Method for evaluating post-earthquake toughness of multi-scale power system

Abstract

The invention discloses a multi-scale power system post-earthquake toughness evaluation method, which comprises the following steps: collecting network topology structure information of a power system and a transformer substation, and collecting damage probability information of key equipment in the transformer substation and a power transmission tower on a power transmission line; establishing an urban power grid linear power flow model, and establishing post-earthquake function and toughness evaluation indexes of a power system and post-earthquake function evaluation indexes of a transformer substation; obtaining the equipment damage and line damage conditions of the transformer substation in each earthquake scene through simulation; evaluating post-earthquake function evaluation indexes and power transmission line functions of the transformer substation based on the damage condition; establishing a system load flow calculation model of the post-earthquake power system, and calculating the post-earthquake function of the power system; and outputting post-earthquake function distribution and toughness evaluation results of the power system. The method can consider the influence of the damage of the earthquake to the infrastructure in the power system such as the transformer substation and the transmission tower on the system function of the power system, and helps a manager comprehensively evaluate the anti-seismic toughness of the power system.

Description

Technical Field

[0001] The invention relates to a multi-scale power system post-earthquake resilience assessment method. Background Art

[0002] The impact of earthquake disasters on power systems has become an important topic that needs to be studied in depth in the field of power engineering. The destructive events caused by earthquakes not only cause direct damage to power facilities, but also lead to extensive economic losses and casualties. According to statistics, major earthquake events often cause economic losses of billions to tens of billions of dollars, which poses a severe challenge to the sustainable development of the country and society.

[0003] At present, the technical means for assessing the resilience of power systems are mostly focused on the damage analysis of lines and nodes. Although this method reveals the vulnerability of power systems under earthquakes to a certain extent, its assessment effect is relatively simple and fails to fully consider the complex structural characteristics of power systems. The power system is not only composed of high-voltage transmission lines and distribution networks, but also involves infrastructure in key hub layers such as substations and switchgear, as well as core equipment such as transformers and transmission towers, ultimately forming a multi-scale complex network structure with multi-level structures and multi-type equipment. There are complex interdependencies between these key elements, and damage to each infrastructure in the power system may lead to more serious systemic failures.

[0004] Therefore, there is an urgent need for a new resilience assessment method that can comprehensively consider the complexity of various infrastructures in the power system, so as to more comprehensively assess the vulnerability, response capability and recovery potential of the power system under earthquake disasters. This will provide a theoretical basis and technical support for improving the seismic resilience of the power system and reducing the cost of post-disaster recovery. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method that can characterize the impact of complex infrastructure such as substations and transmission towers in the power system on the entire power system, help managers fully understand the seismic performance of the power system, and accurately evaluate the seismic resilience of the power system to earthquake disasters.

[0006] The objective of the present invention is achieved through the following technical solution: A multi-scale power system post-earthquake resilience assessment method comprises the following steps:

[0007] Step 1: Collect network topology information of the power system, obtain substation topology information of the power system and equipment damage information in the substation, transmission tower location information and damage probability information on the transmission line;

[0008] Step 2: Establish a linear power flow model of the urban power grid under the condition of no disaster operation; by solving the model, obtain the load supply information of each node of the power system under the condition of no earthquake disaster, establish the post-earthquake function and resilience evaluation index of the power system and the post-earthquake function evaluation index of the substation;

[0009] Step 3: Collect historical earthquake information in the region, simulate earthquake scenarios based on the earthquake information, and obtain the damage to substation equipment and lines in each earthquake scenario;

[0010] Step 4: Evaluate the post-earthquake function evaluation index of the substation based on the damage of the substation equipment, and evaluate the function of the transmission line based on the damage of the transmission towers on the transmission line;

[0011] Step 5: Based on the functional information of substations and transmission lines, establish a system flow calculation model for the post-earthquake power system and calculate the post-earthquake function of the power system under each damage scenario;

[0012] Step 6: Based on the results obtained by the algorithm, output the post-earthquake functional distribution and resilience evaluation results of the power system.

