Distribution network fault recovery method and system considering fault evolution under extreme weather conditions

Abstract

The present invention belongs to the field of distribution network fault recovery and provides a distribution network fault recovery method and system that takes fault evolution into account under extreme weather conditions. The technical solution is to address the problems of inaccurate characterization of the fault evolution mechanism of distribution network equipment under extreme snowy weather and the inability of existing distribution network fault recovery methods to effectively characterize the control mode of distributed power sources. An active distribution network fault recovery strategy that takes fault evolution into account under extreme snowy weather conditions is proposed. First, the impact of the mechanical failure process of distribution network equipment and the uncertainty of distribution network power flow under extreme snowy weather conditions is clarified, the probability of equipment failure and the probability of system state transition are quantified, and a distribution network cascading fault evolution model based on improved random power flow is derived. Second, based on the regional division concept of point localization, the subordinate relationship between the master control node, slave control node, and load node in the island area is comprehensively considered. In combination with the master-slave control logic of the island, the constraints between the master control node, slave control node, and load node are derived, and a distribution network fault recovery model that takes reconstruction and island division into consideration is constructed. The flexible and changeable characteristics of the distribution network topology are utilized while improving the recovery capability of the distribution network.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network fault restoration, and in particular to a distribution network fault restoration method and system taking into account fault evolution 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] When a distribution network fault occurs, reversing the circuit breaker to restore power to the affected loads using the upstream grid, and using distributed generation (DG) to form power islands to restore power to nearby loads, this collaborative approach is a key way to improve the distribution network's resilience to extreme weather and its power recovery capabilities. Therefore, effectively leveraging the flexible and diverse nature of distribution network topology and tapping into the potential for collaborative power supply between the upstream grid and DG are essential measures to enhance the distribution network's resilience to faults.

[0004] During the evolution of distribution network failures under extreme weather conditions, cascading failures can be categorized into three types based on cascading failure models: the complex system approach based on self-organized criticality theory, the complex network theory approach based on network topology analysis, and the pattern search approach exemplified by the accident chain approach. The complex system approach reveals the physical processes of cascading failures and describes the system's self-organized criticality characteristics, but suffers from low computational efficiency and difficulty solving problems. Complex network theory is used to analyze system vulnerabilities and weak links, but it cannot characterize the system's dynamic response mechanisms. The pattern search approach, combining actual physical processes with simulation of cascading failures, enables both quantitative analysis of cascading failures and effectively controls computational complexity, making it the primary method currently used for analyzing cascading failures in distribution networks.

[0005] In the process of distribution network fault evolution under extreme weather, existing technologies have proposed a time-dominated cascading fault evolution model and a dual-time dimension fault evolution model that retains the temporal characteristics of line faults, thereby characterizing the performance change curve of the power grid under typhoon disasters; by simulating the typhoon passage process, the probability of mechanical failure in the system is simulated, and the probability of cascading faults is calculated based on the system power flow distribution and line overload probability; however, its analysis of the fault development and evolution process is only a single time section, ignoring the distinct temporal and spatial persistence characteristics of extreme weather.

[0006] To address these issues, existing research has explored fault recovery methods based on reconstruction and islanding. These methods leverage the flexible and adaptable nature of distribution network topology to restore power to lost loads, or exploit the power support potential of DGs to create power supply islands. Both approaches are crucial for improving distribution network resilience. However, when a large-scale cascading failure occurs in a distribution network, resulting in disconnection from the upstream grid, reconstruction alone fails to fully leverage the power support provided by DGs. Furthermore, islanding methods, which rely solely on DGs providing power support, ignore the key factor in improving distribution network resilience, namely, the upstream grid's ability to supply power to lost loads. Consequently, these approaches have limited impact on improving distribution network resilience.

[0007] To this end, it is an important way to effectively improve the fault recovery capability of the distribution network by simultaneously tapping the potential of coordinated power supply of the upper power grid and power generation resources such as DG and giving full play to the flexible and changeable characteristics of the distribution network topology. "Tang Yida, Wu Zhi, Gu Wei, et al. Unified model of reconstruction and island division for active distribution network fault recovery [J]. Power System Technology, 2020, 44(07): 2731-2740" By tapping the potential of coordinated power supply of the upper power grid, multiple DGs and energy storage, a fault recovery method that coordinates reconstruction and island division is proposed, thereby restoring the power supply of the power-lost load of the distribution network. "Zhou Yu, Jie Huili, Zheng Bolin, et al. Coordination of distribution network fault reconstruction and island operation based on hybrid algorithm [J]. Power System Technology, 2015, 39(01): 136-142" A recovery strategy of coordinated coordination of distribution network reconstruction and island division is proposed. The reconstruction and island are coordinated through the island boundary matrix, thereby obtaining the optimal recovery strategy. "Liu H, Wang C, Ju P, et al. A sequentially preventive model enhancing powersystem resilience against extreme-weather-triggered failures [J]. Renewable and Sustainable Energy Reviews, 2022, 156: 111945" proposes a two-level mathematical programming model that considers reconstruction and islanding. By utilizing the adjustable characteristics of controllable loads, it effectively avoids the power imbalance problem within the island and achieves the maximum range of power restoration in the distribution network. However, all of the above studies focus on improving the fault recovery capability of the distribution network, but few studies consider the change in the control mode of the island, that is, the change in the DG control mode during the transition from grid-connected mode to islanding mode, which causes changes in the DG power output characteristics, resulting in inaccurate characterization of the control operation mode and insufficient exploration of the potential for synergy between reconstruction and islanding. Summary of the Invention

[0008] In order to solve at least one technical problem existing in the above-mentioned background technology, the present invention provides a distribution network fault recovery method and system that takes into account fault evolution under extreme weather conditions. The method and system accurately depict the distribution network fault evolution mechanism under extreme ice and snow weather, effectively characterize the logic of the change in power output characteristics caused by the change in DG control mode, explore the potential for collaborative power supply between the upper power grid and DG, and enhance the recovery capability of the distribution network while giving full play to the flexible and changeable characteristics of the distribution network topology.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] A first aspect of the present invention provides a distribution network fault recovery method taking into account fault evolution under extreme weather conditions, comprising the following steps:

[0011] A rectangular coordinate system is established with the root node of the distribution network as the origin. Combined with the failure mechanism of the distribution network conductors and towers, the overall failure probability of the distribution network line is calculated.

[0012] A linear stochastic power flow model is constructed by characterizing cascading failures in the distribution network through random power flow. Based on the linear stochastic power flow model, a stochastic power flow model considering line disconnection is constructed in combination with a random compensation power method based on sensitivity analysis, and the real-time line outage probability is obtained.

[0013] Combining the overall failure probability of the distribution network line, the real-time outage probability of the line and the determined operating status of the distribution network equipment, the system state change process in continuous time is discretized and the distribution network system state transition probability is calculated;

[0014] Calculate the power output characteristics of the master and slave control units when switching from grid-connected operation to islanded operation, and calculate the power output characteristics of distributed photovoltaic units when switching from grid-connected operation to islanded operation in extreme snowy weather.

[0015] Combining the distribution network system state transition probability, the power output characteristics of the master and slave control units, and the power output characteristics of distributed photovoltaic units, we derive the constraints between the master and slave control nodes and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding.

[0016] The distribution network fault recovery model that takes into account the coordination of reconstruction and island partitioning is solved, and the fault recovery strategy is obtained.

[0017] Furthermore, the establishment of a rectangular coordinate system with the root node of the distribution network as the origin, and the calculation of the overall failure probability of the distribution network line in combination with the failure mechanism of the distribution network conductors and towers, include:

[0018] Based on the movement path of the meteorological center of extreme snow and ice weather, the influence of current electrothermal, ambient temperature, wind speed and precipitation rate on conductor icing is comprehensively considered to obtain the conductor failure rate associated with extreme snow and ice weather.

[0019] Considering the ice load on distribution network towers, calculate the tower failure rate of conductors;

[0020] The overall failure rate of the distribution network lines is calculated by combining the conductor failure rate associated with extreme ice and snow weather and the tower failure rate of the conductor.

