A power system time-delay multi-link complex dynamic network topology identification method based on improved compressed sensing

Abstract

The application discloses a power system time delay multi-link complex dynamic network topology identification method based on improved compressed sensing, and belongs to the field of topology structure identification of power system time delay multi-link complex dynamic network. The method samples network node states, calculates evaluation indexes of internal synchronization and state convergence in the network evolution process, sets a threshold value of triggering random pulse driving, and prevents the network nodes from being internally synchronized or converging to a fixed value. Then, the sampling data is cleaned and integrated, a sensing matrix and a sampling signal suitable for the compressed sensing method are constructed, a mathematical model for identifying the network topology by compressed sensing is established, the network topology signal is obtained by solving the model, and the network topology structure is recovered. The method can avoid the identification failure problem caused by internal synchronization or state convergence of the complex network, has lower control cost compared with the traditional method based on adaptive synchronization, and has smaller disturbance to the system itself.

Description

Technical Field

[0001] This invention belongs to the field of topology identification of complex dynamic networks with time delays and multiple links in power systems, and more specifically, relates to a topology identification method for complex dynamic networks with time delays and multiple links in power systems based on improved compressed sensing. Background Technology

[0002] Power systems exhibit time-delayed multi-link characteristics, with different links possessing different electrical parameters. This multi-link nature leads to complex power flow distribution patterns within the network. Topology identification of complex dynamic networks with time-delayed multi-links in power systems refers to the process of inverting or reconstructing the network topology based on observable network data for networked systems with unknown or difficult-to-measure topologies. Researching topology identification of complex dynamic networks with time-delayed multi-links in power systems is of great significance for improving the stability of the entire power network, optimizing the power flow distribution, and enhancing the fault diagnosis and fault tolerance capabilities of the entire power system.

[0003] Most current methods for identifying complex power system network topologies are based on adaptive synchronization, requiring the design of an auxiliary network of equal size, or assuming that the network to be identified satisfies the assumption of synchronous flow and linear independence, or requiring constant control over the network. However, in practical applications, these assumptions are difficult to meet, and constant control can also cause significant disturbances to the system itself. Summary of the Invention

[0004] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a method for identifying the topology of complex dynamic power system time-delay multi-link networks based on improved compressed sensing. Compared with existing methods, the method provided by this invention has lower control costs, less disturbance to the system itself, and can solve the problem of identification failure caused by internal synchronization or state convergence in complex networks.

[0005] To achieve the above objectives, according to a first aspect of the present invention, a method for identifying the topology of complex dynamic power system time-delay multi-link networks based on improved compressed sensing is provided, comprising:

[0006] S1, Real-time acquisition and determination of whether the range of the l-th state component of network node i is lower than the preset range;

[0007] S2, if so, trigger a random pulse and return to S1; otherwise, determine whether the current acquisition time has reached the preset time. If so, proceed to S4; otherwise, proceed to S3. The random pulse applied to each node uses the node number and time as the random seed.

[0008] S3, calculate the similarity E between the state vector of all nodes in the network at the current sampling time and the state vector at the previous sampling time. If E is greater than the corresponding threshold, trigger the random pulse and return to S1; otherwise, return to S1 directly.

[0009] S4. Collect the state variables of network node i within a preset time period, and clean the data to remove the state variables generated by node i under the random pulse. Use the cleaned data to construct the sensing matrix Φ and the measurement signal matrix y to establish a compressed sensing mathematical model. The topology signal matrix T of the network is obtained by solving it; where the components of the topology signal matrix T are x and the components of the measurement signal matrix y are u.

[0010] According to a second aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor;

[0011] The computer-readable storage medium is used to store executable instructions;

[0012] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0013] According to a third aspect of the invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to perform the method as described in the first aspect.

[0014] According to a fourth aspect of the invention, a computer program product is provided, comprising a computer program or instructions that, when executed by a processor, implement the method described in the first aspect.

