Single / three-phase reliability evaluation method for low-voltage active power distribution network

Abstract

The invention discloses a low-voltage active power distribution network single / three-phase reliability evaluation method, and aims to solve the problem that an existing evaluation method is difficult to adapt to low-voltage power distribution network single / three-phase fault characteristics, complex interconnection topology and a distributed power supply flexible recovery strategy. The method comprises the following steps: firstly, constructing a low-voltage multi-layer power supply topological matrix to represent physical connection among a distribution transformer, a three-phase / single-phase line and a single / three-phase load point, introducing a differential fault recovery influence quantization type, and establishing an explicit expression of a distributed power supply in-situ supply increase rate and a bus / line / phase interlinked supply transfer rate; furthermore, a distribution robust optimization model covering faults of a distribution transformer, a three-phase / N-phase line and a single-phase line is constructed, an optimal recovery strategy is solved by taking minimization of the total power failure time of a system in a worst scene as a target, a load point power failure time matrix is updated based on the optimal recovery strategy, and finally all fault scenes are aggregated through matrix operation, so that the power failure time of the system is recovered. And obtaining the reliability index of the low-voltage active power distribution system.

Description

Technical Field

[0001] This invention relates to the field of reliability assessment technology for low-voltage active distribution networks, and in particular to a method for single / three-phase reliability assessment of low-voltage active distribution networks. Background Technology

[0002] As the final link in the transmission of electrical energy, low-voltage distribution networks directly connect a massive number of end users, and their reliability is crucial to the safety and stability of users' production and daily life. Unlike medium-voltage distribution networks, which primarily handle three-phase balance faults and focus on section isolation and restoration, low-voltage distribution networks differ fundamentally in fault characteristics, network structure, and recovery mechanisms. Firstly, regarding fault characteristics, low-voltage networks commonly exhibit various types of faults, including single-phase grounding, three-phase faults, and neutral line faults, with significant phase-specific differences in their impact. For example, when a single-phase line fault occurs, according to safe operating procedures, the non-faulty phases of the same three-phase line can maintain short-term power supply under constraints such as voltage and load balance. This characteristic has a critical impact on the accurate calculation of load point outage time, a feature often simplified or ignored by traditional methods. Secondly, in terms of network structure, low-voltage distribution networks have diverse topologies. Besides the basic radial structure, they commonly feature interconnection of low-voltage busbars on the distribution transformer side, line-to-line interconnection between three-phase lines, and single-phase line interconnection via phase-changing switches. The fault isolation boundaries, power transfer paths, and operational logic differ under different interconnection structures, resulting in highly differentiated recovery strategies. In addition, with the high penetration of distributed power sources on the low-voltage side, their ability to operate in local islanding after a fault provides a new approach to load recovery, forming a complex recovery mode that coordinates "main grid recovery, distributed power source power supply increase, and interconnection power transfer".

[0003] Existing methods for assessing the reliability of distribution networks mainly include analytical and simulation methods. In recent years, analytical methods based on fault correlation matrices have attracted attention due to their high computational efficiency and ease of integration. These methods characterize the impact of component faults on load point outages through matrix operations, avoiding complex network topology searches. However, existing research and its matrix methods are mainly geared towards medium- and high-voltage distribution networks, making them difficult to apply to the aforementioned low-voltage active distribution networks with their distinct characteristics. Its limitations are mainly reflected in the following aspects: 1) Insufficient adaptability of fault models: Existing methods fail to accurately characterize the differentiated impact mechanisms of single-phase, three-phase, and N-phase faults, especially the short-term continuous power supply logic of non-faulty phases under single-phase faults is not quantitatively characterized; 2) Simplified modeling of recovery strategies: Usually, it is assumed that the network is completely radial or based on a simple global transfer strategy, which fails to effectively integrate and quantify the transfer capacity and operational constraints under bus interconnection, line-to-line interconnection, and phase interconnection topologies; 3) Insufficient source-load collaborative optimization under complex constraints: It fails to establish dynamic collaborative optimization of distributed power output and multi-level transfer strategies under the topological constraints of bus / line / phase interconnection, making it difficult to accurately assess the actual impact of source-load interaction on the reliability of load points.

[0004] Therefore, directly applying existing methods to evaluate low-voltage active distribution networks will lead to distorted reliability indices, failing to accurately reflect their true operational risks, and further hindering the quantitative analysis and optimization of collaborative recovery strategies for multiple types of faults, complex topologies, and distributed power sources. Developing a dedicated reliability assessment and optimization method for low-voltage active distribution networks that integrates single / three-phase differentiated fault models, multi-type interconnected topology recovery mechanisms, and post-fault dynamic recovery strategy optimization has significant theoretical importance and urgent engineering practical value. Summary of the Invention

[0005] This invention aims to provide a single / three-phase reliability assessment method for low-voltage active distribution networks, addressing the challenges of common distribution network reliability assessment methods being ill-suited to low-voltage single / three-phase network structures, fault types, and fault recovery strategies. Through a systematic modeling and solution process, it achieves reliability assessment of low-voltage active distribution networks. Specifically, it includes:

[0006] (1) Based on the connection relationship of distribution transformers, three-phase lines and single-phase lines, a low-voltage multi-layer power supply topology matrix is ​​constructed. A quantitative mechanism for fault types and local power supply / differentiated interconnection and transfer of distributed power sources is introduced to construct a quantitative model of the impact of differentiated faults.

[0007] (2) Based on the differential fault impact quantification model, construct the power outage time matrix of single / three-phase load point under distribution transformer fault, three-phase / N-phase line fault and single-phase line fault, so as to systematically characterize the fault impact of various component faults on load point;

[0008] (3) Construct a unified fault recovery model based on sub-Bruker optimization, with the goal of minimizing the total system outage time under the worst scenario, optimize the recovery strategy after the fault, and update the load point outage time matrix based on the optimal recovery strategy;

[0009] (4) By performing matrix aggregation calculations on all fault scenarios and the load point outage time matrix updated based on the optimal recovery strategy, the reliability index of the low-voltage active power distribution system is obtained.

[0010] The specific process of step (1) is as follows:

[0011] 1) The differentiated fault impact quantification model described in this application specifically includes: constructing a low-voltage multi-layer power supply topology matrix to characterize the physical connection relationship between distribution transformers, three-phase lines, single-phase lines and load points; defining component failure rates to quantify the probability of fault occurrence of distribution transformers, three-phase lines, single-phase lines and N-phase lines; and establishing explicit quantification models of power supply increase rate and power transfer rate to express the local power supply increase capability of distributed power sources, as well as the power transfer capability under the condition of bus / line / phase interconnection.

