Active power distribution network strategy reconstruction method based on improved grey wolf algorithm

Abstract

The invention provides an active power distribution network strategy reconstruction method based on an improved grey wolf algorithm, and the method comprises the following steps: stage 1, reading the electrical data of a power distribution network, confirming the switching state and the access position and constraint conditions of a distributed power supply, and carrying out the reconstruction of a power distribution network strategy on the premise of meeting the power flow constraint, operation constraint and topological structure constraint of the power distribution network; and constructing a mathematical model for static reconstruction of the multi-target active power distribution network. Stage 2: then improving the GWO algorithm, the improved strategy including using improved Tent chaotic mapping to perform population initialization, improving a convergence factor and an adaptive t distribution disturbance variation position updating strategy, and obtaining a TGWO algorithm, according to the method, improved Tent chaotic mapping is introduced to carry out population initialization, an attenuation factor updates an alpha wolf position, and a disturbance variation strategy of adaptive t distribution is improved. The improved grey wolf algorithm is improved in operation speed, solving precision and robustness.

Description

Technical Field

[0001] The invention relates to the technical field of power systems, and in particular to an active distribution network strategy reconstruction method based on an improved grey wolf algorithm. Background Art

[0002] The rapid development of new energy has led to the integration of a large number of distributed generation (DG) represented by photovoltaic, wind power, fuel cells, micro-turbines, etc. into the active distribution network. In 2008, relevant scholars proposed the concept of active distribution network (ADN) for the first time at the International Commission on Large Electric Systems. However, after DG is connected to the active distribution network in large numbers, the uncertainty and intermittency of DG power supply may cause power reverse transmission and increase in power volatility. In this case, the flow of the entire distribution network will change, which will have a greater impact on the economy and stability of the entire distribution network. Given that the control measures such as voltage regulation on the traditional distribution network side are not enough to cope with the impact of high penetration DG on it.

[0003] Nowadays, the optimization research of active distribution network covers a wide range, mainly including the optimization of distributed power access points, the optimization of load absorption capacity of distribution network, reactive power optimization and other fields. Among them, the active distribution network reconstruction strategy has attracted much attention as an efficient optimization method. In the early days, this technology was mainly used for power grid planning to select the best power supply path for new users to achieve the minimum power supply cost. With the continuous development of the research on distribution system performance, subsequent experts and scholars have found that we can control the structure of the distribution network by controlling the switch state in the distribution network through algorithms, and change the power flow distribution of the distribution network. After reconstruction and optimization, the network loss, voltage stability and load balance of the distribution network are significantly improved.

[0004] In the field of distribution network reconstruction, artificial intelligence algorithms have shown more outstanding computing power than traditional mathematical algorithms and heuristic algorithms. The Gray Wolf Algorithm is an innovative artificial intelligence optimization algorithm that theoretically simulates the hunting behavior of gray wolves in nature. The algorithm was proposed by Mirjalili Seyedal in his article "Grey Wolf Optimizer". In this paper, the author elaborated on the origin and operation steps of this algorithm in detail, and it was well verified in some specific problems of optimizing the objective function. Compared with other existing similar artificial intelligence algorithms, such as particle swarm optimization and genetic algorithm, the Gray Wolf Algorithm shows better computing efficiency. Since then, more and more scientific researchers have begun to devote themselves to the in-depth study of the Gray Wolf Algorithm. At present, the Gray Wolf Algorithm has been successfully applied to many fields including industrial automatic control, virtual network architecture design, financial data analysis, etc., but in the electric power industry, the algorithm industry is less involved. Therefore, this invention will focus on the distribution network reconstruction problems faced by the power industry and explore the potential application value and possibility of the Gray Wolf Algorithm. The traditional grey wolf algorithm has some shortcomings, such as insufficient optimization accuracy, easy to fall into local optimal solution, low convergence speed and complex parameter setting, etc., which need to be improved.

[0005] Based on the above, the present invention designs a research strategy for multi-objective reconstruction optimization of active distribution networks based on an improved wolf pack algorithm with higher computational efficiency, better solution accuracy and better robustness, which has important practical value and far-reaching theoretical significance. Summary of the invention

[0006] The purpose of the present invention is to provide an active distribution network strategy reconstruction method based on an improved grey wolf algorithm in order to solve the above problems.

[0007] The present invention achieves the above-mentioned purpose through the following technical scheme, and the active distribution network strategy reconstruction method based on the improved grey wolf algorithm comprises the following steps:

[0008] Phase 1: First, read the electrical data of the distribution network, confirm the switch status and the access location and constraints of the distributed power source, and build a mathematical model for the static reconstruction of the multi-objective active distribution network on the premise of satisfying the distribution network flow constraints, operation constraints, and topological structure constraints.

[0009] Phase 2: Then the GWO algorithm was improved. The improvement strategies included using the improved Tent chaotic map for population initialization, improving the convergence factor, and the adaptive t-distribution perturbation mutation position update strategy to obtain the TGWO algorithm.

[0010] Stage 3: Finally, the present invention proposes to use an external archive (Wset) combined with the Pareto dominance concept to process and update to improve the performance of the Pareto solution, and use an evaluation function to evaluate and select the obtained solutions.

[0011] Firstly, by focusing on the three key factors of optimizing grid loss, minimizing node voltage deviation and minimizing the number of switch operations, a static reconstruction mathematical model of the active distribution network is established under the premise of satisfying the distribution network flow constraints, operation constraints, and topological structure constraints.

