Method for evaluating damage and recovery dynamic process of power distribution system under extreme events

Abstract

This invention discloses a method for evaluating the dynamic process of damage and recovery of a power distribution system under extreme events, overcoming the shortcomings of existing technologies. The method includes the following steps: S1, determining relevant parameters of the power distribution system and disaster information of the extreme event, specifically: S101, determining the network topology parameters of the power distribution system, including line information, user information, and power supply information; S102, determining the disturbance intensity and duration of the extreme event; S103, determining the failure rate of power distribution system components and the repair rate of faulty components during the repair process based on the disturbance intensity of the extreme event and component vulnerability curves; S2, simulating the fault process of the power distribution system; S3, simulating the recovery process of the power distribution system; S4, repeating steps S2 and S3 multiple times to obtain multiple damage and recovery curves under multiple sampling scenarios until the curves converge; S5, calculating reliability indicators based on the obtained component damage curves, user damage curves, component recovery curves, and user recovery curves.

Description

Technical Field

[0001] This invention relates to the field of power distribution system safety technology, and in particular to a method for assessing the dynamic process of power distribution system damage and recovery under extreme events. Background Technology

[0002] With the continuous development of science and technology and the socio-economic landscape, people's reliance on electricity is gradually increasing. In the context of global energy transition and the proposal of dual-carbon goals, electricity is becoming increasingly important. Even brief power outages can have a significant impact on users. Therefore, industrial production and residential activities place higher demands on the continuity of power supply. The distribution system connects the power generation and transmission system with users, directly addressing their electricity needs. Due to its wide distribution and complex structure, most power outages are caused by component failures within the distribution system. While the application of circuit breakers, tie switches, and backup power supplies has enabled the distribution system to cope relatively well with occasional faults under normal operating conditions, extreme events such as typhoons, ice storms, and man-made attacks significantly increase the failure rate of various components. Simultaneous failures of multiple components can lead to widespread power outages. Dynamically assessing the damage process and subsequent recovery process of the distribution system under extreme events can provide theoretical references for governments, power grids, and users in adopting response strategies. Most existing assessment methods use power supply capacity curves or power supply load curves to describe the damage and recovery process of power distribution systems under extreme events, resulting in incomplete results and related indicators. Therefore, proposing a comprehensive and detailed method for assessing the dynamic process of power distribution system damage and recovery under extreme events is a worthy research topic. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies where, under extreme event disturbances, the failure rate of various components increases significantly, leading to power outages for users, but there is a lack of dynamic assessment during the power outage and restoration process, resulting in the inability to effectively restore power supply. This invention provides a method for assessing the dynamic process of power distribution system damage and restoration under extreme events.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A method for assessing the dynamic process of power distribution system damage and recovery under extreme events includes the following steps:

[0006] S1, determine the relevant parameters of the power distribution system and information on extreme event disasters, specifically:

[0007] S101, Determine the network topology parameters of the power distribution system, including line information, user information and power supply information;

[0008] S102, determine the intensity and duration of the disturbance in the extreme event;

[0009] S103, determine the failure rate of power distribution system components and the repair rate of faulty components during the repair process based on the disturbance intensity of extreme events and component vulnerability curves;

[0010] S2 simulates the fault process of the power distribution system;

[0011] S3 simulates the power distribution system recovery process;

[0012] S4. Repeat steps S2 and S3 multiple times to obtain multiple damage and recovery curves under multiple sampling scenarios until the curves converge.

[0013] S5. Calculate the reliability index based on the obtained component damage curve, user damage curve, component recovery curve, and user recovery curve.

[0014] Preferably, the simulation of the fault process of the power distribution system in S2 is specifically as follows:

[0015] S201. Establish a fault model for the components of the power distribution system, where λ is the fault rate of the component and u is the repair rate of the component. Considering that extreme events not only damage the components but also affect the repair work of the maintenance team, the fault and repair processes of the components are separated. It is assumed that the repair process of the faulty components will not be carried out within the disturbance time range of the extreme event. The repair of the faulty components will begin after the impact of the extreme event ends. Furthermore, since the fault rate of the power distribution system during normal operation is relatively small, it is assumed that no new components will fail during the repair process period.

