A method for inverting and restoring a city power grid structure

Abstract

The present application belongs to the field of power system safety, and particularly relates to a kind of inversion reduction method of urban power grid structure, in view of the problems existing in prior art, the typical observable sign of cable and the coupling relationship between cable laying and road network are analyzed, the framework requirement of urban power grid planning principle on power cable laying is considered, the topological inversion double-target optimization model of possible network frame is proposed based on the perspective of attacker, and the inversion reduction method of urban power grid network frame under incomplete topological information is formed.

Description

Technical Field

[0001] This invention belongs to the field of power system security, and specifically relates to a method for inverting and restoring the structure of an urban power grid. Background Technology

[0002] In recent years, research on the methods, processes, and consequences of deliberate attacks on power systems has gradually become a hot topic. Simulating typical deliberate attack processes will help defenders uncover system weaknesses, thereby better serving the formulation of advanced defense concepts and improving the ability of urban power grids to prevent, respond to, and recover from deliberate attacks.

[0003] Existing research generally analyzes the weak links of power systems under deliberate attacks from the perspectives of attack and defense scenarios under complete information and strategy formulation. For example, the literature "Robustness and Vulnerability Analysis of Power Networks Based on Complex Network Theory" (Luo Xiaoru, Southwest Jiaotong University, 2012) and "Vulnerability Assessment Algorithm for Large Power Grids Based on Small-World Topology Model" (Ding Ming and Han Pingping, Automation of Electric Power Systems, 2006(08):7-10+40) summarize several common vulnerability indicators such as maximum connectivity, connectivity factor, and load loss rate, and conduct a comprehensive analysis of the vulnerability of power systems. The literature "Vulnerability Assessment Algorithm for Large Power Grids Based on Small-World Topology Model" (J. Salmerón, K. Wood, Ding Ming and Han Pingping, Automation of Electric Power Systems, 2006(08):7-10+40) and "On the solution of the bilevel programming formulation of the terroristthreat problem" (Arroyo JM, Galina FD, IEEE transactions on Power Systems, 2005, 20(2): (789-797) From the attacker's perspective, it is believed that the optimal strategy under limited attack resources is to maximize the system load loss and take it as the upper-level goal. The optimal emergency scheduling of the system is taken as the lower-level defense response goal. The model is transformed into a single-layer problem using KKT conditions to solve the vulnerable lines of the power system from the attacker's perspective. The literature "Exploring reliable strategies for defending power systems against targeted attacks" (Chen G, Dong Z Y, Hill DJ, et al. "IEEE Transactions on Power Systems", 2010, 26(3):1000-1009) takes the probability and consequences of system components being attacked as the common benefit function of both parties. There is a mixed strategy equilibrium solution in the overall strategy space of both parties, that is, solving the Nash equilibrium problem of minmax F = maxmin F. The equilibrium solution is the weak point of the system.

[0004] However, in reality, attackers often cannot obtain all the information needed to formulate the optimal attack strategy, which greatly increases the difficulty of obtaining the optimal attack state. Existing research has attempted to address the construction of attack strategies in scenarios with incomplete information. The papers "Bilevel model for analyzing coordinated cyber-physical attacks on power systems" (Li Z, Shahidehpour M, Alabdulwahab A, et al., IEEE Transactions on Smart Grid, 2015, 7(5):2260-2272.) and "Modeling cyber-physical vulnerability of the smart grid with incomplete information" (Srivastava A, Morris T, Ernster T, et al., IEEE Transactions on Smart Grid, 2013, 4(1):235-244) address the problem that network attacks often cannot obtain full system measurement information. They utilize observable topological measurement area data to construct a CPPS system information-physical coordinated attack scheme. The papers "Power system structural vulnerability assessment based on an improved maximum flow approach" (Fang J, Su C, Chen Z, et al., IEEE Transactions on Smart Grid, 2016, 9(2):777-785) and "Using graph models" also demonstrate this approach. to analyze the vulnerability of electric power networks》(Holmgren J. *Riskanalysis*, 2006, 26(4): 955-969) addresses the vulnerability of power system structures under incomplete topological element parameter information from the perspectives of maximum flow theory and graph theory, providing model conjectures for attackers regarding attack threats under such incomplete information problems. However, all the above research scenarios are based on the premise that the attack strategy is formulated on the basis that the attacker has complete knowledge of the defender's power grid. In reality, considering factors such as land occupation, reliability, and urban aesthetics, underground cable transmission lines are becoming increasingly common in urban power grids. Therefore, attackers often cannot obtain the complete grid structure, and the formulation of attack strategies under typical deliberate attack forms will face this practical feasibility problem.

