A method and system for improving the resilience of distribution network taking into account isolated islands under extreme weather conditions

Abstract

The present invention belongs to the technical field of electric power systems, and provides a method and system for improving the resilience of a distribution network taking islands into account under extreme weather conditions, comprising: obtaining conductor parameters and extreme weather state parameters of the distribution network; constructing an extreme weather mobility model according to the acquired extreme weather state parameters; constructing a distribution network conductor fault model taking into account the thermal effect of current according to the constructed extreme weather mobility model and the acquired distribution network; constructing a distribution network recovery model taking into account island division and island fusion according to the constructed extreme weather mobility model and the distribution network conductor fault model taking into account the thermal effect of current; solving the constructed distribution network recovery model to complete the recovery and improvement of the distribution network.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and specifically relates to a method and system for improving the resilience of a distribution network taking isolated islands into account under extreme weather conditions. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Extreme snow and ice weather occurs frequently around the world, and the risk of extreme events in distribution networks has increased, making it more difficult to formulate resilience improvement strategies and highlighting operational safety issues. Distributed generation (DG) with black start capability can start independently without relying on external power supplies, forming multiple isolated power grids to achieve power failure recovery, providing a new solution to the problem of improving the resilience of distribution networks. Therefore, it is necessary to take advantage of the flexible and changeable characteristics of distribution network topology and fully tap the power support potential of black start DG to enhance the ability of distribution networks to resist extreme snow and ice weather and improve the resilience of distribution networks.

[0004] According to the inventors, there are two main methods for improving the power supply capacity and resilience of distribution networks under extreme weather conditions: the first is a mathematical programming method that improves the resilience of distribution networks by reinforcing various types of electrical equipment in distribution networks; the second is a method for improving the recovery capacity of distribution networks after failures, which mainly includes two methods: network reconstruction and island operation. The first category mainly simulates extreme weather transit models, chooses to reinforce poles and lines in an economically optimal way, and transforms overhead cables into buried cables to enhance the ability of distribution networks to resist extreme ice and snow weather and improve the resilience of distribution networks; however, the advantages of the flexible and changeable network topology of distribution networks are not brought into play, and there are problems of excessive investment costs and insufficient resilience improvement. The second type of resilience improvement can be achieved by reconstructing the distribution network to restore power supply to the blackout area. Its essence is to change the network structure of the distribution network by adjusting the switching status of the normally closed interconnecting switches and the normally open section switches, so as to achieve reasonable load distribution and quickly restore power supply to the blackout area, which can effectively give play to the advantages of flexible distribution network topology. However, when the distribution network loses connection with the root node, large-scale DG in the distribution network is disconnected from the grid, resulting in large-scale power outages in areas outside the root node of the distribution network, making it difficult to improve the resilience of the distribution network.

[0005] In order to overcome the phenomenon of DG disconnection during the reconstruction of the distribution network, restoring power supply to the blackout area in an island operation mode has become a new approach. According to the IEEE1547-2004 standard, the power support potential of the local DG can be used to divide the fault blackout area into multiple islands for restoration. The existing island division methods are mainly divided into intelligent optimization methods and mathematical programming methods; the intelligent optimization method has low island division accuracy when dealing with problems with precise physical models, and it is difficult to characterize the relationship between the line switch state variables and the island area. It is easy to fall into the local optimum and thus cannot obtain the global optimal solution; the mathematical programming method does not involve the situation of island fusion, ignores some feasible solutions, and has limited effect on improving the resilience of the distribution network.

[0006] As a way to efficiently restore power supply in distribution networks, island fusion can significantly enhance the spatial penetration rate of DG inside the islands by optimizing the combination of different islands so that black-start DGs can be used for collaborative power supply, more efficiently utilize the power generation capacity of multiple sources, and restore power to as many loads as possible under the condition of limited power generation resources, and effectively improve the resilience of the distribution network; by constructing a unified mathematical model for reconstruction and island division, the number of island divisions can be optimized, but the introduction of too many decision variables affects the decision efficiency. The robust discrete optimization theory can be used to propose an island division strategy to form a large island for the distribution network after the fault, but its fusion strategy is relatively simple and cannot cope with the restoration of power supply to multiple islands in the scenario where multiple lines in the distribution network fail at the same time; related studies have considered the multi-source collaborative recovery strategy of distribution systems with island fusion, which can effectively fuse islands, but only fuse pre-divided islands, and cannot perform island division and island fusion at the same time. Summary of the invention

[0007] In order to solve the above problems, the present invention proposes a method and system for improving the resilience of distribution networks taking islands into account under extreme weather conditions. In order to solve the problem that frequent extreme ice and snow weather lead to large-scale power outages in distribution networks, and the problem that existing island division and fusion methods cannot be coordinated and optimized, the island division and fusion are fully considered under extreme ice and snow weather to achieve improved resilience of the distribution network. The distribution network component failure probability model taking into account the thermal effect of current is used to achieve accurate characterization of the ice thickness of distribution network conductors, effectively improve the accuracy of distribution network fault location selection, achieve efficient recovery of the power-off area of ​​the distribution network, and effectively improve the resilience of the distribution network.

