A method for post-earthquake resilience assessment of a multi-scale power system

Abstract

The application discloses a kind of post-earthquake resilience evaluation methods of multi-scale power system, comprising the following steps: collecting the network topology structure information of power system and substation, collecting the damage probability information of key equipment in substation and transmission tower on transmission line;Establish a linear power flow model of urban power grid, establish post-earthquake function and resilience evaluation index of power system and post-earthquake function evaluation index of substation;Through simulation, obtain the damage of substation equipment, line damage condition under each seismic scenario;Based on the damage condition, evaluate the post-earthquake function evaluation index of substation and the function of transmission line;Establish the system power flow calculation model of post-earthquake power system, calculate the post-earthquake function of power system;Output the post-earthquake function distribution and resilience evaluation result of power system.The application can consider the influence of earthquake on the damage of infrastructure in power system, such as substation and transmission tower, on the system function of power system, to help managers to comprehensively evaluate the anti-seismic resilience of power system.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of multi-scale power system post-earthquake resilience evaluation method. BACKGROUND

[0002] The influence of earthquake disaster on power system has become an important issue in the field of power engineering that needs in-depth research. The destructive events caused by earthquakes not only cause direct damage to power facilities, but also lead to widespread economic losses and casualties. According to statistics, major earthquake events often result in billions to tens of billions of dollars in economic losses, which poses a serious challenge to the sustainable development of the country and society.

[0003] Currently, the technical means for power system resilience evaluation mainly focuses on the damage analysis of lines and nodes. Although this method reveals the vulnerability of power system under the action of earthquake to some extent, its evaluation effect is relatively single, and the complex structural characteristics of power system are not fully considered. Power system is not only composed of high-voltage transmission lines and distribution networks, but also involves infrastructure in key hubs such as substations, switch cabinets, and core equipment such as transformers and transmission towers, ultimately forming a multi-level structure, multi-type equipment, and multi-scale complex network structure. There is a complex interdependence between these key elements, and the damage of each infrastructure in the power system may further lead to more serious systemic failures.

[0004] Therefore, there is an urgent need for a new resilience evaluation method that can comprehensively consider the complexity of various infrastructure in power system, so as to more comprehensively evaluate the vulnerability, response capacity and recovery potential of power system under earthquake disaster. This will provide a theoretical basis and technical support for improving the seismic resilience of power system and reducing post-disaster recovery costs. SUMMARY

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

[0006] The purpose of the present application is achieved by the following technical solution: a multi-scale power system post-earthquake resilience evaluation method, comprising the following steps:

[0007] Step 1: Collect the network topology information of the power system, obtain the substation topology information and equipment damage information in the substation, the transmission tower position 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; by solving the model, obtain the load supply information of each node of the power system under the condition of no earthquake disaster, and 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 of the region, simulate earthquake scenarios through the earthquake information, and obtain the damage of substation equipment and line damage under 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 tower on the transmission line;

[0011] Step 5: According to the function information of the substation and the transmission line, establish a system power flow calculation model of the post-earthquake power system, and calculate the post-earthquake function of the power system under each damage scenario;

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

[0013] Further, the linear power flow model of the power system under the condition of no disaster in step 2 adopts a direct current power flow model for calculation, with the goal of maximizing the satisfaction of user required load, which is specifically represented as:

[0014]

[0015] s.t.

[0016]

[0017] Wherein, N represents a set of nodes of the power system, including substation nodes and user load nodes, L represents a set of transmission lines in the power system, w i represents the node weight, d i represents the actual supplied node load, p i represents the power generation of the power generation node, including distributed power supply and substation, represented by set N p , f ij represents the flow through the line (i, j), x ij represents the reactance, θ j represents the phase angle, the maximum power generation, including the maximum allowable output of the substation and the power generation of the distributed power supply, the maximum node demand load, the maximum line load.

[0018] The objective function is to maximize the sum of the weighted loads satisfied by the users. The power supply of each node before the earthquake can be obtained by solving the model

[0019] The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the weighted load satisfied after the earthquake to the weighted load satisfied before the earthquake, which is specifically expressed as:

[0020]

[0021] wherein, represents the load that can be supplied for node i under the post-earthquake scenario ξ.

