A parallel restoration partitioning method for power system based on SIR model

Abstract

The present invention relates to the field of electric power technology, and discloses a power system parallel recovery partitioning method based on a SIR model, the power system parallel partitioning method comprising the following steps: step S1, according to the location and number of black start power supplies, use them as the initial virus infection source, and determine the initial infection matrix F0; step S2, comprehensively consider the topological structure and actual characteristics of the power grid, combine the node degree and the node injection or output power, so as to obtain the node infection probability matrix. The power system parallel recovery partitioning method based on the SIR model comprehensively considers the network topological structure of the power grid and the actual characteristics of the system, proposes a partitioning method suitable for parallel recovery of the power system based on the SIR model in complex network theory, embeds partitioning constraints in the iterative process of the method, and quickly obtains a power system parallel recovery partitioning scheme that meets the requirements of equal sub-area scale, compact internal structure, and power balance.

Description

Technical Field

[0001] The invention relates to the field of electric power technology, and in particular to a parallel restoration partitioning method for an electric power system based on a SIR model. Background Art

[0002] After a major power outage occurs in the power system, a reasonable and effective parallel restoration plan can help shorten the system power outage time and thus reduce economic losses. Sub-area division is a prerequisite for the formulation and implementation of subsequent parallel restoration strategies. How to quickly and effectively formulate a partitioning plan suitable for parallel restoration deserves in-depth study. The parallel restoration partition of the power system has significant community structure characteristics. Therefore, complex network theory can be used to perform parallel restoration partitioning of the power system. Reference [1] uses edge betweenness to represent the degree of connection between nodes. On the premise that there is a black start power supply in each sub-area, the GN (Girven Newman) algorithm is used to use the lines with large edge betweenness as the connecting lines between sub-areas, thereby obtaining a partitioning plan for the power system. The modularity index is used to measure the rationality of the partitioning result. Reference [2] uses the spectral clustering method to map the topological relationship of the network to a space composed of the first and second smallest non-trivial eigenvectors. Then, according to the number of black start power supplies in the system, the Euclidean distance of the corresponding elements of each node in the space is used as the standard for measuring node similarity to cluster and calculate each element to obtain a partitioning plan for the power system.

[0003] Existing methods provide a good theoretical basis for parallel restoration of power grids, but most of them only consider the topological characteristics of the power grid and ignore the normal operation characteristics of the system and the damaged state of the system after the power outage. In addition, there is an inability to ensure the balance of the scale of each restoration sub-area, and there is no detailed consideration of the important issue that the balance between power generation and load in the power system affects the parallel restoration process of the system. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the defects existing in the above-mentioned background technology, the present invention comprehensively considers the network topology structure of the power grid and the actual characteristics of the system, and proposes a partitioning method suitable for parallel recovery of power systems based on the SIR model in complex network theory. Partitioning constraints are embedded in the iterative process of the method to quickly obtain a parallel recovery partitioning scheme for the power system that meets the requirements of equivalent sub-area size, compact internal structure and power balance.

[0006] (II) Technical solution

[0007] The present invention provides the following technical solution: a power system parallel restoration partition method based on the SIR model, the power system parallel partition method comprising the following steps:

[0008] Step S1: According to the location and number of black start power supplies, use them as initial virus infection sources to determine the initial infection matrix F0.

[0009] Step S2, comprehensively considering the topological structure and actual characteristics of the power grid, combining the node degree and the node injection or output power, so as to obtain the node infection probability matrix.

[0010] Step S3: According to the damaged state of the system after the power outage, the severely damaged fault nodes are set as immune nodes to obtain a node infection probability matrix combined with the immune strategy.

[0011] Step S4: According to the node's own infection rate and the status of neighboring nodes, the node's transmission rate during the virus propagation process is obtained.

[0012] Step S5: During the propagation process, the nodes infected with the virus are marked. To avoid cross infection of the nodes already infected with the virus, the infected nodes will be restored to the R state with a probability of δ, so that the nodes will not be infected by the virus again.

[0013] Step S6: embed the partition constraint into the virus propagation process to obtain a set of infected nodes that meet the constraint conditions to ensure the safety and stability of system recovery.

[0014] Step S7: Divide the nodes infected by the same type of virus into the same sub-area, and finally obtain a power system parallel recovery partitioning scheme that meets the requirements of equal sub-area size, compact internal structure, and power balance.

[0015] Preferably, a corresponding propagation threshold is set in step S4 to allow the virus to spread widely.

[0016] Preferably, in an n-node network, nodes can be divided into three states: S represents a susceptible state that is easily infected by a virus; I represents a state that has been infected by a virus; and R represents a node that has recovered from an infected state to a healthy state and will not be infected by a virus again.

