Power distribution system reliability evaluation method under component failure rate variation

Abstract

The application discloses a power distribution system reliability evaluation method under element failure rate change, solves the shortage of the prior art, and comprises the following steps: S1, determining power distribution system topological structure, element failure and maintenance parameters, specifically: S101, determining power distribution system network topological parameters, including: line information, user information and power supply information; S102, determining element failure and maintenance parameters; S2, modeling the element with failure rate change; S3, calculating node reliability indexes under element failure rate change; and S4, calculating system reliability indexes under element failure rate change.

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 reliability of power distribution systems under varying component failure rates. Background Technology

[0002] Against the backdrop of rapid socio-economic development, the introduction of "dual carbon" targets, and the global energy transition, users are increasingly demanding higher reliability from power supply. The power distribution system, connecting the transmission system and loads within the power system, plays a crucial role in determining the level of reliability for users. To ensure power reliability, reliability assessments of the power distribution system are essential, as the assessment results provide theoretical reference for decisions regarding the planning, operation, and upgrading of the power distribution system.

[0003] Most existing reliability assessments focus on the steady-state conditions of long-term system operation, assuming that components are only affected by random failures and that the failure rate is constant. However, in actual operation of power distribution systems, the failure rate of components is not constant due to early failures, aging, wear, and external disturbances. Therefore, conducting reliability assessments of power distribution systems under varying component failure rates provides guidance for maintenance plans, equipment aging and replacement, and fault prevention. This is of positive significance for improving the reliability of power distribution systems and better responding to external disturbances. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing reliability assessments, which assume a fixed component failure rate and have low accuracy, and to provide a method for assessing the reliability of power distribution systems under varying component failure rates.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for assessing the reliability of a power distribution system under varying component failure rates includes the following steps:

[0007] S1, determine the power distribution system topology, component faults, and maintenance parameters, specifically:

[0008] S101, Determine the network topology parameters of the power distribution system, including: line information, user information and power supply information;

[0009] S102, determine component faults and repair parameters;

[0010] S2, modeling components with varying failure rates;

[0011] S3, calculates the node reliability index under varying component failure rates;

[0012] S4 is a system reliability index that calculates the system reliability under varying component failure rates.

[0013] Preferably, in S101, the line information includes the starting node number and the ending node number, the user information includes the node number, the node load, and the number of users at the node, and the power information refers to the power node number.

[0014] Specifically, S102 involves: considering that the component failure rate is a constant λ, determining the change of the component failure rate over time λ(t), and determining the average repair time T of the component. r .

[0015] Preferably, S2 is specifically:

[0016] S201. A two-state reliability model with varying failure rate is used to characterize the component, where u is the component's repair rate, which is equal to the reciprocal of the mean time to repair (MTBL). The expression is:

[0017]

[0018] S202. Define component reliability. First, define a non-negative random variable X to describe the component's lifetime. The corresponding distribution function of X is:

[0019] F(t) = P{X≤t}, t≥0

[0020] F(t) represents the lifetime distribution of the component, from which we can obtain the probability that the component will operate normally before time t, i.e., the survival probability of the product at time t:

[0021] R(t) = P{X≥t} = 1 - F(t)

[0022] R(t) is called the reliability function of a component. R(t) is the probability that the product will not fail within the time interval [0,t]. Therefore, reliability can be defined as the probability that the product will perform its intended function under specified conditions and within a specified time.

[0023] S203. Define the failure rate λ(t) of a component. If the component is still functioning normally at time t, then the probability of it failing in the interval (t, t+Δt) is:

[0024]

[0025] Where f(t) is the probability density function of the component lifetime, the failure rate is:

[0026]

[0027] S204. Derive the relationship between component failure rate and component reliability. According to the above formula:

[0028]

[0029] Solving

[0030]

[0031] If F(0) = 0, then C = 1, and the relationship between component failure rate and component reliability is obtained as follows:

[0032]

[0033] Preferably, the node reliability indicators in S3 include the annual average failure rate, the annual average failure time, and the annual average expected power shortage.