[0022] The resilience evaluation index of the power system is defined as the expected function value of all post-earthquake damage scenarios, which is specifically expressed as:

[0023] R = E ξ (F(ξ)) (9)

[0024] wherein, R represents the resilience evaluation value of the power system, represents the expected value for all post-earthquake damage scenarios ξ.

[0025] 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 is specifically expressed as:

[0026]

[0027] wherein, B represents the post-earthquake system function of the substation, m represents the maximum number of lines working before the earthquake, N i / m represents the maximum number of lines available for use after the earthquake.

[0028] Further, the earthquake scenario simulation in step 3 uses the earthquake activity empirical formula G-R law to statistically analyze historical earthquake data, which is specifically expressed as:

[0029] lgN M = a-bM (11)

[0030] wherein, N M is the number of earthquakes with magnitude greater than or equal to M; a is the earthquake activity level; b reflects the proportional relationship between the magnitude of earthquake activity and the number of earthquakes.

[0031] Based on random numbers, the earthquake magnitude is randomly generated, and the specific calculation formula is:

[0032] N M = -ln(1-z) (12)

[0033]

[0034] wherein z represents a 0-1 random number.

[0035] The calculation method of the ground motion attenuation curve is as follows:

[0036] lgY=A+BM-Clg(R+De EM ) (14)

[0037] wherein Y represents a ground motion parameter, M represents a magnitude, R represents an epicentral distance, A, B, C, D and E represent regression coefficients

[0038] Further, the post-earthquake system function evaluation method of the substation in the step 4 is calculated by calculating the maximum number of lines available for output in the substation, and is specifically represented as:

[0039] maxB ξ (15)

[0040] s.t.

[0041]

[0042]

[0043] wherein N s represents a set of equipment nodes in the substation, D s represents a set of sinks, L s represents a set of lines in the substation, wherein B ξ represents the number of lines available for output in the substation under the post-earthquake damage scenario ξ, represents the flow from the equipment node i to the equipment node j under the post-earthquake damage scenario ξ, s i represents the state of the equipment node i, 1 represents intact, 0 represents damaged, M represents a large enough number, c ij represents the maximum capacity on the line.

[0044] The objective function is to maximize the number of lines available for output B ξ of the substation, and the system function calculation formula of the substation is

[0045] C j represents the maximum system function of the substation.

[0046] Further, the power system linear flow model under the post-earthquake damage scenario ξ in the step 5 considers 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, which can be specifically represented as:

[0047] s.t.

[0048]

[0049] wherein, w i , d i , p i , f ij , x ij , θ j , The meaning is the same as the system flow model in step 2, s ij represents the state of the transmission line (i, j), 1 represents intact, 0 represents damage, and N s represents a set of substations, u j represents the power load capacity that can be output by the substation after the earthquake under the damage scenario ξ.

[0050] The objective function is to maximize the sum of the weighted loads of the nodes that can be met after the earthquake.

[0051] The beneficial effects of the present application are: the method of the present application proposes a multi-scale post-earthquake resilience evaluation method for power systems, which can consider the influence of the damage of infrastructure such as substations and transmission towers in the power system on the system function of the power system, and help managers to comprehensively evaluate the anti-seismic resilience of the power system. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 It is a flowchart of the multi-scale post-earthquake resilience evaluation method for power systems of the present application.

[0053] Figure 2 It is a schematic diagram of the power system used in the present embodiment.

[0054] Figure 3 It is a system schematic diagram of the substation used in the present embodiment.

[0055] Figure 4 It is a post-earthquake system function distribution diagram of the power system of the present embodiment. DETAILED DESCRIPTION

[0056] The technical solutions of the present application will be further described below in combination with the drawings.

[0057] As Figure 1 shown, a multi-scale post-earthquake resilience evaluation method for power systems of the present application includes the following steps:

[0058] Step 1: Collecting network topology information of the power system (load information on network nodes, connection relationship of the network, etc.), obtaining substation topology information of the power system (including position information of the substation in the power system, topology structure inside the substation and system function) and equipment damage information (mean and variance of damage probability) in the substation, tower position information (position information of the tower) and damage probability information (mean and variance of damage probability of the tower) on the transmission line;

[0059] The power system topology structure of 17 nodes shown in Figure 2 is taken as the analysis object. The voltage of the node 15 power supply point is 1.05Un, and the active power of the network is 3.715MW. Among them, Figure 2 The nodes 15, 16 and 17 in

[0060] Figure 2 The network topology information and node information of the power system shown in Table 1 are shown in Table 1, wherein the longitude and latitude information of the first node is expressed by the difference distance from the set zero point position, and the weight of each node is 1.

