Incomplete information attack method and device for virtual power plant flexible pricing mechanism

Abstract

The present application belongs to the technical field of virtual power plant security evaluation, and particularly relates to an incomplete information attack method and device for a virtual power plant elastic pricing mechanism. The method comprises: based on elastic demand response in a virtual power plant, constructing a Stackelberg game model and an optimization objective of the game model; the game model comprises an upper model representing an attacker and a lower model representing a virtual power plant pricing mechanism; based on incomplete information of the elastic pricing mechanism in the virtual power plant, reconstructing the optimization objective of the game model and determining a constraint condition thereof; based on a KKT condition and a large M method, solving the optimization objective of the reconstructed game model to quantitatively evaluate the influence of incomplete information attack on system operation economy in the virtual power plant. The present application discloses the deficiency of the virtual power plant elastic pricing mechanism, and provides guidance for security protection design thereof.

Description

Technical Field

[0001] This invention belongs to the technical field of security assessment of virtual power plants, specifically relating to a method and apparatus for attacking incomplete information targeting the flexible pricing mechanism of virtual power plants. Background Technology

[0002] With the explosive growth of distributed renewable energy and flexible loads, "Virtual Power Plants (VPPs)" have become a key means to improve system flexibility and absorption capacity by aggregating massive amounts of small resources and participating in the spot, ancillary services, and capacity markets under a unified identity. In VPPs, "quantity and price reporting" relies on operating parameters (adjustable capacity, ramp rate, marginal cost, etc.) submitted by end-users. Due to the large number of resources, high measurement costs, and open communication links, operators find it difficult to verify the authenticity of data in a timely manner. Malicious users can inflate market clearing prices or seize winning bids by falsifying parameters, thereby obtaining excessive profits. Attackers can even further exploit the response error amplification mechanism of VPP aggregators to create power deficits during the system's real-time balancing phase, resulting in expensive secondary dispatch costs.

[0003] Existing research largely focuses on post-event detection and static punishment mechanisms, neglecting the dynamic interaction between attackers and defenders, as well as the requirement for obtaining target system information in attack design. Specifically, firstly, attackers can optimize "quotation and pricing" data based on the defender's pricing rules to maximize attack impact. Traditional single-stage models cannot characterize this "attack-defense interaction" process, leading to assessments of virtual power plant vulnerabilities that deviate from reality. Secondly, in real-world systems, attackers rarely obtain pricing information from all end-users. Current attack strategies based on complete system information are difficult to apply to real-world scenarios with incomplete information, resulting in inaccurate security risk analysis of virtual power plants.

[0004] Chinese patent document CN118157122A discloses an attack-defense game model and its application method based on damage analysis of malicious attacks on power grids. It establishes an attacker's destructive capability model based on the correlation propagation of damage to power grid units and the maximum attack equivalent invested by the attacker; considers the associated attack states of power grid units and establishes a defender's power system attack scheduling model; proposes objective functions for the attack-defense game problem based on the optimization objectives of both the attacker and the defender; and successfully transforms the mixed-integer nonlinear two-person zero-sum game problem in the original problem into a mixed-integer linear optimization problem by applying KKT conditions and linear transformations. Finally, it uses a conventional solver to find the attacker's optimal attack path and the defender's optimal scheduling scheme under the scenario of malicious attacks on the power grid.

[0005] Chinese patent document CN119740459A discloses a method for assessing the vulnerability of power systems to external attacks based on a multi-objective zero-sum game. It establishes a power grid unit damage correlation propagation model based on the power grid structure and the types and quantities of actual grid units. Building upon this model, a multi-objective zero-sum game model is established based on the optimization objectives of attackers and defenders for different objective functions, as well as their own resource constraints. This model is represented as a two-level mixed-integer nonlinear optimization problem. Solving the problem yields the minimum attack cost required for an external attacker to cause complete failure of the power system. This invention establishes a multi-objective attack-defense game model that solves for the minimum attack cost required to cause complete failure of the power system from the attacker's perspective, reflecting the overall vulnerability and security of the power system's defense strategy.

