Defense method for optimal deployment of energy storage inverter based on double-layer Stackelberg game and related equipment

Abstract

The invention relates to the technical field of small target detection and identification in images in the power industry, and provides an energy storage inverter optimization deployment defense method based on a double-layer Stackelberg game and related equipment. The method comprises the following steps: constructing a LinDistFlow model based on load power disturbance and reactive power disturbance of each node attacked by LAA; maximizing the voltage deviation of all attacked nodes in the whole attack time period as a first objective function, and combining a first constraint condition to construct a dynamic model of the LAA attack; taking minimization of the operation cost of the energy storage inverter and the voltage deviation of the attacked node as a second objective function, and combining with a second constraint condition to construct a dynamic model of LAA defense; introducing confidence parameters based on load power disturbance and reactive power disturbance of each node, and constructing an optimization model based on opportunity constraint; and if the defender knows / knows the injection power of the attacker, solving the model, and making a defense strategy in advance by using the data of the attacker.

Description

Technical Field

[0001] The present invention relates to the technical field of network security and optimal dispatching of smart grids, and particularly to an optimal deployment and defense method for energy storage inverters based on a two-layer Stackelberg game and related devices. Background Technique

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] With the digital development of the power system, a large number of Internet of Things (IoT) devices are connected to the power grid, improving the intelligence level and operation flexibility of the power grid. However, the remote control characteristics of such devices make the smart grid face new network security threats, especially the Load Altering Attack (LAA). Attackers can manipulate remotely controllable loads (RCLs) to perturb power loads, resulting in increased voltage deviation and even possible large-scale power instability, seriously affecting the security and reliability of the power grid.

[0004] Existing defense methods mainly include static device deployment and detection-based load adjustment, etc. However, in a dynamic attack environment, the above methods still have certain limitations: First, there is a lack of a dynamic optimization mechanism. Current defense schemes are mostly based on static optimization and fail to effectively utilize the real-time dispatching ability of energy storage devices; Second, the changes in the attacker's strategy are not fully considered. Most defense methods are not optimized for the attacker's strategy adjustment at different times, affecting the defense effect; In addition, it is difficult to cope with uncertainties. The attacker's behavior has a high degree of uncertainty, and traditional methods are difficult to provide effective defense strategies in the case of unknown attacks. Summary of the Invention

[0005] To solve the technical problems existing in the above background technique, the present invention provides an optimal deployment and defense method for energy storage inverters based on a two-layer Stackelberg game and related devices. The present invention can optimize the defense strategy in a dynamic environment, fully utilize the real-time dispatching ability of energy storage devices, and combine the changes in the attacker's strategy to improve the adaptability and effectiveness of the defense. In addition, to cope with the uncertainty of attack behaviors, the present invention designs an optimization method that can handle unknown attack situations to ensure the stable operation and security of the smart grid.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The first aspect of the present invention provides an optimal deployment and defense method for energy storage inverters based on a two-layer Stackelberg game.

[0008] A method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game for defense, including:

[0009] Based on the load power perturbation and reactive power perturbation of each node under LAA attack, construct a LinDistFlow model;

[0010] Taking the maximization of the voltage deviation of all attacked nodes during the entire attack period as the first objective function, combined with the first constraint condition, construct a dynamic model of LAA attack;

[0011] Taking the minimization of the operating cost of energy storage inverters and the voltage deviation of attacked nodes as the second objective function, combined with the second constraint condition, construct a dynamic model of LAA defense;

[0012] Based on the load power perturbation and reactive power perturbation of each node, introduce a confidence parameter and construct an optimization model based on chance constraints;

[0013] If the defender knows the injection power of the attacker, according to the LinDistFlow model, solve the dynamic models of LAA attack and LAA defense to maximize the objectives of the attacker and the defender, and formulate a defense strategy in advance based on the attacker's data;

[0014] If the defender cannot master the injection power of the attacker, according to the optimization model based on chance constraints, solve the dynamic model of LAA defense, minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data and formulate a defense strategy in advance.

[0015] In some embodiments, the LinDistFlow model is represented by the following formula:

[0016]

[0017] where P ji represents the active power flowing into node i, P ij represents the active power flowing out of node i, represents the active load of the node, represents the load power perturbation of each node, Q ji represents the reactive power flowing into node i, Q ij represents the reactive power flowing out of node i, represents the reactive power perturbation of each node.

[0018] In some embodiments, the first objective function is represented by the following formula:

[0019]

[0020] where t represents time, T is the set of the entire time range, and N a is the set of all attacked target nodes, and V i (t) represents the actual voltage value of node i at time t, represents the standard voltage value of node i;

[0021] In some embodiments, the first constraint conditions include: the first node power balance constraint, the voltage constraint, the attack perturbation range constraint, and the line power flow constraint.

[0022] In some embodiments, the first node power balance constraint is used to ensure the active power and reactive power balance of each node and introduce the load power perturbation of each node and the reactive power perturbation to characterize the impact of the LAA attack on the power distribution;

[0023] The voltage constraint is used to calculate the voltage deviation according to the line impedance, the active power flowing out of the node, and the reactive power flowing out of the node, and evaluate the impact of the LAA attack on the system voltage stability;

[0024] The second objective function is expressed by the following formula:

[0025]

[0026] where N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charging and discharging power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ i represents the additional fixed operating cost of device i; λ represents the trade-off coefficient used to balance the trade-off between voltage stability and energy storage cost.

[0027] In some embodiments, the second constraint conditions include: the second node power balance constraint, the voltage constraint, the charging and discharging power constraint of the energy storage device, the energy level constraint of the energy storage device, and the power transmission capacity constraint of each line.