[0012] The distribution network reconstruction model is optimized by the improved Grey Wolf Algorithm TGWO, and the Grey Wolf Algorithm is improved. The improvement strategy includes the following steps:

[0013] (1) The improved Tent chaotic map optimizes the initial population of the grey wolf algorithm;

[0014] (2) Update the convergence factor a, calculate the values ​​of A and C, and update the position of the wolf pack;

[0015] (3) Adaptive t-distribution perturbation mutation is used to perturb and mutate the gray wolf individuals to obtain the positions of new individuals;

[0016] The initial population of the grey wolf algorithm is optimized by using the improved Tent chaos map, which includes the following steps:

[0017] The method of incorporating the random element rand(0,1)·1 / N into the initial Tent chaotic mapping formula is expressed as follows:

[0018]

[0019] The expression after Bernoulli transformation is as follows:

[0020]

[0021] Where: N is the size of the algorithm population; x i is the i-th chaotic number, i = 1, 2, ... N; rand (0, 1) is any random number in the interval [0, 1]; mod represents the remainder operation; the specific implementation details and operation steps are as follows:

[0022] 1) Generate a random number x0 between (0,1), i = 0;

[0023] 2) Perform iterative calculation according to formula (2), and add 1 to the value of i each time a chaotic value is generated;

[0024] 3) When i reaches the maximum number of iterations N, save the generated chaotic sequence X;

[0025] 4) Map the chaotic sequence X to the gray wolf initial population search space according to formula (3).

[0026]

[0027] In the formula, Ubj,min and Lbj,max represent the maximum and minimum ranges of the gray wolf search space respectively. The numerical distribution diagram of the improved Tent chaotic mapping sequence is shown in Figure 1 shown.

[0028] The update formula is updated by an update convergence factor a:

[0029]

[0030] In the formula, a initial , a final are the initial value and final value of the convergence factor a respectively; t max The number of iterations is the maximum number of iterations; t is the current number of iterations; k1 and k2 are nonlinear adjustment coefficients. The convergence factor a changes nonlinearly and dynamically with the increase of the number of evolutionary iterations, which helps to balance the global and local search performance.

[0031] By using the adaptive t-distribution perturbation mutation strategy, the Gaussian distribution, t-distribution and Cauchy distribution function distribution graphs are shown in Figure 2 As shown. By using the original gray wolf individual x i Add x to the position i ·t(k) is a perturbation variation term that follows the t distribution, which increases the active search field of the gray wolf individuals, so that they are no longer restricted from obtaining the optimization brought by the gray wolf update. The perturbation variation of the gray wolf position using the adaptive t distribution is shown in formula (5):

[0032] x' i =x i +x i t(k) (5)

[0033] In the formula, represents the position of the gray wolf individual after the disturbance mutation of the t distribution, xi is the position of the i-th gray wolf individual, and t(k) indicates the t distribution that satisfies the number of iterations k as the degree of freedom parameter.

[0034] The gray wolf population is initialized by improved Tent chaotic mapping, and the gray wolf individuals represent each distribution network switch combination;

[0035] The evaluation function is used to select the gray wolf individuals based on the obtained values, and the first three are selected as α wolf, β wolf, and δ wolf, and their positions are recorded as X α ,X β ,X δAfter each iteration, the control variables of the individual gray wolves are updated, and the search range of the prey is determined by these three wolves.

[0036] Update the convergence factor a, calculate the values ​​of A and C, and update the position of the wolf pack.

[0037] The updated gray wolf position is mutated and disturbed by an adaptive t-distribution strategy;

[0038] Calculate the evaluation function value of each gray wolf individual after t distribution mutation, compare the new evaluation function value with the initial evaluation function value, retain the better fitness value, and update the global optimal information

[0039] Finally, the multi-objective reconstruction problem of distribution network is solved by introducing the Pareto optimal criterion, and the external archive (Wset) is used to update and store the selected Pareto alternative solutions in combination with the Pareto dominance concept and evaluation function.

[0040] The beneficial effects of the present invention are:

[0041] 1. The present invention introduces improved Tent chaotic mapping to perform population initialization, attenuation factor to update the position of α wolf and adaptive t distribution disturbance mutation strategy to improve the algorithm. The improved grey wolf algorithm has improved running speed, solution accuracy and robustness.

[0042] 2. The present invention introduces the Pareto optimal criterion to solve the multi-objective reconstruction problem of the distribution network, and uses an external file (Wset) combined with the Pareto dominance concept and the evaluation function to update and select the obtained Pareto candidate solution. The obtained reconstruction optimization result facilitates decision makers to select the optimal solution according to the actual situation, proving that the algorithm of the present invention has excellent practical value and far-reaching theoretical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 To improve the numerical distribution diagram of Tent chaotic mapping sequence before and after;

[0045] Figure 2 Distribution graphs for Gaussian distribution, t distribution and Cauchy distribution functions;

[0046] Figure 3 This is a schematic diagram of the Pareto optimal frontier solution set;

[0047] Figure 4 It is a standard test function optimization curve of an embodiment of the present invention;

[0048] Figure 5 This is a topological diagram of IEEE33 nodes after accessing DG according to an embodiment of the present invention;

[0049] Figure 6 The node voltage distribution before and after reconstruction after adding DG in an embodiment of the present invention;

[0050] Figure 7 The 35kV substation grid structure of the embodiment of the present invention;