[0006] In view of this, the present invention designs an analysis method that can characterize the attack and defense interaction behavior of virtual power plants in scenarios with incomplete information, systematically analyzes the maximum gains that attackers can obtain in scenarios with incomplete information, assesses the security risks faced by virtual power plants, and guides the design of security protection strategies. Summary of the Invention

[0007] This invention aims to overcome at least one of the defects of the prior art and provides an incomplete information attack method for the flexible pricing mechanism of virtual power plants. By constructing a two-layer Stackelberg game model, the impact of attackers on virtual power plants in the context of incomplete information is quantified, revealing the shortcomings of the flexible pricing mechanism of virtual power plants and providing guidance for security protection design.

[0008] The present invention also discloses an apparatus loaded with an incomplete information attack method for a virtual power plant's flexible pricing mechanism.

[0009] The detailed technical solution of this invention is as follows:

[0010] An incomplete information attack method targeting the flexible pricing mechanism of virtual power plants, the method comprising:

[0011] S1. Based on the elastic demand response in a virtual power plant, construct a Stackelberg game model and an optimization objective for the Stackelberg game model; wherein, the Stackelberg game model includes an upper-level model representing the attacker and a lower-level model representing the pricing mechanism of the virtual power plant.

[0012] S2. Based on the incomplete information of the flexible pricing mechanism in the virtual power plant, reconstruct the optimization objective of the Stackelberg game model and determine its constraints.

[0013] S3. Solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the virtual power plant.

[0014] According to a preferred embodiment of the present invention, in S1, the elastic demand response in the virtual power plant is constructed based on a price elasticity matrix, specifically as follows:

[0015]

[0016] In equation (4): Indicates user Load adjustment amount, , This represents the total number of users, including attackers and regular users; Indicates user Basic load; The price elasticity matrix; Indicates user The change in electricity price; Indicates user Base electricity price; function Used to convert vectors Transform it into a diagonal matrix.

[0017] According to a preferred embodiment of the present invention, in S1, the optimization objective of the Stackelberg game model is:

[0018]

[0019] In equation (5): Used to describe the optimization objective of the upper-level model. This indicates a fake elasticity coefficient uploaded by the attacker; This indicates a fake load adjustment uploaded by the attacker; This is the return coefficient for electricity price fluctuations; This indicates the absolute fluctuation range of electricity prices; Indicates the unit cost of falsified load; Used to describe the optimization objective of the lower-level model. Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; This indicates the total load adjustment amount.

[0020] According to a preferred embodiment of the present invention, in S2, the incomplete information of the flexible pricing mechanism in the virtual power plant is constructed as an uncertain set U:

[0021]

[0022] In formula (6): Indicates other users The true elastic coefficient, , For other users True elastic coefficient The lower and upper bounds; Indicates other users The actual load adjustment amount , For other users Actual load adjustment The lower and upper bounds.

[0023] According to a preferred embodiment of the present invention, in S2, the optimization objective of the Stackelberg game model reconstructed based on incomplete information from the flexible pricing mechanism in the virtual power plant is:

[0024]

[0025] In equation (8): This represents the electricity price fluctuation obtained in the worst-case scenario under incomplete information. This represents the operating cost of the virtual power plant; This indicates the attacker's gains; These are the weighting coefficients;

[0026] Furthermore, the following constraints apply to the max objective:

[0027]

[0028]

[0029] In equations (9) and (10): This represents the attacker's base payload; Indicates the base electricity price;

[0030] For the min objective, the following constraints apply:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] In equations (11)-(16): These represent the output power of the gas turbine. The lower and upper limits; These represent wind power output. The lower and upper limits; These represent the power used for interaction with independent operators. The lower and upper limits; These represent the changes in electricity prices. The lower and upper limits; This represents the base load of user n; This represents the number of ordinary users excluding attackers among all users.

[0038] According to a preferred embodiment of the present invention, step S3 includes: using the Lagrange coefficients to construct the Lagrange function of the min objective in the optimization objective of the reconstructed Stackelberg game model, and calculating the gradient of the Lagrange function based on the KKT conditions to obtain the first derivative with respect to each decision variable, so as to limit the range of the optimal solution;

[0039] The decision variables include the real elasticity coefficients of other users, gas turbine output, wind power output, power interacting with independent operators, electricity price change rate, and linearization auxiliary variables.

[0040] According to a preferred embodiment of the present invention, S3 further includes transforming the nonlinear inequality constraints on each decision variable into linear constraints based on the binary auxiliary variables introduced by the Big M method;

[0041] The decision variables include the real elasticity coefficients of other users, gas turbine output, wind power output, power interacting with independent operators, electricity price change rate, and linearization auxiliary variables.

