A power grid key line comprehensive identification method based on the idea of maximum deviation

Abstract

The application discloses a power grid key line comprehensive identification method based on a maximum deviation thought. Based on power grid structure information, combined with current operation state, four line key evaluation indexes of voltage stability, capacity margin, real-time failure rate and topological contact degree are established; based on the maximum deviation thought, a line comprehensive importance identification method considering subjective and objective weighting of different factors is proposed; a power supply capacity evaluation method of the system under line fault is proposed by adopting a control strategy of minimum load shedding amount of system optimal power flow, and it is verified that the identified lines are high-risk lines which will have a key influence on system operation. In the identification of the power grid key line, the application fully considers node voltage, line load, line fault, network topology and other information, considers the special situation of power grid splitting to form an island, excavates the information carried by the identification indexes, improves the identification accuracy of the power grid key line, and has guiding significance for the operation and maintenance management of the power transmission line.

Description

Technical Field

[0001] This invention relates to the field of power system security protection, and in particular to a comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation. Background Technology

[0002] Studies have shown that line faults in power grids can easily trigger a chain reaction, spreading to other equipment and ultimately causing large-scale grid disconnection and major blackouts. Therefore, identifying critical lines in the power grid quickly and effectively is of significant theoretical and practical importance in preventing such blackouts.

[0003] There has been some research on the identification of critical lines in power grids. Existing identification methods are mainly divided into static analysis and dynamic analysis. The representative method of dynamic analysis is entropy theory. Cao Yijia et al. (Cao Yijia, Wang Guangzeng, Cao Lihua, et al. Self-organized critical state judgment model of complex power grid based on power flow entropy [J]. Automation of Electric Power System. 2011.35(7):1-6.) first proposed the concept of power flow entropy to measure the imbalance of power flow in the system. Li Yong et al. (Li Yong, Liu Junyong, Liu Xiaoyu, et al. Vulnerability assessment of power grid cascading fault propagation elements based on power flow entropy [J]. Automation of Electric Power System. 2012.36(19):11-16.) further proposed the power flow distribution entropy and power flow transfer entropy models to measure the vulnerability of lines from the perspectives of impact and consequences. However, dynamic analysis methods generally rely on power flow calculations involving multiple line disconnections, which has a high time cost and cannot meet the real-time requirements of security analysis. Since the power grid has small-world characteristics, static analysis methods based on complex network theory can be used to identify critical lines. Xu Lin et al. (Xu Lin, Wang Xiuli, Wang Xifan. Electrical betweenness and its application in the identification of critical lines in power systems [J]. Proceedings of the CSEE, 2010, 30(1): 33-39.) proposed the "electrical betweenness" index to identify critical lines by injecting a unit current between generator and load nodes and using the smaller value of generator output and load level as the weight. On this basis, Zhang Tao et al. (Zhang Tao, Sun Xiaowei, Xu Xueqin, et al. Identification of critical lines in power grids based on active power flow betweenness [J]. Power System Technology, 2016, 40(1): 193-198.) further considered the usage of transmission lines under the current operating mode and proposed the "active power flow betweenness" index as the identification criterion, but it did not consider the transmission of reactive power in the system. The above indicators or methods can effectively identify the critical path, but the factors considered are relatively singular. Tao Hongfei et al. (Tao Hongfei, Xie Dong, Zhao Fulin, et al. Comprehensive identification of critical path in power system with large-scale wind power grid connection [J]. Power System Protection and Control, 2020, 48(6): 115-123.) adopted a comprehensive indicator of multiple betweenness indicators to identify the critical path.

[0004] Existing critical path identification methods mostly evaluate the importance of a path from a single perspective, without fully considering the information carried by the nodes at both ends of the path. Furthermore, for multi-indicator comprehensive identification methods, the assignment of weights to each indicator is highly subjective and lacks rationality. Summary of the Invention

[0005] Building upon existing research, this invention proposes a comprehensive identification method for critical power grid lines based on the principle of maximizing deviation. First, based on power grid structure information and current operating status, considering local system voltage stability, line transmission capacity, line failure rate, and global topological importance of nodes, critical line evaluation indicators such as voltage stability, capacity margin, real-time failure rate, and topological connectivity are established. Then, based on the principle of maximizing deviation, subjective and objective weights are assigned to each indicator to establish a comprehensive line importance identification method. Finally, a control strategy that minimizes the system's optimal power flow load shedding is adopted to verify the effectiveness of the identification results.

[0006] The objective of this invention is achieved through the following technical solution: a comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation, the method comprising the following steps:

[0007] Step 1: Obtain power grid structure information, line parameters, transformer parameters, generator parameters, and load parameters, and calculate the power grid parameters under the current operating conditions;

[0008] Step 2: Considering the inherent vulnerability of the line, construct the following three indicators:

[0009] A voltage stability index is constructed based on static voltage safety assessment to reflect the local line voltage stability;

[0010] A capacity margin index is constructed based on the line load level to reflect the importance of lines with high local load rates;

[0011] A real-time failure rate index is constructed based on accidental failures under severe weather conditions to reflect the short-term reliability of local lines.

[0012] Step 3: Considering the role of each line in the entire power grid, construct a topology connectivity index based on complex network theory to reflect the interconnection capability of each line in the global power grid;

[0013] Step 4: After proposing independent evaluation indicators for critical power grid lines, the information carried by the indicator values ​​is mined based on the idea of ​​maximizing deviation. Weights are assigned to various indicators, and the comprehensive importance index value of all lines is calculated. The lines with the largest comprehensive importance index values ​​are selected as critical lines in turn.

[0014] Furthermore, in step 1, the grid voltage level and the highest and lowest voltage amplitude of each node are obtained, the connection relationship between nodes and lines is clarified, and the grid topology diagram is drawn; the resistance, reactance and susceptance of each line are obtained, as well as their thermal stability power limit values; the turns ratio of each transformer is obtained; the maximum and minimum power limits of each generator are obtained; and the power values ​​of the load nodes are obtained.