[0013] Furthermore, the linear power flow model of the power system in the non-disaster situation in step 2 is calculated using a DC power flow model, with the goal of maximizing the load required by users, which is specifically expressed as:

[0014]

[0015] Where N represents the set of power system nodes, including substation nodes and user load nodes, L represents the set of transmission lines in the power system, and w i represents the node weight, d i represents the actual node load supplied, p i Represents the power generation of the power generation nodes, including distributed generation and substations, with the set N p It means that f ij represents the flow through line (i, j), x ij represents the reactance, θ j represents the phase angle, Maximum power generation, including the maximum allowable output power of the substation and the power generation of distributed power sources, The maximum required load of the node, Maximum line load.

[0016] The objective function is to maximize the sum of weighted loads of users. By solving the model, we can obtain the power load that the power system can supply to each node before the earthquake.

[0017] The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the weighted load that can be satisfied after the earthquake to the weighted load that can be satisfied before the earthquake, which can be expressed as:

[0018]

[0019] in, represents the load that can be supplied to node i in the post-earthquake scenario ξ.

[0020] The resilience evaluation index of the power system is defined as the expected functional value of all damage scenarios after the earthquake, which is specifically expressed as:

[0021] R=E ξ (F(ξ)) (9)

[0022] Where R represents the resilience evaluation value of the power system, It means taking the expected value of ξ for all post-earthquake damage scenarios.

[0023] The post-earthquake system function of the substation is defined as the ratio of the number of normal output lines after the earthquake to the total number of original output lines, which can be expressed as:

[0024]

[0025] Among them, B represents the post-earthquake system function of the substation, m represents that before the earthquake, the substation has at most m lines working, and N i / m It means that after the substation is shaken, at most i lines are available for use.

[0026] Furthermore, the earthquake scene simulation in step 3 uses the GR law, an empirical formula for earthquake activity, to statistically analyze historical earthquake data, which is specifically expressed as:

[0027] lgN M =a-bM (11)

[0028] Among them, N M is the number of earthquakes with magnitude greater than or equal to M; a is the level of earthquake activity; and b reflects the proportional relationship between the magnitude of earthquake activity and the number of earthquakes.

[0029] The earthquake magnitude is randomly generated based on random numbers. The specific calculation formula is:

[0030] N M =-ln(1-z) (12)

[0031]

[0032] Wherein, z represents a random number between 0 and 1.

[0033] The calculation method of the earthquake motion attenuation curve is as follows:

[0034] lgY=A+BM-Clg(R+De EM ) (14)

[0035] Among them, Y represents the seismic parameters, M is the magnitude, R is the epicenter distance, and A, B, C, D and E are regression coefficients.

[0036] Furthermore, the post-earthquake system function evaluation method of the substation in step 4 is calculated by calculating the maximum number of lines available for output inside the substation, which is specifically expressed as:

[0037] maxB ξ (15)

[0038] st

[0039]

[0040]

[0041] Among them, N s represents the set of equipment nodes in the substation, D s represents the sink set, L s represents the set of lines in the substation, where B ξ It is expressed as the number of lines available for output from the substation under the post-earthquake damage scenario ξ, represents the flow from device node i to device node j in the post-earthquake damage scenario ξ, s i Indicates the status of device node i, 1 indicates intact, 0 indicates damaged, M indicates a sufficiently large number, c ij Indicates the maximum capacity of the line.

[0042] The objective function is to maximize the output line B of the substation ξ , the system function calculation formula of the substation is C j Indicates the maximum system function of the substation.

[0043] Furthermore, the power system linear power flow model under the post-earthquake damage scenario ξ in step 5 takes into account the damage of the transmission line and the substation. The damage of the transmission line causes the line to be unable to transmit power, and the damage of the substation causes the transmission capacity of the substation to be reduced. It can be specifically expressed as:

[0044]

[0045] Among them, w i d i 、p i 、f ij 、x ij ,θ j , The meaning is the same as the system power flow model in step 2, s ij Indicates the status of the transmission line (i, j), 1 means intact, 0 means damaged, N s represents the substation set, u j It represents the power load capacity that the substation can output under the post-earthquake damage scenario.

[0046] The objective function is to maximize the sum of the weighted loads of nodes that can be satisfied after the earthquake.