[0008] According to some embodiments, a first solution of the present invention provides a method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions, using the following technical solutions:

[0009] A method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions, comprising:

[0010] Obtain conductor parameters and extreme weather condition parameters of the distribution network;

[0011] Building an extreme weather movement model based on the acquired extreme weather state parameters;

[0012] Based on the constructed extreme weather movement model and the obtained distribution network, a distribution network conductor fault model taking into account the thermal effect of current is constructed;

[0013] Based on the constructed extreme weather movement model and the distribution network conductor fault model taking into account the thermal effect of current, a distribution network restoration model taking into account island division and island fusion is constructed;

[0014] Solve the constructed distribution network restoration model and complete the restoration and improvement of the distribution network.

[0015] As a further technical limitation, the constructed distribution network recovery model taking into account island division and island fusion considers line switch state variables and node state variables, takes island safety constraints and black start distributed power supply operation constraints as constraints, and constructs an objective function with the goal of minimizing the load loss of the distribution network and the minimum number of switch actions.

[0016] As a further technical limitation, in the process of constructing the distribution network recovery model, the quantitative relationship between the virtual power flow and the node state variables and branch state variables between the isolated areas of the distribution network is determined based on the single commodity flow idea. Combined with the actual operating conditions of the distribution network, the constraints between the virtual power flow and the node state variables and branch state variables are obtained.

[0017] Furthermore, according to the obtained virtual power flow and the constraints between the node state variables and the branch state variables, combined with the weighted values ​​representing the node state variables and the branch state variables, it is determined whether the distribution network line is in an island area.

[0018] Furthermore, when the distribution network is in an island area, auxiliary binary variables are used to constrain the branch state variables in a single direction, forming a radial flow of virtual power flow in the island area line, and forming a distribution network recovery model that takes into account island division and island fusion.

[0019] As a further technical limitation, a rectangular coordinate system is constructed with the root node of the distribution network as the origin, and the moving path of the meteorological center of extreme ice and snow weather is expressed by the coordinates of the meteorological center of extreme ice and snow weather and the moving speed of the meteorological center to obtain an extreme weather movement model; a distribution network conductor icing growth rate model is constructed considering the thermal effect of current, and the change in icing per unit length of the distribution network conductor is calculated; a distribution network conductor icing thickness model is constructed based on the obtained change in icing per unit length of the distribution network conductor, and a distribution network conductor fault model taking into account the thermal effect of current is constructed in combination with the obtained extreme weather movement model to obtain the relationship between the conductor icing thickness and the line failure rate.

[0020] As a further technical limitation, the island division and island fusion considered include at least virtual power flow balance constraints and dominant node constraints within the divided area, power outage area constraints and island area radial constraints.

[0021] According to some embodiments, a second solution of the present invention provides a distribution network resilience improvement system taking into account isolated islands in extreme weather conditions, which adopts the following technical solutions:

[0022] A distribution network resilience enhancement system taking into account isolated islands under extreme weather conditions, comprising:

[0023] An acquisition module, configured to acquire conductor parameters and extreme weather condition parameters of the distribution network;

[0024] A construction module configured to construct an extreme weather mobility model according to the acquired extreme weather state parameters; construct a distribution network conductor fault model taking into account the thermal effect of current according to the constructed extreme weather mobility model and the acquired distribution network; and construct a distribution network restoration model taking into account island division and island fusion according to the constructed extreme weather mobility model and the distribution network conductor fault model taking into account the thermal effect of current;

[0025] The solution module is configured to solve the constructed distribution network restoration model to complete the restoration and improvement of the distribution network.

[0026] According to some embodiments, a third solution of the present invention provides a computer-readable storage medium, which adopts the following technical solution:

[0027] A computer-readable storage medium stores a program thereon, which, when executed by a processor, implements the steps of the method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions as described in the first solution of the present invention.

[0028] According to some embodiments, a fourth solution of the present invention provides an electronic device, which adopts the following technical solution:

[0029] An electronic device comprises a memory, a processor and a program stored in the memory and running on the processor, wherein when the processor executes the program, the steps in the method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions as described in the first scheme of the present invention are implemented.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The present invention takes into account the conductor current-carrying temperature change factor in the distribution network conductor ice coating growth rate model, incorporates the conductor current-carrying temperature change model into the same calculation scale of the distribution network conductor ice coating growth rate model, and proposes a distribution network component failure rate model taking into account the thermal effect of current, thereby achieving accurate characterization of the distribution network conductor ice coating thickness and effectively improving the accuracy of distribution network fault location selection.

[0032] Based on the traditional virtual power flow model based on the single commodity flow concept, the present invention comprehensively considers the quantitative relationship between the virtual power flow and the node state variables and the branch state variables between the isolated island areas, and determines the constraints between the virtual power flow and the node state variables and the branch state variables in combination with the actual operation status of the distribution network. A distribution network resilience improvement method taking into account the island division and fusion is proposed, which gives full play to the flexible and changeable characteristics of the distribution network topology structure, efficiently utilizes the transfer characteristics of the controllable load of the distribution network, realizes the efficient recovery of the power-off area of ​​the distribution network, effectively improves the resilience of the distribution network, and has good applicability to large-scale and complex actual distribution networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings in the specification that constitute a part of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments of this embodiment and their descriptions are used to explain this embodiment and do not constitute improper limitations on this embodiment.