[0017] Preferably, for any t-th virus transmission, there is:

[0018] S(t)+I(t)+R(t)=N(n)

[0019] Where N(n) represents the set of nodes in the network; S(t) represents the set of healthy nodes that are susceptible to infection in the tth transmission; I(t) represents the set of nodes that have been infected in the tth transmission; R(t) represents the set of nodes that have recovered from the infected state to the healthy state in the tth transmission.

[0020] Preferably, in the power grid, the black start power supply node serves as an initial virus infection source, and different black start power supplies represent different types of viruses.

[0021] Preferably, according to the actual operation of the power system after the blackout, when an emergency occurs, the dispatcher will further process the system nodes according to the current state of the system and the availability of components.

[0022] Preferably, partition constraints are embedded into the virus propagation process, including black start power constraints, power balance constraints, sub-area size constraints, and observability constraints.

[0023] Preferably, when the virus propagates, nodes infected by the same type of virus are divided into the same sub-area in each iteration.

[0024] Compared with the prior art, the present invention provides a power system parallel restoration partitioning method based on the SIR model, which has the following beneficial effects:

[0025] 1. The power system parallel recovery partitioning method based on the SIR model comprehensively considers the network topology structure of the power grid and the actual characteristics of the system, proposes a partitioning method based on the SIR model in complex network theory that is suitable for power system parallel recovery, embeds partitioning constraints in the method iteration process, and quickly obtains a power system parallel recovery partitioning scheme that meets the requirements of equivalent sub-area size, compact internal structure, and power balance. Compared with the other two complex network theory methods, the method of the present invention has the shortest running time, so it can obtain feasible partitioning results more quickly and accelerate the recovery process of the power system.

[0026] 2. The SIR model-based power system parallel recovery partitioning method uses the SIR model in virus propagation and combines the damage of the system after the power outage and the partition constraints to obtain a partitioning scheme suitable for parallel recovery. It mainly includes initializing the topology and operating status of the power system after the power outage, and applying the SIR model to obtain the corresponding partitioning scheme. As the number of sub-areas increases, the average running time of the proposed method increases slightly. However, the average running time of each case is not much different. When a power system is divided into more than two sub-areas, the computational efficiency of this paper has great advantages over some existing strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the present invention;

[0028] Figure 2 FIG. 1 is a partitioning scheme diagram of the IEEE 39-node system of the present invention;

[0029] Figure 3 Figure 2 is the SIR node number diagram of the IEEE 39-node system. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] See also Figure 1-3 , a power system parallel restoration partitioning method based on SIR model, the power system parallel partitioning method comprises the following steps:

[0032] Step S1: According to the location and number of black start power supplies, use them as initial virus infection sources to determine the initial infection matrix F0.

[0033] Step S2, comprehensively considering the topological structure and actual characteristics of the power grid, combining the node degree and the node injection or output power, so as to obtain the node infection probability matrix.

[0034] Step S3: According to the damaged state of the system after the power outage, the severely damaged fault nodes are set as immune nodes to obtain a node infection probability matrix combined with the immune strategy.

[0035] Step S4: According to the node's own infection rate and the status of neighboring nodes, the node's transmission rate during the virus propagation process is obtained.

[0036] Step S5: During the propagation process, the nodes infected with the virus are marked. To avoid cross infection of the nodes already infected with the virus, the infected nodes will be restored to the R state with a probability δ, so that the nodes will not be infected by the virus again.

[0037] Step S6: embed the partition constraint into the virus propagation process to obtain a set of infected nodes that meet the constraint conditions to ensure the safety and stability of system recovery.

[0038] Step S7: Divide the nodes infected by the same type of virus into the same sub-area, and finally obtain a power system parallel recovery partitioning scheme that meets the requirements of equal sub-area size, compact internal structure, and power balance.

[0039] Example

[0040] The present invention utilizes the SIR model in virus propagation and combines the damage of the system after power outage and the partition constraints to obtain a partition scheme suitable for parallel recovery. The specific process is shown in the attached figure. Figure 1 As shown, it mainly includes: initializing the topological structure and operating status of the power system after the power outage, and applying the SIR model to obtain the corresponding partitioning scheme.

[0041] 1. Initialization of the virus propagation model

[0042] According to the SIR model theory of virus transmission, in an n-node network, nodes can be divided into three states: S represents the susceptible state that is easily infected by the virus; I represents the state that has been infected by the virus; and R represents the node that has recovered from the infected state to the healthy state and will not be infected by the virus again.

