Power distribution network double-layer multi-target dynamic reconstruction method considering radial constraint of loop opening method

Abstract

The invention discloses a double-layer multi-target dynamic reconstruction optimization method for an active power distribution network, and the innovative technical scheme comprises four core modules: firstly, building a network radial topology constraint model based on an unlinking method, and guaranteeing the basic safety of the operation of the power distribution network; secondly, constructing an equivalent daily load curve dynamic division model based on information entropy, and realizing time period division by quantifying load fluctuation characteristics; load period division, network operation security constraints and active management elements are comprehensively considered, and a double-layer multi-target reconstruction model with time sequence correlation characteristics is established; and finally, providing an improved multi-target electric eel foraging optimization algorithm (IMEEFO) on the basis of a Pareto frontier theory to respectively solve an upper layer model and a lower layer model. Through upper and lower layer nested iterative optimization, an optimal dynamic reconstruction strategy is generated, the operation cost is effectively reduced, the new energy consumption capability is improved, and meanwhile, the real-time operation requirement of the power distribution network is met.

Description

Technical Field

[0001] The present invention relates to an active distribution network reconstruction technology, and in particular to a distribution network double-layer multi-objective dynamic reconstruction method considering radial constraints of a ring decomposition method. Background Art

[0002] With the large-scale integration of renewable energy, dynamic reconfiguration of active distribution networks (ADNs) has become a key approach to improving system efficiency and facilitating renewable energy consumption. This approach alters the network topology by opening and closing section switches and tie switches within the distribution network, thereby changing the power flow distribution within the network to achieve goals such as reducing network losses and improving system reliability. Distribution networks typically operate in open-loop mode, so a mathematical model for radial constraints is necessary when considering reconfiguration. Radial constraint methods for distribution networks include spanning tree constraints, virtual power flow constraints, and radial constraints based on the de-looping method. The de-looping method offers a simpler form, ensuring the generation of an ideal radial topology while also introducing fewer intermediate variables and constraint equations, resulting in higher solution efficiency. Dynamic reconfiguration of distribution networks is particularly important due to the high proportion of distributed generation (DG) and the time-varying nature of loads. This requires coordinating multiple objectives, including switching behavior, voltage quality, and economic efficiency, across multiple timescales. The equivalent load curve period division method based on information entropy does not require the number of segments or comparison thresholds to be given in advance. It can fully consider the information volume of the equivalent daily load data and dynamically determine the optimal number of segments. It can reduce the number of reconstructions while retaining the information volume of the original data as much as possible.

[0003] Most current active distribution network reconfiguration methods focus on a single objective, such as minimizing network losses or maximizing renewable energy consumption, making them difficult to meet the multi-objective optimization needs of active distribution networks. Therefore, it is of great practical significance to develop a multi-objective dynamic reconfiguration method for active distribution networks based on radial constraints using a ring-breaking method and time-segmenting equivalent daily load curves based on information entropy. This method can comprehensively consider multiple objectives, such as the economic efficiency, reliability, and renewable energy consumption of the distribution network, to achieve optimal operation of the distribution network. Summary of the Invention

[0004] The purpose of the present invention is to solve the defects of the existing distribution network reconstruction technology and provide a distribution network double-layer multi-objective dynamic reconstruction method considering the radial constraints of the ring decomposition method.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] The present invention discloses a double-layer multi-objective dynamic reconstruction method for a distribution network considering radial constraints of a ring-breaking method, comprising the following steps:

[0007] S1: Mathematical modeling of radial constraints based on the ring-breaking method;

[0008] S2: Establish an equivalent daily load curve time division model based on information entropy;

[0009] S3: Considering the daily load curve time division, the safe and stable operation constraints of the distribution network and other active management element constraints, a two-layer multi-objective reconstruction model of the active distribution network is established;

[0010] S4: An improved multi-objective electric eel foraging optimization algorithm (IMEEFO) is designed based on Pareto theory. Logistic chaos mapping is introduced in the initial stage to perform chaos initialization on the population; the golden sine algorithm is introduced in the interactive behavior to optimize the search direction; dynamic reverse learning and Cauchy mutation are introduced in the development behavior to enhance the search and avoid local optimality. The improved multi-objective electric eel foraging optimization algorithm is used to solve the upper and lower multi-objective models, and the optimal strategy for dynamic reconstruction of the active distribution network is finally obtained through upper and lower layer cyclic iteration.

[0011] Specifically, the radial constraint modeling analysis based on the ring-breaking method in S1 is as follows:

[0012] The radial constraint of a distribution network can be described using the following two conditions: Condition 1: The number of closed branches in the network is N - Ns; Condition 2: The network is connected. Since Condition 2 is difficult to express analytically, it is replaced by two other conditions: Condition 3: All basic loops in the network must have a switch open. The switches opened in each basic loop are independent of each other, and the same switch cannot be opened simultaneously in multiple basic loops. Condition 4: There are no islands in the network. An island is a connected region that is not directly or indirectly connected to a substation node. The set of branches connecting an island to the main network is called the cut set corresponding to the island. It is easy to see that a network that satisfies Condition 3 necessarily satisfies Condition 1 and contains all feasible solutions. Since a connected network must not have islands, and a network without islands must be connected, Condition 4 is an equivalent condition to Condition 2. Therefore, the simultaneous satisfaction of Conditions 3 and 4 is a necessary and sufficient condition for a network to satisfy the radial constraint.

[0013] Specifically, the construction of the time period division model of the equivalent daily load curve based on information entropy in S2 includes the following steps:

[0014] Calculate the probability distribution of equivalent load in each time period:

[0015]

[0016] Where x i is the equivalent load of period i; Δt i is the duration of time period i in hours; k is the number of equivalent load curve segments; p kis the equivalent load probability in the kth period.