[0034] Figure 1 This is a flow chart of a method for improving the resilience of a distribution network taking isolated islands into account under extreme weather conditions in Embodiment 1 of the present invention;

[0035] Figure 2 This is a schematic diagram of the structure of a single commodity flow implementation in the first embodiment of the present invention;

[0036] Figure 3 Schematic diagram of the value range of the state variable in the first embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the structure of a 69-node power distribution system including a distributed power source in Embodiment 1 of the present invention;

[0038] FIG5( a ) is a schematic diagram of a curve showing a change in ice thickness of a conductor without considering the thermal effect of the conductor current in the first embodiment of the present invention;

[0039] FIG5( b ) is a schematic diagram of a curve showing a change in ice thickness of a conductor taking into account the thermal effect of the conductor current in the first embodiment of the present invention;

[0040] FIG6( a ) is a schematic diagram of a curve showing a change in a failure rate of a distribution network line without considering the thermal effect of conductor current in the first embodiment of the present invention;

[0041] FIG6( b ) is a schematic diagram of a curve showing a change in the failure rate of a distribution network line taking into account the thermal effect of conductor current in the first embodiment of the present invention;

[0042] FIG7( a) is a schematic diagram of the topological structure of the distribution network reconstruction method in Solution 1 in Embodiment 1 of the present invention;

[0043] FIG. 7( b ) is a schematic diagram of the topological structure of the fixed island method in Solution 2 in Embodiment 1 of the present invention;

[0044] FIG7( c ) is a schematic diagram of the topological structure of the traditional island partitioning method in Solution 3 in Embodiment 1 of the present invention;

[0045] FIG7( d ) is a schematic diagram of the topological structure of the island division and fusion method in Solution 4 in Embodiment 1 of the present invention;

[0046] Figure 8 This is a structural block diagram of a distribution network resilience enhancement system taking isolated islands into account under extreme weather conditions in the second embodiment of the present invention. DETAILED DESCRIPTION

[0047] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0048] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0049] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0050] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0051] Embodiment 1

[0052] Embodiment 1 of the present invention introduces a method for improving the resilience of a distribution network taking isolated islands into account under extreme weather conditions.

[0053] like Figure 1 A method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions is shown, comprising:

[0054] Obtain conductor parameters and extreme weather condition parameters of the distribution network;

[0055] Building an extreme weather movement model based on the acquired extreme weather state parameters;

[0056] Based on the constructed extreme weather movement model and the obtained distribution network, a distribution network conductor fault model taking into account the thermal effect of current is constructed;

[0057] Based on the constructed extreme weather movement model and the distribution network conductor fault model taking into account the thermal effect of current, a distribution network restoration model taking into account island division and island fusion is constructed;

[0058] Solve the constructed distribution network restoration model and complete the restoration and improvement of the distribution network.

[0059] This embodiment uses the single commodity flow concept to realize the island division and integration of the distribution network. Figure 2 The single commodity flow concept refers to an efficient management mode that makes the processing time of each process consistent by reasonably formulating standard production processes and reasonably arranging the number of personnel and equipment for each processing process, so as to shorten the processing cycle and reduce operating losses.

[0060] like Figure 2 As shown, assuming that there are 4 steps in the processing process, and the time for each processing process is 1 second, if the transmission time between each process is ignored, the total time spent on processing the goods to be processed into finished products is 4 seconds; when the first piece of goods to be processed enters processing process 2, the second piece of goods to be processed enters processing process 1, and when the first piece of goods to be processed is processed into a finished product, the second piece of goods is in processing process 4, that is, the time interval between the two pieces of goods to be processed into finished products is 1 second.

[0061] Based on the characteristics of the single commodity flow concept, the actual distribution network can be designed as a virtual network, and the virtual network has the same topological structure as the distribution network; the processing time of a single processing step is regarded as the virtual load of the node in the virtual network, that is, the virtual load value is assumed to be 1; the time spent by the processed commodity entering any step in the processing flow can be regarded as the virtual flow value in the virtual network. The total time for processing into finished products can be regarded as the virtual output of the DG with black start capability, that is, the virtual output of the DG depends on the number of virtual loads contained in the island. Based on the above analysis, by constructing the virtual output constraints of the black start DG and the virtual flow, power outage area, and radial constraints of the virtual network, the virtual network can be re-divided and the virtual load can be allocated, thereby realizing the re-planning of the actual distribution network.

[0062] The traditional virtual power flow constraint based on the single commodity flow concept can only set the number of black start DGs to the number of islands, sacrificing the scope of island fusion as a feasible strategy, and cannot be used as the optimal strategy for improving the resilience of the distribution network. Based on the virtual power flow based on the single commodity flow concept, this embodiment fully considers the quantitative relationship between the node state and the branch state and introduces the node state variable and the branch switch state variable. Under the premise of ensuring that the constraint is linear, the island area is divided and the island is merged at the same time; the island division and fusion strategy of this embodiment is:

[0063] (1) Virtual power flow balance constraints within the segmented area

[0064]

[0065]

[0066] (2) Prevent the constraint of having only one dominant node in the segmented area

[0067]

[0068] (3) To avoid the virtual power flow variables violating the disconnection status of the distribution network lines, which would cause the virtual power flow variables to be inconsistent with the actual operating status of the distribution network.

[0069]

[0070]

[0071]

[0072] Among them, Ω n is the set of all nodes; Ω l is the set of all branches; Ω DG is the set of all nodes with black start DG; T is the duration of extreme snowy weather; M is a sufficiently large positive number; is the virtual power flow of line ij at time t; is the virtual power flow sent by node i with black start DG at time t; y i, t is the state variable of node i at time t, y i,t =1 means that node i is powered at time t, otherwise y i,t =0 means that the node i loses power at time t; x ij,t is the state variable of the line from node i to node j at time t, x ij,t =1 means that the circuit is in the switch closed state at time t, otherwise x ij,t =0 indicates that the line switch is in the disconnected state at time t.

