CN113725855B - Electric DebtRank algorithm-based electric power system fragile line identification method - Google Patents

Electric DebtRank algorithm-based electric power system fragile line identification method Download PDF

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CN113725855B
CN113725855B CN202111029428.5A CN202111029428A CN113725855B CN 113725855 B CN113725855 B CN 113725855B CN 202111029428 A CN202111029428 A CN 202111029428A CN 113725855 B CN113725855 B CN 113725855B
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李利娟
李月
曾亦惟
丁钢伟
李沅格
肖闯
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Xiangtan University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
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    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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    • G06F2113/00Details relating to the application field
    • G06F2113/04Power grid distribution networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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    • H02J2203/10Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses an electric power system fragile line identification method based on an electric DebtRank algorithm. Firstly, establishing a dual topology model of the power system, wherein lines in the power system correspond to nodes in the dual topology model, and the connection relationship among the lines corresponds to edges of the dual topology model; then, the three states of the normal state, the heavy load state and the fault state of the line are included in the identification process of the fragile line, and an electric DebtRank algorithm considering the line load flow and the network topological structure is provided for identifying the fragile line of the power system; finally, through power system cascading failure simulation comparative analysis, the weak line identified by the electrical DebtRank algorithm is proved to have larger influence on the power system compared with the existing method. The method can identify the fragile lines in the power system, strengthen and protect the fragile lines, can effectively prevent cascading failures caused by the weak links, and can provide a certain reference value for avoiding blackout accidents.

Description

Electric DebtRank algorithm-based electric power system fragile line identification method
Technical Field
The invention relates to the field of power grid line vulnerability assessment, in particular to an electric power system vulnerable line identification method based on an electric DebtRank algorithm.
Background
With the increase of the scale and the structural complexity of the electric power system, the safety and the stability of the electric power system are more and more obvious, and serious social and economic losses can be caused by large-scale power failure. The power failure accident is usually caused by cascade faults caused by key node or key line faults in the power system, lines are interrupted due to misoperation or operation errors in the operation, control and maintenance processes of the power system, the power lines are interrupted, other elements are further influenced, cascade faults are caused, the probability of line interruption is higher than the node interruption probability, and therefore identification of the key lines is of great significance to prevention and control of major power failure accidents and response of power failure events.
The critical line is also called a "vulnerable line" and represents a line in which a change in operating state has a large effect on the system, is more likely to cause cascading failures, and significantly increases the vulnerability of the system. The existing research methods for identifying the fragile lines of the power system are mainly divided into two types, one type is an identification method based on the running state of the system, and the other type is an identification method based on the network topology structure of the system. The fragile line identification of the system running state is based on load flow calculation, and the vulnerability of the system is judged by simulating and deducing the development trend of the system state, so that the fragile line identification of the power grid is realized. The method for identifying the fragile line of the system network topological structure is mainly based on a complex network theory, and the fragile line is identified by indexes such as application degree and betweenness or combining with electrical characteristic improvement indexes or updating index weights, or the influence of removing the line or changing the running state of the line on the system network is evaluated to measure the vulnerability of the line.
The existing method for identifying the fragile line of the power system considers the influence of two states of normal operation and fault on cascading faults and the influence on the parameters of the line, however, in the power system, a transition process is often formed when the line is transited from the normal state to the complete fault state. Therefore, it is particularly urgent and important to use the electrical DebtRank algorithm to identify vulnerable lines of the power system in consideration of the line transition process.
Disclosure of Invention
Aiming at the problems existing in the technical background, the invention provides an electric power system fragile line identification method based on an electric DebtRank algorithm.
The technical scheme for solving the problems is as follows: firstly, establishing a dual topology model of the power system by taking the line correspondence in the actual power grid as nodes in the dual topology model and taking the relationship formed by the nodes between the lines as the edges of the dual model; then, three states of the line, namely a normal state, a heavy load state and a fault state, are defined according to the complex network characteristics and the line power flow of the power system, and an electric DebtRank algorithm considering the line power flow and the network topological structure is provided.