[0021] Furthermore, the random power flow is used to characterize the cascading failures of the distribution network and to construct a linear random power flow model. Based on the linear random power flow model, a random power flow model considering line disconnection is constructed in combination with a random compensation power method based on sensitivity analysis to obtain the real-time outage probability of the line, including:

[0022] The linear stochastic power flow model is constructed by characterizing the cascading failure of distribution network through stochastic power flow;

[0023] Combining the random compensation power method based on sensitivity analysis, a random power flow model considering line interruption is constructed;

[0024] Solve the stochastic power flow model of line interruption and obtain the probability distribution of power flow in each branch;

[0025] The real-time outage probability of the line is calculated based on the probability distribution of the power flow of each branch.

[0026] Furthermore, the real-time outage probability of the line is expressed as:

[0027]

[0028] Where: f(P l ) is the probability density function of the line active power obtained by random power flow calculation, is the probability of line l being out of service due to overload at time t; To protect the hidden fault probability; P l is the active power of line l; P l r and P l m are the rated power and maximum transmission power of line 1 respectively.

[0029] Furthermore, the distribution network system state transition probability is:

[0030]

[0031] in, The distribution network status is Transfer to probability; and is the state o of the distribution network at time t and time t+1; Ω l,t+1 is the set of devices that may fail at time t+1; The device operating status is Transfer to probability; and They are the probability of equipment ij failing due to extreme ice and snow weather at time t+1 and the probability of equipment l failing due to cascading failures.

[0032] Furthermore, when the grid-connected operation state is converted to the island operation state, the power output characteristics of the main control unit are:

[0033]

[0034] The power output characteristics of the slave control unit when the grid-connected operation state is converted to the island operation state are:

[0035]

[0036] Where: and are the active power and reactive power generated by DG at node i at time t; k i,t k is a 0-1 state variable that indicates whether the DG at node i is in V / f control at time t. i,t =1 means the DG at node i adopts V / f control, otherwise it adopts PQ control, Ω DG is the set of all DG grid-connected nodes; V i,t is the voltage of node i at time t; V0 is the rated voltage of DG as the main control unit; and are the upper limit of active power output and reactive power output of DG at node i at time t; T is the set of fault recovery time; and are the active power reference value and reactive power reference value of DG at node i at time t, respectively.

[0037] Furthermore, in extreme snowy weather, when the system switches from grid-connected operation to island operation, the power output characteristics of the distributed photovoltaic units are as follows:

[0038]

[0039]

[0040] Where: is the ice thickness of distributed photovoltaic at node i at time t; d1, d2, d3 and d4 are constant coefficients; and are the active power and reactive power generated by the distributed photovoltaic at node i at time t; is the radiation intensity at node i at time t; θ PV is the distributed photovoltaic power factor angle, (L x,t ,L y,t ) is the coordinate of the meteorological center of extreme snow and ice weather at time t, and are the x-axis and y-axis coordinates of the distributed photovoltaic at node i.

[0041] Furthermore, the objective function of the distribution network fault recovery model taking into account the coordination of reconstruction and islanding is:

[0042] minF=ω1f1+ω2f2,

[0043]

[0044] Where: F is the overall objective function; f1 and f2 are sub-objective functions that characterize the load loss of the distribution network and the number of switch operations respectively; ω1 and ω2 are the weight coefficients of the sub-objective functions respectively; P LOSS and P ALL are the weighted unload amount and total load amount respectively; Ω n is the set of all nodes in the distribution network; i,t is the 0-1 state variable of node i at time t, y i,t =1 means that node i is powered on at time t, otherwise node i is powered off; ω k1 、ω k2 and ω k3 are the weight coefficients of the primary load, secondary load and tertiary load of the distribution network respectively; and are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; Ω ope and Ω clo are the sets of all tie switches and section switches respectively; x ij,t is the 0-1 state variable of line ij at time t, x ij,t =1 means that line ij is in operation at time t, otherwise it is in disconnection; N line is the total number of switches in the distribution network.

[0045] Furthermore, the constraints of the distribution network fault recovery model taking into account the coordination of reconstruction and islanding include coordination constraints of reconstruction and islanding, distribution network flow constraints, and distribution network security constraints.

[0046] Among them, the coordinated constraints of reconstruction and island division include division area constraints and connectivity and radial constraints;

[0047] The partition area constraints are:

[0048]

[0049] Connectivity and radial constraints:

[0050]

[0051] Constructing distribution network flow constraints:

[0052]

[0053] Distribution network security constraints:

[0054]

[0055] Where: B i,j,t is a 0-1 state variable indicating whether node j is located in the partition area of ​​dominant node i, B i,j,t =1 means node j is located in the region divided by node i, otherwise node j is located outside the region divided by node i; k i,t Ω is a 0-1 state variable that represents whether the DG at node i is in V / f control at time t, DG is the set of all DG grid-connected nodes; Ω sub is the set of nodes connected to the substation; Ω (i) is the set of all nodes in the region formed by node i as the dominant node; N bus is the total number of distribution network nodes; The V / f control DG emits virtual power at node i at time t; F ij,t is the virtual power flow transmitted by branch ij at time t; F ki,t is the virtual power flow transmitted by branch ki at time t; y i,t is the 0-1 state variable of node i at time t, T is the set of fault recovery times; M is a sufficiently large positive number; x ij,t is the 0-1 state variable of line ij at time t; P ij,t and Q ij,t are the active power and reactive power of line ij at time t respectively; P ki,t and Q ki,t are the active power and reactive power of line ki at time t; I ki,t and I ij,t is the current of lines ki and ij at time t; and are the active power and reactive power injected into node i at time t; R ij and X ij are the resistance and reactance of line ij respectively; R ki and X kiare the resistance and reactance of line ki respectively; and are the active power and reactive power output by the substation connected to node i at time t; and are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; and are the reactive powers of the primary load, secondary load and tertiary load of node i at time t respectively; is the square of the voltage at node i at time t; is the square of the voltage at node j at time t; Ω l is the set of all branches; Ω n is the set of all nodes in the distribution network; V i max and V i min are the square values ​​of the upper and lower limits of the voltage amplitude of node i respectively; It is the square value of the upper limit of the current amplitude of branch ij.

[0056] A second aspect of the present invention provides a distribution network fault restoration system that takes fault evolution into account under extreme weather conditions, comprising:

[0057] The fault evolution analysis module establishes a rectangular coordinate system with the root node of the distribution network as the origin, and calculates the overall failure probability of the distribution network line by combining the failure mechanisms of the distribution network conductors and towers. A linear stochastic power flow model is constructed using stochastic power flow to characterize cascading failures in the distribution network. Based on this linear stochastic power flow model, a stochastic power flow model that considers line disconnection is constructed in combination with a stochastic compensation power method based on sensitivity analysis to obtain the real-time outage probability of the line.

[0058] The operation analysis module is used to discretize the system state change process in continuous time by combining the overall failure probability of the distribution network line, the real-time line outage probability, and the determined operating status of the distribution network equipment, and calculate the distribution network system state transition probability. It also calculates the power output characteristics of the master control unit and the slave control unit when the system switches from the grid-connected operation state to the islanded operation state, and calculates the power output characteristics of the distributed photovoltaic unit when the system switches from the grid-connected operation state to the islanded operation state in extreme ice and snow weather.

[0059] The fault recovery module is used to combine the distribution network system state transition probability, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units to derive the constraints between the master control node, the slave control node, and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding; solve the distribution network fault recovery model that takes into account the coordination of reconstruction and islanding to obtain a fault recovery strategy.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] This paper proposes a distribution network cascading failure evolution model based on an improved stochastic power flow under extreme snow and ice weather conditions. This model considers the evolutionary characteristics of distribution network faults and DG output under extreme snow and ice weather conditions, quantifies the probability of mechanical failure of distribution network equipment and the probability of system state transitions, and accurately characterizes the evolutionary mechanism of distribution network faults using a stochastic power flow algorithm that considers line interruptions.

