Key power transmission section identification method, system and equipment of power system and storage medium

Abstract

The invention discloses an identification method, system and device for a key transmission section of a power system and a storage medium, and the method comprises the steps: an initial section identification step: based on a maximum flow minimum cut theory, considering the electrical coupling vulnerability and topological structure vulnerability of a power system line, and combining a power flow consistency constraint condition, completing the identification of the initial transmission section; and a key section identification step: identifying the weak bayonet of the initial power transmission section by considering the power flow operation mode and the line current-carrying capacity, and constructing a transient stability key section identification model based on the multi-channel time sequence convolutional neural network to complete the identification of the transient stability key power transmission section of the power system. According to the method, the initial power transmission section identification method which is based on the maximum flow minimum cut theory, considers the line vulnerability of the power system and combines power flow consistency and other power transmission section constraint conditions is adopted, meanwhile, the data-driven transient safety key section identification model is adopted, and the transient stability key power transmission section identification result can be rapidly and accurately obtained.

Description

Technical Field

[0001] The present application relates to the technical field of power system dispatching operation control, and specifically to a method, system, device and storage medium for identifying key transmission sections of a power system. Background Art

[0002] The traditional method of identifying key power transmission sections based on experience selection is restricted by manual experience, resulting in a relatively rough formulation of the operating status and identification rules of the power grid, and most of them involve transient simulation of the entire system. The calculation process is often complicated and time-consuming. Specifically, the identification method of the key transmission section of transient stability has the following problems: (1) Huge labor cost: Due to the large number of parameters involved in the transient simulation calculation of large power grids, the difficulty of analysis and calculation is increasing day by day, requiring huge human resources; (2) Heavy reliance on expert experience: The identification of key transmission sections mainly depends on the technical level and engineering experience of experts. Complex large power grid simulation analysis tasks are difficult for ordinary technicians to handle; (3) Easy to cause errors and omissions: The traditional identification method of transmission sections mainly relies on manual analysis, and there are more and more errors and omissions when processing data results.

[0003] As the complexity of power grid operation continues to increase, traditional state recognition and identification methods are unable to meet the severe challenges faced by new power systems. Summary of the invention

[0004] In order to solve the problems existing in the traditional power system key transmission section identification technology, the present application provides a power system key transmission section identification method, system, equipment and storage medium. The present application adopts an initial transmission section identification method based on the maximum flow minimum cut theory, taking into account the power system line vulnerability, and combining the transmission section constraints such as power flow consistency. At the same time, taking into account the transient safety and stability constraints, a data-driven transient safety critical section identification model is adopted. The identification results of the critical transmission section for transient stability can be obtained quickly and accurately, guiding the screening of key sections and expanding the application scope of the data-driven model in the power system.

[0005] This application is implemented through the following technical solutions:

[0006] A method for identifying a key transmission section of a power system, the method comprising:

[0007] Initial section identification step: Based on the maximum flow minimum cut theory, the electrical coupling vulnerability and topological structure vulnerability of the power system lines are considered, combined with the power flow consistency constraint condition, the initial transmission section identification is completed to obtain the initial transmission section set of the power system;

[0008] Steps for identifying critical sections: Consider the power flow operation mode and line current carrying capacity to identify the initial transmission section weak points, and use the initial transmission section weak points as input, use the power system comprehensive stability analysis program to simulate and set the transient stability fault sample set, and build a transient stability critical section identification model based on a multi-channel time series convolutional neural network to complete the identification of the critical transmission section for transient stability of the power system.

[0009] In some embodiments, the initial section identification step specifically includes:

[0010] The power grid topology is converted into a directed graph form to obtain a power system directed graph;

[0011] Establish an electrical coupling vulnerability assessment index for power system lines considering the electrical distance of nodes;

[0012] By analyzing the network constraint coefficient of the nodes, the topological structure vulnerability assessment index of the power system line is established;

[0013] Based on the maximum flow theory, the electrical coupling vulnerability and topological structure vulnerability of all lines in the power system are calculated, and the lines with the strongest electrical coupling vulnerability and topological structure vulnerability are removed and recorded;

[0014] Based on the minimum cut theory, determine whether a cut set is generated after the line is removed. If no new cut set is generated, repeat the previous step. If a new cut set is generated, record the cut set as the initial cut set of the power system.

[0015] Based on the initial cut set of the power system and considering the constraint condition of power flow consistency, an initial transmission section set of the power system is constructed.

[0016] In some implementations, the step of establishing an electrical coupling vulnerability assessment index for power system lines taking into account node electrical distances specifically includes:

[0017] The neighbor propagation clustering algorithm is used to construct the classification evaluation index of the electrical coupling degree of the power system line, which is expressed as:

[0018] I i-j =AP(D ij ,R ij ,x ij )

[0019]

[0020] Among them, D ij represents the distance of the transmission line ij, R ij and x ij denote line resistance and reactance, respectively; AP(·) denotes clustering performed using the neighbor propagation clustering algorithm with the features in brackets as input; NAP Indicates the number of clusters; I i-j represents the cluster label of transmission line ij, E i-j Represents the electrical coupling importance of transmission line ij.

[0021] In some implementations, the step of establishing a topological structure vulnerability assessment index for power system lines specifically includes:

[0022] The network constraint coefficients of the nodes at both ends of the power system transmission line are calculated, and the topological structure importance index of the line is constructed by using the index reflecting the topological importance of the node, which is expressed as:

[0023]

[0024] C L (i) = -log2C(i)

[0025] T i-j =C L (i)×C L (j)

[0026] Where C(i) represents the network constraint coefficient of node i, node q is the common adjacent node of nodes i and j, and p ij represents the proportion of transmission line ij to all lines connected to node j, p iq represents the proportion of transmission line iq to all lines connected to node q, p qj represents the proportion of transmission line qj to all lines connected to node j, Γ i represents the set of adjacent nodes of node i, C L (i) represents the topological importance of node i, C L (j) represents the topological importance of node j, T i-j Represents the topological importance of transmission line ij.

