A method and system for preventing and dispatching power cyber-physical systems under extreme weather conditions

Abstract

This invention discloses a preventive scheduling method and system for power cyber-physical systems under extreme weather conditions. Based on the impact of physical-side anomalies on the information-side, an uncertainty set of the power cyber-physical system is constructed. A first-stage objective function is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. First-stage constraints are also established. A second-stage objective function is established with the goal of minimizing unit output costs, wind curtailment costs, and real-time load shedding costs. Second-stage constraints are also established based on the impact of information-side anomalies on the physical-side. The preventive scheduling strategy generation model is solved to obtain the preventive scheduling strategy, thereby effectively improving the resilience and power supply reliability of the power cyber-physical system under extreme weather conditions.

Description

Technical Field

[0001] This invention relates to the field of power cyber-physical system dispatching technology, and in particular to a method and system for preventing the dispatching of power cyber-physical systems under extreme weather conditions. Background Technology

[0002] With the development of smart grids and the energy internet, the digital modern power system, consisting of the primary-side power grid physical system and the secondary-side measurement and control information system and communication network, has been widely regarded as a typical cyber-physical system (CPS).

[0003] In response to extreme weather, power cyber-physical systems (FPS) often enhance system resilience by adjusting generator configurations, preemptively shedding loads, and modifying communication routes. These methods can be collectively referred to as preemptive dispatch strategies for extreme weather. Current preemptive dispatch strategies for power systems under extreme weather conditions typically only consider generator configurations and the preemptive load shedding at each node, while communication routes on the information side are determined using a separate optimization model. However, the resulting generator configuration strategies and communication routing schemes are prone to mismatch, compromising the system's resilience and power supply reliability under extreme weather conditions. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for preventive dispatching of power cyber-physical systems under extreme weather conditions, which can improve the resilience and power supply reliability of power cyber-physical systems under extreme weather conditions.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for preventive dispatching of a power cyber-physical system under extreme weather conditions, comprising the following steps: Constructing the uncertainty set of the power information physical system based on the impact of physical-side anomalies on the information side; The objective function for the first stage is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage costs under the worst-case scenario. The first-stage constraints corresponding to the first-stage objective function are also established. A second-stage objective function is established with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost. A second-stage constraint corresponding to the second-stage objective function is established based on the impact of information-side anomalies on the physical side. Based on the uncertainty set, the first-stage objective function, the first-stage constraints, the second-stage objective function, and the second-stage constraints, a model for generating preventive dispatch strategies for the power cyber-physical system under extreme weather conditions is generated. The preventive scheduling strategy generation model is solved to obtain the preventive scheduling strategy, which includes unit combination, pre-load shedding amount of each load node, and primary and backup routes of each communication substation.

[0006] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows: A power cyber-physical system preventive dispatching system under extreme weather conditions includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the aforementioned power cyber-physical system preventive dispatching method under extreme weather conditions.

[0007] The beneficial effects of this invention are as follows: An uncertainty set of the power cyber-physical system is constructed based on the impact of physical-side anomalies on the information-side. A first-stage objective function is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Corresponding first-stage constraints are also established. A second-stage objective function is established with the goal of minimizing unit output costs, wind curtailment costs, and real-time load shedding costs. Corresponding second-stage constraints are established based on the impact of information-side anomalies on the physical-side. The preventive scheduling strategy generation model is solved to obtain the preventive scheduling strategy. This strategy can simultaneously optimize unit combination, pre-scheduled load amounts at each load node, and primary / backup routing for each communication substation. Furthermore, the impact of physical-side anomalies on the information-side and the impact of information-side anomalies on the physical-side are considered in both the uncertainty set and the second-stage constraints. Therefore, the obtained strategy can effectively improve the resilience and power supply reliability of the power cyber-physical system under extreme weather conditions. Attached Figure Description

[0008] Figure 1 This is a flowchart of a method for preventing and dispatching a power cyber-physical system under extreme weather conditions, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a power cyber-physical system for preventing and dispatching under extreme weather conditions, according to an embodiment of the present invention. Figure 3 This is a modified IEEE 30-node system and typhoon path diagram in a method for preventing and dispatching a power cyber-physical system under extreme weather conditions, according to an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the probability of damage to each line at different times in a power cyber-physical system preventive dispatching method under extreme weather conditions, according to an embodiment of the present invention. Figure 5 In an embodiment of the present invention, a method for preventing and dispatching a power cyber-physical system under extreme weather conditions is described. A schematic diagram illustrating the changes in the upper bound UB and the lower bound LB during the algorithm iteration process when the value is 0.02; Figure 6This is a schematic diagram of the unit combination in the optimal preventive dispatch strategy of a power cyber-physical system preventive dispatch method under extreme weather conditions according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the output of each thermal power unit under the worst-case scenario in a power cyber-physical system preventive dispatching method under extreme weather conditions according to an embodiment of the present invention. Figure 8 This is a schematic diagram comparing the actual output and maximum possible output of two wind farms under the worst-case scenario in a power cyber-physical system preventive dispatching method under extreme weather conditions according to an embodiment of the present invention. Figure 9 This is a schematic diagram of the pre-scheduled load shedding amount in each time period in the optimal preventive scheduling strategy of a power cyber-physical system preventive scheduling method under extreme weather conditions, according to an embodiment of the present invention. Detailed Implementation

[0009] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0010] Before detailing the embodiments of this application, some related concepts will first be explained: Column-and-Constraint Generation (C&CG) is a classic decomposition algorithm for solving optimization problems with uncertainty. Its core logic is to gradually generate key constraints / variables through iterative interaction of "main problem + sub-problems" and finally approach the global optimum.

[0011] In existing technologies, the generation of power system preventive dispatch strategies before extreme weather typically only considers unit combination and pre-load shedding at each node, while communication routing on the information side is determined using a separate optimization model. However, the resulting unit combination strategy and communication routing scheme are prone to mismatch, impairing the system's resilience and power supply reliability under extreme weather conditions.