[0062] 2. This paper proposes a DG operation model that takes into account the transition between V / f control and PQ control. During the transition from grid-connected mode to islanded mode, the change in DG control mode leads to changes in its power output characteristics. An auxiliary binary variable representing the DG control mode is introduced to characterize the DG power output characteristics, enabling accurate characterization of power output changes during the transition between V / f control and PQ control.

[0063] 3. This paper proposes a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding. Based on the regional division concept of "point-based region determination" and combined with the power output characteristics of the DG, the V / f-controlled DG is used as the island master control unit, and this node is used as the regional dominant "node". Judgment variables are introduced to characterize the affiliation between the master control unit, slave control units, and distribution network load. The "regions" to which various nodes in the distribution network belong are derived. While ensuring the connectivity and radial operation of the reconstruction area and the island area, the organic coordination of reconstruction and islanding is achieved, effectively improving the fault recovery capability of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0065] Figure 1 This is a flow chart of a distribution network fault recovery method taking into account fault evolution under extreme weather conditions provided by an embodiment of the present invention;

[0066] Figure 2 The master-slave control and peer-to-peer control structures in an island state provided by an embodiment of the present invention, wherein (a) is a master-slave control structure and (b) is a peer-to-peer control structure;

[0067] Figure 3 The PG&E 69-node active distribution network provided by an embodiment of the present invention;

[0068] Figure 4 is a load fluctuation curve of a distribution network provided by an embodiment of the present invention;

[0069] Figure 5This is a schematic diagram of the failure rate of distribution lines provided by an embodiment of the present invention;

[0070] Figure 6 This is the distribution network fault evolution path provided by the embodiment of the present invention;

[0071] Figure 7 : The cumulative distribution of power flows of line 1 and line 2 provided in the embodiment of the present invention; wherein (a) is the cumulative distribution of power flows of line 1, and (b) is the cumulative distribution of power flows of line 2;

[0072] Figure 8 is a distributed photovoltaic output curve provided by an embodiment of the present invention;

[0073] Figure 9 It is a fault recovery result in a distribution network fault chain scenario provided by an embodiment of the present invention, wherein (a) is a distribution network reconstruction method of scheme 1 at t=18h, (b) is a distribution network reconstruction + islanding method of scheme 2 at t=18h, (c) is a method of the present invention of scheme 3 at t=18h, (d) is a distribution network reconstruction method of scheme 1 at t=19h, 29h, and 40h, (e) is a distribution network reconstruction + islanding method of scheme 2 at t=19h, (f) is a method of the present invention of scheme 3 at t=19h, (g) is a distribution network reconstruction + islanding method of scheme 2 at t=29h, (h) is a method of the present invention of scheme 3 at t=29h, (i) is a distribution network reconstruction + islanding method of scheme 2 at t=40h, and (j) is a method of the present invention of scheme 3 at t=40h;

[0074] Figure 10 It is the load loss in the distribution network accident chain scenario provided by the embodiment of the present invention; wherein, (a) is the total load loss of the distribution network, (b) is the load loss of the first-level load of the distribution network, (c) is the load loss of the second-level load of the distribution network, and (d) is the load loss of the third-level load of the distribution network. DETAILED DESCRIPTION

[0075] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0076] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0077] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0078] In response to the problems of inaccurate characterization of the evolution mechanism of distribution network equipment failures under extreme snowy weather and the inability of existing distribution network fault recovery methods to effectively characterize the control mode of distributed power sources, the present invention proposes an active distribution network fault recovery strategy that takes fault evolution into account under extreme snowy weather. The strategy first clarifies the impact of the mechanical failure process of distribution network equipment and the uncertainty of distribution network power flow under extreme snowy weather, quantifies the probability of equipment failure and the probability of system state transition, and derives a distribution network cascading failure evolution model based on improved random power flow. Secondly, based on the regional division idea of ​​point localization, the subordinate relationship between the master control node, slave control node and load node in the island area is comprehensively considered. Combined with the master-slave control logic of the island, the constraints between the master control node, slave control node and load node are derived, and a distribution network fault recovery model that takes into account the coordination of reconstruction and island division is constructed. The strategy includes the following aspects:

[0079] 1) A distribution network cascading failure evolution model based on an improved stochastic power flow model under extreme snow and ice weather conditions is proposed. Considering the distribution network fault evolution characteristics and DG output characteristics under extreme snow and ice weather conditions, the probability of mechanical failure of distribution network equipment and the probability of system state transition are quantified. Based on a stochastic power flow algorithm for distribution networks that considers line disconnection, the model accurately characterizes the distribution network fault evolution mechanism.

[0080] 2) A DG operation model is proposed that takes into account the transition between V / f control and PQ control. During the transition from grid-connected mode to islanded mode, the change in DG control mode leads to changes in its power output characteristics. An auxiliary binary variable representing the DG control mode is introduced to characterize the DG power output characteristics, enabling a precise characterization of the power output changes during the transition between V / f control and PQ control.

[0081] 3) A distribution network fault recovery model that takes into account the coordination of reconstruction and islanding is proposed. Based on the regional division idea of ​​"point-based region determination" and combined with the power output characteristics of DG, a V / f-controlled DG is used as the island master control unit, and this node is used as the regional dominant "node". Judgment variables that characterize the affiliation between the master control unit, slave control unit, and distribution network load are introduced to deduce the "region" to which various nodes in the distribution network belong. While ensuring the connectivity and radial operation of the reconstruction area and the island area, the organic coordination of reconstruction and islanding is achieved, effectively improving the fault recovery capability of the distribution network.

[0082] Example 1

[0083] like Figure 1 As shown, this embodiment provides a distribution network fault recovery method taking into account fault evolution under extreme weather conditions, including the following steps:

[0084] Step 1: Establish a rectangular coordinate system with the root node of the distribution network as the origin, and calculate the overall failure probability of the distribution network line based on the failure mechanism of the distribution network conductors and towers;

[0085] The specific steps include:

[0086] Step 101: Take the extreme snow weather meteorological center coordinates (L x,t ,L y,t ) and the moving speed of the meteorological center v ice Describe the movement path of the extreme snow and ice weather meteorological center, expressed as:

[0087]

[0088] Where: (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 represents the moving speed of the meteorological center; θ is the angle between the moving speed of the meteorological center and the coordinate axis x-axis.

[0089] Step 102: Comprehensively consider the effects of current and electric heat, ambient temperature, wind speed, and precipitation rate on conductor icing to obtain the relationship between conductor failure rate and extreme snowy weather, expressed as:

[0090]

[0091] Where: m ij is the conductor mass per unit length of wire; is the specific heat capacity of the conductor material of wire ij; τ ij,t is the operating temperature of the conductor ij; R ij is the resistance of circuit ij; I ij,t is the current of line ij at time t; μ1 is the resistance temperature coefficient of the distribution network conductor; τ envir and τ ref They are the current ambient temperature and the rated ambient temperature respectively; 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; is the outer diameter of the conductor ij; is the change in ice coverage per unit length of conductor ij at time t; is the ice thickness of conductor ij at time t; z x and z y are the load parameters of the wire x-axis and y-axis respectively; (x ij ,y ij) is the coordinate of the wire ij; is the failure rate of conductor ij at time t; a1, a2, a3, b1, b2, c1 and c2 are constant coefficients of the equation; n line Design the ice load that the line can withstand.

[0092] Step 103: Calculate the tower failure rate of the conductors by taking into account the ice load on the distribution network towers;

[0093] The ice load on distribution network towers mainly refers to the tension generated when the two ends of the conductor are hung on the tower, which depends on vertical loads such as the conductor's own gravity and the gravity of ice covering the conductor.

[0094]

[0095] Where: is the unit vertical load of conductor ij at time t; is the ice load on a single tower of conductor ij at time t; l1 and l2 are the spans on both sides of the tower; h1 and h2 are the height differences between the two ends of the conductor suspension position; and is the horizontal tension of the lines on both sides of the tower; is the tower failure rate of conductor ij at time t; N pole is the ice load that the tower is designed to withstand; c3 and c4 are constant coefficients.