[0012] 2) Further, to obtain the low-voltage multi-layer power supply topology matrix, the specific steps include: constructing the connection matrix T from the distribution transformer to the three-phase line. Nb×N3p Its element t ij This indicates the connection relationship between the i-th distribution transformer and the j-th three-phase line. When the connection is made, t... ij =1, otherwise 0, where i = 1, ..., N b j = 1, ..., N 3p N b N represents the total number of distribution transformers. 3p Given the total number of three-phase lines; construct the connection matrix L from three-phase lines to single-phase lines. N3p×N1p Its element l jk This indicates the connection relationship between the j-th three-phase line and the k-th single-phase line. When connected, l jk =1, otherwise 0, where k = 1, ..., N 1p N 1p Given the total number of single-phase lines; construct the connection matrix D from the single-phase lines to the load point. N1p×Nd Its element d kd This represents the connection relationship between the k-th single-phase line and the d-th load point. When the connection is made, d... kd =1, otherwise 0, where d = 1, ..., N d N d The total number of load points is represented by the matrix T, which can be applied to both single-phase and three-phase mixed loads. Based on the matrices T and L, a power supply topology matrix T between the distribution transformer and the load points is constructed through matrix operations. DNb×Nd T D =[T·L] T Its element t id This represents the power supply path relationship between the i-th distribution transformer and the d-th load point, when t id =1 indicates that the upstream element of the power supply path to load point d includes distribution transformer i; otherwise, it is 0, i = 1, 2, ..., N b Further construct the power supply topology matrix L of the three-phase lines and load points. D N3p×Nd L D =[L·D] T Its element l jd This represents the power supply path relationship between the j-th three-phase line and the d-th load point. jd =1 indicates that the upstream element of the power supply path to load point d contains three-phase line j; otherwise, it is 0, j = 1, 2, ..., N 3p .

[0013] 3) Further, construct component failure rate vectors, specifically including: distribution transformers, three-phase lines, single-phase lines, and N-phase line components. The distribution transformer failure rate vector is λ. T =[λ T,1, λ T,2,…,λ T,Nb ] T , λ T,i Let λ represent the failure rate of the i-th distribution transformer; the failure rate vector of the three-phase line is: λ 3p =[λ 3p,1, λ 3p,2,…, λ 3p,N3p ] T , λ 3p,j Let represent the failure rate of the j-th three-phase line; the failure rate vectors for the N-phase lines are respectively: λ N =[λ N,1, λ N,2,…, λ N,N3p ] T , λ N,n Let λ represent the failure rate of the nth N-phase line; the failure rate vector for a single-phase line is: λ 1p =[λ 1p,1, λ 1p,2,…, λ 1p,N1p ] T , λ 1p,k This represents the failure rate of the k-th single-phase line.

[0014] 4) Further, calculate the local power supply increase rate of distributed generation, specifically including: defining the total load vector L of the distribution transformer. T =[L T,1 ,L T,2 ,…,L T,Nb ] T Its element L T,i Let L represent the load of the i-th distribution transformer. i The unit is kW; define the distributed power supply access topology capacity vector S. PV =[S PV,1 ,S PV,2 ,…,S PV,Nb ] T Its element S PV,i This indicates that a distributed power source is connected to the i-th distribution transformer with an installed capacity of S. PV,i The unit is kW; the vector of distributed generation local power increase rate is defined as P. DG =[P DG,1 ,P DG,2 ,…,P DG,Nb ] T The value P represents the ratio of the actual output of the distributed power source connected to the distribution transformer node to the total load demand in its power supply area during the fault repair period. DG,i ∈[0,1], its value is determined by the matching of the source load of the distribution transformer.

[0015]

[0016] In the formula, η PVis the output coefficient vector of the distributed power source; ⊙ represents the element-wise multiplication of corresponding positions between vectors.

[0017] 5) Further, define the transfer rates for bus interconnection, line-to-line interconnection, and inter-connection, specifically including:

[0018] (a) Further, define the capacity matrix S of the low-voltage side bus interconnection of the distribution transformer. TNb×Nb Its element S il This represents the interconnection capacity relationship between the i-th distribution transformer and the l-th distribution transformer, where i = 1, ..., N. b l = 1, ..., N b When S il When S > 0, it means that there is a busbar interconnection between the i-th distribution transformer and the l-th distribution transformer, and S il This represents the interconnection capacity in kW; otherwise, it is 0, indicating no bus interconnection. The bus interconnection transfer rate matrix is ​​further defined as P. TRNb×Nb The element P represents the ratio of the low-voltage side busbar interconnection's transferable supply capacity to the remaining load demand, after considering the local increase in supply from the distribution transformer (DG). TR,i ∈[0,1], when the remaining load is 0, the max function is used to avoid the denominator being zero and to ensure that the model is solvable.

[0019]

[0020] In the formula, ε is an infinite decimal greater than 0.

[0021] (b) Further, define the three-phase line interconnection capacity matrix S. 3PN3p×N3p Its element S jm This represents the interconnection capacity relationship between the j-th and m-th three-phase lines, where j = 1, ..., N. 3p m=1,…,N 3p When S jm When S > 0, it means there is a line-to-line interconnection between the j-th and m-th three-phase lines, and S jm The interconnection capacity is expressed in kW; otherwise, it is 0, representing a wireless interconnection. The total load vector L of the three-phase lines is defined. 3p =[L 3p,1 ,L 3p,2 ,…,L 3p,N3p ] T Its element L 3p,j Let L represent the load of the j-th three-phase line. 3p,j The unit is kW; define the three-phase line interconnection and power transfer matrix P. 3P N3p×N3p The element P represents the ability to transfer power to three-phase line loads through three-phase interconnection. 3P,j ∈[0,1].

[0022]

[0023] (c) Further, define the phase-to-phase capacity matrix S of a single-phase line. 1P Its element S kh This represents the connection capacity relationship between the k-th and h-th single-phase lines, where k = 1, ..., N. 1p h = 1, ..., N 1p When S kh When S > 0, it means that there is a mutual connection between the k-th and h-th single-phase lines, and S kh The interconnection capacity is given in kW; otherwise, it is 0, indicating no phase interconnection. The total load vector L for a single-phase line is defined. 1p =[L 1p,1 ,L 1p,2 ,…,L 1p,N1p ] T Its element L 1p,k Let L represent the load of the k-th single-phase line. 1p,k The unit is kW; further define the interconnected power supply matrix P. 1PN1p×N1p The element P represents the ability to transfer power to single-phase loads via phase-switching switches or single-phase line interconnections. 1P,k ∈[0,1].

[0024]

[0025] The specific process of step (2) is as follows:

[0026] 1) Based on the differentiated fault impact quantification model, construct the power outage time matrix of single / three-phase load points under distribution transformer faults, three-phase / N-phase line faults, and single-phase line faults. Specifically, it includes the power outage time matrix of single / three-phase load points under distribution transformer faults, three-phase / N-phase line faults, and single-phase line faults.

[0027] (a) Further, define the load point outage time matrix T under distribution transformer fault. ANb×Nd Its element T A,id This represents the power outage time at the d-th load point after the i-th distribution transformer fails. When a distribution transformer fails, the power outage time at the load point that can be locally supplied via distributed generation is the isolation time t. g The power outage time at the load point that can be supplied via busbar interconnection is the transfer time t. s The power outage time at load points that cannot be transferred or have additional power supplied is the repair time t. r Based on this logic, the outage time matrix T of single / three-phase load points under transformer faults is derived. A .

[0028] T A =t g ·(T D ⊙PDG ·1 1×Nd )

[0029] +t s ·(T D ⊙P TR ·1 Nb×Nd )

[0030] +t r ·(T D ⊙(1 Nd×1 -P DG )⊙(1 Nb×Nd -P TR ))

[0031] In the formula, t g For the quarantine period, t s For the time of transfer, t r This refers to the repair time.

