A power distribution network fault repair strategy optimization method considering wind turbine shutdown under typhoon disaster
By constructing wind speed and power output models for wind turbines and combining them with the dispatching of construction teams and mobile power sources, the emergency repair strategy for the power distribution network was optimized. This solved the power deficit problem caused by wind turbine shutdown during typhoon disasters, and achieved efficient restoration of the power distribution network and minimized load loss.
Patent Information
- Application Number
- CN202211212429.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-29
- Publication Date
- 2026-01-06
- Estimated Expiration
- 2042-09-29
AI Technical Summary
Existing disaster recovery strategies for power distribution networks have failed to effectively address the power deficit caused by wind turbines being shut down during typhoons, resulting in reduced grid recovery efficiency, increased load losses, and exceeding safety limits.
A step model of wind speed and output power of wind turbines is constructed. After linearization, it is combined with the construction team and mobile power dispatch model to construct an optimization model of collaborative wind turbine tripping and distribution network fault repair strategy. The optimization solution is used to solve the repair strategy to reduce the loss of important loads.
Optimizing the emergency repair of power distribution network faults during typhoon disasters can effectively reduce losses of critical loads, ensure the safe operation of the power grid, and improve recovery efficiency.
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Figure CN115759557B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power distribution network restoration, and specifically relates to an optimization method for power distribution network fault repair strategy considering wind turbine shutdown under typhoon disasters. Background Technology
[0002] Extreme weather events, such as typhoons, can severely damage power distribution network facilities, causing widespread power outages and resulting in significant economic losses and social impacts. Therefore, to reduce power outages affecting critical loads, and with the increasing integration of wind power into the distribution network, it can be used to provide power support and enhance grid resilience. However, extreme wind speeds during typhoons can affect the operating status of wind turbines, necessitating further research into their impact on grid recovery.
[0003] Current research on power grid emergency repair and restoration strategies typically assumes that wind turbines operate under normal conditions. However, when wind speed exceeds the tripping speed, wind turbines often trip to ensure hardware safety, causing wind power output to drop instantly from full capacity to zero. This results in a significant active power deficit, leading to critical load losses and even microgrid disconnection, jeopardizing the safe and stable operation of the power grid. Existing emergency repair and restoration methods neglect the issue of wind turbine tripping, leading to reduced grid restoration efficiency, increased load losses, and even exceeding safety constraints.
[0004] Therefore, it is necessary to invent an optimization method for power distribution network fault repair strategy that takes into account wind turbine shutdown during typhoon disasters, in order to improve the efficiency of power distribution network repair, reduce the loss of important loads, and ensure the safe operation of the power grid. Summary of the Invention
[0005] To address the aforementioned problems, the present invention aims to solve the issue that current disaster recovery repairs of power distribution networks do not take into account the significant power deficit caused by wind turbine shutdown, and to provide an optimized method for power distribution network fault repair strategies that takes into account wind turbine shutdown during typhoon disasters.
[0006] The specific technical solution for achieving the objective of this invention is as follows:
[0007] An optimization method for power distribution network fault repair strategy considering wind turbine shutdown under typhoon disasters includes the following steps:
[0008] Step 1: Construct a step model of wind speed and power output of the wind turbine, and linearize the model to obtain the turbine tripping status and power output during the emergency repair process;
[0009] Step 2: Construct a model for dispatching construction teams and mobile power sources during power distribution network emergency repairs;
[0010] Step 3: Based on the construction team and mobile power supply scheduling model in Step 2, construct an optimization model for collaborative wind turbine tripping and distribution network fault repair strategies;
[0011] Step 4: Based on the changes in typhoon wind speed during the power grid emergency repair process, solve the optimization model of coordinated wind turbine tripping and power grid fault repair strategy to obtain the optimal emergency repair scheduling strategy that takes wind turbine tripping into account, so as to minimize the loss of important loads during the recovery process.
[0012] Compared with the prior art, the significant advantages of this invention are:
[0013] (1) The technical solution of the present invention constructs the wind speed and power output function of the wind turbine, describes the wind power output under different wind speeds, and introduces auxiliary variables to linearize the piecewise function. Compared with the traditional method of emergency repair of the distribution network after disaster, it fully considers the output of the wind turbine under extreme wind speed conditions and establishes an optimization model for the coordinated wind turbine tripping and distribution network fault repair strategy.