[0096] Step 104: Equivalently model the entire distribution line as a conductor and tower in series. The overall line failure rate is expressed as:

[0097]

[0098] Where: is the overall failure rate of line ij at time t; u is the number of line conductors; m is the number of towers on the line; is the failure rate of the sth conductor of line ij; is the failure rate of the p-th tower on line ij.

[0099] Step 2: Use random power flow to characterize cascading failures in the distribution network and construct a linear random power flow model. Based on the linear random power flow model, a random power flow model considering line disconnection is constructed in combination with a random compensation power method based on sensitivity analysis to obtain the real-time outage probability of the line.

[0100] The specific steps include:

[0101] Step 201: Construct a linear stochastic power flow model by describing distribution network cascading failures through stochastic power flow.

[0102] The power equation of the stochastic power flow model can be expressed as:

[0103]

[0104] Where W is the active and reactive power variables of the node; Γ is the power equation; X is the state variable consisting of the node voltage and phase angle; Y is the network parameter; Z is the branch power flow random variable; and Η is the branch power flow equation.

[0105] After expanding the power equation at the reference operating point using the Taylor series and ignoring the higher-order terms above the second order, we can obtain:

[0106]

[0107] Where ΔX is the random response to the random disturbance ΔW; ΔZ is the random response of the branch power flow random variable to the random disturbance ΔW.

[0108] J is the Jacobian matrix of the last iteration of the power flow calculation; S0 is the sensitivity matrix, where: S0 = [Γ′ x (X,Y)] -1 , G0=[Η′ x (X,Y)] -1 .

[0109] Step 202: construct a random power flow model considering line disconnection by combining a random compensation power method based on sensitivity analysis;

[0110] In the line-off scenario, the sensitivity matrix method is used to calculate the random power flow. Its essence is to introduce random compensation power at the corresponding nodes of the distribution network to simulate branch off. When the distribution network line network changes ΔY, its state variable will also change ΔX. Equation (15) is expanded using the Taylor series at the operating reference point and converted to:

[0111]

[0112] Ignore (ΔX) 2 Term and higher order term, because Γ(X,Y) is a linear function of Y, so Γ″ yy (X,Y)(ΔY) 2 = 0. When the change of node power injection is not considered, ΔW = 0, so Equation (17) is simplified to:

[0113]

[0114] Where: I is the unit matrix; ΔW y It is the disturbance of the node injection power caused by the disconnection.

[0115] Assuming that the nodes at both ends of the disconnected branch are i and j, it can be written in matrix form:

[0116]

[0117] Where: and ...are the elements in the sensitivity matrix whose rows and columns are related to the endpoints of the disconnection; H ij 、N ij 、J ij and L ij is the corresponding element in the Jacobian matrix; ΔP i , ΔQ i , ΔP j and ΔQ j are the compensation powers when line ij is disconnected.

[0118] Step 203: Solve the stochastic power flow model of line disconnection to obtain the probability distribution of the power flow of each branch;

[0119] In this embodiment, the probabilistic power flow calculation utilizes the semi-invariant method and Gram-Charlier series expansion method. This simplifies the convolution and deconvolution operations required to obtain the probability density function of the sum of random variables into a few semi-invariant algebraic operations, thereby reducing the computational effort. Furthermore, using the Gram-Charlier series expansion, the probability density function (PDF) and cumulative distribution function (CDF) of the desired state variable can be obtained in a single calculation.

[0120] Step 204: Calculate the real-time outage probability of the line based on the probability distribution of the power flow of each branch;

[0121] Various disturbance events, such as line outages caused by extreme snow and ice weather, lead to changes in system status. Therefore, the line overload outage probability can be expressed using a piecewise function:

[0122]

[0123] Where: is the probability of line l being out of service due to overload at time t; To protect the hidden fault probability; P l is the active power of line l; P l r and P l m are the rated power and maximum transmission power of line 1 respectively.

[0124] The line flow obtained by random flow calculation is no longer a fixed value, but a probability distribution of the line flow. It cannot be directly substituted into Equation (22) to obtain the line outage probability. It needs to be further solved in the form of convolution. Therefore, the real-time line outage probability is expressed as:

[0125]

[0126] Where: f(P l ) is the line active power probability density function obtained by random power flow calculation.

[0127] Step 3: Based on the overall failure probability of the distribution network lines, the real-time outage probability of the lines, and the determined operating status of the distribution network equipment, the system state change process in continuous time is discretized to calculate the distribution network system state transition probability;

[0128] The specific steps include:

[0129] Step 301: Determine the operating status of the distribution network equipment;

[0130] Extreme snow and ice weather and current shifts may cause distribution network line failures, thereby causing changes in the distribution network state. The operating status of distribution network equipment is expressed as:

[0131]

[0132] Where: is the state of the distribution network line l at time t, Indicates that the equipment is operating normally, otherwise it indicates a fault; and are the 0-1 state variables of distribution network equipment l at time t after being affected by extreme weather and power flow transfer, and Indicates that the device is operating normally, otherwise it indicates a fault.

[0133] Step 302: Based on the operating status of the distribution network equipment, the overall failure probability of the distribution network lines, and the real-time outage probability of the lines, the distribution network state change process in continuous time is discretized to calculate the distribution network state transition probability;

[0134] Extreme ice and snow weather affects the distribution network lines and photovoltaic units within the affected area, and the resulting changes in system status are time-series.

[0135] Discretizing the distribution network state change process in continuous time can simulate the fault evolution process. In this embodiment, the distribution network state transition process can be regarded as a discrete-time Markov process:

[0136]

[0137] Where: is the state o of the distribution network at time t; The distribution network status is Transfer to probability; and is the state o of the distribution network at time t and time t+1; Ω l,t+1 is the set of devices that may fail at time t+1; The device operating status is Transfer to probability; and They are the probability of equipment ij failing due to extreme ice and snow weather at time t+1 and the probability of equipment l failing due to cascading failures.

[0138] The distribution network continues to evolve from the entry to the end of extreme snow and ice weather, which may include multiple evolution paths. Its occurrence probability is expressed as the sum of the probabilities of each evolution path:

[0139]

[0140] Where: The device's operating status Probability of occurrence; The system evolves from the initial state to the state A set of paths; The system moves from the initial state to the state along path r probability.

[0141] In this embodiment, when the distribution network state transition probability When the probability is greater than the set threshold, in the distribution network fault recovery model in step 5, the 0-1 state variable x of line ij at time t is ij,t Equal to 0, indicating that line ij is disconnected at time t.

[0142] Step 4: When the grid-connected mode is switched to the island mode, the power output characteristics of the master control unit and the slave control unit are calculated respectively when the system switches from the grid-connected operation state to the island operation state, and the power output characteristics of the distributed photovoltaic units are calculated when the system switches from the grid-connected operation state to the island operation state under extreme snow and ice weather conditions;

[0143] In this embodiment, the change in the power output characteristics of the distributed generation caused by the change in the control mode of the distributed generation is considered. An auxiliary binary variable representing the DG control mode is introduced to obtain the power output characteristics of the DG. This allows for an accurate characterization of the power output changes during the conversion process between DG V / f control and PQ control.

[0144] The specific steps include:

[0145] Step 401: Analyze the island and DG operation characteristics of the master-slave control;

[0146] Active distribution network includes multiple energy inputs such as MT, DG and substation, and multiple operating states such as grid-connected and islanded. The islanded operating state includes two control modes: peer control and master-slave control. The two control structures are as follows: Figure 2 shown.

[0147] Peer control means that when the power grid is in island operation mode, all DGs in the system have equal control status. There is no master-slave relationship between the controllers. Each DG is controlled based on local information about the voltage and frequency of the connected system. However, the voltage and frequency of the system may change with load fluctuations, causing island instability.