[0005] To address the aforementioned issues, this paper proposes an inversion and reconstruction method for urban power grid structures under incomplete topological information. The main innovations include: ① Based on observable information of urban transmission cables, a dual-objective optimization model for urban power grid topology inversion and reconstruction is constructed with the objectives of maximizing observability of the inverted network structure and minimizing power supply losses; ② To ensure solution convergence, the constraints of the topology inversion model are linearized based on the Big M method. Summary of the Invention

[0006] To address the aforementioned issues, this invention analyzes typical observable characteristics of cables and the coupling relationship between cable laying and the road network. Considering the framework requirements of urban power grid planning principles for transmission cable laying, and taking the service of urban power system defense strategic planning as the application scenario, it proposes a dual-objective optimization model for topology inversion of possible network structures from the attacker's perspective, forming a method for inverting and restoring urban power grid structures under incomplete topology information.

[0007] A method for inverting and restoring the structure of an urban power grid includes the following steps:

[0008] Step 1: Based on the observability of urban power transmission cables and the line-road coupling relationship between the power grid and the road network, construct a hybrid network model of urban power grid-road network;

[0009] Step 2: Based on the regional differences influencing factors of cable route planning, construct a cable route support scoring function;

[0010] Step 3: Based on cable path support, construct the objective function f1 by inverting the grid support score to obtain the highest score;

[0011] Step 4: Based on the load moment theory, construct the objective function f2 by minimizing the power supply loss of the line network;

[0012] Step 5: Construct a dual-objective optimization model for power grid topology inversion and restoration with f1 and f2 as objective functions, and use the linear weighting method to transform the multi-objective problem into a single-objective problem;

[0013] Step 6: Construct the network node and route planning constraints, and use the Big M method to linearize the constraints. Then, use MATLAB to call the CPLEX solver to solve the problem.

[0014] Preferably, the urban power grid-road network hybrid model in step 1 is represented as follows:

[0015]

[0016] This model includes the power grid model G. E and the main road network model G R Two parts, G R Includes the urban arterial road node set V R direct road set L between nodes R G E Includes the set of power grid nodes V T (Including the power plant set Vg and the substation set Vs), the visible marker set V M And visible overhead line set L E Three parts, of which V M →L R This is a non-full-radial relationship. The power nodes at both ends of transmission lines are often connected to roads, therefore V T →V R There exists a non-surjective relationship in space.

[0017] Preferably, the cable path observability scoring function in step 2 is expressed as:

[0018]

[0019] In the above formula, a ij Indicate l ij The cable has supporting parameters, determined by l ij The quantity, distribution, and rationality of cable routing are determined by factors such as the number of cable markers, their distribution, and the rationality of the cable routing. ij The factors include the considerable number and distribution of signs, as well as the rationality of their route layout.

[0020]

[0021] Among them, mra ij mrbi j ,mrc ij Indicate l ij The number of A / B / C category signs in the vicinity, mra ij ≥0, mrb ij ≥0, mrc ij ≥0, the more flags there are, the more support l is provided. ijThere are underground cables passing through. The three categories of markings (A / B / C) represent the following: maintenance, ventilation openings, inlets / outlets, and alarm / reminder signs for exposed cable sections, cable ducts, and integrated utility tunnels, respectively. σ1, σ2, and σ3 represent the weights of the three categories of markings, with σ1 > σ2 > σ3. Experts indicated that l ij The normalized value of the comprehensive score for the rationality of cable laying indicates that the higher the score, the lower the difficulty of cable laying and the higher the rationality of laying.

