A method and system for improving the controllability of a power system

Abstract

The application discloses a method and system for improving structural controllability of a power system, and belongs to the field of structural controllability optimization of a power system, which comprises the following steps: taking a generator, a transformer substation and a power consumption unit as a node, taking a power transmission line as an edge, the direction of the edge being consistent with the active power flow direction of the power transmission line, establishing an original network model of the power system, deleting the incoming edges of the generator nodes in the original network model to obtain a power network, solving the maximum matching of the power network, merging the edges with the same nodes in the maximum matching to obtain a matching path set and a matching circle set, marking the paths with the generator nodes as starting points in the matching path set as control paths, marking the remaining paths as uncontrollable paths, adding a directed edge between the terminal point of the control path and the starting point of the uncontrollable path, and adding a power transmission line between the nodes corresponding to the added edges. The application makes the power system structurally controllable only when the generator nodes are used as driving nodes, and effectively improves the structural controllability of the power system.

Description

Technical Field

[0001] This invention belongs to the field of power system structure controllability optimization, and more specifically, relates to a method and system for improving the structural controllability of power systems. Background Technology

[0002] With the development of society and the economy, the scale of power systems has become increasingly large. As the most important infrastructure for people's production and life, the reliability, controllability, and stability of their operation have become increasingly important. Before determining how to control a power system, it must be ensured that it is controllable. However, because a power system is a nonlinear, large-scale dynamic system, traditional methods are difficult to apply to the analysis of its dynamic characteristics and motion state.

[0003] A power system can be abstracted into entities such as motors, substations, and power-consuming units, as well as the interconnections between these entities. Therefore, it can be constructed as a complex network for analysis. Research shows that a system is controllable if, within a finite time, appropriate control inputs are selected, it can be guided from any initial state to any target state (Kalman, Rudolf Emil. "Mathematical description of linear dynamical systems." Journal of the Society for Industrial and Applied Mathematics, Series A: Control 1.2 (1963): 152-192.). When the dimension of the system's controllability matrix is ​​small, the Kalman criterion can be used to quickly verify its controllability. However, for complex dynamic networks, it is impossible to accurately obtain the structure matrix A reflecting the connections between nodes, and there is no scalable algorithm that can numerically determine the rank of the controllability matrix C of a large N×NM network, where M represents the number of input signals and N represents the number of nodes in the dynamic network. Therefore, the Kalman criterion cannot be directly applied to complex dynamic networks. Furthermore, for large, complex networks, the rank test performed by the Kalman criterion is susceptible to ill-conditioned conditions and is highly sensitive to rounding errors and uncertainties in matrix elements. In summary, due to the complexity and large scale of power systems, the Kalman criterion cannot be applied to the controllability analysis of power systems.

[0004] To address the aforementioned issues, researchers have proposed a graph theory-based approach to analysis, which systematically avoids these limitations (Lin, Ching-Tai. "Structural controllability." IEEE Transactions on Automatic Control 19.3 (1974): 201-208.). Structural control theory allows us to determine the structural controllability of a controlled network simply by examining its topology, avoiding complex matrix operations. Building upon this, by introducing graph matching theory and methods, and combining them with structural controllability theory, a framework for analyzing the controllability of complex networks based on maximum matching to solve for the minimum set of driving nodes was derived (Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.). The Minimum Inputs Theorem theoretically proves that the set of nodes that can independently control the input to satisfy network structural controllability is the set of unmatched nodes in the network's maximum matching set, known as the minimum driving node set. The ratio of the number of nodes in the minimum driving node set to the total number of nodes in the network is used as a criterion for measuring network controllability. Network controllability n D Defined as the number of network driver nodes N D Divide by the total number of network nodes N, i.e., n D =N d / N, where the total number of network nodes is fixed, is the number of driving nodes N. D The larger the value, the more input signals are needed to control the network, and the worse the network's structural controllability.

[0005] The analytical methods and evaluation criteria for the controllability of complex network structures provide important basis for improving the structural controllability of power systems. In the study of power system structural controllability, the minimum input theorem is used to find the minimum number of driving nodes that make the network structure controllable in an unweighted directed model. By changing the number of driving nodes, critical nodes in the network can be identified (Li, Yu-Shuai, et al. "Critical nodes identification of power systems based on controllability of complex networks." Applied sciences 5.3(2015):622-636.). Combining structural controllability theory with the electrical characteristics of power systems, a directed network model with edge weights is established to effectively measure the maximum controllable range and control capability of nodes (Yang, Dong-Sheng, et al. "Critical nodes identification of complex power systems based on electric cactus structure." IEEE Systems Journal 14.3(2020):4477-4488.).

