A method and apparatus for smart grid robustness evaluation

Abstract

The application discloses a kind of smart grid robustness evaluation method and equipment, it is related to smart grid safety analysis technical field, it is solved that traditional power system safety evaluation method only sets out from electrical characteristic angle, or only sets out from network topological structure angle, and cannot accurately depict the robustness under the evolution law of cascading failure of power network, its technical scheme main point is: on the basis of past alone from topological structure or electrical characteristic angle, the structural robustness of power grid power supply and demand service function and the functional robustness of electrical topological structure characteristics are considered, combined with the efficiency subgraph under different interference modes, from the internal advantage of smart grid invulnerability and the external performance angle of service survivability, a kind of static and dynamic combination smart grid robustness evaluation method is obtained.The evaluation method is the result under the result of multi-aspect quantitative analysis, can more comprehensive more comprehensively reflect the robust characteristic performance of smart grid actual.

Description

Technical Field

[0001] This invention relates to the field of smart grid security analysis technology, and more specifically, to a method and device for assessing the robustness of smart grids. Background Technology

[0002] Power grids have long been plagued by natural disasters, component aging, and human-caused damage, posing significant challenges to their safe and stable operation. With the current vigorous promotion of "Internet+" smart grid construction, ensuring the safe and stable operation of the power system and improving the grid's ability to withstand faults has attracted even greater attention from the entire society. In recent years, the concept of robustness has been widely applied in power network reliability research. Many scholars have given different definitions of power network robustness, and their research approaches also differ. Currently, from the perspective of complex networks, most methods for analyzing power network robustness focus on the structural characteristics of the power grid, such as node survival rate, maximum connected subgraph size, and the number and size of connected subgraphs. These methods only analyze power system robustness from a topological perspective, without considering the impact of the physical operating mechanisms of the smart grid on robustness, especially the influence of power flow distribution and functional characteristics such as electrical properties on the physical power grid. Therefore, the accuracy of these assessment methods is usually not high.

[0003] Traditional power system security assessment methods primarily rely on power flow analysis and the electrical characteristics of power network components to determine network performance at a given moment. However, power network performance is determined by both its topology and electrical characteristics. Focusing solely on electrical characteristics while ignoring the network's topological features fails to accurately characterize the robustness of power networks under the evolution of cascading faults.

[0004] To address the aforementioned shortcomings and accurately assess the robustness of smart grids, this paper considers both grid structural and functional characteristics, and designs a robustness assessment method and device from multiple perspectives. Summary of the Invention

[0005] The purpose of this application is to provide a method and device for evaluating the robustness of smart grids, overcoming the shortcomings of existing robustness evaluation methods that only consider the structural or functional characteristics of smart grids.

[0006] This application first provides a method for evaluating the robustness of smart grids, including the following steps:

[0007] Construct a power grid electrical topology model based on the electrical connections between nodes;

[0008] The number of power supply and demand service paths in the electrical topology model of the power grid is analyzed, and a quantitative model of the structural robustness of the smart grid is constructed. The power transmission efficiency of the power supply and demand service paths and the power supply and demand intensity of the power grid in the electrical topology model of the power grid are analyzed, and a quantitative model of the functional robustness of the smart grid is constructed.

[0009] Based on the aforementioned structural robustness quantification model and functional robustness quantification model of the smart grid, a static robustness evaluation model of the smart grid is constructed. By calculating the number of attack cycles required to completely disconnect the grid and render it unable to provide power supply and demand services, and the efficiency survival rate of the grid under each attack cycle, a dynamic robustness evaluation model of the smart grid is constructed.

[0010] The robustness of the smart grid is evaluated using the aforementioned static robustness evaluation model and the aforementioned dynamic robustness evaluation model.

[0011] By adopting the above technical solution, which takes into account both the structural and functional characteristics of the power grid, the robustness of the smart grid in terms of structural characteristics is effectively evaluated, the robustness of the smart grid in terms of functional characteristics is evaluated, and finally the robustness of the smart grid is accurately evaluated by comprehensively considering both structural and functional characteristics. This overcomes the shortcomings of existing robustness evaluation methods that only consider the structural or functional characteristics of the smart grid.

[0012] Furthermore, the robustness quantification model of the smart grid structure is represented by the product of the average out-degree of the generation node and the average in-degree of the demand node.

[0013] Furthermore, the smart grid functional robustness quantification model is represented by the product of power transmission efficiency and power supply and demand service intensity, including: subgrid individual mean type smart grid functional robustness quantification model and global aggregation type smart grid functional robustness quantification model.

[0014] Furthermore, the power transmission efficiency is as follows:

[0015]

[0016] Among them, E i For the power transmission efficiency of the power grid, L is the mean of the reciprocals of the electrical distances. i The length of the distribution interval is the reciprocal of the electrical distance, M is the number of service paths, and l j This represents the electrical distance of the j-th path.

[0017] Furthermore, the intensity of electricity supply and demand services is as follows:

[0018]

[0019] Among them, R iLet P be the power supply and demand service intensity of grid i, m be the number of generating nodes in grid i, n be the number of demand nodes, and P be the power supply and demand service intensity of grid i. Gg For the output of the power generation node g, P Lr This represents the actual load size of the demand node r.

[0020] Furthermore, the quantitative model for the functional robustness of the smart grid is as follows:

[0021]

[0022]

[0023] Where F is the subgrid-average smart grid functional robustness quantification model. This is a quantitative model for the functional robustness of a globally aggregated smart grid, where K represents the number of stable, isolated power island subgrids that can be decoupled after grid i suffers a fault or failure. For power islanding subnet G K Power transmission efficiency, For power islanding subnet G K The intensity of electricity supply and demand services.

