A reliability evaluation method for direct current distribution system based on state merging by using truncation coefficient

Abstract

The application discloses a kind of based on truncation coefficient and realizes state merging DC distribution system reliability evaluation method, it is related to DC distribution system field.According to the multiple operating states presented by the coupling of DC distribution system "source load", the system state space model is established, according to the internal relationship between different operating states, the state merging condition is optimized, the fault tree analysis method is combined with Markov process, the state merging method based on truncation coefficient is proposed, and the reliability index of DC distribution system is calculated according to the system operating state after merging.The application first applies the state merging idea to the reliability evaluation of DC distribution system, combines the fault tree analysis method with Markov process, determines the truncation coefficient by the convergence process of truncated state probability C While ensuring accuracy, the solving efficiency of merged state transition rate is improved, the system state merging under differentiated transition rate is realized, and the application range of state merging in the reliability evaluation of DC distribution system is expanded.

Description

Technical Field

[0001] This invention relates to the field of DC power distribution system evaluation, specifically to a reliability evaluation method for DC power distribution systems based on state merging using a truncation coefficient. Background Technology

[0002] With the development and application of power electronics technology, DC power distribution systems, due to their advantages such as large power supply capacity, high power quality, and ease of access to new energy sources, are gradually becoming the mainstay of future urban power supply. Reliability assessment of DC power distribution systems is a crucial step in ensuring safe and reliable power consumption for users. Compared to AC power distribution systems, DC power distribution systems have significantly more operating states, mainly in the following two aspects: Firstly, with the development and application of power semiconductor devices, DC power supplies can flexibly adjust their output power according to load demand, possessing multiple output levels. Secondly, DC power distribution systems have various wiring methods, such as true bipolar and pseudo bipolar, allowing loads to operate in either unipolar or bipolar modes, resulting in flexible and varied operating conditions. The multiple combinations of power output levels and load operating modes further increase the number of operating states of the DC power distribution system. Traditional state merging methods assume identical transfer rates (equipment failure rate and repair rate). However, in actual power system operation, even identical equipment under essentially the same operating conditions exhibits differences in failure and repair rates, hindering large-scale application in DC power distribution systems and thus reducing the efficiency of reliability assessment for multi-state DC power distribution systems. Therefore, multi-state DC power distribution systems urgently need a state merging method with a wider range of applications to improve the efficiency of reliability assessment. Summary of the Invention

[0003] To address the problem of reduced reliability assessment efficiency caused by the increasing number of operating states in DC power distribution systems, this invention provides a reliability assessment method for DC power distribution systems based on a truncation coefficient, which overcomes the technical deficiency of traditional state merging methods that require identical state transition rates.

[0004] This invention is achieved through the following technical solution: a reliability assessment method for DC distribution systems based on state merging using a truncation coefficient. Based on the various operating states exhibited by the "source-load" coupling of the DC distribution system, a system state-space model is established. According to the inherent relationships between different operating states, the state merging conditions are optimized. Fault tree analysis is combined with Markov processes to propose a state merging method based on a truncation coefficient. The reliability index of the DC distribution system is calculated based on the merged system operating states. Specifically, the method includes the following steps:

[0005] Step 1: Establish the state-space model of the DC distribution system and solve the system operating state probabilities using a Markov process: First, establish the transition matrix A based on the transition relationship between the operating states of the DC distribution system. The elements of the matrix are as shown in equation (1):

[0006]

[0007] In the formula: i, j are system state numbers and i ≠ j, A ij A represents the off-diagonal elements of a matrix, numerically equal to the transition rate from state i to state j. ii The diagonal element of the matrix is ​​numerically equal to 1 minus the sum of the off-diagonal elements in that row, and n is the number of system running states;

[0008] According to Markov processes, when a system reaches steady-state operation, the state probability does not change with the change of the system's operating state, that is:

[0009] PA = P (2)

[0010] In the formula: P = [p1, p2, ..., p n ] represents the system state probability row vector, p n Let n be the probability that the system is in state n.