[0016] S202. The state of the component is sampled using the Monte Carlo simulation method. During the period of extreme event disturbance, the lifetime of the component is assumed to follow an exponential distribution, i.e.:

[0017] F(t) = 1 - e -λt

[0018] The probability of a component failing per hour is:

[0019] P(t<1)=F(1)=1-e -λ

[0020] Generate a random number U, if U < 1 - e -λ If U > 1 - e, then the component has failed; -λ If the probability of failure is not found, the component will not fail. Since the exponential distribution has no memory, the probability of failure remains unchanged for each subsequent hour. The components that have not failed will continue to be sampled until the disaster ends.

[0021] S203. Record the operating status of each component during the system damage process, determine the consequences of component failure, and plot the damage curves of the components and users.

[0022] Preferably, the simulation of the power distribution system restoration process in S3 specifically involves:

[0023] S301. Based on the damage results of the power distribution system, determine the system fault scenarios, form a set of faulty components, and optimize the system to obtain the optimal maintenance sequence with the minimum cumulative power loss as the optimization objective. The optimization model is as follows:

[0024] Objective function:

[0025]

[0026] The objective function is to minimize the cumulative power outage amount (CPNS), and the decision variable is b. tj Given the state of component j at time t, the formula for calculating the cumulative power outage charge CPNS is:

[0027]

[0028] Among them, l ti Let Δt be the load lost at node i, and Δt be the sampling interval.

[0029] Constraints:

[0030]

[0031]

[0032] Among them, s ij Indicates line b j Is it a load node n? i The power supply path, s ij When it is 1, it indicates line B. j For load node N i The power supply path, s ij When it is 0, it indicates line B. j Not load node N i The power supply path, L i Let δ be the load of node i, δ be a 0-1 variable, M be a large number, and ε be a small number;

[0033] By optimizing the solution of the line state vector at each time step, the optimal maintenance strategy can be obtained.

[0034] S302. Based on the obtained maintenance strategy, the Monte Carlo method is used to repair the components. The maintenance time of the components follows an exponential distribution.

[0035] G(t) = 1 - e -ut

[0036] Where u is the component repair rate, a random number U is generated to simulate the time required for component repair, and the calculation formula is:

[0037]

[0038] Based on the repair sequence, simulate the time required to repair each faulty component in turn;

[0039] S303. Record the repair time of each component during the system recovery process, identify the users whose power is restored due to component repair, and plot the recovery curves of components and users.

[0040] Preferably, the criterion for curve convergence in S4 is that the values ​​at each interval on the curve converge.

[0041] Preferably, the reliability indicators in S5 include the number of faulty components, the number of users experiencing power outages, the amount of power outage load, the number of repaired components, the number of users with restored power, the amount of power restored load, the average failure rate of components, the average failure rate of users, the average failure rate of loads, the average repair rate of components, the average power restoration rate of users, the average power restoration rate of loads, the cumulative number of users with power outages, and the cumulative amount of power outages.

[0042] The beneficial effects of this invention are: it can assess the damage and recovery process of power distribution systems under the influence of extreme events, providing theoretical reference for relevant departments and users, and reducing the impact of extreme events on the normal operation of power distribution systems. This invention establishes a dynamic assessment framework for the damage and recovery process of power distribution systems, decomposing the power distribution system's resilience curve into a fault curve and a recovery curve, analyzing from both component and user perspectives, proposing relevant assessment indicators, and comprehensively analyzing the damage and recovery process of power distribution systems under extreme events. Attached Figure Description

[0043] Figure 1 This is a flowchart of a method for assessing the dynamic process of power distribution system damage and recovery under extreme events;

[0044] Figure 2 It is a fault model diagram of a power distribution system component;

[0045] Figure 3 This is a schematic diagram of the damage curves of power distribution system components;

[0046] Figure 4 This is a schematic diagram of the damage curve for users in the power distribution system;

[0047] Figure 5 This is a schematic diagram of the recovery curve of a power distribution system component;

[0048] Figure 6 This is a schematic diagram of the power distribution system user recovery curve;

[0049] Figure 7This is the topology diagram of the IEEE-37 node test system;

[0050] Figure 8 This is a graph showing the damage curves of components in the example system;

[0051] Figure 9 This is a graph showing the user damage curve of the simulation system;

[0052] Figure 10 This is a graph showing the user load impairment of the simulation system;

[0053] Figure 11 It is a component recovery curve diagram of the simulation system;

[0054] Figure 12 This is a user recovery curve graph of the simulation system;

[0055] Figure 13 This is a user load recovery curve diagram for the simulation system;