[0006] However, these works have not fully considered the physical and electrical characteristics of the power system, nor have they considered the different functions of different nodes in the power system control. This may result in the identified driving nodes including load nodes that do not have control functions, thus failing to effectively guarantee the controllability of the power system. Summary of the Invention

[0007] To address the shortcomings and improvement needs of existing technologies, this invention provides a method and system for improving the structural controllability of power systems. The purpose is to fully consider the physical and electrical characteristics of power systems, restrict only generator nodes to be used as control inputs (i.e., drive nodes) of the power system, and under this constraint, apply the structural controllability theorem to define the control range of generator nodes and correspondingly change the topology of the power system to make the power system structure controllable.

[0008] To achieve the above objectives, according to one aspect of the present invention, a method for improving the structural controllability of a power system is provided, comprising the following steps:

[0009] (S0) The original network model of the power system is established with generators, substations and power-consuming units as nodes and transmission lines as edges. The direction of the edges is consistent with the active power flow direction of the transmission lines.

[0010] (S1) Delete the incoming edges of the generator nodes in the original network model to obtain the power network;

[0011] (S2) Solve for the maximum matching of the power network and merge the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set;

[0012] (S3) The paths in the matching path set that start from the generator node are recorded as control paths, and the remaining paths are recorded as uncontrollable paths. The uncontrollable paths are connected to the end of the control paths by adding directed edges between the end of the control paths and the start of the uncontrollable paths.

[0013] (S4) Add power transmission lines between the nodes corresponding to the added connection edges so that the power system structure is controllable when the generator is the driving node.

[0014] Furthermore, in step (S3), the uncontrollable paths are connected to the endpoints of the control paths by adding directed edges between the endpoints of the control paths and the starting points of the uncontrollable paths, including:

[0015] (S31) If the number of uncontrollable paths m is greater than the number of controllable paths n, then proceed to (S32); otherwise, proceed to (S33).

[0016] (S32) Select n uncontrollable paths, add a directed edge between the end point of each control path and the start point of a selected uncontrollable path, recalculate the number of uncontrollable paths, and then go to (S31).

[0017] (S33) Select m control paths and add a directed edge between the end point of each selected control path and the start point of an uncontrollable path.

[0018] Furthermore, when determining the control paths connected to each uncontrollable path, the goal is to minimize the cost of adding transmission lines.

[0019] Furthermore, the methods for determining the control paths connected to each uncontrollable path include:

[0020] The starting point of each uncontrollable path is designated as an additional driving node, and the topological distance between each additional driving node and the end point of each control path is calculated.

[0021] Determine the control path matched by each additional drive node such that the sum of the topological distances between the additional drive node and the endpoint of the control path is minimized under this matching scheme;

[0022] For each uncontrollable path, determine the control path that matches its starting point as the control path it connects to.

[0023] Furthermore, in step (S2), the maximum matching is solved using the Hopcroft-Karp algorithm.

[0024] According to another aspect of the present invention, a system for improving the structural controllability of a power system is provided, comprising:

[0025] The topology building module is used to establish the original network model of the power system, with generators, substations and power-consuming units as nodes and transmission lines as edges, and the direction of the edges is consistent with the active power flow direction of the transmission lines.

[0026] The topology building module is also used to remove the incoming edges of generator nodes in the original network model to obtain the power network;

[0027] The matching path solving module is used to solve the maximum matching of the power network and merge the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set.

[0028] The edge-connecting module is used to classify the paths in the matching path set that start from the generator node as control paths and the remaining paths as uncontrollable paths. By adding directed edges between the end point of the control path and the start point of the uncontrollable path, the uncontrollable paths are connected to the end point of the control path.

[0029] The line addition device is used to add transmission lines between nodes corresponding to the added connection, so that the power system structure is controllable when the generator is the driving node.

[0030] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0031] (1) In establishing the network topology model of the power system, this invention fully considers the physical and electrical characteristics of the power system. Therefore, the established network model can accurately reflect the behavior of the power system. Specifically, considering that generator nodes are active nodes in the power system, they can influence the operating state of the power system and meet the system's needs by adjusting parameters such as the generator's active power, reactive power, and voltage amplitude; load nodes do not have the ability to directly influence other nodes; generator nodes are fixed and cannot improve the structural controllability of the power system by increasing input signals. In establishing the network model of the power system, this invention sets the direction of the edges to be consistent with the direction of the active power flow on the corresponding transmission line and deletes the incoming edges of generator nodes. The resulting power network has edges whose direction is consistent with the direction of the control action when the generator node acts as a driving node, and ensures that in the subsequent determination of the matching path, the generator node only acts as a source node. This highlights the dominant position of the generator in the power system, so as to effectively control the load nodes and other related nodes of the power system. Based on the established power network, a set of matching paths is determined, where each path starts at a driving node and corresponds to a control input. The matching paths are connected by adding directed edges, ensuring that all retained paths originate from generator nodes. This effectively reduces the number of driving nodes, improves the structural controllability of the power system, and ultimately makes the power system structurally controllable by adding transmission lines corresponding to the added directed edges. In summary, this invention fully considers the physical and electrical characteristics of the power system. By adding a minimum number of directed edges, it achieves structural controllability of the power system only when generator nodes act as driving nodes, effectively improving the structural controllability of the power system.