[0015] Based on the above information, power flow calculations are performed using power system analysis software or programs (such as Matlab-matpower) to obtain the grid node voltage and line power flow data under the current operating conditions.

[0016] Furthermore, in step 2, the voltage stability index is constructed as follows:

[0017] Static voltage security assessment is of great significance for ensuring the normal power supply of the power grid. When conducting static voltage security assessment, the system is often divided into a normal system and a post-fault system. The stability margin of the system before and after the fault is obtained by using repeated calculation power flow or continuous power flow methods after the load increases in a specific direction. For large-scale power systems, the existing repeated calculation power flow or continuous power flow methods have a large simulation workload and cannot meet the real-time requirements of critical line identification. Therefore, starting from the solution conditions of the power flow equation with the terminal voltage as the variable, a voltage stability index is constructed.

[0018] For a typical π-type equivalent line ij, where i is the starting node and j is the ending node, V i ∠δ i and V j ∠δ j V represents the voltage phasors at nodes i and j, respectively. i and δ i V represents the voltage and phase angle at node i, respectively. j and δ j Z represents the voltage and phase angle of node j, respectively; δ represents the phase angle difference between node i and node j; Z represents the line impedance; R represents the line resistance; X represents the line reactance; B / 2 represents the line admittance to ground. and P represents the injected power at node i and the outflow power at node j, respectively. i and Q i P represents the active power injection and reactive power injection at node i, respectively. j and Q j These are the active power outflow and reactive power outflow at node j, respectively. The current flowing through the circuit;

[0019] The power flow equation for line ij, with the terminal voltage as the variable, is as follows:

[0020]

[0021] Expand the above expression separately for the real and imaginary parts:

[0022]

[0023]

[0024] Both equations are about V j A quadratic equation, if the equation has solutions, then satisfies:

[0025] V i 2 sin 2 δ-2BR(P j XQ j R)≥0

[0026]

[0027] According to the voltage V at the end of the line j The voltage stability index L is defined under the condition that a solution exists. V-ij for:

[0028] L V-ij =max(L V1 ,L V2 )

[0029] in,

[0030]

[0031]

[0032] When L V-ij When the index value is greater than 1, the power flow equation with the terminal voltage as the variable has no solution, that is, the line voltage has collapsed and the line is very vulnerable; when the index value is less than 1, the power flow equation with the terminal voltage as the variable has a solution. The closer the index is to 1, the more likely the line ij is to experience voltage collapse under the current operating conditions.

[0033] Furthermore, in step 2, the capacity margin index is constructed as follows:

[0034] Establish the capacity margin index L for line ij S-ij :

[0035]

[0036] Among them, S ij S represents the line transmission power of line ij under its current operating state; ij-max This represents the maximum allowable transmission capacity of line ij, which is limited by the thermal stability power limit.

[0037] The capacity margin index overcomes the shortcomings of existing methods. Traditional methods generally reflect the power flow limitation of a line directly as the ratio of active power to maximum transmission power. These methods have two drawbacks: 1) they ignore the transmission of reactive power, leading to overly optimistic load factor calculations; 2) the importance of a line is directly proportional to its load factor, failing to emphasize the importance of lines with high load factors. This index-defined capacity margin index, L... S-ij Taking into account the reactive power flow carried by the line, it can comprehensively reflect the load level of the line; when the line power flow is close to or has exceeded the line capacity limit, the index value will increase significantly, thus reflecting the difference in importance of lines with different load rates.

[0038] Furthermore, in step 2, the construction of the real-time failure rate indicator is specifically as follows:

[0039] Line faults are not only related to the line's own operating status, but also to accidental factors. In particular, the probability of line faults is much higher under severe weather conditions than under normal weather conditions. Therefore, it is necessary to establish a real-time line fault index based on statistical characteristics and taking into account meteorological factors.

[0040] A three-segment bathtub curve can generally be used to describe the natural aging process of a power line. By statistically analyzing historical fault data, the natural fault rate λ of line ij for a certain period can be obtained. 1-ij ;

[0041] When studying the short-term reliability of a transmission line, the natural failure rate can be used as a benchmark. Considering that severe weather conditions are a highly relevant factor for line failure, the accidental failure rate λ of line ij under severe weather conditions is obtained based on historical statistical data. 2-ij :

[0042]

[0043] in, F represents the statistical average of the failure rate of line ij; ij F represents the probability that line ij will experience extreme weather; ij ′ represents the proportion of line ij that experiences faults under extreme conditions out of the total number of faults;

[0044] The larger of the two failure rates is taken as the real-time failure rate index L of line ij. λ-ij :

[0045] L λ-ij =max{λ 1-ij ,λ 2-ij}

[0046] Furthermore, in step 3, a topological connectivity index is constructed considering the role of the line in the entire power grid, specifically as follows:

[0047] From a network structure perspective, the importance of each node and line is related to its topological position. Based on the definition of node degree in complex network theory—that is, the degree of a node is the sum of the number of edges connected to it, and the larger the value, the more important the node is in the network topology—a topological connectivity index L is established for line ij. K-ij :

[0048]

[0049] Among them, K i K j Let i and j be the node degrees, respectively. The average degree of all nodes in the power grid:

[0050]

[0051] Where M is the set of all nodes in the power grid, N is the total number of power grid nodes, and L is the total number of power grid lines;

[0052] The topological connectivity index, established based on the degree of nodes at both ends of a line, characterizes the line's connectivity in the global power grid. The larger the index value, the more important the line's pivotal role in power transmission in the power grid. Line disconnection can easily cause a significant impact on the power grid structure and have a greater impact on system integrity.