[0012] To at least solve the above problems, please refer to Figure 1 This invention provides a method for preventing and dispatching power cyber-physical systems under extreme weather conditions, comprising the following steps: Constructing the uncertainty set of the power information physical system based on the impact of physical-side anomalies on the information side; The objective function for the first stage is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage costs under the worst-case scenario. The first-stage constraints corresponding to the first-stage objective function are also established. A second-stage objective function is established with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost. A second-stage constraint corresponding to the second-stage objective function is established based on the impact of information-side anomalies on the physical side. Based on the uncertainty set, the first-stage objective function, the first-stage constraints, the second-stage objective function, and the second-stage constraints, a model for generating preventive dispatch strategies for the power cyber-physical system under extreme weather conditions is generated. The preventive scheduling strategy generation model is solved to obtain the preventive scheduling strategy, which includes unit combination, pre-load shedding amount of each load node, and primary and backup routes of each communication substation.

[0013] As can be seen from the above description, the beneficial effects of the present invention are as follows: Based on the impact of physical-side anomalies on the information side, an uncertainty set of the power cyber-physical system is constructed. A first-stage objective function is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Corresponding first-stage constraints are also established. A second-stage objective function is established with the goal of minimizing unit output costs, wind curtailment costs, and real-time load shedding costs. Corresponding second-stage constraints are also established based on the impact of information-side anomalies on the physical side. The preventive scheduling strategy generation model is solved to obtain the preventive scheduling strategy. This allows for simultaneous optimization of unit combination, pre-scheduled load amounts at each load node, and primary / backup routing at each communication substation. Furthermore, the impact of physical-side anomalies on the information side and the impact of information-side anomalies on the physical side are considered in both the uncertainty set and the second-stage constraints. Therefore, the obtained strategy can effectively improve the resilience and power supply reliability of the power cyber-physical system under extreme weather conditions.

[0014] Furthermore, the uncertainty set of the power cyber-physical system, based on the impact of physical-side anomalies on the information-side, includes: Construct a first uncertainty set on the physical side of the power information physical system, the first uncertainty set including the transmission line fault matrix; Define the information branch-physical branch mapping matrix, the primary route reachability matrix, and the backup route reachability matrix; The transmission line fault matrix is ​​mapped to the communication line fault matrix based on the information branch-physical branch mapping matrix. Based on the communication line fault matrix, the primary route reachability matrix, and the backup route reachability matrix, a second uncertainty set is constructed to describe the relationship between the overall route reachability matrix and the communication line fault matrix; The final uncertain set is obtained based on the first uncertain set and the second uncertain set.

[0015] Furthermore, the first uncertainty set on the physical side of the power information physical system is constructed as follows: ; In the formula, Denotes the first uncertainty set on the physical side. Zp Represents the fault matrix of transmission lines. Indicates transmission line l During the period t The probability of failure, Represents auxiliary variables. Indicates transmission line l During the period t The fault status, A threshold representing the probability of line damage scenarios occurring at different time periods. Indicates transmission line l During the period t -1 is a fault status; The transmission line fault matrix is ​​mapped to the communication line fault matrix based on the information branch-physical branch mapping matrix, specifically as follows: ; In the formula, Z c Represents the communication line fault matrix. B Represents the information branch-physical branch mapping matrix; Based on the communication line fault matrix, the primary route reachability matrix, and the backup route reachability matrix, a second uncertainty set is constructed to describe the relationship between the overall route reachability matrix and the communication line fault matrix, specifically: ; In the formula, This represents the second uncertainty set describing the relationship between the overall route reachability matrix and the communication line fault matrix. W Represents the overall route reachability matrix. M ij The elements represent the reachability matrix of the main route. N ij Elements representing the reachability matrix of alternative routes W ij This represents an element of the overall route reachability matrix. This indicates that the main routing matrix of each communication substation is taken as the absolute value of each element. This represents the backup routing matrix for each communication substation, with each element taking its absolute value. The final uncertainty set is obtained based on the first uncertainty set and the second uncertainty set, specifically as follows: ; In the formula, This represents the final, uncertain set.

[0016] As described above, by associating transmission line and communication line faults through a mapping matrix, the mutual influence between the two can be captured, accurately characterizing the physical-information coupling uncertainty, integrating the reachability of primary / backup routes, incorporating the uncertainty of route switching after a fault, improving the completeness of the scenario, and the final uncertainty set can effectively support reliable decision-making.

[0017] Furthermore, the objective function for the first stage is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Specifically: ; In the formula, u g,t Indicates thermal power unit g During the period t Start and stop variables, This indicates the load determined during the preventive scheduling phase. d During the period t The shear load, This represents the main routing matrix for each communication substation. This represents the backup routing matrix for each communication substation. c g u This represents the cost coefficient for unit operation. c g on This represents the cost coefficient for starting up the generator unit. v g,t on Indicates thermal power unit g During the period t The startup operation variables, c g off This represents the cost coefficient for shutting down the generating unit. v g,t off Indicates thermal power unit g During the period t The shutdown operation variable, This represents the cost factor for pre-scheduled load shedding. Indicates the first preset positive number. E i Indicates information node i The importance of c b Indicates information branch b The relative length, X ib This represents an element of the main routing matrix for each communication substation. Y ib These represent the elements of the backup routing matrix for each communication substation. Indicates the second preset positive number.Q () represents a function representing the cost of real-time scheduling when using the current pre-scheduling decision in a scenario with an uncertain set.

[0018] As described above, the objective function of the first stage includes unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage costs under the worst-case scenario. The goal is to select the routing scheme with the minimum overall cost while minimizing the total physical cost, thus ensuring the robustness of the strategy obtained from the model.