[0032] (2) In the preferred embodiment of the present invention, when adding directed edges, the scheme that minimizes the cost of adding transmission lines is given priority, thereby achieving a significant improvement in structural controllability at a lower cost and ultimately maximizing the benefits; in a further preferred embodiment, the scheme for adding directed edges is determined based on the topological distance between nodes, which effectively reduces the computational complexity. Attached Figure Description

[0033] Figure 1 A flowchart illustrating a method for improving the structural controllability of a power system, provided in an embodiment of the present invention.

[0034] Figure 2 This is a diagram of the IEEE 30-node power grid topology provided in an embodiment of the present invention.

[0035] Figure 3 A comparison of network structure controllability under the ICE189 power grid using a random edge addition strategy and the edge addition strategy provided in this invention.

[0036] Figure 4 A comparison of network structure controllability under the ICE189 power grid, using an edge-adding strategy based on node degree values ​​and the edge-adding strategy provided by this invention;

[0037] Figure 5 A comparison of network structure controllability under the ICE189 power grid, using an edge addition strategy based on the out-degree / in-degree of nodes and the edge addition strategy provided by this invention;

[0038] Figure 6 A comparison of network structure controllability under the ICE189 power grid, using an edge-adding strategy based on node centrality and the edge-adding strategy provided by this invention;

[0039] Figure 7 A comparison of the network structure controllability under four different power grids using a random edge addition strategy and the edge addition strategy provided in this invention.

[0040] Figure 8 A comparison of network structure controllability under four different power grids, using an edge-adding strategy based on node degree values ​​and the edge-adding strategy provided by this invention;

[0041] Figure 9 A comparison of network structure controllability under four different power grids, using an edge-adding strategy based on the out-degree / in-degree of nodes and the edge-adding strategy provided by this invention;

[0042] Figure 10 A comparison of network structure controllability under four different power grids, using an edge-adding strategy based on node centrality and the edge-adding strategy provided by this invention;

[0043] Figures 3 to 10 In the middle, the vertical coordinate n D This represents the structural controllability of the power network, with the horizontal axis 'm' representing the proportion of added edges. M represents the number of added edges, N E =N D -N G This represents the additional number of driver nodes, which is the upper limit for increasing the number of edges. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0045] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0046] To improve the structural controllability of power systems, this invention provides a method and system for improving the structural controllability of power systems. The overall idea is that, based on the physical and electrical characteristics of power systems, when performing structural controllability analysis of power systems, only generator nodes can be used as driving nodes. Under the structural controllability theory, by adding connecting edges, the matching paths in the network topology are all source nodes of generator nodes. Finally, by adding corresponding transmission lines, the power system structure becomes controllable.

[0047] The following is an example.

[0048] Example 1:

[0049] A method to improve the structural controllability of power systems, such as Figure 1 As shown, the process includes steps (S0) to (S4). Step (S0) establishes the original network model of the power system. Step (S1) builds a power network that accurately reflects the actual behavior of the power system based on the physical and electrical characteristics of the power system within the original network model. Step (S2) determines the set of matching paths within the power network established in step (S1). Step (S3) connects paths in the matching path set that do not originate from generator nodes to paths that originate from generator nodes by adding edges, ensuring that all matching paths originate from generator nodes. Step (S4) adds actual transmission lines between the corresponding nodes based on the edges added in step (S3), ultimately making the power system structure controllable. The specific implementation methods for each step are further explained below.

[0050] The steps (S0) of this embodiment specifically include: establishing the original network model of the power system with generators, substations and power-consuming units as nodes, and transmission lines as edges, with the direction of the edges consistent with the active power flow direction of the transmission lines.