[0017] Calculate the information entropy of the equivalent daily load curve for different segments:

[0018]

[0019] Where X is a random variable; p(x i ) is the probability of x taking a value, and 0log20=0 is specified.

[0020] Determine the merging scheme that minimizes information entropy reduction: After dividing the time periods, randomly select two adjacent time periods for merging. Compare the information entropy of the different schemes and select the one that minimizes information entropy reduction. If two or more schemes have the same entropy reduction, select one of them. To minimize errors, the equivalent load after merging is the average of the loads of the two adjacent time periods.

[0021] Determination of the optimal number of segments and segment positions: Draw a perpendicular line L at any point on the excess entropy curve, where L is the line connecting the two points with segment numbers 1 and 23. The length of the perpendicular line is:

[0022] h k =23H k -H 24 (k-1) (3)

[0023] Where H k is the information entropy when the number of segments is k. Compare the vertical line h k and h k-1 The size of h k If is larger, then k is the optimal segmentation result.

[0024] In step S3, specific constraints include: DistFlow power flow constraints, node voltage and branch current constraints, PV output constraints, ESS operation constraints, SOP capacity and operation constraints, topology constraints, and switch operation times constraints.

[0025] In step S3, the dual-layer multi-objectives of the active distribution network include: minimizing network losses, minimizing voltage deviations, and minimizing the number of switching operations as upper-layer optimization objectives; and minimizing economic indicators and maximizing renewable energy absorption rates as lower-layer objectives.

[0026] Furthermore, in the upper-level planning objectives, the network loss is minimized 11 , voltage deviation minimized f 12 and the number of switching operations is minimized f 13 Three objective functions, the objective functions are as follows:

[0027] minF1=min(f 11 +f 12+f 13 ) (4)

[0028]

[0029]

[0030] Where N b is the set of all branches including the connecting line; C loss I is the network loss cost; ij,t is the current flowing through line ij at time t; R ij is the resistance value of line ij; m represents the node; n is the number of nodes; V m,i is the actual voltage value of node i at time t; V N is the node rated voltage; N s is the number of switches; S k (t) is the state of the kth switch at time t (0 for open, 1 for closed).

[0031] Specifically, the goal of the lower-level planning is to minimize the economic index and maximize the renewable energy consumption rate. Its objective function is as follows:

[0032] minF2=min(f 21 +(1-f 22 )) (8)

[0033]

[0034] C grid (t)=π grid (t)·P grid (t) (10)

[0035] C DG (t) = a·P DG (t) 2 +b·P DG (t)+c (11)

[0036] C ESS (t) = λ ESS ·|P ESS (t)| (12)

[0037] C SOP (t) = γ SOP ·P SOP (t) (13)

[0038]

[0039] Where C grid is the cost related to the main distribution network at time t; grid(t) is the unit price of electricity purchased from the main grid at time t; P grid (t) is the electric power purchased from the main distribution network at time t; C DG is the cost of distributed generation (DG) at time t; P DG (t) is the power generation of distributed power at time t; a, b, c are the coefficients for distributed power cost calculation; C ESS is the cost of the energy storage system (ESS) at time t; ESS is the unit power cost coefficient of the energy storage system; P ESS (t) is the charge and discharge power of the energy storage system at time t (charging is negative and discharging is positive); C SOP (t) is the cost of flexible switching (SOP) at time t; γ SOP is the unit price of the flexible switch (SOP) operating cost; P SOP (t) is the active power loss of the flexible switch at time t; P DG,ren (t) is the renewable energy (ren) power generation of distributed generation (DG) at time t; P curtail (t) is the curtailed power of renewable energy at time t.

[0040] In step S4, relevant data of the active distribution network is input, including the objective function and relevant variable constraints of the two-layer multi-objective optimization model, and the parameters and decision variables for the dynamic reconstruction of the active distribution network are further derived. The improved EEFO optimization algorithm is combined with the Pareto theory to solve the upper and lower multi-objective models respectively, and the optimal Pareto non-dominated solution is obtained, thereby obtaining the optimal active distribution network reconstruction plan. The steps include:

[0041] Initialize the electric eel population using the Logistic Chaos Map: Set the maximum number of iterations MaxFEs and introduce Logistic Chaos Initialization to the decision variables to generate a group of electric eel individuals. Each individual represents a combination of on and off states. The initialization formula is as follows:

[0042] X i =r×(ub i -lb i )+lb i ,i=1,2,…,n (15)

[0043] x n+1 =μx n (1-x n ) (16)

[0044] Where, X i represents the initial position of the i-th electric eel; ub i and lb idenote the upper and lower bounds of the search space, respectively; r represents a random number between [0,1]; n is the population size; μ is a control parameter, which is usually set to 4 to ensure chaos; x0∈(0,1) is a random initial value.

[0045] Fitness evaluation:

[0046] Fitness(X i )=[f1(X i ),f2(X i ),...,f k (X i )] (17)

[0047] Where, Fitness(X i ) refers to the fitness of each electric eel individual; f k (X i ) indicates that the kth objective function is in X i The value of the solution is determined by the Pareto dominance.

[0048] Solution M a Dominant solution M b If and only if:

[0049]

[0050] Non-dominated sorting and external archive management: Sort the population based on the Pareto dominance relationship and mark non-dominated solutions (i.e., solutions that are not dominated by other solutions). These non-dominated solutions are stored in an external archive. After each iteration, the newly generated non-dominated solutions are compared with the existing solutions in the archive, and all non-dominated solutions are retained. If the archive exceeds the capacity limit, it is pruned using the crowding distance.

[0051] Calculate congestion:

[0052]

[0053] Where, CD(M p ) is the solution of M p The crowding distance, k is the number of objective functions; and are the maximum and minimum values ​​of the j-th target in the current frontier.