[0043] For any t-th virus transmission, we have:

[0044] S(t)+I(t)+R(t)=N(n)

[0045] Where N(n) represents the set of nodes in the network; S(t) represents the set of healthy nodes that are susceptible to infection in the tth transmission; I(t) represents the set of nodes that have been infected in the tth transmission; R(t) represents the set of nodes that have recovered from the infected state to the healthy state in the tth transmission.

[0046] The steps of this program include:

[0047] Step 1: Initialize the node infection matrix F0.

[0048] In the power grid, the black start power supply node is the initial infection source of the virus, and different black start power supplies represent different types of viruses. At the beginning, the remaining nodes are in an uninfected state. During the subsequent virus propagation process, the status of the remaining nodes will be continuously updated until all nodes are infected by the virus. According to the number and location of the black start power supplies, the initial infection matrix F0 can be determined, and the status of the initially infected black start power supply node will not change as the virus spreads.

[0049]

[0050] Where n is the total number of nodes in the power grid, i = 1, 2, ..., n represents the node number. H is the number of virus types, that is, the number of sub-areas. h = 1, 2, ..., H represents different virus types.

[0051] Step 2: The node virus infection probability matrix W = [wi] = ω1[ki] + ω2[si], where ω1 and ω2 are calculated using the entropy weight method; the node degree ki is the number of lines between the remaining nodes connected to point i. The topological structure and actual characteristics of the power grid are comprehensively considered, and the node degree ki and the node injection or output power si are combined as the size of the node virus infection probability.

[0052] The node weight is: si = Si / S0, Where Sij is the rated capacity of all connecting edges between nodes i and j; Si is the sum of the rated capacities of all connecting edges between nodes i and j; S0 is the benchmark capacity of the power system.

[0053] 2. Partitioning strategy based on SIR model

[0054] Step 3: According to the actual operation of the power system after the blackout, when an emergency occurs, the dispatcher will further process the system nodes according to the current state of the system and the availability of components. Using the immune strategy, when the nodes are immune, it means that the edges they are connected to can be removed from the network, which greatly reduces the possible connection paths for virus transmission. Therefore, the immune strategy can be used to correct the node virus infection probability matrix, and the fault nodes that are severely damaged in the system after the power outage are set as immune nodes. The node infection probability matrix combined with the immune strategy can be obtained to deal with emergencies after the blackout.

[0055] The probability matrix of nodes being infected by the virus after combining the immune strategy:

[0056]

[0057] Where c is the immunity probability of the faulty node, ranging from 0 <c≤1。

[0058] Step 4: Node propagation rate:

[0059] Where pi is the element i in the virus node infection probability matrix P; kinfi refers to the number of infected neighbor nodes of the susceptible node i.

[0060] Propagation threshold: λc = min pi

[0061] If the node's propagation rate is greater than the threshold λc, the infected individuals can spread the virus, the virus can persist, and the total number of infected individuals in the entire network will eventually stabilize at a certain equilibrium state; if the node's propagation rate is lower than this threshold, the number of infected individuals will decay and cannot spread over a large area.

[0062] Step 5: During the virus propagation process, the infected nodes obtained in each iteration are marked. The infected nodes will recover to the R state with a probability of δ, and the nodes that have recovered to a healthy state after being infected and are no longer infected by the virus are recorded as Ri.

[0063]

[0064] Where δ is the probability that an infected node recovers to an R-state node, and its value is 0<δ≤1.

[0065] Step 6: Embed partition constraints into the virus propagation process, including black start power constraints, power balance constraints, sub-area size constraints, and observability constraints.

[0066] Black start power constraints

[0067] H≤M

[0068] Where H is the number of subsystems and M is the number of black start power supplies.

[0069] b. Power balance constraints

[0070]

[0071] Where ηi is the minimum technical output coefficient of the unit. Generally, the ηi value of a thermal power unit is 25%-35%, and the ηi value of a hydropower unit is 0; PGi is the rated output power of unit i; PDi is the load value of node i.

[0072] c. Sub-area size constraints

[0073]

[0074] Where DBS,i is the shortest path from the black start power supply to node i, which is obtained by the Dijkstra algorithm; Lmax is the maximum size allowed for the sub-area. If the size difference between sub-areas is too large, the recovery time of each sub-area will be out of sync, which will extend the recovery time of the entire system.

[0075] d. Observability constraints

[0076] ∑z ij r j +r i ≥1i,j∈I(t)

[0077]

[0078] Wherein, when zij=1, it indicates that the line is in the sub-area; when zij=0, it indicates that the line is not in the sub-area; ri indicates whether there is a PMU at node i.

[0079] Step 7: When the virus spreads, the nodes infected by the same type of virus are divided into the same sub-area in each iteration.

