A method for identifying weak equipment in the auxiliary power system of a hydropower plant

Abstract

The present invention belongs to the technical field of identification of weak equipment in the power consumption system, and specifically provides a method for identifying weak equipment in the auxiliary power system of a hydropower plant, including: constructing a four-state reliability model for auxiliary power equipment; refined modeling of the duration of each state: performing refined modeling on the duration of mutual transfer between the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state; constructing a reliability evaluation method for the auxiliary power system based on the equipment four-state reliability model and the reliability operation boundary, and establishing the reliability operation boundary by finding the critical state of system load shedding; identifying weak equipment by determining the load shedding sharing amount of each equipment in the auxiliary power system, and the larger the load shedding sharing amount of the equipment, the weaker the equipment. Through this method, weak equipment in the system can be effectively identified to guide power station operation and maintenance personnel to reasonably select and replace equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of identifying weak equipment in the power consumption system, and specifically relates to a method for identifying weak equipment in the auxiliary power system of a hydropower plant. Background Art

[0002] For large-scale hydropower plants, they have comprehensive benefits such as flood control, power generation, and shipping. On the one hand, they can not only prevent devastating floods but also allow large ships to navigate; on the other hand, they play an important role as a power hub in the power grid and can quickly achieve peak shaving and frequency modulation of the power system.

[0003] It should be noted that the prerequisite for a hydropower plant to exert its comprehensive benefits is to have a reliable auxiliary power supply system to supply equipment such as the gates of the flood discharge dam section, unit excitation, and ship locks. To ensure the safe operation of large-scale hydraulic projects without fail, it is necessary not only to evaluate the reliability level of the entire auxiliary power system. More importantly, it is to accurately identify the weak equipment in the auxiliary power system, which is crucial for guiding power station operation and maintenance personnel to reasonably select and replace equipment and improving the reliability of the auxiliary power system within limited costs. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for identifying weak equipment in the auxiliary power system of a hydropower plant, which can effectively identify the weak equipment in the system to guide power station operation and maintenance personnel to reasonably select and replace equipment.

[0005] To solve the above technical problem, the technical solution adopted by the present invention is: a method for identifying weak equipment in the auxiliary power system of a hydropower plant, including the following steps:

[0006] Step 1: Construct a four-state reliability model for auxiliary power equipment. The four states of auxiliary power equipment include the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state, and the four states of auxiliary power equipment can transfer to each other;

[0007] Step 2: Refined modeling of the duration of each state: Refined modeling is carried out on the duration of the mutual transfer between the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state;

[0008] Step 3: Construct a reliability evaluation method for the auxiliary power system based on the equipment four-state reliability model and the reliability operation boundary. By finding the critical state of the system for load shedding, the reliability operation boundary is established;

[0009] Step 4: Identify the weak equipment by determining the load shedding sharing amount of each equipment in the auxiliary power system. The larger the load shedding sharing amount of the equipment, the weaker the equipment.

[0010] In the preferred solution, in the first step, the four states of the auxiliary power equipment can be transferred to each other. respectively represent the transition rates of the equipment from the normal operation state to the random failure, latent failure, and aging failure states; respectively represent the transition rates of the equipment from the latent failure state to the random failure and aging failure states; represents the repair rate of the equipment from the random failure state to the normal operation state; represents the replacement rate of the equipment from the aging failure state to the normal operation state; respectively represent the durations of the equipment from the normal operation state to the random failure state, from the normal operation state to the latent failure state, and from the normal operation state to the aging failure state; respectively represent the durations of the equipment from the latent failure state to the random failure state and the aging failure state; respectively represent the times for the equipment to recover from the random failure state and the aging failure state to the normal operation state.

[0011] In the preferred solution, in the second step, the refined modeling of the duration of each state includes , , , , , , for modeling: The memoryless exponential function distribution is used to model , and the truncated normal distribution is used to model , and ; The two-parameter Weibull life model is used to model and ; The lognormal distribution is used to model .

[0012] In the preferred solution, the , , , , , , expressions are:

[0013] 1) Time model

[0014] The memoryless exponential function distribution is used to model , The cumulative distribution function of is:

[0015] (1);

[0016] In the formula, represents the cumulative distribution function;

[0017] 2) Time model

[0018] It is modeled using a truncated normal distribution , The probability density function of

[0019] is: (2);

[0020] In the formula, and are respectively the probability density function and the distribution function of the standard normal distribution random variable; respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment, is a constant;

[0021] 3) Time modeling

[0022] It is modeled using a truncated normal distribution , The probability density function is:

[0023] is: (3);

[0024] In the formula, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment; and are respectively the probability density function and the distribution function of the standard normal distribution random variable; is a constant;

[0025] 4) Time modeling

[0026] It is modeled using a two-parameter Weibull lifetime model , The cumulative distribution function is:

[0027] is: (4);

[0028] In the formula, are respectively the scale parameter and the shape parameter;

[0029] 5) Time modeling

[0030] It is modeled using a two-parameter Weibull lifetime model , The cumulative distribution function is:

[0031] (5);

[0032] Wherein, are the scale parameter and the shape parameter respectively;

[0033] 6) Time modeling

[0034] The truncated normal distribution is used for modeling , The cumulative distribution function is:

[0035] (6);

[0036] Wherein, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment;

[0037] 7) Time modeling

[0038] The lognormal distribution is used for modeling , The cumulative distribution function is:

[0039] (7);

[0040] (8);

[0041] Wherein, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment, is the error function, is the variable representation.

[0042] In the preferred solution, in the third step, for two different reasons for load shedding in the system, two different reliability operation boundaries are established, and finally the complete reliability operation boundary is obtained. The system load shedding is caused by two reasons: 1) The transmission line limit determined by the transmission line parameters and the system power flow; 2) The insufficient generating capacity of the units in some system areas or system islands caused by line failures.