[0056] Figure 14 This is a user load elasticity curve diagram of the simulation system. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] Example:

[0059] Methods for assessing the dynamic process of power distribution system damage and recovery under extreme events, such as... Figure 1 As shown, this method first determines the network topology, component faults, and maintenance parameters of the power distribution system, and determines the intensity and duration of extreme event disturbances. Monte Carlo simulation is used to simulate the fault and recovery process, plotting fault and recovery curves from both component and user perspectives. Multiple simulations are performed until the curves converge, and relevant indicators are calculated to complete the dynamic assessment of the power distribution system's damage and recovery process under extreme events. This scheme includes the following steps:

[0060] S1, determine the relevant parameters of the power distribution system and information on extreme event disasters, specifically:

[0061] S101, determine the network topology parameters of the power distribution system. The parameters include line information, user information and power supply information. Among them, the line information includes the starting node number, the ending node number and the line length; the user information includes the node number, the number of users at the node and the load at the node; and the power supply information refers to the power supply node number.

[0062] S102, determine the disturbance intensity and duration of the extreme event; the greater the disturbance intensity and the longer the duration of the extreme event, the greater the probability of power distribution system components failing;

[0063] S103, determine the failure rate of power distribution system components and the repair rate of faulty components during the repair process based on the disturbance intensity of extreme events and component vulnerability curves;

[0064] S2 simulates the fault process of the power distribution system;

[0065] S3 simulates the power distribution system recovery process;

[0066] S4. Repeat steps S2 and S3 multiple times to obtain multiple damage and recovery curves under multiple sampling scenarios until the curves converge.

[0067] S5. Calculate the reliability index based on the obtained component damage curve, user damage curve, component recovery curve, and user recovery curve.

[0068] The S2 simulation of the fault process in the power distribution system specifically involves:

[0069] S201. Establish fault models for power distribution system components, such as... Figure 2 As shown, λ is the component failure rate and u is the component repair rate. Considering that extreme events not only damage components but also affect the repair work of the maintenance team, the component failure and repair process are separated. It is assumed that the repair process of the faulty component will not be carried out within the disturbance time range of the extreme event. The repair of the faulty component will begin after the impact of the extreme event ends. Furthermore, since the failure rate of the power distribution system during normal operation is relatively small, it is assumed that no new component failures will occur during the repair process period.

[0070] S202. The state of the component is sampled using the Monte Carlo simulation method. During the period of extreme event disturbance, the lifetime of the component is assumed to follow an exponential distribution, i.e.:

[0071] F(t) = 1 - e -λt

[0072] The probability of a component failing per hour is:

[0073] P(t<1)=F(1)=1-e -λ

[0074] Generate a random number U, if U < 1 - e -λ If U > 1 - e, then the component has failed; -λ If the probability of failure is not found, the component will not fail. Since the exponential distribution has no memory, the probability of failure remains unchanged for each subsequent hour. The components that have not failed will continue to be sampled until the disaster ends.

[0075] S203. Record the operating status of each component during the system damage process, determine the consequences of component failure, and plot the damage curves for the components and the user, such as... Figure 3 , Figure 4 As shown.

[0076] The simulation of the power distribution system restoration process in S3 specifically involves:

[0077] S301. Based on the damage results of the power distribution system, determine the system fault scenarios, form a set of faulty components, and optimize the system to obtain the optimal maintenance sequence with the minimum cumulative power loss as the optimization objective. The optimization model is as follows:

[0078] Objective function:

[0079]

[0080] The objective function is to minimize the cumulative power outage amount (CPNS), and the decision variable is b. tj Given the state of component j at time t, the formula for calculating the cumulative power outage charge CPNS is:

[0081]

[0082] Among them, l ti Let Δt be the load lost at node i, and Δt be the sampling interval.

[0083] Constraints:

[0084]

[0085]

[0086] Among them, s ij Indicates line b j Is it a load node n? i The power supply path, s ij When it is 1, it indicates line B. j For load node N i The power supply path, s ij When it is 0, it indicates line B. j Not load node N i The power supply path, L i Let δ be the load of node i, δ be a 0-1 variable, M be a large number, and ε be a small number;

[0087] By optimizing the solution of the line state vector at each time step, the optimal maintenance strategy can be obtained.

[0088] S302. Based on the obtained maintenance strategy, the Monte Carlo method is used to repair the components. The maintenance time of the components follows an exponential distribution.