[0015] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0016] The method provided by this invention samples the state of nodes in a complex dynamic multi-link time-delay power system network, calculates evaluation indicators for internal synchronization and state convergence during network evolution, and sets a threshold for triggering random pulse driving to prevent network nodes from internally synchronizing or converging to a fixed value. Then, the sampled data is cleaned and integrated to construct a sensing matrix and sampled signals suitable for compressed sensing methods, establishing a mathematical model for compressed sensing to identify the network topology. By solving this model, the network topology signal is obtained, thereby recovering the network topology structure. This method avoids identification failures caused by internal synchronization or state convergence in complex dynamic multi-link time-delay power systems. Compared with traditional adaptive synchronization-based methods, it has lower control costs and less disturbance to the system itself. It can improve the stability of the entire power network, optimize the power flow distribution, and enhance the fault diagnosis and fault tolerance capabilities of the entire power system.

[0017] As a preferred solution, the present invention designs a solution method for the mathematical model of the above-mentioned compressed sensing identification network topology based on the greedy idea. Compared with the existing compressed sensing method, it requires less data to be sampled when identifying the topology structure, which can further improve the computational efficiency. Attached Figure Description

[0018] Figure 1 Flowchart of a method for identifying complex dynamic network topology of power system time-delay multi-link based on improved compressed sensing, provided in an embodiment of the present invention;

[0019] Figure 2 A flowchart of a network state-triggered random pulse drive provided in an embodiment of the present invention;

[0020] Figure 3 A flowchart for constructing the sensing matrix, sampling signal matrix, and topology signal matrix is ​​provided for embodiments of the present invention;

[0021] Figure 4 This is a flowchart for solving the network topology signal matrix provided in an embodiment of the present invention;

[0022] Figure 5 In the figures (a) and (b), respectively, it is a schematic diagram of the evolution of network node states and the driving triggering situation before and after applying the driving strategy provided in the embodiments of the present invention to the network. Figure 5 (c) in the diagram illustrates the triggering of the driving strategy over time;

[0023] Figure 6 In the above, (a) and (b) are schematic diagrams of the Laplacian matrices of link 1 and link 2 of the 10-node network shown in equation (3) provided in the embodiment of the present invention. Figure 6In the above, (c) and (d) are respectively schematic diagrams of the adjacency matrices of the 10-node network shown in Equation (5) provided in the embodiment of the present invention;

[0024] Figure 7 In the above, (a) and (b) are schematic diagrams of the Laplacian matrix identification results of link 1 and link 2 of the 10-node network shown in equation (3) provided in the embodiment of the present invention. Figure 7 In the above, (c) and (d) are schematic diagrams of the adjacency matrix identification results of the 10-node network shown in Equation (5) provided in the embodiment of the present invention;

[0025] Figure 8 This is a schematic diagram of the topology identification results of a 30-node multi-link complex dynamic network provided in an embodiment of the present invention. Detailed Implementation

[0026] 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.

[0027] Current research has proposed using compressed sensing to identify network topology, but these studies focus on simple networks with single-link connections between nodes. Furthermore, network synchronization can render sampled data unavailable, making it difficult to accurately reconstruct the network topology. Therefore, this invention provides a method for identifying the topology of complex dynamic power system networks with time-delay multi-link connections based on improved compressed sensing. Before introducing this method, some basic terminology related to network graphs will be introduced. A single-layer complex dynamic network can be represented by a graph G = (V, E), where the vertex set V = {v1, v2, ..., v...} n} represents all nodes in a complex network, and the edge set E = {e1, e2, ..., e} m} represents all pairwise information propagation links between network nodes. If it is an undirected graph, information can be transmitted between the nodes at the two vertices of an undirected edge e, and these two nodes are called neighbor nodes; if it is a directed graph, edge e = (v i ,v j ) represents a v j Pointing to v i A one-way edge, in the network, node v i With v j Only one-way information transmission can occur, i.e., node v j Information can be passed to node v i Up, but node vi The information cannot be passed to node v j . Let ω represent the state vector of node i and its derivative, respectively; ij ω represents the edge relationship between nodes i and j. ij =0 indicates that there is no edge between nodes i and j; otherwise, it indicates that there is an edge between nodes i and j. i (x i ) represents the self-dynamic function of node i, C P ,Ξ (P) Let F(X), X, represent the intra-layer coupling strength and intra-layer coupling matrix of the P-th sub-link of the network, respectively. These represent the vectors formed by the dynamics of each node, its state vector, and the derivative of the state vector, respectively.