[0061] Table 1

[0062]

[0063]

[0064] In this embodiment, the response curve of the failure probability of each device in the substation and the tower on the transmission line with the peak ground acceleration is expressed by the logarithmic normal distribution cumulative distribution curve:

[0065]

[0066] Wherein, P represents the failure probability, x represents the value of the peak ground acceleration, Φ(·) represents the normal distribution cumulative distribution function; θ represents the logarithmic mean; β represents the logarithmic standard deviation.

[0067] Figure 2 Each kilometer on each line in contains at least one tower, which is uniformly distributed on the transmission line, and the logarithmic mean of the failure probability curve is 0.52, and the logarithmic variance of the failure probability curve is 0.22.

[0068] In this embodiment, the substation adopts the structure of 220kV substation, Figure 3 The network topology structure of the 220kV substation node is shown, which has 12 output lines without seismic damage, and the damage probability of each device in the substation is shown in Table 2.

[0069] Table 2

[0070]

[0071]

[0072] The parameters used in this embodiment and their meanings are shown in Table 3.

[0073] Table 3

[0074]

[0075]

[0076] Step 2: Establish a linear power flow model of the urban power grid under non-disaster operation, which is specifically expressed as:

[0077]

[0078] s.t.

[0079]

[0080] wherein N represents a node set of the power system, including substation nodes and user load nodes, L represents a transmission line set in the power system, w i represents a node weight, d i represents an actual supplied node load, p i represents a power generation of a node that can generate power, including distributed power supply and substations, and is represented by a set N p represents, f ij represents a flow through the line (i, j), x ij represents a reactance, θ j represents a phase angle, maximum power generation, including maximum allowable output power of the substation and power generation of the distributed power supply, maximum node demand load, maximum line load.

[0081] The objective function is to maximize the sum of the user weighted load. By solving the model, the load supply information of each node of the power system under the condition that no earthquake disaster occurs is obtained, and the results show that in this embodiment, the load demand of all nodes can be met, i.e.

[0082] Establish the post-earthquake function and resilience evaluation index of the power system and the post-earthquake function evaluation index of the substation;

[0083] The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the post-earthquake weighted load that can be met to the pre-earthquake weighted load that can be met, and is specifically expressed as:

[0084]

[0085] where d i (F(ξ)) represents the load that node i can supply under the post-earthquake scenario ξ.

[0086] The resilience evaluation index of the power system is defined as the expected function value of all post-earthquake damage scenarios, which is specifically represented as:

[0087] R = E ξ (F(ξ)) (9)

[0088] where R represents the resilience evaluation value of the power system, which represents the expected value for all post-earthquake damage scenarios ξ.

[0089] The post-earthquake system function of the substation is defined as the ratio of the number of normal output lines to the total number of original output lines, which is specifically represented as:

[0090]

[0091] where B represents the post-earthquake system function of the substation, m represents the maximum number of lines working before the earthquake, N i / m represents the maximum number of lines available for use after the earthquake.

[0092] Step 3: Collect historical earthquake information of the region, and use the empirical formula G-R law of seismic activity to count historical earthquake data, which is specifically represented as:

[0093] lgN M = a - bM (11)

[0094] where N M is the number of earthquakes with magnitude greater than or equal to M; a is the seismic activity level; b reflects the proportional relationship between the magnitude of seismic activity and the number of earthquakes.

[0095] Based on random numbers, the magnitude of the earthquake is randomly generated, and the specific calculation formula is:

[0096] N M = -ln(1-z) (12)

[0097]

[0098] where z represents a random number between 0 and 1.