[0047] The beneficial effect of the present invention is that the method of the present invention proposes a multi-scale power system post-earthquake resilience assessment method, which can consider the impact of earthquake damage to infrastructure in the power system such as substations and transmission towers on the system function of the power system, and help managers comprehensively evaluate the seismic resilience of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic flow chart of the multi-scale power system post-earthquake resilience assessment method of the present invention;

[0049] Figure 2 A schematic diagram of the power system used in this embodiment;

[0050] Figure 3 A system schematic diagram of a substation used in this embodiment;

[0051] Figure 4 This is a post-earthquake system function distribution diagram of the power system of this embodiment. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0053] like Figure 1 As shown, a multi-scale power system post-earthquake resilience assessment method of the present invention comprises the following steps:

[0054] Step 1: Collect the network topology information of the power system (load information on network nodes, network connection relationship, etc.), obtain the substation topology information of the power system (including the location information of the substation in the power system, the topology structure and system function inside the substation) and the equipment damage information in the substation (the mean and variance of the equipment damage probability), the transmission tower location information on the transmission line (the location information of the transmission tower) and the damage probability information (the mean and variance of the damage probability of the transmission tower);

[0055] This embodiment uses Figure 2 The power system topology with 17 nodes shown in the figure is used as the analysis object. The voltage of node 15 power supply point is 1.05Un, and the active power of the network is 3.715MW. Figure 2Nodes 15, 16, and 17 are 220kV substation nodes.

[0056] Figure 2 The network topology information and node information of the power system shown are shown in Table 1, where the longitude and latitude information of the first node are represented by the difference distance from the set zero point position, and the weight of each node is 1.

[0057] Table 1

[0058]

[0059]

[0060] In this embodiment, the failure probability of each device in the substation and the transmission tower on the transmission line is expressed by the response curve of the peak acceleration of the earthquake using the logarithmic normal distribution cumulative distribution curve:

[0061]

[0062] Where P represents the failure probability, x represents the value of the peak acceleration of the earthquake motion, Φ(·) represents the normal distribution cumulative distribution function, θ represents the logarithmic mean, and β represents the logarithmic standard deviation.

[0063] Figure 2 Each line contains at least one transmission tower per kilometer, which is evenly distributed on the transmission line. The logarithmic mean of the failure probability curve is 0.52, and the logarithmic variance of the failure probability curve is 0.22.

[0064] In this embodiment, the substation adopts a 220kV substation structure. Figure 3 The network topology of a 220 kV substation node with 12 output lines without earthquake damage is shown, where the damage probability of each device in the substation is shown in Table II.

[0065] Table 2

[0066]

[0067]

[0068] The parameters used in this embodiment and their meanings are shown in Table 3.

[0069] Table 3

[0070]

[0071]

[0072] Step 2: Establish a linear power flow model of the urban power grid under the condition of no disaster operation, which is specifically expressed as:

[0073]

[0074] Where N represents the set of power system nodes, including substation nodes and user load nodes, L represents the set of transmission lines in the power system, and w i represents the node weight, d i represents the actual node load supplied, p i Represents the power generation of the power generation nodes, including distributed generation and substations, with the set N p It means that f ij represents the flow through line (i, j), x ij represents the reactance, θ j represents the phase angle, Maximum power generation, including the maximum allowable output power of the substation and the power generation of distributed power sources, The maximum required load of the node, Maximum line load.

[0075] The objective function is to maximize the sum of weighted loads of users. By solving the model, the load supply information of each node in the power system is obtained when no earthquake disaster occurs. The results show that the load demand of all nodes can be met in this embodiment, that is,

[0076] Establish post-earthquake function and resilience assessment indicators for power systems and post-earthquake function assessment indicators for substations;

[0077] The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the weighted load that can be satisfied after the earthquake to the weighted load that can be satisfied before the earthquake, which can be expressed as:

[0078]

[0079] Among them, d i (ξ) represents the load that can be supplied to node i in the post-earthquake scenario ξ.

[0080] The resilience evaluation index of the power system is defined as the expected functional value of all damage scenarios after the earthquake, which is specifically expressed as:

[0081] R=E ξ (F(ξ)) (9)

[0082] Where R represents the resilience evaluation value of the power system, It means taking the expected value of ξ for all post-earthquake damage scenarios.

[0083] The post-earthquake system function of the substation is defined as the ratio of the number of normal output lines after the earthquake to the total number of original output lines, which can be expressed as:

[0084]

[0085] Among them, B represents the post-earthquake system function of the substation, m represents that before the earthquake, the substation has at most m lines working, and N i / m It means that after the substation is shaken, at most i lines are available for use.

