Power distribution network fault recovery method and system considering fault evolution in extreme weather

Abstract

The invention belongs to the field of power distribution network fault recovery, and provides a power distribution network fault recovery method and system considering fault evolution in extreme weather. According to the technical scheme, the active power distribution network fault recovery strategy considering fault evolution in the extreme ice and snow weather is provided for solving the problems that a power distribution network equipment fault evolution mechanism is not accurately described in the extreme ice and snow weather and an existing power distribution network fault recovery method cannot effectively represent a distributed power supply control mode. The method comprises the steps that firstly, the influence of the power distribution network equipment mechanical fault process and power distribution network power flow uncertainty in extreme ice and snow weather is clarified, the equipment fault probability and the system state transition probability are quantified, and a power distribution network cascading fault evolution model based on improved random power flow is deduced; secondly, based on a region division thought of localizing by points, comprehensively considering the affiliation relationship among a master control node, a slave control node and a load node in an island region, and combining master-slave control logic of an island to deduce constraints among the master control node, the slave control node and the load node; constructing a power distribution network fault recovery model considering reconstruction and island division cooperation; and the recovery capability of the power distribution network is improved while the characteristics of flexibility and variability of the power distribution network topology are exerted.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network fault recovery, and particularly relates to a distribution network fault recovery method and system considering fault evolution under extreme weather conditions. Background Technique

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

[0003] When a fault occurs in the distribution network, power supply to the de-energized load is restored by switching operations using the superior power grid, and power supply to the nearby de-energized load is restored by forming a power supply island through distributed generation (DG). This two-pronged approach is an important way to promote the distribution network's resistance to extreme weather and improve its power supply restoration ability. Therefore, efficiently leveraging the flexible and variable characteristics of the distribution network topology and deeply exploring the collaborative power supply potential of the superior power grid and DG are necessary measures to enhance the distribution network's fault recovery ability.

[0004] During the fault evolution process of the distribution network under extreme weather conditions, according to the cascading fault model, the distribution network cascading faults can be divided into three categories: the complex system method based on the self-organized criticality theory, the complex network theory method based on network topology structure analysis, and the pattern search method represented by the accident chain. The complex system method reveals the physical process of the system's cascading faults and describes the self-organized critical characteristics of the system, but it has problems such as low computational efficiency and difficult solution. The complex network theory is used to analyze the vulnerability and weak links of the system, but it cannot characterize the dynamic response mechanism of the system. The pattern search method combines the actual physical process to simulate the cascading faults, which can not only quantitatively analyze the cascading faults but also effectively control the computational amount, and it is the main method for analyzing distribution network cascading faults at the present stage.

[0005] During the fault evolution process of the distribution network under extreme weather conditions, the prior art has proposed a time-dominated cascading fault evolution model and a double-time dimension fault evolution model that retains the fault time series characteristics of the lines, thereby characterizing the power grid performance change curve under typhoon disasters; by simulating the typhoon passing process, simulating the probability of mechanical faults occurring in the system, and calculating the occurrence probability of cascading faults based on the system power flow distribution and line overload probability; however, its analysis of the fault development and evolution process is only for a single time section, ignoring the distinct spatio-temporal persistence characteristics of extreme weather.

[0006] To solve the above problems, existing research starts from fault recovery methods of reconstruction and islanding division, and respectively restores the power supply of lost-loads by leveraging the flexible and variable characteristics of the distribution network topology or forms a power supply island by tapping the power support potential of DGs to restore the power supply of lost-loads. Both are of great significance for improving the distribution network recovery ability. However, when large-scale cascading faults occur in the distribution network, resulting in the disconnection of the distribution network from the superior grid, the reconstruction method alone cannot fulfill the due power support responsibility of DGs; if only relying on the islanding division method that DGs provide power support and ignoring the key factor of the superior grid supplying power to lost-loads, which is crucial for improving the distribution network fault recovery ability, the effect of improving the distribution network fault recovery ability will be limited.

[0007] Therefore, simultaneously tapping the collaborative power supply potential of the superior grid and power generation resources such as DGs and leveraging the flexible and variable characteristics of the distribution network topology is an important way to effectively improve the distribution network fault recovery ability. "Tang Yida, Wu Zhi, Gu Wei, et al. A unified model of reconstruction and islanding division for active distribution network fault recovery [J]. Power System Technology, 2020, 44(07): 2731-2740" proposed a fault recovery method that coordinates reconstruction and islanding division by tapping the collaborative power supply potential of the superior grid, various DGs and energy storage, so as to restore the power supply of lost-loads in the distribution network. "Zhou Quan, Xie 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" proposed a recovery strategy that coordinates the reconstruction and islanding division of the distribution network. By using the island boundary matrix, the reconstruction is coordinated with the islanding to obtain the optimal recovery strategy. "Liu H, Wang C, Ju P, et al. A sequentially preventive model enhancing power system resilience against extreme-weather-triggered failures [J]. Renewable and Sustainable Energy Reviews, 2022, 156: 111945" proposed a two-layer mathematical programming model considering reconstruction and islanding division, and utilized the adjustable characteristics of controllable loads to effectively avoid the problem of power imbalance in the island and achieve the maximum range of power supply restoration in the distribution network. However, the above research all focuses on improving the distribution network fault recovery ability, but few studies consider the change in the control mode of the island, that is, the change in the control mode of DGs during the process of switching from the grid-connected mode to the island mode, which causes changes in the power output characteristics of DGs and leads to inaccurate characterization of the control operation mode and insufficient exploration of the collaborative potential of reconstruction and islanding. Summary of the Invention

[0008] To solve at least one of the technical problems existing in the above-mentioned background art, the present invention provides a distribution network fault recovery method and system considering fault evolution under extreme weather conditions. By accurately depicting the fault evolution mechanism of the distribution network under extreme ice and snow weather, effectively representing the logic of the change in power output characteristics caused by the change in the DG control mode, and exploring the collaborative power supply potential between the superior power grid and the DG, while giving full play to the flexible and variable characteristics of the distribution network topology, the recovery ability of the distribution network is improved.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] The first aspect of the present invention provides a distribution network fault recovery method considering fault evolution under extreme weather conditions, including the following steps:

[0011] Establish a rectangular coordinate system with the root node of the distribution network as the origin, and combine the fault mechanisms of the distribution network wires and poles to calculate the overall fault probability of the distribution network lines;

[0012] Characterize the cascading faults of the distribution network through stochastic power flow to construct a linear stochastic power flow model. Based on the linear stochastic power flow model, combine the stochastic compensation power method based on sensitivity analysis to construct a stochastic power flow model considering line outages, and solve to obtain the real-time outage probability of the lines;

[0013] Combine the overall fault probability of the distribution network lines, the real-time outage probability of the lines, and the determined operating states of the distribution network equipment to discretize the system state change process under continuous time, and calculate the distribution network system state transition probability;

[0014] Calculate the power output characteristics of the master control unit and the slave control unit when switching from the grid-connected operation state to the island operation state respectively, and calculate the power output characteristics of the distributed photovoltaic units when the system switches from the grid-connected operation state to the island operation state under extreme ice and snow weather;

[0015] 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 deduce the constraint limitations between the master control node, the slave control node, and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model considering the coordination of reconstruction and island division;

[0016] Solve the distribution network fault recovery model considering the coordination of reconstruction and island division to obtain the fault recovery strategy.