[0080]

[0081] When all non-faulty nodes are infected by the virus, the final partitioning scheme that satisfies the partitioning constraints can be obtained.

[0082] In order to verify the effectiveness of the present invention, IEEE 39 nodes were used for example simulation. The IEEE 39 standard test system includes 10 generator sets, 12 transformers and 34 lines. Units G30, G31 and G34 are used as black start power sources with self-starting capability after a major power outage in the power system. Therefore, the number of sub-areas is 3. Lines 3-4, 14-15, 9-39, 17-18 and 17-27 are used as inter-area interconnection lines. Table 1 shows the node numbers of each sub-area. The number of nodes is relatively balanced, and the partitioning scheme that meets the partitioning constraints is shown in Figure 2.

[0083] Table 1 Nodes in each sub-area

[0084]

[0085] The network diameter T refers to the longest distance between any two nodes. The sub-area Tmax obtained by the method proposed in the present invention is 6, which is smaller than the sub-area Tmax of references [1] and [2]. This indicates that the longest distance that energy may pass through in the network is smaller. The modularity Q value is 0.6354, which is larger than the modularity Q value of references [1] and [2]. This indicates that the partitioning characteristics of the results of the present invention are more obvious.

[0086] Table 2 Comparison of different partitioning methods

[0087]

[0088] The method was run using MATLAB R2018b on a computer with an AMD Ryzen 52600X 3.6GHz processor and 16GB RAM. Compared with the other two complex network theory methods, the method of the present invention has the shortest running time. Therefore, feasible partitioning results can be obtained more quickly, speeding up the restoration process of the power system.

[0089] Table 3. Running time of different methods for IEEE 118-node system

[0090]

[0091] As the number of sub-areas increases, the average running time of the proposed method increases slightly. However, the average running time of each case is not much different. When a power system is divided into more than two sub-areas, the computational efficiency of this paper has a great advantage over some existing strategies.

[0092] Table 4. Running time of the proposed method for IEEE 118-node system

[0093]

[0094] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A parallel restoration partitioning method for power systems based on SIR model, Features: The power system parallel partitioning method comprises the following steps: Step S1, according to the location and number of black start power supplies, use them as initial virus infection sources to determine the initial infection matrix F0; Step S2, comprehensively considering the topological structure and actual characteristics of the power grid, combining the node degree and the node injection or output power, so as to obtain the node infection probability matrix; Step S3: according to the damaged state of the system after the power outage, the severely damaged fault nodes are set as immune nodes, and the node infection probability matrix after combining the immune strategy is obtained; Step S4, according to the node's own infection rate and the state of neighboring nodes, the node's transmission rate during the virus propagation process is obtained; Step S5: During the propagation process, the nodes infected with the virus are marked. In order to avoid cross infection of the nodes already infected with the virus, the infected nodes will be restored to the R state with a probability δ, so that the nodes will not be infected by the virus again; Step S6: embed the partition constraint into the virus propagation process to obtain a set of infected nodes that meet the constraint conditions, so as to ensure the safety and stability of system recovery; Step S7: Divide the nodes infected by the same type of virus into the same sub-area, and finally obtain a power system parallel recovery partitioning scheme that meets the requirements of equal sub-area size, compact internal structure, and power balance.

2. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: In step S4, a corresponding propagation threshold is set.

3. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: In an n-node network, nodes can be divided into three states: S represents the susceptible state that is easily infected by the virus; I represents the state that has been infected by the virus; and R represents the node that has recovered from the infected state to the healthy state and will not be infected by the virus again.

4. The method for parallel restoration of power system based on SIR model according to claim 1, Features: For any t-th virus transmission, we have: S(t)+I(t)+R(t)=N(n) Where N(n) represents the set of nodes in the network; S(t) represents the set of healthy nodes that are susceptible to infection in the tth transmission; I(t) represents the set of nodes that have been infected in the tth transmission; R(t) represents the set of nodes that have recovered from the infected state to the healthy state in the tth transmission.

5. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: In the power grid, black start power supply nodes serve as the initial infection source of the virus, and different black start power supplies represent different types of viruses.

6. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: According to the actual operation of the power system after the blackout, when an emergency occurs, the dispatcher will further process the system nodes according to the current status of the system and the availability of components.

7. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: During the virus propagation process, the infected nodes obtained in each iteration are marked.

8. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: Partition constraints are embedded into the virus propagation process, including black start power constraints, power balance constraints, sub-area size constraints, and observability constraints.

9. A power system parallel restoration partitioning method based on SIR model according to claim 1, Features: When the virus spreads, nodes infected by the same type of virus are divided into the same sub-area in each iteration.

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