[0028] The nodes of a power system's time-delayed multi-link complex dynamic network are either generators or loads within the power network.

[0029] The present invention provides a method for identifying the topology of complex dynamic power system time-delay multi-link networks based on improved compressed sensing, comprising:

[0030] S1, Real-time acquisition and determination of whether the range of the l-th state component of network node i is lower than the preset range;

[0031] S2, if so, trigger a random pulse and return to S1; otherwise, determine whether the current acquisition time has reached the preset time. If so, proceed to S4; otherwise, proceed to S3. The random pulse is a random pulse applied to each node, with the node number and time as the random seed.

[0032] S3, calculate the similarity E between the state vector of all nodes in the network at the current sampling time and the state vector at the previous sampling time. If E is greater than the corresponding threshold, trigger the random pulse and return to S1; otherwise, return directly to S1.

[0033] Compressed sensing methods require sampling a sufficient amount of linearly independent data. However, synchronization phenomena are widespread in complex dynamic networks. Once internal synchronization occurs in a complex network, it leads to linear correlation in the sampled data, making it impossible to recover accurate topology information. Therefore, this method first samples the state information of each node in the network and calculates the range of each state component. The specific calculation method is as follows:

[0034]

[0035] Where x ilLet represent the l-th component of the state vector of node i. When a component converges to a small interval, no further judgment is needed; a pulse control is immediately triggered to break the network's internal synchronization. The pulse signal given to node i at time t is denoted as h. i (i,t) represents a random pulse generated with i,t as a random seed. When this signal is applied to the network (3a), the dynamic expression of the network is as shown in (3b). When the above control is not triggered, the cosine similarity between the node state vector at the sampling time and the node state vector at the previous sampling time is calculated. The calculation method is as follows:

[0036]

[0037] Considering index E, when the calculated result E is greater than a certain threshold, a pulse control is triggered; if neither of the above two judgments triggers control, then resampling is performed and the algorithm is executed again.

[0038] like Figure 2 As shown, in step S1, the state data of the network nodes is sampled, and the range of each component of the node state at the sampling time is calculated. If the range of a certain component is lower than the set threshold, then in step S2, a random pulse drive is triggered. The random signal applied to each node uses the node number and time as the random seed to ensure that the drive signal of each node is different. Otherwise, it is determined whether the current sampling time has reached the preset time. If so, proceed to S3; otherwise, return to S1.

[0039] In step S3, the similarity E between the state vector of all nodes in the network at the current sampling time and the state vector at the previous sampling time is calculated. The index E is compared to see if it exceeds the threshold. If it exceeds the threshold, a random pulse drive is triggered. The random signal applied to each node is also seeded with the node number and sampling time. If it does not exceed the threshold, the random pulse drive is not triggered, and the next round of node state sampling is carried out again.

[0040] S4. Collect the state variables of network node i within a preset time period, and clean the data to remove the state variables generated by node i under the random pulse. Use the cleaned data to construct the sensing matrix Φ and the measurement signal matrix y to establish a compressed sensing mathematical model. The topology signal matrix T of the network is obtained by solving it; where the components of the topology signal matrix T are x and the components of the measurement signal matrix y are u.

[0041] It is understandable that if no random pulse is triggered in steps S2-S3, then no data cleaning is required in step S4. The sensing matrix Φ and the measurement signal matrix y can be constructed directly based on the state variables of the network node i within a preset time.

[0042] For a time-delayed multi-link complex network with dynamics as shown in equation (3a), after modeling and transformation, we obtain the expression shown in equation (4), where X 1:M For the sensing matrix, For sampling signals, It is the topological signal that needs to be solved.