[0017] Further, the step of establishing a rectangular coordinate system with the root node of the distribution network as the origin and combining the fault mechanisms of the distribution network wires and poles to calculate the overall fault probability of the distribution network lines includes:

[0018] Based on the moving path of the meteorological center in extreme ice and snow weather, considering the effects of current electrothermal, ambient temperature, wind speed, and precipitation rate on conductor icing, the failure rate of the conductor associated with extreme ice and snow weather is obtained;

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

[0020] Combining the failure rate of the conductors associated with extreme ice and snow weather and the failure rate of the conductors on the poles and towers, calculate the overall failure rate of the distribution network lines.

[0021] Furthermore, the linear stochastic power flow model is constructed by characterizing the cascading failures of the distribution network through stochastic power flow. Based on the linear stochastic power flow model, a stochastic power flow model considering line outages is constructed by combining the stochastic compensation power method based on sensitivity analysis, and the real-time outage probability of the lines is obtained, including:

[0022] Construct a linear stochastic power flow model by characterizing the cascading failures of the distribution network through stochastic power flow;

[0023] Construct a stochastic power flow model considering line outages by combining the stochastic compensation power method based on sensitivity analysis;

[0024] Solve the stochastic power flow model of line outages to obtain the probability distribution of the power flow of each branch;

[0025] Calculate the real-time outage probability of the lines according to the probability distribution of the power flow of each branch.

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

[0027]

[0028] Where: f(P l ) is the probability density function of the active power of the line obtained by stochastic power flow calculation, is the overload outage probability of line l at time t; is the probability of hidden protection failure; P l is the active power of line l; P l r and P l m are the rated power and the limit transmission power of line l, respectively.

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

[0030]

[0031] Among them, is the probability that the state of the distribution network transfers from to ; and The state of the distribution network at time t and t+1 is o; Ω l,t+1 The set of devices that may fail at time t+1; For the device operating state from Transfer to Probability; And Are the probabilities of device ij failure caused by extreme ice and snow weather and device l failure caused by cascading failures at time t+1, respectively.

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

[0033]

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

[0035]

[0036] In the formula: And Are the active power and reactive power generated by the DG at node i at time t; k i,t Is a 0-1 state variable characterizing whether the DG at node i is under V / f control at time t, k i,t =1 indicates that the DG located at node i adopts V / f control, otherwise it is PQ control, Ω DG Is the set composed of all DG grid-connected nodes; V i,t Is the voltage of node i at time t; V0 is the rated voltage of the DG acting as the master control unit; And Are the upper limits of active power output and reactive power output of the DG at node i at time t, respectively; T is the set composed of the fault recovery time; And Are the active power reference value and reactive power reference value of the DG at node i at time t, respectively.

[0037] Furthermore, under extreme ice and snow weather, and when the system is converted from the grid-connected operation state to the island operation state, the power output characteristics of the distributed photovoltaic unit are:

[0038]

[0039]

[0040] In the formula: Is the ice thickness of the 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 PV at node i at time t, respectively; is the radiation intensity at node i at time t; θ PV is the power factor angle of the distributed PV, (L x,t , L y,t ) are the coordinates of the extreme ice and snow weather meteorological center at time t, and are the x-axis and y-axis coordinates of the distributed PV at node i, respectively.

[0041] Furthermore, the objective function of the distribution network fault recovery model considering the coordination of reconstruction and island division is:

[0042] minF = ω1f1 + ω2f2,

[0043]

[0044] where: F is the total objective function; f1 and f2 are sub-objective functions representing the load shedding amount and the number of switch operations of the distribution network, respectively; ω1 and ω2 are the weight coefficients of the sub-objective functions; P LOSS and P ALL are the weighted load shedding amount and the total load amount, respectively; Ω n is the set composed of all nodes of the distribution network; y i,t is the 0-1 state variable of node i at time t, y i,t = 1 indicates that node i is powered on at time t, otherwise node i is de-energized; ω k1 , ω k2 and ω k3 are the weight coefficients of the first-class load, second-class load and third-class load of the distribution network, respectively; and are the active powers of the first-class load, second-class load and third-class load of node i at time t, respectively; Ω ope and Ω clo are the sets composed of all tie switches and sectional switches, respectively; x ij,t is the 0-1 state variable of line ij at time t, x ij,t = 1 indicates that line ij is in the operating state at time t, otherwise it is in the disconnected state; N line is the total number of switches in the distribution network.

[0045] Furthermore, the constraints of the distribution network fault recovery model considering the coordination of reconstruction and island division include the coordination constraints of reconstruction and island division, the power flow constraints of the distribution network and the security constraints of the distribution network;

[0046] Among them, the coordination constraints of reconstruction and island division include the division area constraint and the connectivity and radiality constraint;

[0047] The partition area is constrained as:

[0048]

[0049] Connectivity and radial constraints:

[0050]

[0051] Construct the power flow constraints of the distribution network:

[0052]

[0053] Distribution network security constraints:

[0054]

[0055] In the formula: B i,j,t is a 0-1 state variable indicating whether node j is within the partition area of the dominant node i. B i,j,t = 1 means that node j is within the partition area of node i, otherwise node j is outside the partition area of node i; k i,t is a 0-1 state variable indicating whether the DG at node i is under V / f control at time t. Ω DG is the set composed of all DG grid-connected nodes; Ω sub is the set composed of the nodes connected to the substation; Ω (i) is the set composed of all the nodes within the area formed with node i as the dominant node; N bus is the total number of distribution network nodes; is the virtual power generated by the V / f controlled DG 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 a 0-1 state variable of node i at time t. T is the set composed of the fault recovery times; M is a sufficiently large positive number; x ij,t is a 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 respectively; I ki,t and I ij,t are the currents of line ki and ij at time t; and are the active power and reactive power injected into node i at time t respectively; R ij and X ij are the resistance and reactance of line ij respectively; R ki and X kiThey are the resistance and reactance of line ki respectively; and They are the active power and reactive power output by the substation connected to node i at time t respectively; and They are the active powers of the primary load, secondary load and tertiary load of node i at time t respectively; and They are the reactive powers of the primary load, secondary load and tertiary load of node i at time t respectively; It is the square of the voltage of node i at time t; It is the square of the voltage of node j at time t; Ω l It is the set composed of all branches; Ω n It is the set composed of all nodes of the distribution network; V i max and V i min They are the squared values of the upper and lower limits of the voltage amplitude of node i respectively; It is the squared value of the upper limit of the current amplitude of branch ij.