[0051] Figure 8 This is a 35kV substation connection equivalent topology diagram according to an embodiment of the present invention;

[0052] Fig. 9 The present invention is a specific flow chart of a distribution network reconstruction method. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] The active distribution network strategy reconstruction method based on the improved grey wolf algorithm includes the following steps:

[0055] Step 1: Read the electrical data of the distribution network, confirm the switch status and the access location and constraints of the distributed power source, and construct a multi-objective reconstruction model of the distribution network according to the objective function. The specific steps are as follows:

[0056] 1. Multi-objective function

[0057] (1) Network loss

[0058] The mathematical model of the objective function to reduce the distribution network loss is as follows:

[0059]

[0060] Where: f1——total network loss of distribution network;

[0061] N——the number of all branches in the system;

[0062] k i ——Switch state, when k i =1 means the branch is closed. i =0 means the branch is disconnected;

[0063] R i ——is the resistance value of branch i;

[0064] P i , Q i ——represent the active power and reactive power of branch i respectively;

[0065] U i ——Indicates the voltage at the end of branch i;

[0066] (2) Node voltage offset

[0067] The smaller the node voltage offset, the more economical, stable and reliable the power supply system will be. The mathematical expression of the objective function corresponding to the node voltage offset index is as follows:

[0068]

[0069] Where: n——number of distribution network nodes;

[0070] Vi, ViN——actual voltage and rated voltage of node i;

[0071] (3) Number of switch operations

[0072] The mathematical model with the number of switching operations as the objective function is as follows:

[0073]

[0074] Where: K1, K2 – the number of section switches and tie switches on the system branch;

[0075] Yi, Zj - the state of the section switch and the tie switch after reconstruction, where the value "1" represents that the switch is in the closed state; conversely, the value "0" represents that the switch is in the open state;

[0076] 2. Constraints for distribution network reconstruction optimization:

[0077] (1) Power balance constraints

[0078]

[0079]

[0080] Where: Pi, Qi – active power and reactive power injected into node i;

[0081] P DGi , Q DGi ——The active power and reactive power injected by DG at node i;

[0082] P Li , Q Li ——active load and reactive load of node i;

[0083] N——Total number of nodes:

[0084] U i , U j——voltage amplitude of nodes i and j;

[0085] Gij, Bij – conductance and susceptance between nodes;

[0086] ε ij ,θ ij ——respectively, the susceptance and voltage phase angle difference between nodes i and j;

[0087] (2) Branch current constraints

[0088] I b，max ≥I b (11)

[0089] Where: l b，max ——The maximum current allowed in branch b;

[0090] I b ——The current flowing through branch b;

[0091] (3) Node voltage constraints

[0092] U d,max ≥U b ≥U d,min (12)

[0093] Where: Udmax——the maximum voltage allowed at node d;

[0094] Udmin——lower limit of voltage at node d.

[0095] (4) DG power generation constraints

[0096] P DGmin ≤P DGi ≤P DGmax (13)

[0097] Q DGmin ≤Q DGi ≤Q DGmax (14)

[0098] Where: P DGi , Q DGi ——The active power and reactive power of the i-th distributed generation;

[0099] P DGmin , P DGmax ————The maximum and minimum active power of the ith distributed generation;

[0100] Q DGmin , Q DGmax ——The maximum and minimum values ​​of reactive power of the i-th distributed generation;

[0101] (5) Network topology constraints

[0102] g k ∈G K (15)

[0103] Where: The distribution network must be a radial structure without islands or loops, g k is the reconstructed distribution network topology, G K Represents the set of all radial topologies formed.

[0104] Step 2: Decode the switch combination corresponding to the gray wolf individual, determine the initial Pareto candidate solution individual, screen the initial generation of candidate solutions and store them in Wset, the number of iterations K = 0.

[0105] Step 3: Calculate the fitness of each wolf in the population, retain the first three and select them as α wolf, β wolf, and δ wolf, and record their positions as X α , X β , X δ After each iteration, the control variables of the individual gray wolves are updated, and the search range of the prey is determined by these three wolves.

[0106] Step 4: The improved strategy includes using the improved Tent chaotic map for population initialization, improving the convergence factor, and the adaptive t-distribution perturbation mutation position update strategy to obtain the TGW0 algorithm.

[0107] As an innovative artificial intelligence optimization algorithm, the Gray Wolf Algorithm has attracted more and more researchers to conduct in-depth research on it. At present, the Gray Wolf Algorithm has been successfully applied to many fields, including industrial automatic control, virtual network architecture design, financial data analysis, etc. However, the algorithm industry is less involved in the electric power industry. Therefore, this chapter will focus on the distribution network reconstruction problem faced by the electric power industry and explore the potential application value and possibility of the Gray Wolf Algorithm.

[0108] First, select the gray wolf individuals based on the obtained values, retain the first three and select them as α wolf, β wolf, and δ wolf, and record their positions as X α , X β , X δ After each iteration, the control variables of the individual gray wolves are updated. These three wolves determine the search range of the prey, and the remaining candidates are all regarded as ω wolves. The ω wolves follow the α, β, and δ wolves to update their positions. After multiple iterations, the alpha wolf pack follows the prey's trail step by step, and finally achieves a comprehensive encirclement and capture of the prey.