[0014] (2) In the process of emergency repair and restoration of power distribution network under typhoon disaster, the technical solution of the present invention combines the analysis of wind turbine output by typhoon wind speed change, optimizes the construction team and mobile power dispatch strategy, and minimizes the important load loss of power distribution network restoration.
[0015] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0016] Figure 1 This is a flowchart of the method steps of the present invention.
[0017] Figure 2 This is a topology diagram of the IEEE 69-node system in an embodiment of the present invention.
[0018] Figures 3-5 This is a schematic diagram of the wind speed of each wind farm in the embodiments of the present invention.
[0019] Figure 6 This is a schematic diagram of the scheduling path for the construction team and mobile power supply in an embodiment of the present invention.
[0020] Figure 7 This is a schematic diagram comparing the repair results of various methods in the embodiments of the present invention. Detailed Implementation
[0021] Combination Figure 1 An optimization method for power distribution network fault repair strategy considering wind turbine shutdown under typhoon disasters includes the following steps:
[0022] Step 1: Construct a step model of wind speed and power output of the wind turbine, and linearize the model to obtain the turbine tripping status and power output during emergency repairs. Specifically:
[0023] Combination Figure 2The operating states of wind turbines under different wind speed conditions can be divided into:
[0024] a) When the wind speed is less than the cut-in wind speed, the wind turbine cannot start and the wind power output is 0.
[0025] b) When the wind speed is between the cut-in wind speed and the rated wind speed, the wind turbine starts to start, and as the wind speed increases, the wind power output gradually increases from 0 to the rated power.
[0026] c) When the wind speed is between the rated wind speed and the wind speed cut-off speed, the wind power is operated at full capacity and the wind power output is the rated power.
[0027] d) When the wind speed is greater than the turbine cutoff speed, in order to ensure the safety of the turbine hardware, the wind turbine will perform a turbine cutoff action, and the wind power output will drop from full power to 0 instantaneously.
[0028] Step 1-1: The power output model of the wind turbine under different wind speed conditions is as follows:
[0029]
[0030] Among them, v t This indicates the wind speed in the current operating environment of the wind turbine, v in v r and v out P represents the wind turbine's cut-in, rated, and cut-off wind speeds, respectively. r P represents the rated power of the fan. t w This indicates the actual power output of the fan at the current wind speed.
[0031] Steps 1-2: Since the power output model of the wind turbine under different wind speeds is nonlinear, in order to ensure the solvability of the model, four auxiliary variables are introduced to linearize the model:
[0032]
[0033] in, The auxiliary variable introduced represents four wind speed ranges with different wind turbine outputs. When the wind speed is in one of these ranges, the corresponding ξ is 1, and the others are 0.
[0034] Step 2: Construct a model for dispatching construction teams and mobile power sources during power distribution network emergency repairs, specifically as follows:
[0035] Step 2-1, Construction Team Scheduling Model:
[0036] Each construction team can only repair one fault point at a time:
[0037]
[0038] in, This indicates the scheduling status of the construction team; a value of 1 indicates that construction team c repairs fault point i at time t.
[0039] Time limit for the construction team's vehicle movement from the warehouse to the first fault location:
[0040]
[0041] in, This indicates the travel time from the warehouse point to each fault point;
[0042] Time constraints for the construction team's movement from fault point i to fault point j:
[0043]
[0044] Among them, tr i,j This represents the travel time of the construction team from fault point i to fault point j;
[0045] Time constraints for the construction team to repair fault points:
[0046]
[0047] Where, r i,c This indicates the repair time required for construction team c to fix fault point i. This indicates the completion status of the fault repair. For example, when the fault requires two time steps to complete the repair, such that x = [0,0,1,1,0], we can obtain z = [0,0,0,1,1].
[0048] State constraints after the construction team repairs the fault point:
[0049]
[0050] The constraint that a fault can only be repaired by a single construction team:
[0051]
[0052] State constraints for fault point repair:
[0053]
[0054] Among them, s i,t This indicates the repair status of fault point i at time t; if the repair is complete, the value is 1.
