Distribution network fault reconstruction method based on improved Hippo optimization algorithm

Abstract

The present invention discloses a distribution network fault reconstruction method based on an improved Hippo optimization algorithm. The method uses connected components to perform fault recovery assessment, determines in advance the loads that can be restored by reconstruction, and reduces the complexity of problem solving. Next, encoding is performed in combination with a minimum ring set to map the solution space of the distribution network fault reconstruction problem to the search space of the algorithm. This encoding method can significantly increase the proportion of effective solutions. Then, the traditional Hippo optimization algorithm is improved in combination with the proposed encoding strategy to enable it to adapt to discrete optimization problems. Finally, the improved Hippo optimization algorithm is used to quickly solve the distribution network fault reconstruction strategy, thereby achieving rapid power supply restoration.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network fault reconstruction, and in particular to a distribution network fault reconstruction method based on an improved Hippo optimization algorithm. Background Art

[0002] In the vast and complex network of power systems, the distribution network, as the final link directly connecting to end users, has a significant impact on the quality and efficiency of power services. In particular, when faced with the common yet daunting challenge of line failures, quickly and efficiently restoring power has become a technical challenge that must be overcome for new power systems.

[0003] Rapid recovery from distribution network line faults is not only a test of technical capabilities but also a direct reflection of the resilience and emergency management capabilities of the power system. In traditional power systems, fault handling is often time-consuming and labor-intensive, relying on manual intervention, which is no longer sufficient in the fast-paced, high-efficiency modern world. Therefore, developing a mechanism that can respond immediately to faults and quickly develop distribution network line reconfiguration strategies is crucial to improving the overall performance of the power system. This can not only significantly shorten outages, reducing the resulting economic losses and social impact, but also enhance the power system's resilience to various risks, ensuring a secure and stable power supply.

[0004] While research on distribution network fault reconstruction has been conducted, several challenges remain. First, some studies fail to consider loads that cannot be restored through network reconstruction strategies. Second, while traditional analytical methods are theoretically rigorous, their computational efficiency is often unsatisfactory when dealing with complex and volatile real-world distribution networks. This is particularly true in large-scale distribution networks, where analytical methods significantly increase solution time, hindering emergency response speed.

[0005] To overcome this challenge, heuristic algorithms have gained popularity in recent years due to their flexibility and efficiency. However, the effectiveness of heuristic algorithms is highly dependent on specific algorithm selection and sophisticated coding strategies. Currently, in the field of distribution network fault reconstruction optimization, heuristic algorithms such as genetic optimization algorithms, ant colony optimization algorithms, and particle swarm optimization algorithms have been widely studied and applied to practical problems. However, each of these algorithms has certain limitations. Although genetic optimization algorithms have good global search capabilities, they tend to converge prematurely during the evolutionary process, resulting in local optimal solutions. When dealing with large-scale problems, the ant colony optimization algorithm may suffer from slow convergence due to the high computational complexity caused by the pheromone update mechanism. Although the particle swarm optimization algorithm has a simple structure and is easy to implement, it is sensitive to the choice of initial parameters during the search process and tends to lose diversity in high-dimensional complex problems, affecting the search effect.

[0006] In response to the shortcomings of these existing algorithms, the Hippopotamus Optimization Algorithm, as an innovative meta-heuristic algorithm, has demonstrated unique advantages. The Hippopotamus Optimization Algorithm simulates the foraging behavior of a hippopotamus group and, through its unique social interaction and environmental adaptation mechanism, achieves a balance between global exploration and local development, effectively avoiding the problem of premature convergence. In addition, the Hippopotamus Optimization Algorithm has a low dependence on parameter settings, which enables it to demonstrate good adaptability and robustness in distribution network fault reconstruction problems of different scales and structures. In terms of computational efficiency, the Hippopotamus Optimization Algorithm's efficient search mechanism ensures its rapid response capability during the solution process, which is crucial for real-time decision-making and grid restoration in emergency situations.