[0024] Furthermore, the static robustness evaluation model for the smart grid is as follows:

[0025] Q = S * F or

[0026] Where S represents the structural robustness of the smart grid, and F(F) is the quantitative model of the functional robustness of the smart grid.

[0027] Furthermore, the smart grid dynamic robustness evaluation model is as follows:

[0028]

[0029] Where, N Dmge Q is the number of attack cycles or fault iterations required to completely disconnect a power grid, rendering it unable to provide power supply and demand services. a / Q represents the power grid's efficiency survival rate under the a-th round of attacks.

[0030] Furthermore, a power grid electrical topology model based on the electrical connections between nodes is constructed, including:

[0031] Construct a physical topology model G = (P, C, E), where P is the power generation node, C is other types of nodes besides the power generation node, and E is the edge connecting all nodes;

[0032] Based on the physical topology model, the flow direction is determined by the power flow distribution direction of the power network, the active power value of each node is used as the node flow magnitude, and the electrical distance between nodes is used as the weight to establish a power network electrical topology model based on the electrical connection relationship between nodes.

[0033] This application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements a smart grid robustness assessment method as described above.

[0034] Compared with existing technologies, this application has the following advantages: The smart grid robustness assessment method and device of this invention simultaneously consider the structural and functional characteristics of the power grid to assess its robustness. Building upon past approaches that solely consider topology or electrical characteristics, this invention combines structural robustness (considering the power supply and demand service functions of the power grid) and functional robustness (considering the electrical topology characteristics) with efficiency subgraphs under different disturbance modes. This results in a combined static and dynamic smart grid robustness assessment method, considering both the inherent advantages of the smart grid's resilience and its external performance in terms of service survivability. The assessment method provided by this invention is the result of multi-faceted quantitative analysis, and can more comprehensively and thoroughly reflect the actual robustness performance of the smart grid. Attached Figure Description

[0035] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0036] Figure 1 A flowchart of the smart grid robustness assessment method provided in Embodiment 1 of the present invention;

[0037] Figure 2 This is the IEEE 39 power network topology model provided in Embodiment 2 of the present invention;

[0038] Figure 3 This is a flowchart of the crash threshold calculation under dynamic attack provided in Embodiment 2 of the present invention. Detailed Implementation

[0039] In the following, the terms “comprising” or “may include” as used in the various embodiments of this application indicate the presence of the claimed function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms “comprising,” “having,” and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or the possibility of adding one or more combinations of the foregoing.

[0040] In various embodiments of this application, the expression "or" or "at least one of B and / or C" includes any combination or all combinations of the words listed simultaneously. For example, the expression "B or C" or "at least one of B and / or C" may include B, may include C, or may include both B and C.

[0041] The terms used in the various embodiments of this application (such as "first," "second," etc.) may modify various constituent elements in the various embodiments, but do not limit the corresponding constituent elements. For example, the above terms do not limit the order and / or importance of the elements. The above terms are only used for the purpose of distinguishing one element from other elements. For example, a first user device and a second user device refer to different user devices, although both are user devices. For example, without departing from the scope of the various embodiments of this application, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element.

[0042] It should be noted that if a description refers to "connecting" a component to another component or "connecting" it to another component, then the first component can be directly connected to the second component, and a third component can be "connected" between the first and second components. Conversely, when a component is "directly connected" to another component or "directly connected" to another component, it can be understood that there is no third component between the first and second components.

[0043] The terminology used in the various embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this application pertain. The terms (such as those defined in a generally used dictionary) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this application.

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this application are only for explaining this application and are not intended to limit this application.

[0045] Example 1

[0046] This embodiment proposes a robustness assessment method for smart grids, taking into account both structural and functional characteristics. It effectively evaluates the robustness of the smart grid in terms of structural characteristics and functional characteristics, and finally comprehensively considers both to accurately assess the overall robustness of the smart grid. This overcomes the shortcomings of existing robustness assessment methods that only consider the structural or functional characteristics of the smart grid. Using the assessment method provided in this embodiment, the inherent ability of a smart grid to withstand fault impacts and ensure the safe and stable operation of the power system under various uncertain disturbances can be accurately evaluated.

[0047] See Figure 1 As shown, Figure 1 A flowchart of a method for evaluating the robustness of smart grids, including the following steps:

[0048] S1. Construct a power grid electrical topology model based on the electrical connection relationships between nodes;

[0049] S2. Analyze the number of power supply and demand service paths in the power grid electrical topology model and construct a quantitative model of smart grid structural robustness; analyze the power transmission efficiency of power supply and demand service paths and the power supply and demand intensity of the power grid in the power grid electrical topology model and construct a quantitative model of smart grid functional robustness.

[0050] S3. Through the structural robustness quantification model and the functional robustness quantification model of the smart grid, a static robustness evaluation model of the smart grid is constructed. By calculating the number of attack rounds required to completely disconnect the grid and make it unable to provide power supply and demand services, and the efficiency survival rate of the grid under each attack round, a dynamic robustness evaluation model of the smart grid is constructed.

[0051] S4. Evaluate the robustness of the smart grid using the aforementioned static robustness evaluation model and the aforementioned dynamic robustness evaluation model.

[0052] The following sections will elaborate on the above methods and steps from four aspects: “Constructing a power grid electrical topology model based on the electrical connection relationship between nodes”, “Constructing a quantitative model of the structural robustness of smart grids”, “Constructing a quantitative model of the functional robustness of smart grids”, and “Constructing a robustness evaluation model of smart grids”.

[0053] A. Constructing a power grid electrical topology model based on the electrical connections between nodes, including the following steps:

[0054] The power network topology model G=(V,E) is improved into a physical topology model G=(P,C,E) that considers both generating nodes and demand nodes, where P is the generating node, C is other types of nodes besides generating nodes, and E is the connection between all nodes.