[0042] In another aspect of the invention, an apparatus is provided for implementing an incomplete information attack method targeting a flexible pricing mechanism for virtual power plants, the apparatus comprising:

[0043] The model building module is used to construct a Stackelberg game model and an optimization objective of the Stackelberg game model based on the elastic demand response in a virtual power plant; wherein, the Stackelberg game model includes an upper-level model representing the attacker and a lower-level model representing the pricing mechanism of the virtual power plant.

[0044] The model reconstruction module is used to reconstruct the optimization objective of the Stackelberg game model based on incomplete information about the flexible pricing mechanism in the virtual power plant, and to determine its constraints.

[0045] The computation module is used to solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method, so as to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the system in the virtual power plant.

[0046] In another aspect of the invention, an electronic device is also provided, comprising:

[0047] At least one processor; and

[0048] The memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform the incomplete information attack method for the virtual power plant flexible pricing mechanism as described above.

[0049] In another aspect of the invention, a machine-readable storage medium is also provided, which stores executable instructions that, when executed, cause the machine to perform the incomplete information attack method for a virtual power plant flexible pricing mechanism as described above.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] This invention provides an incomplete information attack method for the flexible pricing mechanism of virtual power plants. By modeling the flexible demand response in virtual power plants, a two-layer Stackelberg game model representing the attacker-virtual power plant is constructed. A solution strategy based on KKT and Big M method is designed to quantitatively evaluate the impact of incomplete information attacks in virtual power plants on the economic operation of the system, thereby assessing the security risks faced by virtual power plants and guiding the design of security protection strategies. Attached Figure Description

[0052] Figure 1 This is a flowchart of the incomplete information attack method for the flexible pricing mechanism of virtual power plants described in this invention.

[0053] Figure 2 This is a market structure diagram of the virtual power plant in Embodiment 1 of the present invention.

[0054] Figure 3 It is a schematic diagram of the worst - case attack benefit under different elastic ranges in Embodiment 1 of the present invention.

[0055] Figure 4 It is a contour map of the attack benefit in Embodiment 1 of the present invention. Detailed implementation manners

[0056] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0057] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0058] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0059] In the case of no conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0060] Embodiment 1

[0061] Refer Figure 1 , this embodiment provides an incomplete - information attack method for the elastic pricing mechanism of a virtual power plant. The method includes: [[ID=二十九]] [[ID=三十]]

[0062] [[ID=三十一]]S1. Based on the elastic demand response in the virtual power plant, construct a Stackelberg game model and the optimization objective of the Stackelberg game model; wherein, the Stackelberg game model includes an upper - layer model representing the attacker and a lower - layer model representing the pricing mechanism of the virtual power plant. [[ID=三十二]] [[ID=三十三]]

[0063] [[ID=三十四]]Specifically, elastic demand response (DR) is a key mechanism for a virtual power plant (VPP) to coordinate distributed energy, and it motivates users to adjust their loads through electricity price signals. Due to the individual differences of users themselves, different users have different responses to the guidance of electricity price signals, and usually, a price - elasticity matrix model is used to describe the response degree of different users to electricity price signals. [[ID=三十五]] [[ID=三十六]]

[0064] Each element in the price elasticity matrix, i.e. the elasticity coefficient, is usually defined as: the percentage change in demand / the percentage change in price. The change in demand can be positive or negative and generally includes load adjustments, energy storage system output, etc.

[0065] To characterize the interactive influence of users' responses to electricity price signals, the elasticity coefficient is divided into self-elasticity coefficient. With cross elasticity coefficient Specifically defined as:

[0066]

[0067]

[0068] In equations (1) and (2): The self-elasticity coefficient, The cross-elasticity coefficient; Indicates user The actual load adjustment amount; Indicates user Basic load; Indicates user The change in electricity price; Indicates user The base electricity price; Indicates user The change in electricity price; Indicates user The base electricity price.

[0069] It should be understood that the self-elasticity coefficient is always negative and is used to reflect the strength of the load reduction response when electricity prices rise.

[0070] Based on the above, construct a price elasticity matrix. :

[0071]

[0072] In formula (3): This represents the total number of users, including attackers and ordinary users.

[0073] In the price elasticity matrix In the diagram, the diagonal elements are the self-elasticity coefficients, and the remaining elements are the cross-elasticity coefficients.