[0056] The second aspect of the present invention provides a distribution network fault recovery system considering fault evolution under extreme weather, including:

[0057] A fault evolution analysis module, which is used to establish a rectangular coordinate system with the root node of the distribution network as the origin, combine the fault mechanisms of the distribution network wires and poles, and calculate the overall fault probability of the distribution network lines; characterize the cascading faults of the distribution network through stochastic power flow to construct a linear stochastic power flow model, and based on the linear stochastic power flow model, combine the stochastic compensation power method based on sensitivity analysis to construct a stochastic power flow model considering line outages, and solve to obtain the real-time outage probability of the lines;

[0058] An operation analysis module, which is used to discretize the process of system state change under continuous time by combining the overall fault probability of the distribution network lines, the real-time outage probability of the lines and the determined operating states of the distribution network equipment, and calculate the system state transition probability of the distribution network; calculate the power output characteristics of the master control unit and the slave control unit respectively when converting from the grid-connected operation state to the island operation state, and calculate the power output characteristics of the distributed photovoltaic units when the system converts from the grid-connected operation state to the island operation state under extreme ice and snow weather;

[0059] A fault recovery module, which is used to combine the system state transition probability of the distribution network, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units, deduce the constraint limitations between the master control node, the slave control node and the distributed photovoltaic and load nodes, and construct a distribution network fault recovery model considering the coordination of reconstruction and island division; solve the distribution network fault recovery model considering the coordination of reconstruction and island division to obtain the fault recovery strategy.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] 1. The present invention proposes a chain fault evolution model of a distribution network based on improved stochastic power flow under extreme ice and snow weather. Considering the fault evolution characteristics of the distribution network and the DG output characteristics under extreme ice and snow weather, the mechanical fault probability of distribution network equipment and the system state transition probability are quantified, and based on the stochastic power flow algorithm of the distribution network considering line outage, the fault evolution mechanism of the distribution network is accurately characterized.

[0062] 2. The present invention proposes a DG operation model considering the conversion between V / f control and PQ control. In the process of converting from the grid-connected mode to the island mode, considering the change in the power output characteristics of the DG caused by the change in the DG control mode, an auxiliary binary variable representing the DG control mode is introduced to characterize the power output characteristics of the DG, and the accurate characterization of the power output change during the conversion of DG V / f control and PQ control is realized.

[0063] 3. The present invention proposes a distribution network fault recovery model considering the coordination of reconstruction and island division. Based on the regional division idea of "determining the region by a point", combined with the power output characteristics of the DG, the DG with V / f control is used as the main control unit of the island, and this node is used as the regional dominant "node". A judgment variable representing the membership relationship between the main control unit, the slave control unit and the distribution network load is introduced to deduce the "region" to which various nodes of 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 island division is realized, effectively improving the fault recovery ability of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0065] Figure 1 is a flowchart of a distribution network fault recovery method considering fault evolution under extreme weather provided by an embodiment of the present invention;

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

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

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

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

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

[0071] Figure 7 It is the cumulative power flow distribution of Line 1 and Line 2 provided by the embodiment of the present invention; among them, (a) is the cumulative power flow distribution of Line 1, and (b) is the cumulative power flow distribution of Line 2;

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

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

[0074] Figure 10 It is the load shedding amount under the accident chain scenario of the distribution network provided by the embodiment of the present invention; among them, (a) is the total load shedding amount of the distribution network, (b) is the load shedding amount of the primary load of the distribution network, (c) is the load shedding amount of the secondary load of the distribution network, and (d) is the load shedding amount of the tertiary load of the distribution network. Detailed implementation manners

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

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

[0077] It should be noted that the terms used herein are only for describing specific implementation manners 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 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, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0078] Aiming at the problems that the fault evolution mechanism of distribution network equipment under extreme ice and snow weather is inaccurately characterized and the existing distribution network fault recovery methods cannot effectively represent the distributed generation (DG) control mode, the present invention proposes a fault recovery strategy for active distribution networks considering fault evolution under extreme ice and snow weather. First, clarify the mechanical fault process of distribution network equipment and the influence of power flow uncertainty under extreme ice and snow weather, quantify the equipment fault probability and system state transition probability, and deduce a distribution network cascading fault evolution model based on improved stochastic power flow. Secondly, based on the idea of area division by point positioning, comprehensively consider the subordinate relationship between the master control node, slave control node and load node in the island area, combine the master-slave control logic of the island, deduce the constraint limitations between the master control node, slave control node and load node, and construct a distribution network fault recovery model considering the coordination of reconstruction and island division, including the following aspects:

[0079] 1) Propose a distribution network cascading fault evolution model based on improved stochastic power flow under extreme ice and snow weather. Considering the fault evolution characteristics of the distribution network and the DG output characteristics under extreme ice and snow weather, quantify the mechanical fault probability of distribution network equipment and the system state transition probability, and accurately characterize the fault evolution mechanism of the distribution network based on the distribution network stochastic power flow algorithm considering line outage.

[0080] 2) Propose a DG operation model considering the conversion between V / f control and PQ control. During the conversion from grid-connected mode to island mode, considering the change in the power output characteristics of DG caused by the change in the DG control mode, introduce an auxiliary binary variable representing the DG control mode to characterize the power output characteristics of DG, and accurately characterize the change in power output during the conversion of DG V / f control and PQ control.

[0081] 3) Propose a distribution network fault recovery model considering the coordination of reconstruction and island division. Based on the idea of area division by point positioning, combined with the power output characteristics of DG, use the DG with V / f control as the main control unit of the island, and use this node as the regional dominant "node", introduce a judgment variable representing the membership relationship between the main control unit, slave control unit and distribution network load, deduce the attribution "area" of various nodes in the distribution network, and while ensuring the connectivity and radial operation of the reconstruction area and the island area, realize the organic coordination of reconstruction and island division, effectively improving the fault recovery ability of the distribution network.

[0082] Embodiment 1

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

[0084] Step 1: Establish a rectangular coordinate system with the root node of the distribution network as the origin. Combine the fault mechanisms of the distribution network conductors and poles to calculate the overall fault probability of the distribution network lines;

[0085] Specifically, it includes the following steps:

[0086] Step 101: Use the coordinates (L x,t , L y,t ) of the extreme ice and snow weather meteorological center and the moving speed v ice of the meteorological center to describe the moving path of the extreme ice and snow weather meteorological center, which is expressed as:

[0087]

[0088] In the formula: (L x,t , L y,t ) are the coordinates of the extreme ice and snow weather meteorological center at time t; (L x,0 , L y,0 ) are the coordinates of the extreme ice and snow weather meteorological center at the initial time; v ice represents the moving speed of the meteorological center; θ is the angle between the moving speed of the meteorological center and the x-axis of the coordinate axis.