[0051] The accuracy of structural controllability analysis is closely related to the properties of the power system described by the network model. When constructing the model, the physical and electrical characteristics of the power system must be fully considered to ensure that the model accurately reflects the behavior of the power system. Existing methods determine the direction of edges based on voltage, current, impedance, etc., when modeling a power system. In this embodiment, the direction of the edges is set to be consistent with the direction of active power flow on the corresponding transmission lines. Since the direction of active power flow is the direction of control action when a generator node acts as a driving node, the network topology diagram established in this embodiment has edges whose directions are consistent with the direction of control action when a generator node acts as a driving node. This network topology diagram can accurately represent the energy transmission process.

[0052] The specific steps (S1) of this embodiment include: deleting the incoming edges of the generator nodes in the original network model to obtain the power network.

[0053] In this embodiment, after establishing the original network model of the power system, the incoming edges of the generator nodes are further deleted. This ensures that in the subsequently determined matching path, the generator nodes only act as source nodes, thereby highlighting the dominant role of the generators in the power system and enabling effective control of the load nodes and other related nodes of the power system.

[0054] It should be noted that in this embodiment, deleting the incoming edges of the generator nodes is merely a topology-level operation and does not change the actual power transmission lines of the power system. It simply ignores the incoming edges of the generator nodes when finding the maximum matching, and the final optimized network still includes these edges.

[0055] Step (S2) of this embodiment includes: solving for the maximum matching of the power network and merging the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set.

[0056] A maximum matching is a set of directed edges containing as many edges as possible, where no two edges share the same start or end point. That is, for any two edges, if they share a common node, that node must be both the start and end point of one edge. Optionally, in this embodiment, the Hopcroft-Karp algorithm is used to solve for the maximum matching. This algorithm can achieve a time complexity of O(log n). The algorithm finds a maximum matching in a directed network, where N represents the number of nodes and E represents the number of edges. It's easy to understand that the network topology needs to be converted into a bipartite graph before solving for the maximum matching. It should be noted that the Hopcroft-Karp algorithm is only one possible algorithm for finding the maximum matching and should not be construed as the sole limitation of this invention. In other embodiments of this invention, other solution methods such as the Hungarian algorithm and the maximum flow algorithm can also be used.

[0057] By merging edges with the same node, the edges in the maximum matching can be merged into a matching path or a matching circle. A matching path is a simple path starting from a driving node and ending at a matching node, without any connecting edges outside the maximum matching. A matching circle is a directed cycle starting from a matching node and ending at a "parent" node pointing to the starting node. Note that nodes not appearing in the maximum matching M are "isolated" nodes, belonging to the minimum set of driving nodes. They can be considered as the shortest matching path and added to the matching path set. According to structural controllability theory, to control the nodes on a matching path, a control signal needs to be applied to the starting node of the path; therefore, the starting node of the matching path is the driving node. Nodes on a matching circle can be controlled by the same signal applied to the starting driving node of the matching path; therefore, controlling the nodes on the matching circle does not increase the number of driving nodes.

[0058] In the matching path set determined in step (S2) of this embodiment, each matching path starts at a driving node and corresponds to a control input. Since power systems are often large-scale, the driving nodes determined in step (S2) include not only all generator nodes but also some other types of nodes, which are referred to as additional driving nodes in this invention. Large-scale power systems often have more unmatched nodes, i.e., nodes that require control inputs, and maintaining their structural controllability is more costly.

[0059] Generator nodes are active nodes in a power system. They influence the system's operating state and meet system demands by adjusting parameters such as generator active power, reactive power, and voltage amplitude. Load nodes, on the other hand, do not have the ability to directly influence other nodes. Generator nodes are fixed, therefore the structural controllability of the power system cannot be improved by adding input signals.

[0060] Therefore, in order to ensure the controllability of the power system, step (S3) of this embodiment includes: recording the paths in the matching path set that start from the generator node as control paths, and recording the remaining paths as uncontrollable paths, and connecting all uncontrollable paths to the end of the control path by adding directed edges between the end of the control path and the start of the uncontrollable path.

[0061] By adding edges to connect uncontrollable paths driven by other nodes to the endpoints of control paths driven by generator nodes, the uncontrollable paths are combined with the control paths into a matching path. This allows nodes on the matching path with the additional driving node as the source node to be controlled by the generator node, thereby expanding the control range of the generator node and reducing the number of additional driving nodes. Each added edge reduces one driving node, up to N... D and N GLet N represent the number of driving nodes and the number of generator nodes in the original matching path set, respectively. Theoretically, this would require at least an increase of N. D -N G The connection of the edges enables the power system to be structurally controllable when the generator node is used as the driving node.