[0074] According to the price elasticity matrix This allows us to construct a load response equation, i.e., an elastic demand response equation in a virtual power plant, to characterize the relationship between load adjustments and changes in electricity price signals. Its expression is as follows:

[0075]

[0076] In equation (4): Indicates user Load adjustment amount; function To accommodate matrix operations, This vector is transformed into a diagonal matrix.

[0077] After completing the modeling of resilient demand response in the virtual power plant, the next step is to construct an attacker-virtual power plant Stackelberg game model for resilient demand response in the virtual power plant.

[0078] Specifically, since the pricing mechanism of virtual power plants is relatively fixed, attackers (i.e., malicious participants in virtual power plants) can obtain the elastic pricing mechanism and the parameters in the pricing mechanism through prior research, as well as information such as elasticity coefficients and load changes uploaded by other ordinary users. Therefore, in the interaction between attackers and the pricing mechanism of virtual power plants, attackers have a "first-mover advantage," and the pricing mechanism can only respond passively to attackers.

[0079] To characterize the above-mentioned interactive behavior, in this embodiment, a two-layer Stackelberg game framework is preferably adopted, wherein the upper-layer model is the attacker, with the goal of maximizing its own gains; and the lower-layer model is the pricing mechanism of the virtual power plant, with the goal of minimizing operating costs.

[0080] Based on this, the optimization objective of constructing the Stackelberg game model is:

[0081]

[0082] In equation (5): Used to describe the optimization objective of the upper-level model. Indicates the spurious elasticity coefficient; This indicates a fictitious load adjustment. This is the return coefficient for electricity price fluctuations; This indicates the absolute fluctuation range of electricity prices; Indicates the unit cost of falsified load; Used to describe the optimization objective of the lower-level model. Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; This indicates the total load adjustment amount.

[0083] It should be understood that in the two-layer Stackelberg game model, the upper-layer model representing the attacker uploads bid information. At the same time, by reporting false elasticity coefficients and fictitious load adjustment The attacker manipulates the electricity price of a virtual power plant to maximize their attack profits. These profits consist of the electricity price manipulation gains minus the cost of forgery. User-uploaded price quotes are also involved. To participate in market transactions, the price must be higher than the minimum market transaction price. The lower-level model representing the VPP pricing mechanism coordinates gas turbine output. and wind power output and the power of interaction with independent operators. To minimize operating costs.

[0084] Thus, the construction of the two-layer Stackelberg game model and its optimization objective function is completed.

[0085] S2. Based on the incomplete information of the flexible pricing mechanism in the virtual power plant, reconstruct the optimization objective of the Stackelberg game model and determine its constraints.

[0086] During the interaction between the attacker and the virtual power plant, the attacker cannot fully grasp the detailed reported information of all users, namely the actual elasticity coefficient and actual load adjustment of other ordinary users.

[0087] To characterize the aforementioned uncertainties, the unknown elasticity coefficients of other users and the load adjustment amount can be regarded as bounded uncertain variables, that is, the incomplete information of the elastic pricing mechanism in the virtual power plant, which can be represented by the uncertain set U:

[0088]

[0089] In formula (6): Indicates other users The true elastic coefficient, , For other users True elastic coefficient The lower and upper bounds; Indicates other users The actual load adjustment amount , For other users Actual load adjustment The lower and upper bounds.

[0090] It should be understood that the uncertain set U describes the attacker's cognitive limitations regarding other users' information within the virtual power plant. Among them, , , , All of these can be calculated based on historical reported information.

[0091] Based on the above, in scenarios with incomplete information, attackers cannot obtain the accurate elasticity coefficients and load adjustment amounts of other participants, and can only estimate their range based on historical information and other data.

[0092] Considering the impact of the aforementioned incomplete information on the attacker-virtual power plant interaction, the optimization objective of the Stackelberg game model will be reconstructed as follows:

[0093]

[0094] In equation (7): Used to describe the optimization objective of the corresponding upper-level model after reconstruction, where, Used to describe how attackers maximize their gains. Used to describe a worst-case gain for an attacker in an uncertain scenario.

[0095] Based on the above, due to the introduction of uncertainty factors, the optimization objective of the Stackelberg game model representing the attacker-virtual power plant interaction is reconstructed from the original max-min structure to a max-min-min structure.