[0055] Based on the physical topology model, the flow direction is determined by the power flow distribution direction of the power network, the node flow magnitude is determined by the active power value of each node, and the electrical distance between nodes is used as the weight to establish an electrical topology model of the power network based on the electrical connection relationships between nodes. This model can provide real-time topology and real-time power distribution information of the power network.

[0056] B. Constructing a Quantitative Model for the Robustness of Smart Grid Structure: Starting from the electrical topology model of the power grid, this paper analyzes the impact of the distribution characteristics of the "power supply and demand service path" between generation nodes and demand nodes on the robustness of the power grid's power supply and demand services. A quantitative model for the robustness of the smart grid structure based on the average number of power supply and demand service paths is proposed. In reality, the two ends of a power supply and demand service path in a power grid are generation nodes and demand nodes, respectively. Therefore, the distribution characteristics of this service path can be represented by the average out-degree D of the generation nodes. supply Average in-degree D of demand nodes demond These two core parameters describe the robustness of the smart grid structure. Therefore, the quantitative model of smart grid structural robustness can be represented by a combination number expressed by these two core parameters, i.e. Numerically, it equals the product of the average out-degree of generating nodes and the average in-degree of demand nodes. Essentially, the more power supply and demand service paths a power grid has, the stronger its overall resilience to disruptions, and the better it can withstand the impact of partial failures of generating or demand nodes on the grid's power supply and demand services. In other words, the more power supply and demand service paths a power grid has, the stronger its structural robustness.

[0057] C. Constructing a Quantitative Model of Smart Grid Functional Robustness: Considering the characteristics of the power grid's electrical topology and its power flow distribution, this paper analyzes the electrical distance distribution characteristics of power supply and demand service paths within the power grid, as well as the impact of the power supply power of generating nodes / power load distribution of demand nodes on the robustness of the power grid's power supply and demand services. A quantitative model of smart grid functional robustness based on the power transmission efficiency of power supply and demand service paths and the power supply and demand intensity of the power grid is proposed. The construction process of the quantitative model of smart grid functional robustness is detailed below, including:

[0058] C1. Construct a quantitative model of power transmission efficiency along the power supply and demand service path:

[0059] Given that service paths serve as physical channels for power transmission from generation nodes to demand nodes, and the amount of power transmitted through them is inversely proportional to their electrical distance, power flow will be concentrated on service paths with shorter electrical distances. If these service paths fail or malfunction, their power flow will inevitably shift significantly to other service paths with longer electrical distances. This not only directly reduces the power transmission efficiency of the power grid but also indirectly affects the continuity and stability of the power supply and demand services. Assume that power grid i has M service paths, where the electrical distance of the j-th path is l. j Then the power transmission efficiency E of the power grid i It depends on the electrical distance distribution characteristics of the service path, which can be represented by the mean of the inverse of its electrical distance. (Right now: The length L of the distribution interval of the reciprocal of the electrical distance i (Right now: The two core parameters, E and E, are described simply. Therefore, the power transmission efficiency E... i It can be represented as:

[0060]

[0061] From a physical perspective: First, if the length L of the distribution interval of the reciprocal of the electrical distance of the power supply and demand service path is... iThe smaller the distance, the less difference exists between them. Therefore, even if some service paths fail and power flow shifts, the impact on other service paths is smaller. Correspondingly, the power transmission efficiency of the grid is higher. Secondly, since the electrical distance of a service path is essentially defined as the equivalent impedance from the generating node to the demand node, a smaller electrical distance for a service path (correspondingly, a larger inverse of its electrical distance) indicates a stronger electrical coupling between the generating and demand nodes on that path, which is more conducive to improving its power transmission efficiency. Therefore, the larger the mean of the inverses of the electrical distances of all service paths in the grid, the higher the electrical coupling between the generating and demand nodes in the grid, and the higher the overall power transmission efficiency.

[0062] C2. Construct a quantitative model of the power grid's power supply and demand service intensity:

[0063] Power grid robustness, besides considering the impact of power transmission efficiency, must also take into account the influence of the power supply distribution at generating nodes and the load distribution at demand nodes on the intensity of power supply and demand services. Assume there are m generating nodes and n demand nodes in grid i, where the output of generating node g is P. Gg The actual load size of the demand node r is P. Lr Then the power supply and demand service intensity R of the power grid i i It can be represented as:

[0064] From a physical perspective: the power grid must maintain a balance between power supply and demand; therefore, the power supply and demand service intensity R... i Take the minimum value between the total power supplied by the generating nodes and the total power load of the demand nodes. If the power supply and demand service intensity R of grid i is... i The larger the value, the stronger its power supply and demand service capabilities when it returns to a stable operating state after suffering from a fault or failure.

[0065] C3. Based on the quantitative model of power transmission efficiency along the power supply and demand service path and the quantitative model of power grid power supply and demand service intensity, construct a quantitative model of smart grid functional robustness:

[0066] The power transmission efficiency E of the aforementioned power grid i i and the intensity of electricity supply and demand services R i The model then shows the functional robustness F of power grid i. i It can be represented as: F i =E i *R i If power grid i suffers a fault or failure and is split into K stable power island subnetworks {G1, G2, ..., G...}, then... K Assume a power islanded subnet G KThe power transmission efficiency and power supply and demand service intensity are respectively The overall functional robustness F of the decoupled power grid i can be expressed in the following two forms: subgrid individual mean type. or global aggregation type From a physical perspective: the subnet individual mean type functional robustness focuses on quantifying the individual robustness of each isolated power subnet after disconnection, while the global aggregate type functional robustness focuses on quantifying the aggregate robustness of the set of isolated power subnets after disconnection.