[0062] When adding connections, efforts are made to distribute uncontrollable paths evenly among control paths. That is, the number of uncontrollable paths connected to each control path is kept as balanced as possible to avoid exceeding the generator's control capacity limit. Accordingly, in step (S3) of this embodiment, uncontrollable paths are connected to the endpoints of control paths by adding directed edges between the endpoints of control paths and the starting points of uncontrollable paths. This includes:

[0063] (S31) If the number of uncontrollable paths m is greater than the number of controllable paths n, then proceed to (S32); otherwise, proceed to (S33).

[0064] (S32) Select n uncontrollable paths, add a directed edge between the end point of each control path and the start point of a selected uncontrollable path, recalculate the number of uncontrollable paths, and then go to (S31).

[0065] (S33) Select m control paths and add a directed edge between the end point of each selected control path and the start point of an uncontrollable path.

[0066] In practical applications, since the added connections ultimately determine the additional transmission lines, determining the connection relationship between control paths and uncontrollable paths requires comprehensive consideration of various factors such as spatial distance and cost, and must also meet actual operational needs, such as improving transmission capacity and alleviating load congestion. To maximize benefits, in this embodiment, the goal of determining the control paths connected to each uncontrollable path is to minimize the cost of adding transmission lines. Considering the complexity of the factors affecting the cost of adding transmission lines, and to simplify computational complexity, as a preferred implementation method, in this embodiment, the method for determining the control paths connected to each uncontrollable path includes:

[0067] The starting point of each uncontrollable path is designated as an additional driving node, and the topological distance between each additional driving node and the end point of each control path is calculated.

[0068] Determine the control path matched by each additional drive node such that the sum of the topological distances between the additional drive node and the endpoint of the control path is minimized under this matching scheme;

[0069] For each uncontrollable path, determine the control path that matches its starting point as the control path it connects to.

[0070] The topological distance between nodes can be calculated using shortest path algorithms such as Dijkstra's algorithm, which to some extent reflects the spatial distance between entities corresponding to the nodes. In this embodiment, this is used as a basis to determine the connection scheme between uncontrollable paths and control paths. The Hungarian algorithm is applied to solve the allocation problem of control paths, and a better connection scheme is determined with lower computational complexity.

[0071] Step (S4) of this embodiment includes: adding power transmission lines between the nodes corresponding to the added connection edges, so that the power system structure is controllable when the generator is the driving node.

[0072] Step (S4) of this embodiment changes the actual connection relationship between entities in the power system from a physical level by adding transmission lines, and based on this change, the power system structure becomes controllable when the generator node is the driving node.

[0073] In this embodiment, the actual number of transmission lines added is the minimum, i.e., N. D -N G Furthermore, the determination of each transmission line is aimed at minimizing costs. Therefore, this embodiment can effectively improve the structural controllability of the power system at a lower cost.

[0074] The following explanation will further illustrate the relevant steps of this embodiment using a specific power system as an example.

[0075] Figure 2 The diagram shows a schematic of an IEEE 30-node power grid. Its original topology includes 30 nodes and 41 edges. The 30 nodes are numbered 1 to 30. Figure 2 The red nodes in the diagram represent generator nodes, and there are a total of 6 (N) G =6).

[0076] There exists only one incoming edge pointing to the generator node, namely the edge {1-2} connecting generator node 1 to generator node 2. Figure 1 The edge is marked with a black dashed line with an arrow. After deleting this edge, the total number of edges in the network is reduced to 40.

[0077] The Hopcroft-Karp algorithm is used to solve for the maximum matching. The resulting maximum matching M contains 20 connected edges. After merging edges with the same node, 10 matching paths are obtained, but no matching circles are found. Therefore, the IEEE 30-node power grid requires 10 driving nodes (N). D =10). Of the 10 matching paths, 6 are controlled by the generator node, and the remaining 4 are controlled by the additional drive node. Figure 2 In the diagram, the matching path for generator node control is represented by a thick red solid line, and the matching path for additional drive nodes is represented by a thick black solid line.

[0078] Choose the end node of a matching path that originates from a generator node as the starting point for adding an edge, and connect it to an additional driver node, thus combining the two matching paths into a new matching path. The state of all nodes on the new matching path can be controlled by the generator node at the starting position of that path. Therefore, adding N... D -N G With 4 connecting edges, the IEEE 30-node power grid is structurally controllable under the control input of 6 generator nodes.

[0079] Specifically, the distance matrix between the endpoint of the control path and the additional nodes is first obtained using Dijkstra's algorithm, as shown in Table 1:

[0080] Table 1. Topological distance matrix between the additional driving node (s) and the control path endpoint (e).

[0081]

[0082] Then, the Hungarian algorithm is used to assign control path terminators to the additional nodes, transforming the matrices in Table 1 into the matrices shown in Table 2.

