A bas algorithm power distribution network reconfiguration method according to metropolis criterion

Abstract

The application relates to a BAS algorithm power distribution network reconstruction method according to the Metropolis criterion. Considering uncertain factors in the power distribution network, an opportunity constraint reconstruction model is constructed based on probability statistics. A decimal coding mode based on a network loop is adopted to reduce the algorithm search space and reduce the generation of infeasible solutions. In the reconstruction process, network radiation is judged according to an adjacency list storage method. In view of the problems that a single-target reconstruction algorithm is generally low in optimization efficiency and easy to locally converge, a simple and fast BAS algorithm is introduced, the Metropolis criterion in the SA algorithm is added to the BAS algorithm to jump out of local optimization, and the step attenuation mode of the BAS algorithm is improved to make the optimization more flexible. The improved BAS algorithm is higher in optimization efficiency.

Description

Technical Field

[0001] This invention relates to a distribution network reconfiguration method based on the BAS algorithm according to the Metropolis criterion. Background Technology

[0002] During normal operation of a distribution network, the switching status of network line switches is changed to optimize the network's operational structure, thereby altering the power flow distribution and achieving effects such as reducing network losses and improving power quality. Static reconfiguration involves switching the network based on the state of the distribution network at a specific time point.

[0003] Solving the distribution network reconfiguration model relies on the support of intelligent algorithms. The Beetle Beard (BAS) algorithm, with its advantages of low computational cost and fast convergence speed, has been applied to mathematical optimization problems such as distributed generation location and capacity determination, microgrid economic dispatch, indoor positioning, and portfolio optimization. However, there are a large number of switches on the distribution network lines, resulting in many combination schemes. Distribution network reconfiguration is also a complex combinatorial optimization problem in mathematics, requiring a reconfiguration algorithm with higher optimization efficiency. Therefore, the BAS algorithm is introduced. Summary of the Invention

[0004] The purpose of this invention is to provide a distribution network reconfiguration method based on the Metropolis criterion using the BAS algorithm. This invention improves the basic BAS algorithm for solving single-objective static reconfiguration problems, resulting in a more efficient optimization method.

[0005] To achieve the above objectives, the technical solution of this invention is: a distribution network reconfiguration method based on the Metropolis criterion using the BAS algorithm. This method is applied to distribution network reconfiguration, where the location of the longhorn beetle represents the distribution network switch combination scheme, the longhorn beetle search target represents the reconfiguration objective function, and the odor concentrations that the longhorn beetle must receive to its left and right represent the objective function values. The method includes the following steps:

[0006] 1) Initialize the beetle's position x and initial step size δ 0 Step size decay coefficient c1 = 0.95, constant c2 for the relationship between search distance and step size, number of iterations N, number of cooling cycles L;

[0007] 2) Calculate the objective function value f(x) of the initial beetle position x, that is, the objective function value under the initial distribution network switch combination scheme. Store x in xbest and f(x) in fbest as the currently searched optimal scheme.

[0008] 3) Step size control temperature T=δ t ;

[0009] 4) According to d t =δ t / c2 updates the search distance, where t is the number of iterations;

[0010] 5) Calculate the left and right antennae coordinates of the longhorn beetle using the following two formulas;

[0011]

[0012]

[0013] In the formula, x r x l These are the coordinates of the beetle's left and right antennae, respectively; x is the coordinate between the left and right antennae; b is the beetle's search direction, as detailed below:

[0014]

[0015] In the formula, k is the dimension of the solution space; rnd(·) is a random function, and the direction from the right whisker to the left whisker is taken as the search direction of the longhorn beetle;

[0016] 6) Update the position x′ of the longhorn beetle according to the following formula, which is the new switch combination scheme for the distribution network:

[0017]

[0018] In the formula, f(x) l ) and f(x r ) represents the odor concentration received by the left and right antennae of the longhorn beetle, that is, the objective function value corresponding to the coordinates of the left and right antennae; sign(·) is the sign function;

[0019] 7) Calculate the objective function value f(x′) of the longhorn beetle at position x′;

[0020] 8) According to the following formula:

[0021]

[0022] When f(x′) = f(x) t ) <f(x t-1 When p = 1, update the beetle's position, i.e., x = x'. When f(x') = f(x t )≥f(x t-1 If the calculated P is greater than the set random number rand, the position of the longhorn beetle will be updated; otherwise, it will not be updated.