[0043]

[0044] For a time-delayed multi-link complex network with dynamics as shown in equation (5), after modeling and transformation, we obtain the expression shown in equation (6), where... For the sensing matrix, For sampling signals, It is the topological signal that needs to be solved.

[0045]

[0046] like Figure 3 As shown, in step S4, the network node state is sampled within a certain time period, and the external triggering situation at the sampling time is obtained at the same time. Combined with the external driving situation, the data that has been disturbed by the external signal (i.e., random pulse) is cleaned up. That is, the dynamic data generated by the external disturbance applied to the network node state during the evolution process is deleted. Then, the cleaned data is used to construct the sensing matrix and measurement signal to obtain the compressed sensing mathematical model, and then the solution is performed.

[0047] For the network shown in equation (3a), the sensing matrix is ​​X 1:M :=[X(t-τ (1) ); X(t-τ) (2) );…;X(t-τ (M) The measurement signal matrix is: For the network shown in equation (5), the sensing matrix is: The measurement signal matrix is

[0048] Let the sensing matrix be Φ, the components of the topology signal matrix T be x, and the components of the measurement signal matrix y be u. The topology identification problem of multi-link complex networks is transformed into the following zero-norm minimization problem, i.e., the compressed sensing mathematical model:

[0049]

[0050] Since x is a sparse signal, u can be regarded as a linear combination of certain column vectors in matrix Φ. Therefore, solving the above problem is transformed into finding the support set of signal u from the column vectors of matrix Φ.

[0051] By solving the compressed sensing mathematical model described above, the topological signal matrix T of the network can be obtained.

[0052] The aforementioned minimization problem can be solved using existing methods, such as relaxing the 0-norm minimization problem into a 1-norm minimization problem. However, considering that transforming the 0-norm minimization problem into a 1-norm minimization problem with additional conditions that are difficult to verify, as a further preferred embodiment of this invention, a 0-norm minimization solution method based on a greedy algorithm is designed, that is, the above problem is solved in the following way:

[0053] A1, Initialize the set Given the residual signal v = y(k), calculate the inner product of each column vector of Φ with the residual signal, and select the top 2K vectors with the largest inner product. k The indices of the column vectors of Φ are added to Υ in order;

[0054] A2, using the submatrix formed by the column vectors in Φ corresponding to the indices in Υ and y(k), calculate the estimated value of the k-th row vector of the topological signal based on the batch least squares method. And according to the formula Calculate the estimated value of the k-th column vector of the measurement signal matrix y. Determine the current residual signal If the 2-norm of K is less than the corresponding threshold, the process ends; otherwise, proceed to A3. k for sparsity;

[0055] A3, for set Υ, retain The first K in k The index corresponding to the maximum value is removed from the set Y, and the remaining indices are removed.

[0056] A4, calculate the inner product of each column vector of Φ with the current residual signal, and select the top K columns with the largest inner products. k Add the indices of the column vectors to Υ and return A2.

[0057] Preferably, it is obtained according to the following method sparsity K k :

[0058] B1, Initialize the set K k =1, and the sensing matrix Φ is normalized to obtain calculate The inner product of each column vector of y with the k-th column vector of y is calculated, and the values ​​of the inner products are sorted according to their magnitudes. After sorting the column vectors in descending order, Add the index of the column vector

[0059] B2, determine by The first K in k A matrix consisting of column vectors corresponding to each index Does it meet the requirements? Where y(k) is the k-th column vector of y;

[0060] B3, if so, then update. The sparsity is K k Otherwise let K k =K k +1, return to B2.

[0061] Preferably, Where Γ=diag(||Φ1||2) -1 ,||Φ2||2 -1 ,…,||Φ n ||2 -1 ), where n is the length of the recovered topological signal.

[0062] Specifically, such as Figure 4 As shown, the process of solving for the network topology signal is as follows:

[0063] (1) Data initialization: Obtain the measurement signal matrix y and the sensing matrix Φ, and determine the length n of the topology signal to be recovered based on the network size and the state dimension of each node.