[0027] In some implementations, the step of constructing the initial power transmission section set of the power system specifically includes:

[0028] Numbering each node and tie line in the directed graph of the power system;

[0029] Based on the Karger algorithm, the minimum cut search is performed on the power grid. A transmission line is randomly selected and the nodes at both ends are merged until the power grid is divided into two areas.

[0030] Determine whether a new section is generated. If so, repeat the previous step. If no new section is generated, store the cut set in the initial cut set.

[0031] It is determined whether the active power flow directions of all the transmission lines in the initial cut set are consistent. If they are consistent, they are stored in the initial transmission section set; otherwise, the cut set is deleted.

[0032] In some embodiments, the process of identifying the weak points of the initial power transmission section specifically includes:

[0033] Calculate the branching coefficient of the transmission line at its transmission section:

[0034]

[0035] Among them, K i-j It represents the branch coefficient of the transmission line ij in its transmission section, P i-j represents the active power of transmission line ij, represents the active power of transmission section g, which belongs to the initial section set C;

[0036] Considering the power flow operation mode and line current carrying capacity, the ratio of the branching coefficient of the transmission line at its transmission section to its long-term operating current carrying capacity is calculated:

[0037] |P i-j |≤L i-j

[0038]

[0039] |K i-j / L i-j |≤1 / |P g,sum |

[0040] Among them, U N Indicates rated voltage; I max Indicates the current limit of the transmission line; T c represents the temperature correction factor; Indicates power factor; P i-j represents the active power of transmission line ij; L i-j Indicates the long-term allowable current carrying capacity of the transmission line ij;

[0041] Get the compliance The transmission lines serve as the weak points of the transmission sections.

[0042] In some implementations, the process of establishing the transient stability critical transmission section identification model specifically includes:

[0043] The fault sample set is used to generate disturbances on the node voltage and the power angle of the generator set of the power system, and different types of simulation timing curves and stable labels are obtained, and a training set is constructed based on them;

[0044] The node voltage timing curve and the generator power angle timing curve in the training set are used as the input features of the TCN network, and the stable labels in the training set are used as the output features of the TCN network, and a multi-channel TCN network temporary stability discrimination model is obtained by training; wherein the TCN network includes a feature extraction module established for the input node voltage timing curve and the generator power angle timing curve respectively, and a classification module that uses a fully connected layer to realize feature splicing and feature classification;

[0045] The multi-channel TCN network transient stability discrimination model is used for batch identification, and the transmission section judged as unstable by the model is recorded as a transient stability key section. Otherwise, the transmission section is abandoned.

[0046] In a second aspect, the present application proposes a power system key transmission section identification system, the system comprising:

[0047] An initial section identification module, which is based on the maximum flow minimum cut theory, considers the electrical coupling vulnerability and topological structure vulnerability of the power system line, and combines the power flow consistency constraint condition to complete the initial transmission section identification and obtain the initial transmission section set of the power system;

[0048] And, a critical section identification module, which identifies the initial transmission section weak points by considering the flow operation mode and the line current carrying capacity, and takes the initial transmission section weak points as input, uses the power system comprehensive stability analysis program to simulate and set the transient stability fault sample set, and constructs a transient stability critical section identification model based on a multi-channel time series convolutional neural network to complete the identification of the critical transmission section for transient stability of the power system.

[0049] In a third aspect, the present application proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0050] In a fourth aspect, the present application proposes a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0051] The present application proposes a method, system, device and storage medium for identifying key transmission sections of a power system. The method adopts an initial transmission section identification method based on the maximum flow minimum cut theory and line vulnerability assessment index, and calculates the flow value of the network flow graph based on the topological structure vulnerability of the power grid line and the electrical coupling vulnerability. The method can better consider the system load distribution in the section search, and can more comprehensively discover the potential security threats of the power system, and has good search efficiency in different operation scenarios.

[0052] The present application proposes a method, system, device and storage medium for identifying key transmission sections of a power system. The method takes into account transient safety and stability constraints and adopts a data-driven method for identifying key transmission sections. While not being affected by differences in operating modes, the method establishes a mapping relationship between power angle and voltage power system fault timing characteristics and transient stability, thereby improving the accuracy of the model, avoiding mutual influence between different types of characteristics, and improving the interpretability of the model. Compared with traditional transient simulation technology, the present application can improve the computing efficiency and can serve as an effective criterion for identifying key transmission sections for transient stability in different scenarios, providing technical support for related technical engineering applications and theoretical research. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The drawings described herein are used to provide a further understanding of the embodiments of the present application, constitute a part of the present application, and do not constitute a limitation on the embodiments of the present application. In the drawings:

[0054] Figure 1 This is a schematic diagram of the principle of a method for identifying key transmission sections of a power system according to an embodiment of the present application;

[0055] Figure 2 This is a flow chart of a method for identifying key transmission sections of a power system according to an embodiment of the present application;

[0056] Figure 3 A flow chart of power system transmission section discovery based on minimum cut theory and Karger algorithm according to an embodiment of the present application;

[0057] Figure 4 A schematic diagram of the effect of the power transmission section bayonet on the system in an embodiment of the present application;

[0058] Figure 5 This is an overall structural diagram of a transient stability discrimination model based on data-driven according to an embodiment of the present application;

[0059] Figure 6 An IEEE 39-node test system for new energy access according to an embodiment of the present application;

[0060] Figure 7 for Figure 6 Schematic diagram of disturbance curves of the IEEE 39-node test system shown in FIG. 1 ; wherein (a) is the system voltage disturbance curve; (b) is the system power angle disturbance curve;

[0061] Figure 8 for Figure 6 The schematic diagram of the temporary stability judgment result of multi-channel TCN of the IEEE 39-node test system shown;

[0062] Fig. 9 for Figure 6The specific location of the critical transient stability section of the IEEE 39-node test system shown;

[0063] Fig.10 Schematic diagram of the initial section disturbance curve of the L power grid under the Xiada mode; (a) is the voltage disturbance curve; (b) is the power angle disturbance curve;

[0064] Fig.11 This is a schematic diagram of the identification results of the key transmission sections of the L power grid transient stability;

[0065] Fig.12 This is a principle block diagram of the power system key transmission section identification system according to an embodiment of the present application. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with examples and drawings. The illustrative implementation scheme of the present application and its description are only used to explain the present application and are not intended to limit the present application.