[0023] 9) According to δ t =c1δ t-1 Update the inner loop beetle step size;

[0024] 10) Determine if the maximum number of cooling cycles L has been reached. If yes, proceed to the next step; otherwise, return to step 4.

[0025] 11) Update the outer loop step size δ according to the following formula;

[0026]

[0027] 12) Determine if the maximum number of iterations N has been reached. If yes, output the optimal solution; otherwise, return to step 3.

[0028] In one embodiment of the present invention, the distribution network reconfiguration model includes an objective function and constraints. Considering the uncertainties of DG output, EV charging load and system load, the deterministic objective function value is transformed into an expected value, and the deterministic constraints are transformed into opportunistic constraints.

[0029] In one embodiment of the present invention, the expected active power loss is taken as the optimization objective:

[0030]

[0031] In the formula, E represents the expected value; n is the total number of branches in the distribution network; P i,loss P is the random variable representing the active power loss of branch i; i Q i U represents the active and reactive power at the end of the i-th branch; i The voltage amplitude of branch i is a random variable; s i This indicates the state of the i-th branch switch, where 1 represents closed and 0 represents open; r i It is the resistance of the i-th branch.

[0032] In one embodiment of the present invention, the desired load balancing is taken as the optimization objective.

[0033]

[0034] In the formula, E represents the expected value; N b It is the number of closed branches; S i S is the apparent power random variable of branch i; imax This is the maximum allowable power for the corresponding branch.

[0035] In one embodiment of the present invention, the desired node voltage deviation is taken as the optimization objective.

[0036]

[0037] In the formula, E represents the desired value; nd is the total number of nodes in the distribution network; U j U is a random variable representing the voltage amplitude at node j; r That is the rated voltage.

[0038] In one embodiment of the present invention, the constraints are as follows:

[0039] (1) Current constraints

[0040]

[0041] In the formula, P i,k and Q i,k It represents the active and reactive power injected into node i during the k-th power flow calculation; V i,k and V j,k G represents the voltage magnitudes at nodes i and j in the k-th power flow calculation. ij and B ij These are the real and imaginary parts of the nodal admittance matrix; θ ij,k This is the phase angle difference between node i and node j in the k-th power flow calculation;

[0042] (2) Nodal voltage machine constraints

[0043] Pr(V imin ≤V i ≤V imax )≥β V

[0044] In the formula, Pr(·) represents the probability of the event occurring; V i It is a random variable of node voltage, V imax and V imin These are the upper and lower limits of the node voltage; β V It is a set probability;

[0045] (3) Branch power opportunity constraint

[0046] Pr(S j ≤S jmax )≥β S

[0047] In the formula, S j It is a random variable of branch power; S jmax This is the upper limit of branch power; β S It is a set probability;

[0048] (4) Topological constraints

[0049] The distribution network should maintain a radial structure after reconfiguration.

[0050] In one embodiment of the present invention, transforming the power distribution network reconfiguration problem into a mathematical optimization problem requires encoding the network switch states. A loop-based decimal encoding is adopted, with the encoding length being the number of basic loops when all network switches are closed, and the search range being the number of switches within each closed loop.

[0051] Compared with existing technologies, this invention has the following advantages: This invention considers uncertainties in the distribution network and constructs a chance-constrained reconstruction model based on probability statistics. It adopts a decimal encoding method based on network loops to reduce the algorithm's search space and decrease the generation of infeasible solutions. During reconstruction, the network radial shape is determined using the adjacency list storage method. Addressing the common problems of low optimization efficiency and easy local convergence in single-objective reconstruction algorithms, a simple and fast BAS algorithm is introduced. The Metropolis criterion from the SA algorithm is incorporated into the BAS algorithm to escape local optimization, and the improved step size decay method of the BAS algorithm makes optimization more flexible. This invention improves the BAS algorithm, resulting in higher optimization efficiency. Simulation analysis results show that the improved BAS algorithm has an average of only 7.4 iterations, 2.3 fewer than other algorithms, and only 222 power flow calculations, only 30% of other algorithms. The optimization success rate is as high as 98%, 4% higher than other algorithms. Attached Figure Description

[0052] Figure 1 It is an IEEE-33 node system.

[0053] Figure 2 The node structure is stored using the adjacency list method.

[0054] Figure 3 It is an undirected graph.

[0055] Figure 4 Store the undirected graph as an adjacency list.