[0109] (1) Surrounding the prey:

[0110] D=|C·X p(t)-X(t)| (16)

[0111] X(t+1)=X p (t)-A·D (17)

[0112] Where: D is the distance between the wolf pack and the prey;

[0113] A, C——coefficient vector;

[0114] t——current iteration number

[0115] X——position vector of the gray wolf;

[0116] X P ——The position vector of the prey.

[0117] The specific expressions of coefficients A and C are as follows:

[0118] A=2ar1-a (18)

[0119] C=2r2 (19)

[0120] In the formula, r1 and r2 are random numbers with a value range of [0, 1], and a is the convergence factor, which is defined as

[0121]

[0122] Where: n max is the maximum number of iterations of the algorithm. The convergence factor decreases linearly with the increase of the number of iterations, and its value range is [0, 2].

[0123] (2) Approaching prey

[0124] In the gray wolf algorithm, α wolf, β wolf, and δ wolf are the three candidate solutions for the initial design of the algorithm. The positions of these three wolves are generally the gray wolf individuals closest to the prey. The ω wolf will continuously update its own position based on the distance information with α wolf, β wolf, and δ wolf. The distance update between the gray wolves and the overall position update can be specifically expressed by the following formula:

[0125]

[0126] Where: Dα, Dβ, Dδ - represent the distance between the gray wolf individual and the α wolf, β wolf, and δ wolf respectively;

[0127] Xα, Xβ, Xδ——represent the current positions of α wolf, β wolf, and δ wolf respectively;

[0128] C1, C2, C3 – random coefficients;

[0129] X(t)——the current position of the individual gray wolf;

[0130] Under the guidance of gray wolves of various levels, the position of the wolf pack will also be updated. The position vector of the individual ω gray wolf is updated as follows:

[0131]

[0132]

[0133] Where: X1, X2, X3 - represent the step length and direction of the gray wolf under the guidance of α wolf, β wolf, and δ wolf respectively;

[0134] X(t+1)——represents the estimated position of the gray wolf individual after iterative updating.

[0135] The ω wolf basically starts to move only after the α wolf, β wolf, and δ wolf have determined their positions, and updates its own position, ensuring that the wolf pack as a whole continues to move closer to the location of the prey.

[0136] (3) Attacking prey

[0137] The gray wolf keeps approaching the prey. When the approach value reaches a critical value, the wolf pack will attack and kill the prey. In formula (20), the linear change of coefficient a simulates the process of the wolf pack approaching the prey. The value of a is [2, 0]. If the coefficient a decreases linearly, the value range of coefficient A will decrease accordingly. Then the value range of A is calculated to be [-4, 4]. We generally set the absolute value of A to be less than 1, which means that the wolf pack will attack when it falls into the local optimum.

[0138] Compared with other existing similar artificial intelligence algorithms, such as particle swarm optimization and genetic algorithm, the gray wolf algorithm shows better computing efficiency. However, like other swarm intelligence algorithms, GWO has the disadvantages of poor optimization accuracy, easy to fall into local optimal solution, low convergence speed and complex parameter setting. Therefore, the present invention proposes an improved lGWO algorithm. First, the improved Tent chaotic mapping optimizes the initial population of the gray wolf algorithm; then the convergence factor a is updated, the values ​​of A and C are calculated, and the position of the wolf pack is updated; finally, the adaptive t distribution perturbation mutation is used to perturb and mutate the gray wolf individuals to obtain the position of the new individuals. The specific improvement strategy is as follows:

[0139] (1) The improved Tent chaotic map optimizes the initial population of the grey wolf algorithm. The specific measures are as follows:

[0140] Tent mapping is the most commonly used chaotic mapping. The numerical distribution diagram of the chaotic mapping sequence generated by Tent mapping is as follows: Figure 1As shown, it can be seen that although the Tent mapping has good uniformity and a simpler structure, it has the disadvantages of strong autocorrelation and easy to fall into small periodic points and unstable periodic points. Therefore, this chapter proposes an improved Tent chaotic mapping method, which incorporates the random element rand(0,1)·1 / N into the initial Tent chaotic mapping formula. The specific expression is as follows:

[0141]

[0142] The expression after Bernoulli transformation is as follows:

[0143]

[0144] Where: N is the size of the algorithm population; x i is the i-th chaotic number, i = 1, 2, ... N; rand (0, 1) is any random number in the interval [0, 1]; mod represents the remainder operation; the specific implementation details and operation steps are as follows:

[0145] 1) Generate a random number x0 between (0, 1), i.e., i=0;

[0146] 2) Perform iterative calculation according to formula (25), and add 1 to the value of i each time a chaotic value is generated;

[0147] 3) When i reaches the maximum number of iterations N, save the generated chaotic sequence X;

[0148] 4) Map the chaotic sequence X to the gray wolf initial population search space according to formula (26).

[0149]

[0150] Where Ubj,min and Lbj,max represent the maximum and minimum ranges of the gray wolf search space respectively.

[0151] The numerical distribution of the improved Tent chaotic mapping sequence obtained after the improvement is as follows Figure 1 As shown, its mapping ergodicity is strong and the distribution probability volatility is smaller, which can effectively map and generate the initial gray wolf population location.