[0067] Example:

[0068] This embodiment proposes a method for identifying key transmission sections of a power system. Figure 1 As shown, the principle of the method proposed in this embodiment is as follows: first, considering the vulnerability of the topological structure and the vulnerability of the node electrical coupling, an evaluation index system for characterizing the vulnerability of the line is proposed, and the initial transmission section discovery method is constructed in combination with the maximum flow minimum cut theory, and the initial transmission section weak point identification rules are formulated considering the flow operation mode and the line current carrying capacity to realize the initial transmission section identification; then, taking the initial transmission section as input and from the perspective of transient safety and stability, a multi-channel TCN transient stability critical section identification model guided by PSASP simulation is established; finally, based on the transient stability critical section identification results, the corresponding critical dominant labels are generated to achieve the distinction from other traditional types of critical sections, and the quantitative and qualitative analysis of the degree of influence of the initial transmission section on transient stability under multiple flow modes is realized, thereby realizing the identification of transient stability critical transmission sections.

[0069] The method proposed in this embodiment mainly includes two parts: an initial section identification step based on the maximum flow minimum cut theory and line vulnerability evaluation index, and a key section identification step taking into account transient safety and stability constraints. The initial section identification step is mainly based on the maximum flow minimum cut theory, taking into account the electrical coupling vulnerability and topological structure vulnerability of the power system line, and combining the transmission section constraints such as power flow consistency to complete the initial transmission section identification; the key section identification step mainly considers the power flow operation mode and the line current carrying capacity to identify the initial transmission section weak checkpoints, and from the perspective of transient safety and stability, for the initial transmission section weak checkpoints, the power system comprehensive stability analysis program is used to simulate and set the transient stability fault sample set, and a transient stability key section identification model is constructed based on a multi-channel time series convolutional neural network to complete the identification of the power system transient stability key section.

[0070] like Figure 2 As shown, the initial section identification step specifically includes the following steps:

[0071] Step 101, converting the power grid topology into a directed graph. Specifically, the power plant, substation and load nodes in the initial power system can be simplified into topology graph nodes, the transmission lines can be simplified into topology graph tie lines, and multiple transmission lines can be merged to obtain a power system directed graph.

[0072] Step 102: Using a spatial clustering method, establish a system line electrical coupling vulnerability assessment index that takes into account node electrical distances.

[0073] Line impedance is used to characterize the electrical distance between nodes. The transmission line distance is introduced in combination with line impedance to jointly characterize the degree of electrical coupling of the lines, and evaluation principles for the importance of electrical coupling at different levels are formulated.

[0074] This step 102 specifically uses the Affinity Propagation (AP) clustering algorithm to construct a classification evaluation index of the electrical coupling degree of the power system lines.

[0075] The principle of the AP clustering algorithm is:

[0076] s i,k Represents sample point X i With X k The similarity between them is used to judge X k Is it suitable as X i The cluster center is generally represented by the negative value of Euclidean distance.

[0077] s i,k =-||X i -X k || 2 (1)

[0078] s k,k It is called the reference degree, which is the point with the same coordinates on the horizontal and vertical axes in the similarity matrix, indicating the possibility of point k being the cluster center. Before the iteration starts, it is assumed that all sample points have the same probability of becoming cluster centers, so s k,k The initial value of is generally set to the minimum or median of all values ​​in the similarity matrix, s k,k The size of will affect the final number of clusters.

[0079] r i,k and a i,k Represents the sample points X i With X k Angle judgment X k As X i The suitability of cluster centers:

[0080]

[0081]

[0082] Among them, s i,k Based on X i With X k The similarity between i,j represents the attribution value of other points to point i except point k; s i,j represents the attraction of other points to point i except point k; r k,k is the similarity value of point k as the cluster center, r i′,k Indicates the similarity value of point k as the cluster center of other points except point i;

[0083] r i,k and a i,k The convergence speed and stability are adjusted by the damping coefficient γ, which usually takes a value between 0 and 1. i,k and a i,k The update method is as follows:

[0084]

[0085] Through the iterative updating process of formula (4), the cluster center is generated, and each data sample is assigned to the corresponding cluster.

[0086] In step 102, the AP model input feature set is constructed by combining the transmission line distance and line impedance parameters. To avoid the magnitude difference of the input parameters interfering with the clustering results, the input features are normalized with the upper and lower limits of 0.95 and 0.05 respectively. i-j and electrical coupling importance E i-j The calculation method is as follows:

[0087] I i-j =AP(D ij , R ij , x ij ) (5)

[0088]

[0089] Where: D ij represents the distance of the transmission line ij, R ij and x ij denote line resistance and reactance, respectively; AP(·) denotes clustering performed using the features in brackets as input and the AP algorithm; N AP Indicates the number of clusters.

[0090] Step 103, by analyzing the network constraint coefficient of the node, a topological structure vulnerability assessment index of the power system line is established to assess the impact of the target line on the power flow transmission function.

[0091] In step 103, the network constraint coefficients of the nodes at both ends of the power transmission line ij are calculated to propose an index C that reflects the topological importance of node i. L (i) and the index C that reflects the topological importance of node j L (j), and then construct the topological importance index T of line ij i-j , calculated as follows:

[0092]

[0093] C L (i) = -log2 C(i) (8)

[0094] T i-j =C L (i)×C L (j) (9)

[0095] Where C(i) is the network constraint coefficient of node i, node q is the common adjacent node of nodes i and j, and p ij represents the proportion of line ij to all lines connected to node j, p iq represents the proportion of line iq to all lines connected to node q, p qj represents the proportion of line qj to all lines connected to node j; Γ i Represents the set of adjacent nodes of node i.