[0086] Step 3: Collect historical earthquake information in the region and use the GR law, an empirical formula for earthquake activity, to calculate historical earthquake data. Specifically, it can be expressed as:

[0087] lgN M =a-bM (11)

[0088] Among them, N M is the number of earthquakes with magnitude greater than or equal to M; a is the level of earthquake activity; and b reflects the proportional relationship between the magnitude of earthquake activity and the number of earthquakes.

[0089] The earthquake magnitude is randomly generated based on random numbers. The specific calculation formula is:

[0090] N M =-ln(1-z) (12)

[0091]

[0092] Wherein, z represents a random number between 0 and 1.

[0093] The calculation method of the earthquake motion attenuation curve is as follows:

[0094] lgY=A+BM-Clg(R+De EM ) (14)

[0095] Among them, Y represents the seismic parameters, M is the magnitude, R is the epicenter distance, and A, B, C, D and E are regression coefficients.

[0096] In this embodiment, the parameters a=15, b=3, and the random number 0-1 are generated by the system. The calculation method of the earthquake motion attenuation curve in this embodiment is as follows:

[0097] lgPGA=0.583+0.451M-0.8521lg(R+0.182e 0.707M ) (15)

[0098] Among them, PGA is the peak acceleration of the earthquake, and the earthquake center is located at Figure 2 The number of simulations is set to 1000, and the damage of substation equipment and lines under each earthquake scenario is obtained by Monte Carlo simulation.

[0099] Step 4: The post-earthquake system function evaluation method of the substation is calculated by calculating the maximum number of lines available for output inside the substation, which is specifically expressed as:

[0100]

[0101] Among them, N s represents the set of equipment nodes in the substation, D s represents the sink set, L s represents the set of lines in the substation, where B ξ It is expressed as the number of lines available for output from the substation under the post-earthquake damage scenario ξ, represents the flow from device node i to device node j in the post-earthquake damage scenario ξ, s i Indicates the status of device node i, 1 indicates intact, 0 indicates damaged, M indicates a sufficiently large number, c ij Indicates the maximum capacity of the line.

[0102] The objective function is to maximize the output line B of the substation ξ , the system function calculation formula of the substation is C j Indicates the maximum system function of the substation.

[0103] The transmission lines on the power system include multiple transmission towers. If one transmission tower collapses, the transmission line is considered damaged.

[0104] Step 5: Based on the functional information of substations and transmission lines, establish the system flow calculation model of the post-earthquake power system, which is specifically expressed as follows:

[0105]

[0106]

[0107] Among them, w i d i 、p i 、f ij 、x ij ,θ j , The meaning is the same as the system power flow model in step 2, s ij Indicates the status of the transmission line (i, j), 1 means intact, 0 means damaged, N s represents the substation set, u j It represents the power load capacity that the substation can output under the post-earthquake damage scenario.

[0108] The objective function is to maximize the sum of the weighted loads of nodes that can be satisfied after the earthquake.

[0109] This model can be used to calculate the post-earthquake function F(ξ) of the power system under each damage scenario.

[0110] Step 6: Based on the system functions in each scenario calculated in step 5, output the post-earthquake function distribution of the power system, such as Figure 4 As shown, the resilience evaluation value of the power system is calculated by taking the expected value of the system function under all damage scenarios. The resilience evaluation result in this embodiment is 0.2997.

[0111] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A multi-scale power system post-earthquake resilience assessment method, characterized in that: The steps include: Step 1: Collect network topology information of the power system, obtain substation topology information of the power system and equipment damage information in the substation, transmission tower location information and damage probability information on the transmission line; Step 2: Establish a linear power flow model of the urban power grid under the condition of no disaster operation; by solving the model, obtain the load supply information of each node of the power system under the condition of no earthquake disaster, establish the post-earthquake function and resilience evaluation index of the power system and the post-earthquake function evaluation index of the substation; Step 3: Collect historical earthquake information in the region, simulate earthquake scenarios based on the earthquake information, and obtain the damage to substation equipment and lines in each earthquake scenario; Step 4: Evaluate the post-earthquake function evaluation index of the substation based on the damage of the substation equipment, and evaluate the function of the transmission line based on the damage of the transmission towers on the transmission line; Step 5: Based on the functional information of substations and transmission lines, establish a system flow calculation model for the post-earthquake power system and calculate the post-earthquake function of the power system under each damage scenario; Step 6: Based on the results obtained by the algorithm, output the post-earthquake functional distribution and resilience evaluation results of the power system.

