Two-stage anti-seismic toughness optimization method for transformer substation

Abstract

The invention discloses a transformer station two-stage shock resistance toughness optimization method research. The method comprises the following steps: 1, collecting a network topology structure of a transformer station, establishing a network topology graph of the transformer station, collecting equipment fault information, and establishing a fuzzy set of equipment failure probabilities; 2, building a transformer substation toughness index, and building a transformer substation anti-seismic toughness optimization model from a pre-earthquake stage and a post-earthquake stage; 3, reconstructing the two-stage distribution robust optimization model into a two-stage robust optimization model, and performing relaxation processing on state variables in the model; and 4, according to the reconstructed model, solving a two-stage robust optimization model by adopting a nested column and constraint generation algorithm. And step 5, outputting a reinforcement decision of the pre-earthquake stage of the transformer substation, and displaying the reinforcement decision in an image mode. According to the method, a decision maker can be helped to make an optimal transformer substation reinforcement decision, so that the anti-seismic performance of the transformer substation facing uncertain disaster damage and the anti-seismic toughness of the transformer substation are improved to the maximum extent, and the influence of disasters on the transformer substation is reduced.

Description

Technical Field

[0001] The invention relates to a two-stage seismic toughness optimization method for a transformer substation. Background Art

[0002] In recent years, various natural disasters have occurred frequently, causing serious damage and impact on the global power system. Climate change has increased the frequency and intensity of extreme weather events, including typhoons, floods, droughts, and blizzards, which have significantly damaged the power infrastructure and caused serious power outages. Among them, geological disasters represented by earthquakes pose a major threat to the stability of the power system. In this context, improving the resilience and recovery capacity of the power system has become a key issue that needs to be urgently addressed by the power sectors of various countries. In order to meet these challenges, research and application of advanced disaster prevention and mitigation technologies, optimization of power grid design, strengthening of emergency plans, and improving the self-healing capacity of power systems have become important research directions in the field of power engineering. These measures not only help to reduce the impact of natural disasters on the power system, but also improve the overall reliability and sustainability of the system.

[0003] As a key component of the power system, substations convert high-voltage electric energy into voltage levels that meet user needs, and play a vital role in the transmission and distribution of electric energy. Therefore, the reliability of substations directly affects the safety and power supply quality of the entire power system, especially when dealing with grid load fluctuations and sudden failures. The normal operation of substations is particularly important. In this context, an effective substation resilience improvement measure is urgently needed to improve the seismic resilience of substations, protect substations from disaster attacks, and comprehensively improve the resilience of the power system. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for considering the uncertain damage of the substation and finding the best reinforcement decision for improving the seismic resilience of the substation before an earthquake, thereby maximizing the seismic resilience of the substation.

[0005] The object of the present invention is achieved through the following technical solution: A two-stage seismic toughness optimization method for a substation, comprising the following steps:

[0006] Step 1: Collect the network topology of the substation, establish the network topology diagram of the substation, collect equipment failure information, and establish the fuzzy set of equipment failure probability;

[0007] Step 2: Establish the substation resilience index and build the substation seismic resilience optimization model from the two stages before and after the earthquake;

[0008] Step 3: Reconstruct the two-stage distributed robust optimization model into a two-stage robust optimization model, and relax the 0-1 state variables in the model;

[0009] Step 4: Based on the reconstructed model, the nested column and constraint generation algorithm is used to solve the two-stage robust optimization model.

[0010] Step 5: Based on the results obtained by the algorithm, output the reinforcement decision of the substation in the pre-earthquake stage and display it in the form of images.

[0011] Furthermore, the equipment damage fuzzy set in step 1 is established through a set of possible equipment damage scenarios. The feasible equipment damage scenario set can be specifically expressed as:

[0012]

[0013] in, represents the set of feasible damage scenarios, M s represents the number of devices in the substation. Each damage scenario can be represented by an M s Dimensional vector Indicates that the kth parameter defines the device status of the kth device (when it is 1, it means the device is normal, otherwise it is 0), G represents the number of damaged devices in the substation, and the larger G is, the The more damage scenarios can be included.