[0011] Equation (2) is further equivalent to:

[0012] P(AH)=0 (3)

[0013] In the formula: H is the identity matrix;

[0014] By transposing equation (3), the matrix algebraic equation is obtained as follows:

[0015]

[0016] Due to matrix (AH) T The diagonal elements can be represented by off-diagonal elements, therefore it is not a full-rank matrix, and additional constraints are needed to solve for the state probabilities; since the system will always be in some state at any given time, the algebraic sum of all state probabilities should be 1, i.e.:

[0017]

[0018] By combining equations (4) and (5), the system state probabilities can be obtained as follows:

[0019]

[0020] Step Two: Improving Traditional State Merging Conditions Based on a Difference Threshold to Expand the Application Scope of State Merging in DC Distribution Systems. Traditional state merging methods determine the system operating states to be merged based on the same state transition rate. However, in actual power system operation, application scenarios with identical transition rates are almost nonexistent. Nevertheless, in similar or identical scenarios, equipment failure rates and repair rates may be similar. Therefore, this invention proposes a state merging condition based on a difference threshold. Based on calculating the difference between the state transition rate and a reference value, system operating states whose absolute value is less than or equal to the difference threshold are determined as the states to be merged. The selection of the system states to be merged should meet the following conditions:

[0021] {S||λ ij -λ ref |≤δ tr ,i、j∈N} (7)

[0022] In the formula: S is the set of states to be merged, λ ij Let λ be the transition rate from state i to state j. If the system's operating state changes due to a component failure, this transition rate is the failure rate; if the system's operating state changes due to a component recovering its operation, this transition rate is the recovery rate. ref δ is the reference value for the transfer rate. tr Where N is the difference threshold, and N is the set of system operating states;

[0023] It is important to note that while the given state merging conditions mathematically achieve clustering of similar system operating states, to ensure the rationality of the reliability assessment, the system operating states to be merged are generally selected based on similar equipment. In practical engineering applications, merging the states of dissimilar equipment lacks rationality and interpretability.

[0024] Step 3: Solve for the transition rate between the merged state and the state to be transitioned. The transition rate of the merged state includes two forms: the transition rate between the merged state and the independent state, and the transition rate between the merged states.

[0025] ① Transitions between merged and independent states:

[0026] The transition rate λ between independent state i and merged state J iJ Solve using equation (8):

[0027]

[0028] In the formula: j represents an independent state within the merged state J;

[0029] The solution for the transition rate between merged state J and independent state i can be divided into two cases:

[0030] In the first case, when the state transition rate λ jiAt the same time, the transfer rate λ Ji Solve using equation (9):

[0031]

[0032] In the second case, when the state transition rate λ ji At different times, the transfer rate λ Ji Solve using equation (10):

[0033]

[0034] In the formula: C is the cutoff coefficient and C = p j / p k p k This is a reference state, and any state to be merged can be selected.

[0035] ② Transitions between two merged states:

[0036] The solution for the transition rate from merged state I to merged state J is divided into two cases:

[0037] In the first case, when the state transition rate λ ij When they are the same, the merged state transition rate λ IJ Solve using equation (11):

[0038]

[0039] In the formula: i represents an independent state within the merged state I;

[0040] In the second case, when the state transition rate λ ij When they are not the same, the merged state transition rate λ IJ Solve using equation (12):

[0041]

[0042] The process of solving for the transition rate from merged state J to merged state I is similar to that of solving for the transition rate from merged state I to merged state J. To avoid redundancy, when the state transition rate λ... ji When they are the same or different, the merged state transition rate λ JI The solution formulas are given by equations (13) and (14) respectively:

[0043]

[0044]

[0045] Step 4: Solve for the truncation coefficient C. First, determine the truncation function C(t) that varies with time using the fault tree analysis method, as shown in equation (15):

[0046]

[0047] In the formula: p j (t), p k (t) represent the probabilities of the j-th and k-th operating states of the system occurring at time t, respectively, R c (t), R h (t) represents the reliability functions of the c-th and h-th components, respectively; m1 and m2 represent the number of devices operating normally in independent states j and k, respectively; and l represents the total number of system components.