[0032] 2) Further, define the load point outage time matrix T under three-phase / N-phase faults. BN3p×Nd Its element T B,jd This represents the power outage time at the d-th load point after a fault in the j-th three-phase / N-phase line. When a three-phase / N-phase line fault occurs, because the distributed power source connected to the low-voltage line side does not have the capability to support the voltage and frequency after the fault, local power supplementation is not possible. The power outage time at the load point that can be further transferred via line-to-line interconnection is denoted as the transfer time t. s The power outage time at load points that cannot be directly supplied by the line is the repair time t. r Based on this logic, the outage time matrix T of a single / three-phase load point under a three-phase / N-phase fault is derived. B .

[0033] T B =t s ·(L D ⊙P 3P ·1 N3p×Nd )+t r ·(L D ⊙(1 N3p×Nd -P 3p ·1 N3p×Nd ))

[0034] 3) Further, define the load point power outage time matrix T under single-phase fault. CN1p×Nd Its element T C,kd This represents the power outage time at the d-th load point after a single-phase line fault (k-th phase). When a single-phase line fault occurs, and there are no phase interconnections, the power outage time for the faulty phase is the repair time t. r If the other non-faulty phases in the same three-phase line meet the operating requirements, they can remain operational for 2 hours, and their power outage time is t.r -2h; When there are interconnected devices, the power outage time for loads that can be transferred is the transfer time, and the time for repairing loads that cannot be interconnected is the repair time. Based on this logic, the power outage time matrix T for single / three-phase load points under single-phase line faults is derived. C .

[0035] T C =t s ·(D⊙P 1p ·1 N1p×Nd )+(t r -2)·(D⊙M normal )

[0036] +t r ·[D⊙(1 N1p×Nd -P 1p ·1 N1p×Nd )⊙(1 N3p×Nd -M normal )]

[0037] In the formula, M normal An indicator matrix that provides short-term power supply to non-faulty phases.

[0038] The specific process of step (3) is as follows:

[0039] 1) Furthermore, the fault recovery process is divided into three stages: fault isolation period t1, power transfer recovery period t2, repair period t3, and decision-making stage.

[0040] 2) Further, define decision variables, including: distributed power generation output allocation vector. Its elements This represents the actual output ratio of distributed power sources on the i-th distribution transformer during time period t, with a value range of [0,1]; Bus interconnection switch action matrix: Its elements This indicates whether the bus tie interconnection switch between the i-th and l-th distribution transformers is closed during time period t; 1 indicates closed, 0 indicates open; Line-to-line interconnection switch action matrix: Its elements This indicates whether the line-to-line interconnection switch between the j-th and m-th three-phase lines is closed during time period t, with 1 indicating closed and 0 indicating open; the phase interconnection switch action matrix is ​​as follows: Its elements This indicates whether the phase-to-phase interconnection switch between the k-th and h-th single-phase lines is closed during time period t; 1 indicates closed, 0 indicates open; Load switching state vector: Its elements This indicates whether load point d is powered during time period t, with 1 indicating power supply and 0 indicating power outage; it is also a vector summing up the power outage time at the load point. Its elements This represents the cumulative power outage time at load point d up to time period t.

[0041] 3) Furthermore, a fuzzy set considering the uncertainties of distributed power output and load demand is constructed, and the source-load uncertainty vector set is defined:

[0042]

[0043] In the formula, This is the vector of actual output coefficients of distributed power sources; These are the actual load demand vectors for distribution transformers, three-phase lines, and single-phase lines, respectively.

[0044] Constructing fuzzy sets based on moment information

[0045]

[0046] In the formula, μ is the mean vector of the uncertain vector; Σ is the upper bound of the covariance, which is obtained through historical operating data; It represents the set of all possible probability distributions.

[0047] 4) Furthermore, taking minimizing the total system outage time under the worst-case scenario as the objective function, a sub-Bruker optimization model is established, with the objective function expression as follows:

[0048]

[0049] In the formula, This indicates three decision-making stages; Represented as a set of load points; w d The weight of load point d is set according to the load importance level; Let be the decision variable, representing the cumulative power outage time at load point d during the cutoff period t.

[0050] 5) Furthermore, in the optimization model, the matrices and parameters involved in each capacity constraint and topology constraint, specifically the constraint conditions include:

[0051] a) Power outage time recursion constraint:

[0052]

[0053] In the formula, △t t Let Δt1 be the duration of time interval t. g , △t2=t s , △t3=t r .

[0054] b) Constraints on the relationship between power supply status and decision variables:

[0055]

[0056] In the formula, M fault,d This is an indicator variable for the impact of a fault on load d; it is 1 when affected and 0 otherwise.

[0057] c) Busbar / Line / Phase Interconnection Capacity Constraints

[0058]

[0059] d) Switching action and topology consistency constraints:

[0060]

[0061] e) Radial operational constraints:

[0062]

[0063] 6) Furthermore, the column and constraint generation algorithm is used to solve the partial bar optimization model containing the constraints, thereby obtaining the optimal recovery strategy, i.e., the optimal set of decision variables.

[0064] 7) Further, traverse all faulty components and update the load point outage time matrix based on the optimal decision variables, as follows:

[0065]

[0066] 8) Further, the column and constraint generation algorithm includes the following steps:

[0067] (a) Initialization: Set the iteration number k = 0, the upper bound UB = +∞, the lower bound LB = -∞, and the error α;

[0068] (b) Solve the main problem: Given a set of worst-case scenarios, find the optimal recovery strategy.

[0069]

[0070] Outage time recursion constraints, power supply status and decision variable relationship constraints, bus / line / phase interconnection capacity constraints, switch action and topology consistency constraints, and radial operation constraints are applied to each scenario ξ. (s) Established,

[0071] In the formula: θ is an auxiliary variable.

[0072] Obtain the current solution and the objective value obj, and update the next LB = obj;

[0073] (c) Solve the subproblems. Given the solution to the main problem, find the probability distribution that maximizes the expected loss.

[0074]

[0075] Transformed through semidefinite programming duality:

[0076]

[0077] In the formula, y and Z are dual variables, y is a vector, and Z is a positive semi-definite matrix.

[0078] Get the worst-case scenario ξ (k+1) Given the target value sub_obj, update the upper bound UB = min(UB, sub_obj).

[0079] (d) When UB-LB≤α, the algorithm terminates; otherwise, the worst-case scenario is added to the main problem, k=k+1, and the algorithm returns to step (b).

[0080] The specific process of step (4) is as follows:

[0081] 1) The reliability index of the low-voltage active power distribution system is obtained through matrix aggregation operations. The reliability index of the low-voltage active power distribution system is realized by the following expression:

[0082] (a) Calculate the average system outage time (SAIDI)

[0083]

[0084] In the formula, N d,cust Let d be the number of users at load point d.

[0085] (b) Calculate the average power outage frequency of the system (SAIFI)

[0086]

[0087] In the formula, (·) ,d This represents the total frequency affected by component failure at load point d, taken from the d-th column of the matrix.