[0096] To simplify the solution of the reconstructed optimization objective, this embodiment merges the two minimum objectives and retains the maximum objective. Therefore, the optimization objective of the Stackelberg game model will be further reconstructed as follows:

[0097]

[0098] In equation (8): This represents the electricity price fluctuation obtained in the worst-case scenario under incomplete information. This represents the operating costs of the VPP. Indicates the attacker's gains. Weighting coefficients are used for balancing. , Two optimization objectives.

[0099] For the above max objective, it should meet the following constraints:

[0100]

[0101]

[0102] In equations (9) and (10): This represents the attacker's base payload; This indicates the base electricity price.

[0103] Equation (9) represents the false elasticity coefficient reported by the attacker. Must be within the historical statistical range Within; Equation (10) represents the false load adjustment amount reported by the attacker. Need to be combined with spurious elasticity coefficient The attacker's own base load And the worst-case scenario of electricity price fluctuations Strict matching ensures the consistency of falsified data.

[0104] For the above minimum objective, the following constraints should be met:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] In equations (11)-(16): These represent the output power of the gas turbine. The lower and upper limits; These represent wind power output. The lower and upper limits; These represent the power used for interaction with independent operators. The lower and upper limits; These represent the changes in electricity prices. The lower and upper limits; This represents the base load of user n; This represents the number of ordinary users excluding attackers among all users. That is, one of the ordinary users.

[0112] Equations (11)-(13) represent the power limits for gas turbines, wind power, and independent operators, respectively; Equation (14) represents the fluctuation range of electricity price signals; and Equations (15) and (16) represent power balance constraints.

[0113] Thus, the objective function of the two-layer Stackelberg game model is reconstructed, and its constraints are determined.

[0114] S3. Solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the virtual power plant.

[0115] To solve the optimization objective of the Stackelberg game model obtained after further reconstruction, this embodiment preferably adopts the KKT equivalent method, replacing the min objective with its KKT conditions, thus simplifying the max-min two-level optimization problem into a single-level optimization problem. The KKT conditions for the min objective are analyzed as follows:

[0116] Construct the Lagrangian function of the minimizing objective using the Lagrangian coefficients. :

[0117]

[0118] In equation (17): ~ These are the dual terms of the inequality constraints; Denotes the dual variables of inequality constraints; Indicates the rate of change in electricity prices. Electricity price change rate The lower and upper bounds; These are the dual terms of the equality constraint; Indicates other users Basic load; , , All are Lagrange coefficients; It is a linearization auxiliary variable.

[0119] Calculate the gradient of the Lagrange function to obtain its first derivative with respect to the decision variables, which is used to limit the range of the optimal solution:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] .

[0126] Based on formula (17), the Lagrangian function L is constructed. The derivation is based on the principle that the first-order partial derivatives of the Lagrangian function with respect to each decision variable are zero in the KKT conditions: For the true elasticity coefficients of other users... Differentiating yields formula (18); for the gas turbine output Differentiating yields formula (19); for wind power output Differentiating yields formula (20); for power interacting with independent operators Differentiating yields formula (21); for the rate of change in electricity prices Differentiation yields formula (22); for linearized auxiliary variables The derivative yields formula (23). These derived formulas transform the min objective optimization problem into a system of equations, providing a foundation for subsequent simplification and solution of the model.

[0127] To handle inequality constraints in optimization problems, slack variables are introduced to transform them into equality constraints. Considering the nonlinear characteristics of these constraints, this embodiment employs the Big M method to convert nonlinear constraints into linear ones, where the big number introduced is M.

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] In equations (24)-(29): ~ These are binary auxiliary variables introduced based on the Big M method, used to transform nonlinear inequality constraints into linear constraints. The variables they constrain are as follows:

[0135] and Used to constrain elastic coefficient To ensure that it is in Within the range; and Used to constrain the power generation output of gas turbines To satisfy Output limitations; and Used to constrain the power generation output of wind power To satisfy Output limitations; and Power used to constrain interaction with independent operators To make it conform Constraints; and Used to constrain electricity price change rate (Right now ), to ensure it in Scope; and Used to process electricity price change rate The relationship with the linearized auxiliary variable s (i.e. This achieves the linearization transformation of the absolute value function.

[0136] To ensure the physical meaning of the optimization problem and the rationality of the optimal solution, the introduced Lagrange factor must satisfy the non-negativity condition, i.e. , ; .

[0137] Through the simplification, KKT equivalence, and Big M method linearization methods described above, the max-min-min three-layer structure of the attacker-virtual power plant interaction model in the incomplete information scenario is transformed into a single-layer mixed integer programming model, which can be solved using existing commercial solvers.

