CN109687438B - Power grid fragile line identification method considering high-speed rail impact load effect - Google Patents
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Abstract
A power grid fragile line identification method considering the impact load effect of a high-speed rail comprises the following steps: (1) considering the random fluctuation characteristic of the high-speed rail load, establishing a probability model of the high-speed rail load by utilizing the combination of normal distribution and binomial distribution, and then performing N-1 probability load flow calculation in an IEEE39 node system; (2) establishing a correlation network of the power system according to the N-1 probability load flow calculation result; (3) and identifying fragile lines in the power system by adopting a weighted K-kernel decomposition method on the basis of the correlation network. The method performs equivalent description on the high-speed rail load, and the established correlation network can consider the topological structure characteristics and the running state characteristics of the power system and accurately identify the fragile line in the system. The invention provides a weighted K-kernel decomposition method based on Monte Carlo simulation aiming at the characteristics of severe fluctuation and impact of loads of a large-scale high-speed rail accessed to a power grid in China, so as to identify a fragile line in the power grid.
Description
Technical Field
The invention relates to a fragile line identification method in power grid vulnerability analysis, which plays a key role in preventing propagation of power grid cascading failures and preventing occurrence of power grid blackout.
Background
In recent years, blackout accidents occur frequently worldwide. Causing huge economic loss and serious social influence to the country and the society, and arousing the strong attention of people to the reliability of the power system again. Research shows that the general power grid blackout starts from individual element faults, cascading faults are caused in the power flow transfer process, and finally system breakdown is caused, wherein few key lines play a role in promoting the spread of a blackout range. Therefore, how to identify the key lines has important theoretical research and practical application value.
The prior art can be divided into two main categories according to the starting point of modeling. The first type describes the cascading failure propagation process of the power grid by a probability or certainty method based on the state characteristics of the power system and taking load flow calculation as a core, and utilizes an entropy theory method, a risk assessment method, an energy function method and a cascading failure simulation method, thereby achieving the purpose of fragile line identification. The method mainly considers the aspects of line power flow transfer and distribution characteristics, node voltage deviation, virtual injection power disturbance, system load loss and the like under the power grid disturbance. The second type is based on a complex network theory and takes the topological structure of a power grid as a core. And identifying the fragile line by using indexes such as degree values, betweenness and the like in the network structure, wherein the indexes comprise indexes such as gas betweenness, tide betweenness, power betweenness, mixed flow betweenness and the like. Furthermore, identification methods based on K-kernel decomposition, PageRank, maximum flow are proposed in succession. The method fully utilizes physical attributes and static parameters of the power grid and characteristics of power transfer and the like under disturbance, but mainly aims at the traditional load, and the analysis is carried out under the condition of deterministic load in all cases. In consideration of the rapid development of high-speed railways in China, the high-speed rail load ratio is gradually increased. High-speed rail loads have strong impact and randomness, and have non-negligible influence on a power grid. The identification method has the function of considering the load of the high-speed railway.
Disclosure of Invention
The invention aims to provide a power grid fragile line identification method under the action of high-speed rail impact load, which aims to establish a probability model of high-speed rail load based on actual high-speed rail load data, utilize a Monte Carlo simulation method in probability load flow calculation, adopt improved weighted K kernel indexes and consider the fragile line identification under the action of the high-speed rail load.
The object of the invention is achieved in that,
step 1: modeling of high-speed rail load characteristics
First, according to the severe fluctuation, impact characteristics, and probability density distribution of the high-speed rail load, as shown in fig. 1, a probability model of the high-speed rail load is established using a combination of normal distribution and binomial distribution.
Step 2: calculating N-1 Monte Carlo probability load flow considering high-speed rail load characteristics
In combination with the probabilistic model of the high-speed rail load, IEEE39 is used as an analysis object, and as shown in fig. 2, several key loads (red arrows) are replaced by the high-speed rail load. And then carrying out 5000 times of N-1 probability load flow calculation on the system by using a Monte Carlo simulation method to obtain 5000 groups of branch power, and then calculating the mathematical expectation by using a probability statistical method.
And 3, step 3: constructing correlation network of power network according to branch power coupling relation
In order to take into account the topological structure characteristics of the power grid and the state characteristics of the system operation, a correlation network of the power system is established, as shown in fig. 3. The establishment of the correlation network is based on the N-1 probability load flow calculation in the step1, a new network is constructed by taking the transmission line in the original power grid as a node and taking the load flow increase of other lines caused by the disconnection of the line as a side, and the network is called as the correlation network of the original power system. The construction of the correlation network not only considers the topological connection structure between lines, but also quantifies the state relation between the lines. The identification of the fragile line is then translated into the identification of the fragile node.