[0028] In some embodiments, the second node power balance constraint is used to control the active power and reactive power injected into the node, compensate for the power deviation caused by the attack, and ensure the node power balance.

[0029] In some embodiments, the optimization model based on chance constraints is expressed by the following formula:

[0030]

[0031] where, Denote the load power disturbances of each node. Denote the reactive power disturbances of each node. Denote the active load of the node, and η denotes the maximum amplitude of the limited attack disturbance. Denote the reactive power of node i at time t.

[0032] In some embodiments, if the defender cannot grasp the injection power of the attacker, by optimizing, reduce the proportion of the power disturbance exceeding the allowable range so that it does not exceed the set threshold ε:

[0033]

[0034] Among them, φ = 1 indicates that the defender cannot grasp the injection power of the attacker.

[0035] The second aspect of the present invention provides a defense system for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game.

[0036] A defense system for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game, comprising:

[0037] A first model construction module, which is configured to: based on the load power disturbances and reactive power disturbances of each node by LAA attack, construct a LinDistFlow model;

[0038] A second model construction module, which is configured to: take maximizing the voltage deviation of all attacked nodes during the entire attack period as the first objective function, and combine with the first constraint condition to construct a dynamic model of LAA attack;

[0039] A third model construction module, which is configured to: take minimizing the operating cost of the energy storage inverter and the voltage deviation of the attacked nodes as the second objective function, and combine with the second constraint condition to construct a dynamic model of LAA defense;

[0040] A fourth model construction module, which is configured to: based on the load power disturbances and reactive power disturbances of each node, introduce a confidence parameter, and construct an optimization model based on chance constraints;

[0041] A first solving module, which is configured to: if the defender knows the injection power of the attacker, according to the LinDistFlow model, solve the dynamic models of LAA attack and LAA defense to maximize the objectives of the attacker and the defender, and formulate a defense strategy in advance according to the attacker data;

[0042] The second solution module is configured to: if the defender cannot master the injection power of the attacker, solve the dynamic model of LAA defense according to the optimization model based on chance constraints, minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data, and formulate a defense strategy in advance.

[0043] In some embodiments, the LinDistFlow model is represented by the following formula:

[0044]

[0045] where P ji represents the active power flowing into node i, and P ij represents the active power flowing out of node i, represents the active load of the node, represents the load power disturbance of each node, and Q ji represents the reactive power flowing into node i, and Q ij represents the reactive power flowing out of node i, represents the reactive power disturbance of each node.

[0046] In some embodiments, the first objective function is represented by the following formula:

[0047]

[0048] where t represents time, T is the set of the entire time range, and N a is the set of all attack target nodes, and V i (t) represents the actual voltage value of node i at time t, represents the standard voltage value of node i;

[0049] In some embodiments, the first constraint conditions include: the first node power balance constraint, the voltage constraint, the attack disturbance range constraint, and the line power flow constraint.

[0050] In some embodiments, the first node power balance constraint is used to ensure the balance of the active power and reactive power of each node, and introduce the load power disturbance of each node and the reactive power disturbance to characterize the impact of the LAA attack on the power distribution;

[0051] The voltage constraint is used to calculate the voltage deviation according to the line impedance, the active power flowing out of the node, and the reactive power flowing out of the node, and evaluate the impact of the LAA attack on the system voltage stability;

[0052] The second objective function is represented by the following formula:

[0053]

[0054] Among them, N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charging and discharging power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ i represents the additional fixed operating cost of device i; λ represents the trade-off coefficient used to balance the trade-off between voltage stability and energy storage cost.

[0055] In some embodiments, the second constraint condition includes: the second node power balance constraint, the voltage constraint, the charging and discharging power constraint of the energy storage device, the energy level constraint of the energy storage device, and the power transmission capacity constraint of each line.

[0056] In some embodiments, the second node power balance constraint is used to control the active power and reactive power injected into the node, compensate for the power deviation caused by the attack, and ensure node power balance.

[0057] In some embodiments, the optimization model based on chance constraints is expressed by the following formula:

[0058]

[0059] Among them, represents the load power disturbance of each node, represents the reactive power disturbance of each node, represents the active load of the node, η represents the maximum amplitude of the defined attack disturbance, represents the reactive power of node i at time t.

[0060] In some embodiments, if the defender cannot master the injection power of the attacker, by optimizing, reduce the proportion of the power disturbance exceeding the allowable range so that it does not exceed the set threshold ε:

[0061]

[0062] Among them, φ = 1 means that the defender cannot master the injection power of the attacker.

[0063] The third aspect of the present invention provides a computer device, and this device includes:

[0064] A processor, suitable for executing a computer program;

[0065] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps in the optimal deployment and defense method of the energy storage inverter based on the two-layer Stackelberg game described in the first aspect above are implemented.

[0066] The fourth aspect of the present invention provides a computer-readable storage medium that stores a computer program. The computer program is adapted to be loaded and executed by a processor to implement the steps in the optimal deployment and defense method of the energy storage inverter based on the two-layer Stackelberg game described in the first aspect above.

[0067] The fifth aspect of the present invention provides a computer program product or a computer program.

[0068] The present invention provides a computer program product or a computer program. The computer program product or the computer program includes computer instructions that are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions to cause the computer device to implement the steps in the optimal deployment and defense method of the energy storage inverter based on the two-layer Stackelberg game described in the first aspect above.

[0069] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0070] The purpose of the present invention is to provide an optimal deployment and defense method of an energy storage inverter based on a two-layer Stackelberg game and related devices. By combining the optimal deployment of the energy storage inverter, robust optimization technology, and distance matching optimization algorithm, the limitations of existing defense methods in LAA are solved. The present invention can improve the defense ability of the power grid in a dynamic attack environment, optimize the scheduling of energy storage devices, reduce voltage deviation, and ensure the stability and reliability of the system. At the same time, an opportunity-constrained optimization model is used to cope with uncertainties, predict the behavior of attackers, and formulate defense strategies in advance, thereby enhancing the adaptability and security of the power grid.