[0138] Thus, based on the solution results of the optimization objective function of the reconstructed two-layer Stackelberg game model, the impact of incomplete information attacks on the economic operation of the virtual power plant can be quantitatively evaluated.

[0139] The effectiveness of the method of the present invention will be verified by specific experiments below.

[0140] Experimental environment:

[0141] Physical environment: CPU: Intel Core i7-9750H, 6 cores and 12 threads, base frequency 2.60GHz, turbo frequency 4.50GHz;

[0142] GPU: NVIDIA GeForce RTX 2060 (6GB GDDR6);

[0143] Memory: 16GB DDR4-2667MHz dual-channel;

[0144] Storage: 1TB NVMe SSD (Kingston SNV2S1000G);

[0145] Software environment: Windows 10 Professional Edition, MATLAB R2022b.

[0146] Based on the model and solution strategy constructed above, combined with Figure 2 The virtual power plant market structure shown is used to conduct verification work on incomplete information attacks targeting the flexible pricing mechanism of virtual power plants.

[0147] In this embodiment, the virtual power plant is configured as follows: Figure 2 As shown, it includes distributed resources and a gas turbine. Wind power Wait for power generation resources and interact with independent system operators for power generation. This forms a multi-layered collaborative architecture that includes the user layer, the virtual power plant layer, and the external market.

[0148] Analysis of experimental results:

[0149] Figure 3 The core idea is to demonstrate the correlation between the attacker's net gain and the fake elasticity coefficient, with the horizontal axis representing the fake elasticity coefficient fabricated by the attacker. The value ranges from -0.5 to 0; the vertical axis represents the attacker's net gain, intuitively reflecting the magnitude of change in attack profits. When the spurious elasticity coefficient... When the value is in the range of -0.35 to -0.25, the net profit from the attack reaches its peak, with the narrowest range curve showing the highest peak, followed by the medium range curve, and the widest range curve showing a relatively lower peak; while when the false elasticity coefficient... When the return is less than -0.45 or greater than -0.15, the net returns of all three curves decrease significantly, with returns approaching zero in some intervals.

[0150] The curve comparison reveals that the constraint range of the elasticity coefficient has a direct impact on the attack's profitability: the narrower the constraint range (e.g., ... The more prominent the peak return within the optimal range, the steeper the curve fluctuation; the wider the constraint range (e.g. The overall profit level is lower, and the curve trend is flatter. This phenomenon confirms the conclusion in the document that "attackers can maximize profits by optimizing the false elasticity coefficient (focusing on the -0.35 to -0.25 range)," and at the same time reflects the constraint effect of the accuracy of elasticity coefficient information on the attack effect—the more focused the information (the narrower the range), the greater the optimization space for attack profits.

[0151] Figure 4 The "Attack Profit Contour Map" illustrates the synergistic effect between elasticity coefficient and electricity price fluctuation. The areas with dense contour lines, i.e., the range where the elasticity coefficient is between -0.3 and -0.2 and the electricity price fluctuation is between 4 and 6, represent high-profit areas for attacks. This aligns with the mechanism represented in formula (5): "Profit = Electricity Price Manipulation Profit - Forgery Cost," indicating that attackers can manipulate the elasticity coefficient through this method. With False Load Adjustment The matching relationship is used to identify the optimal attack strategy in scenarios with incomplete information.

[0152] By quantifying the differences in the area and profit values ​​of high-yield regions under different levels of information completeness, we can assess the impact of information uncertainty on attack profits. Furthermore, by statistically analyzing the increase in operating costs of virtual power plants under high-yield attack scenarios, we can clarify the extent of damage the attack inflicts on the system's economics. These analyses validate the model's effectiveness in characterizing the dynamic interaction between offense and defense and the impact of incomplete information.

[0153] In summary, the incomplete information attack method for the flexible pricing mechanism of virtual power plants proposed in this invention quantifies the impact of attackers on virtual power plants in incomplete information scenarios by constructing a two-layer Stackelberg game model, revealing the shortcomings of the flexible pricing mechanism of virtual power plants and providing guidance for security protection design.

[0154] Example 2

[0155] This embodiment provides an apparatus for implementing an incomplete information attack method targeting a flexible pricing mechanism for virtual power plants. The apparatus includes:

[0156] The model building module is used to construct a Stackelberg game model and an optimization objective of the Stackelberg game model based on the elastic demand response in a virtual power plant; wherein, the Stackelberg game model includes an upper-level model representing the attacker and a lower-level model representing the pricing mechanism of the virtual power plant.