[0055] Step 2-2, Mobile Power Supply Scheduling Model:
[0056] Determine the power bank's connection status:
[0057]
[0058] in, This indicates the scheduling status of the mobile power supply; a value of 1 indicates that the mobile power supply m is connected to node i at time t. This indicates the connection status of the power bank. If the power bank m is in the operational state at time t, then it equals 1.
[0059] Each power bank can only be connected to one node at a time:
[0060]
[0061] Time limit for the vehicle to travel from the warehouse to the first access point for the power bank:
[0062]
[0063] in, This indicates the travel time of the power bank from the warehouse to each access point;
[0064] Vehicle movement time limit for the power bank from access point i to access point j:
[0065]
[0066] Among them, tr i,j This represents the travel time of the power bank from access point i to access point j;
[0067] Output power constraints of power banks:
[0068]
[0069] In the formula, This represents the output power of the mobile power source m at node i at time t. This indicates the maximum output power of the power bank m.
[0070] Step 3: Based on the construction team and mobile power supply scheduling model in Step 2, construct an optimization model for collaborative wind turbine tripping and distribution network fault repair strategies, specifically as follows:
[0071]
[0072]
[0073]
[0074]
[0075] Where x represents the construction team and mobile energy storage dispatch scheme, and y represents the power output and line switch operation scheme; CL Indicates the cost of load loss. As a cost of load loss, ρ i For load weighting, This represents the demand value of load i at time step t. Let C be the recovery value of load i at time step t, where Δt is the unit time of each time step. M For the unit's power generation cost, The unit power generation cost, This represents the output value of unit i at time step t. C W For the cost of wind curtailment of wind turbines, The unit cost of wind curtailment for wind power W represents the maximum output value of wind turbine i at time step t, considering the turbine shutdown process. i,t This indicates the actual dispatch output of the wind turbine.
[0076] Furthermore, the constraints of the optimization model are as follows:
[0077] (1) Line restoration path constraints:
[0078]
[0079]
[0080]
[0081]
[0082]
[0083] Among them, Z i,j,t This indicates that the recovery path runs from node i to node j at time t. This indicates the available status of the faulty line ij at time t. This indicates the availability of the connection line ij at time t;
[0084] (2) Line power flow capacity constraints:
[0085]
[0086] Among them, P i,j,t This represents the power flow magnitude from node i to node j at time t. The current power flow capacity is the size of the line. The current line can only have power flow if there is a recovery path for the line ij; otherwise, it is 0.
[0087] (3) Power output and load recovery constraints:
[0088]
[0089]
[0090]
[0091]
[0092]
[0093]
[0094]
[0095] in, This represents the power of the mobile power supply at node i at time step t. and Let i be the active and reactive power output of the distributed power source at time t. and RU represents the maximum active and reactive power output of the distributed power source. i and RD i These are the power supply active output ramp-up limits;
[0096] (4) Power balance and voltage safety constraints:
[0097]
[0098]
[0099]
[0100]
[0101]
[0102] Among them, U i,t R represents the voltage magnitude of node i at time step t. i,j and X i,j Let be the impedance value of line ij. U i and These are the upper and lower limits of the node voltage.
[0103] Step 4: Combining the typhoon wind speed changes during the power grid emergency repair process, solve the optimization model of coordinated wind turbine tripping and power grid fault repair strategy to obtain the optimal emergency repair scheduling strategy considering wind turbine tripping, minimizing the loss of critical loads during the recovery process.
[0104] Specifically, firstly, the fault information of the distribution network is analyzed to assess the fault repair time of the distribution network; then, the shortest travel time of vehicles between different nodes is calculated by coupling the roads of the transportation network with the fault nodes of the distribution network and the access points of mobile power sources; finally, the emergency repair resource information during the emergency repair and restoration of the distribution network is considered, and parameters such as the working status and starting position of the construction team, and the initial position and output information of the mobile power source are given.
[0105] Then, based on the predicted wind speed changes during the typhoon disaster and combined with the wind speed-output model of the wind turbine, the turbine tripping status during the repair process was calculated to obtain the turbine output.