[0071] In the lower-level problem, the attacker's optimization strategy is to randomly select attack nodes and adjust the load of the target nodes at different times to maximize the voltage deviation of the system nodes, thereby causing instability of the power grid. To cope with this dynamic behavior, the present invention adopts a time-coupling mechanism to analyze the behavior evolution of the attacker and help the defender identify potential threats in advance. In the upper-level problem, the defender's optimization strategy aims to minimize the voltage deviation in the power grid by optimizing the power output of the energy storage inverter. To cope with uncertainties, an opportunity-constrained optimization model is adopted to ensure that the defense strategy can effectively guarantee the stability of the power grid under various possible attack scenarios.

[0072] The present invention introduces an optimal distance matching optimization algorithm. By analyzing historical attack data, it predicts attack behaviors, calculates the optimal matching distance between the current attack pattern and historical data, and can accurately predict the attacker's strategy to help the defender take countermeasures in advance. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The accompanying drawings forming a part of this invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not unduly limit the present invention.

[0074] Figure 1 is an experimental diagram of the optimal deployment defense method for energy storage inverters based on a two - layer Stackelberg game shown in the embodiments of the present invention;

[0075] Figure 2 is a flowchart of the optimal deployment defense method for energy storage inverters based on a two - layer Stackelberg game shown in the embodiments of the present invention;

[0076] Figure 3 is a structural diagram of a 69 - node test system with an energy storage inverter shown in the embodiments of the present invention;

[0077] Figure 4 is a waveform diagram of the LAA attack effect analysis shown in the embodiments of the present invention;

[0078] Figure 5 is a comparison chart of defense costs shown in the embodiments of the present invention;

[0079] Figure 6 is a bar chart of the inverter operation cost analysis shown in the embodiments of the present invention;

[0080] Figure 7 is a structural diagram of the optimal deployment defense system for energy storage inverters based on a two - layer Stackelberg game shown in the embodiments of the present invention;

[0081] Figure 8 is a structural diagram of a computer device shown in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0082] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0083] It should be noted that the following detailed descriptions are all illustrative and are intended to provide a further explanation 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.

[0084] It should be noted that the terms used herein are only for describing specific embodiments 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 forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0085] To facilitate the understanding of the technical solution of the present invention, some technical terms related to the present invention are introduced below.

[0086] Load Alteration Attack (LAA) is a cyber-physical collaborative attack against the power cyber-physical system. By illegally controlling the controllable loads on the demand side (such as smart appliances, electric vehicle chargers, etc.), it changes the load demand distribution of the power grid, thereby triggering frequency fluctuations, line overloads, or cascading failures, and ultimately threatening the stability of the power system. Its core goal is to disrupt the supply-demand balance of the power grid, interfere with the power market, or cause physical equipment damage.

[0087] The Linearized Distribution Network Power Flow Model (LinDistFlow) is a simplified version of the traditional DistFlow model. By linearizing the power balance equation, it reduces the computational complexity and is suitable for the rapid analysis of radial distribution networks. Its core physical quantities include the node voltage amplitude, line active / reactive power, and network loss. By using the second-order cone relaxation technique to handle the non-linear constraints, it forms an analytic linear or convex optimization problem.

[0088] The two-layer Stackelberg game is a game model that combines hierarchical decision-making and leader-follower interaction, including two levels of optimization problems: (1) The upper layer (leader): Prioritizes formulating strategies and optimizes its own goals based on the responses of the lower-layer participants; (2) The lower layer (follower): Adjusts its own decisions according to the upper-layer strategy to pursue the maximization of individual interests; This model achieves Nash equilibrium through a dynamic game process.

[0089] Based on this, the present invention provides a defense method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game. Referring to Figure 1 , the method described in this embodiment includes a defender (leader) and an attacker (follower). The attacker (follower) randomly selects attack nodes and injects active power and reactive power into the attack nodes; the defender (leader) aims to minimize the voltage difference and the operating cost of the energy storage inverter; the attacker (follower) installs energy storage inverters to achieve the defender's goal, and the attacker aims to maximize the voltage difference. According to this concept, referring to Figure 2 , the defense method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game according to the present invention includes:

[0090] Based on the load power disturbance and reactive power disturbance of each node under the LAA attack, a LinDistFlow model is constructed;

[0091] Taking the maximization of the voltage deviation of all attacked nodes during the entire attack period as the first objective function, combined with the first constraint condition, a dynamic model of the LAA attack is constructed;

[0092] Taking the minimization of the operating cost of the energy storage inverter and the voltage deviation of the attacked nodes as the second objective function, combined with the second constraint condition, a dynamic model of the LAA defense is constructed;

[0093] Based on the load power disturbance and reactive power disturbance of each node, a confidence parameter is introduced to construct an optimization model based on chance constraints;

[0094] If the defender knows the injection power of the attacker, according to the LinDistFlow model, the dynamic models of the LAA attack and the LAA defense are solved to maximize the objectives of the attacker and the defender, and a defense strategy is formulated in advance according to the attacker's data;

[0095] If the defender cannot master the injection power of the attacker, according to the optimization model based on chance constraints, the dynamic model of the LAA defense is solved to minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data and formulate a defense strategy in advance.