[0148] Master-slave control refers to when the power grid is in island mode. One DG in the system acts as the master control unit, employing V / f control to provide voltage and frequency references for the other DGs in the system and to track load fluctuations. The other DGs, on the other hand, act as slaves, employing constant power control (PQ) control. When the system is in grid-connected mode, all DGs use PQ control. However, once the system switches to island mode, the master DG must quickly transition from PQ control to V / f control, while the slaves maintain PQ control. MTs, due to their stable power output and ease of control, were selected as the master control unit in this embodiment.

[0149] Step 402: Calculate the power output characteristics of the main control unit when the computing system switches from the grid-connected operation state to the island operation state;

[0150] In this embodiment, when the system switches from the grid-connected operation state to the island operation state, the main control unit switches from PQ control to V / f control, and its power output characteristics can be expressed as:

[0151]

[0152] Where: Ω DG is the set of all DG grid-connected nodes; T is the set of fault recovery time; and are the active power and reactive power generated by the DG at node i at time t, respectively; and are node i at time t

[0153] DG is at the upper limit of active power output and reactive power output; V i,t is the voltage of node i at time t; V0 is the rated voltage of DG as the main control unit; k i,t k is a 0-1 state variable that indicates whether the DG at node i is in V / f control at time t. i,t=1 indicates that the DG at node i adopts V / f control, otherwise it adopts PQ control.

[0154] Step 403: When the system switches from the grid-connected operation state to the islanded operation state, the power output characteristics of the slave control unit are calculated;

[0155] In this embodiment, when the system switches from the grid-connected operation state to the island operation state, the slave control unit maintains the PQ control unchanged, and its power output characteristics can be expressed as:

[0156]

[0157]

[0158] Where: and are the active power reference value and reactive power reference value of DG at node i at time t, respectively.

[0159] Step 404: Calculate the power output characteristics of the distributed photovoltaic units under extreme snowy weather conditions when the system switches from a grid-connected operation state to an islanded operation state.

[0160] Extreme snow and ice weather can cause icing problems on distributed photovoltaic units. When the system switches from grid-connected operation to island operation, the distributed photovoltaic units maintain PQ control unchanged, and their power output characteristics can be expressed as follows:

[0161]

[0162] Where: is the ice thickness of distributed photovoltaic at node i at time t; d1, d2, d3 and d4 are constant coefficients; and are the active power and reactive power generated by the distributed photovoltaic at node i at time t; is the radiation intensity at node i at time t; θ PV is the distributed photovoltaic power factor angle, and are the x-axis and y-axis coordinates of the distributed photovoltaic at node i.

[0163] Step 5: Combining the distribution network system state transition probability, the power output characteristics of the master and slave control units, and the power output characteristics of the distributed photovoltaic units, derive the constraints between the master control node, slave control nodes, and distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding.

[0164] The specific steps include:

[0165] Step 501: construct an objective function of a distribution network fault recovery model that takes into account coordination between reconstruction and islanding.

[0166] The main task of distribution network fault recovery is to restore as much power as possible while reducing the number of operations of section switches and tie switches. To this end, this embodiment takes the minimum amount of power loss in the distribution network and the minimum number of switch operations as the optimization goal.

[0167] minF=ω1f1+ω2f2 (32),

[0168]

[0169] Where: F is the overall objective function; f1 and f2 are sub-objective functions that characterize the load loss of the distribution network and the number of switch operations respectively; ω1 and ω2 are the weight coefficients of the sub-objective functions respectively; P LOSS and P ALL are the weighted unload amount and total load amount respectively; Ω n is the set of all nodes in the distribution network; i,t is the 0-1 state variable of node i at time t, y i,t =1 means that node i is powered on at time t, otherwise node i is powered off; ω k1 、ω k2 and ω k3 are the weight coefficients of the primary load, secondary load and tertiary load of the distribution network respectively; and are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; Ω ope and Ω clo are the sets of all tie switches and section switches respectively; x ij,t is the 0-1 state variable of line ij at time t, x ij,t =1 means that line ij is in operation at time t, otherwise it is in disconnection; N line is the total number of switches in the distribution network.

[0170] Step 502: Constructing collaborative constraints for reconstruction and island partitioning;

[0171] In this embodiment, based on the regional division idea of ​​"point-based region determination", the V / f controlled DG grid-connected node is used as the dominant "node" of the region, and by introducing auxiliary variables that characterize the logical relationship between the node and the region, it is used to determine the divided "region" where the distribution network node is located. By constructing the node quantity relationship constraint, radial shape and connectivity constraints within the divided region, the coordination of distribution network reconstruction and island division can be achieved.

[0172] Among them, considering that the root node and the V / f controlled DG grid-connected node can be used as the dominant node of the region, the auxiliary variable B is introduced to represent the logical relationship between the node and the region. i,j,t , to realize the division of distribution network areas, and then realize the coordination of reconstruction and island division, including:

[0173] 1) Divide regional constraints

[0174]

[0175] Where: Ω sub is the set of nodes connected to the substation; Ω DG is the set of all DG grid-connected nodes; Ω (i) is the set of all nodes in the region formed by node i as the dominant node; B i,j,t 0, N is whether node j is located in the partition area of ​​dominant node i bus is the total number of distribution network nodes.

[0176]

[0177] Where: Ω l is the set of all branches; The V / f control DG emits virtual power at node i at time t; F ij,t is the virtual power flow transmitted by branch ij at time t; M is a sufficiently large positive number. ki,t is the virtual power flow transmitted by branch ki at time t; Equation (39) indicates that only the DG using V / f control can generate virtual power; Equation (40) represents the virtual power flow balance within the region; Equation (41) is the correlation constraint between the virtual power flow and the switch state variable, which realizes the coupling of the virtual power flow and the switch state variable to avoid the phenomenon that the virtual power flow in the line is still not zero when the switch is disconnected; Equation (42) is the radial constraint, that is, the number of nodes is equal to the number of regions plus the number of operating branches.

[0178] Step 503: Construct distribution network power flow constraints;

[0179] This embodiment adopts the Distflow power flow model of the radial distribution system and introduces 0-1 state variables that characterize the node operating status and branch operating status, converting it into a power flow model suitable for distribution network fault recovery.

[0180]

[0181] Where: P ij,t and Q ij,t are the active power and reactive power of line ij at time t respectively; R ij and X ij are the resistance and reactance of line ij respectively; Iij,t is the current of line ij at time t; and are the active power and reactive power injected into node i at time t respectively; and are the active power and reactive power output by the substation connected to node i at time t; and are the reactive powers of the primary load, secondary load and tertiary load of node i at time t. ki,t and Q ki,t are the active power and reactive power of line ki at time t; R ki and X ki are the resistance and reactance of line ki respectively; is the square of the voltage at node i at time t; is the square of the voltage at node j at time t;

[0182] Step 504: Construct distribution network security constraints;

[0183] During the distribution network fault recovery process, it is necessary to ensure that the node voltage and branch current are within the safe operating range.

[0184]

[0185] Where: V i max and V i min are the square values ​​of the upper and lower limits of the voltage amplitude of node i respectively; It is the square value of the upper limit of the current amplitude of branch ij.

[0186] Step 6: Solve the distribution network fault recovery model that takes into account the coordination of reconstruction and island partitioning, and obtain the fault recovery strategy.

[0187] Since Equation (46) presents non-convex features, it is difficult to solve the fault recovery model proposed in this embodiment. Therefore, we introduce and Perform an equivalent transformation and use the second-order cone relaxation method to transform the model into a mixed integer linear programming model, which is convenient for direct solution. Equation (43) and Equation (41)-Equation (48) can be rewritten as:

[0188]

[0189]

[0190] Where: is the square of the voltage at node i at time t; is the square of the current of line ij at time t; ||·||2 is the two-norm operator.