[0022] E ij Represented as l ij Strong influencing factors of cable laying λ ij With environmental factors e ij Social factors ij The product of the sums of secondary factors:

[0023] E ij =λ ij (s ij +e ij (4)

[0024] Preferably, the objective function f1 constructed in step 3 represents the optimal observability index VF of the inverted network structure, i.e., the highest score. VF is expressed as follows:

[0025]

[0026] In the above formula, for i, j∈V R Define the road segment between nodes i and j as l. ij , l ij ∈L R ,So This means that for p, q∈V T There is a cable line passing through l between power nodes p and q. ij Integer decision variables, Indicate l ij Does a supportive evaluation function exist for the passage of underground cables?

[0027] Preferably, the objective function f2 constructed in step 4 represents the power supply loss index Q of the restored power grid. L Minimum, Q x It consists of the sum of known line power supply loss and restored line power supply loss, expressed by the following formula:

[0028]

[0029] Among them, Q e Let Q represent the known power supply loss of the connecting lines to substation e. If e is connected to its power station by an overhead line, then Q... e Not zero; qe V represents the estimated power supply load of e; es d represents the set of possible power stations that could supply power to e; et d represents the length of the return cable line between e and its power station t. et The calculation formula is:

[0030]

[0031] Where, d ij Indicate l ij The length indicates that the restored cable line between nodes e and t consists of multiple segments l ij The cable is connected together, and the length of each cable segment is d. ij In the above formula, d ij Indicate l ij Length, d ts It is represented as e, the sum of the lengths of each restoration cable line segment between stations t.

[0032] Preferably, in step 5, the inversion and restoration of the bi-objective optimization model is constructed using a linear weighted method with f1 and f2 as objective functions, as shown below:

[0033] A(f)=δ1f1+δ2(-f2) (8)

[0034] Where δ1 and δ2 are linear weighting coefficients, δ1 + δ2 = 1, thus transforming the multi-objective problem into a single-objective problem. Therefore, the overall objective function is:

[0035] max A(f)=δ1·V F +δ2·(-Q L (9)

[0036] Preferably, step 5 includes the following steps:

[0037] Step 5.1: Cable return count constraint;

[0038] Step 5.2: Consider the convergence constraints of road nodes in special grid structures;

[0039] Step 5.3: Constraints on the number of incoming and outgoing power lines to power plants and substations;

[0040] Step 5.4: Terminal substation wiring mode constraints;

[0041] Step 5.5: No independent sub-loop constraints.

[0042] The advantages of this invention are:

[0043] (1) Considering the typical categories, laying conditions and observable indicators of underground cable laying in urban power grids, a coupling relationship model between urban power transmission cable network and transportation network is proposed.

[0044] (2) To optimize the overall observability index of the restored network and minimize the sum of power supply losses of all substations except terminal substations, a dual-objective optimization model for power grid topology inversion and restoration is constructed. The multi-objective problem is transformed into a single-objective problem by using the linear weighting method.

[0045] (3) Construct the network node and line planning constraints, and use the Big M method to linearize the constraints. The whole problem is solved by calling the CPLEX solver in MATLAB. Attached Figure Description

[0046] Figure 1 This is the urban local power grid-main road network coupling network in this invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are some, but not all, of the embodiments of this invention. The embodiments described below are intended to explain this invention and should not be construed as limiting the implementation of this invention.

[0048] First, an undirected network is constructed based on observable cable markers and the coupling relationship between cable laying and the road network. Second, considering the framework requirements of urban power grid planning principles for transmission cable laying, a dual-objective optimization model for topology inversion of the possible network structure is proposed from the attacker's perspective, providing a scenario basis for the formulation of subsequent game theory attack strategies.

[0049] According to one embodiment of the present invention, the urban power grid-road network coupling model based on observable cable marker distribution analysis is as follows.

[0050] Whether using independent pipelines or integrated utility tunnels, the main routes of urban power transmission cables should be laid along the city's main roads, meaning there is a line-road coupling relationship between the power grid and the road network. Visible cable markers are attached to these coupled lines. Therefore, a hybrid urban power grid-road network model is constructed:

[0051]

[0052] In the above formula: G R As the main road network, G E For power grid; G R Including the urban arterial road node set V R direct road set L between nodes R G E Includes the set of power grid nodes V T (including power plant set Vg and substation set Vs), visible marker set V MAnd visible overhead line set L E Three parts, of which V M →L R This is a non-full-radial relationship. The power nodes at both ends of transmission lines are often connected to roads, therefore V T →V R There exists a non-surjective relationship in space.