[0019] Furthermore, the first-stage constraints corresponding to the first-stage objective function include: Establish constraints on thermal power unit start-up and shutdown time, pre-scheduled load shedding, total system reserve, communication routing logic, communication routing topology, and communication routing bandwidth corresponding to the objective function of the first stage; The first stage constraints are obtained based on the thermal power unit start-up and shutdown time constraints, the pre-scheduled load shedding constraints, the system total reserve constraints, the communication routing logic constraints, the communication routing topology constraints, and the communication routing bandwidth constraints.

[0020] As described above, establishing constraints on thermal power unit start-up and shutdown time, pre-scheduled load shedding, total system reserve, communication routing logic, communication routing topology, and communication routing bandwidth corresponding to the objective function of the first stage ensures that the final strategy is practical and effective.

[0021] Furthermore, a second-stage objective function is established with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost, as follows: ; In the formula, p g,t Indicates thermal power unit g During the period t of efforts, Represents renewable energy w During the period t Actual output Indicates load d During the period t Real-time load shedding, c g This represents the cost coefficient of the unit's output. c w This represents the cost coefficient for the curtailment of wind and solar power. Represents renewable energy w During the period t Maximum output This represents the cost coefficient for real-time load shedding.

[0022] As described above, the second stage is equivalent to the real-time scheduling stage. Under a given transmission line fault scenario, the total cost required for real-time scheduling is calculated. Therefore, the objective function of the second stage includes three parts: unit output cost, wind curtailment cost, and real-time load shedding cost, which basically covers all costs of real-time scheduling.

[0023] Furthermore, the second-stage constraints, based on the impact of information-side anomalies on the physical side and corresponding to the second-stage objective function, include: Based on the impact of information-side anomalies on the physical side, establish the following constraints corresponding to the objective function of the second stage: thermal power unit output constraints, thermal power unit ramping constraints, new energy output constraints, real-time load shedding constraints, system power balance constraints, and power flow safety constraints. The second stage constraints are obtained based on the thermal power unit output constraints, the thermal power unit ramping constraints, the new energy output constraints, the real-time load shedding constraints, the system power balance constraints, and the power flow safety constraints.

[0024] As described above, based on the impact of information-side anomalies on the physical side, constraints on thermal power unit output, thermal power unit ramping, new energy output, real-time load shedding, system power balance, and power flow safety are established corresponding to the objective function of the second stage. This accurately models various physical limitations in real-time scheduling and considers the impact of information-side anomalies on the physical side, ensuring the effectiveness and practicality of the overall strategy obtained by the model.

[0025] Furthermore, the preventive scheduling strategy generation model is solved to obtain preventive scheduling strategies including: After linearizing the nonlinear terms in the prevention scheduling strategy generation model, a linearized model is obtained; The linearized model is solved using a column and constraint generation algorithm to obtain a preventive scheduling strategy.

[0026] Furthermore, after linearizing the nonlinear terms in the aforementioned prevention scheduling strategy generation model, a linearized model is obtained, specifically: ; ; ; ; In the formula, x 1 indicates a continuous variable in the first stage of decision-making. x 2 represents the integer variable in the first-stage decision variables. a 1 represents the first coefficient vector. a 2 represents the second coefficient vector. b Represents the third coefficient vector. yThis represents the decision variables for the second stage. u Variables representing an uncertain set, This represents the feasible region of the decision variables in the first stage. A 1 indicates the first coefficient matrix. A 2 represents the second coefficient matrix. q Represents the fourth coefficient vector. ( x 2) Indicates dependence on first-stage decision variables x The uncertain set of 2, B ( x 2) represents the third coefficient matrix. e Represents the fifth coefficient vector. This represents the feasible region of the decision variables in the second stage. E This represents the fourth coefficient matrix. h Represents the sixth coefficient vector. G 1 represents the fifth coefficient matrix. G 2 represents the sixth coefficient matrix. N This represents the seventh coefficient matrix.

[0027] As described above, linearizing the nonlinear terms in the prevention scheduling strategy generation model makes it easier to solve. Using column and constraint generation algorithms to solve the linearized model is more efficient and accurate.

[0028] Please refer to Figure 2 Another embodiment of the present invention provides a power cyber-physical system prevention and dispatching system under extreme weather conditions, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the above-described power cyber-physical system prevention and dispatching method under extreme weather conditions.

[0029] The above-described method and system for preventive dispatching of power cyber-physical systems under extreme weather conditions are applicable to scenarios involving preventive dispatching of power cyber-physical systems under extreme weather conditions. The specific implementation methods described below illustrate these methods: Please refer to Figure 1 One embodiment of the present invention is as follows: A method for preventive dispatching of a power cyber-physical system under extreme weather conditions, comprising the following steps: In extreme weather conditions, line damage, renewable energy output, and load all exhibit significant uncertainties. To ensure power supply reliability under worst-case scenarios, a two-stage robust model is used to optimize preventative scheduling strategies.

[0030] S1. Constructing the uncertainty set of the power information physical system based on the impact of physical-side anomalies on the information side, specifically including S11-S15: S11. Construct the first uncertainty set on the physical side of the power information physical system. The first uncertainty set includes the transmission line fault matrix, specifically: ; In the formula, Denotes the first uncertainty set on the physical side. Z p Represents the fault matrix of transmission lines. Indicates transmission line l During the period t The failure probability can be obtained through methods such as vulnerability curves. This represents an auxiliary variable, such as the transmission line. l During the period t Fault, then It is 1 if it is 1, otherwise it is 0. Indicates transmission line l During the period t The fault state is Z p The elements are 1 for fault and 0 for normal. A threshold representing the probability of line damage scenarios occurring at different time periods. Indicates transmission line l During the period t -1 is the fault state; the left side of the inequality sign in the first equation is... t A scenario where a certain line is damaged during a certain period (by...) The probability of occurrence of a scenario is determined, and only scenarios with a probability greater than a certain threshold are included in the uncertainty set, which reduces the conservatism of the robust optimization model.