[0089] Step 102: Comprehensively consider the effects of current electrothermal, ambient temperature, wind speed, and precipitation rate on conductor icing, and obtain the relationship between conductor failure rate and extreme ice and snow weather, which is expressed as:

[0090]

[0091] In the formula: m ij is the mass of the conductor per unit length of the wire; is the specific heat capacity of the conductor material of wire ij; τ ij,t is the operating temperature of wire ij; R ij is the resistance of line 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 are the current ambient temperature and the rated ambient temperature respectively; is the convective heat transfer coefficient; is the icing growth rate of wire ij at time t; v wind is the ambient wind speed; p rain is the precipitation probability; is the outer diameter of wire ij; is the change in icing per unit length of wire ij at time t; is the icing thickness of wire ij at time t; z x and z y are the load parameters of the wire on the x-axis and y-axis respectively; (x ij , y ij) are the coordinates of wire ij; is the failure rate of wire ij at time t; a1, a2, a3, b1, b2, c1, and c2 are the constant coefficients of the equation; n line is the ice load that the line design can withstand.

[0092] Step 103: Considering the ice load on the distribution network poles and towers, calculate the failure rate of the wires on the poles and towers;

[0093] The ice load on the distribution network poles and towers mainly refers to the tension generated by the wires suspended at both ends on the poles and towers, which depends on the vertical loads such as the self-weight of the wires and the ice weight of the wires.

[0094]

[0095] In the formula: is the unit vertical load of wire ij at time t; is the ice load on a single pole and tower of wire ij at time t; l1 and l2 are the spans on both sides of the pole and tower; h1 and h2 are the height differences at the suspension positions of both ends of the wire; and are the horizontal tensions of the lines on both sides of the pole and tower; is the failure rate of the pole and tower of wire ij at time t; N pole is the ice load that the pole and tower design can withstand; c3 and c4 are constant coefficients.

[0096] Step 104: Equivalent the entire distribution line as a series model of wires and poles and towers, then the overall failure rate of the line is expressed as:

[0097]

[0098] In the formula: is the overall failure rate of line ij at time t; u is the number of strands of the line wire; m is the number of poles and towers on the line; is the failure rate of the s-th strand of wire of line ij; is the failure rate of the p-th pole and tower of line ij.

[0099] Step 2: Characterize the cascading failures of the distribution network through the stochastic power flow to construct a linear stochastic power flow model. Based on the linear stochastic power flow model, combined with the stochastic compensation power method based on sensitivity analysis, construct a stochastic power flow model considering line outages, and solve to obtain the real-time outage probability of the line;

[0100] Specifically, it includes the following steps:

[0101] Step 201: Characterize the cascading failures of the distribution network through the stochastic power flow to construct a linear stochastic power flow model;

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

[0103]

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

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

[0106]

[0107] Where: ΔX is the random response corresponding to the random perturbation ΔW; ΔZ is the random response of the branch power flow random variable corresponding to the random perturbation 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 stochastic power flow model considering line outage in combination with the stochastic compensation power method based on sensitivity analysis;

[0110] In the line outage scenario, the stochastic power flow is calculated using the sensitivity matrix method, whose essence is to introduce stochastic compensation power at the corresponding nodes of the distribution network to simulate the branch outage. When the line network of the distribution network changes by ΔY, its state variable will also change by ΔX. Expand Equation (15) at the reference operating point using the Taylor series and convert it to:

[0111]

[0112] Neglect the (ΔX) 2 term and the high-order terms. Since Γ(X, Y) is a linear function of Y, Γ″ yy (X, Y)(ΔY) 2 = 0. When the change in node power injection is not considered, ΔW = 0, so Equation (17) simplifies to:

[0113]

[0114] Where: I is the identity matrix; ΔW y is the perturbation of the node injection power caused by the line break.

[0115] Assume that the nodes at both ends of the opened branch are i and j, and write it 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 disconnected line; H ij , N ij , J ij and L ij are the corresponding elements in the Jacobian matrix; ΔP i , ΔQ i , ΔP j and ΔQ j are the compensation powers when the line ij is disconnected, respectively.

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

[0119] In this embodiment, the probabilistic power flow calculation adopts the semi-invariant method and the Gram-Charlier series expansion method, which simplifies the convolution and deconvolution calculations when obtaining the probability density function of the sum of random variables into algebraic operations of several semi-invariants, thereby reducing the calculation amount. At the same time, using the Gram-Charlier series expansion, the probability density function (PDF) and cumulative distribution function (CDF) of the desired state variable can be obtained through a single calculation.

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

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

[0122]

[0123] Where: is the overload outage probability of line l at time t; is the probability of hidden protection failure; P l is the active power of line l; P l r and P l m are the rated power and the limit transmission power of line l, respectively.

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

[0125]

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

[0127] Step 3: Combine the overall failure probability of the distribution network lines, the real-time outage probability of the lines, and the determined operating states of the distribution network equipment to discretize the system state change process under continuous time, and calculate the state transition probability of the distribution network system;

[0128] Specifically, it includes the following steps:

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

[0130] Both extreme ice and snow weather and power flow transfer may cause faults in the distribution network lines, thus causing changes in the distribution network state. The operating state of the 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 the distribution network equipment l affected by extreme weather and power flow transfer at time t, and indicate that the equipment is operating normally, otherwise it indicates a fault.

[0133] Step 302: Based on the operating states of the distribution network equipment, the overall failure probability of the distribution network lines, and the real-time outage probability of the lines, discretize the distribution network state change process under continuous time, and calculate the state transition probability of the distribution network;

[0134] Extreme ice and snow weather affects the distribution network lines and photovoltaic units within the affected range, and the resulting system state changes have timeliness.

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

[0136]

[0137] Where: is the state o of the distribution network at time t; is the distribution network state from transferring to Probability; and are the states of the distribution network at times \(t\) and \(t + 1\); \(\Omega\) l,t+1 is the set of devices that may fail at time \(t + 1\); is the probability that the device operating state transfers from to ; and are the probability of device \(ij\) failure caused by extreme ice and snow weather and the probability of device \(l\) failure caused by cascading failures at time \(t + 1\), respectively.

[0138] The state of the distribution network evolves continuously from the entry to the end of the extreme ice and snow weather and may include multiple evolution paths. For a determined system state its occurrence probability is expressed as the sum of the probabilities of each evolution path:

[0139]

[0140] In the formula: is the probability of the occurrence of the device operating state ; is the set composed of the paths of the system evolving from the initial state to the state ; is the probability that the system transfers from the initial state along path \(r\) to the state ;

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

[0142] Step 4: In the process of converting from the grid-connected mode to the island mode, calculate the power output characteristics of the master control unit and the slave control unit when the system converts from the grid-connected operating state to the island operating state, and calculate the power output characteristics of the distributed photovoltaic units when the system converts from the grid-connected operating state to the island operating state under extreme ice and snow weather;

[0143] In this embodiment, considering the change in the power output characteristics caused by the change in the distributed power source control method, an auxiliary binary variable representing the DG control method is introduced to obtain the power output characteristics of the DG; realizing the accurate characterization of the power output change during the conversion between DG V / f control and PQ control.