[0073] Formula (1), (2), (3), (4), (5) and (6) only constrain the island area, but do not make effective constraints on the power-off area. The power-off area should also keep the variables consistent with the actual state while satisfying the constraints of formula (1), (2), (3), (4), (5) and (6).

[0074] It is necessary to constrain the power outage area of ​​the distribution network, such as Figure 3 The variable weighted relationship between the 8 branch states and the node state is shown in Figure 1, and the state variable γ is defined by formula (7): ij,t According to formula (8), the γ of line ij at time t isij,t The value of determines whether it is in the island area. ij,t The states in the power-off region are: γ ij,t =1 state 1, state 2, state 3, γ ij,t =2 state 1; line x ij,t The states in the island region are: γ ij,t =3 state 1; the rest are non-existent states:

[0075]

[0076]

[0077] During the distribution network restoration process, multiple isolated power grids are formed after the black start DG is started. These isolated power grids will be integrated in the subsequent restoration process. It is necessary to ensure that the topological structure of the distribution network is radial, that is,

[0078]

[0079]

[0080]

[0081] Among them, b ij,t is an auxiliary binary variable, b ij,t = 0 means that node i is not the parent node of node j at time t, b ij,t =1 indicates that at time t, node i is the parent node of node j.

[0082] This embodiment establishes a rectangular coordinate system with the root node of the distribution network as the origin, establishes an extreme ice and snow weather movement model, derives a distribution network conductor fault model and a tower fault model that take into account the thermal effect of current, and finally constructs an overall failure rate model of the distribution network line as an evaluation principle for selecting the fault location of the distribution network.

[0083] The extreme snow weather meteorological center coordinates (L x,t ,L y,t ) and the moving speed v of the meteorological center ice Describe the movement path of the extreme ice and snow weather meteorological center:

[0084]

[0085] Among them, (L x,t , L y,t ) is the coordinate of the meteorological center of extreme snow and ice weather at time t; (L x,0 , L y,0 ) is the coordinate of the meteorological center of extreme snow and ice weather at the initial moment; v iceIt is expressed as the moving speed of the meteorological center; θ is expressed as the angle between the moving speed of the meteorological center and the x-axis of the coordinate axis.

[0086] The conductor heat balance equation is improved to the conductor ice growth rate model, and the influence of current thermal effect, ambient temperature, wind speed and precipitation rate are comprehensively considered:

[0087]

[0088]

[0089] Among them, m ij is the conductor mass per unit length of the wire; is the specific heat capacity of the conductor material of wire ij; θ ij,t is the operating temperature of the conductor ij; R ij is the resistance of line ij; I ij,t is the current of the conductor ij at time t; μ1 is the resistance temperature coefficient of the distribution network conductor; θ envir is the current ambient temperature; θ ref is the rated ambient temperature; is the convection heat dissipation coefficient; is the ice growth rate of conductor ij at time t; v wind is the ambient wind speed; p rain is the probability of precipitation; a1, a2, a3 are the constant coefficients of the equation.

[0090] The change in ice coverage per unit length of conductor per unit time is related to the outer diameter of the conductor and the growth rate of ice coverage on the conductor, namely:

[0091]

[0092] Among them, b1 and b2 are constant coefficients of the equation; is the outer diameter of the conductor ij; is the change in ice coverage per unit length of conductor ij at time t.

[0093] The conductor thickness is related to the meteorological center position and the change in ice coverage per unit length of the conductor. The relationship between the ice coverage thickness of a certain section of the distribution network conductor and the meteorological center of extreme ice and snow weather is:

[0094]

[0095] in, is the ice thickness of conductor ij at time t; and are the load parameters of the conductor on the x-axis and y-axis respectively; (x ij ,y ij ) is the coordinate of the wire ij.

[0096] The relationship between the conductor ice thickness and the line failure rate is described in exponential form, that is,

[0097]

[0098] in, is the failure rate of conductor ij at time t; c1 and c2 are constant coefficients; n line Design the lines to withstand ice loads.

[0099] The ice load on the distribution network tower mainly refers to the tension at both ends of the conductor hanging on the tower, which depends on the vertical loads such as the gravity of the distribution network conductor itself and the gravity of the conductor ice load, that is,

[0100]

[0101]

[0102] in, is the unit vertical load of conductor ij at time t; is the ice load of a single tower located in the conductor ij at time t; l1 and l2 are the spacings on both sides of the tower; h1 and h2 are the height differences of the hanging positions at both ends of the conductor respectively; It is the horizontal tension of the lines on both sides of the tower.

[0103] The relationship between the tower ice load and the tower failure rate is described in the form of an exponential function, namely:

[0104]

[0105] in, is the failure rate of the tower located on the conductor ij at time t; c3 and c4 are constant coefficients; N pole Design the tower to withstand ice loads.

[0106] The failure rates of distribution network lines and towers are relatively independent, so the overall failure rate of the line is:

[0107]

[0108] in, is the overall failure rate of the distribution network line ij; n is the number of conductors on the distribution network line; m is the number of towers on the distribution network line.