[0048] Secondly, a Markov process is used to determine the time t for the cutoff function to reach steady state. p As shown in equation (16):

[0049]

[0050] In the formula: ε is an infinitesimal;

[0051] Finally, the steady-state time is substituted into the cutoff function to determine the cutoff coefficient, which is solved by equation (17):

[0052]

[0053] Step 5: Equivalent the power state of the merged system to a two-state system, where the two states are "operating" and "faulting". Before equivalence, the frequency and average outage time of the fault operation state need to be calculated as shown in equations (18) and (19). The equivalence process is shown in equations (20), (21), and (22).

[0054]

[0055]

[0056] In the formula: f i w represents the frequency of occurrence of faulty operating state i. i Let λ be the average power outage time for faulty operating state i. ji Let be the transition rate for leaving state j;

[0057]

[0058]

[0059]

[0060] In the formula: r eq The equivalent mean time to repair (MTBT) is expressed in hours per failure, f. eq The equivalent average failure frequency is expressed in times per year, λ. eqThe equivalent failure rate is expressed in times per year, where F represents the number of faulty operating states.

[0061] After the equivalence is completed, the load reliability index can be calculated using the state enumeration method, and then the reliability index of the entire DC power distribution system can be calculated by combining the user information.

[0062] Compared with existing technologies, the present invention has the following advantages: The reliability assessment method for DC distribution systems based on state merging using a truncation coefficient provided by the present invention, compared with existing technologies, is the first to apply the concept of state merging to the reliability assessment of DC distribution systems. By establishing a state-space model of a multi-state DC distribution system, it merges the system operating states that meet the conditions, reducing the number of system operating states and improving the efficiency of reliability assessment for multi-state DC distribution systems. From a methodological perspective, this method combines fault tree analysis with Markov processes, determining the truncation coefficient C through the convergence process of truncated state probabilities. While ensuring accuracy, it improves the efficiency of solving the merged state transition rate, realizing system state merging under differentiated transition rate conditions, and expanding the application scope of state merging in the reliability assessment of DC distribution systems. Attached Figure Description

[0063] Figure 1 This is a topology diagram of the true bipolar DC power distribution system involved in this invention.

[0064] Figure 2 This is the state-space model of the DC power distribution system involved in this invention.

[0065] Figure 3 This is a schematic diagram illustrating the transition between the merged state and the independent state involved in this invention.

[0066] Figure 4 This is a schematic diagram illustrating the transition between two merged states involved in this invention.

[0067] Figure 5 This is the state probability curve of the DC power distribution system involved in this invention. Detailed Implementation

[0068] The present invention will be further described below with reference to specific embodiments.

[0069] Figure 1 In the DC power distribution system, the high-voltage side voltage level is ±7.5kV, and the low-voltage side voltage level is ±375V. The system adopts a true bipolar connection method. The DC power distribution system has four DC power sources, each with "operating" and "fault" states. The four power sources have a total of 2... 4= 16 states; For the load side, the true bipolar connection method is coupled with the DC power supply state, which increases the load operation mode from 3 to 6, namely the complete bipolar operation, 3 / 4 bipolar unbalanced operation and 1 / 2 bipolar balanced operation derived from bipolar operation, the complete unipolar operation, 1 / 2 unipolar operation derived from unipolar operation, and fault shutdown.

[0070] A reliability assessment method for DC power distribution systems based on state merging using a truncation coefficient is proposed. Figure 1 The system application shown establishes a system state-space model based on the various operating states exhibited by the "source-load" coupling of the DC power distribution system. Based on the inherent relationships between different operating states, the state merging conditions are optimized. A state merging method based on truncation coefficients is proposed by combining fault tree analysis with Markov processes. The reliability index of the DC power distribution system is then calculated based on the merged system operating states. The specific steps include:

[0071] Step 1: Establish the state-space model of the DC distribution system and solve the system operating state probabilities using a Markov process: First, establish the transition matrix A based on the transition relationship between the operating states of the DC distribution system. The elements of the matrix are as shown in equation (1):

[0072]

[0073] In the formula: i, j are system state numbers and i ≠ j, A ij A represents the off-diagonal elements of a matrix, numerically equal to the transition rate from state i to state j. ii The diagonal element of the matrix is ​​numerically equal to 1 minus the sum of the off-diagonal elements in that row, and n is the number of system running states;

[0074] According to Markov processes, when a system reaches steady-state operation, the state probability does not change with the change of the system's operating state, that is:

[0075] PA = P (2)

[0076] In the formula: P = [p1, p2, ..., p n ] represents the system state probability row vector, p n Let n be the probability that the system is in state n.