[0053] Furthermore, in step 4, given m lines, i.e. m evaluation schemes and n evaluation indicators, the set of evaluation indicators is denoted as G = {G1, G2, ..., G...} n Based on the idea of ​​maximizing deviation, the weights of the indicators are determined, and the importance of the route is comprehensively evaluated, specifically as follows:

[0054] The basic idea of ​​deviation maximization is: if the G of all evaluation schemes i If all index values ​​are equal, then G i The indicators have no effect on the ranking of the evaluation schemes, and their weights can be recorded as 0; conversely, if the G of all evaluation schemes has no effect on the ranking of the schemes, the weights can be recorded as 0. i The greater the difference in index values, the more G... i The indicators will play an important role in ranking the evaluation schemes and should be given greater weight.

[0055] The weight vector of each indicator is denoted as W = [w1, w2, ..., w n ] T The weights reflect the information carried by each indicator value. The value of the j-th indicator corresponding to the i-th line is denoted as u. ij U = (u ij )m×n Let W be the decision matrix; the steps to solve for W are as follows:

[0056] 1) Normalize the evaluation indicators; the indicators in steps 2 and 3 are benefit-type indicators, meaning the larger the value, the higher the importance of the route. They can be normalized as follows:

[0057]

[0058] Where: u j max and u j min These are the corresponding indicators G j The maximum and minimum values;

[0059] 2) Obtain the total deviation of all evaluation indicators from the power grid line; for evaluation indicator G j Without considering the influence of weights, the total deviation of line i from other lines k is denoted as d. ij0 , When considering the influence of weights, the total deviation of line i from other lines k is denoted as d. ij , The total deviation between all lines is denoted as d. ij (G j ),

[0060] 3) Solve the optimization model; for all evaluation indicators G, the total deviation between all lines is denoted as D. Based on the idea of ​​maximizing deviation, the choice of W should maximize the total deviation D, i.e., the following optimization model:

[0061]

[0062]

[0063] The solution is obtained using the Lagrange method. j The normalized optimal solution is:

[0064]

[0065] After calculating W, the decision formula E is applied. i =w1u i1 +w2u i2 +…+w n u in Calculate the overall importance index for all routes and sort the results in descending order.

[0066] Furthermore, in step 4, subjective weights based on expert scoring are introduced, and the importance of the route is comprehensively evaluated by combining the idea of ​​maximizing deviation. Specifically:

[0067] The original weight vector W of each indicator obtained based on the idea of ​​maximizing deviation is denoted as the objective weight vector, and the subjective weight vector is denoted as W0. * =[w1 * w2 * ,…,w n * ] T Subjective weights are given by evaluation experts based on their experience and knowledge. The steps for determining subjective weights are as follows:

[0068] 1) Please have P power system experts and on-site operation and maintenance personnel assign weighted scores to the evaluation indicators based on their experience working in the power grid of this region. …, For the evaluation index G j Weighted score w j * satisfy and A higher score for a certain indicator indicates that experts believe that the value of that indicator for the local power grid lines should be given special attention.

[0069] 2) Statistical analysis of expert evaluations was performed, and the subjective weight vector W was calculated by taking the average value. * , …,

[0070] Get U and W * Then, the steps to solve for W are as follows:

[0071] 1) Normalize the evaluation indicators;

[0072] 2) Obtain the total deviation of all evaluation indicators from the power grid line; for evaluation indicator G j When considering both objective and subjective weights, the total deviation of line i from other lines k is denoted as d'. ij , The total deviation between all lines is denoted as d'. ij (G j ),

[0073] 3) Solve the optimization model; for all evaluation indicators G, the total deviation between all lines is denoted as D. Based on the idea of ​​maximizing deviation, the choice of W should maximize the total deviation D, i.e., the following optimization model:

[0074]

[0075]

[0076] Using the Lagrange method, w can be obtained. jThe normalized optimal solution is:

[0077]

[0078] After calculating W, the decision formula E is applied. i =w1 * w1u i1 +w2 * w2u i2 +…+w n * w n u in Calculate the overall importance index for all routes and sort the results in descending order.

[0079] Furthermore, in step 4, after ranking the lines according to their importance based on a comprehensive importance index, and considering the possibility of network disconnection due to line disconnection, a globally optimal power flow load shedding model is proposed. The identified critical lines are disconnected sequentially, and the minimum load loss of the system after line disconnection is calculated to verify the effectiveness of the identification results. Specifically:

[0080] When a line disconnection causes the system to split into two islands, the portion of the system receiving power from the fault can be called the sending-end island, and the other portion the receiving-end island. Generally, under the constraints of power flow calculations, the sending-end island can reach a new equilibrium state by adjusting generator output. However, even by adjusting generator output, the receiving-end island may not be able to avoid node voltage exceeding limits or frequency instability. That is, the sending-end island does not lose load, while the receiving-end island needs to disconnect some load to maintain the safe and stable operation of the system. After a line disconnection, the optimal load shedding amount is calculated; the greater the load loss, the more important the line.

[0081] The objective function for the optimal load shedding is:

[0082]

[0083] Where D is the set of load nodes; P loss-n Let n be the active power loss load.

[0084] The equality constraints for power flow calculation are:

[0085]

[0086]

[0087] Among them, P n and Q n Let P' be the initial active and reactive power of load n, respectively; G is the set of generator nodes; P' is the initial active and reactive power of load n, respectively. m and Q' mLet be the active and reactive power outputs of generator m, respectively; L be the set of lines; ΔP l and ΔQ l These represent the active and reactive power losses of line l, respectively; Q loss-n Let n be the reactive load.

[0088] The inequality constraints for power flow calculation are:

[0089] -S l-max ≤S' l ≤S l-max

[0090] V i min ≤V' i ≤V i max

[0091] P m min ≤P' m ≤P m max

[0092] Q m min ≤Q' m ≤Q m max

[0093] The above equations represent the upper and lower limits of line power flow constraints, the upper and lower limits of voltage at each node, and the upper and lower limits of active and reactive power output of generators, respectively; where S' l S represents the transmission power of line l; l-max V' is the maximum transmission capacity of line l; i V is the voltage at node i; i max and V i min These are the upper and lower voltage limits for node i, respectively; P m max and P m min These represent the upper and lower limits of the active power output of generator m; Q m max and Q m min These are the upper and lower limits of the reactive power output of generator m, respectively;

[0094] If the power factor of the original load is not changed when the load is shelved, then the power factor constraint for load shelving is:

[0095]

[0096] in, Let n be the initial power factor of the load.