[0067] D. Constructing a Smart Grid Robustness Assessment Model: Building upon past assessments of network robustness solely from the perspectives of topological characteristics or electrical functional characteristics, this model combines structural robustness (considering the grid's power supply and demand service functions) and functional robustness (considering electrical topological characteristics) with network disconnection scenarios under different interference modes. From the perspective of the inherent advantages of smart grid resilience and its external performance in service survivability, a combined static and dynamic smart grid robustness assessment model is derived, including:

[0068] D1. Static Robustness Assessment of Smart Grids: Network robustness, as a fundamental attribute of a network, quantifies the different inherent service resilience exhibited by different networks due to variations in their structural and functional characteristics; it is a static attribute. Static robustness analysis and assessment of smart grids involves quantifying the network's robustness performance from the perspective of combining structural and functional characteristics. Therefore, this invention integrates structural robustness based on the average number of power supply and demand service paths with functional robustness based on the power transmission efficiency of power supply and demand service paths and the power supply and demand intensity of the power grid, proposing a static robustness Q to quantify the inherent advantages of the grid's resilience, which can be expressed as Q = S*F or Where S and F(F) represent the structural robustness and functional robustness of this network, respectively.

[0069] From a physical perspective, the performance of a power network is determined by both its topology and electrical characteristics. Static robustness Q comprehensively considers the performance of structural and functional characteristics in terms of robustness. A power network with a higher number of power supply and demand service paths structurally, and better power transmission efficiency and stronger power supply and demand service intensity functionally, will have a stronger overall resilience to power supply and demand service after being affected by faults or failures; thus, the power network is more robust.

[0070] D2. Dynamic Robustness Assessment of Smart Grids: Network robustness, as a manifestation of network resilience, can also quantify the inherent system service survivability of a power network under continuous attack or fault interference modes due to its own structural and functional characteristics; this is called dynamic robustness. Dynamic robustness analysis and assessment of the smart grid, combined with attack scenarios and methods, considers the network robustness performance under each attack or fault evolution, and integrates the robustness performance of all rounds to obtain the network's dynamic robustness throughout the entire attack process. Assuming a continuous attack on the power grid G ​​until the network loses its service function, quantifying the comprehensive robustness performance of the network during this process, the dynamic robustness of the power grid G ​​can be expressed as: Where N Dmge The number of attack cycles or fault iterations required to completely disconnect a power grid, rendering it unable to provide power supply and demand services. Q a / Q represents the power grid's efficiency survival rate under the a-th round of attacks.

[0071] From a physical perspective, the power grid's performance survivability refers to the survival rate of the power network in terms of its topology and the fulfillment rate of its functional characteristics. Numerically, it is represented by a comprehensive robustness index that balances the power network's structure and function. It measures the difference between the attacked network and the original network. The average performance survivability is obtained by summing and averaging the performance survivability of the power grid in each round of continuous attack or fault evolution under that attack scenario. A higher average performance survivability indicates stronger resistance to attacks in its physical topology and more stable system service capabilities in terms of power grid functional characteristics, i.e., better dynamic robustness.

[0072] Finally, the robustness of the smart grid is comprehensively evaluated using the aforementioned static and dynamic robustness evaluation models. This embodiment of the smart grid robustness evaluation method considers both the structural and functional characteristics of the grid. Building upon past approaches that solely consider topology or electrical characteristics, it combines structural robustness (considering the grid's power supply and demand service functions) and functional robustness (considering electrical topology characteristics) with efficiency subgraphs under different disturbance modes. This results in a combined static and dynamic evaluation method that considers both the inherent advantages of the smart grid's resilience and its external performance in service survivability. This evaluation method is the result of multi-faceted quantitative analysis, providing a more comprehensive and complete reflection of the actual robustness of the smart grid.

[0073] Example 2

[0074] This embodiment, based on the IEEE 39 power network topology model, further illustrates the robustness assessment method for smart grids. (See also...) Figure 2 As shown, Figure 2The evaluation method for the IEEE 39 power network topology model diagram includes the following steps:

[0075] Step B1: A method for constructing the electrical topology of a power grid based on the electrical connections between nodes.

[0076] B11. Constructing the electrical topology model of the power grid

[0077] A power system is an integrated system composed of various stages of energy production, transmission, distribution, and consumption. Using graph theory and topological descriptions to represent the power system provides a visual representation of its network structure. Previous studies described power system components, including power plants, substations, and user terminals, as nodes, and the relationships between components, i.e., the cables connecting them, as edges. The graph was represented as G = (V, E), where V is the set of all vertices and E is the set of all edges. This invention represents the graph as G = (P, C, E), where P is the generating node, C represents other types of nodes besides generating nodes, called demand nodes, and E still represents the edges connecting all nodes.

[0078] Traditional power grid models only consider the physical topology connections of the power grid, neglecting the electrical connections between nodes. Therefore, this invention, based on the constructed physical network topology model, considers the dynamic operation of electrons in the power system and constructs an electrical topology diagram of the power grid based on the electrical distances between nodes, comprehensively considering both the physical topology and electrical coupling connections of the power grid.

[0079] The electrical distance between two nodes in a power system is defined as the equivalent impedance between the nodes, numerically equal to the voltage change between the two nodes after a unit current element is injected. Electrical distance describes the degree of electrical connection between nodes in a power grid and reflects the influence relationships between nodes in a real power grid. Based on the established physical topology model G=(P,C,E), the electrical distance is added as a weight to this topology model to obtain the electrical topology model of the power grid.