[0096] The present invention combines the optimal deployment of energy storage inverters, robust optimization technology and distance matching optimization algorithm to solve the limitations of existing defense methods in LAA. The present invention can improve the defense ability of the power grid in a dynamic attack environment, optimize the scheduling of energy storage devices, reduce voltage deviation, and ensure the stability and reliability of the system. At the same time, a chance-constrained optimization model is used to cope with uncertainties, predict the attacker's behavior and formulate a defense strategy in advance, thereby enhancing the adaptability and security of the power grid.

[0097] The following is a detailed description of this embodiment:

[0098] Step (1): In the face of the LAA attack, the intelligent power grid defense method is based on the optimization modeling of the two-layer Stackelberg game to describe the confrontation relationship between the attacker and the defender. The lower-layer model describes that the attacker randomly selects the attacked nodes and maximizes the voltage deviation of the power grid by adjusting the load of the attacked nodes. The upper-layer model formulates the optimal defense strategy by optimizing the power output of the energy storage inverter to minimize the voltage deviation. The present invention can effectively improve the stability and security of the power grid in a dynamic attack environment.

[0099] Specifically, in this step, a linearized distribution network power flow model (LinDistFlow), an energy storage inverter (ESI) model, and an LAA model are adopted to construct an attack-defense game framework for smart grids.

[0100] To describe the power flow relationship in the distribution network, the LinDistFlow model is adopted. The LinDistFlow model can effectively simplify the power flow calculation and is widely used in power grid optimization problems. Its basic equations are as follows:

[0101]

[0102] The above formula represents the conservation of active power at node i, that is, the inflow active power P ji minus the outflow active power P ij is equal to the node load

[0103]

[0104] The above formula represents the conservation of reactive power at node i, that is, the inflow reactive power Q ji minus the outflow reactive power Q ij is equal to the node load

[0105]

[0106] The above formula represents the square difference of voltages between nodes i and j, which is related to the power (P ij , Q ij ) along this line and the line parameters (R ij , X ij ).

[0107] Under the LAA attack, the attacker manipulates high-power devices to quickly change the system load, resulting in grid instability. The energy storage inverter suppresses load fluctuations, maintains voltage and frequency stability, and provides backup power by adjusting charge and discharge, enhancing the anti-attack ability of the power grid.

[0108]

[0109]

[0110] The ESI injects active power P bat,i and reactive power Q bat,i into node i to stabilize the node voltage, relieve the grid fluctuations caused by the LAA attack, and improve system stability.

[0111] The LAA attack disrupts the load power and reactive power The process of changing the power distribution of the power grid and thus affecting system stability. Modify the LinDistFlow model formula to:

[0112]

[0113] Step (2): In view of the dynamic characteristics and time evolution law of the LAA attack, the present invention introduces a time coupling mechanism to describe the system state and attack impact at different times. The attacker can optimize the attack strategy across time periods and adjust the load of the target nodes to maximize the voltage deviation of the power grid and exacerbate system instability. This model reveals the law of attack behavior changing with time and provides a quantitative analysis method for optimizing defense strategies, which helps to improve the adaptability and robustness of the defense system in the face of continuous attacks.

[0114] Specifically, the LAA attack has the characteristics of dynamic evolution. The behavior of the attacker changes with time, and the defense strategy needs to be optimized in real time to adapt to the changing attack patterns. The present invention introduces a time coupling mechanism to accurately depict the system state and the attack evolution process, and realizes a defense strategy optimized across time periods. By dynamically managing energy storage devices, the system can effectively resist the LAA attack at different time points and improve the overall stability. To quantify the impact of the LAA attack on the voltage stability of the system, the present invention takes maximizing the voltage deviation of all attacked nodes during the entire attack period as the objective function and provides a targeted optimization scheme.

[0115] Objective function of the attacker:

[0116]

[0117] Among them, t represents time, and T is the set of the entire time range, indicating that this objective function considers the impact of the attack at multiple moments. N a is the set of all attack target nodes, indicating that the attacker may launch attacks on different nodes. V i (t) represents the actual voltage value of node i at time t. represents the standard voltage value of node i.

[0118] Node power balance constraint:

[0119]

[0120]

[0121] The node power constraint ensures the balance of the active power and reactive power of each node, and introduces attack disturbance terms and to describe the impact of the LAA attack on the power distribution.

[0122] Voltage constraint:

[0123]

[0124] Describe the relationship of the square difference of voltages between adjacent nodes, and calculate the voltage deviation based on the line impedance (R ij 、Q ij ) and power flow (P ij 、Q ij ) to evaluate the impact of the LAA attack on the system voltage stability.

[0125] Attack perturbation range constraint:

[0126]

[0127] Limit the maximum amplitude of the attack perturbation to ensure that the perturbation amount does not exceed η times the node load, and ensure the rationality of the attack impact.

[0128] Line power flow constraint:

[0129]

[0130] Limit the maximum power flow of the line to ensure that the system still maintains physical operation constraints under the attack.

[0131] In this step, through the time coupling mechanism, a dynamic modeling of the LAA attack is constructed to quantify the impact of the attack on the system in the way of maximizing the voltage difference. The attack modeling captures the voltage deviation of each node at all times through the objective function, and the constraint conditions ensure power flow balance, voltage relationship and physical operation limitations, so as to accurately describe the dynamic evolution of the LAA attack.

[0132] Step (3): In the defender's optimization model, the key to coping with the LAA attack lies in optimizing the operation of the energy storage inverter to simultaneously minimize two types of costs: the inverter operation cost and the voltage deviation. By optimizing the scheduling and control of the energy storage device, the defender can effectively reduce the impact of the LAA attack on the distribution network while ensuring the system stability. Under this framework, the defender needs to balance between cost and voltage stability and formulate an optimal operation strategy to improve the overall robustness and anti-interference ability of the distribution system.