[0144] Specifically, it includes the following steps:

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

[0146] The active distribution network includes multiple energy inputs such as MT, DG, and substations, and multiple operating states such as grid-connected and islanded. Among them, the islanded operating state includes two control methods: peer-to-peer control and master-slave control. The two control structures are as Figure 2 shown.

[0147] Peer-to-peer control means that when the power grid is in the islanded operation mode, all DGs in the system have equal status in control, there is no master-slave relationship between the controllers, and each DG is controlled according to the local information of the voltage and frequency of the access system. However, there is a problem that the voltage and frequency of the system will change with the load fluctuation, resulting in the instability of the island.

[0148] Master-slave control means that when the power grid is in the islanded operation mode, one DG in the system is used as the master control unit, adopting V / f control, which is used to provide voltage and frequency references for other DGs in the system and follow the load fluctuation; while other DGs are used as slave control units, adopting constant power control, that is, PQ control. When the system is in the grid-connected mode, all DGs adopt PQ control. Once the system switches to the islanded mode, the DG used as the master control unit needs to quickly switch from PQ control to V / f control, while the slave control units still maintain PQ control. And MT has the characteristics of stable power output and easy control. Therefore, in this embodiment, MT is selected as the master control unit of the island.

[0149] Step 402: When calculating the conversion of the system from the grid-connected operation state to the islanded operation state, calculate the power output characteristics of the master control unit;

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

[0151]

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

[0153] at time t, respectively; V i,t is the voltage of node i at time t; V0 is the rated voltage of the DG used as the master control unit; k i,t is a 0-1 state variable characterizing whether the DG at node i is in V / f control at time t, k i,t= 1 indicates that the DG located at node i adopts V / f control; otherwise, it is PQ control.

[0154] Step 403: When the system switches from the grid-connected operation state to the island operation state, calculate the power output characteristics of the slave control unit.

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

[0159] Step 404: Calculate the power output characteristics of the distributed photovoltaic unit when the system switches from the grid-connected operation state to the island operation state under extreme ice and snow weather.

[0160] Extreme ice and snow weather causes icing problems for the distributed photovoltaic unit. When the system switches from the grid-connected operation state to the island operation state, the distributed photovoltaic unit maintains the PQ control unchanged, and its power output characteristics can be expressed as:

[0161]

[0162] In the formula: is the icing thickness of the 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, respectively; is the radiation intensity at node i at time t; θ PV is the power factor angle of the distributed photovoltaic, and are the x-axis and y-axis coordinates of the distributed photovoltaic at node i, respectively.

[0163] Step 5: Combine the state transition probability of the distribution network system, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic unit to deduce the constraint limitations between the master control node, the slave control node, and the distributed photovoltaic and the load node, and construct a distribution network fault recovery model considering the coordination of reconfiguration and islanding division.

[0164] Specifically, it includes the following steps:

[0165] Step 501: Construct the objective function of the distribution network fault restoration model considering the coordination of network reconfiguration and islanding division;

[0166] The main task of distribution network fault restoration is to minimize the number of sectionalizing switches and tie switches while restoring as many lost loads as possible. For this purpose, in this embodiment, the minimum lost load and the minimum number of switch operations of the distribution network are taken as the optimization objectives.

[0167] minF = ω1f1 + ω2f2 (32),

[0168]

[0169] where: F is the total objective function; f1 and f2 are the sub-objective functions representing the lost load and the number of switch operations of the distribution network respectively; ω1 and ω2 are the weight coefficients of the sub-objective functions; P LOSS and P ALL are the weighted lost load and the total load respectively; Ω n is the set composed of all nodes of the distribution network; y i,t is the 0-1 state variable of node i at time t, y i,t = 1 indicates that node i is powered on at time t, otherwise node i is de-energized; ω k1 、ω k2 and ω k3 are the weight coefficients of the first-class load, the second-class load and the third-class load of the distribution network respectively; and are the active powers of the first-class load, the second-class load and the third-class load of node i at time t respectively; Ω ope and Ω clo are the sets composed of all tie switches and sectionalizing switches respectively; x ij,t is the 0-1 state variable of line ij at time t, x ij,t = 1 indicates that line ij is in the operating state at time t, otherwise it is in the disconnected state; N line is the total number of switches in the distribution network.

[0170] Step 502: Construct the coordination constraints of network reconfiguration and islanding division;

[0171] In this embodiment, based on the regional division idea of "determining the region by points", the DG grid-connected node with V / f control is used as the leading "node" of the region, and by introducing auxiliary variables representing the logical relationship between the node and the region, it is used to judge the division "region" where the distribution network node is located. By constructing the constraint of the number relationship of nodes in the divided region and the radial and connectivity constraints, the coordination of distribution network reconfiguration and islanding division can be realized.

[0172] Among them, considering that the root node and the DG grid-connected node with V / f control can be used as the leading nodes of the area, an auxiliary variable B representing the logical relationship between the nodes and the area is introduced i,j,t , to realize the division of the distribution network area, and then realize the coordination of reconstruction and island division, including:

[0173] 1) Division area constraint

[0174]

[0175] In the formula: 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 forming the area with node i as the leading node; B i,j,t is 0 or N indicating whether node j is within the division area of the leading node i bus is the total number of distribution network nodes.

[0176]

[0177] In the formula: Ω l is the set of all branches; is the virtual power generated by the V / f controlled DG 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. F ki,t is the virtual power flow transmitted by branch ki at time t; Equation (39) indicates that only the DG with V / f control can generate virtual power; Equation (40) indicates the virtual power flow balance within the area; Equation (41) is the correlation constraint between the virtual power flow and the switch state variable, realizing the coupling of the virtual power flow and the switch state variable, and avoiding the phenomenon that the virtual power flow is still non-zero when the switch is disconnected; Equation (42) is the radial constraint, that is, the number of nodes is equal to the number of areas plus the number of operating branches.

[0178] Step 503, construct the distribution network power flow constraint;

[0179] In this embodiment, the Distflow power flow model of the radial distribution system is adopted, and 0-1 state variables representing the operating state of nodes and the operating state of branches are introduced, and it is transformed into a power flow model suitable for distribution network fault restoration.

[0180]

[0181] In the formula: 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 from the substation connected to node i at time t, respectively; and are the reactive powers of the first-class load, second-class load, and third-class load of node i at time t. P ki,t and Q ki,t are the active power and reactive power of line ki at time t, respectively; R ki and X ki are the resistance and reactance of line ki, respectively; is the square of the voltage of node i at time t; is the square of the voltage of node j at time t;

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

[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] In the formula: 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; is the square value of the upper limit of the branch ij current amplitude.