[0191] When the distribution network line switch is in the disconnected state, causing node i and node j to be disconnected, equation (45) becomes invalid. The Big-M method is used to rewrite equation (45) as follows:

[0192]

[0193] Case Analysis

[0194] Taking the PG&E69 node test system as an example, the effectiveness of the active distribution network fault recovery model proposed in this invention considering fault evolution under extreme ice and snow weather is verified. Figure 3 As shown, the load fluctuation curve is as follows Figure 4 As shown in the figure, the distribution network is connected to 6 MTs and 5 distributed photovoltaic units. The detailed parameters of MT are shown in Table 1:

[0195] Table 1 MT parameters

[0196]

[0197] The coordinate system is established with the root node as the origin. The initial position of the extreme snow weather meteorological center is (-150km, -150km), and it moves at a speed of 4.2km / h in a direction of 45° with the horizontal axis. The duration is 50h and the time step is 1h. In the analysis of cascading failures of distribution networks, the line limit transmission power P l m =1.4P l r , the maximum search depth of cascading accidents is 2, and the cascading failure probability threshold is 0.01.

[0198] 5. Simulation of time-varying failure rate and cascading failures of distribution lines

[0199] 5.1. Failure rate of distribution lines in extreme snowy and icy weather

[0200] The overall time-varying failure rate of distribution lines affected by extreme ice and snow weather is as follows: Figure 5 shown.

[0201] Depend on Figure 5 As can be seen, the overall distribution line failure rate increases relatively slowly between hours 0 and 30, but after 30 hours, the failure rates of each line increase exponentially. This is because the extreme snow and ice weather during the hours 0-30 is far from the distribution network, resulting in a slow increase in the failure rate of distribution network conductors and towers. Consequently, the overall failure rate of the distribution network lines increases slowly. After 30 hours, distribution lines 61-63 are affected by the extreme snow and ice weather, and their conductors experience a sharp increase in ice. This leads to an increase in the failure rate of the conductors and towers on lines 61-63, which in turn causes an exponential increase in the overall failure rate of the lines.

[0202] 5.1.2 Distribution network cascading failure simulation

[0203] This paper uses the Markov Chain Monte Carlo (MCMC) method to extract the state of distribution network components time-by-time, identifying faulty lines caused by extreme snow and ice weather. During the simulation, distribution lines 65, 16, 11, and 52 experienced failures at the 18th, 19th, 29th, and 40th hours of the extreme snow and ice weather, respectively, with corresponding failure rates of 48.87%, 48.85%, 49.04%, and 49.90%.

[0204] Distribution network fault evolution path and system response Figure 6 As shown in Figure B Cas is the probability of cascading failure, P loss is the load loss of the distribution network, and the cumulative distribution of power flow of distribution line 1 and line 2 is shown in Figure 7 ,in, Figure 7 (a) is the cumulative distribution of power flow on line 1, and (b) is the cumulative distribution of power flow on line 2. Figure 7 The solid red line in the middle is the rated capacity of the distribution line.

[0205] Depend on Figure 6 It can be seen that when extreme ice and snow weather causes the failure of distribution network line 65, the probability of line 1 and line 2 power flow exceeding the limit outage is 30.37% and 28.67% respectively, and through Figure 7 It can be seen that Lines 1 and 2 are at risk of overload. Furthermore, the distribution network experienced load losses of 5377.84 kW and 5646.61 kW at the 19th and 40th hours, respectively. This is because the failure of Line 65 caused power loss at nodes 66-69 and PV5 to disconnect from the grid. Furthermore, the relatively low load at nodes 66-69 resulted in a system power shift, causing either Line 1 or Line 2 to shut down. Because Node 2 is a zero-injection node, the resulting load loss in the distribution network caused by the cascading failure of either Line 1 or Line 2 at the 19th hour is consistent. Although the probability of overload outages for Lines 1 and 2 is low, if Line 1 or Line 2 were to disconnect, the distribution network would lose connection to the root node, leading to a complete power loss. The subsequent load loss in the distribution network would change with fluctuations in the load forecast curve.

[0206] 5.2 Distribution Network Fault Restoration Topology Analysis

[0207] Typical fault scenarios are generated based on distribution network accident chains 1 and 2. Accident chain 1 is: distribution lines 65, 16, 1, 11, and 52 fail at 18h, 19h, 19h, 29h, and 40h during the extreme snowy weather; accident chain 2 is: distribution lines 65, 16, 2, 11, and 52 fail at 18h, 19h, 19h, 29h, and 40h during the extreme snowy weather. In extreme snowy weather, the thickness of ice covering photovoltaic panels gradually increases, reducing the sunlight intensity on the surface of the photovoltaic panels, resulting in a decrease in photovoltaic output. The output of distributed photovoltaics from 0 to 50 hours is as follows: Figure 8 In order to demonstrate the effectiveness and superiority of the fault recovery strategy proposed in this invention, three schemes are set up for comparison.

[0208] Solution 1: Restore power to the power-lost area by reconfiguring the distribution network.

[0209] Solution 2: Use the reconstruction + islanding method to restore power supply to the power-lost area of ​​the distribution network, in which the islanding operation adopts a peer-to-peer control method.

[0210] Solution 3: Use the distribution network fault recovery method proposed in the present invention that combines reconstruction with islanding to supply power to the power-lost area.

[0211] 5.2.1 Analysis of the topological structure of the fault recovery chain of the distribution network

[0212] The topological structures after power supply restoration at 18h, 19h, 29h and 40h for the three schemes in the distribution network fault chain scenario are as follows: Figure 8 shown.

[0213] Depend on Figure 9 (a) and Figure 9 As shown in (d), at hour 18, the distribution network was able to restore power to nodes 66-68 by closing tie switch S71. When the distribution network lost connection with the root node at hour 19, the traditional reconfiguration model failed to fully utilize the MT's power support capabilities, resulting in a large number of loads in the distribution network losing power.

[0214] Depend on Figure 9 (b) Figure 9 Middle (e), Figure 9 Middle (g) and Figure 9As shown in (i), at hour 18, the distribution network restored power to nodes 66-68 by closing tie switch S71. At hour 19, the primary loads at nodes 9, 35, 37, and 42 lost power; the secondary loads at nodes 29, 34, 38-41, 44, 49, 50, 55, 56, and 66 lost power; and the tertiary loads at nodes 10, 11, 28, 43, 45-48, 59, and 60 lost power. At hour 29, the primary load at node 37 lost power; the secondary loads at nodes 38, 39, 55-56, 66-69 lost power; and the tertiary loads at nodes 11 and 16 lost power. At 40 hours, primary loads at nodes 35, 37, and 57 lost power; secondary loads at nodes 14, 15, 17, 29, 34, 38-41, 44, 49, 50, 53-56, 58, and 66-69 lost power; and tertiary loads at nodes 10, 11, 13, 16, 43, 45-48, 59, and 60 lost power. Restoring power to the lost distribution network area using a reconfiguration + islanding strategy with peer-to-peer control of the islands only restored power to the lost loads around the MT, failing to fully utilize the DG's collaborative power supply capabilities. This resulted in the shedding of a significant number of primary loads.

[0215] Depend on Figure 9 (c) Figure 9 Middle (f), Figure 9 Middle (h) and Figure 9As shown in (j), using the proposed fault recovery method combining reconstruction and islanding, at hour 18, the distribution network restored power to nodes 66-68 by closing tie switch S69. At hour 19, power was lost to the secondary loads at nodes 38, 39, 41, 44, 49, 50, and 58, and to the tertiary loads at nodes 16, 43, 45-48, 59, and 60. The master MTs were MT4 and MT6, respectively. By opening section switch S60 and closing tie switches S70 and S73, an island region was formed, with MT1, MT2, MT3, MT4, and MT5 providing coordinated power, restoring power to more primary loads. At the 29th hour, the secondary loads at nodes 38, 39, 55, 56, and 66 lost power, and the tertiary loads at nodes 10, 11, 16, and 48 lost power. The main control MTs were MT4 and MT6. Since the 29th hour was a low-power period, by opening the section switches S9, S15, S47, and S48 and closing the tie switches S70 and S73, two larger island areas consisting of MT1, MT2, MT5, and MT6 and MT3 and MT5 were formed, restoring more primary and secondary loads. At the 40th hour, the primary loads at nodes 9, 42, and 57 lost power, the secondary loads at nodes 8, 12, 14, 15, 17, 38-41, 44, 49, 50, 53-58, and 66-69 lost power, and the tertiary loads at nodes 7, 10, 11, 13, 16, 43, 45-48 lost power. The main control MTs were MT3, MT4, and MT6. Since the 40th hour was during the peak power consumption period, the section switches S6 and S37 were disconnected, and MT1, MT2, MT5, and MT6 coordinated to supply power, restoring power to the primary loads at nodes 35 and 37.