[0054] Select parent individuals: Parent individuals are selected based on non-dominated rank and crowding, with priority given to solutions in low frontier layers and solutions with high crowding within the same layer to maintain diversity.

[0055] Calculate the energy factor for the current iteration:

[0056]

[0057] Where r7 is a random number in the range of (0, 1). As the number of iterations t increases, E(t) gradually decreases.

[0058] Behavioral judgment and updating: If E>1, the electric eel performs interactive behaviors for global exploration; if E≤1, the electric eel performs resting, hunting or migration behaviors with equal probability for local development.

[0059] Improved EEFO operation to generate children:

[0060] Golden Sine algorithm improves interactive behavior: Golden Sine uses the golden ratio to adjust the search step size and adjust the interactive behavior formula in the original EEFO:

[0061]

[0062] Where τ is the golden ratio coefficient, which is 0.618; is the population center position; x i (t) is the position of the i-th population; C is the chaotic perturbation factor, generated by the Logistic map.

[0063] Dynamic reverse learning strategy: Generates a reverse solution after each iteration and chooses to keep the original solution or the reverse solution based on the dynamic probability, which changes with the number of iterations:

[0064]

[0065] Where ub i and lb i They represent the upper and lower bounds of the search space respectively; t is the current iteration; T is the total number of iterations. opp choose or x i (t) is the better solution.

[0066] Cauchy mutation: Cauchy mutation is applied after the development phase to enhance local escape capability and avoid premature convergence. The updated position of the population after Cauchy mutation is:

[0067]

[0068] Where Cauchy(0,1) is the standard Cauchy distribution random number; σ is the mutation intensity, and σ0=0.1 is the initial mutation intensity.

[0069] Environment selection: First, the parent (P t ) and descendants (Q t ) merged into R t =P t ∪Q t , and then R tReorder and calculate the congestion, then select from low to high according to the frontier layer until the population capacity n is filled. If a layer cannot be fully added, the solution with the largest congestion in that layer is selected.

[0070] External archive maintenance: Each generation adds non-dominated solutions to the archive, removes duplicates, and retains them to the maximum capacity N a If the archive exceeds the limit, the first N files will be retained in descending order of congestion. a A solution.

[0071] Termination condition: When the maximum number of iterations T is reached or the Pareto frontier change rate is less than the threshold ε, the iteration stops:

[0072]

[0073] Where, F new 、F old are the current and previous generation archive target vector sets respectively; ε is the threshold value 10 -6 .

[0074] Technical effects and advantages of the present invention: The present invention proposes a two-layer multi-objective dynamic reconstruction method for distribution networks considering radial constraints of the ring decomposition method. Compared with the existing technology, it has the following advantages:

[0075] First, a radial topology constraint method based on the de-looping idea is adopted. Compared with the currently commonly used spanning tree constraint method, this method has a simple constraint form, which not only ensures the generation of an ideal radial topology, but also introduces fewer intermediate variables and constraint equations, and has higher solving efficiency; secondly, an equivalent load curve time period division method based on information entropy is adopted. Compared with traditional time period division methods (such as K-means clustering), this method does not require a given number of segments or comparison thresholds in advance, can fully consider the information volume of the equivalent daily load data, and the segmentation results are consistent with the changing trend of the equivalent daily load curve; finally, an improved EEFO is designed to solve the upper and lower layer models respectively. Through nested loop iteration of the upper and lower layers, the optimal active distribution network optimization scheduling strategy is finally obtained to meet the operation requirements of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a flow chart of a two-layer multi-objective dynamic reconstruction of a distribution network considering the de-looping method described in the present invention.

[0077] Figure 2 This is a flow chart of the equivalent daily load curve division based on information entropy involved in the present invention.

[0078] Figure 3 This is a flowchart for solving the double-layer multi-objective dynamic reconstruction model of the active distribution network described in the present invention. Specific implementation methods

[0079] In conjunction with the accompanying drawings in the embodiments of the present invention, the relevant technical solutions will be systematically and comprehensively explained below. Figure 1 The overall process of the two-layer multi-objective dynamic reconstruction of active distribution networks is introduced, and the overall framework of the dynamic reconstruction problem of active distribution networks is established based on the process. Figure 2 It is a flow chart for dividing the equivalent daily load curve based on information entropy. According to the intrinsic characteristics of the equivalent daily load curve, the optimal number of segments is dynamically determined, which can reduce the number of reconstructions while retaining the information content of the original data as much as possible. Figure 3 The present invention introduces a flowchart of solving the two-layer multi-objective reconstruction problem of active distribution network based on the multi-objective optimization method of improved EEFO algorithm and Pareto non-dominated solution. By reasonably designing and improving the EEFO algorithm process, it can better solve the two-layer multi-objective dynamic reconstruction problem of active distribution network. It should be noted that the embodiments of the present invention only represent some implementation cases of the present invention and do not cover all possible technical forms. The specific implementation cases listed in this article are only used as explanations of the present invention and should not be regarded as restrictive definitions of the present invention. Based on the contents of the embodiments disclosed in the present invention, all technical solutions derived by technical personnel in the relevant fields without paying creative labor are within the scope of protection of the present invention.

[0080] Reference Figure 1 Establish the overall process of two-layer multi-objective dynamic reconstruction of active distribution network; Figure 2 content, build an equivalent daily load curve partitioning model based on information entropy, and dynamically partition the daily load curve; Figure 3 , a multi-objective optimization method based on the improved EEFO algorithm and Pareto non-dominated solution is used to solve the two-layer multi-objective dynamic reconstruction problem of active distribution network. A two-layer multi-objective dynamic reconstruction method of active distribution network considering the radial constraint of the ring solution method includes the following steps:

[0081] S1: Mathematical modeling of radial constraints based on the ring-breaking method;

[0082] In the embodiment of the present invention, the two necessary and sufficient conditions for satisfying the radial constraint of the distribution network are converted accordingly, and mathematical modeling is performed on the two converted conditions respectively.