[0034] S3 specifically includes:

[0035] S301. Establish a reliability model for the series system under varying component failure rates, and calculate the failure rate of the series system; the lifespan of the series system is:

[0036] X = min{X1,X2,…,X} n}

[0037] Therefore, the reliability of the system is:

[0038]

[0039] When the failure rate of the i-th component is λ i When (t), the reliability of the system is:

[0040]

[0041] The system failure rate is

[0042]

[0043] The system's average annual failure rate is

[0044]

[0045] S302. Calculate the annual average failure time and annual average expected power shortage of the node. The formula for calculating the annual average failure time of the node is:

[0046]

[0047] Where, r i Let i be the node's outage time when component i fails, and let the node's average annual expected power shortage be:

[0048]

[0049] Where P is the load size of the node.

[0050] Preferably, the system reliability indicators in S4 include the system annual average power outage frequency (SAIFI), the system average power outage duration (SAIDI), the average power availability (ASAI), and the expected power shortage (EENS). The specific calculation methods are as follows: The system annual average power outage frequency (SAIFI) refers to the average number of power outage events occurring for each user in the system throughout the year. The calculation formula is as follows:

[0051]

[0052] Where, λ j λ is the annual average failure rate of the j-th load node. i N is the failure rate of the i-th component. j Let S be the number of users on the j-th load node, and S be the set of load nodes in the system. j It is the set of line elements on the power supply path of load node j, N j This represents the number of users at load node j.

[0053] The System Average Annual Outage Duration (SAIDI) refers to the average outage time per user in the system throughout the year. The calculation formula is as follows:

[0054] Average Availability of Electricity (ASAI) is the ratio of the number of hours of normal electricity supply a user receives in a year to the number of hours of electricity supply a user requires. The calculation formula is as follows:

[0055]

[0056] Expected Power Shortage (EENS) refers to the average power shortage for all users in the system over a year, calculated using the following formula:

[0057] The beneficial effects of this invention are as follows: This invention can perform reliability assessments of power distribution systems under varying component failure rates, analyze the system's ability to continuously supply power to users, and provide theoretical references for governments, power grid departments, and users. Existing methods assume a constant component failure rate when assessing the reliability of power distribution systems, thus limiting the applicability of the assessment. This method first establishes a component reliability model under varying component failure rates to characterize these changes; secondly, it proposes a reliability assessment method for power distribution systems under varying component failure rates, overcoming the limitation of existing methods that can only be used under constant component failure rates; thirdly, it proposes a method for calculating reliability indices under varying component failure rates, calculating the reliability indices of the power distribution system, and assessing the system's reliability level. This provides guidance for maintenance planning, equipment aging and replacement, and fault prevention of power distribution system equipment components, and is of positive significance for improving the reliability of power distribution systems and better responding to external disturbances. Attached Figure Description

[0058] Figure 1 This is a block diagram showing the reliability of components under varying failure rates.

[0059] Figure 2 This is a block diagram of the reliability of a series system;

[0060] Figure 3 This is a diagram of the IEEE 37-node test system;

[0061] Figure 4 It is a failure rate curve of the component;

[0062] Figure 5 It is a graph of the probability density function of component lifetime;

[0063] Figure 6 It is a component reliability function curve. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] Example:

[0066] A reliability assessment method for power distribution systems under varying component failure rates is proposed. This method establishes a component reliability model under two states of varying failure rates, and proposes a reliability assessment method for these conditions, calculating node reliability indices and system reliability indices respectively. The scheme includes the following steps:

[0067] S1, determine the power distribution system topology, component faults, and maintenance parameters, specifically:

[0068] S101, Determine the network topology parameters of the power distribution system, including: line information, user information and power supply information;

[0069] S102, determine component faults and repair parameters;

[0070] S2, modeling components with varying failure rates;

[0071] S3, calculates the node reliability index under varying component failure rates;

[0072] S4 is a system reliability index that calculates the system reliability under varying component failure rates.

[0073] The line information in S101 includes the starting node number and the ending node number; the user information includes the node number, node load, and number of users per node; and the power information refers to the power node number.

[0074] Specifically, S102 involves: considering that the component failure rate is a constant λ, determining the change of the component failure rate over time λ(t), and determining the average repair time T of the component. r .