[0043] In the preferred solution, the two different reliability operation boundaries are respectively:

[0044] 1) The first type of reliability operation boundary represents the system power flow limit, and the expression is:

[0045] (9);

[0046] Wherein, Nm is the total number of system nodes; B is the system admittance matrix; is lh the power flow of the line, is lh the maximum power flow of the line; , , , , respectively represent lh the admittance of the line, hk the inverse of the line admittance, the node k generator power generation, the node k load, lk the inverse of the line admittance; represents the node k maximum generator power generation;

[0047] operator is used to scale the right - hand side to a constant, and the expression of the operator is:

[0048] (10);

[0049] In the formula, a represents the variable to be scaled;

[0050] 2) The second - type reliability operation boundary is used to describe the insufficient power generation capacity of a certain system area. The construction method is as follows:

[0051] After detecting an island or a critical system area, establish the second - type reliability operation boundary. In a certain system area, the total load should be less than the sum of the available power generation capacity and the external power transmission line capacity. The expression is:

[0052] (11);

[0053] In the formula, is the node set of the island or the critical system area; is the set of external power transmission lines connected to the system area , represents lh the power flow of the transmission line;

[0054] Since there is no external power transmission line for the island, the second - type reliability operation boundary of the island is simplified as:

[0055] (12).

[0056] In the preferred solution, in step three, the reliability evaluation method of the auxiliary power system includes the following steps:

[0057] Step 1: Initialize the status of all devices;

[0058] Step 2: If the current status of the device is the normal operation status, then sample according to Equations (1), (2), and (5) and judge the size of . If , the device enters the latent fault state. If , the device enters the random failure state. If

[0059] , the device enters the aging failure state; Step 3: If the current status of the device is the random failure operation status, then sample according to Equation (6) ; if the current status of the device is the aging failure state, then sample according to Equation (7) ; if the current status of the device is the latent fault state, then sample according to Equations (3) and (4) and judge the size of . If

[0060] , the device enters the random failure state. If

[0061] , the device enters the aging failure state;

[0062] (13);

[0063] In the formula, respectively represent the original load and the available load after load shedding of the i th node, represents the load shedding size;

[0064] Step 6: Calculate the reliability index.

[0065] In the preferred solution, the reliability index in Step 6 is selected to be measured by the system loss of power probability or / and loss of load frequency or / and expected energy not supplied. The calculation formulas of LOLP, LOLF, and EENS are:

[0066] (14);

[0067] (15);

[0068] (16);

[0069] Wherein, T total represents the total time scale; represents the set of events sampled from the auxiliary power system; represents the duration of state s; is a binary variable, 1 represents load shedding; represents the state s The amount of load shedding; T is a constant, LOLP, LOLF, and EENS respectively represent the system power shortage probability, power shortage frequency, and expected power supply shortage.

[0070] In the preferred solution, in the fourth step, the time-sequence transfer of the auxiliary power system state includes seven cases of Case1 to Case7. Case1 includes the normal operation state and the random fault state, Case2 includes the normal operation state and the aging fault state, Case3 includes the normal operation state and the latent fault state, Case4 includes the normal operation state, the random fault state and the latent fault state, Case5 includes the normal operation state, the random fault state and the aging fault state, Case6 includes the normal operation state, the latent fault state and the aging fault state, Case7 includes the normal operation state, the random fault state, the latent fault state and the aging fault state. According to the state at time T in the time-sequence state transfer process of the auxiliary power system operation, the load shedding sharing is carried out by adopting the multi-level chain sharing principle.

[0071] In the preferred solution, the multi-level chain sharing principle performs load shedding sharing according to the following situations:

[0072] I. First-level sharing: Sharing among random faults, aging faults and latent faults

[0073] 1) If each device at time T only includes the normal operation state and the random fault state, that is, Case1 situation, the sharing is determined as follows:

[0074] ① If neither Case4, Case5, nor Case6 occurs at time T-1 and time T+1, then the risk contribution of device i is: is:

[0075] (17);

[0076] (18);

[0077] (19);

[0078] Wherein, represents device i the probability of failure; Represents the device i The marginal contribution to the load shedding event ; e Represents The sub - event of which does not contain the device i Event; Represents e The number of faulty devices in; And Respectively represent the weight and the fault consequence of the fault event e ; Represents that in the fault event e Adding the faulty device i The fault consequence of the resulting fault event;

[0079] ② If the situation shown in Case 4 occurs at time T - 1 or T + 1, the first occurrence of the hidden fault does not participate in the fault sharing, and the sharing principles for the normal state and the random fault are formula (17); within the next time period, the hidden fault participates in the risk sharing, and the sharing principle is formula (17);

[0080] ③ If the situation shown in Case 5 occurs at time T - 1, then at time T - 1, the aging failure bears the fault, and at time T, the distribution principle is still formula (17);

[0081] ④ If the situation shown in Case 5 occurs at time T + 1, then at time T, the aging failure fault is shared equally with the random fault, and the sharing principle is formula (17), and for the next duration, it is the aging fault that shares the fault;

[0082] ⑤ If the situation shown in Case 6 occurs at time T - 1, then at time T - 1, the aging failure bears the fault, and at time T, the distribution principle is still the one in formula (17), and the hidden fault bears the fault together with the random fault and the aging failure fault;

[0083] ⑥ If the situation shown in Case 6 occurs at time T + 1, then at time T, the aging failure fault is shared equally with the random fault, and the sharing principle is formula (17), and within the next 8 time instants, it is the aging failure that bears the responsibility;

[0084] ⑦ If the situation shown in Case 7 occurs at time T - 1, then at time T - 1, the aging failure state is treated as the random fault state, and for the next duration of the state, it is all treated as the aging failure state;

[0085] ⑧ If the situation shown in Case 7 occurs at time T + 1, then at time T, the risk sharing is carried out according to formula (17); at time T + 1, the aging failure is treated as a random failure, and the sharing principle is formula (17), and within the next T + 8 time instants, it is the aging failure state that shares the fault.

[0086] 2) When the situations described in Case 2 and Case 3 occur at time T, the sharing criteria can be obtained by the same method as in 1) above.

[0087] II. Second - layer sharing: Sharing within random failures, aging failures, or latent failures

[0088] For aging failure states, random failure states, or latent failure states that occur, sharing is carried out in accordance with the proportional sharing principle, and the sharing principle is shown in the following formula:

[0089] (20);

[0090] In the formula, is the risk amount shared by equipment A in load shedding; respectively represent the failure rates of equipment A, B... N; H A represents the risk contribution of equipment A, which is obtained through the first - layer sharing calculation.