[0133] Specifically, this step is based on a two-layer optimization framework to dynamically adjust the operation strategy of the energy storage inverter to simultaneously minimize the inverter operation cost and the voltage deviation. By optimizing the power injection of the energy storage inverter, the power balance between nodes is ensured, and the system stability is maintained under the attack perturbation. The model constraints include power balance constraints, energy storage capacity limitations, voltage relationships and power flow constraints to ensure the feasibility of the system in a dynamic attack environment, enhance the system's ability to resist the LAA attack, and at the same time reduce the operation cost of the energy storage inverter.

[0134] Defender's objective function:

[0135]

[0136] Among them, N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charging and discharging power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ i represents the additional fixed operating cost of device i; λ represents the trade-off coefficient, which is used to balance the trade-off between voltage stability and energy storage cost.

[0137] Node power balance constraint:

[0138]

[0139] The energy storage inverter compensates for the power deviation caused by the attack by controlling P bat,i (t) and Q bat,i (t) to inject additional active and reactive power, thereby ensuring node power balance, reducing voltage fluctuations, improving the anti-interference ability of the system, and reducing the impact of LAA attacks on the system operation.

[0140] Voltage constraint:

[0141]

[0142] Describes the energy evolution of the energy storage device. The current energy storage level depends on the energy at the previous moment and the current charging and discharging power:

[0143]

[0144] Constrains the charging and discharging power of the energy storage device to ensure that it does not exceed the set ratio:

[0145]

[0146] Ensures that the energy level of the energy storage device remains within the allowable range:

[0147]

[0148] Restricts the power transmission capacity of each line to prevent overload:

[0149]

[0150] This defense optimization model compensates for LAA attack disturbances by regulating the power output of energy storage inverters, maintaining power balance and voltage stability. The constraint conditions ensure the safe operation of energy storage, prevent line overload, thereby improving the anti-attack ability and stability of the power grid while reducing the defense cost.

[0151] Step (4): In view of the uncertainty of LAA attacks, the present invention constructs an optimization model based on chance constraints to enhance the adaptability and robustness of defense strategies. A robust optimization model based on optimal distance matching is proposed and combined with the chance constraint optimization method. By optimizing the model parameters, an optimal balance is achieved between system stability and minimization of operating costs. Compared with traditional deterministic methods, this method can adaptively adjust defense strategies and enhance the reliability and anti-interference ability of the distribution system in complex attack environments.

[0152] Specifically, the present invention adopts an optimization model based on chance constraints to cope with the uncertain disturbances brought by LAA attacks. The optimization method is enhanced by introducing uncertain disturbances. Specifically, it is ensured that the power disturbances ( and ) of each node are kept within an acceptable tolerance range to cope with the impact of LAA on the normal load and power flow of the system. This tolerance range is proportional to the load of each node, enabling the system to withstand larger disturbances under high load conditions and automatically tightening the tolerance range under low load, thereby maintaining system stability.

[0153] In addition, the parameter ε is introduced to quantify the system's tolerance to uncertainty. The defense cost under uncertain attacks is higher than that under deterministic attacks. By adjusting ε, it can be ensured that there is a certain deviation between the real data and the predicted data, and this deviation is controlled within an acceptable range, enabling the system to remain stable when facing uncertain attacks. Although the defense cost is slightly higher than that under deterministic attacks, it can effectively enhance the robustness of the system and ensure the balance between security and economy in a more complex attack environment.

[0154]

[0155] Among them, η represents the maximum amplitude of the limited attack disturbance. The tolerance range is proportional to the load of each node, enabling the system to accommodate larger disturbances when the load is high and narrowing the tolerance range when the load is low, thereby ensuring the stability of the system under different load conditions. represents the reactive power of node i at time t.

[0156] The present invention effectively enhances the defense ability of the power grid against uncertain attack behaviors through the chance constraint optimization method, ensures that the system can maintain stable operation under different load conditions, and optimizes the defense cost while ensuring security. The present invention not only enhances the robustness of the power grid but also improves the adaptability and practicality of defense strategies.

[0157] Step (5): To cope with unknown attack types and enhance the robustness of the defense, the present invention proposes a minimum matching distance algorithm. This algorithm optimizes the matching degree between the predicted result and the actual attack pattern, enabling the defense system to more accurately identify and understand the attacker's behavior. By reducing the matching error, the defense system can effectively improve its attack pattern recognition ability, avoid misjudgment caused by prediction deviation, and thus ensure more precise defense measures when facing different attack types.

[0158] Specifically, in the smart grid defense system, in view of the uncertainty of the attacker's behavior, a robust optimization method based on chance constraints is adopted to improve the robustness and stability of the system. By introducing a binary variable φ, the situations of known and unknown attacker behaviors are respectively dealt with. When φ = 0, the defender knows the injection power of the attacker, and a two-layer Stackelberg game optimization framework can be used for solution; when φ = 1, the defender cannot accurately grasp the injection power of the attacker, so a chance-constrained robust optimization method is adopted. By searching 100 attack scenarios, the current attack nodes are matched, and the injection power of the attacker is determined. During the optimization process, first, the matching distance is minimized, and the optimal matching metric is used to compare the predicted data with the data of the closest attack scenario to ensure that the matching error does not exceed the threshold ρ. Secondly, probability constraints are used to ensure that the power perturbation and deviation does not exceed the set tolerance range and and ensure that this constraint holds with a probability of at least 1 - ε. Specifically, the optimization objective is to minimize the probability that the power deviation violates the tolerance range and ensure that this probability does not exceed 1 - ε, that is:

[0159]

[0160] In the case of φ = 1, the defender cannot accurately grasp the power injection of the attacker, so it is necessary to optimize to reduce the proportion of power perturbation exceeding the allowable range so that it does not exceed the set threshold ε:

[0161]

[0162] In addition, to improve the accuracy of attack behavior prediction, the optimization process also needs to minimize the matching distance between the predicted attack data and the actual attack data and ensure that this distance does not exceed the threshold ρ:

[0163]

[0164] Through the above-mentioned optimization constraints, the defense strategy of the present invention can maintain robustness in the face of uncertain attacks, ensure the stable operation of the power grid system, and effectively reduce unnecessary defense costs caused by prediction errors. Specifically, the present invention limits the probability of power deviation through the opportunity constraint mechanism, so that the system can still be maintained within the safe operating range, thereby improving the reliability of the defense strategy. In addition, by minimizing the matching distance between the predicted attack data and the actual attack data, the ability to identify attack patterns can be enhanced, allowing defenders to more accurately assess potential threats and avoid excessive or insufficient defense due to information asymmetry.

[0165] The present invention installs an energy storage inverter in the IEEE69 node system, such as Figure 3 shown.

[0166] To evaluate the effectiveness of the LAA attack, we first establish a baseline model based on the system load data before the attack, and compare and analyze the load changes observed after the attack. By implementing the LAA attack at different nodes in the distribution network, we monitor and record the corresponding load change trends. Figure 4 As shown in the figure, the LAA attack causes a significant increase in the load on the distribution network, further verifying the effectiveness of the designed attack model.

[0167] In the LAA attack environment, ESI plays a key role in weakening the impact of the attack by adjusting the output power and stabilizing the grid voltage, thereby greatly improving the stability and security of the distribution network. These inverters can provide additional active and reactive power to help maintain load balance, reduce voltage fluctuations, and optimize system power flow, effectively resisting LAA attacks and ensuring the continuous operation of the grid. However, this process is accompanied by frequent power adjustments and inverter operations, resulting in certain operating costs.

[0168] like Figure 5 As shown, the method proposed in the present invention not only successfully mitigates the impact of LAA attacks, but also significantly reduces operating costs compared to unprotected solutions, showing better economic benefits and technical advantages.

[0169] Analysis of inverter operation cost in different scenarios, such as Figure 6 As shown in the figure, the operating costs of the inverter under deterministic and uncertain attack environments are compared and analyzed, aiming to evaluate the impact of the uncertainty of attack behavior on the system operating efficiency. In the case of deterministic attacks, since the attacker's behavior is predictable, the system can optimize the response strategy in a targeted manner, thereby effectively reducing the operating cost. In the uncertain attack scenario, since the attack mode is difficult to predict, the inverter needs to adjust the output power more frequently to maintain system stability, which will lead to higher operating costs. This analysis emphasizes how to strike a balance between cost control and the robustness of the defense strategy when facing uncertain threats.

[0170] Combined above Figure 1 The method for optimizing the deployment and defense of a storage inverter based on a two - layer Stackelberg game provided by the embodiments of the present invention has been introduced in detail. Next, the system for optimizing the deployment and defense of a storage inverter based on a two - layer Stackelberg game provided by the embodiments of the present invention will be introduced with reference to the accompanying drawings.

[0171] Figure 4 is a schematic structural diagram of a system for optimizing the deployment and defense of a storage inverter based on a two - layer Stackelberg game shown in the embodiments of the present invention. Referring to Figure 7 , the system of the present invention includes:

[0172] A system for optimizing the deployment and defense of a storage inverter based on a two - layer Stackelberg game includes:

[0173] A first model - building module, which is configured to: based on the load power perturbation and reactive power perturbation of each node under LAA attacks, build a LinDistFlow model;

[0174] A second model - building module, which is configured to: taking maximizing the voltage deviation of all attacked nodes during the entire attack period as the first objective function, and combining with the first constraint condition, build a dynamic model of LAA attacks;

[0175] A third model - building module, which is configured to: taking minimizing the operating cost of the storage inverter and the voltage deviation of the attacked nodes as the second objective function, and combining with the second constraint condition, build a dynamic model of LAA defense;

[0176] A fourth model - building module, which is configured to: based on the load power perturbation and reactive power perturbation of each node, introduce a confidence parameter, and build an optimization model based on chance - constrained;

[0177] A first solving module, which is configured to: if the defender knows the injection power of the attacker, according to the LinDistFlow model, solve the dynamic models of LAA attacks and LAA defense to maximize the objectives of the attacker and the defender, and formulate a defense strategy in advance according to the attacker's data;

[0178] A second solving module, which is configured to: if the defender cannot master the injection power of the attacker, according to the optimization model based on chance - constrained, solve the dynamic model of LAA defense, minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data and formulate a defense strategy in advance.

[0179] In some possible embodiments, the LinDistFlow model is represented by the following formula:

[0180]

[0181] Among them, P ji represents the active power flowing into node i, and P ij represents the active power flowing out of node i. represents the active load of the node. represents the load power disturbance of each node. Q ji represents the reactive power flowing into node i, and Q ij represents the reactive power flowing out of node i. represents the reactive power disturbance of each node.

[0182] In some possible embodiments, the first objective function is represented by the following formula:

[0183]

[0184] Among them, t represents time, T is the set of the entire time range, and N a is the set of all attacked target nodes, and V i (t) represents the actual voltage value of node i at time t. represents the standard voltage value of node i;

[0185] In some possible embodiments, the first constraint conditions include: the first node power balance constraint, the voltage constraint, the attack perturbation range constraint, and the line power flow constraint.