[0186] Step 6: Solve the distribution network fault recovery model considering the coordination of reconfiguration and islanding division to obtain the fault recovery strategy.

[0187] Since formula (46) presents non-convex characteristics, it is difficult to solve the fault recovery model proposed in this embodiment. Therefore, and are introduced for equivalent transformation, and the second-order cone relaxation method is used to transform the model into a mixed-integer linear programming model for easy direct solution. Formulas (43), (41)-(48) can be rewritten as:

[0188]

[0189]

[0190] In the formula: is the square of the voltage of 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 line switch of the distribution network is in the off state, causing nodes i and j to be disconnected, Equation (45) fails. The Big-M method is used to rewrite Equation (45) as follows:

[0192]

[0193] Case Study

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

[0195] Table 1 MT Parameters

[0196]

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

[0198] 5. Time-Varying Failure Rate of Distribution Lines and Cascading Fault Simulation

[0199] 5.1 Time-Varying Failure Rate of Distribution Lines under Extreme Ice and Snow Weather

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

[0201] As can be seen from Figure 5 , the overall failure rate of the distribution lines increases relatively slowly at 0-30 hours. After 30 hours, the failure rates of each line increase rapidly in an exponential form. This is because the extreme ice and snow weather is far from the distribution network at 0-30 hours, and the ice accretion on the distribution network conductors increases slowly, resulting in a slow increase in the failure rates of the distribution network conductors and poles. Therefore, the overall failure rate of the distribution network lines increases slowly. After 30 hours, the distribution lines 61-63 are affected by the extreme ice and snow weather, and the ice accretion on their conductors increases sharply, resulting in an increase in the failure rates of the conductors and poles of lines 61-63, and further leading to a rapid increase in the overall failure rate of the lines in an exponential form.

[0202] 5.1.2 Simulation of Cascading Failures in Distribution Network

[0203] The present invention uses the Markov Chain Monte Carlo method (MCMC) to extract the states of distribution network components hour by hour and obtain the faulty lines caused by extreme ice and snow weather. During the simulation, distribution lines 65, 16, 11, and 52 failed at the 18th hour, 19th hour, 29th hour, and 40th hour respectively during the passage of extreme ice and snow weather, and their corresponding failure rates were 48.87%, 48.85%, 49.04%, and 49.90% respectively.

[0204] The fault evolution path and system response of the distribution network are as Figure 6 shown. In the figure, B Cas is the probability of cascading failure, and P loss is the load loss of the distribution network. The cumulative distribution of the power flows of distribution lines 1 and 2 is shown in Figure 7 , where Figure 7 (a) is the cumulative distribution of the power flow of line 1, and (b) is the cumulative distribution of the power flow of line 2. Figure 7 The red solid line in it is the rated capacity of the distribution line.

[0205] It can be seen from Figure 6 that after the failure of distribution line 65 due to extreme ice and snow weather, the probability of over-limit outage of the power flows of lines 1 and 2 is 30.37% and 28.67% respectively, and it can be seen from Figure 7 that there is a risk of over-limit power flow for lines 1 and 2. In addition, the load losses of the distribution network at the 19th hour and 40th hour are 5377.84 kW and 5646.61 kW respectively. This is because when line 65 fails, the loads at nodes 66 - 69 lose power and PV5 is disconnected from the network, and due to the small loads at nodes 66 - 69, the system power flow is transferred, resulting in the outage of line 1 or line 2. Since node 2 is a zero-injection node, the load losses of the distribution network caused by the cascading failures of line 1 or line 2 at the 19th hour are the same. Although the probability of overloading and outage of lines 1 and 2 is low, once line 1 or line 2 is disconnected, the distribution network loses connection with the root node, resulting in all the loads of the distribution network losing power, and the load losses of the distribution network at subsequent moments will change with the fluctuation of the load prediction curve.

[0206] 5.2 Topological Analysis of Distribution Network Fault Restoration

[0207] Generate typical fault scenarios based on distribution network accident chains 1 and 2. Accident chain 1 is as follows: Distribution lines 65, 16, 1, 11, and 52 fail at the 18th hour, 19th hour, 19th hour, 29th hour, and 40th hour respectively during the passage of extreme ice and snow weather. Accident chain 2 is as follows: Distribution lines 65, 16, 2, 11, and 52 fail at the 18th hour, 19th hour, 19th hour, 29th hour, and 40th hour respectively during the passage of extreme ice and snow weather. Under extreme ice and snow weather, the ice thickness on the photovoltaic panels gradually increases, reducing the sunlight intensity on the surface of the photovoltaic panels, thereby resulting in a decrease in photovoltaic power output. The power output of the distributed photovoltaic system from 0 to 50 hours is as Figure 8 shown. To demonstrate the effectiveness and superiority of the fault recovery strategy proposed in the present invention, three scenarios are set for comparison.

[0208] Scenario 1: Use the distribution network reconfiguration method to restore power supply to the power outage area.

[0209] Scenario 2: Use the reconfiguration + islanding method to restore power supply to the power outage area of the distribution network, where the island operation adopts the peer-to-peer control method.

[0210] Scenario 3: Use the distribution network fault recovery method proposed in the present invention, which coordinates reconfiguration and island division, to supply power to the power outage area.

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

[0212] The topological structures of the three scenarios after power supply recovery at the 18th hour, 19th hour, 29th hour, and 40th hour in the distribution network accident chain scenario are as Figure 8 shown.

[0213] From Figure 9 (a) in and Figure 9 (d) in, it can be seen that at the 18th hour, the distribution network can restore power supply to the power outage nodes 66 - 68 by closing the tie switch S71. When the distribution network loses connection with the root node at the 19th hour, the traditional reconfiguration model cannot exert the power support ability of the MT, resulting in a large number of loads in the distribution network losing power.

[0214] From Figure 9 (b) in, Figure 9 (e) in, Figure 9 (g) in, and Figure 9As can be seen from Fig. (i), at the 18th hour, the power supply to the power-loss nodes 66 - 68 of the distribution network can be restored by closing the tie switch S71. At the 19th hour, the primary loads at nodes 9, 35, 37, and 42 lose power, the secondary loads at nodes 29, 34, 38 - 41, 44, 49, 50, 55, 56, and 66 lose power, and the tertiary loads at nodes 10, 11, 28, 43, 45 - 48, 59, and 60 lose power. At the 29th hour, the primary load at node 37 loses power, the secondary loads at nodes 38, 39, 55 - 56, 66 - 69 lose power, and the tertiary loads at nodes 11 and 16 lose power. At the 40th hour, the primary loads at nodes 35, 37, and 57 lose power, the secondary loads at nodes 14, 15, 17, 29, 34, 38 - 41, 44, 49, 50, 53 - 56, 58, 66 - 69 lose power, and the tertiary loads at nodes 10, 11, 13, 16, 43, 45 - 48, 59, and 60 lose power. When reconstructing + islanding and the islanding adopts the peer-to-peer control method to restore the power supply to the power-loss area of the distribution network, only the power-loss loads around the MT can be restored, and the DG collaborative power supply ability cannot be exerted, resulting in the excision of more primary loads.