[0056] Figure 5 To determine the flowchart of a radial network.

[0057] Figure 6 It is a 12-node network containing loops and islands.

[0058] Figure 7 The flowchart for the optimization process of the basic BAS algorithm.

[0059] Figure 8 Flowchart for improving the BAS algorithm optimization process. Detailed Implementation

[0060] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0061] During normal operation of a distribution network, the switching status of network line switches is changed to optimize the network's operational structure, thereby altering the power flow distribution and achieving effects such as reducing network losses and improving power quality. Static reconfiguration involves switching the network based on the state of the distribution network at a specific time point.

[0062] This invention improves the basic BAS algorithm for solving single-objective static reconstruction problems.

[0063] The distribution network reconfiguration model includes an objective function and constraints. Considering the uncertainties of DG output, EV charging load, and system load, the deterministic objective function value is transformed into the expected value, and the deterministic constraints are transformed into opportunity constraints.

[0064] (1) The optimization objective is to take the expected active power loss as the target:

[0065]

[0066] In the formula, E represents the expected value; n is the total number of branches in the distribution network; P i,loss P is the random variable representing the active power loss of branch i; i Q i U represents the active and reactive power at the end of the i-th branch; i The voltage amplitude of branch i is a random variable; s i This indicates the state of the i-th branch switch, where 1 represents closed and 0 represents open; r i It is the resistance of the i-th branch.

[0067] (2) Taking the expected load balance as the optimization objective

[0068]

[0069] In the formula, E represents the expected value; N b It is the number of closed branches; S i S is the apparent power random variable of branch i; imax This is the maximum allowable power for the corresponding branch.

[0070] (3) The optimization objective is to take the expected node voltage deviation.

[0071]

[0072] In the formula, E represents the desired value; nd is the total number of nodes in the distribution network; U j U is a random variable representing the voltage amplitude at node j; r That is the rated voltage.

[0073] The constraints are as follows:

[0074] (1) Current constraints

[0075]

[0076] In the formula, P i,k and Q i,k It represents the active and reactive power injected into node i during the k-th power flow calculation; V i,k and V j,k G represents the voltage magnitudes at nodes i and j in the k-th power flow calculation. ij and B ijThese are the real and imaginary parts of the nodal admittance matrix; θ ij,k This is the phase angle difference between node i and node j in the k-th power flow calculation;

[0077] (2) Nodal voltage machine constraints

[0078] Pr(V imin ≤V i ≤V imax )≥β V (5)

[0079] In the formula, Pr(·) represents the probability of the event occurring; V i It is a random variable of node voltage, V imax and V imin These are the upper and lower limits of the node voltage; β V It is a set probability;

[0080] (3) Branch power opportunity constraint

[0081] Pr(S j ≤S jmax )≥β S (6)

[0082] In the formula, S j It is a random variable of branch power; S jmax This is the upper limit of branch power; β S It is a set probability;

[0083] (4) Topological constraints

[0084] The distribution network should maintain a radial structure after reconfiguration.

[0085] Transforming the power distribution network reconfiguration problem into a mathematical optimization problem requires encoding the network switch states. Using binary encoding, the encoding length is equal to the total number of switches in the network branches. Due to this excessive length, the search space is extremely large. Despite various simplification measures, each reconfiguration operation requires the participation of all switches in the calculation, resulting in too many ineffective computations. This invention employs a loop-based decimal encoding, with the encoding length equal to the number of basic loops when all network switches are closed. The search range is the number of switches within each closed loop, significantly reducing the search space. Furthermore, because only one switch is disconnected in each loop, the generation of infeasible solutions is reduced.

[0086] by Figure 1 The IEEE-33 node system shown is an example.

[0087] Close all switches to form 5 basic loops (L1, L2, L3, L4, L5).

[0088] L1 = [S2,S3,S4,S5,S6,S7,S...] 18,S 19 ,S 20 ,S 33 ]

[0089] L2=[S9,S 10 ,S 11 ,S 12 ,S 13 ,S 14 ,S 34 ]

[0090] L3 = [S8,S9,S] 10 ,S 11 ,S 21 ,S 33 ,S 35 ]

[0091] L4 = [S6,S7,S8,S] 15 ,S 16 ,S 17 ,S 25 ,S 26 ,S 27 ,S 28 ,S 29 ,S 30 ,S 31 ,S 32 ,S 34 ,S 36 ]

[0092] L5 = [S3,S4,S5,S] 22 ,S 23 ,S 24 ,S 25 ,S 26 ,S 27 ,S 28 ,S 37 ]

[0093] It can be seen that switch S1, which is not in a loop, must be closed; otherwise, the network will become isolated, failing to satisfy the radial structure. The radial structure of the distribution network also requires that the number of disconnected switches equals the total number of tie switches, which is also the number of basic loops. Selecting one switch to disconnect from each loop, with an encoding length of 5, results in a search space of 10*7*7*16*11 = 86240, which is significantly larger than the search space of binary encoding. It has been greatly reduced.