[0157] The model reconstruction module is used to reconstruct the optimization objective of the Stackelberg game model based on incomplete information about the flexible pricing mechanism in the virtual power plant, and to determine its constraints.

[0158] The computation module is used to solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method, so as to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the system in the virtual power plant.

[0159] Example 3

[0160] This embodiment also provides an electronic device, including:

[0161] At least one processor; and

[0162] The memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform the incomplete information attack method for the virtual power plant flexible pricing mechanism as described above.

[0163] In this embodiment, the electronic device may include, but is not limited to: personal computer, server computer, workstation, desktop computer, laptop computer, notebook computer, mobile computing device, smartphone, tablet computer, cellular phone, personal digital assistant (PDA), handheld device, messaging device, wearable computing device, consumer electronic device, etc.

[0164] Example 4

[0165] This embodiment also provides a machine-readable storage medium storing executable instructions that, when executed, cause the machine to perform the incomplete information attack method for the flexible pricing mechanism of virtual power plants as described above.

[0166] Specifically, a system or apparatus equipped with a readable storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer or processor of the system or apparatus can read and execute the instructions stored in the readable storage medium.

[0167] In this case, the program code read from the readable medium itself can perform the functions of any of the above embodiments, and therefore the machine-readable code and the readable storage medium storing the machine-readable code constitute a part of this specification.

[0168] Examples of readable storage media include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD-RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer or the cloud via a communication network.

[0169] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0170] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0172] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0173] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the specific implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for attacking incomplete information regarding the flexible pricing mechanism of virtual power plants, characterized in that, The method includes: S1. Based on the elastic demand response in a virtual power plant, construct a Stackelberg game model and an optimization objective for the Stackelberg game model; wherein, the Stackelberg game model includes an upper-level model representing the attacker and a lower-level model representing the pricing mechanism of the virtual power plant. The elastic demand response in the virtual power plant is constructed based on a price elasticity matrix, specifically as follows: In equation (4): Indicates user Load adjustment amount, , This represents the total number of users, including attackers and regular users; Indicates user Basic load; The price elasticity matrix; Indicates user The change in electricity price; Indicates user Base electricity price; function Used to convert vectors Transform it into a diagonal matrix; The optimization objective of the Stackelberg game model is: In equation (5): Used to describe the optimization objective of the upper-level model. This indicates a fake elasticity coefficient uploaded by the attacker; This indicates a fake load adjustment uploaded by the attacker; This is the return coefficient for electricity price fluctuations; This indicates the absolute fluctuation range of electricity prices; Indicates the unit cost of falsified load; Used to describe the optimization objective of the lower-level model. Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; Indicates the total load adjustment amount; S2. Based on the incomplete information of the flexible pricing mechanism in the virtual power plant, reconstruct the optimization objective of the Stackelberg game model and determine its constraints. Specifically, the incomplete information regarding the flexible pricing mechanism in the virtual power plant is constructed as an uncertain set U: In formula (6): Indicates other users The true elastic coefficient, , For other users True elastic coefficient The lower and upper bounds; Indicates other uses; The optimization objective of the Stackelberg game model based on the incomplete information reconstruction of the flexible pricing mechanism in virtual power plants is: In equation (8): This indicates a fake elasticity coefficient uploaded by the attacker; This indicates a fake load adjustment uploaded by the attacker; This is the return coefficient for electricity price fluctuations; This represents the electricity price fluctuation obtained in the worst-case scenario under incomplete information. Indicates the unit cost of falsified load; Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; This represents the operating cost of the virtual power plant; This indicates the attacker's gains; These are the weighting coefficients; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; Indicates the total load adjustment amount; Furthermore, the following constraints apply to the max objective: In equations (9) and (10): This represents the attacker's base payload; Indicates the base electricity price; For the min objective, the following constraints apply: In equations (11)-(16): These represent the output power of the gas turbine. The lower and upper limits; These represent wind power output. The lower and upper limits; These represent the power used for interaction with independent operators. The lower and upper limits; These represent the changes in electricity prices. The lower and upper limits; This represents the base load of user n; This represents the number of ordinary users excluding attackers among all users. S3. Solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the virtual power plant.