And 4, step 4: identification of fragile lines using weighted K-kernel decomposition
The traditional K core decomposition is based on an undirected network, and the importance degree is higher when the K core value is larger. However, the correlation network established in step2 is a bidirectional weighting network, and improves the conventional K-core decomposition, as shown in fig. 4, in the weighted K-core decomposition, only the association strength of the node to the adjacent node is subtracted when the node is removed, and the influence of the adjacent node on the node is retained. And decomposing layer by layer from the node with the minimum weighting degree to obtain the K core value of each node in the correlation network. The larger the K core value is, the more fragile the node is, and then according to the establishment process of the correlation network in the step2, the node in the correlation network corresponds to the vulnerability of the line in the original power system.
The correlation network established in the step 3 is a bidirectional weighting network, the traditional K-kernel decomposition is improved, in the weighted K-kernel decomposition, only the correlation strength of the node to the adjacent node is subtracted when the node is removed, and the influence of the adjacent node to the node is reserved; decomposing layer by layer from the node with the minimum weighting degree to obtain a K core value of each node in the correlation network; because the nodes at the edge of the network still can present a high accumulation phenomenon, namely a high K core value, the influence is small; so that the K kernel values of the node and its adjacent node and secondary adjacent node are used to raise the identification precision, i.e.
In the formula, Ks _ d (i) is a depth K core value of the node i and reflects the influence of the node i; ks (i) is the K core value of the node i; i.e. ijThe jth node, Ω, in the set of adjacent nodes representing node iiA set of contiguous nodes that are nodes i;
represents a node ijThe k-th adjacent node of (2),
represents a node ijM is a set of adjacent nodes0Represents the K kernel weight, m, of node i1Weight, m, representing sum of kernel values of K adjacent nodes of node i2Represents the weight of the sum of the kernel values of the next adjacent node K of node i, and m0+m1+m 21 is ═ 1; obviously, the larger the value of Ks _ d, the more fragile the corresponding transmission line is;
and taking the IEEE-39 node system as an example for analysis, calculating the weighted K core value of each line in the topological structure of the node system, and sequencing the lines in a descending order according to the weighted K core value, thereby determining the key line of the system.
The invention has the beneficial effects that:
(1) according to the method, based on the high-speed rail load characteristic, a probability density model of the high-speed rail load impact characteristic is established, and a foundation is laid for power flow calculation of a power grid under the action of the high-speed rail load;
(2) according to the method, constraint information of the active power flow of the network among the transmission lines is considered, and a fragile line identification method based on the physical attributes and static parameters of the power network has better identification accuracy and effectiveness;
(3) the method can provide a new idea for guiding the evolution of the power network and searching for a strategy for inhibiting the propagation of the cascading failure, and has important significance for the planning and safe and stable operation of the power system.
Drawings
Fig. 1(a) shows the daily high-speed rail load probability density, and fig. 1(b) shows the daily high-speed rail load probability density after zero load rejection.
Fig. 2 is a system diagram of IEEE39 nodes.
FIG. 3 is a diagram of physical wiring and correlation network mapping.
FIG. 4 is a weighted K-kernel decomposition process.
Fig. 5 is a diagram of a network adjacent node structure.
Fig. 6 is a histogram of the weighted K-kernel values of the transmission line.
FIG. 7 is a system off-load duty line graph after a deliberate attack.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a fragile line identification method considering high-speed rail fluctuating load based on the defect that the high-speed rail fluctuating load is only rarely considered in the conventional fragile line identification. The method is based on real-time high-speed rail load data, utilizes a Monte Carlo simulation method in probability load flow calculation and adopts an improved weighted K-kernel index, and provides a fragile line identification method considering the high-speed rail load effect. The specific implementation mode is as follows:
step 1: calculating N-1 Monte Carlo probability load flow considering high-speed rail load characteristics
(1) Analysis of impact load characteristics of high-speed rail
The load of the high-speed rail traction substation is characterized by frequent random fluctuation. According to measured data of a certain transformer substation, the average proportion of high-speed rail loads in 3 months in 2018 in the total load of a power system is 10.21%, the maximum proportion is 33.82%, and the maximum load reaches 49.6 MW. Thus, high iron loads have random fluctuating, impact characteristics.