[0077] Equation (2) is further equivalent to:

[0078] P(AH)=0 (3)

[0079] In the formula: H is the identity matrix;

[0080] By transposing equation (3), the matrix algebraic equation is obtained as follows:

[0081]

[0082] Due to matrix (AH) T The diagonal elements can be represented by off-diagonal elements, therefore it is not a full-rank matrix, and additional constraints are needed to solve for the state probabilities; since the system will always be in some state at any given time, the algebraic sum of all state probabilities should be 1, i.e.:

[0083]

[0084] By combining equations (4) and (5), the system state probabilities can be obtained as follows:

[0085]

[0086] Step Two: Improving Traditional State Merging Conditions Based on a Difference Threshold to Expand the Application Scope of State Merging in DC Distribution Systems. Traditional state merging methods determine the system operating states to be merged based on the same state transition rate. However, in actual power system operation, application scenarios with identical transition rates are almost nonexistent. Nevertheless, in similar or identical scenarios, equipment failure rates and repair rates may be similar. Therefore, this invention proposes a state merging condition based on a difference threshold. Based on calculating the difference between the state transition rate and a reference value, system operating states whose absolute value is less than or equal to the difference threshold are determined as the states to be merged. The selection of the system states to be merged should meet the following conditions:

[0087] {S||λ ij -λ ref |≤δ tr ,i、j∈N} (7)

[0088] In the formula: S is the set of states to be merged, λ ij Let λ be the transition rate from state i to state j. If the system's operating state changes due to a component failure, the transition rate is the failure rate; if the system's operating state changes due to a component recovering its operation, the transition rate is the recovery rate. ref δ is the reference value for the transfer rate. tr Where N is the difference threshold, and N is the set of system operating states;

[0089] It is important to note that while the given state merging conditions mathematically achieve clustering of similar system operating states, to ensure the rationality of the reliability assessment, the system operating states to be merged are generally selected based on similar equipment. In practical engineering applications, merging the states of dissimilar equipment lacks rationality and interpretability.

[0090] Step 3: Solve for the transition rate between the merged state and the state to be transitioned. The transition rate of the merged state includes two forms: the transition rate between the merged state and the independent state, and the transition rate between the merged states.

[0091] ① Transitions between merged and independent states:

[0092] The transition rate λ between independent state i and merged state J iJ Solve using equation (8):

[0093]

[0094] In the formula: j represents an independent state within the merged state J;

[0095] The solution for the transition rate between merged state J and independent state i can be divided into two cases:

[0096] In the first case, when the state transition rate λ ji At the same time, the transfer rate λ Ji Solve using equation (9):

[0097]

[0098] In the second case, when the state transition rate λ ji At different times, the transfer rate λ Ji Solve using equation (10):

[0099]

[0100] In the formula: C is the cutoff coefficient and C = p j / p k p k This is a reference state, and any state to be merged can be selected.

[0101] ② Transitions between two merged states:

[0102] The solution for the transition rate from merged state I to merged state J is divided into two cases:

[0103] In the first case, when the state transition rate λ ij When they are the same, the merged state transition rate λ IJ Solve using equation (11):

[0104]

[0105] In the formula: i represents an independent state within the merged state I;

[0106] In the second case, when the state transition rate λ ij When they are not the same, the merged state transition rate λ IJ Solve using equation (12):

[0107]

[0108] The process of solving for the transition rate from merged state J to merged state I is similar to that of solving for the transition rate from merged state I to merged state J. To avoid redundancy, when the state transition rate λ... ji When they are the same or different, the merged state transition rate λ JI The solution formulas are given by equations (13) and (14) respectively:

[0109]

[0110]

[0111] Step 4: Solve for the truncation coefficient C. First, determine the truncation function C(t) that varies with time using the fault tree analysis method, as shown in equation (15):

[0112]

[0113] In the formula: p j (t), p k (t) represent the probabilities of the j-th and k-th operating states of the system occurring at time t, respectively, R c (t), R h (t) represents the reliability functions of the c-th and h-th components, respectively; m1 and m2 represent the number of devices operating normally in independent states j and k, respectively; and l represents the total number of system components.