[0186] In some possible embodiments, the first node power balance constraint is used to ensure the active power and reactive power balance of each node, and introduces the load power disturbance of each node and the reactive power disturbance to describe the impact of the LAA attack on the power distribution;

[0187] The voltage constraint is used to calculate the voltage deviation based on the line impedance, the active power flowing out of the node, and the reactive power flowing out of the node, and evaluate the impact of the LAA attack on the system voltage stability;

[0188] The second objective function is represented by the following formula:

[0189]

[0190] Among them, N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charge and discharge power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ iDenote the additional fixed operating cost of device i; λ represents the trade-off coefficient used to balance the trade-off between voltage stability and energy storage cost.

[0191] In some possible embodiments, the second constraint condition includes: the second node power balance constraint, the voltage constraint, the charge and discharge power constraint of the energy storage device, the energy level constraint of the energy storage device, and the power transmission capacity constraint of each line.

[0192] In some possible embodiments, the second node power balance constraint is used to control the active power and reactive power injected into the node, compensate for the power deviation caused by the attack, and ensure the node power balance.

[0193] In some possible embodiments, the optimization model based on chance constraint is expressed by the following formula:

[0194]

[0195] Wherein, represents the load power perturbation of each node, represents the reactive power perturbation of each node, represents the active load of the node, η represents the maximum amplitude of the limited attack perturbation, represents the reactive power of node i at time t.

[0196] In some possible embodiments, if the defender cannot master the injection power of the attacker, by optimizing, reduce the proportion of the power perturbation exceeding the allowable range so that it does not exceed the set threshold ε:

[0197]

[0198] Wherein, φ = 1 indicates that the defender cannot master the injection power of the attacker.

[0199] According to the embodiment of the present invention, the optimized deployment defense system of the energy storage inverter based on the two-layer Stackelberg game can correspond to executing the method described in the embodiment of the present invention, and the above and other operations and / or functions of each module of the optimized deployment defense system of the energy storage inverter based on the two-layer Stackelberg game are respectively for realizing Figure 2 the corresponding processes of the respective methods in, for the sake of brevity, will not be elaborated here.

[0200] See Figure 8Structural diagram of the computer device shown. The computer device includes a processor, a communication interface, and a computer-readable storage medium. Among them, the processor, the communication interface, and the computer-readable storage medium can be connected through a bus or other means. Among them, the communication interface is used to receive and send data. The computer-readable storage medium can be stored in the memory of the computer device. The computer-readable storage medium is used to store computer programs. The computer programs include program instructions. The processor is used to execute the program instructions stored in the computer-readable storage medium. The processor (or CPU (Central Processing Unit, central processor)) is the computing core and control core of the computer device, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding steps in the embodiment of the optimization deployment defense method of the energy storage inverter based on the double-layer Stackelberg game.

[0201] This embodiment provides a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in the computer device and is used to store programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and, of course, the extended storage medium supported by the computer device. The computer-readable storage medium provides a storage space, and this storage space stores the processing system of the computer device.

[0202] Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in this storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory; optionally, it can also be at least one computer-readable storage medium located far from the aforementioned processor.

[0203] In one embodiment, one or more instructions are stored in the computer-readable storage medium; the processor loads and executes one or more instructions stored in the computer-readable storage medium to implement the corresponding steps in the embodiment of the optimization deployment defense method of the energy storage inverter based on the double-layer Stackelberg game.

[0204] This embodiment provides a computer program product or a computer program. The computer program product or the computer program includes computer instructions, and the computer instructions are stored in the computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the corresponding steps in the embodiment of the optimization deployment defense method of the energy storage inverter based on the double-layer Stackelberg game.

[0205] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories and optical memories, etc.) that contain computer-usable program code.

[0206] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0207] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0208] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0209] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above various methods. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0210] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An optimized deployment defense method for energy storage inverters based on a two-layer Stackelberg game, characterized in that Including: Construct a LinDistFlow model based on the load power disturbance and reactive power disturbance of each node under the LAA attack; Taking the maximization of the voltage deviation of all attacked nodes during the entire attack period as the first objective function, combined with the first constraint condition, construct a dynamic model of the LAA attack; Taking the minimization of the energy storage inverter operation cost and the voltage deviation of the attacked nodes as the second objective function, combined with the second constraint condition, construct a dynamic model of the LAA defense; Based on the load power disturbance and reactive power disturbance of each node, introduce a confidence parameter to construct an optimization model based on chance constraints; If the defender knows the injection power of the attacker, according to the LinDistFlow model, solve the dynamic models of the LAA attack and the LAA defense to maximize the objectives of the attacker and the defender, and formulate a defense strategy in advance according to the attacker's data; If the defender cannot master the injection power of the attacker, according to the optimization model based on chance constraints, solve the dynamic model of the LAA defense, minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data and formulate a defense strategy in advance.

2. The defense method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game according to claim 1, wherein The LinDistFlow model is represented by the following formula: Among them, P ji represents the active power flowing into node i, and P ij represents the active power flowing out of node i, represents the active load of the node, represents the load power disturbance of each node, and Q ji represents the reactive power flowing into node i, and Q ij represents the reactive power flowing out of node i, represents the reactive power disturbance of each node.

3. The defense method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game according to claim 1, wherein The first objective function is represented by the following formula: where t represents time, T is the set of the entire time range, and N a is the set of all attacked target nodes, and V i (t) represents the actual voltage value of node i at time t, represents the standard voltage value of node i; Or, The first constraint condition includes: the first node power balance constraint, voltage constraint, attack disturbance range constraint, and line power flow constraint; Or, The first node power balance constraint is used to ensure the active power and reactive power balance of each node and introduce the load power disturbance of each node and reactive power disturbance which is used to characterize the impact of LAA attacks on power distribution; The voltage constraint is used to calculate the voltage deviation according to the line impedance, the active power flowing out of the node, and the reactive power flowing out of the node, and evaluate the impact of the LAA attack on the system voltage stability.