[0083] S2: Establish an equivalent daily load curve time division model based on information entropy;

[0084] In the embodiment of the present invention, the equivalent daily load curve division result based on information entropy mainly meets the two requirements of minimizing the number of switching actions and minimizing the amount of data loss information.

[0085] S3: Considering the daily load curve time division, the safe and stable operation constraints of the distribution network and other active management element constraints, a two-layer multi-objective reconstruction model of the active distribution network is established;

[0086] In an embodiment of the present invention, the upper layer takes minimizing network loss, minimizing voltage deviation, and minimizing the number of switching operations as optimization goals, and adopts a radial constraint method based on the ring decomposition method to optimize the topology of the distribution network. Based on the operation results of the upper layer, the lower layer takes minimizing economic indicators and maximizing renewable energy utilization as goals, and uses a time division method based on information entropy to determine the time period for reconstruction and the switching operation status within each time period. The topology structure of each time period is then returned to the upper layer for iterative solution. Constraints include DistFlow power flow constraints, node voltage and branch current constraints, PV output constraints, ESS operation constraints, SOP capacity and operation constraints, topology constraints, and switch operation number constraints.

[0087] S4: Based on the Pareto theory, an improved multi-objective electric eel foraging optimization algorithm (IMEEFO) is designed. Logistic chaos mapping is introduced to initialize the population in the initial stage. The golden sine algorithm is used in the interactive behavior to optimize the search direction. Dynamic reverse learning and Cauchy mutation are introduced in the development behavior to enhance the search and avoid local optimality. The improved multi-objective electric eel foraging optimization algorithm is used to solve the upper and lower multi-objective models. Through upper and lower layer iterations, the optimal strategy for the dynamic reconstruction of the active distribution network is ultimately derived.

[0088] In an embodiment of the present invention, the improved EEFO algorithm introduces Logistic chaos mapping, dynamic reverse learning strategy, Cauchy mutation and golden sine strategy. In the initialization stage, the Logistic chaos mapping is used to generate the initial population to improve the diversity of the population and the global search capability; in the development behavior stage, the dynamic reverse learning strategy is used to generate the reverse solution, increase the search range, apply Cauchy mutation to the individuals, enhance the local escape capability, and avoid premature convergence; in the position update, the golden sine formula is applied to optimize the migration step size and balance the development accuracy and speed. In order to solve the double-layer multi-objective reconstruction problem of the distribution network, the improved EEFO optimization algorithm is expanded to multiple objectives by adding the Pareto non-dominated solution, and the optimal reconstruction strategy of the active distribution network is obtained through the iterative cycle of the upper and lower layers.

[0089] Specifically, step S1 includes the following steps:

[0090] S11. From the above analysis, we can see that satisfying both conditions 3 and 4 is a necessary and sufficient condition for the network to satisfy the radial constraint. The following mathematical modeling of conditions 3 and 4 is as follows:

[0091] S12. The mathematical model that meets condition 3 is:

[0092]

[0093] Where C k is the kth basic cycle set; l ij is the branch between nodes i and j; l r b after conversion r The corresponding branch; a ij For branch l ij The switch state is 0 for open state and 1 for closed state; b r is the auxiliary variable introduced. In each common branch, only one switch can be opened at most. r To replace the switches contained therein, so that there are no common variables in different basic loops, so that condition 3 can be met.

[0094] S13. To better represent condition 4 using a mathematical model, possible islands are divided into two categories: the first category, which contains no nodes with a degree greater than or equal to 3; and the second category, which contains nodes with a degree greater than or equal to 3. The degree of a node refers to the number of branches connected to it in the basic circuit.

[0095] S14. The mathematical model that meets condition 4 is:

[0096]

[0097] Where, is the set of common branches between different basic loops, that is b r is the auxiliary variable introduced, and finally b is converted into r The state is converted back to a ij Status; r b after conversion r The corresponding branch; ij is the branch between nodes i and j; η m is the cut set corresponding to the mth second-type island in the network; is the number of edges in the cut set corresponding to the second type of islands.

[0098] S15, where equations (1)-(3) ensure that the switches in the cut set corresponding to the first type of island are not all turned on; equation (4) ensures that the switches in the cut set corresponding to the second type of island are not all turned on, and the auxiliary variable b is used. r To reduce recurrence.

[0099] Specifically, step S2 includes the following steps:

[0100] S21. Calculate the probability distribution of equivalent load in each period. The formula for the probability distribution of equivalent load in each period is:

[0101] The probability distribution formula of equivalent load in each period is:

[0102]

[0103] Where x i is the equivalent load of period i; Δt i is the duration of time period i in hours; k is the number of equivalent load curve segments; p k is the equivalent load probability in the kth period.

[0104] S22. Calculate the information entropy of the equivalent daily load curve for different segments:

[0105]

[0106] Where X is a random variable; p(x i ) is the probability of x taking a value, and 0log20=0 is specified.

[0107] S23. Determine the merging scheme that minimizes information entropy:

[0108] After dividing the time periods, two adjacent time periods are randomly combined. The information entropy of different schemes is compared, and the scheme with the smallest entropy reduction is selected. If two or more schemes have the same entropy reduction, one of them is selected. To minimize errors, the combined equivalent load is the average of the loads of the two adjacent time periods.

[0109] S24. Determination of the optimal number of segments and segment positions:

[0110] Draw a perpendicular line L at any point on the excess entropy curve, where L is the line connecting the two points with segment numbers 1 and 23. The length of the perpendicular line is:

[0111] h k =23H k -H 24 (k-1) (7)

[0112] Where H k is the information entropy when the number of segments is k. Compare the vertical line h k and h k-1 The size of h k If is larger, then k is the optimal segmentation result.