[0064] (2) Normalized sensor matrix.

[0065] Calculate the normalized matrix Γ = diag(||Φ1||2) -1 ,||Φ2||2 -1 ,…,||Φ n ||2 -1 Normalization of the sensing matrix

[0066] (3) Estimate the sparsity of the topological signal.

[0067] For each topological signal that needs to be recovered, i.e., the k-th row vector of the topological signal matrix, denoted as T(k), its sparsity is K. k Perform the following steps:

[0068] 1) Initialize the collection Calculate matrix The inner product of each column vector with the k-th column vector in the measurement signal matrix y is calculated, and the values ​​of the inner products are then sorted according to their magnitudes. The column vectors in the array are sorted in descending order.

[0069] 2) Following the order in 1), convert the inner product results to their corresponding values. The index of the column vector is added to the set. In the initialization, the topological signal sparsity, i.e., K, is determined. k The value is 1.

[0070] 3) Examine the sequence formed by the indices in the set. submatrix Does it meet the requirements? If satisfied, then update the sparsity to K. k Proceed to step (4); otherwise, let K = K + 1 and repeat step (3).

[0071] (4) Recover the topology signal. For each topology signal to be recovered, define the topology signal matrix as T, and the k-th row vector of the topology signal matrix as T(k), and perform the following steps:

[0072] 1) Initialize set Y to an empty set, define For the estimated value of T(k), define the use of When replacing T(k), the estimated value of the k-th column vector of the measured signal matrix y is... Define the residual signal as Initialize the residual signal as the measurement signal, i.e., let v = y(k). Calculate the inner product of each column vector of matrix Φ with the residual signal, and select the top 2K columns with the largest inner product. k The indices of the column vectors Φ are added to the set Υ.

[0073] 2) Using the submatrix formed by the column vectors in Φ corresponding to the indices in set Y, calculate the estimated value of the k-th row vector of the topological signal based on the batch least squares method. renew Calculate the new residual signal Check if the 2-norm of the residual signal is less than an acceptable threshold; if acceptable, end step 4 and obtain the topology estimation signal. If not, continue to step 3.

[0074] 3) For set Y, retain the first K of the estimated signals. k The index corresponding to the maximum value is used to remove the remaining indices from set Y.

[0075] 4) Calculate the inner product of each column vector of matrix Φ with the current residual signal. Select the top K columns with the largest inner products. k Add the indices of the column vectors to set Y, and repeat step 2).

[0076] The method provided by the present invention will be further illustrated below with a specific example.

[0077] In this example, a time-delayed multi-link complex network with dynamics as shown in equation (5) is used, where M = 2 and N = 10. Figure 5Figure (a) illustrates the node dynamics evolution of a complex multi-link dynamic network as shown by the following dynamic equations:

[0078]

[0079] from Figure 5 As can be seen in (a), the node states quickly tend to internal synchronization. At this point, traditional topology identification methods based on adaptive synchronization need to construct an auxiliary network of the same size and apply continuous control signals to each node. Existing methods based on compressed sensing, on the other hand, will fail to identify nodes because they cannot sample enough linearly independent data. Figure 5 Figure (b) illustrates the evolution of network node states after applying the driving strategy of this invention. Figure 5 (c) shows the triggering of the external driving strategy over time. It can be seen that the present invention successfully breaks the internal synchronization of the network with fewer external driving times. Compared with the adaptive synchronization method, it reduces the control cost and reduces the disturbance to the network to be identified.

[0080] The method provided by this invention is compared with existing methods based on adaptive control and compressed sensing for topology identification of complex dynamic networks. As shown in Table 1, when identifying networks with different nodes, the 0-norm minimization method based on a greedy algorithm provided by this invention requires fewer sampling times compared to the relaxation methods in previous studies that used 1-norm minimization instead of 0-norm minimization. It can be seen that the method provided by this invention effectively reduces the number of sampling times, especially on large-scale networks.