[0031] Among them, the transmission line fault matrix Z p Its dimension is the number of transmission lines. b p ×Number of time periods T Each row of this matrix represents a transmission line in the system, and each column represents a time period, specifically: .

[0032] Due to the application of Optical Fiber Composite Overhead Ground Wire (OPGW), there is coupling between transmission lines and communication lines.

[0033] S12. Define the information branch-physical branch mapping matrix, the primary route reachability matrix, and the backup route reachability matrix.

[0034] Among them, the elements of the main route reachability matrix M ijRepresents a node i During the period j The primary route reachability is represented by 1, indicating that the primary route is reachable, and 0, indicating that the primary route is unreachable. The elements of the backup route reachability matrix are also shown. N ij Similarly. The specific elements of each matrix are: ; .

[0035] S13. Map the transmission line fault matrix to the communication line fault matrix according to the information branch-physical branch mapping matrix, specifically as follows: ; In the formula, Z c This represents a communication line fault matrix, with its dimension being the number of communication lines. b c ×Number of time periods T , Its matrix elements and Z p Similarly, 1 indicates a fault, and 0 indicates normal operation. B The information branch-physical branch mapping matrix has the following dimensions: b c × b p The element corresponding to the coupled branch is 1, and the other elements are 0.

[0036] S14. Based on the communication line fault matrix, the primary route reachability matrix, and the backup route reachability matrix, construct a second uncertain set describing the relationship between the overall route reachability matrix and the communication line fault matrix, specifically: ; In the formula, This represents the second uncertainty set describing the relationship between the overall route reachability matrix and the communication line fault matrix. W Represents the overall route reachability matrix. M ij The elements represent the reachability matrix of the main route. N ij Elements representing the reachability matrix of alternative routes W ij This represents an element of the overall route reachability matrix. This indicates that the main routing matrix of each communication substation is taken as the absolute value of each element. This represents the backup routing matrix for each communication substation, with each element taking its absolute value.

[0037] S15. Obtain the final uncertainty set based on the first uncertainty set and the second uncertainty set, specifically as follows: ; In the formula, This represents the final, uncertain set.

[0038] S2. Establish a first-stage objective function with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Establish first-stage constraints corresponding to the first-stage objective function, specifically including S21-S23: S21. Establish the first-stage objective function with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Specifically: ; In the formula, u g,t Indicates thermal power unit g During the period t Start and stop variables, This indicates the load determined during the preventive scheduling phase. d During the period t The shear load, This represents the main routing matrix for each communication substation. This represents the backup routing matrix for each communication substation. c g u This represents the cost coefficient for unit operation. c g on This represents the cost coefficient for starting up the generator unit. v g,t on Indicates thermal power unit g During the period t The startup operation variables, c g off This represents the cost coefficient for shutting down the generating unit. v g,t off Indicates thermal power unit g During the period t The shutdown operation variable, This represents the cost factor for pre-scheduled load shedding. Indicates the first preset positive number. E i Indicates information node i The importance of c b Indicates information branch bThe relative length (cost) is obtained by comprehensively considering indicators such as latency, bandwidth, and reliability. X ib This represents an element of the main routing matrix for each communication substation. Y ib These represent the elements of the backup routing matrix for each communication substation. Indicates the second preset positive number. Q () represents a function representing the cost of real-time scheduling when using the current pre-scheduling decision in a scenario with an uncertain set.

[0039] Among them, the start / stop variable, start operation variable, and stop operation variable are all 0-1 variables. The first and second preset positive numbers are both sufficiently small positive numbers. The economic cost of unit combination and pre-scheduled load shedding is prioritized over routing link cost in the optimization process. This ensures that the primary route link cost takes precedence over the backup route in optimization.

[0040] The main routing matrix and backup routing matrix of each communication substation are as follows: ; X and Y The dimension is the number of nodes in the communication network. N c Number of communication lines b c . X Elements in the matrix X ij Indicator Node i Does the main route pass through a communication line? j 1 indicates that the route passes through the branch and the routing direction is the same as the branch reference direction; -1 indicates that the route passes through the branch but the routing direction is opposite to the branch reference direction; 0 indicates that the route does not pass through the branch. (Alternative routing matrix) Y The meanings of the elements are similar.

[0041] Information Node i Importance E i Specifically: ; In the formula, Represents a node i Control commands y i The maximum adjustable value refers to the adjustable range of active power injected into the node by the active power flow correction control. , SI ( x ) represents a state variable xThe vector composed of the importance of each component in the active power flow can be defined as follows: SI ( x )= P l / , Represents physical-side state variables x For information-side control decision variables y i Sensitivity.

[0042] S22. Establish the start-up and shutdown time constraints, pre-scheduled load shedding constraints, total system reserve constraints, communication routing logic constraints, communication routing topology constraints, and communication routing bandwidth constraints corresponding to the objective function of the first stage.

[0043] Specifically, the start-up and shutdown time constraints of the thermal power units are as follows: ; ; ; In the formula, u g,t-1 Indicates thermal power unit g During the period t -1 is the start / stop variable. UT g Indicates thermal power unit g The minimum allowed continuous running time, DT g Indicates thermal power unit g The minimum allowable continuous downtime IU g Indicates thermal power unit g The initial state needs to be maintained for a certain period of time. ID g Indicates thermal power unit g The initial shutdown state needs to be maintained for a certain period of time. Indicates thermal power unit g During the period The startup operation variables, Indicates thermal power unit g During the period The shutdown operation variable.

[0044] The first formula in this constraint is for the decision variables. u g,t , v g,t on , v g,t offThe first constraint is a logical constraint, the second constraint limits the minimum interval between unit start-up and shutdown operations, and the third constraint limits the duration of the unit's initial state.

[0045] The pre-scheduled load shedding constraints are specifically as follows: ; In the formula, Indicates load during preventive scheduling d During the period t The upper limit of the amount that can be removed.

[0046] The total system reserve constraint is specifically as follows: ; In the formula, Indicates thermal power unit g The upper limit of output, p d,t Indicates time period t load d Size, R t Indicates time period t The amount of backup demand.