[0096] Based on the network constraint coefficient of the structural hole theory, a topological structure importance T that reflects the importance of the line is proposed from the perspective of power grid topology characteristics. i-j . T i-jIt can characterize the connection tightness between line ij and other lines. The larger the value is, the more important line ij is in the system, the stronger the power transmission role it undertakes, and the greater the possibility of causing safety and stability problems.

[0097] In addition, the value of the network constraint coefficient C is between 0 and 1. The smaller the value, the more important the target node is in the topology. In order to better characterize the influence of C, the negative logarithm of C with base 2 is taken as the node importance index C L From formula (8), we can see that when C(i) = 0.5, C L (i) = 1, that is, C(i) is bounded by 0.5, and if it is lower than 0.5, then T i-j A positive effect is produced, otherwise a negative effect is produced. C(i) is 1, which means that the node is a hanging node.

[0098] Step 104 , based on the maximum flow theory, the electrical coupling vulnerability and topological structure vulnerability of all lines in the power system are calculated, and the lines with the strongest electrical coupling vulnerability and topological structure vulnerability are removed and recorded.

[0099] In step 104, the network constraint coefficient is used to characterize the maximum flow of the system, and the line importance evaluation index B is constructed by comprehensively considering the two types of line vulnerabilities, combining the topological structure vulnerability and the electrical coupling vulnerability evaluation index. i-j , calculated as follows:

[0100] B i-j =T i-j ·E i-j (10)

[0101] By calculating the electrical coupling vulnerability assessment index and topological structure vulnerability assessment index of all lines in the power system, the line importance assessment index is obtained. According to the line importance assessment index value, the line with the strongest vulnerability is identified, removed and recorded.

[0102] Step 105, based on the minimum cut theory, determine whether a cut set is generated after removing the line. If no new cut set is generated, repeat the previous step (i.e., step 400). If a new cut set is generated, record the cut set as the initial cut set of the power system. Based on the initial cut set of the power system, consider the transmission section constraints such as power flow consistency, and construct the initial transmission section set of the power system.

[0103] This step 105 adopts a power grid partitioning method based on the minimum cut theory and the Karger algorithm to realize the power grid area division and construct an initial transmission section set, such as Figure 3 As shown, the specific process is as follows:

[0104] Step 501, numbering each node and tie line in the power system directed graph;

[0105] Step 502, performing minimum cut search on the power grid based on the Karger algorithm, randomly selecting a line, merging the nodes at both ends thereof, until the network is divided into two areas;

[0106] Step 503, determining whether a new section is generated, if so, repeating step 502; if no new section is generated, storing the cut set value in the initial cut set;

[0107] Step 504, determining whether the active power flow directions of all lines in the initial cut set are consistent, if the power flow directions are consistent, storing them in the initial transmission section set, if the power flow directions are inconsistent, deleting the cut set;

[0108] Step 505: obtain the initial transmission section set C = {C1, C2, C3, ... C k-1}.

[0109] The key section identification step specifically includes the following steps:

[0110] Step 201, based on the initial transmission section set of the power system, identifying the weak points of the initial transmission section taking into account the flow operation mode and the line current carrying capacity.

[0111] The power transmission section of the power system distributes active power based on the impedance of each line. This step 201 uses the branching coefficient to define the ratio of the active power of any line in the transmission section to the power of the transmission section. Therefore, the line branching coefficient in the fully connected operation mode can be approximated as a constant, which is calculated as follows:

[0112]

[0113] Among them, K i-j It represents the branch coefficient of line ij in the transmission section to which it belongs, P i-j represents the active power of line ij, Represents the active power of transmission section g, which belongs to the initial section set C.

[0114] Under normal operation, the active power P i-j Not higher than its long-term allowable current carrying capacity L i-j . When the line type is the same, L i-j Determined by current limit, ambient temperature and wire operating temperature.

[0115] |P i-j |≤L i-j (12)

[0116]

[0117] Among them, U N Indicates rated voltage; I maxIndicates the current limit of the line; T c It is the temperature correction coefficient, which is affected by the ambient temperature and the conductor working temperature. Usually, the ambient temperature is 25℃ and the conductor temperature is 80℃. In this case, T c is 1; Indicates the power factor, usually 0.9 or 0.95.

[0118] K in the transmission section i-j With L i-j The line with the largest ratio is not overloaded, and the other lines in this section can operate safely and stably, so the line that meets the conditions The line is defined as the weak point of the transmission section. The schematic diagram of the impact of the weak point of the transmission section on the system is as follows: Figure 4 As shown. Figure 4 It can be seen that the transmission section is composed of lines L1 and L4. The impact of disconnecting the weak stopper line L1 in the transmission section on the entire system is much greater than disconnecting the non-stopper line L4 in the section. When L1 is disconnected, the impact on the system includes but is not limited to overload of lines L2 and L4, reverse flow of line L5, etc. On the contrary, when L4 is disconnected, the operation of the system is not greatly impacted. Therefore, more attention should be paid to the operating status of weak stoppers in the transmission section.

[0119] Step 202, taking the initial transmission section weak points as input and taking into account the transient safety and stability constraints of the online safe and stable operation of the power system, a data-driven transient stability key transmission section identification model is established.

[0120] In step 202, the process of establishing the transient stability key transmission section identification model is as follows:

[0121] By analyzing the transient stability judgment mechanism of the power system, the Power System Analysis Software Package (PSASP) is used to simulate the fault sample set to generate disturbances on the system node voltage and the power angle of the generator set, and different types of simulation timing curves (input features) and stability labels (output features: instability and stability) are obtained to construct a training set.

[0122] The temporal convolutional network (TCN) is used as the model infrastructure, in which TCN uses dilated convolution operations to achieve interaction between neurons. The mathematical expression of the dilated convolution operation is shown in the following formula:

[0123]

[0124] Where F(t) represents the dilated convolution operation, X tRepresents sequence data, f(v) represents the filter function, u is the length of the input sequence data, and v is the value of the vth element in the input sequence data.

[0125] TCN is used to establish feature extraction modules for the system node voltage timing curve and the generator power angle timing curve, and then the fully connected layer (Fully Connected Layer, FCL) is used to realize feature splicing and feature classification. Each input feature curve is denoted as x i , each TCN network is denoted as ψ Ti , the fully connected layer is denoted as Γ N , the transient stability discrimination model can be expressed by formula (16).