[0080] B12. Constructing a dynamic power flow calculation model for power networks

[0081] Based on the aforementioned power grid electrical topology model, the dynamic flow of electrons in the power system is considered. In power systems, to monitor the operating status in real time, extensive and rapid power flow calculations are required. The distribution of voltage, current, and power from the power source through the network to the loads is called the power flow distribution. Incorporating the magnitude and direction of the power flow distribution into the electrical topology model results in a weighted directed graph. It uses the direction of the power flow distribution to determine the flow direction, the active power value of each node as the node flow magnitude, and the electrical distance between nodes as the weight of the transmission lines. Therefore, this invention yields a power grid electrical topology model based on the electrical connections between nodes.

[0082] Natural disasters and other destructive events can directly cause failures in system nodes or edges. Removing these faulty nodes or edges, along with their associated faulty components, alters the system topology, leading to power flow calculations and flow redistribution. This can cause some nodes or components to exceed their limits, resulting in cascading failures. The power grid electrical topology model established in this invention reflects the changes in the electrical characteristics of power grid nodes or lines during the evolution of cascading failures.

[0083] Step B2: Defining and evaluating the robustness of the structural characteristics considering the power grid's power supply and demand service functions.

[0084] Most past robustness studies have focused on the topological characteristics of networks. Common metrics include node survival rate, maximum connected subgraph size, and the number and size of connected subgraphs. When using node survival rate as a robustness metric, it focuses on the number of remaining nodes and fails to reflect the internal topological connections of the network. Robustness measured by this metric cannot account for the impact of network topology density or sparsity. While using maximum connected subgraph size as a robustness metric is relevant for large power grids, when disintegrated into multiple subnets after an attack, many smaller subnets besides the largest connected subgraph will still survive and continue operating. However, the maximum connected subgraph metric does not consider the impact of these normally operating subnets on system robustness. Although the number and size of connected subgraphs avoid the drawbacks of using maximum connected subgraphs as a robustness metric, they still fail to reflect the actual physical connections within each subnet and cannot perceive the impact of network density on robustness. Furthermore, traditional connected subgraphs only consider the survival relationships of nodes and edges in terms of topology. However, for a network like a power grid that follows basic circuit laws and actual operating mechanisms, it cannot be simply regarded as a homogeneous network. Defining a subnetwork using connected subgraphs solely from the perspective of topology does not conform to the actual situation of the power grid.

[0085] To address practical concerns, this invention proposes the concept of an "efficiency subgraph," defined as follows: When a power grid is split into multiple isolated systems operating independently of the main grid due to faults or interference, the isolated system capable of stable operation under supply-demand balance is called an efficiency subgraph. Compared to connected subgraphs, efficiency subgraphs can eliminate invalid subgraphs that remain valid in the topology graph but have lost their functional characteristics, thus avoiding the phenomenon of "artificially high" robustness values ​​in the calculation. Therefore, in the following research, efficiency subgraphs are used instead of connected subgraphs to reflect the topological connections and actual operating mechanisms of subnetworks.

[0086] The power grid electrical topology model established in step B1 is a directed graph, and its direction is the actual power flow distribution direction, represented by arrows pointing from one vertex to another. Thus, the number of arrows pointing to each vertex is its in-degree, and the number of arrows pointing outwards from that vertex is its out-degree.

[0087] First, we consider the impact of the structural characteristics of power generation nodes on robustness, specifically considering the power generation nodes in each performance subgraph after a network attack. As source nodes, power generation nodes only have outflows and no inflows. Therefore, when assessing their robustness, we only consider the out-degree of the power generation nodes. In the performance subgraph, the larger the out-degree of a power generation node, the more demanding nodes it directly connects to. Thus, as the starting point of a service, it can provide more service paths. When subjected to external interference, even if some paths fail, other paths can continue to provide service, allowing the network to maintain basic power supply functions and exhibiting stronger anti-interference capabilities; that is, the performance subgraph is more robust. Therefore, this invention starts from the perspective of the starting point of paths in the topology, using the average out-degree D of the power generation nodes... supply The robustness of the topology of the power generation nodes in the network is measured as shown in Equation 1.

[0088]

[0089] Where G represents the power network, p is the generating node in this network, and D... p N represents the out-degree of the generator node p in the network. p This represents the number of power-generating nodes in the network. The average out-degree D of the power-generating nodes in the network is obtained by summing the out-degrees of all power-generating nodes and then dividing by the number of nodes. supply .

[0090] Next, considering the impact of the structural characteristics of demand nodes on robustness, the network of nodes in the demand nodes that play roles in transmission, distribution, and consumption is regarded as a large whole, all serving the ultimate power supply function. This invention considers the demand nodes in each performance subnet after the network has been attacked, to measure the impact of the connection relationships between demand nodes on the network structural robustness. Research shows that when the average in-degree of demand nodes in the network is higher, there are more paths in the network that can provide power distribution and transmission services, and thus more paths to consumption nodes. Therefore, the tighter the connection between demand nodes in the network, the stronger its ability to resist external interference. Therefore, this invention uses the average in-degree D of demand nodes. demond Equation 2 measures the tightness of the topological connections of all nodes in a power network except for the generating nodes. This indicator can also clearly perceive the impact of the tightness or sparsity of the network on its robustness.

[0091]

[0092] Where G represents the power network, c is the demand node in this network, and D... c N represents the in-degree of the demand node c in the network. c This represents the number of demand nodes in the network. The average in-degree D of the demand nodes in the network is obtained by summing the in-degrees of all demand nodes and then dividing by the number of nodes. demond .