[0091] A method for identifying weak equipment in the auxiliary power system of a hydropower plant provided by the present invention has the following beneficial effects:

[0092] 1. It can calculate and analyze the reliability of the auxiliary power system under different auxiliary power supply schemes, and finally accurately and effectively identify the weak equipment in the system to guide the power station operation and maintenance personnel to reasonably select and replace equipment, and seek an auxiliary power system scheme that is not affected by the operation mode and unit maintenance arrangement and can quickly restore power supply after disconnection within a limited cost, which can ensure the safe and stable operation of the power station units and other facilities.

[0093] 2. Step 1 of the present invention comprehensively considers all possible operating states of the equipment in actual operation, and establishes a time - series state transition process under the coupling action of the aging failure state, random failure state, and latent failure state of the equipment, which more realistically simulates the operation of the equipment.

[0094] 3. Step 2 of the present invention analyzes the causes of various failure states, and finely models the random variables of the duration of each state through the probability distribution that matches them, which can avoid the masking effect of different failure modes on its state transition process and can more accurately simulate the actual state transition process of the equipment.

[0095] 4. Step 3 proposes a reliability assessment method for the auxiliary power system of a hydropower plant based on the four - state reliability model of the equipment and the reliability operation boundary, which covers more system states with fewer reliability operation boundaries, and proposes a fast load - shedding calculation method based on the approximate distance model, which well solves the problem of long calculation time of traditional reliability assessment methods.

[0096] 5. Step 4 proposes a multi-level chain sharing principle, redefines the reliability allocation principle considering the differences in the four-state reliability models of equipment, and enables a more reasonable allocation of the load shedding risk among the equipment in the auxiliary power system. Description of the Drawings

[0097] The present invention will be further described below in conjunction with the drawings and embodiments:

[0098] Figure 1 is the four-state Markov state transition diagram of the equipment of the present invention;

[0099] Figure 2 is the timing state transition process diagram of the equipment and system in the embodiment;

[0100] Figure 3 is the summary diagram of the timing state transition of the auxiliary power system;

[0101] Figure 4 is the auxiliary power system diagram in the embodiment;

[0102] Figure 5 The flowchart of the present invention. Detailed Embodiment

[0103] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0104] Embodiment 1:

[0105] As Figure 5 shown, the present invention provides a method for identifying weak equipment in the auxiliary power system of a hydropower plant, which is described in detail as follows:

[0106] Step 1: Construct a four-state reliability model for the auxiliary power equipment. The four states of the auxiliary power equipment include the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state. The four states of the auxiliary power equipment can be transferred to each other.

[0107] During the operation life cycle of the equipment, there are generally two independent failure modes: the random failure mode and the aging failure mode. The difference between the two is that the random failure can be repaired and the equipment can return to the normal operation state after repair, while the aging failure means the end of the life and the equipment must be replaced to return to the normal operation state.

[0108] At present, hidden faults such as non-metallic short circuits, poor contact of cable heads, insulation damage, internal discharge, and unbalanced load operation are initially manifested as small-amplitude zero-sequence or negative-sequence components. However, neither the relay protection device nor the fault recorder can respond to these small components. Usually, it can only be detected through manual patrols and methods such as temperature measurement. Therefore, the equipment will continue to operate for some time. If the hidden fault is detected in time, the operator can stop the equipment for maintenance and let it enter the random outage state. If the hidden fault is not detected in time, many cases have shown that such faults will cause violent explosions of the load or cable, resulting in short circuits, which will trigger more switch tripping, causing adverse effects, and thus entering the aging failure state. The equipment needs to be replaced to continue operating.

[0109] Based on the above analysis, Figure 1 the four-state Markov state transition diagram of the equipment considering random faults, aging faults, and hidden faults is drawn. Among them, the random failure state includes the state where the equipment is stopped by the operation and maintenance staff due to hidden faults and the equipment outage caused by traditional random faults; the aging fault state, also known as the aging failure state, includes the serious faults such as equipment explosion caused by hidden faults and the equipment outage caused by aging faults.

[0110] Figure 1 In respectively represent the transition rates of the equipment from the normal operation state to the random fault, hidden fault, and aging fault states; respectively represent the transition rates of the equipment from the hidden fault state to the random fault and aging fault states; represents the repair rate of the equipment from the random fault state to the normal operation state; represents the replacement rate of the equipment from the aging fault state to the normal operation state; respectively represent the durations of the equipment from the normal state to the random failure state, from the normal state to the hidden fault state, and from the normal state to the aging failure state; respectively represent the durations of the equipment from the hidden fault state to the random failure state and aging failure state; respectively represent the times for the equipment to recover from the random fault state and aging state to the normal operation state.

[0111] Step 2: Fine-grained modeling of the duration of each state: Fine-grained modeling is carried out on the duration of the mutual transition between the equipment aging fault state, equipment random fault state, equipment hidden fault state, and equipment normal operation state.

[0112] According to Figure 1 the characteristics of the durations of different states in and based on the historical data collected from the equipment ledger, the present invention proposes an accurate modeling method for the state duration, and then establishes a comprehensive four-state reliability model for the auxiliary power equipment.

[0113] (1) Time model

[0114] For the random faults of auxiliary power equipment, which are independent of the equipment operation time and completely caused by external accidental factors, and any equipment fault is independent of each other. Therefore, the present invention uses an exponential function distribution without memory to model as follows, and its cumulative distribution function is:[[]]

[0115] (1);

[0116] In the formula,[[]] represents the cumulative distribution function.[[]]

[0117] (2) Time model

[0118] For the latent faults of auxiliary power equipment, which are independent of the equipment operation time, but due to the different qualities of each maintenance personnel and the inconsistent mental states during the maintenance on the same day, it may lead to incomplete maintenance of cable heads or switches during maintenance, resulting in not being completely stable. Therefore, the present invention uses a truncated normal distribution to model to prevent the phenomenon of negative values during sampling, and its probability density function is:[[]]

[0119] (2);

[0120] In the formula,[[]] and are respectively the probability density function and the distribution function of the standard normal distribution random variable; respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of auxiliary power equipment,[[]] is a constant.[[]]

[0121] (3) Time modeling

[0122] For the latent faults that the auxiliary power equipment has entered, even if the power plant arranges special personnel to measure the temperature and check for such faults, the time to discover the latent faults is related to the personnel quality, inspection frequency, and temperature measurement device sensitivity, etc., making have a certain degree of uncertainty. Therefore, the present invention uses a truncated normal distribution to model as follows, and its probability density function is:[[]]

[0123] (3);

[0124] In the formula,[[]] represent the location and scale parameters of the general normal distribution respectively, and the specific values can be obtained from the historical records of auxiliary power equipment.