[0109] Considering the extreme snowy weather conditions, we must first ensure the power supply of important loads in the distribution network and reduce the number of switch operations. Therefore, the objective function is to minimize the amount of load loss in the distribution network and the number of switch operations; that is,

[0110]

[0111]

[0112] minF=ω1f1+ω2f2 (24)

[0113] Among them, ω l1 ,ω l2 ,ω l3 They are the weight coefficients of primary load, secondary load and tertiary load respectively; are the active powers of the primary uncontrollable, secondary uncontrollable, and tertiary uncontrollable loads at node i at time t respectively; are the upper limits of active power of the primary controllable, secondary controllable, and tertiary controllable loads at node i at time t respectively; are the active powers of the primary controllable, secondary controllable, and tertiary controllable loads at node i at time t; Ω ope is the set of distribution network lines with section switches; Ω close is the distribution network line set including tie switches; n sw is the total number of all switches; ω1 and ω2 are the weight coefficients of the sub-objective function, satisfying ω1+ω2=1.

[0114] This embodiment adopts the Distflow power flow model applicable to the radial distribution system, and introduces the line switch state variables and node state variables, namely:

[0115]

[0116]

[0117]

[0118]

[0119] Among them, X ij is the reactance of line ij; are the reactive power of the uncontrollable primary load, uncontrollable secondary load, and uncontrollable tertiary load of node i at time t respectively; are the reactive power of the controllable primary load, controllable secondary load, and controllable tertiary load of node i at time t; P ij,t and Q ij,t are the active power and reactive power flowing from node i to node j at time t; V i,t is the voltage of node i at time t; I ij,t is the current of line ij at time t; and is the active and reactive power generated by the substation connected to node i at time t; and are the active and reactive power generated by DG at node i at time t respectively.

[0120] Within the island range, it is necessary to ensure that the node voltage and branch current are within the safe operating range, that is,

[0121]

[0122]

[0123] in, and are the square values ​​of the upper and lower limits of the voltage amplitude of node i respectively; is the square of the current amplitude in branch ij.

[0124] The black start DG operation constraints are:

[0125]

[0126]

[0127] in, is the upper limit of the active output of the black-start DG at node i at time t; is the upper limit of reactive power output of the black start DG at node i at time t.

[0128] Since the Distflow model is a non-convex nonlinear model due to formula (26), formula (27), formula (28), formula (30) and formula (31), it is difficult to solve the model. Therefore, this embodiment uses second-order cone relaxation and Big-M method to convert the model into a mixed integer second-order cone programming model, which is convenient for directly solving it with the help of mature commercial solvers.

[0129] Introduced in formula (26), formula (27), formula (28), formula (30) and formula (31) Perform an equivalent transformation and use second-order cone relaxation to transform the original non-convex model into a convex relaxation model, that is:

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] in, is the square of the voltage at node i at time t; is the square of the current of line ij at time t, and ||g||2 is the second norm equation.

[0138] The Big-M method shown in formula (40) is used for formula (28) to transform the original nonlinear model into a linear model, that is,

[0139]

[0140]

[0141] Among them, E i,t is a continuous variable; G i,t is an auxiliary variable, whose value is G i,t =e i,t E i,t ;e i,t is a 0-1 variable; is the upper limit of continuous variables; are auxiliary variables, which are M is a sufficiently large positive integer.

[0142] In order to avoid the failure of formula (37) when nodes i and j are not connected, the Big-M method is used to rewrite formula (37) as follows:

[0143]

[0144] Case Analysis

[0145] This embodiment takes the PG&E69 node distribution network as an example to verify the effectiveness of the proposed island partitioning and fusion recovery model, and verifies the applicability of the recovery model taking into account island partitioning and fusion in large-scale, multi-DG complex distribution networks using a certain 185-node actual distribution network. In this embodiment, the model is solved by calling the GUROBI solver using MATLAB2022a software. The computer configuration is Win11 system, the CPU is Intel Core i9-12900H, the main frequency is 2.5GHz, and the memory is 16GB. The duration of extreme ice and snow weather is 50h, and the length of each period is 1h.

[0146] PG&E69 node test system Figure 4As shown, the distribution network related parameters refer to the literature, the load level and controllable load are shown in Table 1, and 6 black start DGs are connected to the distribution network, and their parameters are shown in Table 2. The coordinate axis is established with the root node as the origin. The coordinates of the meteorological center of extreme ice and snow weather are (-150km, -150km), moving at a speed of 4.2km / h in a direction of 45° with the horizontal axis, and the duration is 50 hours; in formula (14), a1 = 0.02, a2 ​​= 0.0133, a3 = 0.000558, in formula (15), b1 = 0.0277, b2 = 1.088, in formula (17), c1 = 0.18, c2 = 20, in formula (20), c3 = 0.1, c4 = 10.

[0147] Table 1 Load level and controllable type

[0148]

[0149]

[0150] Table 2 Black start DG parameters

[0151]

[0152] According to the extreme snow and ice weather meteorological center moving model and the distribution network conductor ice thickness model, the relationship curves between ice thickness and extreme snow and ice weather transit process can be obtained as shown in Figure 5(a) and Figure 5(b).

[0153] In Figure 5(a), when the current thermal effect is not considered, as the meteorological center of extreme snow and ice weather moves toward the distribution network, the conductor ice coating first shows a slow growth trend, and the ice coating thickness increases rapidly in an exponential form after 15 hours. After the extreme snow and ice weather lasts for 47 hours, the growth of the conductor ice coating thickness gradually slows down. In Figure 5(b), when the current thermal effect is considered, due to the time delay of the current thermal effect, the conductor ice coating thickness increases slowly from 0 to 25 hours, and the conductor ice coating thickness increases rapidly in an exponential form after 25 hours, and the conductor ice coating growth rate is significantly lower than the conductor ice coating growth rate without considering the current thermal effect. Compared with the scheme in Figure 5(a), the conductor ice coating thickness model derived in this embodiment taking into account the current thermal effect more accurately describes the interaction mechanism between the extreme snow and ice weather moving path and the distribution network conductor ice coating thickness, realizes the accurate characterization of the conductor ice coating thickness, and the conductor ice coating thickness curve obtained by it is closer to the actual distribution network conductor ice coating thickness change trend.