[0075] Specifically, S2 is:

[0076] S201. Use a two-state reliability model with varying failure rates to characterize components, such as... Figure 1 As shown, u represents the component repair rate, which is equal to the reciprocal of the mean time between repairs (MTBL). The expression is:

[0077]

[0078] S202. Define component reliability. First, define a non-negative random variable X to describe the component's lifetime. The corresponding distribution function of X is:

[0079] F(t) = P{X≤t}, t≥0

[0080] F(t) represents the lifetime distribution of the component, from which we can obtain the probability that the component will operate normally before time t, i.e., the survival probability of the product at time t:

[0081] R(t) = P{X≥t} = 1 - F(t)

[0082] R(t) is called the reliability function of a component. R(t) is the probability that the product will not fail within the time interval [0,t]. Therefore, reliability can be defined as the probability that the product will perform its intended function under specified conditions and within a specified time.

[0083] S203. Define the failure rate λ(t) of a component. If the component is still functioning normally at time t, then the probability of it failing in the interval (t, t+Δt) is:

[0084]

[0085] Where f(t) is the probability density function of the component lifetime, the failure rate is:

[0086]

[0087] S204. Derive the relationship between component failure rate and component reliability. According to the above formula:

[0088]

[0089] Solving

[0090]

[0091] If F(0) = 0, then C = 1, and the relationship between component failure rate and component reliability is obtained as follows:

[0092]

[0093] The node reliability metrics in S3 include annual average failure rate, annual average failure time, and annual average expected power shortage; S3 specifically includes:

[0094] S301. Establish a reliability model for the series system under varying component failure rates, and calculate the failure rate of the series system; the reliability block diagram of the series system is as follows: Figure 2 As shown, the lifetime of the series system is:

[0095] X = min{X1,X2,…,X} n}

[0096] Therefore, the reliability of the system is:

[0097]

[0098] When the failure rate of the i-th component is λ i When (t), the reliability of the system is:

[0099]

[0100] The system failure rate is

[0101]

[0102] The system's average annual failure rate is

[0103]

[0104] S302. Calculate the annual average failure time and annual average expected power shortage of the node. The formula for calculating the annual average failure time of the node is:

[0105]

[0106] Where, r i Let i be the node's outage time when component i fails, and let the node's average annual expected power shortage be:

[0107]

[0108] Where P is the load size of the node.

[0109] The system reliability indicators in S4 include the system's annual average power outage frequency (SAIFI), the system's average power outage duration (SAIDI), the average power availability (ASAI), and the expected power shortage (EENS). The specific calculation methods are as follows:

[0110] The system's annual average power outage frequency (SAIFI) refers to the average number of power outage events that occur per user in the system throughout the year. The calculation formula is as follows:

[0111]

[0112] Where, λ j λ is the annual average failure rate of the j-th load node. i N is the failure rate of the i-th component. j Let S be the number of users on the j-th load node, and S be the set of load nodes in the system. j It is the set of line elements on the power supply path of load node j, N j This represents the number of users at load node j.

[0113] The System Average Annual Outage Duration (SAIDI) refers to the average outage time per user in the system throughout the year. The calculation formula is as follows:

[0114] Average Availability of Electricity (ASAI) is the ratio of the number of hours of normal electricity supply a user receives in a year to the number of hours of electricity supply a user requires. The calculation formula is as follows:

[0115]

[0116] Expected Power Shortage (EENS) refers to the average power shortage for all users in the system over a year, calculated using the following formula:

[0117] The method of the present invention will be further illustrated below with specific examples.

[0118] A modified IEEE-37 node test system is used as a case study, such as... Figure 3 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.

[0119] Table 1

[0120] 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

[0121] The lengths of each line are shown in Table 2.

[0122] Table 2

[0123] 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

[0124] The failure rate, lifetime probability density function, and reliability function of the component are respectively as follows: Figure 4 , Figure 5 and Figure 6 As shown, the average repair time for the components is 5 hours. The node reliability indices were calculated, and the reliability indices for some nodes are shown in Table 3.

[0125] Table 3

[0126] Node number Average annual failure rate Average annual downtime / hours Average annual expected power shortage / kW 701 0.5503 2.7513 83.6408 712 1.0262 5.1309 108.0564 724 1.8352 9.1761 269.5021 731 1.6449 8.2243 200.5081 733 1.6568 8.2838 49.5370 735 2.0375 10.1874 126.8332 740 2.3111 11.5556 85.6273 775 1.6151 8.0756 327.8679

[0127] The system's reliability indicators are shown in Table 4.