[0215] From Figure 9 in (c), Figure 9 in (f), Figure 9 in (h) and Figure 9As can be seen from (j), by adopting the fault recovery method that coordinates the reconstruction and islanding division proposed in the present invention, at the 18th hour, the power supply of the de-energized nodes 66-68 can be restored by closing the tie switch S69 in the distribution network. At the 19th hour, the secondary loads at nodes 38, 39, 41, 44, 49, 50, and 58 are de-energized, and the tertiary loads at nodes 16, 43, 45-48, 59, and 60 are de-energized. The main controls MT are MT4 and MT6 respectively. By opening the sectionalizing switch S60 and closing the tie switches S70 and S73, an islanding area is formed with the coordinated power supply of MT1, MT2, MT3, MT4, and MT5, and the power supply of more primary loads is restored. At the 29th hour, the secondary loads at nodes 38, 39, 55, 56, and 66 are de-energized, and the tertiary loads at nodes 10, 11, 16, and 48 are de-energized. The main controls MT are MT4 and MT6. Since the 29th hour is in the low electricity consumption period, by opening the sectionalizing switches S9, S15, S47, and S48 and closing the tie switches S70 and S73, two larger islanding areas of MT1, MT2, MT5, and MT6 and MT3 and MT5 can be formed, and more primary and secondary loads can be restored. At the 40th hour, the primary loads at nodes 9, 42, and 57 are de-energized, the secondary loads at nodes 8, 12, 14, 15, 17, 38-41, 44, 49, 50, 53-58, and 66-69 are de-energized, and the tertiary loads at nodes 7, 10, 11, 13, 16, 43, 45-48 are de-energized. The main controls MT are MT3, MT4, and MT6. Since the 40th hour is in the peak electricity consumption period, the sectionalizing switches S6 and S37 are opened, and MT1, MT2, MT5, and MT6 supply power in coordination to restore the power supply of the primary loads at nodes 35 and 37.

[0216] In summary, the distribution network fault recovery method that coordinates the reconstruction and islanding division proposed in the present invention uses the MT with V / f control as the main control unit of the islanding. While realizing the connectivity and radial operation of the reconstruction area and the islanding area, it ensures the organic coordination of the reconstruction and the islanding division, and effectively improves the fault recovery ability of the distribution network.

[0217] 5.2.2 Analysis of the operating characteristics of the MT with the conversion between V / f control and PQ control under the accident chain scenario of the distribution network

[0218] To verify the influence of the operating characteristics of the MT with the conversion between V / f control and PQ control proposed in the present invention on the active power output of the MT, taking three schemes under the accident chain scenario of the distribution network as examples, the active power outputs of the MT at the 18th hour, the 19th hour, the 29th hour, and the 40th hour are shown in Table 2.

[0219] Table 2 Active power output of the MT in the accident chain 1 of the distribution network

[0220]

[0221] As can be seen from the comparison in Table 2, at the 18th hour, the MTs of the reconstruction method in Scheme 1 all adopt PQ control, and the output power of the MTs is the rated power. At the 19th hour, the 29th hour, and the 40th hour, the output power of the MTs in the distribution network reconstruction mode is 0. This is because when the distribution network loses connection with the root node at the 19th hour, the traditional reconstruction method cannot exert the power support ability of the MTs, resulting in the active power output by the MTs being 0 kW.

[0222] At the 18th hour, for the MTs in Scheme 2 with reconstruction + islanding and the islanding adopting the peer-to-peer control mode, all adopt PQ control, and the output power of the MTs is the rated power. At the 19th hour, the 29th hour, and the 40th hour, for the MTs with reconstruction + islanding and the islanding adopting the peer-to-peer control mode, they have the same status in control, and the active power output changes with the fluctuation of the load prediction curve near the MTs.

[0223] At the 18th hour, for the DG operation model with the conversion between V / f control and PQ control proposed in the present invention, the MTs all adopt PQ control, and the output power of the MTs is the rated power. At the 19th hour and the 29th hour, the main control MTs are MT4 and MT6 respectively, which adopt V / f control to follow the load fluctuation, and the remaining MTs adopt PQ control with the output power being the rated power. At the 40th hour, the main control MTs 3, 4, and 6 are used to follow the load fluctuation, and the output power of MT1, MT2, and MT5 is the rated power.

[0224] In summary, the DG operation model with the conversion between V / f control and PQ control proposed in the present invention can effectively characterize the characteristics of the change in power output characteristics caused by the change in the DG control mode, and realizes the accurate description of the power output change during the conversion between V / f control and PQ control.

[0225] 5.3 Analysis of the Restoration Effect of the Distribution Network

[0226] To verify the advantage of the fault restoration strategy for the coordination of reconstruction and islanding division proposed in the present invention in terms of the restored amount of the lost load in the distribution network, the three schemes proposed in 5.2 are used for comparative analysis.

[0227] The lost load amounts of the three schemes in the distribution network accident chain scenario are as Figure 10 shown.

[0228] As Figure 10 shown in (a) of it, from the 19th hour to the 50th hour, the total lost load amount of the fault restoration method for the coordination of reconstruction and islanding division proposed in the present invention is much lower than that of Scheme 1, and is also lower than that of Scheme 2. This is because the fault method for the coordination of reconstruction and islanding division proposed in the present invention fully exploits the power support potential of the MTs and gives full play to the collaborative power supply ability of the MTs to achieve the efficient restoration of the lost load in the distribution network. As Figure 10It can be seen from Fig. (b) that except that the first-level load recovery rate of the fault recovery method combining reconstruction and islanding division proposed in the 33h of the present invention is lower than that of Scheme 2, from the 18h to 32h and from the 34h to 50h, the first-level load loss power of the fault recovery method combining reconstruction and islanding division proposed in the present invention is much lower than that of Scheme 1 and Scheme 2. This is because the method combining reconstruction and islanding division proposed in the present invention can realize MT collaborative power supply, and then realize the transfer of load, giving priority to ensuring the power supply of important loads. From Figure 10 It can be seen from Fig. (c) that at the 26-28h, 31h, 32h, 38h, 39h and 40-50h, the second-level load loss power of the fault recovery method combining reconstruction and islanding division proposed in the present invention is slightly higher than that of Scheme 2, but much lower than that of Scheme 1. This is because the fault recovery method combining reconstruction and islanding division in the present invention gives priority to restoring the power supply of important loads through the collaborative power supply of MT, thus sacrificing the power supply of some second-level loads.