[0014] Then the damage state fuzzy set of substation equipment is established Specifically expressed as:

[0015]

[0016] Among them, y represents the equipment reinforcement decision, and its kth parameter represents the reinforcement of the kth equipment; It represents the reinforcement factor of the equipment, that is, the percentage by which the probability of equipment failure can be reduced through reinforcement; It represents the Hadamard product, which is to multiply the elements of vector a and vector b at corresponding positions, and the vector is obtained by arranging them in the original position after multiplication; represents the failure probability of the equipment, ξ max Indicates the upper limit of the probability of equipment failure.

[0017] Furthermore, the substation resilience index in step 2 is defined as the number of lines in the substation that can operate normally after T time after the earthquake, which is specifically expressed as:

[0018] f(T)=N i / p (T) (3)

[0019] Among them, f(T) represents the resilience of the substation after T time after the earthquake, p represents the number of normally working lines of the substation before the earthquake, N i / p (T) means that i lines can work normally after T time after the earthquake.

[0020] The two-stage resilience optimization model in step 2 is established from the pre-earthquake and post-earthquake stages. In the pre-earthquake stage, the substation resilience optimization is specifically expressed as:

[0021]

[0022] st

[0023]

[0024]

[0025] in, Represents the objective function in the post-earthquake stage, namely, the resilience loss value. It means to find the expectation under all disaster scenarios in the brackets, a i represents the cost of reinforcing device i, and C represents the total budget.

[0026] The objective function in the pre-earthquake stage is to minimize the expected value of the substation resilience loss under the worst damage scenario distribution;

[0027] The objective function of the post-earthquake stage is to repair the damaged equipment based on the spare parts in the substation after the disaster occurs. The objective function is the minimum value of the substation resilience loss after T time after the earthquake. It is specifically expressed as

[0028]

[0029] st

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] Among them, p represents the number of lines that can work normally before the earthquake, and f represents the number of lines that can work normally after T time after the earthquake. Represents the set of substation equipment connection lines. represents the set of substation source points, represents the substation sink set, N represents the total number of substation equipment, O represents the number of equipment types inside the substation, and [Z] represents the set {1, 2, ..., Z}; x ij represents the flow from device i to device j; d i Indicates the status of the i-th device after T time after the earthquake, 1 indicates normal operation, and 0 indicates device failure; is a 0-1 variable, 1 means that the equipment i was repaired for the kth time after the disaster, otherwise it is 0; represents a 0-1 variable, 1 means that the equipment i is in good condition before the kth maintenance after the disaster, otherwise it is 0; v o Indicates the number of spare parts for the oth type of equipment; z k represents a 0-1 variable, 1 means the kth repair can be completed within T time after the earthquake, otherwise it is 0; q i represents the maintenance time of equipment i;

[0042] The objective function of the post-earthquake stage is to minimize the resilience loss value of the substation after T time after the earthquake.

[0043] Furthermore, the two-stage distributed robust optimization model described in step 3 is reconstructed into a two-stage robust optimization model, which is specifically expressed as:

[0044]

[0045] st

[0046] (5) to (6), (8) to (18)

[0047]

[0048] Among them, β is the dual variable, which is an N-dimensional variable;

[0049] For the nonlinear term β in the objective function (19), i y i Through the auxiliary variable σ i Linearize and transform the problem into the following:

[0050]

[0051] st

[0052] (5)~(6), (8)~(18),

[0053]

[0054]

[0055]

[0056]

[0057] In order to achieve efficient solution of the model, the 0-1 decision variables Perform relaxation and modify constraint (12) to the following form:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Furthermore, the nested column and constraint generation algorithm in step 4 is specifically implemented as follows:

[0064] Step 41: Initialize parameters, input algorithm tolerance ε, define optimization algorithm lower bound LB, algorithm upper bound UB, number of iterations R, damage scenario set O, set