2. The multi-scale power system post-earthquake resilience assessment method according to claim 1 is characterized in that: The linear power flow model of the power system in the non-disaster situation in step 2 is calculated using the DC power flow model, with the goal of maximizing the load required by users, which can be specifically expressed as: st Where N represents the set of power system nodes, including substation nodes and user load nodes, L represents the set of transmission lines in the power system, and w i represents the node weight, d i represents the actual node load supplied, p i Represents the power generation of the power generation nodes, including distributed generation and substations, with the set N p It means that f ij represents the flow through line (i, j), x ij represents the reactance, θ j represents the phase angle, Maximum power generation, including the maximum allowable output power of the substation and the power generation of distributed power sources, The maximum required load of the node, Maximum line load; The objective function is to maximize the sum of weighted loads of users. By solving the model, we can obtain the power load that the power system can supply to each node before the earthquake. The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the weighted load that can be satisfied after the earthquake to the weighted load that can be satisfied before the earthquake, which can be expressed as: in, represents the load that can be supplied to node i in the post-earthquake scenario ξ; The resilience evaluation index of the power system is defined as the expected functional value of all damage scenarios after the earthquake, which is specifically expressed as: R=E ξ (F(ξ)) (9) Where R represents the resilience evaluation value of the power system, represents the expected value of ξ for all post-earthquake damage scenarios; The post-earthquake system function of the substation is defined as the ratio of the number of normal output lines after the earthquake to the total number of original output lines, which can be expressed as: Among them, B represents the post-earthquake system function of the substation, m represents that before the earthquake, the substation has at most m lines working, and N i / m It means that after the substation is shaken, at most i lines are available for use.

3. The multi-scale power system post-earthquake resilience assessment method according to claim 1 is characterized in that: The earthquake scenario simulation in step 3 uses the GR law, an empirical formula for earthquake activity, to calculate historical earthquake data, which is specifically expressed as: lgN M =a-bM (11) Among them, N M is the number of earthquakes with magnitude greater than or equal to M; a is the level of earthquake activity; b reflects the proportional relationship between the magnitude of earthquake activity and the number of earthquakes; The earthquake magnitude is randomly generated based on random numbers. The specific calculation formula is: N M =-ln(1-z) (12) Among them, z represents a 0-1 random number; The calculation method of the earthquake motion attenuation curve is as follows: lgY=A+BM-Clg(R+De EM ) (14) Among them, Y represents the seismic motion parameter, M is the magnitude, R is the epicenter distance, and A, B, C, D and E are regression coefficients.

4. The multi-scale power system post-earthquake resilience assessment method according to claim 1, characterized in that: The post-earthquake system function evaluation method of the substation in step 4 is calculated by calculating the maximum number of lines available for output inside the substation, which is specifically expressed as: maxB ξ (15)s.t. Among them, N s represents the set of equipment nodes in the substation, D s represents the sink set, L s represents the set of lines in the substation, where B ξ It is expressed as the number of lines available for output from the substation under the post-earthquake damage scenario ξ, represents the flow from device node i to device node j in the post-earthquake damage scenario ξ, s i Indicates the status of device node i, 1 indicates intact, 0 indicates damaged, M indicates a sufficiently large number, c ij Indicates the maximum capacity of the line; The objective function is to maximize the output line B of the substation ξ , the system function calculation formula of the substation is C j Indicates the maximum system function of the substation.

5. The multi-scale power system post-earthquake resilience assessment method according to claim 1, characterized in that: The linear power flow model of the power system under the post-earthquake damage scenario ξ in step 5 takes into account the damage of the transmission lines and substations. The damage of the transmission lines causes the lines to be unable to transmit power, and the damage of the substations reduces the transmission capacity of the substations. It can be specifically expressed as: st Among them, w i d i 、p i 、f ij 、x ij ,θ j , The meaning is the same as the system power flow model in step 2, s ij Indicates the status of the transmission line (i, j), 1 means intact, 0 means damaged, N s represents the substation set, u j It represents the power load capacity that the substation can export under the post-earthquake damage scenario ξ; The objective function is to maximize the sum of the weighted loads of nodes that can be satisfied after the earthquake.

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