[0047] The specific communication routing logic constraints are as follows: ; In the formula, X i,k Represents a node i Does the main route use a communication line? k , Y i,k Represents a node i Is the backup route via communication line? k .

[0048] This constraint restricts the primary and backup routes of each node from passing through the same branch.

[0049] The specific communication routing topology constraints are as follows: ; ; In the formula, Represents the node-branch correlation matrix of a communication network A c The i OK, X j Representation matrix X The j OK, Y j Representation matrix Y The j OK, CC It refers to the Control Center.

[0050] The physical meaning of this constraint is: if node i and j If they are the same, then the inner product of the corresponding matrix row vectors is the number of branches originating from that node in the route, which should be 1; if the node i If the control center is the matrix, then the inner product of the corresponding matrix row vectors is the node. j The negative of the number of branches in the route that terminate at the control center should be -1; if the node i and j If they are different and none of them are control centers, then the inner product of the corresponding matrix row vectors is the node. j Nodes in the route i The net number of outgoing branches should be 0.

[0051] The specific communication routing bandwidth constraint is as follows: ; In the formula, b k Indicates information branch k The bandwidth limit. This constraint ensures that the amount of information transmitted by each branch does not exceed its bandwidth limit.

[0052] S23. The first stage constraints are obtained based on the thermal power unit start-up and shutdown time constraints, the pre-scheduled load shedding constraints, the system total reserve constraints, the communication routing logic constraints, the communication routing topology constraints, and the communication routing bandwidth constraints.

[0053] S3. Establish a second-stage objective function with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost. Based on the impact of information-side anomalies on the physical side, establish second-stage constraints corresponding to the second-stage objective function, specifically including S31-S33: In the second stage (real-time dispatch), the transmission line fault matrix Z p and overall route reachability matrix W It has been determined that, based on this, the unit output, the amount of wind curtailment of renewable energy, and the real-time load shedding amount need to be determined in order to meet the power balance and power flow security constraints of the power system and minimize the total cost.

[0054] S31. Establish the second-stage objective function with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost, as follows: ; In the formula, p g,t Indicates thermal power unit g During the periodt of efforts, Represents renewable energy w During the period t Actual output Indicates load d During the period t Real-time load shedding, c g This represents the cost coefficient of the unit's output. c w This represents the cost coefficient for the curtailment of wind and solar power. Represents renewable energy w During the period t Maximum output This represents the cost coefficient for real-time load shedding.

[0055] S32. Based on the impact of information-side anomalies on the physical side, establish the thermal power unit output constraints, thermal power unit ramping constraints, new energy output constraints, real-time load shedding constraints, system power balance constraints, and power flow safety constraints corresponding to the objective function of the second stage.

[0056] Specifically, the output constraint of the thermal power unit is as follows: ; In the formula, W g,t Indicates thermal power unit g The node in the time period t The reachability of the route, if the route is unreachable (i.e. W g,t (If the value is 0), the unit is out of control, and the protection device will disconnect the unit from the grid. p g,t Equal to 0, Indicates thermal power unit g The lower limit of the output. This formula is actually an approximation of the physical process after the unit loses communication, mainly to take into account the impact of communication interruption on the power generation side in the second stage.

[0057] The specific climbing constraints for thermal power units are as follows: ; In the formula, p g,t-1 Indicates thermal power unit g During the period t -1 output, RD g and RU g They represent thermal power units g The maximum downhill slope and the maximum uphill slope, SD g and SUg They represent thermal power units g Maximum allowable output during the period before shutdown and the period after startup.

[0058] The specific constraints on the output of new energy sources are as follows: ; In the formula, W w,t Represents renewable energy w The node in the time period t The formula considers the impact of communication interruptions on the output of new energy sources, ensuring their reachability.

[0059] The real-time load shedding constraint is specifically as follows: ; In the formula, W d,t Indicates load d The node in the time period t The formula considers the impact of communication interruption on the load. This formula is equivalent to assuming that when a load node loses communication, all of its load must be disconnected.

[0060] The specific system power balance constraint is as follows: ; In the formula, G i Represents a node i The collection of thermal power units at the location, W i Represents a node i A collection of renewable energy sources, D i Represents a node i The load set at the location, L i Representation and Node i A set of connected branches, f l,t Indicates a branch l The active power flow is ensured by this formula, which guarantees the power balance of each node.

[0061] The power flow safety constraints are specifically as follows: ; ; In the formula, Represents a node i During the period t voltage phase angle, Represents a node j During the period t voltage phase angle,X l Indicates a branch l Reactance, Indicates a branch l The maximum permissible active power flow. This formula uses a DC power flow model, if the branch... l During the period t Normal operation (i.e.) (equal to 0), the active power flow of the branch must satisfy the voltage phase angle relationship at both ends of the node, and be between the upper and lower limits; if the line l During the period t Fault (i.e.) (Equal to 1), the active power flow of the branch is 0.

[0062] S33. The second stage constraints are obtained based on the thermal power unit output constraints, the thermal power unit ramping constraints, the new energy output constraints, the real-time load shedding constraints, the system power balance constraints, and the power flow safety constraints.

[0063] S4. Generate a model for generating preventive dispatch strategies for the power cyber-physical system under extreme weather conditions based on the uncertainty set, the first-stage objective function, the first-stage constraints, the second-stage objective function, and the second-stage constraints.

[0064] The first stage of the model is equivalent to the preventive scheduling stage, which generates a preventive scheduling strategy before the uncertain central scenario is determined, minimizing the sum of the strategy's own cost and the cost of the second stage under the worst scenario; the second stage is equivalent to the real-time scheduling stage, which makes real-time adjustments based on the preventive scheduling decisions after the scenario is determined, minimizing the cost of real-time adjustments.