(2) Establishing a high-speed rail load probability model
The probability density statistical chart of the high-speed rail load characteristic can be obtained by setting the high-speed rail load as a random variable X, as shown in fig. 1 (a). From the probability density statistical chart, it can be seen that the high-speed rail load is totally in binomial distribution, and an extremely strong spike exists, and the spike is located at the position where the load is zero, which indicates that the probability of zero load occurrence is very high. When an actual high-speed rail line runs, because the lengths of the two power supply arms of one AT power supply system are about 60km, a motor train unit does not run on the two power supply arms of one traction substation every moment, so that the load of the traction substation is intermittent and the intermittent operation is frequent.
Meanwhile, if the zero load is removed from the data, the high-speed rail load shows a clear normal distribution, as shown in fig. 1 (b). As can be seen from fig. 1(b), the high-speed rail load density function is more fit to the normal distribution. Therefore, the probability density of the high iron load is decomposed into a combination of a normal distribution and a binomial distribution. There are only two possible outcomes in each trial of the binomial distribution, and whether both outcomes occur or do not occur independently of each other. The load of one traction substation is either zero or non-zero, the probability of occurrence of the high-speed rail load is assumed to be p, the probability of occurrence of the high-speed rail load in the non-zero state is assumed to be 1-p, and under the probability of 1-p, the high-speed rail load obeys that the mean value is mu and the variance is sigma2Normal distribution of (u, a)2). The probability density function for high iron loads can therefore be expressed as equation (1).
The generation of the high-speed rail load simulation data can be carried out in the following two steps, and the values of the random variables are independent each time.
Step 1: and firstly generating a random number R between 0 and 1, and if R < p, setting the high-speed rail load value X to be 0, and ending. Otherwise, the step2 is carried out.
Step 2: randomly taking a obedient mathematical expectation as mu and a variance as sigma2And (3) taking the normal distribution value as a high-speed rail load value, if X is equal to 0, discarding the value, and turning to the step1, otherwise, ending.
(3) Calculating N-1 power flow based on Monte Carlo simulation method
In order to take into account the fluctuations, the jerkiness of the high-speed railway load, several representative loads (1, 8, 20, 39, as shown in fig. 2) in the IEEE nodal system are replaced by high-speed railway loads in combination with a probabilistic model of the high-speed railway loads. And then generating a group of load data according to the high-speed rail load probability model by utilizing a Monte Carlo simulation method, and carrying out N-1 probability load flow calculation to obtain the active power value of each branch. And repeating the calculation for 5000 times to obtain the calculation result of 5000 groups of branch power. And solving the mathematical expectation of each branch by using a probability statistical method.
Step 2: constructing correlation network of power network according to branch power coupling relation
According to the N-1 check, if the active power of one branch can be changed due to the fact that the branch is disconnected, the two transmission lines can be considered to have correlation. As shown in fig. 3, a power transmission branch in an original power grid is used as a node of a correlation network; and (4) taking the power increment of other branches caused by the disconnection of the branch as the side weight in the correlation network, thereby constructing a bidirectional weighting network.
And step 3: identification of fragile lines using weighted K-kernel decomposition
The classical K-kernel decomposition process is a recursive removal of nodes in the network with all values less than or equal to K. The conventional K-core decomposition is improved as follows in consideration of the weighting characteristics of the correlation network, as shown in fig. 4. In the weighted K-kernel decomposition, only the association strength of the node to the adjacent node is subtracted when the node is removed, and the influence of the adjacent node to the node is reserved. And decomposing layer by layer from the node with the minimum weighting degree to obtain the K core value of each node in the correlation network. Since the nodes at the edge of the network may still exhibit a high accumulation phenomenon, i.e. a high K kernel value, small impact. The K-kernel values of the node and its neighboring and next neighboring nodes are used to improve the recognition accuracy, as shown in FIG. 5, i.e.
In the formula, Ks _ d (i) is a depth K core value of the node i and reflects the influence of the node i; ks (i) is the K core value of the node i; i.e. ijThe jth node, Ω, in the set of contiguous nodes representing node iiA set of contiguous nodes that are nodes i;
represents a node ijThe k-th adjacent node of (a),
represents a node ijM is a set of adjacent nodes0K kernel weight, m, representing node i1Weight, m, representing sum of kernel values of K adjacent nodes of node i2Represents the weight of the sum of the kernel values of the next adjacent node K of node i, and m0+m1+m 21 is ═ 1; obviously, the larger the value of Ks _ d, the more fragile the corresponding transmission line is;
the analysis is carried out by taking an IEEE-39 node system as an example, and the topological structure is shown in figure 2. The weighted K kernel value for each line is calculated according to the method of the present invention as shown in fig. 6. And sorting the lines in a descending order according to the weighted K kernel value, thereby determining the key line of the system. If the line with a large weighting K kernel value is damaged, a large-scale power failure accident is likely to be caused. Table 1 shows the top 10 critical lines in the recognition ranking results.