[0088] The advantages and positive effects of this invention are:

[0089] This invention first constructs a low-voltage multi-layer power supply topology matrix to characterize the physical connections between distribution transformers, three-phase / single-phase lines, and single / three-phase load points. It then introduces differentiated fault recovery impact quantification types and establishes explicit expressions for the local power supply increase rate of distributed generation and the bus / line / phase interconnection transfer rate. Furthermore, it constructs a distributed bar optimization model covering faults in distribution transformers, three-phase / N-phase lines, and single-phase lines. With the objective of minimizing the total system outage time under the worst-case scenario, it solves for the optimal recovery strategy and updates the load point outage time matrix based on this optimal recovery strategy. Finally, it aggregates all fault scenarios through matrix operations to obtain the reliability index of the low-voltage active power distribution system.

[0090] This invention can effectively address the assessment challenges brought about by the diverse fault types, complex topological interconnections, and uncertainties of source and load in low-voltage distribution networks. While ensuring assessment accuracy, it improves assessment calculation efficiency, thereby significantly enhancing the practicality and efficiency of reliability assessment and operation optimization of large-scale low-voltage active distribution networks. Attached Figure Description

[0091] Appendix Figure 1 This is a flowchart illustrating the single / three-phase reliability assessment method for low-voltage active distribution networks provided by the present invention.

[0092] Appendix Figure 2 This is a schematic diagram of a low-voltage active distribution network topology provided by the present invention, including distribution transformers, three-phase lines, single-phase lines, load points and distributed power sources. The diagram also illustrates bus interconnection, line-to-line interconnection and phase-to-phase interconnection lines, which are used to illustrate the low-voltage diversified interconnection structure involved in the present invention. Detailed Implementation

[0093] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that these drawings are designed for illustrative purposes only and are not intended to limit the scope of the present invention. Furthermore, these drawings are only intended to conceptually illustrate the processes and illustrations described herein and are not necessarily drawn to scale.

[0094] The implementation process of the low-voltage active distribution network single / three-phase reliability assessment method described in this invention can be achieved by those skilled in the art based on the following description and in conjunction with specific power grid data.

[0095] Step 1: Based on the connection relationships of distribution transformers, three-phase lines, and single-phase lines, construct a low-voltage multi-layer power supply topology matrix. Introduce a quantitative mechanism for fault types and local power supply enhancement / differentiated interconnection and transfer of power from distributed sources, and construct a quantitative model for the impact of differentiated faults. Specifically, this includes:

[0096] (1) Determine the system scale and construct the low-voltage connection matrix: Construct the connection matrix T from the distribution transformer to the three-phase line. Nb×N3p Three-phase line to single-phase line connection matrix L N3p×N1p Single-phase line to load point connection matrix D N1p×Nd Specifically, this includes: constructing the connection matrix T from the distribution transformer to the three-phase line. Nb×N3p Its element t ij This indicates the connection relationship between the i-th distribution transformer and the j-th three-phase line. When the connection is made, t... ij =1, otherwise 0, where i = 1, ..., N b j = 1, ..., N 3p N b N represents the total number of distribution transformers. 3pGiven the total number of three-phase lines; construct the connection matrix L from three-phase lines to single-phase lines. N3p×N1p Its element l jk This indicates the connection relationship between the j-th three-phase line and the k-th single-phase line. When connected, l jk =1, otherwise 0, where k = 1, ..., N 1p N 1p Given the total number of single-phase lines; construct the connection matrix D from the single-phase lines to the load point. N1p×Nd Its element d kd This represents the connection relationship between the k-th single-phase line and the d-th load point. When the connection is made, d... kd =1, otherwise 0, where d = 1, ..., N d N d This represents the total number of load points, which can be applied to single-phase and three-phase mixed loads.

[0097] (2) Derive the power supply topology matrix: Obtain the power supply topology matrix T between the distribution transformer and the load point. DNb×Nd Power supply topology matrix L of three-phase lines and load points DN3p×Nd Specifically, based on the matrices T and L, a power supply topology matrix T between the distribution transformer and the load point is constructed through matrix operations. DNb×Nd T D =[T·L] T Its element t id This represents the power supply path relationship between the i-th distribution transformer and the d-th load point, when t id =1 indicates that the upstream element of the power supply path to load point d includes distribution transformer i; otherwise, it is 0, i = 1, 2, ..., N b Further construct the power supply topology matrix L of the three-phase lines and load points. DN3p×Nd L D =[L·D] T Its element l jd This represents the power supply path relationship between the j-th three-phase line and the d-th load point. jd =1 indicates that the upstream element of the power supply path to load point d contains three-phase line j; otherwise, it is 0, j = 1, 2, ..., N 3p .

[0098] (3) Input component reliability parameters: Input transformer failure rate vector is λ T =[λ T,1, λ T,2 ,…,λ T,Nb ] T The fault rate vector of a three-phase line is: λ 3p =[λ 3p,1, λ 3p,2 ,…,λ 3p,N3p ] TThe fault rate vectors of the input N-phase lines are respectively: λ N =[λ N,1, λ N,2 ,…,λ N,N3p ] T The fault rate vector of the input single-phase line is: λ 1p =[λ 1p,1, λ 1p,2 ,…,λ 1p,N1p ] T Specifically, these include: distribution transformers, three-phase lines, single-phase lines, and N-phase line components. The failure rate vector for distribution transformers is λ. T =[λ T,1 ,λ T,2 ,…,λ T,Nb ] T , λ T,i Let λ represent the failure rate of the i-th distribution transformer; the failure rate vector of the three-phase line is: λ 3p =[λ 3p,1 ,λ 3p,2 ,…,λ 3p,N3p ] T , λ 3p,j Let represent the failure rate of the j-th three-phase line; the failure rate vectors for the N-phase lines are respectively: λ N =[λ N,1, λ N,2 ,…,λ N,N3p ] T , λ N,n Let λ represent the failure rate of the nth N-phase line; the failure rate vector for a single-phase line is: λ 1p =[λ 1p,1, λ 1p,2 ,…,λ 1p,N1p ] T , λ 1p,k This represents the failure rate of the k-th single-phase line.

[0099] (4) Input load, distributed generation and interconnection capacity parameters: Input static transformer total load vector L T =[L T,1 ,L T,2 ,…,L T,Nb ] T Distributed power supply access topology capacity vector S PV =[S PV,1 ,S PV,2 ,…,S PV,Nb ] T , Transformer low-voltage side bus interconnection capacity matrix S TNb×Nb Three-phase line interconnection capacity matrix S 3PN3p×N3p Single-phase line phase-to-phase capacity matrix S 1P， Its element L T,iLet L represent the load of the i-th distribution transformer. i The unit is kW, and its element is S. PV,i This indicates that a distributed power source is connected to the i-th distribution transformer with an installed capacity of S. PV,i The unit is kW;

[0100] (5) Without considering source load uncertainty, calculate the static power increase rate and various interconnection and transfer rates, specifically including: calculating the distributed power generation local power increase rate matrix P. DG The bus interconnection transfer rate matrix is ​​P. TR Three-phase line interconnection power transfer matrix P 3P Interconnected supply matrix P 1P .