[0097] After the line is disconnected, the optimal load loss of the system is calculated. The greater the load loss, the more important the line is.

[0098] The beneficial effects of this invention are:

[0099] 1) The critical path identification fully considers the node information at both ends of the line. Based on the idea of ​​maximizing the deviation by combining subjective and objective weighting, a comprehensive evaluation index is established that considers node voltage, line load, line failure rate and network topology, making the identification results of critical power grid lines more reasonable.

[0100] 2) The proposed optimal power flow load shedding model takes into account the situation of grid disconnection forming islands, which can effectively verify the identification results of critical lines and has practical value for the operation and maintenance management of power grid lines. Attached Figure Description

[0101] Figure 1 This is a flowchart of the comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation in an embodiment of the present invention.

[0102] Figure 2 This is a schematic diagram of the power grid structure in an embodiment of the present invention.

[0103] Figure 3 This is the result of identifying critical power grid lines considering objective weights in an embodiment of the present invention.

[0104] Figure 4 for Figure 3 The optimal load shedding result in the example.

[0105] Figure 5 This is the result of identifying critical power grid lines in the embodiments of the present invention, taking into account both subjective and objective weights.

[0106] Figure 6 for Figure 5 The optimal load shedding result in the example. Detailed Implementation

[0107] The present invention will be further described in detail below with reference to specific embodiments.

[0108] This invention provides a comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation. The method includes the following steps:

[0109] Step 1: Obtain power grid structure information, line parameters, transformer parameters, generator parameters, and load parameters, and calculate the power grid parameters under the current operating conditions; specifically:

[0110] Obtain the grid voltage level and the highest and lowest voltage amplitudes of each node, clarify the connection relationships between nodes and lines, and draw the grid topology diagram; obtain the resistance, reactance, and susceptance of each line, as well as their thermal stability power limits; obtain the turns ratio of each transformer; obtain the maximum and minimum power limits of each generator; obtain the power values ​​of the load nodes;

[0111] Based on the above information, power flow calculations are performed using power system analysis software or programs (such as Matlab-matpower) to obtain the grid node voltage and line power flow data under the current operating conditions.

[0112] Step 2: Considering the inherent vulnerability of the line, construct the following three indicators:

[0113] A voltage stability index is constructed based on static voltage safety assessment to reflect the local line voltage stability;

[0114] A capacity margin index is constructed based on the line load level to reflect the importance of lines with high local load rates;

[0115] A real-time failure rate index is constructed based on accidental failures under severe weather conditions to reflect the short-term reliability of local lines.

[0116] (1) Voltage stability index

[0117] For large-scale power systems, the existing repetitive calculation power flow or continuous power flow simulation methods have too large a computational load and cannot meet the real-time requirements for critical line identification. Therefore, starting from the solution conditions of the power flow equation with the terminal voltage as the variable, a voltage stability index is constructed.

[0118] For a typical π-type equivalent line ij, where i is the starting node and j is the ending node, V i ∠δ i and V j ∠δ j V represents the voltage phasors at nodes i and j, respectively. i and δ i V represents the voltage and phase angle at node i, respectively. j and δ j Z represents the voltage and phase angle of node j, respectively; δ represents the phase angle difference between node i and node j; Z represents the line impedance; R represents the line resistance; X represents the line reactance; B / 2 represents the line admittance to ground. and P represents the injected power at node i and the outflow power at node j, respectively. i and Q i P represents the active power injection and reactive power injection at node i, respectively. j and Q j These are the active power outflow and reactive power outflow at node j, respectively. The current flowing through the circuit;

[0119] The power flow equation for line ij, with the terminal voltage as the variable, is as follows:

[0120]

[0121] Expand the above expression separately for the real and imaginary parts:

[0122]

[0123]

[0124] Both equations are about V j A quadratic equation, if the equation has solutions, then satisfies:

[0125] V i 2 sin 2 δ-2BR(P j XQ j R)≥0

[0126]

[0127] According to the voltage V at the end of the line j The voltage stability index L is defined under the condition that a solution exists. V-ij for:

[0128] L V-ij =max(L V1 ,L V2 )

[0129] in,

[0130]

[0131]

[0132] When L V-ij When the index value is greater than 1, the power flow equation with the terminal voltage as the variable has no solution, that is, the line voltage has collapsed and the line is very vulnerable; when the index value is less than 1, the power flow equation with the terminal voltage as the variable has a solution. The closer the index is to 1, the more likely the line ij is to experience voltage collapse under the current operating conditions.

[0133] (2) Capacity margin index

[0134] Establish the capacity margin index L for line ij S-ij :

[0135]

[0136] Among them, S ijS represents the line transmission power of line ij under its current operating state; ij-max This represents the maximum allowable transmission capacity of line ij, which is limited by the thermal stability power limit.

[0137] The capacity margin index overcomes the shortcomings of existing methods. Traditional methods generally reflect the power flow limitation of a line directly as the ratio of active power to maximum transmission power. These methods have two drawbacks: 1) they ignore the transmission of reactive power, leading to overly optimistic load factor calculations; 2) the importance of a line is directly proportional to its load factor, failing to emphasize the importance of lines with high load factors. This index-defined capacity margin index, L... S-ij Taking into account the reactive power flow carried by the line, it can comprehensively reflect the load level of the line; when the line power flow is close to or has exceeded the line capacity limit, the index value will increase significantly, thus reflecting the difference in importance of lines with different load rates.