[0053] According to one embodiment of the present invention, the dual-objective optimization model for power grid topology inversion and restoration is as follows.

[0054] Urban local power grid-main road network coupled network, such as Figure 1 As shown.

[0055] Figure 1 In the diagram, solid lines represent visible overhead lines, and dashed lines represent invisible cable lines; power system node T a ,…,T e For substations of different voltage levels, the ring represents the high voltage level and the circle represents the low voltage level. Meanwhile, T... a ,…,T e Respectively with road node R 10 ,…,R 14 Overlap; T a T c A cable line passes through road nodes R1, R6, and R7 in sequence. Considering the needs of ventilation and maintenance, there are some visible ground markings along the line.

[0056] When some power nodes and lines are visible, cable segments are added to different road sections to form cable lines, thus completing the incomplete information network topology. The goal of completing the network should mainly follow the following principles: ① The restored cable lines should pass through sections with dense cable markings as much as possible; ② The completed network should meet the principle of minimizing power supply loss in the power system planning.

[0057] Therefore, the objective function of the bi-objective optimization problem for power grid topology completion in this section consists of two parts: f1 and f2. f1 represents the highest observability compliance, and f2 represents the minimum load moment of the completed network (characterizing the attacker's estimate of the power supply network loss). The two objectives are added together using a linear weighted method, and the bi-objective optimization model is established as follows:

[0058] A(f)=δ1f1+δ2(-f2) (2)

[0059] Where δ1 and δ2 are linear weighting coefficients, δ1 + δ2 = 1, thus transforming the multi-objective problem into a single-objective problem. Therefore, the overall objective function is:

[0060] max A(f)=δ1·V F +δ2·(-Q L(3)

[0061] Objective function f1 analysis

[0062] For i,j∈V R Define the road segment between nodes i and j as l. ij , l ij ∈L R Then for p, q∈V T Define a cable line passing through power nodes p and q. ij The integer decision variables are Its value represents the number of times the cable line has been restored. For example... Figure 1 China T a T c There is a cable line r ac Equivalent to If it does not exist, then Therefore, the objective function f1 represents the goal of having as many and more reasonable cable markings as possible in each road segment through which the restored cable lines pass in the completed network structure.

[0063] Therefore, the objective function f1 represents the goal of having as many and more reasonable cable markings as possible in each road segment through which the restored cable lines pass in the completed network structure.

[0064]

[0065] In the formula: Indicate l ij Does a supportive evaluation function exist for the passage of underground cables? Represented as:

[0066]

[0067] In the formula: a ij Indicate l ij The cable has supporting parameters, determined by l ij The number, distribution, and rationality of cable markings are all factors that determine the cable's strength. Since different types of visible markings offer varying degrees of support to the cable, V is ranked from highest to lowest support. M The elements are classified into three levels: A, B, and C, as shown in Table 1.

[0068] Table 1 Classification of Visible Markings for Cables

[0069]

[0070] Therefore, in equation (5) a ij It is expressed as follows:

[0071]

[0072] Among them, mra ij mrb ij ,mrc ij Indicate l ij The number of A / B / C category signs in the vicinity, mra ij ≥0, mrb ij ≥0, mrc ij ≥0, the more flags there are, the more support l is provided. ij There are underground cables passing through. The three categories of markings (A / B / C) represent the following: maintenance, ventilation, inlet / outlet, and alarm / reminder signs for exposed cable sections, cable ducts, and integrated utility tunnels, respectively. σ1, σ2, and σ3 represent the weights of the three categories of markings, with σ1 > σ2 > σ3. Experts indicated that l ij The normalized value of the comprehensive score for the rationality of cable laying indicates that the higher the score, the lower the difficulty of cable laying and the higher the rationality of laying.

[0073] E ij Represented as l ij Strong influencing factors of cable laying λ ij With environmental factors e ij Social factors ij The product of the sums of secondary factors:

[0074] E ij =λ ij (s ij +e ij (7)

[0075] The factors influencing the scores are shown in Table 2:

[0076] Table 2 ij Factors affecting the rationality of laying

[0077]

[0078] Table 2 shows the regional differences in cable route planning, therefore E ij The acquisition of this information can only rely on expert judgment; that is, this section aims to build a general framework applicable to all regions, rather than a special structure applicable to individual regions.