In order to achieve the purpose, the following technical scheme is adopted to achieve the purpose:
step 1: carrying out dual modeling on the power system, and corresponding lines in the power system to be nodes in a dual topology model, wherein each actual line is represented by one node in the dual topology model; taking the relation formed by nodes between transmission lines in an actual power grid as an edge of a dual model; in order to embody the electrical performance of the power system, defining the power flow direction of the power transmission line as the direction of an edge in the topological graph, and establishing a directed dual graph of the power grid;
step 2: electric system fragile line sequencing research of an electric DebtRank algorithm;
2-1: three states of the line are defined: normal state, heavy load state, fault state;
the fault rate of the electric power system circuit is related to the circuit load rate, the load rate of the circuit can be increased due to the increase of the tidal current in the circuit, further, the heating of the circuit is increased, the probability of the fault is increased, the shutdown probability of the circuit is increased when the tidal current of the circuit crosses the overheat stability limit, the three set states are respectively a normal state U, an abnormal state D and a fault state F, the load rate of the circuit is used as an evaluation index of the running state according to the running state of the electric power system circuit, and when the circuit is in a heavy load state, the circuit is in a running state but in a poor running state due to the fact that the load rate of the circuit is increased, and therefore the abnormal state in the electric DebtRank algorithm can be defined as a heavy load state O.
2-2: establishing an influence matrix of the line k brought by the line l fluctuation;
in the power system, a line l is connected with a line k, and an influence matrix brought to the line k by the fluctuation of the line l is Y lk To show that:
Figure GDA0003789181840000021
in the formula (1), P l 、P k The power flow, Sigma P, of the line l and k after the line l of the power system fluctuates k For the line connected to line k, including the total power flow of line k, Y lk The maximum value is 1.
2-3: each line R derived by the electrical DebtRank algorithm l A value;
to avoid introducing a continuous variable h i And state s i The influence of (c) is repeatedly calculated resulting in an overestimation of the influence caused by the initial perturbation. In the electrical DebtRank algorithm, h is defined l (t) is the state variable s of line l at time t and line k k Associated continuous variables, the description representing dynamic changes in the power system in continuous changes:
Figure GDA0003789181840000022
in the formula (2), h l The value of (t) is equal to h l (t-1) adding the sum of the products of the influence of the line k and the line l on all the lines in the heavy load state at the time t-1. h is k (t-1) represents a continuous variable of the line k at the time t-1; the more line k connected to line l falls into a heavy load state at time t-1, the more h l The larger the value of (t), h l (t) the maximum value in dynamic variation is 1.
Figure GDA0003789181840000023
In the formula (3), the continuous variable h l Determining a state variable s l State variable s l Three states of the line l are respectively a U normal state, and the line l can normally run; o represents that the line l is in a heavy load state, the line l can continue to operate but the operating state exceeds a certain thermal stability area, and the fault probability and the risk are improved; f represents a fault condition in which line i is completely inoperable.
The conversion relationship between 3 states is expressed by equation (3), for the state variable s l (t) when the continuous variable h of the line l l (t) greater than the mean outage probability of the line at time t
Figure GDA0003789181840000024
And s l (t) previous state s l (t-1) not in the failure state, s l (t) the state variable is converted into a heavy load state O; when the state variable s of the node l l (t-1) in the heavy load state O, s l (t-1) Next State s l (t) the state variable is converted into a fault state F; in other cases, when the variable h is continuous l (t) less than average line outage probability
Figure GDA0003789181840000025
Or s l (t-1) in the event of a failure, s l (t) state variable inheritance s l The value of the state variable at time t-1.
According to the correspondence of equations (1) - (3) and the three defined states, the electrical DebtRank algorithm is described as shown in equation (4):
R l =∑ k h k (t)p k -h l (1)p l (4)
Figure GDA0003789181840000026
Figure GDA0003789181840000027
in the formula p k 、p l The ratios of the total power flows of the line k and the line l to the total power flows flowing into the line k and the line l are respectively shown as a formula (5) and a formula (6); according to the formula (4), the R of each line calculated based on the electrical DebtRank algorithm can be obtained l Value R l The larger the value, the more fragile the line is, and the sorting result of the fragile line in the power system can be obtained.
2-4: calculating flow of an electric DebtRank algorithm;
based on the above analysis, the flow of the weak line sequencing of the power system is as follows:
1) establishing a power grid dual topology model: establishing a dual topology model of the power system by taking the line correspondence in the actual power grid as nodes in the dual topology model and taking the relationship formed by the nodes between the lines as the edges of the dual model;
2) selecting an initial disturbance line: selecting the line to be set in a heavy load state in sequence from small to large according to the line number, using the line as an initial disturbance node in a dual model of the power system, and calculating the power flow after node fluctuation;
3) distribution of continuous variable h l And a state variable s l : continuous variable h of each node of dual topological model l And a state variable s l Assigning an initial value: continuous variable h of each node l The value being a fixed random value, the state variable s l Are all in a normal state U; distributing a continuous variable h and a state variable s to each node in the dual model, and ensuring the independence and the accuracy of each calculation;
4) calculating an influence matrix Y: calculating the influence Y among all lines according to the line connection matrix of the dual model lk Obtaining an influence matrix Y;
5) the electrical DebtRank algorithm calculates: calculating R of each node of the dual topology model through formulas (1) to (6) l A value;
node R l Value sorting: according to the calculated R l The numerical values are sorted, and the larger the numerical value is, the greater the influence on the performance of the power system is, the more important the numerical value is.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a topology diagram of an IEEE-39 node system.