[0126] y′=Γ N (ψ T1 (x1),ψ T2 (x2),…,ψ Tn (x n )) (16)

[0127] Among them, y i ′ is the temporary stable discriminant prediction value, and n is the number of input features.

[0128] The overall structure of the data-driven transient stability judgment model is as follows: Figure 5 As shown, the node voltage curve and the generator power angle curve are selected as the input characteristics.

[0129] The model loss function uses the binary cross-entropy loss (BCE) function, which is calculated as follows:

[0130]

[0131] Among them, y is the transient stable true label, and N is the number of label categories.

[0132] Considering that the number of transient stability instability samples is relatively small, it is easy to have an unbalanced sample distribution. Therefore, by adjusting the weight of the loss function, the attention of the samples is balanced to improve the classification performance of the model on the unbalanced data set, reduce the risk of overfitting, and improve the generalization ability of the model. Based on this, the loss function is modified to:

[0133]

[0134]

[0135] in, and are the weights corresponding to the i-th positive / negative samples respectively; N i,train Represents the total number of samples of the i-th label; and Respectively represent the number of positive / negative samples of the i-th label.

[0136] The Adam optimization algorithm is used to control the parameter update rate by designing an adaptive learning rate to correct the prediction error until the error converges to the expected range or reaches the maximum iteration round.

[0137] When the same section is affected by disturbance, the power of each line in the section has similar dynamic response characteristics. Therefore, a fault set is preset for each weak point of the initial transmission section, and batch identification is performed based on the multi-channel TCN network transient stability discrimination model. The transmission section judged as unstable by the data-driven transient stability discrimination model is recorded as a critical section of transient stability. Otherwise, the section is abandoned.

[0138] Step 203: Use the transient stability critical transmission section identification model to identify the transmission section that is greatly affected by transient stability, and generate corresponding critical dominant labels to complete the identification of the critical transmission section.

[0139] The key sections identified by taking into account transient stability safety constraints are the key transmission sections from the perspective of transient safety, and can then be deduced to the key sections corresponding to different power flow modes. After the power system is disturbed, if its power flow distribution changes and presents different operating modes, it is necessary to further determine the key sections corresponding to the target system under different power flow modes, and then analyze the operating characteristics of the key transmission sections under transient stability safety constraints based on the section criticality identification method from the perspective of transient safety, and establish the key dominant labels of different key transmission sections based on the transient stability safety theme, that is, determine whether the key section is susceptible to transient stability under a specific operating mode.

[0140] This embodiment uses two examples to verify the above method, as follows:

[0141] (1) Calculation example 1:

[0142] In order to verify the effectiveness and adaptability of the key transmission section identification technology proposed in this embodiment, Example 1 uses the IEEE 39-node system with new energy access as a test example. First, based on the IEEE 39-node system, the traditional units connected to nodes 35 and 37 are replaced with wind turbines (W) and photovoltaic units (P) respectively, so as to test the proposed method and verify the comprehensive performance of the proposed key section identification method. Figure 6 .

[0143] In this embodiment, the output of the traditional unit is modified according to the ±15% fluctuation of the standard working condition, and the uncertain wind and solar station applies ±30% disturbance to randomly generate scenarios according to the wind and solar characteristics, and a total of 5000 sets of tidal samples are obtained. The tidal samples of the scenarios where the tidal directions of each line are completely consistent are eliminated, and 349 sets of typical scenarios are obtained. The changes in the tidal flow direction of each line and the probability of occurrence are recorded, as shown in Table 1 and Table 2.

[0144] Table 1 Changes and probability of non-fixed line flow direction in different scenarios of renewable energy access to IEEE 39-node system

[0145]

[0146] Table 2 Flow directions of fixed lines in different scenarios of IEEE 39-bus system with renewable energy access

[0147]

[0148] Considering the importance of the line and the edge betweenness, the importance of the power lines is quantitatively ranked, as shown in Table 3. Considering the impact of the unit output volatility on the line power flow direction, the initial transmission section is traversed based on the Karger algorithm proposed in this embodiment. In addition, the power flow consistency of the lines in each cut set under different operating modes is analyzed for different scenarios, and the probability of power flow consistency is calculated. The cut set with a power flow consistency rate exceeding 70% is regarded as the initial transmission section, so the lines with a probability of power flow direction change exceeding 30% are preferentially eliminated. Therefore, the sections containing the four lines 3-4, 8-9, 9-39, and 17-27 are eliminated in the verification stage.

[0149] Table 3 Importance ranking of IEEE 39-node system lines for renewable energy access

[0150]

[0151] Taking the transmission section characteristics as the basic condition, considering the line importance and power flow consistency rate, the Karger algorithm is used to identify all the initial transmission section sets for the new energy access to the IEEE 39-bus system. The initial section results composed of different numbers of lines are shown in Table 4.

[0152] Table 4 Initial section identification results of IEEE 39-bus system with renewable energy access

[0153]

[0154] Based on the initial transmission sections found, taking into account the transient safety and stability constraints, the key transmission sections susceptible to transient safety and stability are identified. Considering that the lines in the IEEE 39-bus system are all single-circuit lines, the initial sections containing no more than 2 lines will be operated in sections when performing "N-1" or "N-2" stability checks. Therefore, all key transmission sections containing no more than 2 lines are shown in Table 5.

[0155] Table 5 Identification results of key sections of the IEEE 39-bus system with no more than 2 lines for renewable energy access

[0156]

[0157]

[0158] As shown in Table 5, the critical section identification method constructed in this embodiment considering the uncertainty of unit output and the power flow consistency constraint found a total of 1 "N-1" critical section and 11 "N-2" critical sections. At the same time, considering the influence of the excessive frequency of power flow direction changes or the limit of the line with the opposite power flow direction, in order to avoid the section not meeting the power flow consistency constraint condition, this embodiment eliminates the critical sections that do not meet the power flow consistency constraint. Next, based on formula (14), the weak checkpoints of each initial section containing more than 2 lines are calculated. The initial sections containing more than 2 lines and the corresponding weak checkpoints can be found in Table 6.