[0113] Specifically, step S3 includes the following steps:

[0114] S31. In the upper-level planning objectives, consider minimizing network loss f 11 , voltage deviation minimized f 12and the number of switching operations is minimized f 13 Three objective functions, the objective functions are as follows:

[0115] minF1=min(f 11 +f 12 +f 13 ) (8)

[0116]

[0117] Where N b is the set of all branches including the connecting line; C loss I is the network loss cost; ij,t is the current flowing through line ij at time t; R ij is the resistance value of line ij; m represents the node; n is the number of nodes; V m,i is the actual voltage value of node i at time t; V N is the node rated voltage; N s is the number of switches; S k (t) is the state of the kth switch at time t (0 for open, 1 for closed).

[0118] S32. The goal of the lower-level planning is to minimize the economic index and maximize the renewable energy consumption rate. Its objective function is as follows:

[0119] minF2=min(f 21 +(1-f 22 )) (12)

[0120]

[0121] C grid (t)=π grid (t)·P grid (t) (14)

[0122] C DG (t) = a·P DG (t) 2 +b·P DG (t)+c (15)

[0123] C ESS (t) = λ ESS ·|P ESS (t)| (16)

[0124] C SOP (t) = γ SOP ·P SOP (t) (17)

[0125]

[0126] Where C grid is the cost related to the main distribution network at time t; grid (t) is the unit price of electricity purchased from the main grid at time t; P grid (t) is the electric power purchased from the main distribution network at time t; C DG is the cost of distributed generation (DG) at time t; P DG (t) is the power generation of distributed power at time t; a, b, c are the coefficients for distributed power cost calculation; C ESS is the cost of the energy storage system (ESS) at time t; ESS is the unit power cost coefficient of the energy storage system; P ESS (t) is the charge and discharge power of the energy storage system at time t (charging is negative and discharging is positive); C SOP (t) is the cost of flexible switching (SOP) at time t; γ SOP is the unit price of the flexible switch (SOP) operating cost; P SOP (t) is the active power loss of the flexible switch at time t; P DG,ren (t) is the renewable energy (ren) power generation of distributed generation (DG) at time t; P curtail (t) is the curtailed power of renewable energy at time t.

[0127] S33. Specific constraints are as follows:

[0128] S331, DistFlow flow constraint:

[0129] The commonly used branch power flow model for AC distribution network is:

[0130]

[0131] Where α(j) is the set of downstream nodes with node j as the upstream node of the branch; β(j) is the set of upstream nodes with node j as the downstream node of the branch; P ij,t , Q ij,t are the active and reactive powers flowing through branch ij at time t; P jk,t , Q jk,t are the active and reactive powers flowing through the downstream branch with node j as the head end at time t; are the net active and reactive power injected into node j at time t, respectively; are the charging and discharging power of the energy storage device at node j at time t; are the active and reactive power injected into node j by the substation at time t, respectively; is the reactive load of node j at time t; U j,t is the effective voltage at node j at time t; Rij 、X ij are the equivalent resistance and reactance of branch ij respectively.

[0132] Since there are nonlinear terms in the above tidal current equation, it is generally difficult to solve it directly, so we introduce intermediate variables and second-order cone relaxation to transform it linearly. Substituting the square terms in equations (19) to (22) is:

[0133]

[0134] There is a nonlinear term in Equation (28), which is converted into a second-order cone constraint using the second-order cone relaxation method, namely:

[0135]

[0136] After the ADN dynamic reconstruction, since some branches are in a disconnected state, not all branches can satisfy Equation (27). Therefore, the large-M method is introduced to further transform Equation (27) into:

[0137]

[0138] Where M is a sufficiently large positive number; a ij,t It is a Boolean variable, indicating the open and closed state of branch ij at time t. ij,t = 0, branch ij is closed; when a ij,t =1, branch ij is disconnected.

[0139] S332, node voltage and branch current constraints:

[0140]

[0141] Where U j,max 、U j,min is the maximum and minimum voltage allowed at node j; I ij,max is the maximum current allowed to flow through branch ij.

[0142] S333, PV output constraint:

[0143] In order not to affect the upper power grid, the present invention does not allow power to be fed back to the upper power grid, and does not consider the uncertainty of PV output and its reactive output.

[0144]

[0145] Where, is the maximum PV adjustable power at node j at time t.

[0146] S334, ESS operation constraints:

[0147]

[0148]

[0149] Where, They are the charging and discharging states of the ESS at node j at time t, and their values ​​are Boolean variables, which are used to limit the ESS to be in the charging or discharging state; are the maximum and minimum charging power of ESS at time t respectively; are the maximum and minimum discharge power of ESS at time t respectively; is the ESS storage capacity at node j at time t; are the maximum and minimum storage capacities of ESS respectively; are the ESS charging and discharging efficiency coefficients respectively.

[0150] S335, SOP capacity constraints:

[0151]

[0152] Where, The number of SOPs installed for branch ij; is the unit capacity of SOP; The maximum capacity of SOP installed for branch ij; is the decision variable for whether to install SOP on branch ij.

[0153] S336, SOP operation constraints:

[0154]

[0155] Where, are the active power output by SOP at nodes i and j at time t in scenario s, respectively; is the transmission loss of SOP at time t in scenario s; is the loss coefficient of SOP port i, j; μ is the power coefficient of SOP; are the reactive power output by SOP at nodes i and j at time t in scenario s.

[0156] S337, Topology Constraints:

[0157]

[0158] Where, ψ k is the set of all branches in the kth basic circuit; is the set of common branches in adjacent basic loops, that is, b r The intermediate variable introduced replaces the common branch variable a in the adjacent basic loop ijstate, making the switches of each basic circuit disconnected independent of each other, and finally b is converted by formula (50) r Transform back to a ij state; r is the intermediate variable b after conversion r corresponding branch; They are respectively the set of cut sets corresponding to the node degrees greater than or equal to 3 in the network and the number of branches in the corresponding cut sets.