[0065] Step 42: Solve the constrained master problem based on the limited set of damage scenarios O to obtain the optimal equipment reinforcement strategy in the pre-earthquake stage, denoted as y*, the objective function value is Ψ*, and the updated lower bound is LB=max{LB,Ψ*};

[0066] Step 43: Define subproblems based on the optimal reinforcement strategy obtained in the pre-earthquake stage, use the column and constraint generation algorithm to solve the subproblems, solve the worst equipment damage scenario, denoted as ξ*, the objective function is Υ*, and the updated upper bound is UB=min{UB, Υ*};

[0067] Step 44: if UB-LB≤ε, return the optimal solution y*; otherwise, add the damage scenario ξ* into the damage scenario set O, R=R+1, and return to step 42;

[0068] The beneficial effects of the present invention are as follows: the method of the present invention proposes a two-stage seismic resilience optimization method for substations, which can take into account the uncertainty of damage caused to substations by extreme disasters, formulate resilience enhancement strategies from both the pre-earthquake and post-earthquake stages, and help engineering personnel determine the best pre-earthquake equipment reinforcement decisions, thereby maximizing the seismic resistance and seismic resilience of substations, and improving the ability of substations to operate stably under extreme disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a schematic flow chart of the two-stage seismic resilience optimization method for a substation of the present invention;

[0070] Figure 2 A schematic diagram of the substation network topology used in this embodiment;

[0071] Figure 3 This is the optimal toughness improvement strategy for the case of the present invention. DETAILED DESCRIPTION

[0072] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0073] like Figure 1 As shown, a two-stage seismic resilience optimization method for a substation of the present invention comprises the following steps:

[0074] Step 1: Collect the network topology of the substation (equipment information in the substation, including equipment type, possible reinforcement methods and reinforcement effects, and connection relationships between equipment), establish a network topology diagram of the substation (establish a directed graph to represent the topology of the substation), collect equipment failure information (estimate the upper limit of the failure probability of equipment under extreme disasters), and establish a fuzzy set of equipment failure probability;

[0075] This embodiment adopts Figure 2 The substation network topology diagram shown in the figure is Figure 2 All equipment shown in can be reinforced by reinforcement measures, and the specific information of each type of equipment is shown in Table 1. There is only one spare part available for each type of equipment in the substation after the earthquake, with a total budget of 120,000 yuan. Before the disaster, there were 6 lines in the substation that could work normally.

[0076] Table 1

[0077]

[0078] The parameters used in this embodiment and their meanings are shown in Table 2:

[0079] Table 2

[0080]

[0081] The equipment damage fuzzy set is established through the possible equipment damage scenario set. The feasible equipment damage scenario set can be specifically expressed as:

[0082]

[0083] in, represents the set of feasible damage scenarios, M s represents the number of devices in the substation. Each damage scenario can be represented by an M S Dimensional vector Indicates that the kth parameter defines the device status of the kth device (when it is 1, it means the device is normal, otherwise it is 0), G represents the number of damaged devices in the substation, and the larger G is, the The more damage scenarios can be included.

[0084] Then the damage state fuzzy set M(y) of substation equipment is established, which is specifically expressed as:

[0085]

[0086] Among them, y represents the equipment reinforcement decision, and its kth parameter represents the reinforcement of the kth equipment; It represents the reinforcement factor of the equipment, that is, the percentage by which the probability of equipment failure can be reduced through reinforcement; It represents the Hadamard product, which is to multiply the elements of vector a and vector b at corresponding positions, and the vector is obtained by arranging them in the original position after multiplication; represents the failure probability of the equipment, ξ max Indicates the upper limit of the probability of equipment failure.

[0087] Step 2: The substation resilience index is defined as the number of lines that can operate normally in the substation after T time after the earthquake, which is specifically expressed as:

[0088] f(T)=N i / p (T) (3)

[0089] Where f(T) represents the resilience of the substation after T time after the earthquake, p represents that the substation has p normally functioning lines before the earthquake, and N i / p (T) means that i lines can work normally after T time after the earthquake.