[0106] Finally, considering the wind turbine tripping status, an optimization model for distribution network fault repair strategy considering wind turbine tripping is solved to obtain the optimal fault repair scheduling strategy, minimizing the loss of critical loads during distribution network restoration.
[0107] An optimization system for power distribution network fault repair strategies considering wind turbine shutdown during typhoon disasters includes the following modules:
[0108] Wind turbine output module: used to build a step model of wind speed and output power of wind turbine units, and to determine the turbine tripping status and output status during emergency repairs;
[0109] Construction team and mobile power supply module: used to build a construction team and mobile power supply dispatch model for emergency repairs of power distribution networks;
[0110] Emergency Repair Strategy Optimization Model: This model is used to construct and solve the optimization model for coordinated wind turbine tripping and distribution network fault emergency repair strategies, thereby obtaining the optimal emergency repair scheduling strategy that takes wind turbine tripping into account, and minimizing the loss of critical loads during the recovery process.
[0111] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, performs the following steps:
[0112] Step 1: Construct a step model of wind speed and power output of the wind turbine, and linearize the model to obtain the turbine tripping status and power output during the emergency repair process;
[0113] Step 2: Construct a model for dispatching construction teams and mobile power sources during power distribution network emergency repairs;
[0114] Step 3: Based on the construction team and mobile power supply scheduling model in Step 2, construct an optimization model for collaborative wind turbine tripping and distribution network fault repair strategies;
[0115] Step 4: Based on the changes in typhoon wind speed during the power grid emergency repair process, solve the optimization model of coordinated wind turbine tripping and power grid fault repair strategy to obtain the optimal emergency repair scheduling strategy that takes wind turbine tripping into account, so as to minimize the loss of important loads during the recovery process.
[0116] A computer-storable medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:
[0117] Step 1: Construct a step model of wind speed and power output of the wind turbine, and linearize the model to obtain the turbine tripping status and power output during the emergency repair process;
[0118] Step 2: Construct a model for dispatching construction teams and mobile power sources during power distribution network emergency repairs;
[0119] Step 3: Based on the construction team and mobile power supply scheduling model in Step 2, construct an optimization model for collaborative wind turbine tripping and distribution network fault repair strategies;
[0120] Step 4: Based on the changes in typhoon wind speed during the power grid emergency repair process, solve the optimization model of coordinated wind turbine tripping and power grid fault repair strategy to obtain the optimal emergency repair scheduling strategy that takes wind turbine tripping into account, so as to minimize the loss of important loads during the recovery process.
[0121] The present invention will be further described below with reference to the embodiments.
[0122] Example
[0123] The topology of the IEEE 69-node system is as follows: Figure 3 As shown in Table 1, wind turbines are installed at nodes 24, 43, and 50 of the distribution network. Specific parameters of the wind farms are also shown. Since individual wind turbines cannot support a microgrid, each wind farm is combined with energy storage to form a wind-storage system. Considering the movement of the typhoon during distribution network repairs, the wind speed changes at each wind farm are as follows: Figure 4 As shown.
[0124] F1-F7 represent line faults in the distribution network caused by the typhoon. Two construction teams and one mobile power supply participated in the post-disaster repair of the distribution network. The power supply was limited to 400kW and its initial location was at node 48. The connection point of the mobile power supply in the distribution network is represented by the green node.
[0125] Table 1 Wind Farm Parameters
[0126]
[0127] Figure 5 This is a schematic diagram of the dispatching routes for construction teams and mobile power sources. The shaded area represents the microgrid supported by the wind-storage system, which is used to reduce critical load losses.
[0128] As the typhoon's path changed, wind turbines 50, 43, and 24 at the wind farm were successively tripped due to extreme wind speeds. To minimize the loss of critical loads in the microgrid, mobile power supplies were connected to nodes 48, 44, and 23 to provide stable power support and prevent the power reduction caused by turbine tripping from leading to microgrid disconnection. Meanwhile, Team 2 repaired faults F1, F4, and F5, connecting each microgrid to the substation nodes. Team 1 repaired faults F6, F3, F7, and F2, restoring other loads in the distribution network and restoring the original distribution network topology.