[0083] Table 2 Topological distance matrix after processing with the Hungarian algorithm

[0084]

[0085] Based on Table 2, the directed edges that need to be added can be determined. It should be noted that the optimal scheme for adding edges may not be unique. In this example, there are 5 optimal schemes, such as {7-11,14-16,21-26,8-29}, {8-11,14-16,21-26,24-29}, etc. Figure 2 In the diagram, the added edges are represented by thick yellow solid lines. The following comparison of the impact of existing edge-adding strategies and the edge-adding strategy in this embodiment on the controllability of the power system structure further verifies the beneficial effects achievable by this embodiment.

[0086] The existing edge-adding strategies compared include: random edge-adding strategy, random edge-adding strategy based on node degree value, edge-adding strategy based on node out-degree and in-degree values, and edge-adding strategy based on node centrality. For ease of description, in the following comparison, the edge-adding strategy in this embodiment will be referred to as the optimal edge-adding strategy.

[0087] First, taking the ice189 power grid as an example, we determine the impact of different edge addition strategies on its structural controllability. The ice189 power grid consists of 189 nodes and 203 edges. After deleting all incoming edges from generator nodes, the total number of edges is reduced to 197. This power grid has 35 generator nodes and requires 94 driver nodes (N...). D=94). Therefore, in addition to the generator nodes, 59 additional nodes are needed as driving nodes. By using the optimal edge-adding strategy, a maximum of 59 edges can be added, enabling the ICE189 power grid to be controllable through the generator node structure. A comparative experiment is as follows:

[0088] (1) Random edge addition is a widely used edge addition method. In complex network research, it is often used to simulate random connection phenomena in networks, thereby better understanding the evolution and properties of networks. Existing research results show that the controllability change curve of any edge addition strategy that enhances network controllability lies between the effect curve of random edge addition strategy and the "optimal edge addition strategy" (Wang, Wen-Xu, et al. Optimizing controllability of complex networks by minimum structural perturbations. Physical Review E 85.2(2012):026115.). If randomly adding an edge can reduce the number of driving nodes, then the edge will be retained, while a "redundant edge" will be deleted (Lvlin, Hou, et al. Enhancing complex network controllability by rewiring links. 2013 Third International Conference on Intelligent System Design and Engineering Applications. IEEE, 2013.).

[0089] When applying the random edge addition strategy, the number of added edges gradually increases from 1 to 59. After each edge addition, the number of driving nodes in the network is calculated and recorded. The experiment is repeated 1000 times to eliminate the randomness of the results. A mean curve with standard deviation is plotted. Figure 3 The red curve and the red-covered area are shown in the middle. Comparing the two edge-adding strategies, when adding the same number of edges, the random edge-adding strategy only improves controllability by 1 / 4 of the effect of the optimal edge-adding strategy.

[0090] (2) Existing research results indicate that the number of driving nodes in a real network is mainly determined by the network's degree distribution, and driving nodes tend to avoid nodes with high degrees. Under the same average degree, ER networks, with a relatively uniform distribution of node degree values, have better structural controllability than SF networks. There are four different edge-adding strategies based on node degree values: "high degree-high degree", "high degree-low degree", "low degree-high degree", and "low degree-low degree". Taking "high degree-low degree" as an example, the starting point for adding an edge is preferentially selected from nodes with higher degree values. The probability of a node being selected is related to the degree value k of that node. i The degree of a node is directly proportional to its degree value. If a node has not been visited, it is used as the starting point of a new edge. The endpoint of an added edge is preferentially chosen from nodes with smaller degree values; the probability of a node being selected is proportional to the reciprocal of its degree value (1 / k). i Proportional. If the node has not been visited, is not a generator node, and the newly added edge does not overlap with any existing edge in the power grid, then the node is selected as the starting point of the new edge. A directed edge is added between the starting and ending points.

[0091] When adding edges randomly based on the degree of nodes, the number of edges added gradually increases from 1 to 59. After each edge addition, the number of driving nodes in the network is calculated and recorded. The experiment is repeated 1000 times to eliminate the randomness of the results. The mean curves of the four edge addition strategies are plotted against the controllability optimization curve of the optimal edge addition strategy. Figure 4 As shown in the figure, the "small degree - small degree" edge addition method is the most effective, improving controllability by 40% compared to the optimal edge addition strategy.