[0094] The safe operation of a power distribution network requires maintaining a radial network structure; therefore, the network topology needs to be determined radially during the reconstruction process. This invention employs an adjacency list storage method with a time complexity of O(n) to determine the power distribution network structure based on node degree.

[0095] The adjacency list storage method combines arrays and linked lists to store the network structure. Vertices are stored using a one-dimensional array, and all adjacent vertices of each vertex form a linked list. Therefore, as shown below... Figure 2 The adjacency list shown has two parts: a vertex list and an edge list. Figure 2 (a) stores vertex data in the data field and points to the first edge field of the edge table. Figure 2 (b) The adjvex field stores the index of the adjacent point of the vertex, and the next field points to the next node in the edge list.

[0096] Suppose Figure 3 If the undirected graph shown is used as the description object, then the adjacency list storage method is used to store the undirected graph as follows: Figure 4 As shown.

[0097] The process of determining whether a network has a radial structure based on network topology data stored using the adjacency list method is as follows: Figure 5 As shown.

[0098] To illustrate how to determine network topology using the adjacency list storage method, let's assume... Figure 6 A 12-node network containing loops and islands is used as the description object. This network is stored using an adjacency list as shown in Table 1. For ease of explanation, the edge list directly stores the node number instead of the array index.

[0099] Table 1 Adjacency List Storage

[0100]

[0101] according to Figure 5 Following the process sequence and referring to Table 1, node 3 in the first column of the vertex table has no adjacent nodes and its degree is 0, indicating that this node is an isolated node. After removing this node, the analysis continues. The nodes with a degree of 1 in the first column of the vertex table are 1, 2, 5, 8, and 11, with their corresponding adjacent nodes being 4, 5, 2, 7, and 10 respectively. Among these adjacent nodes, nodes 2 and 5 have a degree of 1, indicating that nodes 2 and 5 form an isolated node. All data in the row containing the nodes with a degree of 1 in the first column of the vertex table are removed, and all nodes with a degree of 1 in the edge tables starting from the second column are also removed. Then, the search for nodes with a degree of 1 in the first column of the vertex table is continued, and the above operations are repeated. Finally, 5 nodes remain in the first column of the vertex table, and all of these nodes have a degree of 2, indicating that a cycle exists in the network.

[0102] Solving the distribution network reconfiguration model relies on the support of intelligent algorithms. This invention introduces and improves the BAS algorithm, which has advantages in solving single-objective reconfiguration problems.

[0103] BAS, a novel algorithm proposed in 2017, simulates the foraging behavior of longhorn beetles in nature. These beetles have two antennae; when searching for food, if the scent received by the left antennae is stronger, they fly to the left; if the scent received by the right antennae is stronger, they fly to the right, continuing this process to approach their target. Compared to common intelligent algorithms such as particle swarm optimization and genetic algorithms, BAS uses only one individual beetle, resulting in simpler parameters, less computation, and faster convergence. The algorithm's modeling process is as follows:

[0104] (1) Random search direction of the longhorn beetle

[0105]

[0106] In the formula, k is the dimension of the solution space; rnd(·) is a random function. Here, the direction from the right whisker to the left whisker is taken as the search direction of the longhorn beetle.

[0107] (2) The longhorn beetle needs to be positioned left and right.

[0108]

[0109]

[0110] In the formula, t is the number of iterations; x is the coordinate between the left and right antennae; and d is the distance between the left and right antennae of the longhorn beetle, which is also the search distance.

[0111] (3) Longhorn beetle location update

[0112]

[0113] In the formula, f(x) l ) and f(x r ) represents the odor concentration received by the left and right antennae of the longhorn beetle, i.e., the objective function value corresponding to the coordinates of the left and right antennae; sign(·) is the sign function; δ t The step size for the longhorn beetle optimization is used. To improve the convergence of the algorithm, this invention employs a variable step size.