[0152] (2) Update the convergence factor a, calculate the values ​​of A and C, and update the position of the wolf pack. The specific measures are as follows:

[0153] The convergence factor a of the traditional grey wolf algorithm ranges from [0, 2]. The convergence factor shows a linear downward trend as the number of iterations increases, and the value of A in the corresponding formula (16) also changes accordingly. When the parameter |A|>1, the wolf pack will be forced to restart the global search to avoid falling into the local optimal solution. When |A|<1, the wolf pack will shrink its encirclement and fall into the local optimal solution, that is, the wolf pack will launch an attack. Therefore, controlling the balance of the convergence factor a will determine the global search capability and local development capability of the algorithm. However, since the convergence factor in the basic grey wolf algorithm decreases linearly, this will limit the algorithm from effectively coordinating between global and local searches. Therefore, the present invention proposes a new nonlinear convergence factor update formula:

[0154]

[0155] In the formula, a initial , a final are the initial value and final value of the convergence factor a respectively; t max The number of iterations is the maximum number of iterations; t is the current number of iterations; k1 and k2 are nonlinear adjustment coefficients. The convergence factor a changes nonlinearly and dynamically with the increase of the number of evolutionary iterations, which helps to balance the global and local search performance.

[0156] (3) Adaptive t-distribution perturbation variation. The specific measures are as follows:

[0157] Perturbation mutation is an auxiliary method for artificial intelligence algorithms to generate new individuals. This paper proposes a t-distribution perturbation mutation strategy to mutate gray wolf individuals. The t-distribution mathematically satisfies the probability density function with k degrees of freedom. Figure 2 is the function distribution graph, and formula (28) is the probability density formula.

[0158]

[0159] When the degree of freedom n is equal to 1, the t distribution turns into the standard Cauchy distribution, that is, t(n=1)→C(0,1); when n≥30, the offset can be ignored, and as n increases, the t distribution gradually turns into the standard Gaussian distribution, that is, t(n=∞)→N(0,1). From this, we can analyze that the standard cauchy distribution and the standard Gaussian distribution are special cases of the two boundary values ​​of the t distribution. Therefore, as the degree of freedom n changes, the t distribution has the advantages of both the Gaussian distribution and the Cauchy distribution.

[0160] Therefore, the present invention uses an adaptive t-distribution perturbation mutation strategy to add a perturbation mutation term xi·t(k) that obeys t-distribution to the original position of the gray wolf individual xi, thereby increasing the active search field of the gray wolf individual, so that they are no longer restricted from obtaining the optimization brought by the gray wolf update. The perturbation mutation of the gray wolf position using the adaptive t-distribution is shown in formula (21):

[0161] x′ j =x i +x i ·t(k) (29)

[0162] In the formula, represents the position of the gray wolf individual after the disturbance mutation of the t distribution, x i is the position of the i-th gray wolf individual, and t(k) indicates the t distribution with the number of iterations k as the degree of freedom parameter.

[0163] In the early stage of optimization, due to the limited search range of the algorithm, it is easy for individual wolves to fall into the local optimal solution. At this time, the perturbation variation term t(k)xi produces a large disturbance, which can cause the individual gray wolf to suddenly change its position, which helps the algorithm to jump out of the local extreme value; in the later stage of optimization, the main work of the algorithm is to conduct local and detailed optimization until the optimal solution is found, thereby improving the optimization accuracy of the algorithm. In this case, the number of iterations k is large, and the mutation effect of the t distribution at this time is equivalent to a Gaussian distribution. The random number generated by this mutation is close to the origin, and the perturbation variation term t(k)xi produces a small disturbance at this time. The gradual change of position of the individual gray wolf can increase the diversity of the population. At this time, the algorithm has a strong local search capability, and the optimization accuracy of the algorithm is improved.

[0164] Step 5: Maintain and update the external memory Wset, and update the dominance sorting according to the Pareto dominance relationship, such as Figure 3 As shown; if the external archive is full, then use the evaluation function to calculate the evaluation function values ​​of all Pareto alternative solutions in the solution set, sort them in descending order, and delete the parts that exceed the maximum capacity of Wset. The specific steps are as follows:

[0165] The present invention uses the Pareto optimal criterion to solve the multi-objective reconstruction optimization problem and uses the evaluation function to evaluate the obtained reconstruction combination. After each iteration of the reconstruction algorithm, a set of Pareto alternative solutions will be generated. However, in the multi-objective optimization problem of the distribution network, the optimization targets of each objective function are inconsistent, which makes it impossible to intuitively compare the quality of any two alternative solutions in the constraint set. Therefore, we need to establish an evaluation function formula (30) to select the obtained solution.

[0166]

[0167] Where, f(n) is the evaluation function value of the nth Pareto non-inferior solution; ω1, ω2, ω3 are the weight coefficients of multiple objectives, and satisfy ω1+ω2+ω3=1; f1(n), f2(n), f3(n) are the fitness function values ​​of the nth alternative solution under the three objective functions; f1 min 、f2 min 、f3 min They are the optimal fitness function values ​​of the three objective functions; f1 max 、f2 max 、f3 max They are the worst fitness function values ​​of the three objective functions respectively.

[0168] The present invention adopts the hierarchical analysis method to transform qualitative problems into quantitative problems for analysis through the levels of objectives, criteria, and schemes. The hierarchical analysis method is selected to calculate the weight coefficients of each part of the objective function. For the reconstruction optimization problem of the present invention, each objective can be graded according to its importance, with active network loss as the first-level objective, node voltage offset index as the second-level objective, and the number of switch operations as the third-level objective. It is calculated that ω1=0.562, ω2=0.312, and ω3=0.126.

[0169] Step 6: If the maximum number of iterations is reached, output the Pareto optimal solution set in Wset; otherwise, return to Step 2.