[0216] In summary, the distribution network fault recovery method with coordinated reconstruction and islanding proposed in the present invention uses the V / f-controlled MT as the island master control unit, achieving connectivity and radial operation between the reconstruction area and the island area while ensuring the organic coordination of reconstruction and islanding, effectively improving the fault recovery capability of the distribution network.

[0217] 5.2.2 Analysis of MT Operation Characteristics of V / f Control and PQ Control Conversion in Distribution Network Fault Chain Scenario

[0218] To verify the impact of the MT operating characteristics of the proposed V / f control and PQ control conversion on the MT active output, three schemes under the distribution network fault chain scenario are taken as examples. The MT active output at the 18th hour, 19th hour, 29th hour, and 40th hour is shown in Table 2.

[0219] Table 2 Distribution network fault chain 1MT active output

[0220]

[0221] Table 2 shows that at hour 18, all MTs in Scheme 1's reconstruction method use PQ control, and their output power is rated. At hours 19, 29, and 40, the MT output power in the distribution network reconstruction method is zero. This is because at hour 19, when the distribution network loses connection with the root node, the traditional reconstruction method cannot fully utilize the MT's power support capacity, resulting in 0 kW of active power output from the MT.

[0222] At hour 18, all MTs in Scheme 2, which uses reconfiguration and islanding with peer-to-peer control, use PQ control, and their output power is rated. At hours 19, 29, and 40, MTs in Scheme 2, which uses reconfiguration and islanding with peer-to-peer control, have equal control status, and their active output varies with the fluctuations of the load forecast curve near the MT.

[0223] At hour 18, in the proposed DG operation model for switching between V / f control and PQ control, all MTs adopted PQ control, with their output power at rated power. At hours 19 and 29, the master MTs, MT4 and MT6, respectively, adopted V / f control to follow load fluctuations, while the remaining MTs adopted PQ control and maintained their output power at rated power. At hour 40, the master MTs, MT3, MT4, and MT6, followed load fluctuations, while MT1, MT2, and MT5 maintained their output power at rated power.

[0224] In summary, the DG operation model proposed in this invention, which takes into account the conversion between V / f control and PQ control, can effectively characterize the changes in power output characteristics caused by changes in the DG control mode, and achieves accurate characterization of power output changes during the conversion between V / f control and PQ control.

[0225] 5.3 Analysis of distribution network restoration effect

[0226] In order to verify the advantages of the fault recovery strategy of coordinated reconstruction and island partitioning proposed in this invention in terms of the amount of load recovery after power outages in the distribution network, the three schemes proposed in 5.2 are used for comparative analysis.

[0227] The load loss of the three schemes under the distribution network fault chain scenario is as follows Figure 10 shown.

[0228] Depend on Figure 10 As can be seen in (a), from the 19th hour to the 50th hour, the total load loss of the fault recovery method of the present invention with coordinated reconstruction and island partitioning is much lower than that of Solution 1 and also lower than that of Solution 2. This is because the fault recovery method of the present invention with coordinated reconstruction and island partitioning deeply taps the MT power support potential, fully utilizes the MT's coordinated power supply capabilities, and achieves efficient recovery of the distribution network's lost load. Figure 10It can be seen from (b) that except for the 33rd hour, the first-level load recovery rate of the fault recovery method of coordinated reconstruction and island division proposed by the present invention is lower than that of Scheme 2. From the 18th to the 32nd hour and from the 34th to the 50th hour, the first-level load loss of the fault recovery method of coordinated reconstruction and island division proposed by the present invention is much lower than that of Scheme 1 and Scheme 2. This is because the method of coordinated reconstruction and island division proposed by the present invention can realize MT coordinated power supply, and then realize load transfer, which gives priority to ensuring the power supply of important loads. Figure 10 As can be seen in (c), at hours 26-28, 31, 32, 38, 39, and 40-50, the secondary load power loss in the proposed fault recovery method with coordinated reconstruction and islanding is slightly higher than that in Scheme 2, but much lower than that in Scheme 1. This is because the proposed fault recovery method with coordinated reconstruction and islanding prioritizes power supply to important loads through the coordinated power supply of the MTs, thereby sacrificing the power supply to some secondary loads.

[0229] Depend on Figure 10 As can be seen in (d), at time points 23, 25, 27-29, 42, and 44, the power loss of the tertiary loads using the proposed fault recovery method with coordinated reconstruction and islanding is higher than that of Scheme 2, but much lower than that of Scheme 1. This is because the proposed fault recovery method with coordinated reconstruction and islanding prioritizes restoring power to important loads by adjusting the switch states, thereby sacrificing the power supply to some tertiary loads.

[0230] In summary, the above further verifies that the distribution network fault recovery method of coordinated reconstruction and islanding proposed in this invention can fully utilize the power support potential of MT while ensuring the power supply of important loads, and efficiently restore the power supply to the power-lost area of ​​the distribution network.

[0231] Example 2

[0232] This embodiment provides a distribution network fault recovery system that takes fault evolution into account under extreme weather conditions, including:

[0233] The fault evolution analysis module establishes a rectangular coordinate system with the root node of the distribution network as the origin, and calculates the overall failure probability of the distribution network line by combining the failure mechanisms of the distribution network conductors and towers. A linear stochastic power flow model is constructed using stochastic power flow to characterize cascading failures in the distribution network. Based on this linear stochastic power flow model, a stochastic power flow model that considers line disconnection is constructed in combination with a stochastic compensation power method based on sensitivity analysis to obtain the real-time outage probability of the line.

[0234] The operation analysis module is used to discretize the system state change process in continuous time by combining the overall failure probability of the distribution network line, the real-time line outage probability, and the determined operating status of the distribution network equipment, and calculate the distribution network system state transition probability. It also calculates the power output characteristics of the master control unit and the slave control unit when the system switches from the grid-connected operation state to the islanded operation state, and calculates the power output characteristics of the distributed photovoltaic unit when the system switches from the grid-connected operation state to the islanded operation state in extreme ice and snow weather.

[0235] The fault recovery module is used to combine the distribution network system state transition probability, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units to derive the constraints between the master control node, the slave control node, and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding; solve the distribution network fault recovery model that takes into account the coordination of reconstruction and islanding to obtain a fault recovery strategy.

[0236] Example 3

[0237] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the distribution network fault recovery method taking into account fault evolution under extreme weather conditions as described above are implemented.

[0238] Example 4

[0239] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the distribution network fault recovery method taking into account fault evolution under extreme weather conditions as described above are implemented.

[0240] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A distribution network fault recovery method taking into account fault evolution under extreme weather conditions, characterized in that: The steps include: A rectangular coordinate system is established with the root node of the distribution network as the origin. Combined with the failure mechanism of the distribution network conductors and towers, the overall failure probability of the distribution network line is calculated. A linear stochastic power flow model is constructed by characterizing cascading failures in the distribution network through random power flow. Based on the linear stochastic power flow model, a stochastic power flow model considering line disconnection is constructed in combination with a random compensation power method based on sensitivity analysis, and the real-time line outage probability is obtained. Combining the overall failure probability of the distribution network line, the real-time outage probability of the line and the determined operating status of the distribution network equipment, the system state change process in continuous time is discretized and the distribution network system state transition probability is calculated; Calculate the power output characteristics of the master and slave control units when switching from grid-connected operation to islanded operation, and calculate the power output characteristics of distributed photovoltaic units when switching from grid-connected operation to islanded operation in extreme snowy weather. Combining the distribution network system state transition probability, the power output characteristics of the master and slave control units, and the power output characteristics of distributed photovoltaic units, we derive the constraints between the master and slave control nodes and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding. The distribution network fault recovery model that takes into account the coordination of reconstruction and island partitioning is solved, and the fault recovery strategy is obtained.

2. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The method of establishing a rectangular coordinate system with the root node of the distribution network as the origin and calculating the overall failure probability of the distribution network line in combination with the failure mechanism of the distribution network conductors and towers includes: Based on the movement path of the meteorological center of extreme snow and ice weather, the influence of current electrothermal, ambient temperature, wind speed and precipitation rate on conductor icing is comprehensively considered to obtain the conductor failure rate associated with extreme snow and ice weather. Considering the ice load on distribution network towers, calculate the tower failure rate of conductors; The overall failure rate of the distribution network lines is calculated by combining the conductor failure rate associated with extreme ice and snow weather and the tower failure rate of the conductor.

3. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The method uses random power flow to characterize the cascading failures of the distribution network and construct a linear random power flow model. Based on the linear random power flow model, a random power flow model considering line disconnection is constructed in combination with a random compensation power method based on sensitivity analysis to solve the real-time line outage probability, including: The linear stochastic power flow model is constructed by characterizing the cascading failure of distribution network through stochastic power flow; Combining the random compensation power method based on sensitivity analysis, a random power flow model considering line interruption is constructed; Solve the stochastic power flow model of line interruption and obtain the probability distribution of power flow in each branch; The real-time outage probability of the line is calculated based on the probability distribution of the power flow of each branch.

4. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 3, characterized in that: The real-time outage probability of the line is expressed as: Where: f(P l ) is the probability density function of the line active power obtained by random power flow calculation, is the probability of line l being out of service due to overload at time t; To protect the hidden fault probability; P l is the active power of line l; P l r and P l m are the rated power and maximum transmission power of line 1 respectively.

5. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The state transition probability of the distribution network system is: in, The distribution network status is Transfer to probability; and is the state o of the distribution network at time t and time t+1; Ω l,t+1 is the set of devices that may fail at time t+1; The device operating status is Transfer to probability; and They are the probability of equipment ij failing due to extreme ice and snow weather at time t+1 and the probability of equipment l failing due to cascading failures.

6. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The power output characteristics of the main control unit when the grid-connected operation state is converted to the island operation state are: The power output characteristics of the slave control unit when the grid-connected operation state is converted to the island operation state are: Where: and are the active power and reactive power generated by DG at node i at time t; k i,t k is a 0-1 state variable that indicates whether the DG at node i is in V / f control at time t. i,t =1 means the DG at node i adopts V / f control, otherwise it adopts PQ control, Ω DG is the set of all DG grid-connected nodes; V i,t is the voltage of node i at time t; V0 is the rated voltage of DG as the main control unit; and are the upper limit of active power output and reactive power output of DG at node i at time t respectively; T is the set of fault recovery times; and are the active power reference value and reactive power reference value of DG at node i at time t, respectively.

7. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: In extreme snowy weather, when the system switches from grid-connected operation to island operation, the power output characteristics of the distributed photovoltaic units are as follows: Where: is the ice thickness of distributed photovoltaic at node i at time t; d1, d2, d3 and d4 are constant coefficients; and are the active power and reactive power generated by the distributed photovoltaic at node i at time t; is the radiation intensity at node i at time t; θ PV is the distributed photovoltaic power factor angle, (L x,t ,L y,t ) is the coordinate of the meteorological center of extreme snow and ice weather at time t, and are the x-axis and y-axis coordinates of the distributed photovoltaic at node i.

8. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The objective function of the distribution network fault recovery model considering the coordination of reconstruction and islanding is: minF=ω1f1+ω2f2, Where: F is the overall objective function; f1 and f2 are the sub-objective functions that characterize the load loss of the distribution network and the number of switch operations respectively; ω1 and ω2 are the weight coefficients of the sub-objective functions respectively; P LOSS and P ALL are the weighted unload amount and total load amount respectively; Ω n is the set of all nodes in the distribution network; i,t is the 0-1 state variable of node i at time t, y i,t =1 means that node i is powered on at time t, otherwise node i is powered off; ω k1 、ω k2 and ω k3 are the weight coefficients of the primary load, secondary load and tertiary load of the distribution network respectively; and are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; Ω ope and Ω clo are the sets of all tie switches and section switches respectively; x ij,t is the 0-1 state variable of line ij at time t, x ij,t =1 means that line ij is in operation at time t, otherwise it is in disconnection; N line is the total number of switches in the distribution network.

9. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions according to claim 1, characterized in that: The constraints of the distribution network fault recovery model taking into account the coordination of reconstruction and islanding include coordination constraints of reconstruction and islanding, distribution network flow constraints, and distribution network security constraints. Among them, the coordinated constraints of reconstruction and island partitioning include partitioning area constraints and connectivity and radial constraints; The partitioning area constraints are: Connectivity and radial constraints: Constructing distribution network flow constraints: Distribution network security constraints: Where: B i,j,t is a 0-1 state variable indicating whether node j is located in the partition area of ​​dominant node i, B i,j,t =1 means node j is located in the region divided by node i, otherwise node j is located outside the region divided by node i; k i,t Ω is a 0-1 state variable that represents whether the DG at node i is V / f controlled at time t, DG is the set of all DG grid-connected nodes; Ω sub is the set of nodes connected to the substation; Ω (i) is the set of all nodes in the region formed by node i as the dominant node; N bus is the total number of distribution network nodes; The V / f control DG emits virtual power at node i at time t; F ij,t is the virtual power flow transmitted by branch ij at time t; F ki,t is the virtual power flow transmitted by branch ki at time t; y i,t is the 0-1 state variable of node i at time t, T is the set of fault recovery times; M is a sufficiently large positive number; x ij,t is the 0-1 state variable of line ij at time t; P ij,t and Q ij,t are the active power and reactive power of line ij at time t respectively; P ki,t and Q ki,t are the active power and reactive power of line ki at time t; I ki,t and I ij,t is the current of lines ki and ij at time t; and are the active power and reactive power injected into node i at time t; R ij and X ij are the resistance and reactance of line ij respectively; R ki and X ki are the resistance and reactance of line ki respectively; and are the active power and reactive power output by the substation connected to node i at time t; and are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; and are the reactive powers of the primary load, secondary load and tertiary load of node i at time t respectively; is the square of the voltage at node i at time t; is the square of the voltage at node j at time t; Ω l is the set of all branches; Ω n is the set of all nodes in the distribution network; V i max and V i min are the square values ​​of the upper and lower limits of the voltage amplitude of node i respectively; It is the square value of the upper limit of the current amplitude of branch ij.

10. A distribution network fault restoration system taking into account fault evolution in extreme weather conditions, characterized by: include: The fault evolution analysis module establishes a rectangular coordinate system with the root node of the distribution network as the origin, and calculates the overall failure probability of the distribution network line by combining the failure mechanisms of the distribution network conductors and towers. A linear stochastic power flow model is constructed using stochastic power flow to characterize cascading failures in the distribution network. Based on this linear stochastic power flow model, a stochastic power flow model that considers line disconnection is constructed in combination with a stochastic compensation power method based on sensitivity analysis to obtain the real-time outage probability of the line. The operation analysis module is used to discretize the system state change process in continuous time by combining the overall failure probability of the distribution network line, the real-time line outage probability and the determined operating status of the distribution network equipment, and calculate the distribution network system state transition probability; Calculate the power output characteristics of the master and slave control units when switching from grid-connected operation to islanded operation, and calculate the power output characteristics of distributed photovoltaic units when switching from grid-connected operation to islanded operation in extreme snowy weather. The fault recovery module is used to combine the distribution network system state transition probability, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units to derive the constraints between the master control node, the slave control node, and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model that takes into account the coordination of reconstruction and islanding; solve the distribution network fault recovery model that takes into account the coordination of reconstruction and islanding to obtain a fault recovery strategy.

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