[0092] (3) The out-degree and in-degree distribution of nodes are important factors affecting the controllability of network structure. Some studies have shown that the positive correlation between out-degree and in-degree can improve the controllability of the network (Nepusz T, Vicsek T. Controlling edge dynamics in complex networks[J]. Nature Physics,2012,8(7):568-573.). In studies on improving structural controllability, some methods have removed redundant links and added a link between the node with the highest in-degree and the node with the highest out-degree (if neither is connected) (Xu, Jiuqiang, et al. "Improving controllability of complex networks by rewiring links regularly." The 26th Chinese Control and Decision Conference (2014CCDC). IEEE,2014.). Another study is based on the concept of node residual degree (NRD), which selects nodes to change the direction of the connection based on the difference between the out-degree and in-degree of a node (Xiao, Yan-Dong, et al. "Edge orientation for optimizing controllability of complex networks." Physical Review E 90.4 (2014): 042804.).

[0093] Taking the "larger out-degree - larger in-degree" edge addition method as an example. First, based on the out-degree and in-degree values ​​of the nodes, groups nodes with the same degree value together. This results in four grouping sorts: D1 by out-degree value from largest to smallest; D2 by out-degree value from smallest to largest; D3 by in-degree value from largest to smallest; and D4 by in-degree value from smallest to largest. Prioritizing nodes with larger out-degree values ​​as the starting point for adding edges, in grouping sort D1, the edge is added from the group with the largest out-degree value. 1,0 Randomly select a node from D; if that node has not been visited, it becomes the starting point of a new edge. Assume that when D... 1,0 If all nodes in the list have been visited, then sort them by their out-degree values, starting from D. 1,1 Randomly select a node from the grid, and so on. Prioritize selecting nodes with large in-degree as the endpoints for adding edges, using the same method, but ensure that the endpoint and start point of the new edge are not duplicates, and that the new edge does not belong to a generator node, while also ensuring that the newly added edge does not duplicate any existing edges in the power grid.

[0094] When adding edges based on the out-degree and in-degree values ​​of nodes, the number of edges added gradually increases from 1 to 59. After each edge addition, the number of driving nodes in the network is calculated and recorded. The mean curves of a total of 16 edge addition strategies are plotted against the controllability optimization curve of the optimal edge addition strategy. Figure 5 As can be seen, the effect of the edge-adding strategy of "small out-degree - small in-degree" is closest to that of the optimal edge-adding strategy, and its improvement in controllability can reach 3 / 4 of that of the optimal edge-adding strategy.

[0095] (4) The centrality index of complex networks is a measure of the importance and influence of nodes in the network. Different centrality indices focus on different aspects. There are four commonly used node centrality indices: degree centrality (DC), betweenness centrality (BC), proximity centrality (CC), and eigenvector centrality (EC).

[0096] Taking betweenness centrality (BC) as an example, this section explains how to add edges based on the betweenness centrality of nodes. Using a "large betweenness centrality - small betweenness centrality" approach, first, calculate the betweenness centrality of all nodes and sort them by betweenness centrality value from largest to smallest and vice versa. First, prioritize nodes with large betweenness centrality as the starting point for adding edges, selecting them in descending order. Second, prioritize nodes with small betweenness centrality as the ending point for adding edges, selecting them in ascending order of betweenness centrality value. Choose the first unvisited node as the ending point of the new edge, ensuring that the ending point and starting point of the new edge are not duplicates, that it does not belong to a generator node, and that the newly added edge does not overlap with any existing edges in the power grid.

[0097] When adding edges based on node centrality, the number of edges added gradually increases from 1 to 59. After each edge addition, the number of driving nodes in the network is calculated and recorded. The mean curves of all 16 edge addition strategies are plotted against the controllability optimization curve of the optimal edge addition strategy. Figure 6 As can be seen, the effects of the two edge-adding strategies, "small degree centrality - small degree centrality" and "small betweenness centrality - small betweenness centrality", are closest to the optimal edge-adding strategy, and their improvement in controllability can reach 60% of that of the optimal edge-adding strategy.

[0098] The above comparison results demonstrate that the edge-adding strategy provided in this embodiment, due to its full consideration of the dominant position of generator nodes in the power system, can more effectively improve the structural controllability of the power system compared with existing edge-adding strategies.

[0099] Next, different edge-addition strategies were compared on four different power grids: IEEE47, IEEE118, Shandong340, and GB2224. The impact of random and optimal edge-addition strategies on the structural controllability of these four power grids is as follows: Figure 7 As shown, the impact of edge-adding strategies based on node degree values ​​and the optimal edge-adding strategy on the structural controllability of these four power grids is as follows: Figure 8 As shown, the impact of edge-adding strategies based on node out-degree / in-degree and the optimal edge-adding strategy on the structural controllability of these four power grids is as follows: Figure 9 As shown, the impact of edge-adding strategies based on node centrality and the optimal edge-adding strategy on the structural controllability of these four power grids is as follows: Figure 10 As shown.