[0159] S338, switch operation times constraint:

[0160] In order to reduce the switching loss caused by multiple reconstructions, the number of switch reconstructions is limited. The constraints are as follows:

[0161]

[0162] Where s k,max is the maximum number of switch k operations; s max It is the maximum value of all switch operations.

[0163] Specifically, step S4 includes the following steps:

[0164] S41. Input relevant data of the active distribution network, including the objective function and relevant variable constraints of the double-layer multi-objective optimization model, and further derive parameters and decision variables for dynamic reconstruction of the active distribution network.

[0165] S42, upper and lower multi-objective model solution:

[0166] S421. Initialize the electric eel population using Logistic Chaos Mapping: Set the maximum number of iterations MaxFEs and introduce Logistic Chaos Mapping to the decision variables to generate a group of electric eel individuals. Each individual represents a combination of on and off states. The initialization formula is as follows:

[0167] X i =r×(ub i -lb i )+lb i ,i=1,2,…,n (52)

[0168] x n+1 =μx n (1-x n ) (53)

[0169] Where, X i represents the initial position of the i-th electric eel; ub i and lb i denote the upper and lower bounds of the search space, respectively; r represents a random number between [0,1]; n is the population size; μ is a control parameter, which is usually set to 4 to ensure chaos; x0∈(0,1) is a random initial value.

[0170] S422, fitness evaluation:

[0171] Fitness(X i )=[f1(X i ),f2(X i ),...,f k (X i )] (54)

[0172] Where, Fitness(X i ) refers to the fitness of each electric eel individual; f k (X i ) indicates that the kth objective function is in X i The value of the solution is determined by the Pareto dominance.

[0173] S423. Non-dominated sorting and external archive management: Sort the population according to the Pareto dominance relationship and mark non-dominated solutions (i.e., solutions that are not dominated by other solutions). Store non-dominated solutions in an external archive. After each iteration, compare the newly generated non-dominated solutions with the existing solutions in the archive, and retain all non-dominated solutions. If the archive exceeds the capacity limit, prune it using the crowding distance.

[0174] S424. Calculate the congestion degree:

[0175]

[0176] Where, CD(M p ) is the solution of M p The crowding distance, k is the number of objective functions; and are the maximum and minimum values ​​of the j-th target in the current frontier.

[0177] S425. Select parent individuals: Select parents based on non-dominated rank and crowding, give priority to solutions in low frontier layers, and select solutions with high crowding within the same layer to maintain diversity.

[0178] S4251. Calculate the energy factor of the current iteration:

[0179]

[0180] Where r7 is a random number in the range of (0, 1). As the number of iterations t increases, E(t) gradually decreases.

[0181] S4252. Behavior judgment and update: If E>1, the electric eel performs interactive behaviors for global exploration; if E≤1, the electric eel performs resting, hunting or migration behaviors with equal probability for local development.

[0182] S426. Improved EEFO operation to generate offspring:

[0183] S4261. Golden Sine Algorithm Improves Interactive Behavior: Golden Sine uses the golden ratio to adjust the search step size and adjust the interactive behavior formula in the original EEFO:

[0184]

[0185] Where τ is the golden ratio coefficient, which is 0.618; is the population center position; x i (t) is the position of the i-th population; C is the chaotic perturbation factor, generated by the Logistic map.

[0186] S4262, Dynamic Reverse Learning Strategy: Generates a reverse solution after each iteration and chooses to retain the original solution or the reverse solution based on the dynamic probability, which changes with the number of iterations:

[0187]

[0188] Where ub i and lb i Represent the upper and lower bounds of the search space respectively; t is the current iteration, and T is the total number of iterations. opp choose or x i (t) is the better solution.

[0189] S4263, Cauchy mutation: Cauchy mutation is applied after the development phase to enhance local escape capability and avoid premature convergence. The updated position of the population after Cauchy mutation is:

[0190]

[0191] Where Cauchy(0,1) is the standard Cauchy distribution random number; σ is the mutation intensity, and σ0=0.1 is the initial mutation intensity.

[0192] S427, environment selection: first the parent (P t ) and descendants (Q t ) merged into R t =P t ∪Q t , and then R t Reorder and calculate the congestion, then select from low to high according to the frontier layer until the population capacity n is filled. If a layer cannot be fully added, the solution with the largest congestion in that layer is selected.

[0193] S428, External archive maintenance: Each generation adds non-dominated solutions to the archive, removes duplicates and retains them to the maximum capacity Na If the archive exceeds the limit, the first N files will be retained in descending order of congestion. a A solution.

[0194] S429, termination condition: When the maximum number of iterations T is reached, or the Pareto frontier change rate is less than the threshold ε, the iteration is stopped and the Pareto optimal solution is output:

[0195]

[0196] Where, F new 、F old are the current and previous generation archive target vector sets respectively; ε is the threshold value 10 -6 .