FIG. 3 is a dual topology diagram of an IEEE-39 node system power system.
FIG. 4 is a line R of an IEEE-39 node power system l The value is obtained.
FIG. 5 is a graph comparing line ripple load loss for an IEEE-39 node power system.
FIG. 6 is a R of an IEEE-118 node power system line l The value is obtained.
FIG. 7 is a graph comparing line ripple load loss for an IEEE-118 node power system.
FIG. 8 is a graph comparing the load loss of the first 10 vulnerable lines of the IEEE-118 node power system removed step by step.
Detailed Description
The invention is further described below with reference to the figures and examples.
Taking IEEE-39 and IEEE-118 node power systems as examples, the effectiveness of the application of the method in vulnerability assessment is verified in three aspects of utilizing an electrical DebtRank algorithm to perform simulation identification on a key line and comparing a sequencing result with the existing method; the method comprises the following specific steps:
step 1: according to the topological graph and the dual graph of the IEEE-39 node system, the circuit sequencing of the power system is simulated;
the example simulation parameters are set as follows: taking the average statistical value of the line load rate more than or equal to 0.8 and less than 1 as the heavy load state and the line outage probability
Figure GDA0003789181840000031
Setting initial variable s of line k (1) For normal operation U, the initial variable s of the disturbed line l (1) For the heavy load state O, the system load power changes randomly when other random factors are considered, and the continuous variable h l (1) The system load power random variation is taken to be 0,0.8 when other random factors are considered]A random number in between.
Using equations (1) - (6) and referring to FIG. 1, R of 46 lines of the IEEE-39 node power system, namely 46 nodes in a dual topology, is obtained l The values are shown in figure 4. According to R thereof l The lines are sorted according to the value, and the obtained key line identification result is compared with the first 10 lines of the fragile line sorting identified by the improved PageRank method, the improved LeaderRank algorithm and the electrical betweenness method, and the comparison result is shown in a table 1; respectively removing the first 10 fragile lines identified by the four methods in Table 1 according to the sorting condition of each method, and performing 5The percentage of load loss and the cumulative probability of load loss caused by the 00 cascading failure simulations are shown in fig. 5.
TABLE 1 IEEE-39 node electric power system 3 fragile line identification method comparison
Figure GDA0003789181840000032
Figure GDA0003789181840000041
As can be obtained from table 1, 2 lines in the first 10 lines of the sequence obtained by the improved electrical DebtRank algorithm are outgoing lines of the generator No. 31 and the generator No. 35 respectively, and a line fault will seriously affect the insufficient active power output of the system, thereby causing a blackout accident; 3 lines which are connected with important load nodes in the power system bear heavier power transmission tasks, and the connection of the power system can be reduced after the lines are disconnected, so that the safe and stable operation of the system is threatened, and the power balance of the power system is damaged. If line number 29, which is ranked first, is the connection line between load node 16 and load node 24, and load node 16 connects 5 nodes in the power system, which is one of the most important nodes in the system, disconnection will cause the system to be divided into two parts, causing power flow fluctuation and causing a large change in the topology of the system.
As can be seen from fig. 5, the percentage of the maximum load loss resulting from removing the 10 fragile lines identified using the electrical DebtRank algorithm is 31%, which is significantly better than the 25% and 26% maximum load loss of the modified PageRank algorithm and the modified leaderrrank algorithm, respectively, and also better than the 29% maximum load loss of the electrical permittivity method. When the load loss percentage of the system is (0, 13%), the cumulative probability of the load loss is slightly higher than that of the improved LeaderRank algorithm and that of the improved PageRank algorithm due to the first ten line fluctuations identified by the electrical DebtRank algorithm; when the load loss percentage of the system is (13, 17%), the cumulative probability of the load loss is equivalent to the improved LeaderRank algorithm and the improved PageRank algorithm; when the load loss is larger than 17%, the load loss cumulative probability is obviously higher than that of an improved PageRank algorithm, an improved LeaderRank algorithm and an electrical betweenness method, and the electrical DebtRank algorithm initially has obvious advantages; the cumulative probability of load loss greater than 12% is stably higher than the improved PageRank algorithm and the improved LeadeRank algorithm. It can be seen that the fragile lines identified using the electrical DebtRank algorithm may lead to a greater probability of cascading failure.