[0093] This paper considers the impact of both generation and demand nodes on robustness. Based on the electrical topology of the power grid, it quantifies the structural robustness of the grid from the perspective of power flow service paths between generation and demand nodes, referred to as "power supply and demand service paths." The more service paths between generation and demand nodes, the stronger the grid's ability to withstand the impact of partial generation or demand node failures on power supply and demand services. In other words, the more power supply and demand service paths within the grid, the stronger its structural robustness. Therefore, a stable power island (i.e., the defined efficiency subgraph) within or outside the main grid can be considered a bipartite graph composed of generation and demand nodes. The average number of service paths between them can be defined as: = (Average out-degree of generation node D) supp y* Average in-degree of demand node D demond Its physical meaning is: given that a service path ends with a power generation node and a demand node, how many possible combinations are possible for this path? This can be expressed as a combination. The average number of service paths S in subgraph i of performance i As shown in Equation 3.

[0094] S i =D supply *D demond(Equation 3)

[0095] When a power grid is subjected to external interference or attack, it is decomposed into K efficiency subgraphs. The average number of service paths in all subgraphs can be used to obtain the robustness performance S of the network in terms of structural characteristics, as shown in Equation 4.

[0096]

[0097] Step B3: Definition and evaluation of functional characteristic robustness considering electrical topology characteristics.

[0098] The structural robustness quantification model proposed in this invention mainly explores the relationship between the supply and demand service paths between generation nodes and demand nodes and network robustness. However, in actual power grids, these paths cannot be simply quantified by connections in the topology diagram. Instead, they should be quantified and analyzed based on topological relationships, comprehensively considering the power flow distribution characteristics and electrical properties of the physical power grid. Furthermore, the structural robustness analysis above has already considered the "quantity" of supply and demand service paths. Therefore, in functional robustness analysis, their "quality" needs to be considered.

[0099] Therefore, this invention comprehensively considers the characteristics of the electrical topology of the power grid and its power flow distribution, analyzes the electrical distance distribution characteristics of the power supply and demand service paths within the power grid, and proposes a functional robustness quantification model based on the power transmission efficiency of the power supply and demand service paths. Furthermore, considering the impact of the power supply distribution of generating nodes and the power load distribution of demand nodes on the power supply and demand service intensity, a power grid power supply and demand service intensity quantification model is proposed.

[0100] B31. Quantitative Model of Power Transmission Efficiency in Power Supply and Demand Service Path

[0101] As physical channels for transmitting electrical energy, power supply and demand service paths become increasingly vulnerable, experience greater energy loss, and suffer from poorer transmission capacity with longer distances. The amount of power transmitted via a service path is inversely proportional to its electrical distance, leading to a concentration of power flow on shorter service paths. Failure or breakdown of these shorter paths causes a significant transfer of power flow to other, longer-distance service paths. This directly reduces the power transmission efficiency of the power grid and indirectly affects the continuity and stability of power supply and demand services. Furthermore, large-scale power flow transfers can easily lead to power flow exceeding limits and cascading faults, significantly impacting grid security. Therefore, this invention, based on the electrical distance distribution characteristics of power supply and demand service paths, proposes a power transmission efficiency E... i Its robustness in power supply and demand services is measured as shown in Equation 5.

[0102]

[0103] Where M represents the number of service paths in grid i, l j Let l represent the electrical distance of the j-th path. min With l max Let represent the minimum and maximum electrical distances in grid i, respectively.

[0104] Power transmission efficiency of the power grid E i The mean of the reciprocals of their electrical distances (Right now: The length L of the distribution interval of the reciprocal of the electrical distance i (Right now: This can be simply described using two core parameters. One is the length L of the distribution interval of the reciprocal of the electrical distance of the power supply and demand service path. i This represents the difference in electrical efficiency between supply and demand service paths in power grid i. The smaller the value, the smaller the difference between them, and the stronger the balance of electrical efficiency in the network. Therefore, when some service paths fail due to faults or disturbances, the power flow transfer caused by them has a smaller impact on other service paths. Correspondingly, the power transmission efficiency of the power grid is higher, the stability of the power grid against disturbances is stronger, and its robustness is better. Furthermore, since the electrical distance of a power supply and demand service path is essentially defined as the equivalent impedance between the generating node and the demand node, a smaller electrical distance of a service path (correspondingly, a larger inverse of its electrical distance) indicates a higher electrical coupling strength between the generating node and the demand node on that path, resulting in higher electrical efficiency. This indicates a better ability of the network to ensure safe and stable power transmission, naturally improving its power transmission efficiency. Therefore, if the average inverse of the electrical distance of all supply and demand service paths in the power grid is larger, it indicates that there is generally a higher electrical coupling strength between the generating node and the demand node in the power grid, resulting in higher overall power transmission efficiency. The higher the power transmission efficiency, the more stable the supply and demand services provided by the network, and the better the robustness of the power network in terms of supply and demand services.

[0105] B32. Quantitative Model of Power Supply and Demand Service Intensity in Power Grids

[0106] As a crucial infrastructure, the power grid's core significance lies in its power supply function. A generally accepted definition of robustness in the industry is its ability to maintain certain performance characteristics under uncertain disturbances. If a power grid can still guarantee good safe and stable operation under uncertain disturbances, providing users with high-quality, wide-area power supply, then its robustness is naturally better. Therefore, this invention, in addition to considering the impact on power transmission efficiency, also considers the impact of the power distribution at generation nodes and the load distribution at demand nodes on the intensity of power supply and demand services from the perspective of the actual function of the power grid, and uses "power supply and demand service intensity" to measure the robustness of the power grid in terms of supply and demand services.

[0107] Electricity supply and demand service intensity R i It can be represented by the power supply area and power supply volume of the network. The larger the power supply area and the greater the power supply volume, the more users the power network serves, indicating a higher power supply and demand service intensity. Specifically, the power supply and demand service intensity is the minimum value of the sum of the power supply power of the network's generating nodes and the sum of the power load of the demand nodes after a system failure, as shown in Equation 6.

[0108]

[0109] Where m and n represent the number of generating nodes and demand nodes in power grid i, respectively, and the output of generating node g is P. Gg The actual load size of the demand node r is P. Lr .