[0229] From Figure 10 It can be seen from Fig. (d) that at the 23h, 25h, 27-29h, 42h and 44th moments, the third-level load loss power of the fault recovery method combining reconstruction and islanding division proposed in the present invention is higher than that of Scheme 2, but much lower than that of Scheme 1. This is because the fault recovery method combining reconstruction and islanding division proposed in the present invention gives priority to restoring the power supply of important loads by adjusting the switch state, thus sacrificing the power supply of some third-level loads.

[0230] To sum up, it is further verified that the distribution network fault recovery method combining reconstruction and islanding division proposed in the present invention gives full play to the power support potential of MT on the premise of ensuring the power supply of important loads, and efficiently restores the power supply of the power outage area of the distribution network.

[0231] Embodiment 2

[0232] The present embodiment provides a distribution network fault recovery system considering fault evolution under extreme weather, including:

[0233] A fault evolution analysis module, which is used to establish a rectangular coordinate system with the root node of the distribution network as the origin, calculate the overall fault probability of the distribution network line in combination with the fault mechanism of the distribution network wire and tower; characterize the cascading faults of the distribution network through stochastic power flow to construct a linear stochastic power flow model, and based on the linear stochastic power flow model, construct a stochastic power flow model considering line outages in combination with the stochastic compensation power method based on sensitivity analysis, and solve to obtain the real-time outage probability of the line;

[0234] An operation analysis module, which is used to discretize the system state change process under continuous time by combining the overall fault probability of the distribution network line, the real-time outage probability of the line, and the determined operation state of the distribution network equipment, and calculate the state transition probability of the distribution network system; respectively calculate the power output characteristics of the master control unit and the slave control unit when switching from the grid-connected operation state to the island operation state, and calculate the power output characteristics of the distributed photovoltaic unit when the system switches from the grid-connected operation state to the island operation state under extreme ice and snow weather.

[0235] A fault recovery module, which is used to deduce the constraint limitations between the main control node, the slave control node, and the distributed photovoltaic and load nodes by combining the state transition probability of the distribution network system, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic unit, and construct a distribution network fault recovery model considering the coordination of reconstruction and island division; solve the distribution network fault recovery model considering the coordination of reconstruction and island division to obtain a fault recovery strategy.

[0236] Embodiment III

[0237] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps in the distribution network fault recovery method considering fault evolution under extreme weather as described above.

[0238] Embodiment IV

[0239] This embodiment provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps in the distribution network fault recovery method considering fault evolution under extreme weather as described above.

[0240] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope 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, and the overall failure probability of the distribution network line is calculated based on the failure mechanism of the distribution network conductors and towers; A linear random power flow model is constructed by describing the cascading failures of the distribution network through random power flow. 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, and the real-time outage probability of the line 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 control unit and the slave control unit when the system switches from the grid-connected operation state to the islanded operation state, and calculate the power output characteristics of the distributed photovoltaic units when the system switches from the grid-connected operation state to the islanded operation state in extreme ice and snow weather; Combining the state transition probability of the distribution network system, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units, the constraints between the master control node, the slave control node, and the distributed photovoltaic and load nodes are derived, and a distribution network fault recovery model that takes into account the coordination of reconstruction and island division is constructed; 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 under extreme weather conditions as claimed in 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 moving 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 the distribution network towers, calculate the tower failure rate of the conductors; The overall failure rate of the distribution network line is calculated by combining the conductor failure rate associated with extreme ice and snow weather and the conductor tower failure rate.

3. The distribution network fault recovery method taking into account fault evolution under extreme weather conditions as claimed in claim 1, characterized in that: The linear random power flow model is constructed by describing the cascading failure of the distribution network through random power flow. 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 outage probability of the line, including: The linear random power flow model is constructed by describing the cascading failures of distribution networks through random power flow; A random power flow model considering line disconnection is constructed by combining the random compensation power method based on sensitivity analysis; Solve the random power flow model of line disconnection 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 under extreme weather conditions as claimed in 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 overload outage probability of line l 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 the maximum transmission power of line l respectively.

5. The distribution network fault recovery method taking into account fault evolution under extreme weather conditions as claimed in claim 1, characterized in that: The distribution network system state transition probability is: in, The distribution network status is Transfer to The probability of 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 The probability of and They are respectively the probability of equipment ij failure caused by extreme ice and snow weather at t+1 and the probability of equipment l failure caused by cascading failure.

6. The distribution network fault recovery method taking into account fault evolution under extreme weather conditions as claimed in 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: When the grid-connected operation state is converted to the island operation state, the power output characteristics of the slave control unit 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 that 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 They are respectively the upper limit of active power output and reactive power output of DG at node i at time t; T is a 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 under extreme weather conditions as claimed in 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 respectively; 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, respectively.

8. The distribution network fault recovery method taking into account fault evolution in extreme weather conditions as claimed in claim 1, characterized in that: The objective function of the distribution network fault recovery model considering the coordination of reconstruction and island partitioning is: minF=ω1f1+ω2f2, Where: F is the total objective function; f1 and f2 are sub-objective functions that characterize the load loss of the distribution network and the number of switch operations; ω1 and ω2 are the weight coefficients of the sub-objective functions; P LOSS and P ALL are the weighted load loss and total load 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 power 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 disconnected; 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 as claimed in claim 1, characterized in that: The constraints of the distribution network fault recovery model taking into account the coordination of reconstruction and island division include coordination constraints of reconstruction and island division, distribution network flow constraints and distribution network safety constraints; Among them, the coordinated constraints of reconstruction and island partitioning include partitioning area constraints and connectivity and radial constraints; The partition 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 region 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 outside the region divided by node i; k i,t is a 0-1 state variable representing whether the DG at node i is V / f controlled at time t, Ω 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 at node i at time t controls the DG to emit virtual power; 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 respectively; 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, respectively; 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 power of 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 recovery system taking into account fault evolution under extreme weather conditions, characterized in that: include: The fault evolution analysis module is used to 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 by combining the failure mechanism of the distribution network conductors and towers; a linear random power flow model is constructed by describing the cascading failures of the distribution network through random power flow. Based on the linear random power flow model, a random power flow model considering line disconnection is constructed by combining the random compensation power method based on sensitivity analysis, and the real-time outage probability of the line is obtained by solving it; 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 outage probability of the line 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 control unit and the slave control unit when the system switches from the grid-connected operation state to the islanded operation state, and calculate the power output characteristics of the distributed photovoltaic units when the system switches from the grid-connected operation state to the islanded operation state in extreme ice and snow weather; A fault recovery module is used to combine the state transition probability of the distribution network system, the power output characteristics of the master control unit and the slave control unit, and the power output characteristics of the distributed photovoltaic units, 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 island division; solve the distribution network fault recovery model that takes into account the coordination of reconstruction and island division, and obtain a fault recovery strategy.

Images