[0159] Table 6 Initial section and bayonet identification results of improved IEEE 39-node system

[0160]

[0161] To ensure that the sample set covers different operating modes and fault conditions as comprehensively as possible, the output of traditional units is modified according to the ±15% fluctuation of standard operating conditions, and the uncertain wind and solar power stations impose ±30% disturbances according to the characteristics of wind and solar power to randomly generate scenarios. Afterwards, PSASP is used to set a three-phase short-circuit grounding fault in the system. The fault location is selected at 2% and 98% of the length of the weak section line. The occurrence time is selected as 0.1s, the removal time is selected as 0.2s, and the total simulation time is selected as 10s. The 3000 sets of transient simulation samples generated are labeled according to the PSASP transient stability calculation criteria, including 1885 stable samples and 1115 unstable samples. The voltage disturbance curve in the model input characteristics can be referred to Figure 7 (a), the power angle disturbance curve can be referred to Figure 7 (b) is the timing curve from fault occurrence to fault removal, including node voltage curve and generator power angle curve. The training set, validation set and test set are divided into 70%, 15% and 15% ratios.

[0162] The proposed temporary stability discrimination model based on multi-channel TCN is verified, and the prediction results are as follows Figure 8 As shown, the dark part in the legend represents the proportion of correctly predicted samples.

[0163] The accuracy of the proposed model in batch processing of transient stability identification problems is shown in Table 7, and is compared with the transient stability identification results of the transient stability discrimination model proposed in recent years. The prediction performance of the proposed model is improved to varying degrees compared with other models or classical models proposed in recent years, which further proves that the proposed model has excellent prediction performance when performing transient stability judgment and can be used as a basis for judging the key section of transient stability.

[0164] Table 7 Performance comparison of the proposed method and different transient stability assessment models

[0165]

[0166] PSASP is used to preset faults for each of the 40 initial sections. The location of each transient safe and stable section in the IEEE 39 system for new energy access can be found in Fig. 9 PSASP was used to calculate the transient stability criteria of each initial section as a verification. The four sections found all had transient instability risks. Otherwise, the remaining sections passed the safety verification. The comparison of the calculation time of the two methods for analyzing the 40 initial sections can be found in Table 8.

[0167] Table 8 Comparison of the time taken by the proposed method and the traditional method to analyze the target sample

[0168]

[0169] As shown in Table 8, considering that the traditional method requires repeated flow adjustment and "N-1" verification, the data-driven method has higher efficiency than the traditional calculation criteria, and as the number of calculation samples increases, the difference in calculation efficiency will further increase. Considering the identification accuracy and calculation efficiency, the proposed data-driven method can be used as an effective criterion for the identification of critical sections of transient stability.

[0170] (2) Calculation example 2

[0171] In order to verify the effectiveness and adaptability of the method proposed in this embodiment in actual power grid applications, a power grid in L City in the southwest (hereinafter referred to as L power grid) is selected as the test target. Among them, L power grid consists of 51 nodes and 60 transmission lines above 220kV, with a network load of 5835MW, a total of 11 hydropower units, and a total installed power capacity of 3550MW.

[0172] Based on the PSASP simulation software, a fault set is set for each initial section checkpoint. The three-phase short circuit is selected as the fault type. The checkpoint power angle and voltage timing characteristic curves are generated. The training results of the fault curve generated by combining historical data are used to perform transient stability judgment on the initial section.

[0173] Grid dispatching and operation personnel usually choose the Xiada mode, which is a relatively severe scenario among typical operating modes, for safety and stability verification. Therefore, this paper first identifies the key transmission sections for the Xiada operating mode of the L power grid.

[0174] First, obtain the initial transmission section set under the Xiada operation mode of the L power grid, and obtain the initial section "checkpoint", as shown in Table 9 for details.

[0175] Table 9 Initial section and bayonet identification results of L power grid Xiada mode

[0176]

[0177] As shown in Table 9, considering the importance of the lines and the community division strategy, the L power grid obtains 15 initial transmission sections, which reduces the workload of identifying the criticality of the sections to a certain extent.

[0178] First, the key transmission sections are identified for the summer operation mode of the L power grid. Since the stability / instability time sequence characteristics of the power angle and voltage curve of the power system are similar, the temporary stability judgment of the L power grid is uniformly processed in batches. The voltage input characteristics can be found in Fig.10 (a), the power angle input characteristics can be found in Fig.10 (b).

[0179] According to the temporary stability identification model proposed by the above method of this embodiment, there is no risk of temporary stability over-limit in the 15 initial transmission sections of the L power grid under the Xiada method. Considering that the power installed capacity of the L power grid is composed of hydropower units, considering the characteristics of hydropower output, the key transmission sections shift with time series characteristics, and the Xiada method cannot represent all extreme scenarios. Therefore, there is a possibility of missing selection when the L power grid only identifies the key transmission sections in the Xiada method.

[0180] In view of the omission of key sections of the L power grid, the output of the units is modified by starting and stopping the hydropower units, taking into account the characteristics of hydropower flood and drought and the load-power balance constraints. Based on the three modes of full-on, half-on, and full-off, 11 hydropower plants are operated, and the coupling relationship between the plant and the station (such as some plants and stations need to maintain the same operation mode) and their own characteristics (such as some plants and stations only have two operation modes: full-on and full-off) are considered to generate 288 typical scenarios.

[0181] Based on the model proposed by the above method of this embodiment, the key transmission sections are identified for different scenarios, and their importance is measured by calculating the probability of occurrence of the key sections, and the specific scenarios where the key sections appear are marked. The identification results of the key sections of transient stability in multiple operation scenarios of the L power grid are shown in Table 10, and are compared with the key transmission sections that are included in the key monitoring by computing experts in the actual operation of the L power grid.