[0114] (4) Step size and search distance update expressions

[0115] δ t =c1δ t-1 (11)

[0116] d t =c2d t-1 +d0 (12)

[0117] In the formula, c1 and c2 are the step size and search distance attenuation coefficients, which are generally taken as 0.95; d0 is a user-defined constant. This invention links the step size and search distance according to the following formula (13), and calculates the search distance through the step size, which is more convenient.

[0118] d t =δ t / c2 (13)

[0119] wherein c2 is a self-set constant.

[0120] When the algorithm is applied to distribution network reconfiguration, the position of the beetle corresponds to the distribution network switch combination scheme, the beetle search objective corresponds to the reconfiguration objective function, and the odor concentration received by the left and right antennae of the beetle corresponds to the objective function value. The optimization steps of the algorithm are as follows, and the flow chart is Figure 7 shown as follows.

[0121] 1) Initialize the beetle position x, initial step size δ 0 , step size attenuation coefficient c1, search distance attenuation coefficient c2, and number of iterations N.

[0122] 2) Calculate the objective function value f(x) of the initial position x, that is, the objective function value under the initial switch combination scheme, store x in xbest and f(x) in fbest, which are saved as the currently searched optimal scheme.

[0123] 3) Update the search distance according to formula (13).

[0124] 4) Calculate the coordinates of the current left and right antennae of the beetle according to formula (8) and formula (9).

[0125] 5) Pre-update the beetle position x′ according to formula (10), which corresponds to the new switch combination scheme of the distribution network, serving as a probe for the next optimization direction.

[0126] 6) Calculate the objective function value f(x′) of the beetle at position x′ at this time, that is, the objective function value under the new switch combination scheme.

[0127] 7) When f(x′)<fbest, on the premise that a smaller objective function value indicates better performance, it indicates that the current new switch combination scheme is better than all historically searched schemes, so the beetle position and the objective function value are updated and saved, that is, xbest=x′, fbest=f(x′), otherwise no update is performed.

[0128] 8) Update the beetle step size according to formula (11), so that the search range of the beetle is continuously reduced, and the search gradually becomes local optimization, which accelerates convergence.

[0129] 9) Determine whether the maximum number of iterations N is reached, if yes, output the optimal solution, otherwise return to step 3).

[0130] The BAS algorithm benefits from its fast convergence speed due to its optimization mechanism. However, since it only uses one beetle, it is prone to getting stuck in local optimization when dealing with complex problems and cannot find the true global optimum. This section addresses this shortcoming by introducing the Metropolis criterion from the Simulated Annealing (SA) algorithm into the beetle's optimization process. This allows the beetle to accept a less desirable solution with a certain probability, thus escaping local optimization. Furthermore, the step size variation method is improved, making the search process more flexible and the optimization effect better.

[0131] SA is a global optimization algorithm that simulates the solid annealing process. Based on the Metropolis criterion, it assumes that the energy at state i is E. i The energy of the next state j is E. j If E j <E i Then replace state i with state j, if E j >E i The probability that state j replaces state i is exp[(E i -E j ) / T], where T represents temperature, then the expression for probability p is shown in equation (14).

[0132]

[0133] When the Metropolis criterion is introduced into the beetle whisker search algorithm, the energy value E i The fitness value f(x) corresponding to the previous iteration of BAS t-1 Energy value E j The corresponding fitness value f(x) in the current iteration t If the probability p of the beetle algorithm accepting a poor solution during the optimization process is shown in equation (15), then the probability p is as shown in equation (15).

[0134]

[0135] In the formula, f(x) t ) indicates that the longhorn beetle is at its current position x. t The corresponding objective function value; f(x) t-1 The expression represents the objective function value corresponding to the position of the longhorn beetle in the previous iteration; T is the annealing temperature, which gradually decreases as the algorithm searches deeper. It can be seen that during the initial optimization phase, because T is relatively large, p is also relatively large, giving the algorithm a strong ability to escape local optima. However, in the later stages of optimization, as the temperature T decreases, p also decreases, weakening the algorithm's ability to escape local optima and potentially causing it to converge to a non-optimal solution. To address this issue, it is necessary to consider appropriately increasing the temperature when the algorithm gets stuck in local optimization, i.e., annealing to raise the temperature, so that the algorithm has a greater chance of escaping local extrema again.