[0138] (3) Real-time failure rate index

[0139] A three-segment bathtub curve can generally be used to describe the natural aging process of a power line. By statistically analyzing historical fault data, the natural fault rate λ of line ij for a certain period can be obtained. 1-ij ;

[0140] When studying the short-term reliability of a transmission line, the natural failure rate can be used as a benchmark. Considering that severe weather conditions are a highly relevant factor for line failure, the accidental failure rate λ of line ij under severe weather conditions is obtained based on historical statistical data. 2-ij :

[0141]

[0142] in, F represents the statistical average of the failure rate of line ij; ij F represents the probability that line ij will experience extreme weather; ij ′ represents the proportion of line ij that experiences faults under extreme conditions out of the total number of faults;

[0143] The larger of the two failure rates is taken as the real-time failure rate index L of line ij. λ-ij :

[0144] L λ-ij =max{λ 1-ij ,λ 2-ij}

[0145] Step 3: Considering the role of each line in the entire power grid, construct a topological connectivity index based on complex network theory to reflect the interconnection capability of each line in the global power grid.

[0146] From a network structure perspective, the importance of each node and line is related to its topological position. Based on the definition of node degree in complex network theory—that is, the degree of a node is the sum of the number of edges connected to it, and the larger the value, the more important the node is in the network topology—a topological connectivity index L is established for line ij. K-ij :

[0147]

[0148] Among them, K i K j Let i and j be the node degrees, respectively. The average degree of all nodes in the power grid:

[0149]

[0150] Where M is the set of all nodes in the power grid, N is the total number of power grid nodes, and L is the total number of power grid lines;

[0151] The topological connectivity index, established based on the degree of nodes at both ends of a line, characterizes the line's connectivity in the global power grid. The larger the index value, the more important the line's pivotal role in power transmission in the power grid. Line disconnection can easily cause a significant impact on the power grid structure and have a greater impact on system integrity.

[0152] Step 4: After proposing independent evaluation indicators for critical power grid lines, the information carried by the indicator values ​​is mined based on the idea of ​​maximizing deviation. Weights are assigned to various indicators, and the comprehensive importance index value of all lines is calculated. The lines with the largest comprehensive importance index values ​​are selected as critical lines in turn.

[0153] Given m routes, i.e. m evaluation schemes and n evaluation indicators, the set of evaluation indicators is denoted as G = {G1, G2, ..., G...} n Based on the idea of ​​maximizing deviation, the weights of the indicators are determined. Objective weights are considered individually or a combination of subjective and objective weights are taken into account to comprehensively evaluate the importance of the route. Specifically:

[0154] The basic idea of ​​deviation maximization is: if the G of all evaluation schemes i If all index values ​​are equal, then G i The indicators have no effect on the ranking of the evaluation schemes, and their weights can be recorded as 0; conversely, if the G of all evaluation schemes has no effect on the ranking of the schemes, the weights can be recorded as 0. i The greater the difference in index values, the more G... i The indicators will play an important role in ranking the evaluation schemes and should be given greater weight.

[0155] In one embodiment, the weight vector of each indicator is denoted as W = [w1, w2, ..., w n ] TThe weights reflect the information carried by each indicator value. The value of the j-th indicator corresponding to the i-th line is denoted as u. ij U = (u ij ) m×n Let W be the decision matrix; the steps to solve for W are as follows:

[0156] 1) Normalize the evaluation indicators; the indicators in steps 2 and 3 are benefit-type indicators, meaning the larger the value, the higher the importance of the route. They can be normalized as follows:

[0157]

[0158] Where: u j max and u j min These are the corresponding indicators G j The maximum and minimum values;

[0159] 2) Obtain the total deviation of all evaluation indicators from the power grid line; for evaluation indicator G j Without considering the influence of weights, the total deviation of line i from other lines k is denoted as d. ij0 , When considering the influence of weights, the total deviation of line i from other lines k is denoted as d. ij , The total deviation between all lines is denoted as d. ij (G j ),

[0160] 3) Solve the optimization model; for all evaluation indicators G, the total deviation between all lines is denoted as D. Based on the idea of ​​maximizing deviation, the choice of W should maximize the total deviation D, i.e., the following optimization model:

[0161]

[0162]

[0163] The solution is obtained using the Lagrange method. j The normalized optimal solution is:

[0164]

[0165] After calculating W, the decision formula E is applied. i =w1u i1 +w2u i2 +…+w n u in Calculate the overall importance index for all routes and sort the results in descending order.

[0166] In this embodiment, the weight vector W is an objective weight vector.

[0167] In another embodiment, subjective weights based on expert scoring are introduced, and the importance of the route is comprehensively evaluated by combining the idea of ​​maximizing deviation, specifically as follows:

[0168] The original weight vector W of each indicator obtained based on the idea of ​​maximizing deviation is denoted as the objective weight vector, and the subjective weight vector is denoted as W0. * =[w1 * w2 * ,…,w n * ] T Subjective weights are given by evaluation experts based on their experience and knowledge. The steps for determining subjective weights are as follows:

[0169] 1) Please have P power system experts and on-site operation and maintenance personnel assign weighted scores to the evaluation indicators based on their experience working in the power grid of this region. …, For the evaluation index G j Weighted score w j * satisfy And A higher score for a certain indicator indicates that experts believe that the value of that indicator for the local power grid lines should be given special attention.

[0170] 2) Statistical analysis of expert evaluations was performed, and the subjective weight vector W was calculated by taking the average value. * , …,

[0171] Get U and W * Then, the steps to solve for W are as follows:

[0172] 1) Normalize the evaluation indicators;

[0173] 2) Obtain the total deviation of all evaluation indicators from the power grid line; for evaluation indicator G j When considering both objective and subjective weights, the total deviation of line i from other lines k is denoted as d'. ij , The total deviation between all lines is denoted as d'. ij (G j ),

[0174] 3) Solve the optimization model; for all evaluation indicators G, the total deviation between all lines is denoted as D. Based on the idea of ​​maximizing deviation, the choice of W should maximize the total deviation D, i.e., the following optimization model:

[0175]

[0176]

[0177] Using the Lagrange method, w can be obtained. j The normalized optimal solution is:

[0178]

[0179] After calculating W, the decision formula E is applied. i =w1 * w1u i1 +w2 * w2u i2 +…+w n * w n u in Calculate the overall importance index for all routes and sort the results in descending order.