[0154] The overall time-varying failure rate of the distribution network line affected by the movement of the meteorological center of extreme ice and snow weather is shown in Figure 6. Specifically, in Figure 6(a), when the current thermal effect is not considered, the overall failure rate of the distribution network line increases slowly from 0 to 25 hours, and after 25 hours, the failure rate of the distribution network line increases rapidly in an exponential form. In Figure 6(b), when the current thermal effect is taken into account, the time-varying failure rate of the distribution network line increases slowly from 0 to 30 hours, and after 30 hours, it increases rapidly in an exponential form, and the growth rate is significantly lower than that of the line failure rate without considering the current thermal effect. This is because, on the one hand, the ice thickness of the distribution network conductor is reduced when the current thermal effect is taken into account, resulting in a reduction in the failure rate of the distribution network conductor and the tower; on the other hand, due to the time delay characteristics of the current thermal effect and the slow growth of the ice thickness of the conductor, the failure rate of the distribution network line increases with time delay. The overall failure rate of distribution network line 2 is higher than that of the other lines. The reason is that the distribution network line 2 contains multiple strands of conductors. It can be deduced from formula (21) that the more strands of conductors, the higher the failure rate.

[0155] In summary, the feasibility and optimality of the resilience improvement method proposed in this paper are verified by taking a three-phase grounding fault in distribution network line 2 as an example. In this embodiment, four different schemes are set to compare the recovery conditions:

[0156] 1) Solution 1: Restore power to the power outage area by reconfiguring the distribution network;

[0157] 2) Solution 2: Use fixed islands to restore power to the power-off areas of the distribution network, forming each black-start DG into an island, and the islands will not be merged during the restoration process;

[0158] 3) Solution 3: Traditional island division method;

[0159] 4) Solution 4: The island division and fusion method in this embodiment.

[0160] The topological structures of the distribution networks after restoration of the four schemes are shown in Figure 7(a), Figure 7(b), Figure 7(c) and Figure 7(d) respectively. As shown in Figure 7(a), when the distribution network loses connection with the root node, the traditional distribution network reconstruction model cannot unify the radial constraints of the distribution network with the branch switch variables and node state variables in the power-off area, resulting in the failure of the radial constraints, causing large-scale disconnection of the black-start DG, and thus failing to exert the black-start capability of the black-start DG, causing the power supply to be unable to be restored in the power-off area.

[0161] In Figure 7(b), the uncontrollable loads at nodes 10, 12, 29, 37, 45, 46, 47, 49, 59, and 60 in the distribution network lose power; the controllable loads at nodes 11, 38, 39, 43, 44, 48, 54, 55, 56, 57, and 58 are removed. Restoring power to the blackout area of ​​the distribution network in a fixed island mode can only restore power to the power-lost nodes around the black-start DG, but not to the power-lost nodes far from the black-start DG, and the flexibility of the controllable loads cannot be brought into play, resulting in more controllable loads being removed.

[0162] As can be seen from Figure 7(c), by using the traditional island division and island fusion method based on rooted tree search, the uncontrollable loads at nodes 10, 12, 28, 29, 30, 31, 45, 46, 47, 49, 59, 60, and 61 in the distribution network lose power; the controllable loads at nodes 11, 48, 54, 55, 56, 57, and 58 are removed; and the section switches S3, S9, S12, S31, S37, S44, S49, S53, and S61 in the line are disconnected. Compared with scheme 2, by merging the islands formed by DG1 and DG2, a large island area is formed, and the power supply of node 37 containing the primary load is restored by losing the power supply of node 3 and node 28. However, in the island area formed by DG5, the power supply of node 30 and node 31 loads is not restored. Because this method does not fully consider the controllability of the controllable load, it causes the power loss of some primary loads.

[0163] As can be seen from Figure 7(d), by adopting the island division and island fusion method proposed in this embodiment, in the distribution network, the uncontrollable loads at nodes 28, 29, and 50 lose power; the controllable loads at nodes 55 and 56 lose power; the section switches S6, S14, S19, S27, S29, S49, S50, and S54 in the line are disconnected; and the connecting switches S70-S73 are closed. When a three-phase ground short circuit fault occurs in line 2, by disconnecting the section switches S6, S14, S19, and S38 and closing the connecting switch S71, DG1, DG2, DG3, and DG6 form a large island area, thereby restoring the power supply of the primary load nodes 6, 37, and 18. In the island area formed by DG4, by disconnecting the section switches S49 and S50, the node containing a large secondary load at node 50 is cut off to ensure that more primary important loads are restored to power supply.

[0164] Therefore, the distribution network island division and fusion method based on the single commodity flow concept proposed in this embodiment, through the constraints between virtual power flow and node state variables and branch state variables, utilizes the role of segmented switches to achieve the fusion of multiple islands, give full play to the flexible scheduling potential of controllable loads, and ultimately achieve efficient transfer of electric energy, ensuring the restoration of power supply for more primary important loads.