[0136] The step size δ directly affects the convergence speed and accuracy of the BAS algorithm. In the basic BAS algorithm, the step size decreases continuously with a constant decay coefficient according to equation (11), transforming from a global search to a local search. Considering that a slow step size decay results in a strong global search capability, while a fast step size decay results in a fast convergence speed, it is necessary to consider making the step size decay faster when the optimization effect is good, thus accelerating convergence to the optimum, and increasing the step size and slowing down the step size decay rate when the optimization effect is poor, thereby improving the global search capability.

[0137] Based on the application of the Metropolis criterion and the requirements of tempering and temperature decay, the algorithm improvement direction needs to be that when the optimization effect is good, the step size decays quickly to accelerate convergence, and when the optimization effect is poor, both the step size and temperature need to be increased to escape local optimization. Therefore, the improved algorithm sets up two loops. In the inner loop, the beetle updates its position according to the Metropolis criterion, and has a certain chance to escape local extrema. After several cooling cycles, the searched solution is output to the outer loop for judgment. In the outer loop, the step size controls the temperature to decay in the same way, and the expression for the beetle step size δ decay changes from equation (11) of the basic BAS to equation (16), where t is the current iteration number and δ is the current iteration number. 0 It is the initial step size, f(x) t f(x) is the objective function value corresponding to the current position of the longhorn beetle found by the inner loop, and f(xbest) is the objective function value corresponding to the optimal position of the longhorn beetle stored by the outer loop. When the inner loop performs well in finding the optimal position, i.e., f(x) = 0, f(xbest) = 0. t When f(x) ≤ f(xbest), the step size decreases rapidly in an exponential decay manner, accelerating the convergence speed. t When f(xbest) > f(xbest), it may be trapped in a local optimization. In this case, the step size of the next iteration should be δ. 0 ×0.95 t The calculation shows that this double-loop approach, which allows the algorithm to escape local optimization twice, increases the likelihood of finding the global optimum. The variable step size decay method makes the optimization process more flexible.

[0138]

[0139] The improved BAS algorithm optimization steps are as follows, and the flowchart is shown below. Figure 8 As shown.

[0140] 1) Initialize the beetle's position x and initial step size δ 0 Step size decay coefficient c1 = 0.95, constant c2 for the relationship between search distance and step size, number of iterations N, number of cooling cycles L.

[0141] 2) Calculate the objective function value f(x) at the initial position x, and store x in xbest.

[0142] 3) Temperature is controlled by step size, T = δ;

[0143] 4) Update the search distance according to equation (13), d = δ / c2.

[0144] 5) Calculate the left and right coordinates according to equations (8) and (9).

[0145] 6) Update the position x′ of the longhorn beetle according to equation (10).

[0146] 7) Calculate the objective function value f(x′) of the longhorn beetle at position x′.

[0147] 8) According to equation (15), when f(x′) = f(x) t ) <f(x t-1 When p = 1, update the beetle's position, i.e., x = x'. When f(x') = f(x t )≥f(x t-1 If the calculated P is greater than the set random number rand, the position of the longhorn beetle will be updated; otherwise, it will not be updated.

[0148] 9) Update the inner loop beetle step size according to equation (11), δ t =0.95δ t-1 .

[0149] 10) Determine if the maximum number of cooling cycles L has been reached. If yes, proceed to the next step; otherwise, return to step 4.

[0150] 11) Update the outer loop step size δ according to equation (16).

[0151] 12) Determine if the maximum number of iterations N has been reached. If yes, output the optimal solution; otherwise, return to step 3.

[0152] This invention considers uncertainties in power distribution networks and constructs a chance-constrained reconfiguration model based on probability statistics. A decimal encoding method based on network loops is used to reduce the algorithm's search space and decrease the generation of infeasible solutions. During the reconfiguration process, the network radial state is determined using an adjacency list storage method. Addressing the common problems of low optimization efficiency and local convergence in single-objective reconfiguration algorithms, this invention introduces the simple and fast BAS algorithm for the first time. The Metropolis criterion from the SA algorithm is incorporated into the BAS algorithm to escape local optimization. The improved step size decay method of the BAS algorithm makes optimization more flexible. Simulation results show that the improved BAS algorithm has an average of only 7.4 iterations, 2.3 fewer than other algorithms, and only 222 power flow calculations, only 30% of other algorithms. The optimization success rate is as high as 98%, 4% higher than other algorithms.