[0079] Objective function f2 analysis

[0080] Since system operating parameters are often not directly obtainable, attackers can only approximate the power supply loss of the complete power grid based on the information they have. Therefore, drawing on the concept of load moment in power grid planning, the power supply loss of a transmission line is estimated as the product of the estimated load of the low-voltage side substation of that line and the line length. Thus, the objective function f2 represents minimizing the estimated load moment of the complete power grid.

[0081]

[0082] Among them, Q e Let Q represent the known power supply loss of the connecting lines to substation e. If e is connected to its power station by an overhead line, then Q... e Not zero; q e V represents the estimated power supply load of e; es d represents the set of possible power stations that could supply power to e; et d represents the length of the return cable line between e and its power station t. et The calculation formula is:

[0083]

[0084] Where, d ij Indicate l ij The length indicates that the restored cable line between nodes e and t consists of multiple segments l ij The cable is connected together, and the length of each cable segment is d. ij .

[0085] Constraint generation

[0086] In the topology completion model, the cable path segments are connected to form a complete cable line, while ensuring the structural rationality of the completed network, constraining the number of incoming and outgoing lines at power nodes, and avoiding problems such as the absence of independent sub-circuits. The main constraints are as follows:

[0087] 1) Path l ij Cable return count constraint

[0088] Path l ij It can often accommodate multiple cables, and the sum of their turns is less than or equal to the upper limit, as expressed by the following constraint:

[0089]

[0090] In the formula: Indicate l ij Maximum number of cable lines that can be accommodated.

[0091] 2) Road node convergence constraints

[0092] When multiple cable lines pass through a road node, the r that merges into that node pqThe return number should be equal to r of the node that outputs the data. pq The number of rounds is represented as follows:

[0093]

[0094] 3) Constraints on the number of incoming and outgoing power lines to power plants and substations

[0095] The number of incoming and outgoing power lines to power plants and substations should be less than the upper limit, and there should be no incoming lines.

[0096]

[0097] In the formula, This indicates the upper limit of the p-outgoing line of the power plant. This indicates the number of visible overhead lines from power plant p. Similarly, there is an upper limit to the number of incoming and outgoing cables at a substation.

[0098]

[0099] In the formula, as well as These represent the upper limits of the incoming and outgoing lines of the substation, respectively. as well as These represent the number of visible overhead incoming and outgoing lines at substation p, respectively.

[0100] 4) Terminal substation wiring mode constraints

[0101] Urban power transmission network terminal substations belong to high-voltage distribution networks. The supply methods from upstream substations to terminal substations typically involve different wiring configurations, such as π-connection, n-loop chain, and radial configuration. Therefore, for terminal substations with V... l ∈V s For q∈V l All of them satisfy the condition of being connected to a maximum of two power nodes.

[0102] Therefore, assuming substation q and n q (n q If ≤2) nodes are connected by known overhead lines, then q can be connected to at most 2-n nodes. q There are cable connections between the power nodes:

[0103]

[0104] In the formula: p∈V T m pq This indicates a criterion for determining whether there is a cable connection between nodes p and q. Clearly, m pq Between nodes p and q Value determination:

[0105]

[0106] Introducing a larger number M transforms the above equation:

[0107]

[0108] 5) No independent sub-loop constraints

[0109] Any r pq The starting point should be p, and the ending point should be q. It is unacceptable for both the starting and ending points to be p simultaneously. That is, the independent sub-loop situation, similar to that in the TSP problem, should be avoided. Therefore, this paper adopts the Miller-Tucker-Zemlin (MTZ) constraint method for i, j∈G. P Introducing 0-1 decision variable μ i μ j Construct the MTZ inequality:

[0110]

[0111] In the formula: M = N V N V Represents the set of power nodes G E and the main road node set G R The sum of the number of elements in the middle. Constraint (17) is the tightened MTZ inequality.