4. The defense method for optimizing the deployment of energy storage inverters based on a two-layer Stackelberg game according to claim 1, wherein The second objective function is represented by the following formula: Among them, N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charging and discharging power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ i represents the additional fixed operating cost of device i; λ represents the trade-off coefficient used to balance the trade-off between voltage stability and energy storage cost; Or, The second constraint condition includes: the second node power balance constraint, voltage constraint, charge and discharge power constraint of the energy storage device, energy level constraint of the energy storage device, and power transmission capacity constraint of each line; Or, The second node power balance constraint is used to control the active power and reactive power of the injection node, compensate for the power deviation caused by the attack, and ensure node power balance.

5. The defense method for optimizing the deployment of energy storage inverters based on the two-layer Stackelberg game according to claim 1, wherein The optimization model based on chance constraints is represented by the following formula: Among them, represents the load power disturbance of each node, represents the reactive power disturbance of each node, represents the active load of the node, and η represents the maximum amplitude of the limited attack disturbance, represents the reactive power of node i at time t; Or, If the defender cannot master the injection power of the attacker, optimize to reduce the proportion of power disturbance exceeding the allowable range so that it does not exceed the set threshold ε: Where φ = 1 indicates that the defender cannot master the injection power of the attacker.

6. An optimized deployment defense system for energy storage inverters based on a two-layer Stackelberg game, characterized in that, Including: The first model construction module is configured to: construct a LinDistFlow model based on the load power disturbance and reactive power disturbance of each node under the LAA attack; The second model construction module is configured to: taking the maximization of the voltage deviation of all attacked nodes during the entire attack period as the first objective function, combined with the first constraint condition, construct a dynamic model of the LAA attack; The third model construction module is configured to: taking the minimization of the energy storage inverter operation cost and the voltage deviation of the attacked nodes as the second objective function, combined with the second constraint condition, construct a dynamic model of the LAA defense; The fourth model construction module is configured to: introduce a confidence parameter based on the load power disturbance and reactive power disturbance of each node, and construct an optimization model based on chance-constrained programming. The first solution module is configured to: if the defender knows the attacker's injection power, solve the dynamic models of the LAA attack and the LAA defense according to the LinDistFlow model, maximize the objectives of the attacker and the defender, and formulate a defense strategy in advance according to the attacker's data. The second solution module is configured to: if the defender cannot master the attacker's injection power, solve the dynamic model of the LAA defense according to the optimization model based on chance-constrained programming, minimize the matching distance between the predicted attack data and the actual attack data, predict the attacker's data, and formulate a defense strategy in advance.

7. The defense system for optimizing the deployment of energy storage inverters based on the two-layer Stackelberg game according to claim 6, wherein The LinDistFlow model is expressed by the following formula: Among them, P ji represents the active power flowing into node i, and P ij represents the active power flowing out of node i, represents the active power load of the node, represents the load power disturbance of each node, and Q ji represents the reactive power flowing into node i, and Q ij represents the reactive power flowing out of node i, represents the reactive power disturbance of each node; Or, The first objective function is expressed by the following formula: where t represents time, T is the set of the entire time range, and N a is the set of all attacked target nodes, and V i (t) represents the actual voltage value of node i at time t, represents the standard voltage value of node i; Or, The first constraint conditions include: the first node power balance constraint, the voltage constraint, the attack disturbance range constraint, and the line power flow constraint. Or, The first node power balance constraint is used to ensure the active power and reactive power balance of each node, and introduce the load power disturbance of each node and reactive power disturbance is used to describe the impact of LAA attacks on power distribution; The voltage constraint is used to calculate the voltage deviation according to the line impedance, the active power flowing out of the node, and the reactive power flowing out of the node, and evaluate the impact of the LAA attack on the system voltage stability. The second objective function is expressed by the following formula: Among them, N der represents the set of nodes where energy storage inverters are installed; P bat,i (t) represents the charging and discharging power of energy storage inverter i at time t; γ i represents the unit power cost coefficient of energy storage device i; δ i represents the additional fixed operating cost of device i; λ represents the trade-off coefficient used to balance the trade-off between voltage stability and energy storage cost; Or, The second constraint conditions include: the second node power balance constraint, the voltage constraint, the charge and discharge power constraint of the energy storage device, the energy level constraint of the energy storage device, and the power transmission capacity constraint of each line. Or, The second node power balance constraint is used to control the active power and reactive power of the injection node, compensate for the power deviation caused by the attack, and ensure the node power balance. Or, The optimization model based on chance-constrained programming is expressed by the following formula: Among them, represents the load power disturbance of each node, represents the reactive power disturbance of each node, represents the active load of the node, and η represents the maximum amplitude of the limited attack disturbance, represents the reactive power of node i at time t; Or, If the defender cannot master the attacker's injection power, optimize to reduce the proportion of power disturbance exceeding the allowable range so that it does not exceed the set threshold ε: Where φ = 1 indicates that the defender cannot master the attacker's injection power.

8. A computer device, characterized in that a processor adapted to execute a computer program; a computer-readable storage medium storing a computer program, which when executed by the processor, implements the steps in the defense method for optimizing the deployment of the energy storage inverter based on the two-layer Stackelberg game according to any one of claims 1-5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and the computer program is adapted to be loaded and executed by the processor to implement the steps in the defense method for optimizing the deployment of the energy storage inverter based on the two-layer Stackelberg game according to any one of claims 1-5.

10. A computer program product, characterized in that, The computer program product includes a computer program, which when executed by the processor, implements the steps in the defense method for optimizing the deployment of the energy storage inverter based on the two-layer Stackelberg game according to any one of claims 1-5.

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