[0197] It is obvious to those skilled in the art that the invention is not limited to the specific details involved in the above-mentioned exemplary embodiments. The invention may have other specific forms without violating the spirit or basic characteristics of the invention. These embodiments are for illustrative purposes only and are not restrictive. The scope of the invention is defined by the appended claims and is intended to cover all changes within the meaning and scope of the equivalent elements of the claims. The reference numerals in the claims do not affect the scope of the claims. The specification describes the embodiments, but the technical solutions of the various embodiments can be combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A two-layer multi-objective dynamic reconfiguration method for distribution networks considering radial constraints of a ring-breaking method, comprising the following steps: S1: Mathematical modeling of radial constraints based on the ring-breaking method; S2: Establish an equivalent daily load curve time division model based on information entropy; S3: Considering the daily load curve time division, the safe and stable operation constraints of the distribution network and other active management element constraints, a two-layer multi-objective reconstruction model of the active distribution network is established; S4: An improved multi-objective electric eel foraging optimization algorithm (IMEEFO) is designed based on Pareto theory. Logistic chaos mapping is introduced in the initial stage to perform chaos initialization on the population; the golden sine algorithm is introduced in the interactive behavior to optimize the search direction; dynamic reverse learning and Cauchy mutation are introduced in the development behavior to enhance the search and avoid local optimality. The improved multi-objective electric eel foraging optimization algorithm is used to solve the upper and lower multi-objective models, and the optimal strategy for dynamic reconstruction of the active distribution network is finally obtained through upper and lower layer cyclic iteration.

2. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 1, characterized in that: The two necessary and sufficient conditions for satisfying the radial constraint of the distribution network were converted accordingly, and mathematical modeling was carried out for the two converted conditions respectively.

3. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 1, characterized in that: The equivalent daily load curve division method based on information entropy is adopted, and its result mainly meets the two requirements of minimizing the number of switching operations and minimizing data loss information.

4. The method of claim 2, wherein the method comprises: The mathematical model construction considering the radial constraint of the ring solution method includes the following steps: The radial constraint of a distribution network can be described using the following two conditions: Condition 1: The number of closed branches in the network is N - Ns; Condition 2: The network is connected. Since Condition 2 is difficult to express analytically, it is replaced by two other conditions: Condition 3: All basic loops in the network must have a switch open. The switches opened in each basic loop are independent of each other, and the same switch cannot be opened simultaneously in multiple basic loops. Condition 4: There are no islands in the network. An island is a connected region that is not directly or indirectly connected to a substation node. The set of branches connecting an island to the main network is called the cut set corresponding to the island. It is easy to see that a network that satisfies Condition 3 necessarily satisfies Condition 1 and contains all feasible solutions. Since a connected network must not have islands, and a network without islands must be connected, Condition 4 is an equivalent condition to Condition 2. Therefore, the simultaneous satisfaction of Conditions 3 and 4 is a necessary and sufficient condition for a network to satisfy the radial constraint. The mathematical model that meets condition 3 is: Where C k is the kth basic cycle set; l ij is the branch between nodes i and j; l r b after conversion r The corresponding branch; a ij For branch l ij The switch state is 0 for open state and 1 for closed state; b r is the auxiliary variable introduced. In each common branch, only one switch can be opened at most. r To replace the switches contained therein, so that there are no common variables in different basic loops, so that condition 3 can be met. To better represent condition 4 using a mathematical model, possible islands are divided into two categories: the first category, which contains no nodes with a degree greater than or equal to 3; and the second category, which contains nodes with a degree greater than or equal to 3. The degree of a node refers to the number of branches connected to it in the basic circuit. The mathematical model that meets condition 4 is: Where, is the set of common branches between different basic loops, that is b r is the auxiliary variable introduced, and finally b is converted into r The state is converted back to a ij Status; r b after conversion r The corresponding branch; ij is the branch between nodes i and j; η m is the cut set corresponding to the mth second-type island in the network; is the number of edges in the cut set corresponding to the second type of islands. Among them, formulas (1)-(3) ensure that the switches in the cut set corresponding to the first type of island are not all turned on; formula (4) ensures that the switches in the cut set corresponding to the second type of island are not all turned on, and the auxiliary variable b is used r To reduce recurrence.

5. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 3 is characterized by: The equivalent daily load curve time division model based on information entropy includes the following steps: Calculate the probability distribution of equivalent load in each time period: Where x i is the equivalent load of period i; Δt i is the duration of time period i in hours; k is the number of equivalent load curve segments; p k is the equivalent load probability in the kth period. Calculate the information entropy of the equivalent daily load curve for different segments: Where X is a random variable; p(x i ) is the probability of x taking a value, and 0log20=0 is specified. Determine the merging scheme that minimizes information entropy reduction: After dividing the time periods, randomly select two adjacent time periods for merging. Compare the information entropy of the different schemes and select the one that minimizes information entropy reduction. If two or more schemes have the same entropy reduction, select one of them. To minimize errors, the equivalent load after merging is the average of the loads of the two adjacent time periods. Determination of the optimal number of segments and segment positions: Draw a perpendicular line L at any point on the excess entropy curve, where L is the line connecting the two points with segment numbers 1 and 23. The length of the perpendicular line is: h k = 23H k - H 24 (k-1) (7) Where H k is the information entropy when the number of segments is k. Compare the vertical line h k and h k-1 The size of h k If is larger, then k is the optimal segmentation result.

6. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 1, characterized in that: Specific constraints include DistFlow power flow constraints, node voltage and branch current constraints, PV output constraints, ESS operation constraints, SOP capacity and operation constraints, topology constraints, and switch operation times constraints.

7. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 1, characterized in that: The dual-layer multi-objectives of the active distribution network include: minimizing network losses, minimizing voltage deviations, and minimizing the number of switching operations as the upper-layer optimization objectives; minimizing economic indicators and maximizing renewable energy absorption rates as the lower-layer objectives. In the upper planning objective, the network loss is minimized 11 , voltage deviation minimized f 12 and the number of switching operations is minimized f 13 , three objective functions, the objective functions are as follows: minF1=min(f 11 +f 12 +f 13 ) (8) Where N b is the set of all branches including the connecting line; C loss I is the network loss cost; ij,t is the current flowing through line ij at time t; R ij is the resistance value of line ij; m represents the node; n is the number of nodes; V m,i is the actual voltage value of node i at time t; V N is the node rated voltage; N s is the number of switches; S k (t) is the state of the kth switch at time t (0 for open, 1 for closed). The goal of the lower-level planning is to minimize the economic index and maximize the renewable energy consumption rate. Its objective function is as follows: minF2=min(f 21 +(1-f 22 )) (12) C grid (t)=π grid (t)·P grid (t) (14) C DG (t)=a·P DG (t) 2 +b·P DG (t)+c (15) C ESS (t)=λ ESS ·|P ESS (t)| (16) C SOP (t)=γ SOP ·P SOP (t) (17) Where C grid is the cost related to the main distribution network at time t; grid (t) is the unit price of electricity purchased from the main grid at time t; P grid (t) is the electric power purchased from the main distribution network at time t; C DG is the cost of distributed generation (DG) at time t; P DG (t) is the power generation of distributed power at time t; a, b, c are the coefficients for distributed power cost calculation; C ESS is the cost of the energy storage system (ESS) at time t; ESS is the unit power cost coefficient of the energy storage system; P ESS (t) is the charge and discharge power of the energy storage system at time t (charging is negative and discharging is positive); C SOP (t) is the cost of flexible switching (SOP) at time t; γ SOP is the unit price of the flexible switch (SOP) operating cost; P SOP (t) is the active power loss of the flexible switch at time t; P DG,ren (t) is the renewable energy (ren) power generation of distributed generation (DG) at time t; P curtail (t) is the curtailed power of renewable energy at time t.

8. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 1, characterized in that: The system inputs relevant data about the active distribution network, including the objective function and relevant variable constraints of the two-layer multi-objective optimization model, to derive the parameters and decision variables for the dynamic reconfiguration of the active distribution network. The improved EEFO optimization algorithm, combined with Pareto theory, solves the upper and lower multi-objective models separately, obtaining the optimal Pareto non-dominated solution and, consequently, the optimal active distribution network reconfiguration scheme.

9. The method for dynamic reconfiguration of a distribution network with two layers and multiple objectives considering radial constraints of a ring-breaking method according to claim 8, characterized in that: The multi-objective optimization steps based on the improved EEFO algorithm and Pareto non-dominated solution are as follows: Initialize the electric eel population using the Logistic Chaos Map: Set the maximum number of iterations MaxFEs and introduce Logistic Chaos Initialization to the decision variables to generate a group of electric eel individuals. Each individual represents a combination of on and off states. The initialization formula is as follows: X i =r×(ub i -lb i )+lb i ,i=1,2,…,n (19) x n+1 =μx n (1-x n ) (20) Where, X i represents the initial position of the i-th electric eel; ub i and lb i denote the upper and lower bounds of the search space, respectively; r represents a random number between [0,1]; n is the population size; μ is a control parameter, which is usually set to 4 to ensure chaos; x0∈(0,1) is a random initial value. Fitness evaluation: Fitness(X i )=[f1(X i ),f2(X i ),...,f k (X i )] (21) Where, Fitness(X i ) refers to the fitness of each electric eel individual; f k (X i ) indicates that the kth objective function is in X i The value of the solution is determined by the Pareto dominance. Solution M a Dominant solution M b If and only if: Non-dominated sorting and external archive management: Sort the population based on the Pareto dominance relationship and mark non-dominated solutions (i.e., solutions that are not dominated by other solutions). These non-dominated solutions are stored in an external archive. After each iteration, the newly generated non-dominated solutions are compared with the existing solutions in the archive, and all non-dominated solutions are retained. If the archive exceeds the capacity limit, it is pruned using the crowding distance. Calculate congestion: Where, CD(M p ) is the solution of M p The crowding distance, k is the number of objective functions; and are the maximum and minimum values ​​of the j-th target in the current frontier. Select parent individuals: Parent individuals are selected based on non-dominated rank and crowding, with priority given to solutions in low frontier layers and solutions with high crowding within the same layer to maintain diversity. Calculate the energy factor for the current iteration: Where r7 is a random number in the range of (0, 1). As the number of iterations t increases, E(t) gradually decreases. Behavioral judgment and updating: If E>1, the electric eel performs interactive behaviors for global exploration; if E≤1, the electric eel performs resting, hunting or migration behaviors with equal probability for local development. Improved EEFO operation to generate children: Golden Sine algorithm improves interactive behavior: Golden Sine uses the golden ratio to adjust the search step size and adjust the interactive behavior formula in the original EEFO: Where τ is the golden ratio coefficient, which is 0.618; is the population center position; x i (t) is the position of the i-th population; C is the chaotic perturbation factor, generated by the Logistic map. Dynamic reverse learning strategy: Generates a reverse solution after each iteration and chooses to keep the original solution or the reverse solution based on the dynamic probability, which changes with the number of iterations: Where ub i and lb i Represent the upper and lower bounds of the search space respectively; t is the current iteration; T is the total number of iterations. With probability p opp choose or x i (t) is the better solution. Cauchy mutation: Cauchy mutation is applied after the development phase to enhance local escape capability and avoid premature convergence. The updated position of the population after Cauchy mutation is: Where Cauchy(0,1) is the standard Cauchy distribution random number; σ is the mutation intensity, and σ0=0.1 is the initial mutation intensity. Environment selection: First, the parent (P t ) and descendants (Q t ) merged into R t =P t ∪Q t , and then R t Reorder and calculate the congestion, then select from low to high according to the frontier layer until the population capacity n is filled. If a layer cannot be fully added, the solution with the largest congestion in that layer is selected. External archive maintenance: Each generation adds non-dominated solutions to the archive, removes duplicates, and retains them to the maximum capacity N a If the archive exceeds the limit, the first N files will be retained in descending order of congestion. a A solution. Termination condition: When the maximum number of iterations T is reached or the Pareto frontier change rate is less than the threshold ε, the iteration stops: Where, F new 、F old are the current and previous generation archive target vector sets respectively; ε is the threshold value 10 -6 .

Images