[0170] Embodiment 1:

[0171] To verify the performance of the TGWO algorithm, the present invention compares the improved gray wolf algorithm (TGWO) with the standard gray wolf search algorithm (GWO), the gray wolf search algorithm with improved convergence mode (NGWO), and the chaotic gray wolf search algorithm (CGWO). Set the population size N = 30, the convergence factor range is [0, 2], r 1、 r2∈[0,1], maximum number of iterations T=100.

[0172] (1) Test the improved Grey Wolf Algorithm (TGWO) to test the solving ability of the function in different dimensions. The present invention sets the test dimensions to d=10, d=30, and d=50 respectively. Table 1 records the best optimization results obtained by independently running the four optimization algorithms 30 times on two single-modal benchmark test functions, multi-modal benchmark test functions, and composite benchmark test functions. The size of the mean value and standard deviation in the table can reflect the optimization accuracy and robustness of the algorithm. The closer the mean value is to the optimal solution, the better the optimization accuracy of the algorithm. The closer the standard deviation is to 0, the better the robustness of the algorithm. Function

[0173]

[0174] Table 1 Test function optimization results

[0175] From the analysis of the above table, it can be seen that TGWO has solved the theoretical optimal value in the single-mode benchmark test functions F1, F2 and the composite benchmark test functions F5, F6 compared with the other three algorithms. Even if the theoretical optimal value is not solved under some multi-modal benchmark test functions F3 and F4, a solution very close to the theoretical optimal value can still be obtained. By comparison, it can be seen that the algorithm proposed in the present invention has higher optimization accuracy.

[0176] As the dimension increases, the mean and standard deviation of GWO, NGWO, and CGWO are greatly reduced. This is mainly because these algorithms themselves have the disadvantage of being easily trapped in local extreme values, and are more susceptible to the influence of local extreme values ​​in high-dimensional space, resulting in a decrease in optimization performance. In the process of improving the TGWO algorithm, improved Tent chaotic mapping, improved convergence factor, and adaptive t-distribution perturbation mutation strategy are introduced to improve the global search and local search capabilities of the algorithm. Even if the dimension of the test function continues to increase, the mean and standard deviation obtained by the optimization solution of the algorithm of the present invention do not change much, and the mean and standard deviation are closer to 0 than those of the other three algorithms, indicating that the improved Tent chaotic mapping, improved convergence factor, and adaptive t-distribution perturbation mutation strategy introduced in the process of algorithm improvement by TGWO not only improve the algorithm optimization accuracy and convergence speed, but also make the algorithm more robust.

[0177] (2) In order to more intuitively compare the convergence rate and optimization accuracy of the four algorithms, the present invention introduces the concept of convergence curve. In the convergence curves corresponding to the six test functions (all with a dimension of 30), the horizontal axis represents the number of iterations, and the vertical axis represents the fitness value, that is, the value of the test function. The earlier the inflection point appears on the curve, the faster the convergence speed, and the closer the fitness value is to the theoretical optimal value, the higher the search accuracy. At the same time, the ability of the algorithm to escape the local optimal solution can also be seen from the convergence curve.

[0178] The test function results are as follows Figure 4As shown, the fitness value in the figure is the test function value. It can be seen from the convergence curve that the TGWO algorithm has solved the theoretical optimal value on F1, F5, and F6, and an inflection point appears within a very short number of iterations. Compared with the convergence curves of other algorithms, the GWO convergence curve is relatively gentle, with few inflection points, and the algorithm falls into the local extreme value early in the optimization process and cannot jump out; although the convergence curves of NGWO and CGWO have inflection points earlier, the algorithm falls into the local optimal solution and cannot jump out when the number of iterations is very small, resulting in weak convergence performance of the algorithm. Although the TGWO algorithm did not find the theoretical optimal value on F2, F3, and F4, compared with the GWO, NGWO, and CGWO algorithms, the algorithm proposed in the present invention has solved a solution very close to the theoretical optimal value under the same number of iterations. By comparison, it is known that the algorithm proposed in the present invention has better optimization accuracy and convergence speed.

[0179] From the above analysis, it can be concluded that TGWO introduces improved Tent chaotic mapping, improved convergence factor, and adaptive t-distribution perturbation mutation strategy in the algorithm improvement process, which not only improves the algorithm optimization accuracy and convergence speed, but also makes the algorithm more robust.

[0180] Embodiment 2:

[0181] In this experiment, the convergence factor of the improved grey wolf algorithm is set in the range of [0,2], the initial population N = 50, and the maximum number of iterations T = 100. In order to summarize the effectiveness of the algorithm, the following experimental design is carried out. In order to verify the superiority of the present invention, the experiment is first carried out on the IEEE33 standard node. First, different types of DGs are connected to the IEEE-33 node system. The structural topology after connection is shown in the figure below. Figure 5 As shown, the DG access points, types and parameters are shown in Table 2.

[0182] Table 2 Parameters for connecting to different types of DG

[0183]

[0184]

[0185] The improved grey wolf algorithm is used to perform multi-objective static reconstruction of the active distribution network for the three objective functions of active power loss, voltage deviation index, and switch operation. The reconstruction is performed and solved, and finally a set of Pareto optimal solutions containing reconstruction schemes is obtained. The corresponding branch switch set after reconstruction, network loss, average number of iterations, and voltage deviation index are shown in Table 3.