Step 2: simulating a line sequence of the IEEE-118 node power system;
by using the formulas (1) to (6) and according to the flow shown in the attached figure 2, the R of 179 lines is obtained by carrying out simulation operation on an IEEE-118 node power system l The values are shown in FIG. 6, where R of the line l The larger the value, the more influential it has in the system, the more important the line.
To verify the effectiveness of the method for identifying fragile lines presented herein, the key line identification results obtained herein in table 1 were compared to the top ten lines of the fragile line sequence identified by the electrical medium. According to R thereof l The lines are sorted according to the value, and the transmission lines with the simulation results listed at the top 10 are shown in table 2.
TABLE 2 IEEE-118 node power system 2 identification method comparison
Figure GDA0003789181840000042
As can be seen from table 2, 5 of the important lines obtained by the improved electrical DebtRank algorithm are outgoing lines of the generator, and 5 of the important lines are lines connecting important load nodes in the power system, and bear a heavy power transmission task, and these lines will bring huge load loss after being disconnected. If the line 33 with the first sequence is an outlet line between the generator No. 25 and the generator No. 27, the power output of the generator No. 27 is severely limited once the generator No. 27 is disconnected, and the disconnection can cause large-scale power flow transfer and cause cascading failure.
The first 10 fragile lines identified by the two methods in table 2 were removed and cascading failure simulation was performed 500 times, and fig. 7 shows the change and comparison of the percentage of load loss and the cumulative probability of load loss caused by the two methods removing the first 10 fragile lines.
As can be seen from fig. 7, the cumulative probability of load loss is slightly higher for the first ten line fluctuations identified by the electrical DebtRank algorithm when the system load loss percentage is (0, 8%); the cumulative probability after load loss greater than 8% is steadily higher than the electrical betweenness method, and the electrical DebtRank algorithm starts to exhibit significant advantages. And, the percentage of the maximum load loss caused by removing the 10 fragile lines identified by the electrical DebtRank algorithm is 21%, which is obviously better than that of the electrical betweenness method, and it can be seen that the fragile lines identified by the electrical DebtRank algorithm are more fragile, and the probability of cascading failures possibly caused by the fragile lines is higher.
Then, the first 10 lines identified by the two methods in Table 2 are identified according to the vulnerable line value R l And electrical medians are ordered for removal. Fig. 8 shows the change in load loss resulting from the gradual removal of the first 10 vulnerable lines of the two methods sequence. In fig. 8, the load loss of the electrical DebtRank algorithm is close to that of the electrical betweenness method when the first 5 vulnerable lines are removed, which indicates that the influence on the power system when the first 5 vulnerable lines are removed is almost the same. However, after the important lines are continuously removed, the load loss caused by the electrical DebtRank algorithm is obviously larger than that based on the electrical outage method, and it can be seen that the influence of the fragile lines identified based on the electrical DebtRank algorithm is higher than that based on the electrical outage method, especially in terms of preventing large-scale power outage accidents.