[0099] The calculation method of the ground motion attenuation curve is as follows:

[0100] lgY = A + BM - Clg(R + De EM ) (14)

[0101] Wherein, Y represents the ground motion parameter, M is the magnitude, R is the epicentral distance, A, B, C, D and E are regression coefficients

[0102] The parameters a=15, b=3 in the embodiment, and the 0-1 random number is generated by the system. The ground motion attenuation curve in the embodiment is calculated as follows:

[0103] lgPGA=0.583+0.451M-0.8521lg(R+0.182e 0.707M ) (15)

[0104] Wherein, PGA is the peak ground acceleration, and the earthquake center is randomly generated in a 20kMx20kM space. Figure 2 The simulation number is set to 1000, and the Monte Carlo simulation is used to obtain the substation equipment damage and line damage under each earthquake scenario.

[0105] Step 4: The post-earthquake system function evaluation method of the substation is calculated by calculating the maximum number of lines that can be output in the substation, which is specifically represented as:

[0106] maxB ξ (16)

[0107] s.t.

[0108]

[0109] Wherein, N s represents the set of equipment nodes in the substation, D s represents the set of sinks, L s represents the set of lines in the substation, wherein B ξ represents the number of lines that can be output by the substation under the post-earthquake damage scenario ξ, represents the flow from equipment node i to equipment node j under the post-earthquake damage scenario ξ, s i represents the state of equipment node i, 1 represents intact, 0 represents damaged, M represents a large enough number, and c ij represents the maximum capacity of the line.

[0110] The objective function is to maximize the output line B ξ of the substation, and the system function calculation formula of the substation is

[0111] C j represents the maximum system function of the substation.

[0112] The transmission line on the power system includes multiple transmission towers, and the collapse of a transmission tower is considered as damage to the transmission line.

[0113] Step 5: According to the substation and transmission line function information, the system power flow calculation model of the post-earthquake power system is established, which is specifically expressed as:

[0114] s.t.

[0115]

[0116] wherein, w i , d i , p i , f ij , x ij , θ j , The meaning is the same as that of the system power flow model in step 2, s ij represents the state of the transmission line (i, j), 1 represents intact, 0 represents damaged, N s represents the set of substations, u j represents the power load capacity that can be output by the substation under the post-earthquake damage scenario ξ.

[0117] The objective function is to maximize the sum of the weighted loads of the nodes that can be met after the earthquake.

[0118] Through the model, the post-earthquake function F(ξ) of the power system under each damage scenario can be calculated.

[0119] Step 6: According to the system function under each scenario calculated in step 5, the post-earthquake function distribution of the power system is output, as shown in Figure 4 The resilience evaluation result in the embodiment is 0.2997.

[0120] Those skilled in the art will appreciate that the embodiments described herein are intended to help the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspirations disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. A method for multi-scale power system post-earthquake resilience assessment, characterized in that, The method comprises the following steps: Step 1: Collecting network topology information of the power system, obtaining substation topology information and equipment damage information in the substation, transmission tower position information and damage probability information on the transmission line of the power system; Step 2: Establishing a linear power flow model of the power system under the condition of no disaster; by solving the model, the load supply information of each node of the power system under the condition of no earthquake disaster is obtained, and the post-earthquake function and resilience evaluation index of the power system and the post-earthquake function evaluation index of the substation are established; Step 3: Collecting historical earthquake information of the region, simulating earthquakes through the earthquake information, and obtaining substation equipment damage and line damage under each earthquake, i.e. the damage scenario corresponding to each earthquake; Step 4: Evaluating the post-earthquake function evaluation index of the substation based on the equipment damage of the substation, and evaluating the function of the transmission line based on the damage of the transmission tower on the transmission line; Step 5: According to the function information of the substation and the transmission line, a system power flow calculation model of the post-earthquake power system is established, and the post-earthquake function of the power system under each damage scenario is calculated; Step 6: According to the results obtained by solving the algorithm, the post-earthquake function distribution and resilience evaluation results of the power system are output.