[0110] After a system failure, power flow calculations are performed. During this process, the power grid adjusts its output and load shedding ratio according to the power flow calculation rules to maintain power supply and demand balance. Once the system reaches steady state, the power supply and demand service intensity (Ri) effectively reflects the severity of the failure's impact on the power system's supply performance. i The larger the value, the stronger its power supply and demand service capabilities when it returns to a stable operating state after suffering from a fault or failure, indicating that the network has strong robustness in terms of supply and demand services.

[0111] B33. Quantitative Model of Power Grid Functional Robustness

[0112] Considering the characteristics of the power grid's electrical topology and power flow distribution, this paper analyzes the electrical distance distribution characteristics of power supply and demand service paths within the power grid, as well as the impact of the power supply power of generating nodes / power load distribution of demand nodes on the robustness of the power grid's power supply and demand services. It then proposes using power transmission efficiency E... i and the intensity of electricity supply and demand services R i The functional robustness of grid i is comprehensively quantified as shown in Equation 7.

[0113] F i =E i *R i (Equation 7)

[0114] When power grid i is attacked or affected by a fault, it is split into K stable power island subnets {G1, G2, ..., G...} K When, assume the power islanded subnet G K The power transmission efficiency and power supply and demand service intensity are respectively The overall functional robustness F of the decoupled power grid i can be expressed in the following two forms:

[0115] a. Subnet Individual Mean Type

[0116]

[0117] b. Global Aggregation Type

[0118]

[0119] From a physical perspective: the subnet individual mean type functional robustness focuses on quantifying the individual robustness of each isolated power subnet after disconnection, while the global aggregate type functional robustness focuses on quantifying the aggregate robustness of the set of isolated power subnets after disconnection.

[0120] The subnet individual mean quantization model and the global aggregation quantization model provided by this invention can be applied from different perspectives depending on the emphasis.

[0121] Step B4: Definition and evaluation of the comprehensive robustness of smart grids, taking into account both grid structural and functional characteristics.

[0122] Based on the definitions and assessments of structural and functional robustness of power networks in steps B2 and B3, a comprehensive robustness assessment method for smart grids that simultaneously considers both structural and functional characteristics is proposed. Building upon past assessments of network robustness solely from the perspectives of topological or electrical functional characteristics, this method combines structural robustness (considering the power supply and demand service functions of the grid) and functional robustness (considering the electrical topology characteristics) with network disconnection scenarios under different interference modes. This results in a combined static and dynamic robustness assessment method for smart grids, considering both the inherent resilience of the smart grid and its external performance in terms of service survivability. Static robustness refers to the fundamental attribute of the network, used to quantify the overall robustness performance of the original network in terms of structure and function. Dynamic robustness refers to the network's resilience to attacks and the stability of its service capabilities under different attack scenarios.

[0123] B41. Static Robustness Assessment of Smart Grids

[0124] Network robustness, as a fundamental attribute of networks, quantifies the varying inherent service resilience of different networks due to their structural and functional characteristics; it is a static attribute. Therefore, this invention simultaneously considers the structural characteristics of power networks in terms of power supply and demand service functions, as well as their functional characteristics in terms of power transmission efficiency and power supply and demand intensity, defining a static evaluation method for smart grid robustness, as shown in Equation 10.

[0125]

[0126] Among them, S, These represent the structural robustness and functional robustness of this network, respectively.

[0127] B42. Dynamic Robustness Assessment of Smart Grids

[0128] Network robustness, as a manifestation of network resilience, can also quantify the inherent system service survivability of a network under different attack or fault interference modes due to its own structural and functional characteristics; it is a dynamic attribute. Therefore, this invention proposes a dynamic evaluation method for smart grid robustness, as shown in Equation 11, which integrates the average performance of the network's anti-attack capability in its physical topology and its system service capability in terms of power grid functional characteristics under continuous attack or fault interference.

[0129]

[0130] Where N Dmge The number of attack cycles or fault iterations required to completely disconnect a power grid, rendering it unable to provide power supply and demand services. Q a / Q represents the power grid's performance survivability under the a-th round of attack. Its physical meaning is the power grid's survivability in terms of topology and the fulfillment rate of its functional characteristics. Numerically, it is represented by a comprehensive robustness index that balances the power grid's structure and function, measuring the difference between the attacked network and the original network. The smaller the difference between the attacked network and the original network, the higher the power grid's performance survivability, i.e., the better its robustness.

[0131] By summing the power grid's performance survivability in each round of continuous attacks and then dividing by the number of attack rounds, we can obtain the average performance survivability of the power grid under this attack scenario, as shown in Equation 11. This average performance survivability is used to represent dynamic robustness. The higher the average performance survivability of the power grid, the stronger its resistance to attacks in terms of physical topology, and the more stable the system service capability in terms of power grid functional characteristics, that is, the better the dynamic robustness of the smart grid.

[0132] The dynamic robustness evaluation process includes:

[0133] (1) Establish a network model that takes into account the actual operation mechanism of the power network: that is, a power network electrical topology model based on the electrical connection relationship between nodes;

[0134] (2) Calculate the original robustness assessment value of this power network based on its structural and functional characteristics, i.e., the static robustness Q;

[0135] (3) Set the method of continuous attack on this power network, such as continuously attacking the node with the maximum degree value or the node with the maximum betweenness centrality in the network.

[0136] (4) Based on the attack method, launch a continuous attack on the power grid, and calculate the number of attack rounds required to completely disconnect the power grid so that it can no longer provide power supply and demand services. Let N be the number of attack rounds required. Dmge .