[0125] (4) Time modeling

[0126] For auxiliary power equipment that has entered the latent failure state, the time to enter the aging failure is related to the development process speed of the latent failure and also has a certain correlation with the equipment operation time. The longer the operation time, the greater the probability of its entering the aging failure, resulting in a certain degree of uncertainty. The two-parameter Weibull lifetime model can flexibly characterize the relationship between the equipment failure rate and its operation age. Therefore, it is selected as the lifetime distribution of the equipment. Thus, its cumulative distribution function is:

[0127] (4);

[0128] In the formula, are the scale parameter and the shape parameter respectively.

[0129] (5) Time modeling

[0130] The aging failure state means the end of the equipment life, which has a strong correlation with the equipment operation time. In other words, its cumulative distribution function is related to the equipment operation time. The two-parameter Weibull lifetime model can flexibly characterize the relationship between the equipment failure rate and its operation age. Therefore, it is selected as the lifetime distribution of the equipment. Thus, its cumulative distribution function is:

[0131] (5);

[0132] In the formula, are the scale parameter and the shape parameter respectively;

[0133] (6) Time modeling

[0134] If the auxiliary power equipment fails, the equipment repair time is related to the personnel efficiency and quality. Therefore, the present invention uses the truncated normal distribution for modeling , and its cumulative distribution function is:

[0135] (6);

[0136] In the formula, represent the location and scale parameters of the general normal distribution respectively, and the specific values are obtained from the historical records of auxiliary power equipment.

[0137] (7) Time modeling

[0138] If the auxiliary power equipment fails, the equipment replacement time is related to the auxiliary power production speed, transportation time, installation time, etc. Therefore, the present invention uses the lognormal distribution to model , and its cumulative distribution function is:[[]]

[0139] (7);

[0140] (8);

[0141] In the formula, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment, is the error function, is the variable representative.[[]]

[0142] Step 3: Construct a reliability evaluation method for the auxiliary power system based on the four-state reliability model of the equipment and the reliability operation boundary, and establish the reliability operation boundary by finding the critical state of the system for load shedding.[[]]

[0143] Aiming at the deficiencies that the existing system state analysis methods cannot pre-judge the system state adequacy, the calculation complexity of load shedding is high, and the methods for accelerating system state analysis cannot adapt to large load fluctuations, the present invention establishes a reliability operation boundary model for reliability evaluation, and on this basis, proposes a system state analysis method based on the reliability operation boundary, which improves the efficiency of system state analysis.[[]]

[0144] In order to establish a reliability operation boundary for reliability evaluation, it is necessary to analyze the reasons for the system to shed load, and establish the reliability operation boundary by finding the critical state of the system for load shedding. The system shedding load is mainly caused by two reasons: ① The transmission line limit determined by the transmission line parameters and system power flow; ② The insufficient generating capacity of the units in some system areas or system islands generated due to line failures. Therefore, the present invention establishes two different types of reliability operation boundaries for these two different reasons for the system to shed load, and finally combines them to obtain a complete reliability operation boundary.[[]]

[0145] 1) The first type of reliability operation boundary[[]]

[0146] The first type of reliability operation boundary is to characterize the system power flow limit. For each system state, the DC power flow is used to determine whether the system state is a load shedding state. If so, the system load shedding amount is determined, and the expression is:[[]]

[0147] (9);[[]]

[0148] (10);[[]]

[0149] (11);[[]]

[0150] (12);

[0151] (13);

[0152] (14);

[0153] Wherein, N m is the total number of system nodes; B is the system admittance matrix; is lh the power flow of the line, is lh the maximum power flow of the line; represents node l 's maximum annual load; represents node l 's cutting load; is node l the percentage of the load that can be shed in the total load; is node l 's active power output of the generator; and respectively represent the maximum and minimum output powers of the generator at node l ; , respectively represent the admittance of line lh , the voltage phase angle of node h .

[0154] Assuming that the load shedding variable in the optimal power flow model is 0, then the voltage phase angles of each node are obtained from Equations (10) and (11):

[0155] (15);

[0156] Wherein: , and respectively represent the power generation and load magnitude of node h.

[0157] Combining Equations (11) and (15) to calculate the branch power flow as:

[0158] (16);

[0159] , , , respectively represent hk the inverse of the line admittance, node kGenerator power generation, node k load of lk the inverse of the line admittance.

[0160] Considering the capacity limit of the transmission line and combining with Equation (12), a set of inequalities representing power flow constraints is obtained:

[0161] (17);

[0162] An operator is proposed to scale the on the right side to a constant, and the expression is:

[0163] (18);

[0164] In the formula, a represents the variable to be scaled;

[0165] Therefore, combining Equation (14), Equation (17) and Equation (18) gives:

[0166] (19);

[0167] In the formula, represents the generator capacity of node k.

[0168] Therefore, Equation (17) is scaled to:

[0169] (20);

[0170] In Equation (20), the left side of the inequality is a set of linear functions of the load, and the right side of the inequality is a set of constants determined by the system topology and equipment parameters. Therefore, Equation (20) is the first type of reliability operation boundary characterizing the power flow limit.

[0171] 2) The second type of reliability operation boundary

[0172] The second type of reliability operation boundary is used to describe the insufficient power generation capacity in a certain system area. In the present invention, only the system islands and key system areas caused by transmission line failures are considered, and the key system area is defined as the system area with only one external transmission line left due to transmission line failures. The second type of reliability operation boundary is obtained by the depth-first search method.