[0180] Step 5: After ranking the lines according to their importance based on a comprehensive importance index, considering the network disconnection caused by line disconnection, a globally optimal power flow load shedding model is proposed. The identified critical lines are disconnected sequentially, and the minimum load loss of the system after a line disconnection is calculated to verify the effectiveness of the identification results. Specifically:

[0181] The objective function for the optimal load shedding is:

[0182]

[0183] Where D is the set of load nodes; P loss-n Let n be the active power loss load.

[0184] The equality constraints for power flow calculation are:

[0185]

[0186]

[0187] Among them, P n and Q n Let P' be the initial active and reactive power of load n, respectively; G is the set of generator nodes; P' is the initial active and reactive power of load n, respectively. m and Q' m Let be the active and reactive power outputs of generator m, respectively; L be the set of lines; ΔP l and ΔQ l These represent the active and reactive power losses of line l, respectively; Q loss-n Let n be the reactive load.

[0188] The inequality constraints for power flow calculation are:

[0189] -S l-max ≤S' l ≤S l-max

[0190] V i min ≤V' i ≤V i max

[0191] P m min ≤P' m ≤P m max

[0192] Q m min ≤Q' m ≤Q m max

[0193] The above equations represent the upper and lower limits of line power flow constraints, the upper and lower limits of voltage at each node, and the upper and lower limits of active and reactive power output of generators, respectively; where S' l S represents the transmission power of line l; l-max V' is the maximum transmission capacity of line l; i V is the voltage at node i; i max and V i min These are the upper and lower voltage limits for node i, respectively; P m max and P m min These represent the upper and lower limits of the active power output of generator m; Q m max and Q m min These are the upper and lower limits of the reactive power output of generator m, respectively;

[0194] If the power factor of the original load is not changed when the load is shelved, then the power factor constraint for load shelving is:

[0195]

[0196] in, Let n be the initial power factor of the load.

[0197] After the line is disconnected, the optimal load loss of the system is calculated. The greater the load loss, the more important the line is.

[0198] Example

[0199] Based on the comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation, using the standard IEEE 39-bus system (such as...) Figure 2 Taking the example shown, we identify the critical path in the system. The example assumes the maximum transmission capacity of the path is the thermal stability limit, and the real-time failure rate of the path is proportional to its impedance.

[0200] Based on the definitions of the four categories of indicators selected—voltage stability, capacity margin, real-time failure rate, and topology connectivity—the values ​​of each indicator were calculated, and the top 10 lines of importance in the system were identified as critical lines in descending order. The results are shown in Table 1.

[0201] Table 1 Key Path Identified by Single Indicator

[0202] Sort <![CDATA[L V ]]> <![CDATA[L S ]]> <![CDATA[L λ ]]> <![CDATA[L K ]]> 1 26-29 16-19 26-29 16-17 2 23-24 21-22 26-28 16-19 3 16-19 6-11 11-12 2-3 4 21-22 2-3 12-13 5-6 5 1-2 23-24 1-2 6-11 6 26-28 28-29 8-9 2-25 7 2-3 10-11 23-24 25-26 8 28-29 16-21 25-26 26-29 9 6-7 10-13 14-15 15-16 10 8-9 4-14 3-4 16-21

[0203] Based on the aforementioned single identification index, the values ​​of each index are normalized. Using the deviation maximization decision model, the objective weights of each index are obtained as W = [0.0889, 0.3290, 0.2511, 0.3311]. T Therefore, the overall importance index value of the system's lines can be obtained, such as... Figure 3 As shown.

[0204] The critical lines identified were disconnected one by one, and the system load shedding was calculated using the optimal power flow load shedding model. The results were compared with existing identification methods, and four calculation examples were constructed. C1-C4 represent the critical lines identified by disconnecting one by one according to the method of this invention, electrical betweenness (Xu Lin, Wang Xiuli, Wang Xifan. Electrical betweenness and its application in the identification of critical lines in power systems [J]. Proceedings of the CSEE, 2010, 30(1): 33-39.), active power flow betweenness (Zhang Tao, Sun Xiaowei, Xu Xueqin, et al. Identification of critical lines in power grids based on active power flow betweenness [J]. Power System Technology, 2016, 40(1): 193-198.), and power flow entropy (Li Yong, Liu Junyong, Liu Xiaoyu, et al. Vulnerability assessment of power grid cascading fault propagation elements based on power flow entropy [J]. Automation of Electric Power Systems, 2012, 36(19): 11-16.). The changes in the optimal load shedding of the system under different operating conditions are as follows: Figure 4 As shown.

[0205] It can be seen that when the first 10 critical lines are disconnected sequentially according to the identification results of the method of this invention, the optimal power flow load shedding is the highest, the average growth rate is the fastest, and the system load loss reaches 1981.7MW after disconnecting the 10 critical lines. The system load loss after disconnecting the other three methods is 1424.3MW, 1864.2MW, and 1461.5MW, respectively.

[0206] According to the identification results of the method of this invention, when the first line 16-19 is disconnected, the system will split into two parts, resulting in a significant change in the power grid structure. Furthermore, the generators at nodes 33 and 34 will be disconnected from the main grid, hindering power transmission. While the isolated islands disconnected from the main grid (including nodes 19, 20, 33, and 34) can maintain power balance by adjusting generator output, the main grid needs to cut off 447.6 MW of load, leading to a sharp increase in system load loss. After disconnecting the fifth line 23-24 and the seventh line 21-22, the island formed by nodes 22, 23, 35, and 36 is disconnected from the main grid, and the power transmission channels for the generators at nodes 35 and 36 are completely cut off, causing another increase in the main grid load loss. Disconnecting the eighth line 16-21 cuts off the power supply to the load at node 21, requiring the complete disconnection of this load, resulting in an additional loss of 274 MW of load. When the tenth line is disconnected, nodes 16 and 24 are completely disconnected from the grid, and because there is no generator power supply, the load at both nodes is completely lost.