[0137] (5) Calculate the robustness evaluation value Q after each round of attack. a The ratio of the original network robustness assessment value Q to the power grid's performance survival rate Q under each round of attack is obtained. a / Q, until the attack rounds reach N. Dmge The power grid collapses completely, losing its ability to provide supply and demand services.

[0138] (6) The performance survival rate Q after each attack a Sum the results of / Q and then divide by the number of attack rounds N. Dmge The dynamic robustness assessment value Q′ of this power network is obtained.

[0139] N Dmge Calculation process:

[0140] Suppose that a power grid is continuously attacked by attacking the node with the highest degree value until the entire network collapses and no longer has the ability to supply power.

[0141] (1) Find the node with the maximum degree and start the first round of attack, with the number of attacks set to 'a'. Set the attacked node to an invalid state, delete the invalid node and the edges connected to it, and perform power flow calculation;

[0142] (2) Determine whether any lines have exceeded the power flow limit, delete the lines that have exceeded the limit, update the power grid, and perform a new round of power flow calculation until the power flow of all lines is within its carrying capacity.

[0143] Determine if there are any isolated nodes. If so, set the isolated nodes to a failed state, and the power grid will reach a temporary stable state.

[0144] (4) Determine if the network can provide power supply and demand services. If yes, return to step (1) to continue a new round of attack, with the attack round number set to a = a + 1. If no, proceed to step (5).

[0145] (5) The entire network crashes, and there is no longer any power supply and demand service capability. The final attack round 'a' is output, which is N under this dynamic and continuous attack. Dmge .

[0146] The calculation flowchart is attached later. Figure 2 Explanation. Use N. Dmge This is used to measure the network's ability to defend against dynamic and persistent attacks. Its physical meaning is: for a network, the more times it can withstand attacks—that is, the more nodes or edges need to be deleted to completely collapse the network and lose its power supply and demand service capabilities—the more robust the network is.

[0147] The dynamic robustness index Q ′ This is a comprehensive robustness index from multiple perspectives. It considers both the structural and functional characteristics of the power grid, as well as the network disconnection situation under continuous attacks. Compared with traditional robustness indices, the proposed dynamic robustness evaluation index for power networks based on structural and functional characteristics is the result of multi-faceted evaluation and analysis of continuous dynamic attacks, topological characteristics, and power grid functional characteristics. It can more comprehensively and accurately reflect the robustness performance of power networks in the face of continuous attacks or iterative faults.

[0148] This embodiment also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a smart grid robustness assessment method as described above.

[0149] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating the robustness of smart grids, characterized by: Includes the following steps: Construct a power grid electrical topology model based on the electrical connections between nodes; The number of power supply and demand service paths in the electrical topology model of the power grid is analyzed, and a quantitative model of the structural robustness of the smart grid is constructed. The power transmission efficiency of the power supply and demand service paths and the power supply and demand intensity of the power grid in the electrical topology model of the power grid are analyzed, and a quantitative model of the functional robustness of the smart grid is constructed. Based on the aforementioned structural robustness quantification model and functional robustness quantification model of the smart grid, a static robustness evaluation model of the smart grid is constructed. By calculating the number of attack cycles required to completely disconnect the grid and render it unable to provide power supply and demand services, and the efficiency survival rate of the grid under each attack cycle, a dynamic robustness evaluation model of the smart grid is constructed. The robustness of the smart grid is evaluated using the aforementioned static robustness evaluation model and the aforementioned dynamic robustness evaluation model. The smart grid functional robustness quantification model is represented by the product of power transmission efficiency and power supply and demand service intensity, including: subgrid individual mean type smart grid functional robustness quantification model and global aggregation type smart grid functional robustness quantification model; The power transmission efficiency is: in, For power grid Power transmission efficiency, The mean of the reciprocals of the electrical distance. The length of the distribution interval is the reciprocal of the electrical distance. For the number of service paths, Indicates the first Electrical distance along the path; The intensity of electricity supply and demand services is: in, For power grid The intensity of electricity supply and demand services, For power grid The number of power generation nodes, The number of nodes required. For power generation nodes of effort, For demand nodes The actual load size; The quantitative model for the functional robustness of the smart grid is as follows: in, For the quantitative model of functional robustness of subgrid-average smart grid, A quantitative model for the functional robustness of a globally aggregated smart grid. For power grid The number of stable, isolated power island subgrids that are disconnected after a fault or failure. For power island subgrids Power transmission efficiency, For power island subgrids The intensity of electricity supply and demand services.

2. The method for evaluating the robustness of a smart grid according to claim 1, characterized in that: The robustness quantification model of the smart grid structure is represented by the product of the average out-degree of the generating nodes and the average in-degree of the demand nodes.

3. The method for evaluating the robustness of a smart grid according to claim 1, characterized in that: The static robustness evaluation model for the smart grid is as follows: or in, For the robustness of smart grid structure, ( () is a quantitative model for the functional robustness of smart grids.

4. The method for evaluating the robustness of a smart grid according to claim 1, characterized in that: The dynamic robustness evaluation model for the smart grid is as follows: in, The number of attack cycles or fault iterations required to completely disconnect a power grid, rendering it unable to provide power supply and demand services. For the first The efficiency survival rate of the power grid under round attack.

5. The method for evaluating the robustness of a smart grid according to claim 1, characterized in that: Constructing a power grid electrical topology model based on the electrical connections between nodes, including: Constructing a physical topology model ,in For power generation nodes, For nodes other than power generation nodes, Connect all nodes with edges; Based on the physical topology model, the flow direction is determined by the power flow distribution direction of the power network, the active power value of each node is used as the node flow magnitude, and the electrical distance between nodes is used as the weight to establish a power network electrical topology model based on the electrical connection relationship between nodes.

6. A computer device 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 a smart grid robustness assessment method as described in any one of claims 1 to 5.

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