2. The incomplete information attack method for the flexible pricing mechanism of virtual power plants according to claim 1, characterized in that, S3 includes using the Lagrange coefficients to construct the Lagrange function of the min objective in the optimization objective of the reconstructed Stackelberg game model, and calculating the gradient of the Lagrange function based on the KKT conditions to obtain the first derivative with respect to each decision variable, so as to limit the range of the optimal solution. The decision variables include the real elasticity coefficients of other users, gas turbine output, wind power output, power interacting with independent operators, electricity price change rate, and linearization auxiliary variables.

3. The incomplete information attack method for the flexible pricing mechanism of virtual power plants according to claim 1, characterized in that, The S3 also includes, based on the binary auxiliary variables introduced by the Big M method, transforming the nonlinear inequality constraints on each decision variable into linear constraints; The decision variables include the real elasticity coefficients of other users, gas turbine output, wind power output, power interacting with independent operators, electricity price change rate, and linearization auxiliary variables.

4. An apparatus for implementing an incomplete information attack method for a flexible pricing mechanism for virtual power plants, characterized in that, The device includes: The model building module is used to construct a Stackelberg game model and an optimization objective of the Stackelberg game model based on the elastic demand response in a virtual power plant; wherein, the Stackelberg game model includes an upper-level model representing the attacker and a lower-level model representing the pricing mechanism of the virtual power plant. The elastic demand response in the virtual power plant is constructed based on a price elasticity matrix, specifically as follows: In equation (4): Indicates user Load adjustment amount, , This represents the total number of users, including attackers and regular users; Indicates user Basic load; The price elasticity matrix; Indicates user The change in electricity price; Indicates user Base electricity price; function Used to convert vectors Transform it into a diagonal matrix; The optimization objective of the Stackelberg game model is: In equation (5): Used to describe the optimization objective of the upper-level model. This indicates a fake elasticity coefficient uploaded by the attacker; This indicates a fake load adjustment uploaded by the attacker; This is the return coefficient for electricity price fluctuations; This indicates the absolute fluctuation range of electricity prices; Indicates the unit cost of falsified load; Used to describe the optimization objective of the lower-level model. Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; Indicates the total load adjustment amount; The model reconstruction module is used to reconstruct the optimization objective of the Stackelberg game model based on incomplete information about the flexible pricing mechanism in the virtual power plant, and to determine its constraints. Specifically, the incomplete information regarding the flexible pricing mechanism in the virtual power plant is constructed as an uncertain set U: In formula (6): Indicates other users The true elastic coefficient, , For other users True elastic coefficient The lower and upper bounds; Indicates other uses; The optimization objective of the Stackelberg game model based on the incomplete information reconstruction of the flexible pricing mechanism in virtual power plants is: In equation (8): This indicates a fake elasticity coefficient uploaded by the attacker; This indicates a fake load adjustment uploaded by the attacker; This is the return coefficient for electricity price fluctuations; This represents the electricity price fluctuation obtained in the worst-case scenario under incomplete information. Indicates the unit cost of falsified load; Indicates the output power of the gas turbine; Indicates wind power output; Indicates the power used for interaction with independent operators; Indicates the change in electricity price; This represents the operating cost of the virtual power plant; This indicates the attacker's gains; These are the weighting coefficients; , , These correspond to the unit costs of load adjustment, gas turbine output, and wind power output, respectively. This indicates the market electricity price for an independent system operation; Indicates the total load adjustment amount; Furthermore, the following constraints apply to the max objective: In equations (9) and (10): This represents the attacker's base payload; Indicates the base electricity price; For the min objective, the following constraints apply: In equations (11)-(16): These represent the output power of the gas turbine. The lower and upper limits; These represent wind power output. The lower and upper limits; These represent the power used for interaction with independent operators. The lower and upper limits; These represent the changes in electricity prices. The lower and upper limits; This represents the base load of user n; This represents the number of ordinary users excluding attackers among all users. The computation module is used to solve the optimization objective of the reconstructed Stackelberg game model based on KKT conditions and the Big M method, so as to quantitatively evaluate the impact of incomplete information attacks on the economic operation of the system in the virtual power plant.

5. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform an incomplete information attack method for a virtual power plant flexible pricing mechanism as described in any one of claims 1 to 3.

6. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores executable instructions that, when executed, cause the machine to perform an incomplete information attack method for a virtual power plant flexible pricing mechanism as described in any one of claims 1 to 3.

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