[0065] S5. Solve the preventive scheduling strategy generation model to obtain the preventive scheduling strategy, which includes unit combination, pre-load shedding amount of each load node, and primary / backup routing of each communication substation, specifically including S51-S52: S51. After linearizing the nonlinear terms in the prevention scheduling strategy generation model, a linearized model is obtained.

[0066] Specifically, a routing matrix appears in the first-stage objective function, communication routing logic constraints, and communication routing bandwidth constraints. X and Y The absolute value of the arithmetic function is linearized by defining an auxiliary matrix. X + , X - , Y + , Y - and replace the model X , ,Y , Specifically: ; ; The first equation in the uncertain set can be linearized by taking the logarithm of both sides, resulting in: ; The fifth equation for uncertain sets can be solved by introducing auxiliary 0-1 variables. Linearization is then performed using the Big M method, which replaces the fifth equation with the following set of equations, where... M big For a sufficiently large positive number, the linearization method of the sixth equation in the uncertainty set is similar.

[0067] ; After simplification, the linear model can be obtained as follows: ; ; ; ; In the formula, x 1 indicates a continuous variable in the first stage of decision-making. x 2 represents the integer variable in the first-stage decision variables. a 1 represents the first coefficient vector. a 2 represents the second coefficient vector. b Represents the third coefficient vector. y The decision variables for the second stage are all continuous variables. u The variables representing the uncertain set are all integer variables. This represents the feasible region of the decision variables in the first stage. A 1 indicates the first coefficient matrix. A 2 represents the second coefficient matrix. q Represents the fourth coefficient vector. ( x 2) Indicates dependence on first-stage decision variables x The uncertainty set of 2 has decision-dependent uncertainty (DDU). B ( x 2) represents the third coefficient matrix. e Represents the fifth coefficient vector. This represents the feasible region of the decision variables in the second stage. E This represents the fourth coefficient matrix. h Represents the sixth coefficient vector.G 1 represents the fifth coefficient matrix. G 2 represents the sixth coefficient matrix. N This represents the seventh coefficient matrix.

[0068] S52. Solve the linearized model using a column and constraint generation algorithm to obtain a prevention scheduling strategy.

[0069] The column and constraint generation algorithm divides the original problem into a master problem (MP) and a subproblem (SP). It iteratively solves the two problems to update the upper and lower bounds of the optimal value of the original problem until the upper and lower bounds converge, thus obtaining the optimal solution to the original problem.

[0070] Specifically, for the original problem (i.e., the linearized model), the first... n The principal problem (MP) in the round iteration is: ; st ; ; ; In the formula, y k , Represents decision variables, Indicates the ( k -1) The worst-case scenario obtained by the subproblem (SP) in round-1 iteration.

[0071] The main problem is a mixed-integer linear programming (MILP) problem, which can be solved efficiently using existing commercial solvers such as gurobi.

[0072] No. n The subproblems in the round iteration are: ; In the formula, , This represents the result obtained from solving the main problem in the same iteration. x 1 and x The optimal solution for 2.

[0073] Finding the dual of the inner-level min problem in the above equation, the subproblem can be transformed into the following form: ; st ; ; In the formula, This represents the dual variable.

[0074] The above formula contains decision variables. u and The product. Because u For integer variables, Since it is a continuous variable, the Big M method can be used to linearize this term, and the subproblem after linearization is also a MILP problem.

[0075] Based on the constructed main problem and subproblems, the optimal solution to the original problem, i.e., the prevention scheduling strategy, can be obtained by iterative calculation using the column and constraint generation algorithm.

[0076] A numerical example analysis is performed on the method described above, considering the preventative scheduling problem of the power information physical system for the next 24 hours before a typhoon: The following modifications are made to the IEEE 30-node system: One wind farm is added at busbars 7 and 25; multiple buses connected to transformers are treated as a single substation, with each substation considered a communication substation, and each busbar (excluding substations) considered a communication substation; the substations at buses 6, 9, and 10 are designated as control centers. The modified system and typhoon path are as follows: Figure 3 As shown.

[0077] The probability of damage to each line at different times has been determined in advance, such as... Figure 4 As shown in the figure, only the time periods and lines affected by the typhoon are listed. Overall, the probability of line damage gradually decreases over time, simulating the characteristic that typhoon intensity weakens over time.

[0078] The optimization calculations were performed on a laptop with an 11th-generation Intel i5-1135G7 CPU (4 cores, 8 logic processors, 2.40GHz). The program was written in MATLAB, and the optimization solver was Gurobi 11.0.2.

[0079] Select different probability thresholds for line damage scenarios By using the C&CG algorithm to solve the optimization problem, different results can be obtained. The objective function value, number of iterations, and time consumption are shown in Table 1. As the uncertainty decreases, the number of scenarios within the uncertainty set increases, leading to a larger objective function value. The algorithm converges in just 2-3 iterations, making it very fast.

[0080] Table 1 Differences Number of iterations and time consumption required for the algorithm

[0081] by Taking 0.02 as an example, the changes in the upper bound UB and the lower bound LB during the algorithm iteration process are as follows: Figure 5 As shown.

[0082] As can be seen from the data in Table 1, when When the value is decreased from 0.10 to 0.08, the objective function value increases significantly, indicating that... When the value is less than or equal to 0.08, the solution obtained by the model may be too conservative. The optimal value is 0.10. All results below are based on... It was obtained based on 0.10.

[0083] The worst-case scenario for line damage identified by the model is: t When the value is 6, line (5, 7) is damaged; t When the value is 7, line (2, 6) is damaged; t When the value is 12, line (16, 17) is damaged; t When the value is 13, line (10, 17) is damaged; other lines remain normal.

[0084] In the optimal preventive scheduling strategy obtained from the model, the unit combination is as follows: Figure 6 As shown. Figure 6 In the diagram, a "1" on a red background indicates that the unit is running, and a "0" on a green background indicates that the unit is shut down. This result satisfies constraints such as minimum continuous operation / shutdown time and initial state maintenance time.