[0100] according to Figures 7-10 The results also show that the edge-adding strategy provided in this embodiment can more effectively improve structural controllability on these four power grids.

[0101] Example 2:

[0102] A system for improving the structural controllability of a power system, comprising:

[0103] The topology building module is used to establish the original network model of the power system, with generators, substations and power-consuming units as nodes and transmission lines as edges, and the direction of the edges is consistent with the active power flow direction of the transmission lines.

[0104] The topology building module is also used to remove the incoming edges of generator nodes in the original network model to obtain the power network;

[0105] The matching path solving module is used to solve the maximum matching of the power network and merge the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set.

[0106] The edge-connecting module is used to classify the paths in the matching path set that start from the generator node as control paths and the remaining paths as uncontrollable paths. By adding directed edges between the end point of the control path and the start point of the uncontrollable path, the uncontrollable paths are connected to the end point of the control path.

[0107] The line addition device is used to add transmission lines between nodes corresponding to the added connection edges, making the power system structure controllable when the generator acts as the driving node. In this embodiment, the specific implementation methods of each module can be referred to the description in Embodiment 1 above, and will not be repeated here.

[0108] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 improving the structural controllability of a power system, characterized in that, Includes the following steps: S0: Establish the original network model of the power system with generators, substations and power-consuming units as nodes and transmission lines as edges, with the direction of the edges consistent with the active power flow direction of the transmission lines. S1: Remove the incoming edges of the generator nodes in the original network model to obtain the power network; S2: Solve for the maximum matching of the power network, and merge the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set; S3: The paths starting from the generator node in the matching path set are recorded as control paths, and the remaining paths are recorded as uncontrollable paths. The uncontrollable paths are connected to the end of the control paths by adding directed edges between the end of the control paths and the start of the uncontrollable paths. When determining the control paths connected to each uncontrollable path, the goal is to minimize the cost of adding transmission lines. The methods for determining the control paths connected to each uncontrollable path include: The starting point of each uncontrollable path is designated as an additional driving node, and the topological distance between each additional driving node and the end point of each control path is calculated. Determine the control path matched by each additional drive node such that the sum of the topological distances between the additional drive node and the endpoint of the control path is minimized under this matching scheme; For each uncontrollable path, determine the control path that matches its starting point as the control path it is connected to. S4: Add power transmission lines between the nodes corresponding to the added connecting edges, so that the power system structure is controllable when the generator is the driving node.

2. The method for improving the structural controllability of a power system as described in claim 1, characterized in that, In step S3, the uncontrollable paths are connected to the endpoints of the control paths by adding directed edges between the endpoints of the control paths and the starting points of the uncontrollable paths, including: S31: If the number of uncontrollable paths m is greater than the number of controllable paths n, then go to S32; otherwise, go to S33. S32: Select n uncontrollable paths, add a directed edge between the end point of each control path and the start point of a selected uncontrollable path, recalculate the number of uncontrollable paths, and then go to S31. S33: Select m control paths and add a directed edge between the end point of each selected control path and the start point of an uncontrollable path.

3. The method for improving the structural controllability of a power system as described in claim 1 or 2, characterized in that, In step S2, the maximum matching is solved using the Hopcroft-Karp algorithm.

4. A system for improving the structural controllability of a power system, characterized in that, include: The topology building module is used to establish the original network model of the power system with generators, substations and power-consuming units as nodes and transmission lines as edges, with the direction of the edges consistent with the active power flow direction of the transmission lines. The topology construction module is also used to delete the incoming edges of generator nodes in the original network model to obtain the power network; The matching path solving module is used to solve the maximum matching of the power network and merge the edges with the same node in the maximum matching to obtain the matching path set and the matching circle set. The edge-connecting module is used to denote the paths starting from the generator node in the matching path set as control paths and the remaining paths as uncontrollable paths. The uncontrollable paths are connected to the end of the control paths by adding directed edges between the end of the control paths and the start of the uncontrollable paths. A line addition device is used to add transmission lines between nodes corresponding to the added connection, so that the power system structure is controllable when the generator is the driving node. When determining the control paths connected to each uncontrollable path, the goal is to minimize the cost of adding transmission lines. The methods for determining the control paths connected to each uncontrollable path include: The starting point of each uncontrollable path is designated as an additional driving node, and the topological distance between each additional driving node and the end point of each control path is calculated. Determine the control path matched by each additional drive node such that the sum of the topological distances between the additional drive node and the endpoint of the control path is minimized under this matching scheme; For each uncontrollable path, determine the control path that matches its starting point as the control path it connects to.

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