[0173] After detecting the islands and key system areas, the second type of reliability operation boundary can be established as shown in the following formula:

[0174] (21);

[0175] In the formula, A set of nodes for an island or a critical system area; For the system area A set of external power transmission lines connected.

[0176] What is represented by Equation (21) is that within a certain system area, the total load should be less than the sum of the available power generation capacity and the capacity of the external power transmission lines. It should be noted that there are no external power transmission lines in an island, so the second - type reliability operation boundary of the island can be simplified as:

[0177] (22);

[0178] After establishing the first - type reliability operation boundary through the system power flow equation derivation and the second - type reliability operation boundary through island search respectively, and combining the two types of reliability operation boundaries, a complete reliability operation boundary model can be obtained.

[0179] The reliability assessment method based on the reliability operation boundary includes the following steps:

[0180] Step 1: Initialize the states of all devices, generally assuming them to be in the operating state.

[0181] Step 2: If the current state of the device is the normal operating state, then sample according to Equations (1), (2), and (5) That is, sample the time for each device in the auxiliary power system to maintain the current state. And judge the magnitude of, and then judge which failure type the device will be in the next stage. If , the device enters the latent failure state, and other states are deduced similarly.

[0182] Step 3: If the current state of the device is the random failure operating state, then sample according to Equation (6) ; if the current state of the device is the aging failure operating state, then sample according to Equation (7) ; if the current state of the device is the latent failure state, then sample according to Equations (3) and (4) , judge the magnitude of, if , the device enters the random failure state, and other states are deduced similarly.

[0183] Step 4: At the specified time scale, continuously repeat Steps 2 and 3, then the state transition process of all devices at this time scale can be obtained, and the time - series process of the operation of the auxiliary power system can be combined, as Figure 2 shown.

[0184] Step 5: According to the reliability operation boundary determined in 1) and 2), calculate the magnitude of the shed load for each system state using the Manhattan distance.

[0185] The calculation of the minimum load shedding of the system based on the reliability operation boundary is to calculate the minimum Manhattan distance from the load point to the feasible region:

[0186] (23);

[0187] In the formula, respectively represent the original load of the i-th node and the available load after load shedding.

[0188] Step 6: Calculate the reliability index:

[0189] The calculation formulas of LOLP, LOLF and EENS are:

[0190] (24);

[0191] (25);

[0192] (26);

[0193] In the formula, T total represents the total time scale; represents the event set sampled from the auxiliary power system; represents the duration of state s; is a binary variable, 1 represents load loss; represents the state s load shedding amount; T is a constant, usually 8760 hours, and LOLP, LOLF and EENS respectively represent the system loss of power probability, loss of power frequency, and expected energy not supplied.

[0194] Step 4: Identify the weak equipment by determining the share of each equipment in the load shedding in the auxiliary power system. The larger the share of the equipment in the load shedding, the weaker the equipment.

[0195] The identification of equipment weak links lies in determining the "contribution" of each equipment in the system to the load shedding. At present, most existing studies adopt the proportional sharing principle, with the equipment failure probability as the sharing basis, reflecting the responsibility of the equipment for the probability of failure events. If the failure probabilities of the equipment are the same, the risk sharing is the same. Such a sharing principle will have the phenomenon of masking the load loss risk. For example, if the failure of a certain component does not cause the system to shed load, then this component should not participate in the risk sharing. Moreover, the previous methods for identifying weak links have not considered the cross-influence under multiple failure modes. Therefore, the present invention proposes a multi-level chain sharing method for reliability tracking of the auxiliary power system considering the multi-state model as:

[0196] Note: According to the above analysis, random failures are repairable, and the equipment will return to the normal operating state after repair. Assume the repair time is T1; while aging failures mean the end of the life, and the equipment must be replaced to return to the normal operating state. The replacement time is often ten times the repair time. In this invention, it is assumed to be 10T1. The duration of latent faults is assumed to be T2.

[0197] 1) If the failure of a certain device has no impact on the consequences caused by the system failure event, then this device does not participate in the risk sharing of this failure event.

[0198] 2) If a certain failure event simultaneously has the normal operating state, aging failure state, latent fault state, and random failure state of the device: ① When the aging failure first appears, it is regarded as a random failure and participates in the risk sharing; ② Within the time of (10T1 - 1) after the first appearance of the aging failure, the aging failure device shall bear the risk; ③ When the latent fault first appears, it does not participate in the risk sharing; ④ Within the time of (T2 - 1) after the first appearance of the latent fault, it is recorded as the latent fault sharing the risk.

[0199] 3) If a certain failure event simultaneously has the normal operating state, latent fault state, and random failure state of the device: ① When the latent fault first appears, it does not participate in the risk sharing; ② Within the time of (T2 - 1) after the first appearance of the latent fault, it is recorded as the latent fault sharing the risk; ③ When the random failure first appears, it is regarded as a random failure and participates in the risk sharing;

[0200] 4) If a certain failure event simultaneously has the normal operating state and random failure state of the device, then this device shares the risk according to the random failure.

[0201] Therefore, the multi-level chain sharing method for the reliability tracking of the auxiliary power system proposed in this invention is as follows:

[0202] Both the normal state and the latent fault state can transform into aging faults and random faults. The time for the aging fault to return to the normal state is much longer than the recovery time of the random fault. Therefore, the aging fault should bear all the consequences of the failure; for the aging state, although the aging failure rates in different states are different, the resulting failure consequences are all that the equipment needs to be replaced. Therefore, for the equipment entering the aging state, the same consequences should be borne.

[0203] Such as Figure 3As shown, the time-sequential transfer of the auxiliary power system status includes seven cases from Case1 to Case7. Case1 includes the normal operation state and the random fault state, Case2 includes the normal operation state and the aging fault state, Case3 includes the normal operation state and the latent fault state, Case4 includes the normal operation state, the random fault state and the latent fault state, Case5 includes the normal operation state, the random fault state and the aging fault state, Case6 includes the normal operation state, the latent fault state and the aging fault state, and Case7 includes the normal operation state, the random fault state, the latent fault state and the aging fault state. According to the state at time T in the time-sequential state transfer process of the auxiliary power system operation, the hierarchical chain sharing principle is adopted for load shedding sharing.