[0085] In the worst-case scenario, the output of each thermal power unit is as follows: Figure 7 As shown. In the first half of the period, due to the lower output of wind power, the output of thermal power units was relatively higher, and the output of each unit was allocated according to the principle of economy. In the second half of the period, the output of wind power increased and the load shedding increased, resulting in a decrease in the output of thermal power units. Unit 3 operated during the period 7-13 but had zero output because, under the worst-case scenario, both the primary and backup communication routes of bus 5, where Unit 3 is located, were interrupted.

[0086] Comparison of the actual output and maximum possible output of the two wind farms in the worst-case scenario Figure 8 As shown. Due to the typhoon, the maximum output of wind farm 1 was 0 during the period from 5 to 9. The actual output of wind farm 1 was equal to the maximum output during each period, and no wind curtailment occurred; wind farm 2 experienced some wind curtailment during the period of system power surplus from 17 to 21.

[0087] In the optimal preventive scheduling strategy, the pre-scheduled load shedding amount for each time period is as follows: Figure 9 As shown, the peak in the curve during periods 6-9 is mainly due to the interruption of critical transmission lines (5, 7) and (2, 6) during this period. The total pre-scheduled load shedding accounts for 7.11% of the total load.

[0088] Since the cost of load shedding during the real-time scheduling phase is much higher than that during the pre-scheduling phase, in the worst-case scenario, only buses 5 and 17 are forced to shed load during the real-time scheduling phase due to communication interruption, while other load nodes do not experience real-time load shedding.

[0089] The model has been verified to satisfy the logical, topological, and bandwidth constraints for the primary and backup routes of each communication substation. Figure 3 Table 2 shows the primary and backup routes for the communication substations corresponding to each busbar on the left side of the typhoon's path. In the worst-case scenario, only the substations corresponding to buses 5 and 17 experience communication interruption, while communication for other substations remains normal.

[0090] Table 2. Primary and backup routes for some communication substations in the optimal preventive scheduling strategy.

[0091] Therefore, it can be seen that the preventive scheduling strategy and the results under the worst scenario obtained by the model are reasonable, and the designed algorithm has a fast convergence speed and short running time, which proves the correctness and practicality of the power CPS preventive scheduling strategy generation model under extreme weather conditions established in this invention.

[0092] In summary, the proposed method for preventive dispatching of a power cyber-physical system under extreme weather conditions constructs an uncertainty set of the power cyber-physical system based on the impact of physical-side anomalies on the information-side. A first-stage objective function is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario, along with corresponding first-stage constraints. A second-stage objective function is established with the goal of minimizing unit output costs, wind curtailment costs, and real-time load shedding costs, along with corresponding second-stage constraints based on the impact of information-side anomalies on the physical-side. The preventive dispatching strategy generation model is then solved to obtain the preventive dispatching strategy. This strategy simultaneously optimizes unit combination, pre-scheduled load amounts at each load node, and primary / backup routing for each communication substation. Furthermore, the impact of physical-side anomalies on the information-side and the impact of information-side anomalies on the physical-side are considered in both the uncertainty set and the second-stage constraints, thereby effectively improving the resilience and power supply reliability of the power cyber-physical system under extreme weather conditions. Additionally, linearizing the nonlinear terms in the preventive dispatching strategy generation model facilitates solving, and using a column and constraint generation algorithm to solve the linearized model is more efficient and accurate.

[0093] According to another aspect of the invention, Figure 2 This is a schematic diagram illustrating a power cyber-physical system preventive dispatching system under extreme weather conditions according to an embodiment of the present invention. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the power cyber-physical system preventive dispatching method under extreme weather conditions as described above.

[0094] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for preventive dispatching of a power cyber-physical system under extreme weather conditions, characterized in that, Including the following steps: Constructing the uncertainty set of the power information physical system based on the impact of physical-side anomalies on the information side; The objective function for the first stage is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage costs under the worst-case scenario. The first-stage constraints corresponding to the first-stage objective function are also established. A second-stage objective function is established with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost. A second-stage constraint corresponding to the second-stage objective function is established based on the impact of information-side anomalies on the physical side. Based on the uncertainty set, the first-stage objective function, the first-stage constraints, the second-stage objective function, and the second-stage constraints, a model for generating preventive dispatch strategies for the power cyber-physical system under extreme weather conditions is generated. Solving the preventive scheduling strategy generation model yields the preventive scheduling strategy, which includes unit combination, pre-load shedding amount for each load node, and primary / backup routing for each communication substation. The objective function for the first stage is established with the goal of minimizing unit operation and start-up / shutdown costs, pre-scheduled load shedding costs, routing link costs, and the second-stage cost under the worst-case scenario. Specifically: ； In the formula, u g,t Indicates thermal power unit g During the period t Start and stop variables, This indicates the load determined during the preventive scheduling phase. d During the period t The shear load, This represents the main routing matrix for each communication substation. This represents the backup routing matrix for each communication substation. c g u This represents the cost coefficient for unit operation. c g on This represents the cost coefficient for starting up the generator unit. v g,t on Indicates thermal power unit g During the period t The startup operation variables, c g off This represents the cost coefficient for shutting down the generating unit. v g,t off Indicates thermal power unit g During the period t The shutdown operation variable, This represents the cost factor for pre-scheduled load shedding. Indicates the first preset positive number. E i Indicates information node i The importance of c b Indicates information branch b The relative length, X ib This represents an element of the main routing matrix for each communication substation. Y ib These represent the elements of the backup routing matrix for each communication substation. Indicates the second preset positive number. Q () represents a function of the cost required for real-time scheduling when using the current pre-scheduling decision in a scenario with an uncertain set. Z p Represents the fault matrix of transmission lines. W Represents the overall route reachability matrix. This represents the final, uncertain set.