[0114] Secondly, a Markov process is used to determine the time t for the cutoff function to reach steady state. p As shown in equation (16):

[0115]

[0116] In the formula: ε is an infinitesimal;

[0117] Finally, the steady-state time is substituted into the cutoff function to determine the cutoff coefficient, which is solved by equation (17):

[0118]

[0119] Step 5: Equivalent the power state of the merged system to a two-state system, where the two states are "operating" and "faulting". Before equivalence, the frequency and average outage time of the fault operation state need to be calculated as shown in equations (18) and (19). The equivalence process is shown in equations (20), (21), and (22).

[0120]

[0121]

[0122] In the formula: f iw represents the frequency of occurrence of faulty operating state i. i Let λ be the average power outage time for faulty operating state i. ji Let be the transition rate for leaving state j;

[0123]

[0124]

[0125]

[0126] In the formula: r eq The equivalent mean time to repair (MTBT) is expressed in hours per failure, f. eq The equivalent average failure frequency is expressed in times per year, λ. eq The equivalent failure rate is expressed in times per year, where F represents the number of faulty operating states.

[0127] After the equivalence is completed, the load reliability index can be calculated using the state enumeration method, and then the reliability index of the entire DC power distribution system can be calculated by combining the user information.

[0128] Figure 2 In the middle: a state-space model of a true bipolar DC power distribution system is established using a Markov process, where i1 to i16 represent system state numbers, and γ1 to γ4 and μ1 to μ4 represent the failure rate and repair rate of each DC power source, respectively.

[0129] Figure 3 and Figure 4 In the diagram: j1~j4 are the independent states contained in the merged state J, and i1~i4 are the independent states contained in the merged state I.

[0130] Figure 5 In this context, the system state probability function is a monotonic function with a fast convergence rate. When the state probability function p... i (t) and p i When the absolute value of the difference (t+Δt) first becomes less than ε (an infinitesimal quantity), the system is considered to have reached steady-state operation. At this time, the independent variable t is the steady-state time t. p Even if the failure rate and repair rate of the equipment are different, the time for the state probability function to reach steady state only fluctuates within a small range.