Claims

1. A method for inverting and reconstructing the structure of an urban power grid, characterized in that, Includes the following steps: Step 1: Based on the observability of urban power transmission cables and the line-road coupling relationship between the power grid and the road network, construct a hybrid network model of urban power grid-road network; Step 2: Based on the regional differences influencing factors of cable route planning, construct a cable route observability scoring function; Step 3: Based on the observability of the cable path, construct the objective function f1 by inverting the network observability score; Step 4: Based on the load moment theory, construct the objective function f2 by minimizing the power supply loss of the line network; Step 5: Construct a dual-objective optimization model for power grid topology inversion and restoration with f1 and f2 as objective functions, and use the linear weighting method to transform the multi-objective problem into a single-objective problem; Step 6: Construct the nodes and route planning constraints of the restored network structure, and use the Big M method to linearize the constraints. Use MATLAB to call the CPLEX solver to solve the topology of the inverted network structure. The urban power grid-road network hybrid model in step 1 is represented as follows: (1) This model includes the power grid model G. E and the main road network model G R Two parts, G R Includes the urban arterial road node set V R direct road set L between nodes R G E Includes the set of power grid nodes V T Visible flag set V M And visible overhead line set L E Three parts, of which V M →L R Because it is not a full-radial relationship, the power nodes at both ends of the transmission line are often connected to roads, therefore V T →V R There exists a non-surjective relationship in space; The inversion and restoration bi-objective optimization model uses f1, which has the strongest observability, and f2, which minimizes the load moment of the completed grid structure, as objective functions. It is constructed using a linear weighting method, and the bi-objective optimization model is expressed as follows: (2) Where δ1 and δ2 are linear weighting coefficients, δ1 + δ2 = 1, thus transforming the multi-objective problem into a single-objective problem. Therefore, the overall objective function is: (3) Among them, V F To indicate compliance indicators, Q L This is a load moment estimation index.

2. The method for inverting and restoring the urban power grid structure according to claim 1, characterized in that, Step 3: Marker compliance index V F Represented as: (4) Where, for i, j∈V R Define the road segment between nodes i and j as l. ij , l ij ∈L R ,So This means that for p, q∈V T There is a cable line passing through l between power nodes p and q. ij Integer decision variables, φ(i,j) represent l ij Does a supportive evaluation function exist for the passage of underground cables? φ(i,j) is represented as: (5) Among them, a ij Indicate l ij The cable has supporting parameters, determined by l ij The quantity, distribution, and rationality of cable markings are determined by l ij The considerable number of signs, their distribution, and the rationality of their route layout constitute the following: (6) Among them, mra ij mrb ij ,mrc ij Indicate l ij The number of A / B / C category signs in the vicinity, mra ij ≥0, mrb ij ≥0, mrc ij ≥0, the more flags there are, the more support l is provided. ij There are underground cables passing through. The three types of signs, A, B and C, respectively represent the maintenance, ventilation opening, entrance and exit, alarm and reminder signs of the exposed cable section, cable network, and integrated pipe gallery. σ1, σ2 and σ3 represent the weight of the three types of signs, with σ1>σ2>σ3. Experts indicated that l ij The normalized comprehensive score for the rationality of cable laying indicates that a higher score signifies lower cable laying difficulty and greater rationality. ij Represented as l ij Strong influencing factors of cable laying λ ij With environmental factors e ij Social factors ij The product of the sums of secondary factors: (7)。 3. The method for inverting and restoring the urban power grid structure according to claim 1, characterized in that, Step 3: Complete the grid structure compliance index Q L Represented as: (8) Among them, Q e Let Q represent the known power supply loss of the connecting lines to substation e. If e is connected to its power station by an overhead line, then Q... e Not zero; q e V represents the estimated power supply load of e; es d represents the set of possible power stations that could supply power to e; et d represents the length of the return cable line between e and its power station t. et The calculation formula is: (9) Where, d ij Indicate l ij The length indicates that the restored cable line between nodes e and t consists of multiple segments l. ij The cable is connected together, and the length of each cable segment is d. ij .

4. The method for inverting and restoring the urban power grid structure according to claim 1, characterized in that, The constraints of the bi-objective optimization model in step 5 include the following steps: Step 5.1: Cable return count constraint; Step 5.2: Consider the convergence constraints of road nodes in special grid structures; Step 5.3: Constraints on the number of incoming and outgoing power lines to power plants and substations; Step 5.4: Terminal substation wiring mode constraints; Step 5.5: No independent sub-loop constraints.

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