2. The method for preventing and dispatching a power information physical system under extreme weather conditions according to claim 1, characterized in that, The uncertainty set of a power cyber-physical system, based on the impact of physical-side anomalies on the information-side, includes: Construct a first uncertainty set on the physical side of the power information physical system, the first uncertainty set including the transmission line fault matrix; Define the information branch-physical branch mapping matrix, the primary route reachability matrix, and the backup route reachability matrix; The transmission line fault matrix is ​​mapped to the communication line fault matrix based on the information branch-physical branch mapping matrix. Based on the communication line fault matrix, the primary route reachability matrix, and the backup route reachability matrix, a second uncertainty set is constructed to describe the relationship between the overall route reachability matrix and the communication line fault matrix; The final uncertain set is obtained based on the first uncertain set and the second uncertain set.

3. A method for preventing and dispatching power information physical systems under extreme weather conditions according to claim 2, characterized in that, The first uncertainty set of the physical side of the power information physical system is constructed as follows: ； In the formula, Denotes the first uncertainty set on the physical side. Indicates transmission line l During the period t The probability of failure, Represents auxiliary variables. Indicates transmission line l During the period t The fault status, A threshold representing the probability of line damage scenarios occurring at different time periods. Indicates transmission line l During the period t -1 is a fault status; The transmission line fault matrix is ​​mapped to the communication line fault matrix based on the information branch-physical branch mapping matrix, specifically as follows: ； In the formula, Z c Represents the communication line fault matrix. B Represents the information branch-physical branch mapping matrix; Based on the communication line fault matrix, the primary route reachability matrix, and the backup route reachability matrix, a second uncertainty set is constructed to describe the relationship between the overall route reachability matrix and the communication line fault matrix, specifically: ； In the formula, This represents the second uncertainty set describing the relationship between the overall route reachability matrix and the communication line fault matrix. M ij The elements of the main route reachability matrix, i.e., nodes. i During the period j The primary route reachability is indicated by a value of 1 (1 indicates the primary route is reachable) and 0 (0 indicates the primary route is unreachable). N ij The elements representing the reachability matrix of alternative routes, and M ij Similar, W ij Represents the elements of the overall route reachability matrix, and M ij Similar, This indicates that the main routing matrix of each communication substation is taken as the absolute value of each element. This represents the backup routing matrix for each communication substation, with each element taking its absolute value. The final uncertainty set is obtained based on the first uncertainty set and the second uncertainty set, specifically as follows: 。 4. A method for preventing and dispatching power information physical systems under extreme weather conditions according to claim 1, characterized in that, The first-stage constraints corresponding to the first-stage objective function include: Establish constraints on thermal power unit start-up and shutdown time, pre-scheduled load shedding, total system reserve, communication routing logic, communication routing topology, and communication routing bandwidth corresponding to the objective function of the first stage; The first stage constraints are obtained based on the thermal power unit start-up and shutdown time constraints, the pre-scheduled load shedding constraints, the system total reserve constraints, the communication routing logic constraints, the communication routing topology constraints, and the communication routing bandwidth constraints.

5. A method for preventing and dispatching power information physical systems under extreme weather conditions according to claim 1, characterized in that, The second-stage objective function is established with the goal of minimizing unit output cost, wind curtailment cost, and real-time load shedding cost, as follows: ； In the formula, p g,t Indicates thermal power unit g During the period t of efforts, Represents renewable energy w During the period t Actual output Indicates load d During the period t Real-time load shedding, c g This represents the cost coefficient of the unit's output. c w This represents the cost coefficient for the curtailment of wind and solar power. Represents renewable energy w During the period t Maximum output This represents the cost coefficient for real-time load shedding.

6. A method for preventing and dispatching a power information physical system under extreme weather conditions according to claim 1, characterized in that, The second-stage constraints, based on the impact of information-side anomalies on the physical side and corresponding to the second-stage objective function, include: Based on the impact of information-side anomalies on the physical side, establish the following constraints corresponding to the objective function of the second stage: thermal power unit output constraints, thermal power unit ramping constraints, new energy output constraints, real-time load shedding constraints, system power balance constraints, and power flow safety constraints. The second stage constraints are obtained based on the thermal power unit output constraints, the thermal power unit ramping constraints, the new energy output constraints, the real-time load shedding constraints, the system power balance constraints, and the power flow safety constraints.

7. A method for preventing and dispatching power information physical systems under extreme weather conditions according to claim 1, characterized in that, Solving the aforementioned preventive scheduling strategy generation model yields preventive scheduling strategies including: After linearizing the nonlinear terms in the prevention scheduling strategy generation model, a linearized model is obtained; The linearized model is solved using a column and constraint generation algorithm to obtain a preventive scheduling strategy.

8. A method for preventing and dispatching a power information physical system under extreme weather conditions according to claim 7, characterized in that, After linearizing the nonlinear terms in the aforementioned prevention scheduling strategy generation model, a linearized model is obtained, specifically: ； ； ； ； In the formula, x 1 indicates a continuous variable in the first stage of decision-making. x 2 represents the integer variable in the first-stage decision variables. a 1 represents the first coefficient vector. a 2 represents the second coefficient vector. b Represents the third coefficient vector. y This represents the decision variables for the second stage. u Variables representing an uncertain set, This represents the feasible region of the decision variables in the first stage. A 1 indicates the first coefficient matrix. A 2 represents the second coefficient matrix. q Represents the fourth coefficient vector. ( x 2) Indicates dependence on first-stage decision variables x The uncertain set of 2, B ( x 2) represents the third coefficient matrix. e Represents the fifth coefficient vector. This represents the feasible region of the decision variables in the second stage. E This represents the fourth coefficient matrix. h Represents the sixth coefficient vector. G 1 represents the fifth coefficient matrix. G 2 represents the sixth coefficient matrix. N This represents the seventh coefficient matrix.

9. A power information physical system prevention and dispatching system under extreme weather conditions, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements each step of the method for preventing and dispatching a power cyber-physical system under extreme weather conditions, as described in any one of claims 1 to 8.

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