[0101] Calculating the local boost rate of distributed generation specifically includes: defining the local boost rate vector of distributed generation as P. DG =[P DG,1 ,P DG,2 ,…,P DG,Nb ] T The value P represents the ratio of the actual output of the distributed power source connected to the distribution transformer node to the total load demand in its power supply area during the fault repair period. DG,i ∈[0,1], its value is determined by the matching of the source load of the distribution transformer.

[0102]

[0103] In the formula, η PV is the output coefficient vector of the distributed power source; ⊙ represents the element-wise multiplication of corresponding positions between vectors.

[0104] Define the transfer rate for bus interconnection, line interconnection, and phase interconnection, specifically including:

[0105] Define the capacity matrix S of the low-voltage side bus interconnection of the distribution transformer. TNb×Nb Its element S il This represents the interconnection capacity relationship between the i-th distribution transformer and the l-th distribution transformer, where i = 1, ..., N. b l = 1, ..., N b When S il When S > 0, it means that there is a busbar interconnection between the i-th distribution transformer and the l-th distribution transformer, and S il This represents the interconnection capacity in kW; otherwise, it is 0, indicating no bus interconnection. The bus interconnection transfer rate matrix is ​​further defined as P. TRNb×Nb The element P represents the ratio of the low-voltage side busbar interconnection's transferable supply capacity to the remaining load demand, after considering the local increase in supply from the distribution transformer (DG). TR,i ∈[0,1], when the remaining load is 0, the max function is used to avoid the denominator being zero and to ensure that the model is solvable.

[0106]

[0107] In the formula, ε is an infinite decimal greater than 0.

[0108] Furthermore, define the three-phase line interconnection capacity matrix S. 3PN3p×N3p Its element S jm This represents the interconnection capacity relationship between the j-th and m-th three-phase lines, where j = 1, ..., N. 3p m=1,…,N 3p When S jm When S > 0, it means there is a line-to-line interconnection between the j-th and m-th three-phase lines, and S jm The interconnection capacity is expressed in kW; otherwise, it is 0, representing a wireless interconnection. The total load vector L of the three-phase lines is defined. 3p =[L 3p,1 ,L 3p,2 ,…,L 3p,N3p ] T Its element L 3p,j Let L represent the load of the j-th three-phase line. 3p,j The unit is kW; define the three-phase line interconnection and power transfer matrix P. 3P N3p×N3p The element P represents the ability to transfer power to three-phase line loads through three-phase interconnection. 3P,j ∈[0,1].

[0109]

[0110] Furthermore, define the phase-to-phase capacity matrix S of a single-phase line. 1P Its element S kh This represents the connection capacity relationship between the k-th and h-th single-phase lines, where k = 1, ..., N. 1p h = 1, ..., N 1p When S kh When S > 0, it means that there is a mutual connection between the k-th and h-th single-phase lines, and S kh The interconnection capacity is given in kW; otherwise, it is 0, indicating no phase interconnection. The total load vector L for a single-phase line is defined. 1p =[L 1p,1 ,L 1p,2 ,…,L 1p,N1p ] T Its element L 1p,k Let L represent the load of the k-th single-phase line. 1p,k The unit is kW; further define the interconnected power supply matrix P. 1PN1p×N1p The element P represents the ability to transfer power to single-phase loads via phase-switching switches or single-phase line interconnections. 1P,k ∈[0,1].

[0111]

[0112] Step 2: Based on the differentiated fault impact quantification model, construct the power outage time matrix for single / three-phase load points under distribution transformer faults, three-phase / N-phase line faults, and single-phase line faults. This matrix is ​​used to systematically characterize the fault impact of various component faults on load points. Specifically, this includes:

[0113] Based on the distribution transformer fault recovery logic and P DG and P TR Calculate the initial matrix T of the load point power outage time under distribution transformer fault. A Nb×Nd Based on the three-phase line fault recovery logic and P 3P Calculate the initial matrix T of the load point power outage time under a three-phase line fault. BN3p×Nd According to the single-phase line fault recovery logic, P 1P and M normal Calculate the initial matrix T of the load point power outage time under a single-phase line fault. CN1p×Nd Based on the differentiated fault impact quantification model, a power outage time matrix for single / three-phase load points under distribution transformer faults, three-phase / N-phase line faults, and single-phase line faults is constructed. Specifically, it includes the power outage time matrix for single / three-phase load points under distribution transformer faults, three-phase / N-phase line faults, and single-phase line faults.

[0114] 1) Define the load point power outage time matrix T under distribution transformer fault. ANb×Nd Its element T A,id This represents the power outage time at the d-th load point after the i-th distribution transformer fails. When a distribution transformer fails, the power outage time at the load point that can be locally supplied via distributed generation is the isolation time t. g The power outage time at the load point that can be supplied via busbar interconnection is the transfer time t. s The power outage time at load points that cannot be transferred or have additional power supplied is the repair time t. r Based on this logic, the outage time matrix T of single / three-phase load points under transformer faults is derived. A .

[0115] T A =t g ·(T D ⊙P DG ·1 1×Nd )

[0116] +t s ·(T D ⊙P TR ·1 Nb×Nd )

[0117] +t r ·(T D ⊙(1 Nd×1-P DG )⊙(1 Nb×Nd -P TR ))

[0118] In the formula, t g For the quarantine period, t s For the time of transfer, t r This refers to the repair time.

[0119] 2) Define the load point power outage time matrix T under three-phase / N-phase faults. BN3p×Nd Its element T B,jd This represents the power outage time at the d-th load point after a fault in the j-th three-phase / N-phase line. When a three-phase / N-phase line fault occurs, because the distributed power source connected to the low-voltage line side does not have the capability to support the voltage and frequency after the fault, local power supplementation is not possible. The power outage time at the load point that can be further transferred via line-to-line interconnection is denoted as the transfer time t. s The power outage time at load points that cannot be directly supplied by the line is the repair time t. r Based on this logic, the outage time matrix T of a single / three-phase load point under a three-phase / N-phase fault is derived. B .

[0120] T B =t s ·(L D ⊙P 3P ·1 N3p×Nd )+t r ·(L D ⊙(1 N3p×Nd -P 3p ·1 N3p×Nd ))

[0121] 3) Define the load point power outage time matrix T under single-phase fault. CN1p×Nd Its element T C,kd This represents the power outage time at the d-th load point after a single-phase line fault (k-th phase). When a single-phase line fault occurs, and there are no phase interconnections, the power outage time for the faulty phase is the repair time t. r If the other non-faulty phases in the same three-phase line meet the operating requirements, they can remain operational for 2 hours, and their power outage time is t. r -2h; When there are interconnected devices, the power outage time for loads that can be transferred is the transfer time, and the time for repairing loads that cannot be interconnected is the repair time. Based on this logic, the power outage time matrix T for single / three-phase load points under single-phase line faults is derived. C .

[0122] T C =t s ·(D⊙P 1p ·1 N1p×Nd )+(t r-2)·(D⊙M normal )

[0123] +t r ·[D⊙(1 N1p×Nd -P 1p ·1 N1p×Nd )⊙(1 N3p×Nd -M normal )]

[0124] In the formula, M normal An indicator matrix that provides short-term power supply to non-faulty phases.