[0089] G(t) = 1 - e -ut

[0090] Where u is the component repair rate, a random number U is generated to simulate the time required for component repair, and the calculation formula is:

[0091]

[0092] Based on the repair sequence, simulate the time required to repair each faulty component in turn;

[0093] S303. Record the repair time of each component during the system recovery process, identify the users affected by the component repairs, and plot the recovery curves for components and users, such as... Figure 5 , Figure 6 As shown.

[0094] The criterion for curve convergence in S4 is that the values ​​at each interval on the curve converge.

[0095] The reliability indicators in S5 include the number of faulty components, the number of users experiencing power outages, the amount of power outage load, the number of repaired components, the number of users with restored power, the amount of power restored load, the average failure rate of components, the average failure rate of users, the average failure rate of loads, the average repair rate of components, the average power restoration rate of users, the average power restoration rate of loads, the cumulative number of users with power outages, and the cumulative amount of power outages.

[0096] A modified IEEE-37 node test system is used as a case study, such as... Figure 7 As shown, the original system had 37 load nodes, 35 lines, and 1 transformer. To facilitate the demonstration of the method proposed in this paper, the following modifications were made: load node 799 was changed to a low-voltage substation node, i.e., the power supply node of the distribution network; and the transformer between load nodes 709 and 775 was replaced with line L35. The load capacity and number of users of each load node are shown in Table 1.

[0097] Table 1

[0098] node Load / kW Number of users node Load / kW Number of users node Load / kW Number of users 701 30.4 85 713 37.61 88 732 48.5 130 702 18.61 48 714 31.51 74 733 5.98 10 703 38.84 103 718 18.89 50 734 7.49 15 704 26.39 65 720 12.17 30 735 12.45 23 705 12.58 30 722 15.36 42 736 35.12 58 706 29.58 72 724 29.37 70 737 11.03 18 707 31.09 75 725 33.82 80 738 46.84 145 708 22.57 20 727 43.9 125 740 7.41 12 709 43.08 128 728 41.18 110 741 31.86 90 710 12.57 23 729 35.71 89 742 12.73 32 711 48.23 140 730 43.98 114 744 19.04 54 712 21.06 52 731 24.38 56 775 40.6 108

[0099] The lengths of each line are shown in Table 2.

[0100] Table 2

[0101] line Length / m line Length / m line Length / m line Length / m line Length / m L1 960 L9 320 L17 320 L25 600 L33 200 L2 400 L10 240 L18 200 L26 280 L34 280 L3 360 L11 280 L19 1280 L27 200 L35 500 L4 1320 L12 760 L20 400 L28 560 L36 1850 L5 240 L13 120 L21 200 L29 640 L6 600 L14 320 L22 520 L30 520 L7 80 L15 320 L23 520 L31 400 L8 800 L16 600 L24 920 L32 400

[0102] Given an extreme event with a component failure rate of 10 hours and an average repair time of 5 hours, the component damage curves, user damage curves, user load damage curves, component recovery curves, user recovery curves, and user load recovery curves for the power distribution system are as follows: Figures 7-14 As shown.

[0103] The system's reliability indicators are shown in Table 3.

[0104] Reliability indicators Calculation results Number of faulty components 13.2512 Number of users experiencing power outages (households) 2.4266e+03 Power outage load (kW) 9.6755e+02 Mean failure rate of components (number of components / hour) 1.3251 Average failure rate per user (users / hour) 2.4266e+02 Mean Failure Rate (kW / h) 96.7552 Average component repair rate (pieces / hour) 0.1312 Average repair rate per user (users / hour) 24.0262 Average repair rate per load (kW / h) 9.5797 Total number of households affected by power outages (households per hour) 1.1978e+05 Total power outage amount (kW·h) 4.8136e+04

[0105] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Other variations and modifications are possible without departing from the technical solutions described in the claims.