[0131] The scope of protection claimed by this invention is not limited to the specific embodiments described above. Moreover, for those skilled in the art, this invention can have various modifications and alterations. Any modifications, improvements, and equivalent substitutions made within the concept and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A reliability assessment method for a DC power distribution system based on state merging using a truncation coefficient, characterized in that: Specifically, the steps include the following: Step 1: Establish the state-space model of the DC distribution system and solve the system operating state probabilities using a Markov process: First, establish the transition matrix A based on the transition relationship between the operating states of the DC distribution system. The elements of the matrix are as shown in equation (1): (1) In the formula: i, j are system state numbers and i ≠ j, A ij A represents the off-diagonal elements of a matrix, numerically equal to the transition rate from state i to state j. ii The diagonal elements of the matrix are numerically equal to 1 minus the sum of the off-diagonal elements in the i-th row, and n is the number of system running states; According to Markov processes, when a system reaches steady-state operation, the state probability does not change with the change of the system's operating state, that is: (2) In the formula: P = [p1, p2, ..., p n ] represents the system state probability row vector, p n Let n be the probability that the system is in state n. Equation (2) is further equivalent to: (3) In the formula: H is the identity matrix; By transposing equation (3), the matrix algebraic equation is obtained as follows: (4) Due to matrix (AH) T The diagonal elements can be represented by off-diagonal elements, therefore it is not a full-rank matrix, and additional constraints are needed to solve for the state probabilities; since the system will always be in some state at any given time, the algebraic sum of all state probabilities should be 1, i.e.: (5) By combining equations (4) and (5), the system state probabilities can be obtained as follows: (6) Step Two: Improve the traditional state merging conditions based on the difference threshold, and expand the application scope of state merging in DC distribution systems. Based on the calculation of the difference between the state transition rate and the reference value, determine the system operating states whose absolute value of the difference is less than or equal to the difference threshold as the states to be merged. The selection of the system states to be merged should meet the following conditions: (7) In the formula: S is the set of states to be merged, λ ij Let be the transition rate from state i to state j. If the system's operating state changes due to a component failure, then the transition rate is the failure rate. If the system's operating state changes due to the recovery of a component, then the transfer rate is the repair rate, λ. ref δ is the reference value for the transfer rate. tr Where N is the difference threshold, and N is the set of system operating states; Step 3: Solve for the transition rates between the merged state and the state to be transitioned, including two forms: the transition rate between the merged state and the independent state, and the transition rate between merged states. ① Transitions between merged and independent states: The transition rate λ between independent state i and merged state J iJ Solve using equation (8): (8) In the formula: j represents an independent state within the merged state J; The solution for the transition rate between merged state J and independent state i can be divided into two cases: In the first case, when the state transition rate λ ji At the same time, the transfer rate λ Ji Solve using equation (9): (9) In the second case, when the state transition rate λ ji At different times, the transfer rate λ Ji Solve using equation (10): (10) In the formula: C is the cutoff coefficient and C=p j / p k p k This is a reference state, and any state to be merged can be selected. ② Transitions between two merged states: The solution for the transition rate from merged state I to merged state J is divided into two cases: In the first case, when the state transition rate λ ij When they are the same, the merged state transition rate λ IJ Solve using equation (11): (11) In the formula: i represents an independent state within the merged state I; In the second case, when the state transition rate λ ij When they are not the same, the merged state transition rate λ IJ Solve using equation (12): (12) The process of solving for the transition rate from merged state J to merged state I is similar to that of solving for the transition rate from merged state I to merged state J. To avoid redundancy, when the state transition rate λ... ji When they are the same or different, the merged state transition rate λ JI The solution formulas are given by equations (13) and (14) respectively: (13) (14) Step 4: Solve for the truncation coefficient C. First, determine the truncation function C(t) that varies with time using the fault tree analysis method, as shown in equation (15): (15) In the formula: p j (t), p k (t) represent the probabilities of the j-th and k-th operating states of the system occurring at time t, respectively, R c (t), R h (t) represents the reliability functions of the c-th and h-th components, respectively; m1 and m2 represent the number of devices operating normally in independent states j and k, respectively; and l represents the total number of system components. Secondly, a Markov process is used to determine the time t for the cutoff function to reach steady state. p As shown in equation (16): (16) In the formula: ε is an infinitesimal; Finally, the steady-state time is substituted into the cutoff function to determine the cutoff coefficient, which is solved by equation (17): (17) Step 5: Equivalent the power state of the merged system to a two-state system, where the two states are "operating" and "faulting". Before equivalence, the frequency and average power outage time of the faulting operation state need to be calculated as shown in Equations (18) and (19). The equivalence process is shown in Equations (20), (21), and (22). (18) (19) In the formula: f i w represents the frequency of occurrence of faulty operating state i. i Let λ be the average power outage time for faulty operating state i. ji Let be the transition rate for leaving state j; (20) (21) (22) In the formula: r eq The equivalent mean time to repair (MTBT) is expressed in hours per failure, f. eq The equivalent average failure frequency is expressed in times per year, λ. eq The equivalent failure rate is expressed in times per year, where F represents the number of faulty operating states. After the equivalence is completed, the load reliability index can be calculated using the state enumeration method, and then the reliability index of the entire DC power distribution system can be calculated by combining the user information.

2. The reliability assessment method for a DC power distribution system based on state merging using a truncation coefficient as described in claim 1, characterized in that: The state merging conditions in step two are based on selecting the system operating states to be merged from similar devices.

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