[0186] Table 3 Pareto optimal reconstruction solution set after adding DG reconstruction

[0187]

[0188] In the multi-objective static reconstruction, the improved TGWO algorithm is used to generate simulation results of 12 schemes in only 17.58 seconds. Scheme 8 can minimize network loss, scheme 11 has the lowest voltage deviation, and scheme 7 has the smallest number of switch operations. There are 9 other solutions with relatively balanced performance and good optimization effects. The efficiency of the algorithm is greatly improved, and a variety of combination schemes also facilitate decision makers to better select the optimal solution according to actual conditions. When considering the maximum economic benefit and the minimum network loss, scheme 8 can be selected; when focusing on the life of the switch and operational safety, scheme 7 can be selected; when emphasizing the system voltage stability and reliability, scheme 11 with the smallest voltage deviation can be selected; when considering comprehensively, schemes 4 and 11 are two good choices. In terms of practical application, different schemes can be selected to solve different problems according to actual needs, which has certain practical significance.

[0189] According to the target fitness function value, we conclude that the distribution network architecture corresponding to optimization scheme 4 is a better reconstruction scheme. At this time, the set of branches disconnected from the grid structure is {S9, S12, S21, S32, S3}. Figure 6 It is the voltage per unit value of each node in the IEEE33-node system after the access to distributed generation (DG). Overall, after the access to DG, the node voltage of the network has increased. Especially in places where the original node voltage value is low, the voltage increase is particularly significant. On the contrary, the voltage of nodes with originally higher voltage values, such as node 1 and node 20, has hardly changed. This is because these nodes are close to the reference voltage node, so the voltage drop is small and the impact of DG is not obvious. Before the system reconstruction, the DG connected to the 8th node can effectively increase the voltage of the node and its surroundings (nodes 7, 8, and 9). In addition, node 31, as a branch terminal node, significantly increases the voltage of nodes 32 and 33 connected to it.

[0190] After the network reconstruction of the active distribution network containing DG, the node voltage of the network generally increased, and the overall voltage was closer to the rated voltage than before the reconstruction. The lowest voltage of the node before the reconstruction was 0.9131pu, and it reached 0.9582pu after the reconstruction. Compared with the reconstruction results before the DG distribution network was connected to the grid, the voltage stability standard level reached higher after the reconstruction in this section of the experiment was higher, the voltage distribution was more uniform after the reconstruction, and the network voltage quality was better improved. It can also be seen from the table that after the network reconstruction is implemented using the method proposed in the present invention, the network loss reduction rate reached 49.1%, which is also better than the performance in the previous section. It proves that the reconstruction algorithm is also applicable to the active distribution network containing DG, which helps to improve its economic benefits and safety performance. Therefore, the reconstruction strategy we proposed can significantly improve the various indicators of the active distribution network containing DG, proving the effectiveness and feasibility of the algorithm.

[0191] Embodiment 3:

[0192] Figure 7 The grid structure of Shuyuan Station and Donghai Station in a certain area. Both stations are 35kV substations, and each has 2 sections of 10kV busbars. Shuyuan Station has 10 10KV lines, and Donghai Station has 7 10KV lines. The present invention reconstructs and analyzes Shuyuan Station and Donghai Station. The entire distribution network structure meets the radial constraints, such as Figure 8 shown.

[0193] Table 4 DG grid-connected parameters

[0194]

[0195] Table 5 Pareto optimal reconstruction scheme set after actual distribution network reconstruction

[0196]

[0197]

[0198] It can be seen from Table 5 that after adopting the strategy proposed in the present invention, the network loss under the grid structure corresponding to the actual distribution network switch combination 11 under this operation mode is the smallest, which is 478.39kW, which is 31.04% less than before reconstruction; the node voltage offset under the grid structure corresponding to the switch combination 6 is the smallest, which is 0.0412, which is 55.87% less than before reconstruction; the number of switch operations under the grid corresponding to the switch combination 7 is the least.

[0199] Through in-depth research and analysis, we first made a comprehensive comparison of the experiments on the reconstruction of distribution networks with and without DG standard nodes, and then performed reconstruction optimization in the actual distribution network. The experiment shows that the algorithm of the present invention has extremely high efficiency and accuracy whether it is applied to standard nodes or actual distribution networks, and effectively solves the reconstruction problem in the power system, thereby significantly reducing the economic losses of the distribution network and improving the voltage quality, safety and stability of the power grid.

[0200] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. An active distribution network strategy reconstruction method based on an improved grey wolf algorithm is characterized in that: The following steps are involved: S1. First, read the electrical data of the distribution network, confirm the switch status and the access location and constraint conditions of the distributed power source, and build a mathematical model of multi-objective active distribution network static reconstruction under the premise of satisfying the power flow constraints, operation constraints, and topological structure constraints of the distribution network; S2. In view of some problems existing in the standard grey wolf algorithm in distribution network reconstruction, such as slow convergence speed, insufficient accuracy and weak robustness, the grey wolf algorithm is improved. The improvement strategy includes using improved Tent chaotic mapping for population initialization, improving convergence factor and adaptive t-distribution perturbation mutation position update strategy; S3. Use external files (Wset) combined with the Pareto dominance concept to update and improve the performance of the Pareto solution, and use the evaluation function to evaluate and select the obtained solutions.

2. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 1 is characterized in that: The gray wolf algorithm improvement strategy in step S2 includes the following steps: S2.1, optimize the initial population of the grey wolf algorithm through the improved Tent chaos map; S2.2, by improving and updating the convergence factor a, calculate the values ​​of A and C and update the position of the wolf pack; S2.

3. The positions of new individuals are obtained by perturbing and mutating the gray wolf individuals through adaptive t-distribution perturbation mutation.

3. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 1 is characterized in that: In step S2.1, the initial population of the grey wolf algorithm is optimized by using the improved Tent chaotic mapping method, which incorporates the random element rand (0, 1) 1 / N into the initial Tent chaotic mapping formula. The specific expression is as follows: The expression after Bernoulli transformation is as follows: Where: N is the size of the algorithm population; x i is the i-th chaotic number, i=1, 2, ...N; rand(0, 1) is any random number in the interval [0, 1]; mod represents the remainder operation.

4. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 3 is characterized by: The initial population of the grey wolf algorithm is optimized by using the improved Tent chaotic mapping. The random element rand(0, 1)·1 / N is incorporated into the initial Tent chaotic mapping formula. The operation steps are as follows: 1) Generate a random number x0 between (0, 1), i.e., i=0; 2) Perform iterative calculation according to formula (2), and add 1 to the value of i each time a chaotic value is generated; 3) When i reaches the maximum number of iterations N, save the generated chaotic sequence X; 4) Map the chaotic sequence X to the gray wolf initial population search space according to formula (3). Where Ubj,min and Lbj,max represent the maximum and minimum ranges of the gray wolf search space respectively.

5. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 2 is characterized in that: In S2.2, the convergence factor a formula is updated by improving: In the formula, a initial , a final are the initial value and final value of the convergence factor a respectively; t max The number of iterations is the maximum number of iterations; t is the current number of iterations; k1 and k2 are nonlinear adjustment coefficients. The convergence factor a changes nonlinearly and dynamically with the increase of the number of evolutionary iterations, which helps to balance the global and local search performance.

6. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 2 is characterized in that: In S2.3, the adaptive t-distribution perturbation mutation strategy is used by i Add x to the position i t(k) is a perturbation variation term that follows the t distribution, which increases the active search field of the gray wolf individuals, so that they are no longer restricted from obtaining the optimization brought by the gray wolf update.

7. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 6 is characterized in that: In S2.3, the position of the gray wolf is disturbed and mutated using adaptive t distribution as shown in formula (5): x′ i =x i +x i ·t(k) (5) In the formula, represents the position of the gray wolf individual after the disturbance mutation of the t distribution, xi is the position of the i-th gray wolf individual, and t(k) indicates the t distribution that satisfies the number of iterations k as the degree of freedom parameter.

8. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 1 is characterized in that: The specific steps are as follows: S1.

1. Multi-objective function S1 . 2 , constraints for distribution network reconstruction optimization.

9. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 8 is characterized in that: In the multi-objective function of S1.1, (1) Network loss The mathematical model of the objective function to reduce the distribution network loss is as follows: Where: f1——total network loss of distribution network; N—the number of all branches in the system; k i ——Switch state, when k i =1 means the branch is closed. i =0 means the branch is disconnected; R i ——is the resistance value of branch i; P i , Q i ——represent the active power and reactive power of branch i respectively; U i ——Indicates the voltage at the end of branch i; (2) Node voltage offset The smaller the node voltage offset, the more economical, stable and reliable the power supply system will be. The mathematical expression of the objective function corresponding to the node voltage offset index is as follows: Where: n——number of distribution network nodes; Vi, ViN——actual voltage and rated voltage of node i; (3) Number of switch operations The mathematical model with the number of switching operations as the objective function is as follows: Where: K1, K2 – the number of section switches and tie switches on the system branch; Yi, Zj - the state of the section switch and the tie switch after reconstruction, where the value "1" represents that the switch is in the closed state; conversely, the value "0" represents that the switch is in the open state.

10. The active distribution network strategy reconstruction method based on the improved grey wolf algorithm according to claim 8 is characterized in that: In the constraints of S1.2 and distribution network reconstruction optimization, (1) power balance constraint Where: Pi, Qi – active power and reactive power injected into node i; P DGi , Q DGi ——The active power and reactive power injected by DG at node i; P Li , Q Li ——active load and reactive load of node i; N——total number of nodes; U i , U j ——voltage amplitude of nodes i and j; Gij, Bij – conductance and susceptance between nodes; ε ij ,θ ij ——respectively, the susceptance and voltage phase angle difference between nodes i and j; (2) Branch current constraints I b，max ≥I b (11) Where: I b，max ——The maximum current allowed in branch b; I b ——The current flowing through branch b; (3) Node voltage constraints IN d，max ≥U b ≥U d，min (12) Where: Udmax——the maximum voltage allowed at node d; Udmin——lower limit of voltage at node d. (4) DG power generation constraints P DGmin ≤P DGi ≤P DGmax (13) Q DGmin ≤Q DGi ≤Q DGmax (14) Where: P DGi , Q DGi ——The active power and reactive power of the i-th distributed generation; P DGmin , P DGmax ——The maximum and minimum active power of the ith distributed generation; Q DGmin , Q DGmax ——The maximum and minimum values ​​of reactive power of the i-th distributed generation; (5) Network topology constraints g k ∈G K (15) Where: The distribution network must be a radial structure without isolated islands or loops, g k is the reconstructed distribution network topology, G K Represents the set of all radial topologies formed.

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