[0182] Table 10 Identification results of critical sections of transient stability in multi-scenario power grid

[0183]

[0184] like Fig.11 As shown, the L power grid obtains a total of 5 transient stability critical transmission sections under multiple operation scenarios. After comparison with the actual production and operation results, the key sections identified based on the method proposed in this embodiment completely correspond to the above 4 key sections, and 1 new transient stability critical section (42-32, 42-23) is newly discovered. After data-driven transient stability verification, the probability of transient stability exceeding the limit of Section 2 is 4.17%. While avoiding omissions, sections with potential risks can also be summarized to obtain better monitoring effects. Although the occurrence scenario of Section 2 is relatively harsh and the probability of occurrence does not exceed 5%, it is still at risk of exceeding the limit and should also be included in the key transmission sections for monitoring.

[0185] The calculation time of analyzing 15 initial sections in a large power grid by the method proposed in this embodiment is further compared with that of the PSASP calculation criterion, as shown in Table 11.

[0186] Table 11 Comparison of the time taken by the proposed method and the PSASP calculation criteria to analyze large power grid samples

[0187]

[0188] As shown in Table 11, considering that the traditional method requires repeated flow adjustment and “N-1” verification, the data-driven method has higher efficiency than the traditional calculation criteria, and as the number of calculation samples increases, the difference in calculation efficiency will further increase.

[0189] The method proposed in this embodiment is first based on the maximum flow minimum cut theory, taking into account the electrical coupling vulnerability and topological structure vulnerability of the power system lines, and combining the transmission section constraints such as power flow consistency to achieve initial transmission section identification; then considering the power flow operation mode and line current carrying capacity to identify the initial transmission section weak checkpoints, and finally from the perspective of transient safety and stability, for the weak checkpoints of the transmission section, the power system comprehensive stability analysis program is used to simulate and set a stable fault sample set, and a transient stability critical section identification model is constructed based on a multi-channel time series convolutional neural network to complete the transient stability critical section identification and generate corresponding critical dominant labels. The method proposed in this embodiment helps researchers obtain transient stability critical section identification results, while guiding the screening of critical sections and expanding the application scope of data-driven models in power systems.

[0190] The method proposed in this embodiment adopts an initial transmission section identification method based on the maximum flow minimum cut theory and line vulnerability evaluation index. It can better consider the system load distribution in the section search, while more comprehensively discovering potential security threats to the power system, reducing the cumbersomeness of the section discovery process, and having good search efficiency in different operating scenarios.

[0191] The method proposed in this embodiment adopts a mechanism-guided and data-driven transient safety critical section identification method that takes into account transient complete stability constraints. It has both identification accuracy and computational efficiency while not being affected by differences in operating modes. It can serve as an effective criterion for identifying transient stability critical sections in different scenarios, and provide technical support for engineering applications and theoretical research.

[0192] Based on the same technical concept as above, this embodiment also proposes a key transmission section identification system for a power system, such as Fig.12 As shown, the system proposed in this embodiment includes:

[0193] The initial section identification module is mainly based on the maximum flow minimum cut theory, taking into account the electrical coupling vulnerability and topological structure vulnerability of the power system lines, and combining the transmission section constraints such as power flow consistency to complete the initial transmission section identification.

[0194] And the key section identification module, which mainly considers the flow operation mode and line current carrying capacity to realize the weak checkpoints of the initial transmission section, and from the perspective of transient safety and stability, for the weak checkpoints of the initial transmission section, the power system comprehensive stability analysis program is used to simulate the setting of transient stability fault sample sets, and a transient stability key section identification model is constructed based on a multi-channel time series convolutional neural network to complete the identification of the key sections of transient stability of the power system.

[0195] Furthermore, the initial section identification module specifically includes:

[0196] The graph conversion unit converts the power grid topology into a directed graph. Specifically, the power plant, substation and load nodes in the initial power system can be simplified into topology graph nodes, the transmission lines can be simplified into topology graph tie lines, and multiple transmission lines can be merged to obtain a directed graph of the power system.

[0197] The index construction unit adopts the spatial clustering method to establish the system line electrical coupling vulnerability assessment index considering the node electrical distance; and establishes the topological structure vulnerability assessment index of the power system line by analyzing the network constraint coefficient of the node.

[0198] And, a power grid division identification unit, which calculates the electrical coupling vulnerability and topological structure vulnerability of all lines in the power system based on the maximum flow theory, removes and records the lines with the strongest electrical coupling vulnerability and topological structure vulnerability; based on the minimum cut theory, determines whether a cut set is generated after removing the line. If no cut set is generated, repeat the operation of calculating the vulnerability and removing and recording the lines with the strongest vulnerability based on the maximum flow theory. If a new cut set is generated, record the cut set as the initial cut set of the power system. Based on the initial cut set of the power system, consider the transmission section constraints such as power flow consistency to construct the initial transmission section set of the power system. It should be noted that the specific implementation method of each functional unit in this module is the same as steps 101 to 105 in the above method, and will not be repeated here.

[0199] Furthermore, the key section identification module specifically includes:

[0200] The checkpoint identification unit identifies the weak checkpoints of the initial transmission sections based on the initial transmission section set of the power system, taking into account the flow operation mode and line current carrying capacity.

[0201] The transient stability identification unit takes the initial weak points of the transmission section as input, and takes into account the transient complete stability constraints of the online safe and stable operation of the power system, and establishes a data-driven transient stability key transmission section identification model.

[0202] And, a critical section identification unit, which uses a transient stability critical transmission section identification model to identify the transmission section that is greatly affected by transient stability, and generates corresponding critical dominant labels to complete the identification of critical transmission sections. It should be noted that the specific implementation of each functional unit of this module is the same as step 201 to step 203 in the above method, and will not be repeated here.

[0203] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0204] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0205] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0206] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0207] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only the specific implementation method of the present application and is not intended to limit the scope of protection of the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for identifying key transmission sections of a power system, characterized in that: The method comprises: Initial section identification step: Based on the maximum flow minimum cut theory, the electrical coupling vulnerability and topological structure vulnerability of the power system lines are considered, combined with the power flow consistency constraint condition, the initial transmission section identification is completed to obtain the initial transmission section set of the power system; Steps for identifying critical sections: Consider the power flow operation mode and line current carrying capacity to identify the initial transmission section weak points, and use the initial transmission section weak points as input, use the power system comprehensive stability analysis program to simulate and set the transient stability fault sample set, and build a transient stability critical section identification model based on a multi-channel time series convolutional neural network to complete the identification of the critical transmission section for transient stability of the power system.