[0165] The power-off load recovery amounts of the above four schemes are shown in Table 3. The island division and fusion method proposed in this embodiment is much higher than schemes 1, 2 and 3 in the recovery amount of the primary load; weaker than schemes 2 and 3 in the recovery amount of the secondary load; higher than schemes 1, 2 and 3 in the recovery amount of the 3rd load; much higher than schemes 1, 2 and 3 in the controllable load margin; higher than schemes 1 and 2 in the total recovery amount, but worse than scheme 3. This is because the method proposed in this embodiment removes the secondary load at node 50, and the load of this node is much higher than that of other nodes, and at the expense of the load of this node, more primary load power supply and tertiary load power supply are restored.

[0166] Table 3 Comparison of power failure load recovery

[0167]

[0168] This embodiment uses the recovery rate to evaluate the distribution network resilience indicators of the four schemes, namely:

[0169]

[0170] Among them, Ω reco is the load recovery amount; w k1 is the primary load weight coefficient, w k1 =100; w k2 is the secondary load weight coefficient, w k2 =10; w k3 is the third-level load weight coefficient, w k3 =1.

[0171] The distribution network resilience levels of the four restoration schemes can be obtained by formula (41) as shown in Table 4.

[0172] Table 4 Comparison of toughness levels

[0173]

[0174] As can be seen from Table 2, in terms of the resilience level of the distribution network, the island division and fusion method proposed in this embodiment is 72.50%, which is 72.50% higher than that of Solution 1, 14.63% higher than that of Solution 2, and 18.94% higher than that of Solution 3. Since the method proposed in this embodiment restores more primary loads, and the weight coefficient of the primary load is much higher than that of the secondary load and the tertiary load, when evaluating the resilience of the distribution network after restoration, the distribution network restoration solution of the method proposed in this embodiment is higher than other solutions in terms of its resilience level, which can effectively improve the resilience level of the distribution network and enhance the ability of the distribution network to cope with extreme ice and snow weather.

[0175] This embodiment adopts the island division and fusion based on the single commodity flow concept to improve the resilience of the distribution network. On the basis of the traditional virtual power flow model based on the single commodity flow concept, the quantitative relationship between the virtual power flow and the node state variables and the branch state variables between the island areas is clarified. Combined with the actual operation status of the distribution network, the constraints between the virtual power flow and the node state variables and the branch state variables are derived, and the weighted values ​​representing the node state variables and the branch state variables are introduced to judge whether the distribution network line is located in the island area or the power-off area to ensure the unity of the virtual power flow and the state of the divided area, and introduce auxiliary binary variables to constrain the branch state variables in a single direction to ensure the radial flow of the virtual power flow of the island area line, and finally form a unified model of island division and island fusion. The recovery strategy that takes into account the island division and fusion can significantly improve the recovery capability of the distribution network and improve the resilience level of the distribution network.

[0176] This embodiment adopts a distribution network component failure rate model that takes into account the thermal effect of current. By analyzing the thermal balance equation of the distribution network line and the ice growth mechanism of the distribution network line, the conductor current-carrying temperature change model is incorporated into the same calculation scale of the distribution network conductor ice growth rate model, accurately describing the impact of extreme ice and snow weather on the failure rate of distribution network components, and improving the rationality of the selection of distribution network line fault locations.

[0177] Embodiment 2

[0178] Embodiment 2 of the present invention introduces a distribution network resilience enhancement system taking isolated islands into account under extreme weather conditions.

[0179] like Figure 8 A distribution network resilience enhancement system for taking isolated islands into account under extreme weather conditions is shown, comprising:

[0180] An acquisition module, configured to acquire conductor parameters and extreme weather condition parameters of the distribution network;

[0181] A construction module configured to construct an extreme weather mobility model according to the acquired extreme weather state parameters; construct a distribution network conductor fault model taking into account the thermal effect of current according to the constructed extreme weather mobility model and the acquired distribution network; and construct a distribution network restoration model taking into account island division and island fusion according to the constructed extreme weather mobility model and the distribution network conductor fault model taking into account the thermal effect of current;

[0182] The solution module is configured to solve the constructed distribution network restoration model to complete the restoration and improvement of the distribution network.

[0183] The detailed steps are the same as the method for improving the resilience of the distribution network taking into account isolated islands under extreme weather conditions provided in Example 1, and will not be repeated here.

[0184] Embodiment 3

[0185] Embodiment 3 of the present invention provides a computer-readable storage medium.

[0186] A computer-readable storage medium stores a program thereon, which, when executed by a processor, implements the steps of the method for improving the resilience of a distribution network taking isolated islands into account under extreme weather conditions as described in Embodiment 1 of the present invention.

[0187] The detailed steps are the same as the method for improving the resilience of the distribution network taking into account isolated islands under extreme weather conditions provided in Example 1, and will not be repeated here.

[0188] Embodiment 4

[0189] A fourth embodiment of the present invention provides an electronic device.

[0190] An electronic device comprises a memory, a processor and a program stored in the memory and running on the processor, wherein when the processor executes the program, the steps in the method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions as described in the first embodiment of the present invention are implemented.

[0191] The detailed steps are the same as the method for improving the resilience of the distribution network taking into account isolated islands under extreme weather conditions provided in Example 1, and will not be repeated here.

[0192] The above description is only a preferred embodiment of the present embodiment and is not intended to limit the present embodiment. For those skilled in the art, the present embodiment may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment shall be included in the protection scope of the present embodiment.