TABLE 1
From the recognition result, the lines 46, 33, 37, 20, 34, 39 are outlet lines of the generators, and therefore structurally they are in the important power transmission path. However, the system has 10 generator outlet lines, of which the 39 generator generates 1000MW active power, and the generators connected to the above lines generate 500 or 600MW active power at most, but the branches 2 and 17 connected to the 39 generator do not belong to the important branches. Because a large load (1104MW) is connected to node 39, the generator load is taken up nearby and the power transmitted on legs 2 and 17 is not really large. This shows that the method not only considers the structural characteristics of the line, but also considers the state characteristics of the line, reflecting the correctness of the identification method.
In order to analyze the effectiveness of the identification result of the method, static deliberate attack is carried out on the power network according to the sequence of the identification result and the mode of randomly selecting the attack line, and the lost load of the system and the power out-of-limit condition of other branches after each line is attacked are counted. And taking the load loss condition of the system after a certain line is disconnected as a measurement index influencing the safety of the system, and comparing the load loss condition of the system under the two conditions.
The method comprises the following specific steps:
step 1: and selecting an initial attack line according to the identification result of the fragile line.
Step 2: and recording a fault line and updating a network structure.
And 3, step 3: and (5) carrying out island processing and carrying out alternating current load flow calculation.
And 4, step 4: and (4) judging whether a line power flow is out of limit, if so, cutting off the line with the power out of limit, and turning to the step2, otherwise, turning to the step 5.
And 5: the system load loss situation caused by the initial line fault and the accident chain caused by the line are calculated. And then judging whether the line is attacked or not, if so, ending the process, and otherwise, turning to the step 1.
Fig. 7 lists the attack results of the first 5 key lines and the random line, and it can be seen from the attack results of the first 5 key lines that after the first 5 lines of the method are attacked, the system load loss is much larger than the result of the random attack, which illustrates the effectiveness of the identification method.
There are a small number of remote connection lines in the grid so that the rated load nodes and generator nodes in the network maintain a small electrical distance. When these lines fail, the power transmission capacity of the network is greatly reduced. The line 27 in the IEEE39 node system belongs to the type of line, and its disconnection directly causes the system to be disconnected, forming two islands, wherein the nodes 19, 20, 33, 34 form small islands, and the islands contain two generators and a load, and approximately half of the generated energy needs to be cut off to maintain the normal operation of the system. On the other hand, the other island has insufficient power generation, which leads to the necessity of cutting off a large amount of load and also leads to the cutting off of a subsequent line. Therefore, the normal operation of the line 27 ensures that the power of the No. 33 and No. 34 generators can be normally sent out and positioned at the key power transmission position, thereby illustrating the effectiveness of the method.
In the simulation of cascading failures, the probability of each line appearing in an accident chain is counted, wherein the probability of each non-generator line 3, 27 and 23 appearing in the accident chain is 0.67,0.43 and 0.49 respectively, which shows that the three lines are easily interfered by other failures, and the method is a weak link of a system and shows the correctness of the method.
The fragile line identification algorithm provided by the invention takes the high-speed rail load fluctuation characteristic into account, takes the structural characteristics and the state characteristics of the line into consideration, and adopts an improved K kernel decomposition method to identify the fragile line. The identification results are all weak links in the system, and show larger load loss than randomly selected lines in the process of deliberate attack. Therefore, the method has important significance for searching the cascading failure blocking strategy of the power system, improving the safe operation level of the system and preventing the occurrence of the large power failure of the power grid.