[0125] Step 3: Construct a unified fault recovery model based on distributed bar optimization. With the objective of minimizing the total system outage time under the worst-case scenario, optimize the recovery strategy after a fault and update the load point outage time matrix based on the optimal recovery strategy. Specifically, this includes:

[0126] (1) Set the fault isolation time t g Transfer operation time t s Repair time t r Divide the decision-making stages.

[0127] (2) Considering the uncertainty of the source load, define the decision variables, including: the distributed power generation output allocation vector. Its elements This represents the actual output ratio of distributed power sources on the i-th distribution transformer during time period t, with a value range of [0,1]; Bus interconnection switch action matrix: Its elements This indicates whether the bus tie interconnection switch between the i-th and l-th distribution transformers is closed during time period t; 1 indicates closed, 0 indicates open; Line-to-line interconnection switch action matrix: Its elements This indicates whether the line-to-line interconnection switch between the j-th and m-th three-phase lines is closed during time period t, with 1 indicating closed and 0 indicating open; the phase interconnection switch action matrix is ​​as follows: Its elements This indicates whether the phase-to-phase interconnection switch between the k-th and h-th single-phase lines is closed during time period t; 1 indicates closed, 0 indicates open; Load switching state vector: Its elements This indicates whether load point d is powered during time period t, with 1 indicating power supply and 0 indicating power outage; it is also a vector summing up the power outage time at the load point. Its elements This represents the cumulative power outage time at load point d up to time period t. A source-load fuzzy set is constructed, considering the uncertainties in distributed power generation output and load demand. The source-load uncertainty vector set is defined as follows:

[0128]

[0129] In the formula, This is the vector of actual output coefficients of distributed power sources; Given the actual load demand vectors for distribution transformers, three-phase lines, and single-phase lines, a fuzzy set based on moment information is constructed.

[0130]

[0131] In the formula, μ is the mean vector of the uncertain vector; Σ is the upper bound of the covariance, which is obtained through historical operating data; It represents the set of all possible probability distributions.

[0132] A partial Bruker optimization model is established with the objective function of minimizing the total system outage time under the worst-case scenario. The objective function expression is as follows:

[0133]

[0134] In the formula, This indicates three decision-making stages; Represented as a set of load points; w d The weight of load point d is set according to the load importance level; Let be the decision variable, representing the cumulative power outage time at load point d during the cutoff period t.

[0135] In the optimization model, the matrices and parameters involved in each capacity constraint and topology constraint, and the specific constraint conditions include:

[0136] a) Power outage time recursion constraint:

[0137]

[0138] In the formula, △t t Let Δt1 be the duration of time interval t. g , △t2=t s , △t3=t r .

[0139] b) Constraints on the relationship between power supply status and decision variables:

[0140]

[0141] In the formula, M fault,d This is an indicator variable for the impact of a fault on load d; it is 1 when affected and 0 otherwise.

[0142] c) Busbar / Line / Phase Interconnection Capacity Constraints

[0143]

[0144] d) Switching action and topology consistency constraints:

[0145]

[0146] e) Radial operational constraints:

[0147]

[0148] (3) The column and constraint generation algorithm is used to solve the sub-Bruker optimization model to obtain the optimal set of recovery strategies.

[0149] (4) Traverse all faulty components and update the corresponding load point outage time matrix based on the optimal strategy. Specifically as follows:

[0150]

[0151] The column and constraint generation algorithm includes the following steps:

[0152] (a) Initialization: Set the iteration number k = 0, the upper bound UB = +∞, the lower bound LB = -∞, and the error α;

[0153] (b) Solve the main problem: Given a set of worst-case scenarios, find the optimal recovery strategy.

[0154]

[0155] Outage time recursion constraints, power supply status and decision variable relationship constraints, bus / line / phase interconnection capacity constraints, switch action and topology consistency constraints, and radial operation constraints are applied to each scenario ξ. (s) Established,

[0156] In the formula: θ is an auxiliary variable.

[0157] Obtain the current solution and the objective value obj, and update the next LB = obj;

[0158] (c) Solve the subproblems. Given the solution to the main problem, find the probability distribution that maximizes the expected loss.

[0159]

[0160] Transformed through semidefinite programming duality:

[0161]

[0162] In the formula, y and Z are dual variables, y is a vector, and Z is a positive semi-definite matrix.

[0163] Get the worst-case scenario ξ (k+1) Given the target value sub_obj, update the upper bound UB = min(UB, sub_obj).

[0164] (d) When UB-LB≤α, the algorithm terminates; otherwise, the worst-case scenario is added to the main problem, k=k+1, and the algorithm returns to step (b).

[0165] Step 4: By performing matrix aggregation calculations on all fault scenarios and the updated load point outage time matrix based on the optimal recovery strategy, the reliability index of the low-voltage active power distribution system is obtained. Specifically, this includes:

[0166] (1) Updated By aggregating the corresponding failure rate vectors column by column, the total outage time vector for each load point is obtained.

[0167] (2) Calculate the system average outage time SAIDI and the system average outage frequency SAIFI according to the formula. (a) Calculate the system average outage time SAIDI

[0168]

[0169] In the formula, N d,cust Let d be the number of users at load point d.

[0170] (b) Calculate the average power outage frequency of the system (SAIFI)

[0171]

[0172] In the formula, (·) ,d This represents the total frequency affected by component failure at load point d, taken from the d-th column of the matrix.

[0173] (3) Output system indicators such as SAIDI and SAIFI, as well as indicators of each load point. These results can be used to assess the current reliability of the power grid, compare planning schemes, identify weak links, and provide quantitative decision support for distribution automation configuration, optimized access of distributed power sources, and grid structure planning.

[0174] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments and should not be considered as limiting the scope of the invention. They also include technical solutions composed of any combination of the above technical features. All equivalent changes and improvements made within the scope of this invention should fall within the patent coverage of this invention. This embodiment is beneficial for providing guidance on single / three-phase reliability assessment of low-voltage active distribution networks. The above descriptions are merely embodiments of this invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for assessing the reliability of single / three-phase low-voltage active distribution networks, characterized in that, The method includes the following steps: (1) Based on the connection relationship of distribution transformers, three-phase lines and single-phase lines, a low-voltage multi-layer power supply topology matrix is ​​constructed. A quantitative mechanism for fault types and local power supply / differentiated interconnection and transfer of distributed power sources is introduced to construct a quantitative model of the impact of differentiated faults. (2) Based on the differential fault impact quantification model, construct the power outage time matrix of single / three-phase load point under distribution transformer fault, three-phase / N-phase line fault and single-phase line fault, so as to systematically characterize the fault impact of various component faults on load point; (3) Construct a unified fault recovery model based on sub-Bruker optimization, with the goal of minimizing the total system outage time under the worst scenario, optimize the recovery strategy after the fault, and update the load point outage time matrix based on the optimal recovery strategy; (4) By performing matrix aggregation calculations on all fault scenarios and the load point outage time matrix updated based on the optimal recovery strategy, the reliability index of the low-voltage active power distribution system is obtained.

