setting subunit is used to set operation constraints for each load resource based on the operation data of each load resource on the demand side in the load data. The constraint integration subunit is used to integrate and unify the operational constraints of each load resource to generate a second operational constraint. The second objective function construction subunit is used to construct a second objective function for each load resource based on the second operating constraints and pricing strategy, with the goal of minimizing the operating cost of individual load resources; wherein, the second objective function includes the load regulation strategy of the corresponding load resource; The lower-level model generation subunit is used to construct the lower-level model based on the second running constraints and each of the second objective functions; The model solving module includes: a reconstruction unit, a second initialization unit, and a second iteration unit; The reconfiguration unit is used to characterize the average power of all load resources on the demand side as the average effect of load resources, and reconfigure the linear expression of the pricing strategy and each second objective function according to the average effect to obtain the second pricing strategy and each third objective function; wherein, the third objective function includes the load regulation strategy of the corresponding load resources; The second initialization unit is used to initialize the second pricing strategy, the load control strategy set and the average effect, as well as the approximate Jacobian matrix of the distributed supergradient descent algorithm; The second iteration unit is used to iteratively update the second pricing strategy according to the distributed super gradient descent algorithm, the current second pricing strategy, the load control strategy set, and the approximate Jacobian matrix, until the upper-level model converges, and output the load control strategy set after the lower-level model converges. Furthermore, after each iteration of the second pricing strategy, the load control strategy set of the lower-level model is iterated according to the current second pricing strategy until a preset number of iterations or the average effect converges. The approximate Jacobian matrix is ​​then iteratively updated according to the converged load control strategy set until convergence. After each iteration of the load control strategy set, the average effect is iteratively updated according to the preset Mann acceleration theory algorithm.

6. A distributed super-gradient demand response control device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the steps of a distributed super-gradient demand response control method according to any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the distributed super-gradient demand response control method according to any one of claims 1-4.

Images