Claims (2)
1. A power grid fragile line identification method considering the high-speed rail impact load effect is characterized in that the random fluctuation characteristic of the high-speed rail load is considered at first, a probability model of the high-speed rail load is established, and then N-1 probability load flow calculation is carried out in an IEEE39 node system; establishing a correlation network of the power system according to the N-1 probability load flow calculation result; finally, identifying a fragile line in the power system by adopting a weighted K kernel decomposition method on the basis of the correlation network; the method comprises the following steps:
step 1: modeling of high-speed rail load characteristics
Firstly, according to the characteristic of severe fluctuation of the high-speed rail load and the probability density distribution thereof, establishing a probability model of the high-speed rail load by utilizing the combination of normal distribution and binomial distribution, as shown in a formula (1);
wherein f (x) represents the probability density of the high-speed rail load, x represents the value of the high-speed rail load, p represents the probability of zero high-speed rail load, mu represents the mean value of the high-speed rail load, and sigma represents the variance of the high-speed rail load;
the method comprises the following two steps when high-speed rail load simulation data are generated, and values of random variables are independent each other;
step 1: firstly, generating a random number R between 0 and 1, and if R is less than p, setting the high-speed rail load value X to be 0, and ending; otherwise, turning to the step 2;
step 2: randomly taking a obedient mathematical expectation as mu and a variance as sigma2If X is equal to 0, discarding the value, and turning to the step1, otherwise, ending;
step 2: calculating N-1 Monte Carlo probability load flow considering high-speed rail load characteristics
Replacing a plurality of key loads with the high-speed rail loads by taking IEEE39 as an analysis object in combination with a probability model of the high-speed rail loads; then 5000 times of N-1 probability load flow calculation is carried out on the system by utilizing a Monte Carlo simulation method to obtain 5000 groups of branch active power values, and the mathematical expectation of the branch active power values is calculated by utilizing a probability statistical method;
and 3, step 3: constructing correlation network of electric power system according to branch power coupling relation
In order to consider the topological structure characteristics of the power grid and the state characteristics of system operation, a correlation network of the power system is established; establishing the correlation network by taking the N-1 Monte Carlo probability load flow calculation in the step2 as a basis, taking the power transmission line in the original power grid as a node, and taking the load flow increase of other lines caused by the disconnection of the line as an edge weight to construct a new network, which is called the correlation network of the original power system;
and 4, step 4: identification of fragile lines using weighted K-kernel decomposition
The correlation network established in the step 3 is a bidirectional weighting network, the traditional K-kernel decomposition is improved, in the weighted K-kernel decomposition, only the correlation strength of the node to the adjacent node is subtracted when the node is removed, and the influence of the adjacent node to the node is reserved; decomposing layer by layer from the node with the minimum weighting degree to obtain a K core value of each node in the correlation network; the nodes at the edge of the network still can present a high accumulation phenomenon, namely a high K core value and small influence; so that the K kernel values of the node and its adjacent node and secondary adjacent node are used to raise the identification precision, i.e.
In the formula, Ks _ d (i) is a depth K core value of the node i and reflects the influence of the node i; ks (i) is the K core value of the node i; i.e. ijThe jth node, Ω, in the set of adjacent nodes representing node iiA set of contiguous nodes that are nodes i;
represents a node ijThe k-th adjacent node of (2),
represents a node ijM is a set of adjacent nodes0Represents the K kernel weight, m, of node i1Weight, m, representing sum of kernel values of K adjacent nodes of node i2Represents the weight of the sum of the kernel values of the next adjacent node K of node i, and m0+m1+m21 is ═ 1; obviously, the larger the value of Ks _ d, the more fragile the corresponding transmission line is;
and analyzing by taking the IEEE-39 node system as an example, calculating the weighted K core value of each line in the topological structure of the node system, and sequencing the lines in a descending order according to the weighted K core value, thereby determining the key line of the system.
2. A power grid fragile line identification method as claimed in claim 1, characterized in that, in order to analyze the validity of the identification result of the method, static deliberate attack is carried out on the power network according to the sequence of the identification result and the mode of randomly selecting attack lines, and the lost load of the system and the power out-of-limit condition of other branches after each line is attacked are counted; taking the load loss condition of the system after a certain line is disconnected as a measurement index influencing the safety of the system, and comparing the load loss condition of the system under the two conditions;
the method comprises the following specific steps:
step 1: selecting an initial attack line according to the identification result of the fragile line;
step 2: recording a fault line and updating a network structure;
and 3, step 3: carrying out island processing and carrying out alternating current power flow calculation;
and 4, step 4: judging whether a line power flow is out of limit or not, if so, switching off the line with out-of-limit power, and turning to the step2, otherwise, turning to the step 5;
and 5: calculating the system load loss condition caused by the initial line fault and an accident chain caused by the line; and then judging whether the line is attacked or not, if so, ending the process, and otherwise, turning to the step 1.
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| CN110350522B (en) * | 2019-07-10 | 2022-04-29 | 西南交通大学 | Electric power system fragile line identification method based on weighted H index |
| CN111313408B (en) * | 2020-03-05 | 2022-04-29 | 西南交通大学 | Power grid fragile line identification method considering transient energy correlation |
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