[0204] The reliability hierarchical chain sharing principle of the four-state model of the equipment proposed by the present invention is as follows:

[0205] I. First-level sharing: Sharing among random faults, aging faults and latent faults

[0206] 1) For Figure 2 the state at time T in the time-sequential state transfer process, which only includes the normal operation state and the random fault state, as shown in Case1 of Figure 3 :

[0207] ① If neither Case4, Case5 nor Case6 occurs at T-1 and T+1, the sharing principle is Equation (27);

[0208] ② If Case4 occurs at T-1 or T+1, the latent fault that appears for the first time does not participate in the fault sharing, and the sharing principle for the normal state and the random fault is Equation (27); in the following time, the latent fault should also participate in the risk sharing, and the sharing principle is Equation (27);

[0209] ③ If Case5 occurs at T-1, then the aging failure bears the fault at T-1, and the distribution principle in Equation (27) is still used at T;

[0210] ④ If Case5 occurs at T+1, then the aging failure fault at T is equivalent to the random fault for sharing, and the sharing principle is Equation (27), and the aging failure shares the fault for the following duration;

[0211] ⑤ If Case6 occurs at T-1, then the aging failure bears the fault at T-1, and the distribution principle in Equation (27) is still used at T, and the latent fault shares the fault together with the random fault and the aging failure fault;

[0212] ⑥ If the situation shown in Case 6 occurs at time T+1, the aging failure fault at time T is treated as a random fault for sharing, and the sharing principle is Equation (27); and the aging failure is responsible for the next 8 time instants.

[0213] ⑦ If the situation shown in Case 7 occurs at time T-1, the aging failure state at time T-1 is treated as a random failure state, and the subsequent state durations are all treated as aging failure states.

[0214] ⑧ If the situation shown in Case 7 occurs at time T+1, the risk is shared according to Equation (27) at time T; the aging failure is treated as a random failure at time T+1, and the sharing principle is Equation (27), and the aging failure state shares the fault within the next T+8 time instants.

[0215] 2) For Figure 2 the situation where the Case 2 and Case 3 described in Figure 3 occur at time T during the time sequence state transition process in

[0216] (27);

[0217] (28);

[0218] (29);

[0219] In the formula, represents the probability of the device i having a fault; represents the marginal contribution of the device i to the load shedding event ; e represents the event that does not include the device i in the sub-events of ; e represents the number of faulty devices in and respectively represent the weight and fault consequence of the fault event e ; represents the fault consequence of the fault event obtained by adding the faulty device e to the fault event i . It can be found from Equation (27) that the devices with high fault probability or large changes in the fault event consequences caused by the fault should share a greater risk.

[0220] II. Second-layer sharing: Sharing within random faults, aging faults, or hidden faults

[0221] For those in the aging failure state, random failure state or latent failure state, they are all allocated according to the proportional sharing principle, and the sharing principle is as shown in the formula.

[0222] (30);

[0223] In the formula, is the risk amount allocated by component A in load shedding; respectively represent the failure rates of components A, B, and N.

[0224] To illustrate the difference between the sharing criterion proposed in the present invention and proportional sharing, the following example is given for illustration:

[0225] Taking the event E{A,B} caused by equipment A and B as an example, the difference between the two sharing methods is illustrated. Suppose the failure probabilities of equipment A and B are both 0.01, and the lost load amount EENS is 20 MWh. The load shedding amount caused by the failure event of equipment A is 5 MW, the load shedding amount caused by the failure event of equipment B is 0 MW, and the load shedding amount in the normal state is 0 MW.

[0226] (1)Proportional sharing

[0227] (31);

[0228] (32);

[0229] (2)The sharing method of the present invention

[0230] 1) The subordinate sub-events of event E{A,B} include: ① The event e{A} where only equipment A fails; ② The event e{B} where only equipment B fails; ③ The normal state e{0};

[0231] ① Calculate the weights of the subordinate sub-events without event e{A}:

[0232] (33);

[0233] (34);

[0234] ② Use formula (28) to calculate the marginal contribution coefficients of equipment A and B to event E{A,B} respectively as:

[0235] (35);

[0236] (36);

[0237] Therefore, according to formula (27), the risk contributions of equipment A and B can be obtained as:

[0238] (37);

[0239] (38);

[0240] Therefore, the values allocated from EENS for Equipment A and Equipment B are respectively:

[0241] (39);

[0242] (40);

[0243] It can be seen that since it is assumed in the premise of the present invention that the failure of only Equipment B will not cause load shedding, it should not participate in risk sharing. From the above analysis, in the proportional sharing criterion, Equipment B shares a load shedding amount of 10 MWh, while in the method proposed by the present invention, Equipment B does not share the load shedding amount. Therefore, the sharing method proposed by the present invention is more fair and reasonable, and the identification of weak equipment is more accurate, and the masking effect can be avoided.

[0244] Embodiment 2:

[0245] To verify the effectiveness of the weak equipment identification method proposed by the present invention, the analysis is carried out taking the auxiliary power supply wiring of a certain power plant as an example. As Figure 4 shown, Figure 4 The switch states in are only for illustration. In the calculation of the present invention, the original reliability parameters are shown in Table 1. In the present invention, it is assumed that Substation B is the main power supply, and the generator terminal auxiliary power, Substation A, and the load are used as backups. In this mode, both 3M and 8M respectively use the 10 kV busbars 4M and 5M of Substation A as the main power supply. In addition, 1M is connected to the 10 kV busbar of Substation B, 2M is respectively connected by one circuit from the 10 kV busbar of Substation B and the 10 kV busbar of the load (10M), 6M is connected to the 10 kV busbar of Substation B, and 7M is respectively connected by one circuit from the 10 kV busbar of Substation B and the 10 kV busbar of the load (15M).

[0246]

[0247] Note: λ a : Short-circuit failure rate; λ p : Open-circuit failure rate; P s : Circuit breaker refusal rate; r : Fault repair time; λ ", r ": Are the planned maintenance rate and planned maintenance time respectively; L: Line length.