[0128] Table 4

[0129]

[0130]

[0131] 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 assessing the reliability of a power distribution system under varying component failure rates, characterized by: Includes the following steps: S1, determine the power distribution system topology, component faults, and maintenance parameters, specifically: S101, Determine the network topology parameters of the power distribution system, including: line information, user information and power supply information; S102, determine component faults and repair parameters; S2, modeling components with varying failure rates; S3, calculates the node reliability index under varying component failure rates; S4 is a system reliability index under varying component failure rates. Specifically, S2 is: S201. A two-state reliability model with varying failure rate is used to characterize the component, where u is the component's repair rate, which is equal to the reciprocal of the mean time to repair (MTBL). The expression is: S202. Define component reliability. First, define a non-negative random variable X to describe the component's lifetime. The corresponding distribution function of X is: F(t) = P{X≤t}, t≥0 F(t) represents the lifetime distribution of the component, from which we can obtain the probability that the component will operate normally before time t, i.e., the survival probability of the product at time t: R(t) = P{X≥t} = 1 - F(t) R(t) is called the reliability function of a component. R(t) is the probability that the product will not fail within the time interval [0,t]. Therefore, reliability can be defined as the probability that the product will perform its intended function under specified conditions and within a specified time. S203. Define the failure rate λ(t) of a component. If the component is still functioning normally at time t, then the probability of it failing in the interval (t, t+Δt) is: Where f(t) is the probability density function of the component lifetime, the failure rate is: t∈{t:F(t)<1} S204. Derive the relationship between component failure rate and component reliability. According to the above formula: Solving If F(0) = 0, then C = 1, and the relationship between component failure rate and component reliability is obtained as follows:

2. The method for assessing the reliability of a power distribution system under varying component failure rates according to claim 1, characterized in that, The line information in S101 includes the starting node number and the ending node number; the user information includes the node number, node load, and number of users per node; and the power information refers to the power node number. Specifically, S102 involves: considering that the component failure rate is a constant λ, determining the change of the component failure rate over time λ(t), and determining the average repair time T of the component. r .

3. The method for assessing the reliability of a power distribution system under varying component failure rates according to claim 1, characterized in that, The node reliability metrics in S3 include the annual average failure rate, the annual average failure time, and the annual average expected power shortage. S3 specifically includes: S301. Establish a reliability model for the series system under varying component failure rates, and calculate the failure rate of the series system; the lifespan of the series system is: X=min{X1,X2,…,X n } Therefore, the reliability of the system is: When the failure rate of the i-th component is λ i When (t), the reliability of the system is: The system failure rate is The average annual failure rate of the system is S302. Calculate the annual average failure time and annual average expected power shortage of the node. The formula for calculating the annual average failure time of the node is: Where, r i Let i be the node's outage time when component i fails, and let the node's average annual expected power shortage be: Where P is the load size of the node.

4. The method for assessing the reliability of a power distribution system under varying component failure rates according to claim 3, characterized in that, The system reliability indicators in S4 include the system's annual average power outage frequency (SAIFI), the system's average power outage duration (SAIDI), the average power availability (ASAI), and the expected power shortage (EENS). The specific calculation methods are as follows: The system's annual average power outage frequency (SAIFI) refers to the average number of power outage events that occur per user in the system throughout the year. The calculation formula is as follows: Where, λ j λ is the annual average failure rate of the j-th load node. i N is the failure rate of the i-th component. j Let S be the number of users on the j-th load node, and S be the set of load nodes in the system. j It is the set of line elements on the power supply path of load node j, N j This represents the number of users at load node j. The System Average Annual Outage Duration (SAIDI) refers to the average outage time per user in the system throughout the year. The calculation formula is as follows: Average Availability of Electricity (ASAI) is the ratio of the number of hours of normal electricity supply a user receives in a year to the number of hours of electricity supply a user requires. The calculation formula is as follows: Expected Power Shortage (EENS) refers to the average power shortage for all users in the system over a year, calculated using the following formula:

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