[0081] Table 1 compares the number of samples required for complete topological structure identification using the proposed method and the 1-norm relaxation solution.

[0082]

[0083] This invention provides an electronic device, including: a computer-readable storage medium and a processor;

[0084] The computer-readable storage medium is used to store executable instructions;

[0085] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0086] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0087] This invention provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the method described in any of the above embodiments.

[0088] 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 identifying the topology of complex dynamic power system networks with time delays and multiple links based on improved compressed sensing, characterized in that, include: S1, real-time data collection and analysis of network nodes. i The l Whether the range of each state component is lower than a preset range; where, for complex dynamic networks with a single layer, a graph is used. This indicates that the vertex set Represents all nodes and edge sets in a complex network. This represents all pairwise information propagation links between network nodes; in a complex dynamic network of time-delayed multi-link power systems, the nodes are generators or loads within the power network. S2, if so, trigger a random pulse and return to S1; otherwise, determine whether the current acquisition time has reached the preset time. If so, proceed to S4; otherwise, proceed to S3. The random pulse applied to each node uses the node number and time as the random seed. S3, Calculate the similarity between the state vectors of all nodes in the network at the current sampling time and their state vectors at the previous sampling time. E ,like E If the value is greater than the corresponding threshold, the random pulse is triggered and the process returns to S1; otherwise, the process returns directly to S1. S4, Collect network nodes i The state data within a preset time period is processed, and the data is cleaned to remove nodes. i The state variables generated under the action of the random pulse; the sensing matrix is ​​constructed using the cleaned data. and measurement signal matrix To establish a mathematical model for compressed sensing The topological signal matrix of the network is obtained by solving the problem. T ; where, topological signal matrix T The component is Measurement signal matrix The component is ; If the dynamics formula of the network is: ； Then its sensing matrix Measurement signal matrix ; If the dynamics formula of the network is: ； Then its sensing matrix Measurement signal matrix ; in, For nodes The state vector, For nodes Its own dynamic function, For nodes exist The state vector at time t, For the first p The time delay of each sub-link, For all nodes in the network The vector formed by the state vectors at each moment. For the first M The time delay of each sub-link, M The number of network time-delay links. N The number of nodes in the network. Let be the intra-layer coupling strength and intra-layer coupling matrix of the i-th sub-link of the network, respectively. For nodes In the The connection weights of each link; This represents a vector composed of the derivatives of the state vectors of each node.

2. The method as described in claim 1, characterized in that, Step S4 includes: A1, Initialize the set , residual signal ,calculate The inner product of each column vector with the residual signal, and the top 2 with the largest inner product. K k indivual The column vectors are added in order. middle; A2, Use The serial number in Submatrices formed by column vectors in and The first step of calculating the topological signal based on batch least squares method. k The estimated values ​​of each row vector And according to the formula Calculate the measurement signal matrix The k Estimates of column vectors Determine the current residual signal If the 2-norm is less than the corresponding threshold, the process ends; otherwise, proceed to A3. K k for sparsity; A3, for sets ,reserve The front of the middle K k The index corresponding to the maximum value, from the set Remove the remaining serial numbers from the middle; A4, Calculation The inner product of each column vector with the current residual signal will have the largest inner product among the top columns. K k Add the indices of the column vectors to Return to A2.

3. The method as described in claim 2, characterized in that, Obtain using the following methods sparsity K k : B1, Initialize the set , K k =1, for the sensing matrix After unitization, the following is obtained ;calculate Each column vector and The k The inner product of the column vectors, and sorted by the size of the inner product. After sorting the column vectors in descending order, Add the index of the column vector ; B2, determine by The front of the middle K k A matrix consisting of column vectors corresponding to each index Does it meet the requirements? d; where, for The k Column vectors; B3, if so, then update. The sparsity is K k Otherwise K k = K k +1, return to B2.

4. The method as described in claim 3, characterized in that, ;in, , n The length of the recovered topology signal.

5. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-4.

7. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method as described in any one of claims 1 to 4.

Images