[0207] Furthermore, three experts were introduced to assign weighted scores, and the calculated average subjective weights were W. * =[0.3,0.35,0.05, 0.3] T Based on the deviation maximization decision model with comprehensive subjective and objective weighting, the objective weights of each indicator are obtained as W = [0.1747, 0.5034, 0.0400, 0.2775]. T Therefore, the overall importance index value of the system's lines can be obtained, such as... Figure 5 As shown.

[0208] Disconnect the identified critical paths one by one. The changes in the optimal load shedding amount of the system under different operating conditions in the C1-C4 examples are as follows: Figure 6 As shown, when the first 10 critical lines are disconnected sequentially according to the identification results of the method of the present invention, the optimal power flow load shedding is the highest, the average growth rate is the fastest, and the system load loss reaches 2317.3MW after disconnecting the 10 critical lines.

[0209] According to the identification results of the method of this invention, when the first line 16-19 is disconnected, the system will split into two parts, resulting in a significant change in the power grid structure. Furthermore, the generators at nodes 33 and 34 will be disconnected from the main grid, hindering power transmission. While the isolated islands disconnected from the main grid (including nodes 19, 20, 33, and 34) can maintain power balance by adjusting generator output, the main grid needs to cut 447.6 MW of load, leading to a sharp increase in system load loss. When the fourth line 21-22 is disconnected, the generators at nodes 35 and 36 will have their power transmission hindered, only able to transmit power through line 23-24. However, limited by the maximum transmission power of line 23-24 (600 MW), generator output will decrease, and the system load loss will also increase significantly. When the sixth line 23-24 is disconnected, the island formed by nodes 22, 23, 35, and 36 will be disconnected from the main grid, and the power transmission channels for the generators at nodes 35 and 36 will be completely cut off, causing another increase in main grid load loss. Disconnecting the seventh line (16-21) cut off power supply to the load at node 21, necessitating the complete disconnection of that load and resulting in an additional load loss of 274MW. When the tenth line was disconnected, the island formed by nodes 10, 11, 12, 13, and 32 was disconnected from the main grid. The generator at node 32 only needed to supply power to the load at node 12 (8.53MW), and the excess output could not be transmitted to the main grid, causing a significant increase in the main grid's load loss.

[0210] The above analysis shows that, compared with existing methods, the comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation provided by this invention fully considers the local and global characteristics of the power grid, mines the information carried by various identification indicators, improves the identification accuracy of critical power grid lines, and has guiding significance for the operation and maintenance management of transmission lines.

[0211] The above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A comprehensive identification method for critical power grid lines based on the idea of ​​maximizing deviation, characterized in that, Includes the following steps: Step 1: Obtain power grid structure information, line parameters, transformer parameters, generator parameters, and load parameters, and calculate the power grid parameters under the current operating conditions; Step 2: Considering the inherent vulnerability of the line, construct the following three indicators: A voltage stability index is constructed based on static voltage safety assessment to reflect the local line voltage stability; A capacity margin index is constructed based on the line load level to reflect the importance of lines with high local load rates; A real-time failure rate index is constructed based on accidental failures under severe weather conditions to reflect the short-term reliability of local lines. Step 3: Considering the role of each line in the entire power grid, construct a topology connectivity index based on complex network theory to reflect the interconnection capability of each line in the global power grid; Step 4: After proposing independent evaluation indicators for critical power grid lines, the information carried by the indicator values ​​is mined based on the idea of ​​maximizing deviation. Weights are assigned to various indicators, and the comprehensive importance index value of all lines is calculated. The lines with the largest comprehensive importance index values ​​are selected as critical lines in turn. Specifically: Given m routes, i.e. m evaluation schemes and n evaluation indicators, the set of evaluation indicators is denoted as G = {G1, G2, ..., G...} n Based on the idea of ​​maximizing deviation and taking into account both subjective and objective weights, a comprehensive evaluation of the importance of the route is conducted, specifically as follows: The objective weight vector of each indicator is denoted as W = [w1, w2, ..., w n ] T The objective weights reflect the information carried by each indicator value; the value of the j-th indicator corresponding to the i-th line is denoted as u. ij U = (u ij ) m×n For decision matrix; Let the subjective weight vector be denoted as W. * =[w1 * w2 * ,…,w n * ] T Subjective weights are given by evaluation experts based on their experience and knowledge. The steps for determining subjective weights are as follows: 1) Please have P power system experts and on-site operation and maintenance personnel assign weighted scores to the evaluation indicators based on their experience working in the power grid of this region. For the evaluation index G j Weighted score w j * satisfy and A higher score for a certain indicator indicates that experts believe that the value of that indicator for the local power grid lines should be given special attention. 2) Statistical analysis of expert evaluations was performed, and the subjective weight vector W was calculated by taking the average value. * , The steps to solve for the objective weight vector W are as follows: 1) Normalize the evaluation indicators; 2) Obtain the total deviation of all evaluation indicators from the power grid line; for evaluation indicator G j Taking into account both objective and subjective weights, the total deviation of line i from other lines k is denoted as d′. i ' j , The total deviation between all lines is denoted as d′. ij (G j ), 3) Solve the optimization model; For all evaluation indicators G, the total deviation between all lines is denoted as D. Based on the idea of ​​maximizing deviation, the choice of W should maximize the total deviation D, i.e., the following optimization model: Using the Lagrange method, w can be obtained. j The normalized optimal solution is: After calculating the objective weight vector W, the decision formula E is applied. i =w1 * w1u i1 +w2 * w2u i2 +…+w n * w n u in Calculate the overall importance index for all routes and sort the results in descending order.

2. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 1, the grid voltage level and the highest and lowest voltage amplitude of each node are obtained, the connection relationship between nodes and lines is clarified, and the grid topology is drawn; the resistance, reactance and susceptance of each line are obtained, as well as their thermal stability power limit values; the turns ratio of each transformer is obtained; the maximum and minimum power limits of each generator are obtained; and the power values ​​of the load nodes are obtained. Based on the above information, power flow calculations are performed using power system analysis software or programs to obtain the grid node voltage and line power flow data under the current operating conditions.

3. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 2, the voltage stability index is constructed as follows: Starting from the solution conditions of the power flow equation with the terminal voltage as the variable, a voltage stability index is constructed. For a typical π-type equivalent line ij, where i is the starting node and j is the ending node, V i ∠δ i and V j ∠δ j V represents the voltage phasors at nodes i and j, respectively. i and δ i V represents the voltage and phase angle at node i, respectively. j and δ j Z represents the voltage and phase angle of node j, respectively; δ represents the phase angle difference between node i and node j; Z represents the line impedance; R represents the line resistance; X represents the line reactance; B / 2 represents the line admittance to ground. and Let P be the injected power at node i and the outflow power at node j, respectively; i and Q i P represents the active power injection and reactive power injection at node i, respectively. j and Q j These are the active power outflow and reactive power outflow at node j, respectively. The current flowing through the circuit; The power flow equation for line ij, with the terminal voltage as the variable, is: Expand the above expression separately for the real and imaginary parts: Both equations are about V j A quadratic equation, if the equation has solutions, then satisfies: V i 2 sin 2 δ-2BR(P j XQ j R)≥0 According to the voltage V at the end of the line j The voltage stability index L is defined under the condition that a solution exists. V-ij for: L V-ij <max(L V1 ,L V2 ) in, When L V-ij When the index value is greater than 1, the power flow equation with the terminal voltage as the variable has no solution, that is, the line voltage has collapsed and the line is very vulnerable; when the index value is less than 1, the power flow equation with the terminal voltage as the variable has a solution. The closer the index is to 1, the more likely the line ij is to experience voltage collapse under the current operating conditions.

4. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 2, the capacity margin index is constructed as follows: Establish the capacity margin index L for line ij S-ij : Among them, S ij S represents the line transmission power of line ij under its current operating state; ij-max This represents the maximum allowable transmission capacity of line ij, which is limited by the thermal stability power limit. Capacity margin index L S-ij It takes into account the reactive power flow carried by the line, and can comprehensively reflect the load level of the line; when the line power flow is close to or has exceeded the line capacity limit, the index value will increase significantly.

5. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 2, the construction of the real-time failure rate indicator is specifically as follows: A three-segment bathtub curve is used to describe the natural aging process of the line. The natural failure rate λ of line ij for a certain period is obtained by statistically analyzing historical fault data of the line. 1-ij ; Based on historical statistical data, the accidental failure rate λ of line ij under severe weather conditions was obtained. 2-ij : in, F represents the statistical average of the failure rate of line ij; ij F represents the probability that line ij will experience extreme weather; ij ′ represents the proportion of line ij that experiences faults under extreme conditions out of the total number of faults; The larger of the two failure rates is taken as the real-time failure rate index L of line ij. λ-ij : L λ-ij =max{λ 1-ij ,l 2-ij }。 6. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 3, a topological connectivity index is constructed considering the role of the line in the entire power grid, specifically as follows: Establish the topological connectivity index L for line ij K-ij : Among them, K i K j Let i and j be the node degrees, respectively. The average degree of all nodes in the power grid: Where M is the set of all nodes in the power grid, N is the total number of power grid nodes, and L is the total number of power grid lines; The topological connectivity index, established based on the degree of nodes at both ends of a line, characterizes the line's connectivity in the global power grid. The larger the index value, the more important the line's pivotal role in power transmission in the power grid. Line disconnection can easily cause a significant impact on the power grid structure and have a greater impact on system integrity.

7. The method for comprehensive identification of critical power grid lines based on the idea of ​​maximizing deviation, as described in claim 1, is characterized in that... In step 4, after ranking the lines according to their importance based on a comprehensive importance index, and considering the network disconnection caused by line disconnection, a globally optimal power flow load shedding model is proposed. The identified critical lines are disconnected sequentially, and the minimum load loss of the system after a line disconnection is calculated to verify the effectiveness of the identification results. Specifically: The objective function for the optimal load shedding is: Where D is the set of load nodes; P loss-n Let n be the active power loss load. The equality constraints for power flow calculation are: Among them, P n and Q n Let P' be the initial active and reactive power of load n, respectively; G is the set of generator nodes; P' is the initial active and reactive power of load n, respectively; m and Q' m Let be the active and reactive power outputs of generator m, respectively; L be the set of lines; ΔP l and ΔQ l These represent the active and reactive power losses of line l, respectively; Q loss-n Let n be the reactive load. The inequality constraints for power flow calculation are: -S l-max ≤S′ l ≤S l-max In i min ≤V i '≤V i max P m min ≤P′ m ≤P m max Q m min ≤Q' m ≤Q m max The above equations represent the upper and lower limits of line power flow constraints, the upper and lower limits of voltage at each node, and the upper and lower limits of active and reactive power output of generators, respectively; where S′ l S represents the transmission power of line l; l-max V represents the maximum transmission capacity of line l; i 'V' represents the voltage at node i; i max and V i min These are the upper and lower voltage limits for node i, respectively; P m max and P m min These represent the upper and lower limits of the active power output of generator m; Q m max and Q m min These are the upper and lower limits of the reactive power output of generator m, respectively; If the power factor of the original load is not changed when the load is shelved, then the power factor constraint for load shelving is: in, Let n be the initial power factor of the load. After the line is disconnected, the optimal load loss of the system is calculated. The greater the load loss, the more important the line is.

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