[0090] The two-stage resilience optimization model in step 2 is established from the pre-earthquake and post-earthquake stages. In the pre-earthquake stage, the substation resilience optimization is specifically expressed as:

[0091]

[0092] st

[0093]

[0094]

[0095] in, Represents the objective function in the post-earthquake stage, namely, the resilience loss value. It means to find the expectation under all disaster scenarios in the brackets, a i represents the cost of reinforcing device i, and C represents the total budget.

[0096] The objective function in the pre-earthquake stage is to minimize the expected value of the substation resilience loss under the worst damage scenario distribution;

[0097] The objective function of the post-earthquake stage is to repair the damaged equipment based on the spare parts in the substation after the disaster occurs. The objective function is the minimum value of the substation resilience loss after T time after the earthquake. It is specifically expressed as

[0098]

[0099] st

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] Among them, p represents the number of lines that can work normally before the earthquake, and f represents the number of lines that can work normally after T time after the earthquake. Represents the set of substation equipment connection lines. represents the set of substation source points, represents the substation sink set, N represents the total number of substation equipment, O represents the number of equipment types inside the substation, and [Z] represents the set {1, 2, ..., Z}; xij represents the flow from device i to device j; d i Indicates the status of the i-th device after T time after the earthquake, 1 indicates normal operation, and 0 indicates device failure; is a 0-1 variable, 1 means that the equipment i was repaired for the kth time after the disaster, otherwise it is 0; represents a 0-1 variable, 1 means that the equipment i is in good condition before the kth maintenance after the disaster, otherwise it is 0; v o Indicates the number of spare parts for the oth type of equipment; z k represents a 0-1 variable, 1 means the kth repair can be completed within T time after the earthquake, otherwise it is 0; q i represents the maintenance time of equipment i;

[0112] The objective function of the post-earthquake stage is to minimize the resilience loss value of the substation after T time after the earthquake.

[0113] Step 3: Reconstruct the two-stage distributed robust optimization model into a two-stage robust optimization model, which is specifically expressed as:

[0114]

[0115] st

[0116] (5)~(6), (8)~(18),

[0117]

[0118] Among them, β is the dual variable, which is an N-dimensional variable;

[0119] For the nonlinear term β in the objective function (19), i y i Through the auxiliary variable σ i Linearize and transform the problem into the following:

[0120]

[0121] st

[0122] (5)~(6), (8)~(18),

[0123]

[0124]

[0125]

[0126]

[0127] In order to achieve efficient solution of the model, the 0-1 decision variables Perform relaxation and modify constraint (12) to the following form:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Step 4: Simplify the reconstructed model into the following form:

[0134]

[0135] st

[0136]

[0137] Uy+Wβ≤h1 (33)

[0138]

[0139]

[0140] Among them, y and β represent the decision variables in the pre-earthquake stage; represents the uncertainty parameters in the model, that is, the equipment state variables after the disaster occurs; n represents the 0-1 decision variable in the post-earthquake stage; ω represents the continuous variable in the post-earthquake stage; the matrix B and vectors b1, b2 represent the coefficient matrix and vector in the objective function; the matrices U, W, D, K, J and vectors e1, e2, h1, h2 represent the coefficient matrix and vector in the constraints.

[0141] The problem is solved by using a nested column and constraint generation algorithm, where the outer column and constraint generation algorithm is specifically expressed as:

[0142] Step 41: Initialize parameters, input algorithm tolerance ε, define optimization algorithm lower bound LB, algorithm upper bound UB, number of iterations R, damage scenario set O, set

[0143] Step 42: Define the restricted master problem based on the finite set of damage scenarios O, which can be specifically expressed as

[0144] MP: minΨ(36)

[0145] st

[0146] Ay≤C (37)

[0147] Uy+Wβ≤h1 (38)

[0148]