[0129] To demonstrate the advantages of the power grid fault repair method considering wind turbine shutdown proposed in this invention, this method is compared with methods that do not consider mobile power sources, wind turbine shutdown, and grid reconfiguration. In this comparison, Method A is the method of this application, Method B is the method without considering mobile power sources, Method C is the method without considering wind turbine shutdown, and Method D is the method without considering grid reconfiguration.
[0130] The results of the four methods are as follows: Figure 6 As shown.
[0131] Combination Figure 6 Load loss accounts for a large portion of the total cost because load restoration has the highest priority compared to other economic costs during the post-disaster recovery phase. Method B, by not considering the power support of mobile power sources, leads to higher generator costs and load loss. Method C, by not considering measures to address sudden power shortages caused by wind turbine tripping, results in large-scale load reduction to ensure the safe and stable operation of the distribution network. Method D, by not considering network reconfiguration, leads to the greatest outage loss because the outage load cannot be transferred to other feeders through network reconfiguration; the outage load can only be restored after all faults are repaired. In summary, the method proposed in this invention outperforms the other three methods, and by considering mobile power sources, wind turbine tripping, and network reconfiguration, it effectively reduces load loss during distribution network emergency repair and restoration.
[0132] The above embodiments illustrate and describe the basic principles and main features of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.
Claims
1. A method for optimizing a power distribution network fault repair strategy considering a wind turbine shutdown under a typhoon disaster, characterized in that, The method comprises the following steps: Step 1, constructing a wind speed and output power step model of a wind turbine, and linearizing the model to obtain a wind turbine cutting state and output condition during repair; Step 1-1, the output power model of the wind turbine under different wind speed conditions is: ; Wherein, v t represents the current fan working environment wind speed, v in , v r and v out respectively represent the cut-in, rated and cut-out wind speed of the fan, P r represents the rated power of the fan, represents the actual power of the fan at the current wind speed; Step 1-2, four auxiliary variables are introduced to linearize the above output power model: ; wherein, , , , is an auxiliary variable introduced, representing four wind speed intervals of different fan outputs, when the wind speed is in one of the wind speed intervals, the corresponding is 1, and others is 0; Step 2, constructing a construction team and mobile power dispatching model during distribution network repair; Step 3, based on the construction team and mobile power dispatching model of step 2, constructing a collaborative wind turbine cutting and distribution network fault repair strategy optimization model: ; ; ; ; where x represents the construction team and mobile energy storage scheduling scheme, y represents the power output and line switch action scheme; represents the load loss cost, is the load loss cost, is the load weight, represents the demand value of load i at time step t, is the recovery value of load i at time step t, is the unit time of each time step, is the unit generation cost of each unit, is the unit generation cost of each unit, represents the output value of unit i at time step t, is the wind turbine abandonment cost, is the unit wind turbine abandonment cost, represents the maximum output value of wind turbine i at time step t considering wind turbine tripping, represents the actual dispatch output of the wind turbine. Step 4, combining the typhoon wind speed change during distribution network repair, solving the collaborative wind turbine cutting and distribution network fault repair strategy optimization model, obtaining the optimal repair scheduling strategy considering wind turbine cutting, and realizing the minimum important load loss during the recovery process.