[0153] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A distribution network reconfiguration method based on the BAS algorithm according to the Metropolis criterion, characterized in that, This method is applied to distribution network reconfiguration. The location of the longhorn beetle represents the distribution network switch combination scheme, the target of the longhorn beetle search represents the reconfiguration objective function, and the odor concentrations that the longhorn beetle must receive to its left and right represent the objective function values. It includes the following steps: 1) Initialize the beetle's position x and initial step size. Step size decay coefficient c1=0.95, constant c2 for the relationship between search distance and step size, maximum number of iterations N, number of cooling iterations L; 2) Calculate the objective function value of the initial beetle position x. That is, the objective function value x under the initial distribution network switch combination scheme is stored in... , deposit Save it as the best solution found so far; 3) Temperature control by step size ; 4) According to Update the search distance, where t is the number of iterations; 5) Calculate the left and right antennae coordinates of the longhorn beetle using the following two formulas; In the formula, , These are the coordinates of the beetle's left and right whiskers, respectively; b represents the beetle's search direction, as detailed below: In the formula, k is the dimension of the solution space; It is a random function; here, the direction from the right whisker to the left whisker is taken as the search direction of the longhorn beetle. 6) Pre-update the position of the longhorn beetle according to the following formula. That is, a new switch combination scheme for the power distribution network: In the formula, and This represents the odor concentration received by the left and right antennae of the longhorn beetle, i.e., the objective function value corresponding to the coordinates of the left and right antennae; It is a symbolic function; 7) Calculate the location of the longhorn beetle objective function value ; 8) According to the following formula: when = < When p=1, update the beetle's position, i.e., x= ,when = ≥ If the calculated P is greater than the set random number rand, the position of the longhorn beetle is updated; otherwise, it is not updated. 9) According to Update the inner loop beetle step size; 10) Determine if the maximum number of cooling cycles L has been reached. If yes, proceed to the next step; otherwise, return to step 4. 11) Update the outer loop step size according to the following formula ; 12) Determine if the maximum number of iterations N has been reached. If yes, output the optimal solution; otherwise, return to step 3.

2. The distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 1, characterized in that, The distribution network reconfiguration model includes an objective function and constraints. Considering the uncertainties of DG output, EV charging load, and system load, the deterministic objective function value is transformed into the expected value, and the deterministic constraints are transformed into opportunity constraints.

3. The distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 2, characterized in that, The optimization objective is to optimize the expected active power loss. In the formula, E represents the expected value; It is the total number of branches in the distribution network; It is the random variable of active power loss in branch i; , These are the active and reactive power at the end of the i-th branch; It is a random variable representing the voltage amplitude of branch i; This indicates the state of the i-th branch switch, where 1 represents closed and 0 represents open. It is the resistance of the i-th branch.

4. The distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 2, characterized in that, The optimization objective is to balance the expected load. In the formula, E represents the expected value; It is the number of closed branches; The apparent power of branch i is a random variable; This is the maximum allowable power for the corresponding branch.

5. A distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 2, characterized in that, The optimization objective is the expected node voltage deviation. In the formula, E represents the expected value; nd is the total number of nodes in the distribution network; The voltage amplitude at node j is a random variable. That is the rated voltage.

6. The distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 2, characterized in that, The constraints are as follows: (1) Current constraints In the formula, and The active and reactive power injected into node i during the k-th power flow calculation; and V j,k G represents the voltage magnitudes at nodes i and j in the k-th power flow calculation. ij and B ij These are the real and imaginary parts of the nodal admittance matrix; θ ij,k This is the phase angle difference between node i and node j in the k-th power flow calculation; (2) Nodal voltage machine constraints In the formula, Indicates the probability of an event occurring; It is a random variable of node voltage. and These are the upper and lower limits of the node voltage; It is a set probability; (3) Branch power opportunity constraints In the formula, S j It is a random variable of branch power; This is the upper limit of branch power; It is a set probability; (4) Topological constraints The distribution network should maintain a radial structure after reconfiguration.

7. The distribution network reconfiguration method based on the Metropolis criterion and BAS algorithm according to claim 1, characterized in that, Transforming the power distribution network reconfiguration problem into a mathematical optimization problem requires encoding the network switch states. A loop-based decimal encoding is used, with the encoding length being the number of basic loops when all network switches are closed, and the search range being the number of switches within each closed loop.

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