[0248] According to the method proposed by the present invention, the reliability calculation results can be obtained as shown in Table 2.

[0249]

[0250] It can be seen that the method proposed in the present invention can calculate and analyze the reliability of the auxiliary power system under different auxiliary power supply schemes, and can provide a certain data basis for identifying weak equipment.

[0251] In order to verify the effectiveness of the proposed sharing method, the present invention specifically compares and analyzes the differences in weak components obtained by this method and the existing proportional sharing method. The results are shown in Table 3.

[0252]

[0253] To illustrate the effectiveness of the method of the present invention, the failure rates of the equipment in Table 3 are reduced proportionally to simulate the improvement of system reliability. Specifically, the reliability indicators ranked 1-3 are reduced by 60%, and the reliability of the equipment ranked 4-6 is reduced by 20%. Then, the system reliability indicators of the present invention are calculated again, as shown in Table 4.

[0254]

[0255] It can be found that after the equipment failure rate is reduced, the reliability obtained by both methods is improved. However, the LOLP obtained by proportional sharing is still greater than the LOLP of the method proposed in the present invention. Therefore, compared with the proportional sharing method, the sharing method of the present invention is more fair and reasonable, and the identification of weak equipment is more accurate.

[0256] In order to prove the accuracy and efficiency of the reliability operation boundary offline modeling - online operation proposed in the present invention. The optimal power flow model and the reliability operation boundary proposed in the present invention are respectively used to analyze a certain system state, and the calculation time is shown in Table 5.

[0257]

[0258] As can be seen from Table 5, under the condition of ensuring consistent reliability or accuracy, the reliability operation boundary improves the calculation time of system state analysis by about 2 times.

[0259] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for identifying weak equipment in the auxiliary power system of a hydropower plant, characterized in that, It includes the following steps: Step 1: Construct a four-state reliability model for auxiliary power equipment. The four states of auxiliary power equipment include the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state. The four states of auxiliary power equipment can transfer to each other; Step 2: Fine-grained modeling of the duration of each state: Fine-grained modeling of the duration of the mutual transfer between the equipment aging failure state, the equipment random failure state, the equipment hidden failure state, and the equipment normal operation state; Step 3: Construct a reliability assessment method for the auxiliary power system based on the equipment four-state reliability model and the reliability operation boundary: By finding the critical state of system load shedding, establish the reliability operation boundary. System load shedding is caused by two reasons: 1) Transmission line over-limit determined by transmission line parameters and system power flow; 2) Insufficient generating capacity of units in some system areas or system islands caused by line faults. For these two different reasons of system load shedding, establish two different reliability operation boundaries, and finally merge them to obtain the complete reliability operation boundary; According to the reliability operation boundary, use the Manhattan distance to calculate the load shedding size of each system state: （13）； In the formula, respectively represent the i original load and the available load after load shedding of the th node, and represents the amount of load shedding; Step 4. Identify weak equipment by determining the load shedding sharing amount of each equipment in the auxiliary power system. The larger the load shedding sharing amount of the equipment, the weaker the equipment. The multi-level chain sharing principle is adopted for load shedding sharing, including the first-level sharing, which is the sharing among random faults, aging faults, and hidden faults, and the risk contribution of the equipment i is as follows: （17）； （18）； （19）； Wherein, represents the probability of equipment i failure; represents the marginal contribution of equipment i to the load shedding event ; e represents the event whose sub - events do not include equipment i ; represents the number of faulty equipment e in; and respectively represent the weight and the failure consequence of the failure event e ; represents the failure consequence of the failure event obtained by adding the faulty equipment e to the failure event i ; It also includes the second - layer sharing, which is the sharing within random failures, aging failures or hidden failures. For the occurrence of aging failure states, random failures or hidden failure states, the sharing is carried out according to the proportional sharing principle. The sharing principle is shown in the following formula: （20）； In the formula, is the risk amount allocated to equipment A during load shedding; respectively represent the failure rates of equipment A, B... N; H A represents the risk contribution of equipment A, which is obtained through the first-layer allocation calculation.

2. The method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 1, wherein In the first step described above, the four states of the auxiliary power equipment can be transferred to each other. They respectively represent the transition rates of the equipment from the normal operation state to the random failure state, the latent failure state, and the aging failure state. They respectively represent the transition rates of the equipment from the latent failure state to the random failure state and the aging failure state. It represents the repair rate of the equipment from the random failure state to the normal operation state. It represents the replacement rate of the equipment from the aging failure state to the normal operation state. They respectively represent the durations of the equipment from the normal operation state to the random failure state, from the normal operation state to the latent failure state, and from the normal operation state to the aging failure state. They respectively represent the durations of the equipment from the latent failure state to the random failure state and the aging failure state. They respectively represent the times for the equipment to recover from the random failure state and the aging failure state to the normal operation state.

3. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 2, characterized in that, In the second step, the refined modeling of the duration of each state includes , , , , , , for modeling: The memoryless exponential function distribution is used to model , and the truncated normal distribution is used to model , and ; The two-parameter Weibull lifetime model is used to model and ; The lognormal distribution is used to model .

4. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 3, characterized in that The said , , , , , , The expression of: 1) Time model Use a memoryless exponential function distribution to perform modeling, The cumulative distribution function of （1）； In the formula, represents the cumulative distribution function; 2) Time model Modeling is performed using a truncated normal distribution , The probability density function of which is as follows: （2）； In the formula, and are the probability density function and the distribution function of the standard normal distribution random variable respectively; represent the location and scale parameters of the general normal distribution respectively, and the specific values are obtained from the historical records of the auxiliary power equipment, is a constant; 3) Time modeling Model using the truncated normal distribution , The probability density function is as follows: （3）； In the formula, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of auxiliary power equipment; 4) Time modeling Use a two-parameter Weibull lifetime model for modeling , The cumulative distribution function is as follows: （4）； wherein, are the scale parameter and the shape parameter respectively; 5) Time modeling Use the two-parameter Weibull lifetime model for modeling , The cumulative distribution function is as follows: （5）； wherein, are the scale parameter and the shape parameter, respectively; 6) Time modeling Modeled using a truncated normal distribution , The cumulative distribution function is as follows: （6）； In the formula, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of the auxiliary power equipment; 7) Time modeling Modeling using the lognormal distribution , The cumulative distribution function is as follows: （7）； （8）； In the formula, respectively represent the location and scale parameters of the general normal distribution, and the specific values are obtained from the historical records of auxiliary power equipment. is the error function. is the variable representative.

5. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 1, characterized in that, The two different reliability operation boundaries are respectively: 1) The first type of reliability operation boundary represents the system power flow limit, and the expression is: （9）； wherein, N m is the total number of system nodes; B is the system admittance matrix; is lh the power flow of the line, is lh the maximum power flow of the line; and and and and respectively represent lh the admittance of the line, hk the inverse of the line admittance, node k the power generation of the generator, node k load, lk the inverse of the line admittance; represents the maximum power generation of the generator at node k ; Operator used to scale the right side to a constant. The expression of the operator is: （10）； In the formula, a represents the variable to be scaled; 2) The second type of reliability operation boundary is used to describe the insufficient generating capacity of a certain system area. The construction method is: After detecting an island or a key system area, establish the second type of reliability operation boundary. In a certain system area, the total load should be less than the sum of the available generating capacity and the external transmission line capacity. The expression is: （11）； In the formula, is the set of nodes in the island or critical system area; is the set of external transmission lines connected to the system area ; represents lh the power flow of the transmission line; There is no external transmission line in the island, so the second type of reliability operation boundary of the island is simplified as: （12）。 6. The method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 1, wherein In Step 3, the reliability assessment method for the auxiliary power system includes the following steps: Step 1: Initialize the states of all equipment; Step 2: If the current state of the device is the normal operating state, then sample according to Equations (1), (2), and (5) and judge and determine the magnitude of. If , then the device enters the latent fault state. If , then the device enters the random failure state. If , then the device enters the aging failure state; Step 3: If the current state of the device is the random failure operation state, then sample according to Equation (6) for ; if the current state of the device is the aging failure state, then sample according to Equation (7) for ; if the current state of the device is the latent fault state, then sample according to Equations (3) and (4) for , and judge the magnitude of . If , then the device enters the random failure state; if , then the device enters the aging failure state. Step 4: At the specified time scale, continuously repeat Steps 2 and 3, then the state transfer process of all equipment at this time scale can be obtained, and the time sequence process of the operation of the auxiliary power system can be combined; Step 5: According to the reliability operation boundary, use the Manhattan distance to calculate the load shedding size of each system state; Step 6: Calculate the reliability index.

7. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 6, characterized in that, The reliability index in Step 6 is selected to be measured by the system loss of power probability or / and loss of power frequency or / and expected energy not supplied. The calculation formulas of LOLP, LOLF, and EENS are: （14）； （15）； （16）； Wherein, T total represents the total time scale; represents the set of events sampled from the auxiliary power system; represents the duration of state s; is a binary variable, where 1 represents load shedding; represents the state s The amount of load shedding; T is a constant, and LOLP, LOLF, and EENS represent the loss of load probability, loss of load frequency, and expected energy not supplied of the system respectively.

8. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 1, characterized in that In step 4, according to the state at time T of the operation time-sequence state transition process of the auxiliary power system, the load shedding is allocated using the multi-level chain sharing principle. The state at time T of the operation time-sequence state transition process of the auxiliary power system includes seven cases, namely Case1 to Case7. Case1 includes the normal operation state and the random fault state, Case2 includes the normal operation state and the aging fault state, Case3 includes the normal operation state and the latent fault state, Case4 includes the normal operation state, the random fault state and the latent fault state, Case5 includes the normal operation state, the random fault state and the aging fault state, Case6 includes the normal operation state, the latent fault state and the aging fault state, and Case7 includes the normal operation state, the random fault state, the latent fault state and the aging fault state. According to the state at time T of the operation time-sequence state transition process of the auxiliary power system, the load shedding is allocated using the multi-level chain sharing principle.

9. A method for identifying weak equipment in the auxiliary power system of a hydropower plant according to claim 8, characterized in that, For the seven cases of the state at time T of the operation time-sequence state transition process of the auxiliary power system, the first-level sharing operation of the multi-level chain sharing principle is as follows: 1) If each device at time T only includes the normal operation state and the random fault state, that is, Case1, the sharing is determined as follows: ① If neither Case 4, Case 5, nor Case 6 occurs at both the T-1 and T+1 times, then the risk contribution of device i is calculated according to Equation (17); ② If the situation shown in Case4 occurs at time T-1 or T+1, the latent fault that appears for the first time does not participate in the fault sharing, and the sharing principle for the normal state and the random fault is Equation (17); in the following time, the latent fault participates in the risk sharing, and the sharing principle is Equation (17); ③ If the situation shown in Case5 occurs at time T-1, then the aging failure bears the fault at time T-1, and the distribution principle at time T is still Equation (17); ④ If the situation shown in Case5 occurs at time T+1, then the aging failure fault at time T is shared as a random fault, and the sharing principle is Equation (17), and the following continuous time is the aging fault sharing the fault; ⑤ If the situation shown in Case6 occurs at time T-1, then the aging failure bears the fault at time T-1, and the distribution principle in Equation (17) is still used at time T, and the latent fault bears the fault together with the random fault and the aging failure fault; ⑥ If the situation shown in Case6 occurs at time T+1, then the aging failure fault at time T is shared as a random fault, and the sharing principle is Equation (17), and the aging failure bears the responsibility within the next 8 time instants; ⑦ If the situation shown in Case7 occurs at time T-1, then the aging failure state at time T-1 is treated as a random fault state, and the following state duration is treated as the aging failure state; ⑧ If the situation shown in Case7 occurs at time T+1, then the risk sharing is carried out according to Equation (17) at time T; the aging failure is treated as a random failure at time T+1, and the sharing principle is Equation (17), and the aging failure state shares the fault within the next T+8 time instants; 2) When the situations described in Case2 and Case3 occur at time T, the sharing criteria can be obtained by the same method as in 1) above.

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