Claims

1. A method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions, characterized in that: include: Obtain conductor parameters and extreme weather condition parameters of the distribution network; Building an extreme weather movement model based on the acquired extreme weather state parameters; Based on the constructed extreme weather movement model and the obtained distribution network, a distribution network conductor fault model taking into account the thermal effect of current is constructed; Based on the constructed extreme weather movement model and the distribution network conductor fault model taking into account the thermal effect of current, a distribution network restoration model taking into account island division and island fusion is constructed; Solve the constructed distribution network restoration model and complete the restoration and improvement of the distribution network; The distribution network restoration model considering island division and island fusion takes into account the line switch state variables and node state variables, takes island safety constraints and black start distributed power supply operation constraints as constraints, and constructs the objective function with the minimum load loss of the distribution network and the minimum number of switch actions as the goals; In the process of constructing the distribution network restoration model, the quantitative relationship between the virtual power flow and the node state variables and branch state variables between the isolated areas of the distribution network is determined based on the single commodity flow method. The constraints between the virtual power flow and the node state variables and branch state variables are obtained in combination with the actual operating conditions of the distribution network. The island division and island fusion considered include at least the virtual power flow balance constraint and dominant node constraint within the divided area, the power failure area constraint and the island area radial constraint; A rectangular coordinate system is established with the root node of the distribution network as the origin, an extreme snow and ice weather movement model is established, and the distribution network conductor fault model and tower fault model taking into account the thermal effect of current are derived. Finally, an overall fault rate model of the distribution network line is constructed as the evaluation principle for selecting the fault location of the distribution network. The extreme snow weather meteorological center coordinates (L x,t ,L y,t ) and the moving speed v of the meteorological center ice Describe the movement path of the extreme ice and snow weather meteorological center: Among them, (L x,t , L y,t ) is the coordinate of the meteorological center of extreme snow and ice weather at time t; (L x,0 , L y,0 ) is the coordinate of the meteorological center of extreme snow and ice weather at the initial moment; v ice It is expressed as the moving speed of the meteorological center; θ is expressed as the angle between the moving speed of the meteorological center and the x-axis of the coordinate axis; The conductor heat balance equation is improved to the conductor ice growth rate model, and the influence of current thermal effect, ambient temperature, wind speed and precipitation rate are comprehensively considered: Among them, m ij is the conductor mass per unit length of the wire; is the specific heat capacity of the conductor material of wire ij; θ ij,t is the operating temperature of the conductor ij; R ij is the resistance of line ij; I ij,t is the current of conductor ij at time t; μ1 is the resistance temperature coefficient of the distribution network conductor; θ envir is the current ambient temperature; θ ref is the rated ambient temperature; is the convection heat dissipation coefficient; is the ice growth rate of conductor ij at time t; v wind is the ambient wind speed; p rain is the probability of precipitation; a1, a2, a3 are constant coefficients of the equation; The change in ice coverage per unit length of conductor per unit time is related to the outer diameter of the conductor and the growth rate of ice coverage on the conductor. Among them, b1 and b2 are constant coefficients of the equation; is the outer diameter of the conductor ij; is the change in ice coverage per unit length of conductor ij at time t; T is the duration of extreme ice and snow weather; The conductor thickness is related to the meteorological center position and the change in ice coverage per unit length of the conductor. The relationship between the ice coverage thickness of a certain section of the distribution network conductor and the meteorological center of extreme ice and snow weather is: in, is the ice thickness of conductor ij at time t; and are the load parameters of the conductor on the x-axis and y-axis respectively; (xij, yij) is the coordinate of the conductor ij; The relationship between the conductor ice thickness and the line failure rate is described in exponential form. in, is the failure rate of conductor ij at time t; c1 and c2 are constant coefficients; n line Design the lines to withstand ice loads; The tension at both ends of the distribution network tower ice load guide wire hanging on the tower depends on the gravity of the distribution network conductor itself and the gravity of the conductor ice load. in, is the unit vertical load of conductor ij at time t; is the ice load of a single tower located in the conductor ij at time t; l1 and l2 are the spacings on both sides of the tower; h1 and h2 are the height differences of the hanging positions at both ends of the conductor respectively; is the horizontal tension of the lines on both sides of the tower; The relationship between the tower ice load and the tower failure rate is described in the form of an exponential function. in, is the failure rate of the tower located on the conductor ij at time t; c3 and c4 are constant coefficients; N pole Design the tower to withstand ice loads; The failure rates of distribution network lines and towers are relatively independent, so the overall failure rate of the line is: in, is the overall failure rate of the distribution network line ij; n is the number of conductors on the distribution network line; m is the number of towers on the distribution network line.

2. A distribution network resilience improvement system taking into account isolated islands in extreme weather conditions, using the steps of the distribution network resilience improvement method taking into account isolated islands in extreme weather conditions as described in claim 1, characterized in that: include: An acquisition module, configured to acquire conductor parameters and extreme weather condition parameters of the distribution network; A construction module configured to construct an extreme weather mobility model according to the acquired extreme weather state parameters; construct a distribution network conductor fault model taking into account the thermal effect of current according to the constructed extreme weather mobility model and the acquired distribution network; and construct a distribution network restoration model taking into account island division and island fusion according to the constructed extreme weather mobility model and the distribution network conductor fault model taking into account the thermal effect of current; The solution module is configured to solve the constructed distribution network restoration model to complete the restoration and improvement of the distribution network.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for improving the resilience of a distribution network taking into account isolated islands under extreme weather conditions as described in claim 1 are implemented.

4. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, the steps of the method for improving the resilience of the distribution network taking into account isolated islands under extreme weather conditions as described in claim 1 are implemented.

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