[0149] Where Ψ is an auxiliary variable. Solving this problem obtains the optimal equipment reinforcement strategy in the pre-earthquake stage, denoted as y*, and obtains the optimal solution β* of the auxiliary variable. The objective function value is Ψ*, and the updated lower bound is LB=max{LB,Ψ*};

[0150] Step 43: Define sub-problems based on the best reinforcement strategy obtained in the pre-earthquake phase. The column and constraint generation algorithm is used to solve the subproblem and solve the worst equipment damage scenario, which is denoted as ξ*, the objective function is Υ*, and the updated upper bound is UB=min{UB,Y*};

[0151] Step 44: If UB-LB≤ε, return the optimal solution y*; otherwise, add the disaster scenario ξ* into the damage scenario set O, R=R+1, and add the following constraints to the main problem:

[0152]

[0153] Return to step 42;

[0154] In step 43, a column and constraint generation algorithm is used to solve the subproblem, which is specifically expressed as follows:

[0155] Step 431: Initialize parameters, input algorithm tolerance ε, define optimization algorithm lower bound LB, algorithm upper bound UB, number of iterations R, maintenance decision set set up

[0156] Step 432: Based on a limited set of maintenance decisions Solve the definition of the main problem, which is specifically expressed as

[0157]

[0158] st

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165] Where Υ is an auxiliary variable. Solving this problem obtains the worst damage scenario under a finite set of maintenance decisions, denoted as ξ*, the objective function value is Υ*, and the update upper bound is

[0166] Step 433: Define sub-problems based on the obtained worst damage scenario, which is specifically expressed as:

[0167]

[0168] st

[0169]

[0170] Solve this problem to obtain the optimal maintenance decision, denoted as n * , the objective function is γ*, and the update upper bound is LB=max{LB, γ *};

[0171] Step 434: If UB-LB≤ε, return the optimal solution ξ*; otherwise, add the maintenance decision γ* into the maintenance decision set L = L + 1, and add the following constraints to the main problem:

[0172]

[0173] K T π L+1 ≤b2 (51)

[0174]

[0175]

[0176] Return to step 432;

[0177] Step 5: According to the results obtained by the algorithm, the reinforcement decision y* of the substation before the earthquake is output to obtain the optimal reinforcement strategy of the substation. The optimal reinforcement decision in this embodiment is as follows: Figure 3 As shown, the black part is the reinforced equipment.

[0178] 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 two-stage seismic resilience optimization method for a substation, characterized in that: The steps include: Step 1: Collect the network topology of the substation, establish the network topology diagram of the substation, collect equipment failure information, and establish the fuzzy set of equipment failure probability; Step 2: Establish the substation resilience index and build the substation seismic resilience optimization model from the two stages before and after the earthquake; Step 3: Reconstruct the two-stage distributed robust optimization model into a two-stage robust optimization model, and relax the 0-1 state variables in the model; Step 4: Based on the reconstructed model, the nested column and constraint generation algorithm is used to solve the two-stage robust optimization model; Step 5: Based on the results obtained by the algorithm, output the reinforcement decision of the substation in the pre-earthquake stage and display it in the form of images.

2. A two-stage seismic resilience optimization method for a substation according to claim 1, characterized in that: The equipment damage fuzzy set in step 1 is established through a set of possible equipment damage scenarios. The feasible equipment damage scenario set can be specifically expressed as: in, represents the set of feasible damage scenarios, M s represents the number of devices in the substation. Each damage scenario can be represented by an M s Dimensional vector Indicates that the kth parameter defines the status of the kth device (when it is 1, it means the device is normal, otherwise it is 0), G represents the number of damaged devices in the substation, and the larger G is, the The more damage scenarios can be included in the fuzzy set of damage states of substation equipment Specifically expressed as: Among them, y represents the equipment reinforcement decision, and its kth parameter represents the reinforcement of the kth equipment; represents the reinforcement coefficient of the equipment, that is, the percentage by which the probability of equipment failure can be reduced through reinforcement; aob represents the Hadamard product, which is the multiplication of the elements at the corresponding positions of vector a and vector b, and the vector is obtained by arranging them in the original position after multiplication; represents the failure probability of the equipment, ξ max Indicates the upper limit of the probability of equipment failure.