2. The method for optimizing the power distribution network fault repair strategy considering the typhoon disaster and fan cutting according to claim 1, characterized in that, The construction of the construction team and mobile power dispatching model during distribution network repair in step 2 is specifically: Step 2-1, construction team dispatching model: Each construction team can only repair one fault point at the same time at most: ; wherein, represents the construction crew dispatch state, equal to 1 indicates that the construction crew c repairs the fault point i at time t; The vehicle movement time limit of the construction team from the warehouse point to the first fault point: ; wherein, represents the movement time from the warehouse point to each failure point; The vehicle movement time limit of the construction team from fault point i to fault point j: ; wherein, represents the movement time of the construction team between the fault points i and j; The repair time limit of the construction team for repairing the fault point: ; wherein, represents the repair time required by the construction team c to repair the fault point i, represents the repair completion status of the fault point; The state constraint of the construction team after repairing the fault point: ; The constraint that the fault point can be repaired by at most one construction team: ; The state constraint of the fault point repair: ; wherein, represents the repair status of the fault point i at time t, and if completed, the value = 1; Step 2-2, mobile power dispatching model: Determine the access state of the mobile power: ; wherein, denotes the mobile power dispatching state, equal to 1 indicates that the mobile power m accesses the node i at time t, denotes the access state of the mobile power, equal to 1 if the mobile power m is in the operation state at time t; Each mobile power can only access one node at the same time at most: ; The vehicle movement time limit of the mobile power from the warehouse point to the first access point: ; wherein, represents the movement time of the mobile power source from the warehouse point to each access point; The vehicle movement time limit of the mobile power between access points i and j: ; wherein, denotes the movement time of the mobile power supply between the access point i and the access point j; The output power constraint of the mobile power: ; wherein represents the output power of the mobile power supply m at the i-th node at the time t, represents the maximum output power of the mobile power supply m.
3. The method for optimizing the power distribution network fault repair strategy considering the typhoon disaster and fan cutting according to claim 1, characterized in that, The constraint condition of the optimization model is: (1) line recovery path constraint: ; ; ; ; ; wherein, denotes the restoration path from node i to node j at time t, denotes the available state of the fault line ij at time t, denotes the available state of the tie line ij at time t; (2) line flow capacity constraint: ; wherein, Pij(t) represents the power flow magnitude from node i to node j at time t, Cij represents the power flow capacity of line ij, which is the power flow magnitude that the current line can have when there is a restoration path for line ij, otherwise it is 0; (3) power output and load recovery constraint: ; ; ; ; ; ; ; wherein, Pm, i(t) denotes the mobile power source power size of node i at time step t, and Pd, i(t) is the active and reactive power output of the t time step distributed power i, and Pd, i(t) is the maximum value of the active and reactive power output of the distributed power, and are the active power output ramping limits of the power source, respectively; (4) power balance and voltage safety constraint: ; ; ; ; ; wherein, V (i, t) denotes the voltage magnitude of node i at time step t, and Z (i, j) is the impedance value of line ij, and Vmin(i) and Vmax(i) are the lower and upper bounds of the node voltage.
4. A power distribution network fault repair strategy optimization system considering wind turbine shutdown under typhoon disaster, characterized in that, The method comprises the following modules: Wind turbine output module: for constructing a wind speed and output power step model of a wind turbine, determining the cutting state and output condition of the wind turbine during repair, comprising: The output power model of the wind turbine under different wind speed conditions is: ; Wherein, v t represents the current fan working environment wind speed, v in , v r and v out respectively represent the fan cut-in, rated and cut-out wind speed, P r represents the rated power of the fan, represents the actual power of the fan at the current wind speed; Four auxiliary variables are introduced to linearize the above output power model: ; wherein, , , , is an auxiliary variable introduced, representing four wind speed intervals of different fan outputs, when the wind speed is in one of the wind speed intervals, the corresponding is 1, and others is 0; Construction team and mobile power module: for constructing a construction team and mobile power dispatching model during distribution network repair; Repair strategy optimization model: for constructing a collaborative wind turbine cutting and distribution network fault repair strategy optimization model and solving, obtaining the optimal repair scheduling strategy considering wind turbine cutting, and realizing the minimum important load loss during the recovery process: The collaborative wind turbine cutting and distribution network fault repair strategy optimization model is: ; ; ; ; where x represents the construction team and mobile energy storage scheduling scheme, y represents the power output and line switch action scheme; represents the load loss cost, is the load loss cost, is the load weight, represents the demand value of the load i at time step t, is the recovery value of the load i at time step t, is the unit time of each time step, is the unit generation cost of the unit, is the unit generation cost of the unit, represents the output value of the unit i at time step t, is the wind turbine abandoned wind cost, is the unit wind turbine abandoned wind cost, represents the maximum output value of the wind turbine i at time step t considering the wind turbine tripping, represents the actual scheduling output of the wind turbine.
5. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the method in any one of claims 1-3.
6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method in any one of claims 1-3.
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