2. A method for identifying key transmission sections of a power system according to claim 1, characterized in that: The initial section identification step specifically includes: The power grid topology is converted into a directed graph form to obtain a power system directed graph; Establish an electrical coupling vulnerability assessment index for power system lines considering the electrical distance of nodes; By analyzing the network constraint coefficient of the nodes, the topological structure vulnerability assessment index of the power system line is established; Based on the maximum flow theory, the electrical coupling vulnerability and topological structure vulnerability of all lines in the power system are calculated, and the lines with the strongest electrical coupling vulnerability and topological structure vulnerability are removed and recorded; Based on the minimum cut theory, determine whether a cut set is generated after the line is removed. If no new cut set is generated, repeat the previous step. If a new cut set is generated, record the cut set as the initial cut set of the power system. Based on the initial cut set of the power system and considering the constraint condition of power flow consistency, an initial transmission section set of the power system is constructed.

3. A method for identifying key transmission sections of a power system according to claim 2, characterized in that: The steps of establishing an electrical coupling vulnerability assessment index for power system lines taking into account node electrical distances specifically include: The neighbor propagation clustering algorithm is used to construct the classification evaluation index of the electrical coupling degree of the power system line, which is expressed as: I i-j =AP(D ij ,R ij ,x ij ) Among them, D ij represents the distance of the transmission line ij, R ij and x ij denote line resistance and reactance, respectively; AP(·) denotes clustering performed using the neighbor propagation clustering algorithm with the features in brackets as input; N AP Indicates the number of clusters; I i-j represents the cluster label of transmission line ij, E i-j Represents the electrical coupling importance of transmission line ij.

4. A method for identifying key transmission sections of a power system according to claim 2, characterized in that: The step of establishing the topological structure vulnerability assessment index of the power system line specifically includes: The network constraint coefficients of the nodes at both ends of the power system transmission line are calculated, and the topological structure importance index of the line is constructed by using the index reflecting the topological importance of the node, which is expressed as: C L (i)=-log2C(i) T i-j =C L (i)×C L (j) Where C(i) represents the network constraint coefficient of node i, node q is the common adjacent node of nodes i and j, and p ij represents the proportion of transmission line ij to all lines connected to node j, p iq represents the proportion of transmission line iq to all lines connected to node q, p qj represents the proportion of transmission line qj to all lines connected to node j, Γ i represents the set of adjacent nodes of node i, C L (i) represents the topological importance of node i, C L (j) represents the topological importance of node j, T i-j Represents the topological importance of transmission line ij.

5. A method for identifying key transmission sections of a power system according to claim 2, characterized in that: The steps of constructing the initial power transmission section set of the power system specifically include: Numbering each node and tie line in the directed graph of the power system; Based on the Karger algorithm, the minimum cut search is performed on the power grid. A transmission line is randomly selected and the nodes at both ends are merged until the power grid is divided into two areas. Determine whether a new section is generated. If so, repeat the previous step. If no new section is generated, store the cut set in the initial cut set. It is determined whether the active power flow directions of all the transmission lines in the initial cut set are consistent. If they are consistent, they are stored in the initial transmission section set; otherwise, the cut set is deleted.

6. A method for identifying key transmission sections of a power system according to any one of claims 1 to 5, characterized in that: The identification process of the weak points of the initial power transmission section specifically includes: Calculate the branching coefficient of the transmission line at its transmission section: Among them, K i-j It represents the branch coefficient of the transmission line ij in its transmission section, P i-j represents the active power of transmission line ij, represents the active power of transmission section g, which belongs to the initial section set C; Considering the power flow operation mode and line current carrying capacity, the ratio of the branching coefficient of the transmission line at its transmission section to its long-term operating current carrying capacity is calculated: P i-j |≤L i-j K i-j / L i-j |≤1 / |P g,sum | Among them, U N Indicates rated voltage; I max Indicates the current limit of the transmission line; T c represents the temperature correction factor; Indicates power factor; P i-j Represents the active power of transmission line ij; L i-j Indicates the long-term allowable current carrying capacity of the transmission line ij; Get the compliance The transmission lines serve as the weak points of the transmission sections.

7. A method for identifying key transmission sections of a power system according to claim 6, characterized in that: The process of establishing the transient stability key transmission section identification model specifically includes: The fault sample set is used to generate disturbances on the node voltage and the power angle of the generator set of the power system, and different types of simulation timing curves and stable labels are obtained, and a training set is constructed based on them; The node voltage timing curve and the generator power angle timing curve in the training set are used as the input features of the TCN network, and the stable labels in the training set are used as the output features of the TCN network, and a multi-channel TCN network temporary stability discrimination model is obtained by training; wherein the TCN network includes a feature extraction module established for the input node voltage timing curve and the generator power angle timing curve respectively, and a classification module that uses a fully connected layer to realize feature splicing and feature classification; The multi-channel TCN network transient stability discrimination model is used for batch identification, and the transmission section judged as unstable by the model is recorded as a transient stability key section. Otherwise, the transmission section is abandoned.

8. A power system key transmission section identification system, characterized in that: The system comprises: An initial section identification module, which is based on the maximum flow minimum cut theory, considers the electrical coupling vulnerability and topological structure vulnerability of the power system line, and combines the power flow consistency constraint condition to complete the initial transmission section identification and obtain the initial transmission section set of the power system; And, a critical section identification module, which identifies the initial transmission section weak points by considering the flow operation mode and the line current carrying capacity, and takes the initial transmission section weak points as input, uses the power system comprehensive stability analysis program to simulate and set the transient stability fault sample set, and constructs a transient stability critical section identification model based on a multi-channel time series convolutional neural network to complete the identification of the critical transmission section for transient stability of the power system.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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