Claims (1)

1. A method for identifying a fragile line of an electric power system based on an electric DebtRank algorithm comprises the following steps:
step 1: carrying out dual modeling on the power system, and corresponding lines in the power system to be nodes in a dual topology model, wherein each actual line is represented by one node in the dual topology model; taking the relation formed by nodes between transmission lines in an actual power grid as an edge of a dual model; in order to embody the electrical performance of the power system, defining the power flow direction of the power transmission line as the direction of an edge in the topological graph, and establishing a directed dual graph of the power grid;
step 2: considering the power system line flow, three states of the line are defined: identifying a fragile line of the power system by using an electric DebtRank algorithm in a normal state, a heavy load state and a fault state; the step 2 specifically comprises:
2-1: three states of the line are defined: normal state, heavy load state, fault state;
the fault rate of the electric power system circuit is related to the circuit load rate, the load rate of the circuit can be increased due to the increase of the tidal current in the circuit, further, the heating of the circuit is increased, the probability of the fault is increased, the probability of the circuit shutdown is increased when the tidal current of the circuit crosses the overheat stability limit, the three set states are respectively a normal state U, an abnormal state D and a fault state F, according to the operation state of the electric power system circuit, the load rate of the circuit is used as an operation state evaluation index, when the circuit is in a heavy load state, the circuit is in a state of operation but poor operation state due to the fact that the load rate of the circuit is increased, and therefore the abnormal state in the electric DebtRank algorithm can be defined as a heavy load state O;
2-2: establishing an influence matrix of the line k brought by the line l fluctuation;
in the power system, a line l is connected with a line k, and an influence matrix brought to the line k by the fluctuation of the line l is Y lk To show that:
Figure FDA0003789181830000011
in the formula (1), P l 、P k The power flow, Sigma P, of the line l and k after the line l of the power system fluctuates k For the line connected to line k, including the total power flow of line k, Y lk The maximum value is 1;
2-3: each line R derived by the electrical DebtRank algorithm l A value;
to avoid introducing a continuous variable h l And a state variable s l Is repeatedly calculated resulting in an overestimation of the effect caused by the initial perturbation, at electrical DebtIn the Rank algorithm, h is defined l (t) is the state variable s of line l at time t and line k k Associated continuous variables, the description representing dynamic changes in the power system in continuous changes:
Figure FDA0003789181830000012
in the formula (2), h l The value of (t) is equal to h l (t-1) adding the sum of the products of the influence of the line k and the line l on the line k in the heavy load state at the moment of t-1; h is a total of k (t-1) represents a continuous variable of the line k at the time t-1; the more line k connected to line l falls into a heavy load state at time t-1, the more h l The larger the value of (t), h l (t) a maximum value of 1 in dynamic variation;
Figure FDA0003789181830000013
in the formula (3), the continuous variable h l Determining a state variable s l State variable s l Three states of the line l are respectively a U normal state, and the line l can normally run; o represents that the line l is in a heavy load state, the line l can continue to operate but the operating state exceeds a certain thermal stability area, and the fault probability and the risk are improved; f represents a fault state in which line i is completely inoperable;
the conversion relationship between 3 states is expressed by equation (3), for the state variable s l (t) when the continuous variable h of the line l l (t) greater than the mean outage probability of the line at time t
Figure FDA0003789181830000014
And s l (t) previous state s l (t-1) not in the failure state, s l (t) the state variable is converted into a heavy load state O; when the state variable s of the node l l (t-1) in the heavy load state O, s l (t-1) Next State s l (t) state variables are converted to fault statesState F; in other cases, when the variable h is continuous l (t) less than average line outage probability
Figure FDA0003789181830000015
Or s l (t-1) in the event of a failure, s l (t) State variable inheritance s l The value of the state variable at time t-1;
according to the correspondence of equations (1) - (3) and the three defined states, the electrical DebtRank algorithm is described as shown in equation (4):
R l =∑ k h k (t)p k -h l (1)p l (4)
Figure FDA0003789181830000021
Figure FDA0003789181830000022
in the formula p k 、p l The ratios of the total power flows of the line k and the line l to the total power flows of the line k and the line l are respectively shown as a formula (5) and a formula (6); according to the formula (4), the R of each line calculated based on the electrical DebtRank algorithm can be obtained l Value R l The larger the value is, the more fragile the line is, and further the sorting result of the fragile line in the power system can be obtained;
2-4: calculating flow of an electric DebtRank algorithm;
based on the above analysis, the flow of the fragile line sequencing of the power system is as follows:
1) establishing a power grid dual topology model: establishing a dual topology model of the power system by taking the line correspondence in the actual power grid as nodes in the dual topology model and taking the relationship formed by the nodes between the lines as the edges of the dual model;
2) selecting an initial disturbance line: selecting the line to be set in a heavy load state in sequence from small to large according to the line number, using the line as an initial disturbance node in a dual model of the power system, and calculating the power flow after node fluctuation;
3) distribution of continuous variable h l And a state variable s l : continuous variable h of each node of dual topological model l And a state variable s l Assigning an initial value: continuous variable h of each node l The value being a fixed random value, the state variable s l Are all in a normal state U; distributing a continuous variable h and a state variable s to each node in the dual model, and ensuring the independence and the accuracy of each calculation;
4) calculating an influence matrix Y: calculating the influence Y among all lines according to the line connection matrix of the dual model lk Obtaining an influence matrix Y;
5) the electrical DebtRank algorithm calculates: calculating R of each node of the dual topology model through formulas (1) to (6) l A value;
node R l Value sorting: according to the calculated R l The numerical values are sorted, and the larger the numerical value is, the greater the influence on the performance of the power system is, the more important the numerical value is.
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