3. A two-stage seismic resilience optimization method for a substation according to claim 1, characterized in that: The substation resilience index in step 2 is defined as the number of lines that can operate normally in the substation after T time after the earthquake, which is specifically expressed as: f(T)=N i / p (T) (3) Among them, f(T) represents the resilience of the substation after T time after the earthquake, p represents the number of normally working lines of the substation before the earthquake, N i / p (T) means that i lines can work normally after T time after the earthquake; The two-stage resilience optimization model in step 2 is established from the pre-earthquake and post-earthquake stages. In the pre-earthquake stage, the substation resilience optimization is specifically expressed as: st in, Represents the objective function in the post-earthquake stage, namely, the resilience loss value. It means to find the expectation under all disaster scenarios in the brackets, a i represents the cost required to reinforce equipment i, and C represents the total budget; The objective function in the pre-earthquake stage is to minimize the expected value of the substation resilience loss under the worst damage scenario distribution; The objective function of the post-earthquake stage is to repair the damaged equipment based on the spare parts in the substation after the disaster occurs. The objective function is the minimum value of the substation resilience loss after T time after the earthquake. It is specifically expressed as st Among them, p represents the number of lines that can work normally before the earthquake, and f represents the number of lines that can work normally after T time after the earthquake. Represents the set of substation equipment connection lines. represents the set of substation source points, represents the substation sink set, N represents the total number of substation equipment, O represents the number of equipment types inside the substation, and [Z] represents the set {1, 2, ..., Z}; x ij represents the flow from device i to device j; d i Indicates the status of the i-th device after T time after the earthquake, 1 indicates normal operation, and 0 indicates device failure; is a 0--1 variable, 1 means that the equipment i was repaired for the kth time after the disaster, otherwise it is 0; represents a 0--1 variable, 1 means that the equipment i is in good condition before the kth maintenance after the disaster, otherwise it is 0; v o Indicates the number of spare parts for type O equipment; k represents a 0-1 variable, 1 means the kth repair can be completed within T time after the earthquake, otherwise it is 0; q i Indicates the maintenance time of equipment i; The objective function of the post-earthquake stage is to minimize the resilience loss value of the substation after T time after the earthquake.

4. A two-stage seismic resilience optimization method for a substation according to claim 1, characterized in that: The two-stage distributed robust optimization model described in step 3 is reconstructed into a two-stage robust optimization model, which is specifically expressed as: st (5)～(6)，(8)～(18) Among them,, are dual variables, and is an N-dimensional variable; For the nonlinear term β in the objective function (19), i y i Through the auxiliary variable σ i Linearize and transform the problem into the following: st (5)～(6)，(8)～(18)， In order to achieve efficient solution of the model, the 0--1 decision variables Perform relaxation and modify constraint (12) to the following form:

5. A two-stage seismic resilience optimization method for a substation according to claim 1, characterized in that: The nested column and constraint generation algorithm in step 4 is specifically implemented as follows: Step 41: Initialize parameters, input algorithm tolerance ε, define optimization algorithm lower bound LB, algorithm upper bound UB, number of iterations R, damage scenario set O, set LB = -∞, UB = +∞, R = 0, Step 42: Solve the constrained master problem based on the limited set of damage scenarios O to obtain the optimal equipment reinforcement strategy in the pre-earthquake stage, denoted as y*, the objective function value is Ψ*, and the updated lower bound is LB=max{LB,Ψ*}; Step 43: Define subproblems based on the optimal reinforcement strategy obtained in the pre-earthquake stage, use the column and constraint generation algorithm to solve the subproblems, solve the worst equipment damage scenario, denoted as ξ*, the objective function is γ*, and the updated upper bound is UB=min{UB,γ*}; Step 44: If UB-LB≤ε, return the optimal solution y*; otherwise, add the damage scenario ξ* into the damage scenario set O, R=R+1, and return to step 42.

Images