Claims

1. A method for evaluating the dynamic process of damage and recovery of a power distribution system under extreme events, characterized in that, Includes the following steps: S1, determine the relevant parameters of the power distribution system and information on extreme event disasters, specifically: S101, Determine the network topology parameters of the power distribution system, including line information, user information and power supply information; S102, determine the intensity and duration of the disturbance in the extreme event; S103, determine the failure rate of power distribution system components and the repair rate of faulty components during the repair process based on the disturbance intensity of extreme events and component vulnerability curves; S2 simulates the fault process of the power distribution system, specifically as follows: S201. Establish fault models for power distribution system components; S202. The Monte Carlo simulation method is used to sample the state of the component. During the period of extreme event disturbance, the lifetime of the component is assumed to follow an exponential distribution. S203. Record the operating status of each component during the system damage process, determine the consequences of component failure, and plot the damage curves of components and users; S3 simulates the power distribution system recovery process, specifically: S301. Based on the damage results of the power distribution system, determine the system fault scenario, form a set of faulty components, and optimize the system to obtain the optimal maintenance sequence with the minimum cumulative power loss as the optimization objective. S302. Based on the obtained maintenance strategy, the Monte Carlo method is used to maintain the components, and the maintenance time of the components follows an exponential distribution. S303. Record the repair time of each component during the system recovery process, identify the users whose power was restored due to component repair, and plot the recovery curves of components and users; S4. Repeat steps S2 and S3 multiple times to obtain multiple damage and recovery curves under multiple sampling scenarios until the curves converge. S5. Calculate the reliability index based on the obtained component damage curve, user damage curve, component recovery curve, and user recovery curve.

2. The method for assessing the dynamic process of power distribution system damage and recovery under extreme events according to claim 1, characterized in that, The S2 simulation of the fault process in the power distribution system specifically involves: S201. Establish fault models for power distribution system components. For the failure rate of components, To assess the component repair rate, considering that extreme events not only damage components but also impact the repair work of maintenance teams, the component failure and repair process are separated. It is assumed that the repair process for faulty components will not commence within the disturbance timeframe of the extreme event, and will only begin after the impact of the extreme event has subsided. Furthermore, since the failure rate of the power distribution system during normal operation is relatively low, it is assumed that no new components will fail during the repair process period. S202. The state of the component is sampled using the Monte Carlo simulation method. During the period of extreme event disturbance, the lifetime of the component is assumed to follow an exponential distribution, i.e.: The probability of a component failing per hour is: Generate random numbers ,like If the component fails, then the component has malfunctioned; if If the probability of failure is not found, the component will not fail. Since the exponential distribution has no memory, the probability of failure remains unchanged for each subsequent hour. The components that have not failed will continue to be sampled until the disaster ends. S203. Record the operating status of each component during the system damage process, determine the consequences of component failure, and plot the damage curves of the components and users.

3. The method for assessing the dynamic process of power distribution system damage and recovery under extreme events according to claim 2, characterized in that, The simulation of the power distribution system restoration process in S3 specifically involves: S301. Based on the damage results of the power distribution system, determine the system fault scenarios, form a set of faulty components, and optimize the system to obtain the optimal maintenance sequence with the minimum cumulative power loss as the optimization objective. The optimization model is as follows: Objective function: Select the minimum cumulative power outage amount As the objective function, decision variables For components exist Real-time status, cumulative power outage amount The calculation formula is: in, For nodes Lost load, This is the sampling interval; Constraints: in, Indicates the line Is it a load node? The power supply path, When it is 1, it indicates the line For load nodes The power supply path, When it is 0, it indicates the line Not a load node The power supply path, For nodes The load capacity, For 0-1 variables, For a large number, It is a decimal; By optimizing the solution of the line state vector at each time step, the optimal maintenance strategy can be obtained. S302. Based on the obtained maintenance strategy, the Monte Carlo method is used to repair the components. The maintenance time of the components follows an exponential distribution. in, Generate random numbers for the component repair rate. The time required for simulating component repair is calculated using the following formula: Based on the repair sequence, simulate the time required to repair each faulty component in turn; S303. Record the repair time of each component during the system recovery process, identify the users whose power is restored due to component repair, and plot the recovery curves of components and users.

4. The method for assessing the dynamic process of power distribution system damage and recovery under extreme events according to claim 1, characterized in that, The criterion for curve convergence in S4 is that the values ​​at each interval on the curve converge.

5. The method for assessing the dynamic process of power distribution system damage and recovery under extreme events according to claim 1, characterized in that, The reliability indicators in S5 include the number of faulty components, the number of users experiencing power outages, the amount of power outage load, the number of repaired components, the number of users with restored power, the amount of power restored load, the average failure rate of components, the average failure rate of users, the average failure rate of loads, the average repair rate of components, the average power restoration rate of users, the average power restoration rate of loads, the cumulative number of users with power outages, and the cumulative amount of power outages.

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