2. The method of claim 1, wherein, The linear power flow model of the power system under the condition of no disaster in step 2 is calculated by using the direct current power flow model, and the target is to maximize the total sum of the user weighted load, which can be specifically represented as: where i, j, k represent index symbols, N represents a set of nodes of a power system, including substation nodes and user load nodes, i ∈ N represents any node i in the set N, L represents a set of transmission lines in the power system, (i, j) ∈ L represents any line (i, j) in the line set L, w i represents a node weight, d i represents an actual supplied node load, p i represents a power generation capacity of a power-generating node, and a set of substation nodes is represented by N p , i ∈ N p represents any node i in the set N p , f ij , f ji , and f ik respectively represent flows through the line (i, j), the line (j, i), and the line (i, k), x ij represents a reactance, θ i and θ j respectively represent phase angles of the node i and the node j, represents a maximum power generation capacity, including a maximum allowable output power of a substation and a power generation capacity of a distributed power supply, represents a maximum node demand load, represents a maximum line load; The objective function is to maximize the sum of the user weighted loads; by solving the model, the power system can supply each node with power load before the earthquake The post-earthquake system function index F(ξ) of the power system is defined as the ratio of the post-earthquake weighted load that can be met to the pre-earthquake weighted load that can be met, which is specifically represented as: wherein, represents the load that can be supplied by node i in the post-earthquake scenario ξ; The resilience evaluation index of the power system is defined as the expected function value of all damage scenarios after the earthquake, which is specifically represented as: R = E ξ (F(ξ)) (9) where R represents the resilience evaluation value of the power system, E ξ () represents the expectation value for all post-earthquake damage scenarios ξ; 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 is specifically represented as: where B represents the post-earthquake system function of the substation, m represents that there are at most m lines working in the substation before the earthquake, and N i / m represents that there are at most i lines available for use in the substation after the earthquake.

3. The method of claim 1, wherein, The earthquake simulation in step 3 uses the earthquake activity empirical formula, i.e. Gutenberg-Richter law, to statistically analyze historical earthquake data, which is specifically represented as: lgN M = a - bM (11) where M represents the earthquake magnitude, N M is the number of earthquakes with magnitude greater than or equal to M; a is the seismicity level; and b reflects the proportional relationship between the magnitude of seismic activity and the number of earthquakes. The earthquake magnitude is randomly generated based on random numbers, and the specific calculation formula is: N M = -ln(l - z) (12) wherein z denotes a 0-1 random number, M s denotes a randomly generated earthquake magnitude; Based on the randomly generated earthquake magnitude M s The calculation method of ground motion attenuation curve is as follows: Where Y represents the ground motion parameter, R is the epicentral distance, A, B, C, D and E are regression coefficients.

4. The method of claim 1, wherein, The post-earthquake system function evaluation method of the substation in step 4 is calculated by calculating the maximum number of lines that can be output in the substation, which is specifically represented as: maxB ξ (15) s.t. where i, j represent index symbols, N s represents a set of equipment nodes in a substation, i ∈ N s represents a set N s represents any one node i in the set N s represents a set of sinks, i ∈ D s represents a set D s represents any one node i in the set D s represents a set of lines in a substation, (i, j) ∈ L s represents a set L s represents any one line (i, j) in the set L represents the flow from equipment node i to equipment node j under post-earthquake damage scenario ξ, represents the flow from equipment node j to equipment node i under post-earthquake damage scenario ξ, represents the flow from equipment node i to sink node v under post-earthquake damage scenario ξ, s i represents the state of equipment node i, 1 represents intact, 0 represents damaged, s j represents the state of equipment node j, 1 represents intact, 0 represents damaged, M represents a large enough number, c ij represents the maximum capacity on 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 m represents that before the earthquake, the substation has at most m lines working, C j represents the maximum system function of the substation.

5. The method for multi-scale power system post-earthquake resilience assessment according to claim 2, wherein, The linear power flow model of the power system under the post-earthquake damage scenario ξ considers the damage of the transmission line and the substation, and the damage of the transmission line leads to the inability of the line to transmit power, and the damage of the substation leads to the reduction of the transmission capacity of the substation, which can be specifically represented as: where i, j, k, N, L, N p , w i , d i , p i , f ij , f ji , f ik , x ij , θ i , θ j , The meaning is the same as the power system flow model in step 2, s ij represents the state of the transmission line (i, j), 1 represents intact, 0 represents damaged, N s represents the substation equipment node set, u j represents the power load capacity that the substation can output under the post-earthquake damage scenario ξ; The objective function is to maximize the sum of the post-earthquake node weighted load.

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