2. The method for assessing the single / three-phase reliability of a low-voltage active distribution network according to claim 1, characterized in that, The differential fault impact quantification model described in step (1) is as follows: a low-voltage multi-layer power supply topology matrix is ​​constructed to characterize the physical connection relationship between distribution transformers, three-phase lines, single-phase lines and load points; then, the component failure rate is defined to quantify the probability of fault occurrence of distribution transformers, three-phase lines, single-phase lines and N-phase lines; finally, an explicit quantification model of the power supply increase rate and the power transfer rate is established to express the local power supply increase capability of distributed power sources, as well as the power transfer capability under the condition of bus / line / phase interconnection.

3. The method for assessing the single / three-phase reliability of a low-voltage active distribution network according to claim 2, characterized in that, The low-voltage multi-layer power supply topology matrix is ​​specifically as follows: Constructing the connection matrix T from the distribution transformer to the three-phase line. Nb×N3p Its element t ij This indicates the connection relationship between the i-th distribution transformer and the j-th three-phase line. When the connection is made, t... ij =1, otherwise 0, where i = 1, ..., N b j = 1, ..., N 3p N b N represents the total number of distribution transformers. 3p Given the total number of three-phase lines; construct the connection matrix L from three-phase lines to single-phase lines. N3p×N1p Its element l jk This indicates the connection relationship between the j-th three-phase line and the k-th single-phase line. When connected, l jk =1, otherwise 0, where k = 1, ..., N 1p N 1p Given the total number of single-phase lines; construct the connection matrix D from the single-phase lines to the load point. N1p×Nd Its element d kd This represents the connection relationship between the k-th single-phase line and the d-th load point. When the connection is made, d... kd =1, otherwise 0, where d = 1, ..., N d N d The total number of load points is given, and these load points are applicable to mixed single-phase and three-phase loads. Based on the aforementioned matrices T and L, the power supply topology matrix T between the distribution transformer and the load points is constructed through matrix operations. DNb×Nd T D =[T·L] T Its element t id This represents the power supply path relationship between the i-th distribution transformer and the d-th load point, when t id =1 indicates that the upstream element of the power supply path to load point d includes distribution transformer i; otherwise, it is 0, i = 1, 2, ..., N b Further derive the power supply topology matrix L of the three-phase line and the load point. DN3p×Nd L D =[L·D] T Its element l jd This represents the power supply path relationship between the j-th three-phase line and the d-th load point. jd =1 indicates that the upstream element of the power supply path to load point d contains three-phase line j; otherwise, it is 0, j = 1, 2, ..., N 3p .

4. The method for assessing the single / three-phase reliability of a low-voltage active distribution network according to claim 2, characterized in that, The component failure rates include those for distribution transformers, three-phase lines, single-phase lines, and N-phase lines, with the distribution transformer failure rate vector being λ. T ＝ [λ T,1, λ T,2,…, λ T,Nb ] T , λ T,i Let λ represent the failure rate of the i-th distribution transformer; the failure rate vector of the three-phase line is: λ 3p ＝ [λ 3p,1, λ 3p,2,…, λ 3p,N3p ] T , λ 3p,j Let represent the failure rate of the j-th three-phase line; the failure rate vectors for the N-phase lines are respectively: λ N ＝ [λ N,1, λ N,2,…, λ N,N3p ] T , λ N,n Let λ represent the failure rate of the nth N-phase line; the failure rate vector for a single-phase line is: λ 1p ＝ [λ 1p,1, λ 1p,2,…, λ 1p,N1p ] T , λ 1p,k This represents the failure rate of the k-th single-phase line.

5. The method for assessing the single / three-phase reliability of a low-voltage active distribution network according to claim 2, characterized in that, The explicit quantification model of the supply increase rate is quantified in the following way: defining the total load vector L of the distribution transformer. T ＝ [L T,1 ,L T,2 ,…,L T,Nb ] T Its element L T,i Let L represent the load of the i-th distribution transformer. i The unit is kW; define the distributed power supply access topology capacity vector S. PV ＝ [S PV,1 ,S PV,2 ,…,S PV,Nb ] T Its element S PV,i This indicates that a distributed power source is connected to the i-th distribution transformer with an installed capacity of S. PV,i The unit is kW; the vector of distributed generation local power increase rate is defined as P. DG =[P DG,1 ,P DG,2 ,…,P DG,Nb ] T The value P represents the ratio of the actual output of the distributed power source connected to the distribution transformer node to the total load demand in its power supply area during the fault repair period. DG,i ∈[0,1], its value is determined by the matching of the source load of the distribution transformer: In the formula, η PV is the output coefficient vector of the distributed power source; ⊙ represents the element-wise multiplication of corresponding positions in the vector; The explicit quantification model for the transfer rate includes the quantification of the following three types of interconnection transfer capabilities: (1) Define the capacity matrix S of the low-voltage side bus interconnection of the distribution transformer. TNb×Nb Its element S il This represents the interconnection capacity relationship between the i-th distribution transformer and the l-th distribution transformer, where i = 1, ..., N. b l = 1, ..., N b When S il When S > 0, it means that there is a busbar interconnection between the i-th distribution transformer and the l-th distribution transformer, and S il The busbar interconnection capacity is expressed in kW; otherwise, it is 0, indicating no busbar interconnection. The busbar interconnection transfer rate matrix is ​​further defined as P. TRNb×Nb The element P represents the ratio of the low-voltage side busbar interconnection's transferable supply capacity to the remaining load demand, after considering the local increase in supply from the distribution transformer (DG). TR,i ∈[0,1], when the residual load is 0, the max function is used to avoid the denominator being zero and to ensure that the model is solvable. In the formula, ε is an infinite decimal greater than 0; (2) Define the capacity matrix S for interconnection of three-phase lines. 3PN3p×N3p Its element S jm This represents the interconnection capacity relationship between the j-th and m-th three-phase lines, where j = 1, ..., N. 3p m=1,…,N 3p When S jm When S > 0, it means there is a line-to-line interconnection between the j-th and m-th three-phase lines, and S jm The interconnection capacity is expressed in kW; otherwise, it is 0, representing a wireless interconnection. The total load vector L of the three-phase lines is defined. 3p ＝ [L 3p,1 ,L 3p,2 ,…,L 3p,N3p ] T Its element L 3p,j Let L represent the load of the j-th three-phase line. 3p,j The unit is kW; define the three-phase line interconnection and power transfer matrix P. 3PN3p×N3p The element P represents the ability to transfer power to three-phase line loads through three-phase interconnection. 3P,j ∈[0,1]: (3) Define the phase-to-phase capacity matrix S of a single-phase line. 1P Its element S kh This represents the connection capacity relationship between the k-th and h-th single-phase lines, where k = 1, ..., N. 1p h = 1, ..., N 1p When S kh When S > 0, it means that there is a mutual connection between the k-th and h-th single-phase lines, and S kh The interconnection capacity is given in kW; otherwise, it is 0, indicating no phase interconnection. The total load vector L for a single-phase line is defined. 1p ＝ [L 1p,1 ,L 1p,2 ,…,L 1p,N1p ] T Its element L 1p,k Let L represent the load of the k-th single-phase line. 1p,k The unit is kW; further define the interconnected power supply matrix P. 1PN1p×N1p The element P represents the ability to transfer power to single-phase loads via phase-switching switches or single-phase line interconnections. 1P,k ∈[0,1]:

6. The method for assessing the single / three-phase reliability of a low-voltage active distribution network according to claim 1, characterized in that, The single / three-phase load point power outage time matrix mentioned in step (2) is as follows: ① Load point power outage time matrix T under distribution transformer fault ANb×Nd Its element T A,id The formula for calculating the power outage time at the d-th load point after the i-th transformer fails is as follows: T A =t g ·(T D ⊙P DG ·1 1×Nd ) +t s ·(T D ⊙P TR ·1 Nb×Nd ) +t r ·(T D ⊙(1 Nd×1 -P DG )⊙(1 Nb×Nd -P TR )) In the formula, t g For the quarantine period, t s For the time of transfer, t r For repair time; ② Define the load point power outage time matrix T under three-phase / N-phase faults BN3p×Nd Its element T B,jd The formula for calculating the power outage time at the d-th load point after a fault in the j-th three-phase / N-phase line is as follows: T B =t s ·(L D ⊙P 3P ·1 N3p×Nd )+t r ·(L D ⊙(1 N3p×Nd -P 3p ·1 N3p×Nd )) ③ Define the load point power outage time matrix T under single-phase fault. CN1p×Nd Its element T C,kd The formula for calculating the power outage time at the d-th load point after a fault in the k-th single-phase line is as follows: T C =t s ·(D⊙P 1p ·1 N1p×Nd )+(t r -2)·(D⊙M normal ) +t r ·[D⊙(1 N1p×Nd -P 1p ·1 N1p×Nd )⊙(1 N3p×Nd -M normal )] In the formula, M normal An indicator matrix for short-term power supply to non-faulty phases.

7. The method for assessing the reliability of single / three-phase low-voltage active distribution networks according to claim 1, characterized in that, The sub-Bruker optimization model described in step (3) specifically includes the following steps: ① Divide the fault recovery process into three stages: fault isolation period t1, power transfer and recovery period t2, repair period t3, and decision-making stage. ② Define decision variables, including: distributed power generation output allocation vector Its elements This represents the actual output ratio of distributed power sources on the i-th distribution transformer during time period t, with a value range of [0,1]; Bus interconnection switch action matrix: ∈{0,1} Nb×Nb Its elements This indicates whether the bus tie interconnection switch between the i-th and l-th distribution transformers is closed during time period t; 1 indicates closed, 0 indicates open; Line-to-line interconnection switch action matrix: Its elements This indicates whether the line-to-line interconnection switch between the j-th and m-th three-phase lines is closed during time period t, with 1 indicating closed and 0 indicating open; the phase interconnection switch action matrix is ​​as follows: Its elements This indicates whether the inter-phase switch between the k-th and h-th single-phase lines is closed during time period t; 1 indicates closed, 0 indicates open; Load switching state vector: Its elements This indicates whether load point d is powered during time period t, with 1 indicating power supply and 0 indicating power outage; it is also a vector summing up the power outage time at the load point. Its elements This represents the cumulative power outage time at load point d up to time period t. ③ Construct a fuzzy set considering the uncertainties of distributed power output and load demand, and define the source-load uncertainty vector set: In the formula, This is the vector of actual output coefficients of distributed power sources; These are the actual load demand vectors for distribution transformers, three-phase lines, and single-phase lines, respectively. Constructing fuzzy sets based on moment information: In the formula, μ is the mean vector of the uncertain vector; Σ is the upper bound of the covariance, which is obtained through historical operating data; Represents the set of all possible probability distributions; ④ Taking minimizing the total system outage time under the worst-case scenario as the objective function, a sub-Bruker optimization model is established, and its objective function expression is: In the formula, This indicates three decision-making stages; Represented as a set of load points; w d The weight of load point d is set according to the load importance level; Let be the decision variable, representing the cumulative power outage time at load point d during the cutoff period t; ⑤ In the optimization model, the matrices and parameters involved in each capacity constraint and topology constraint, and the specific constraint conditions include: a) Power outage time recursion constraint: In the formula, △t t Let Δt1 be the duration of time interval t. g , △t2=t s , △t3=t r ; b) Constraints on the relationship between power supply status and decision variables: In the formula, M fault,d This is an indicator variable for the impact of a fault on load d; it is 1 when affected and 0 otherwise. c) Busbar / Line / Phase Interconnection Capacity Constraints: d) Switching action and topology consistency constraints: e) Radial operational constraints: ⑥ Use the column and constraint generation algorithm to solve the partial Bruker optimization model with constraints to obtain the optimal recovery strategy, i.e., the optimal set of decision variables. The specific algorithm is as follows: Initialization: Set the iteration count k = 0, upper bound UB = +∞, lower bound LB = -∞, and error α; Solve the main problem: Given a set of worst-case scenarios, find the optimal recovery strategy. min θ Outage time recursion constraints, power supply status and decision variable relationship constraints, bus / line / phase interconnection capacity constraints, switch action and topology consistency constraints, and radial operation constraints are applied to each scenario ξ. (s) Established, In the formula: θ is an auxiliary variable. Obtain the current solution and the objective value obj, and update the next LB = obj; Solve the subproblems: Given a solution to the main problem, find the probability distribution that maximizes the expected loss. Transformed through semidefinite programming duality: Z＞0 In the formula, y and Z are dual variables, y is a vector, and Z is a positive semi-definite matrix. Get the worst-case scenario ξ (k+1) Given the target value sub_obj, update the upper bound UB = min(UB, sub_obj). When UB-LB≤α, the algorithm terminates; otherwise, the worst-case scenario is added to the main problem, k=k+1, and the algorithm returns to step - solving the main problem. Iterate through all faulty components and update the load point outage time matrix based on the optimal decision variables, as follows:

8. The method for assessing the reliability of single / three-phase low-voltage active distribution networks according to claim 1, characterized in that, The reliability index of the low-voltage active power distribution system obtained through matrix aggregation operation in step (4) is specifically achieved through the following expression: ① Calculate the system's average outage time (SAIDI) In the formula, N d,cust Let d be the number of users at load point d. ② Calculate the average power outage frequency of the system (SAIFI) In the formula, (·) ,d This represents the total frequency affected by component failure at load point d, taken from the d-th column of the matrix.

9. A low-voltage active distribution network reliability assessment device for implementing the single / three-phase reliability assessment method for low-voltage active distribution networks according to any one of claims 1 to 8, characterized in that, The device includes: a low-voltage multilayer topology modeling module for constructing matrices T, L, D, T D L D The component fault modeling module is used to establish the fault rate λ for distribution transformers, three-phase, single-phase, and N-phase lines. T , λ 3P , λ 1P , λ N Interconnectivity and augmented computing modules are used to build S PV D T D 3p D 1P And calculate P DG P TR P 3P P 1P The power outage time assessment module is used to calculate the load point outage time T under different fault scenarios and recovery strategies. A T B T C The fault recovery optimization module is used to construct and solve the sub-Bruker optimization model and update the load point outage time matrix. The index aggregation module is used to output reliability indicators of low-voltage active power distribution systems based on matrix aggregation operations.

10. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the single / three-phase reliability assessment method for low-voltage active distribution networks as described in any one of claims 1 to 8.

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