[0007] However, the native Hippo optimization algorithm, primarily designed for continuous variable optimization problems, has inherent limitations when dealing with problems with distinct discrete characteristics, such as distribution network fault reconfiguration. This involves a large number of switch state selections, a typical discrete optimization problem requiring the algorithm to find the optimal reconfiguration solution within a limited set of switch combinations. Summary of the Invention

[0008] The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and provide a distribution network fault reconstruction method based on an improved Hippo optimization algorithm. This method uses connected components to perform fault recovery assessment, determines in advance the loads that can be restored by reconstruction, and reduces the complexity of problem solving. Next, the solution space of the distribution network fault reconstruction problem is mapped to the search space of the algorithm in combination with the minimum ring set for encoding. This encoding method can greatly increase the proportion of effective solutions. Then, the traditional Hippo optimization algorithm is improved in combination with the proposed encoding strategy so that it can adapt to discrete optimization problems. Finally, the improved Hippo optimization algorithm is used to quickly solve the distribution network fault reconstruction strategy, thereby achieving rapid power restoration.

[0009] To achieve the above objectives, the present invention provides a technical solution: a distribution network fault reconstruction method based on an improved Hippo optimization algorithm, comprising the following steps:

[0010] S1: Abstract the power source and load as the vertices of the graph, and the lines and tie switches between the loads as the edges of the graph to construct an undirected graph model of the distribution network;

[0011] S2: Remove the edges corresponding to the fault line in the undirected graph model and use the connected components to perform fault recovery evaluation to determine the load that can be restored through reconstruction;

[0012] S3: Based on the loads that can be restored through reconstruction, a subgraph of the undirected graph model of the distribution network is constructed. This subgraph is then encoded using a minimal cycle set. The encoding strategy is to extract an edge from each minimal cycle to form different candidate solutions, thus forming a search space. This encoding strategy maps the solution space of the distribution network fault reconstruction problem to the algorithm's search space.

[0013] S4: Combined with the proposed encoding strategy, the initial population of the Hippo optimization algorithm is generated. Then, according to the characteristics of the candidate solutions obtained by the encoding strategy, the continuous search process of the Hippo optimization algorithm is improved through crossover and circular search methods, so that the Hippo optimization algorithm can be adapted to discrete optimization problems.

[0014] S5: Construct a mathematical model for distribution network fault reconstruction, including the maximum load recovery rate target, minimum number of switching operations target, minimum active power loss target, minimum voltage offset target, flow constraints, voltage constraints, branch current constraints and radial constraints. Use the improved Hippo optimization algorithm to solve the mathematical model of distribution network fault reconstruction, and thus obtain the optimal distribution network fault reconstruction strategy.

[0015] Furthermore, in step S1, the power source and the load are abstracted as the vertices V of the graph, and the lines and tie switches between the loads are abstracted as the edges E of the graph, and an undirected graph model G(V,E) is constructed.

[0016] Furthermore, the specific operation steps of step S2 are as follows:

[0017] S21: Remove the edge e corresponding to the fault line in the undirected graph model G(V,E) o , thus obtaining the distribution network model G after the fault o ;

[0018] S22: Solving for G o The Laplace matrix L(G o ):

[0019] L(G o )=D(G o )-A(G o )

[0020] Where: D(G o ) is G o The degree matrix of A(G o ) is G o The adjacency matrix of

[0021] S23: Determine the number of independent connected components: o) eigenvalues, the number of zero eigenvalues ​​is equal to the number of independent connected components, and the zero eigenvalue corresponds to k linearly independent eigenvectors, each representing an independent connected component. Therefore, solving L(G o ) can be used to obtain independent connected components:

[0022] L(G o )p=0

[0023] p=c1p1+c2p2+…+c k p k

[0024] Where: p is the characteristic vector; c k represents the coefficient of the kth linearly independent eigenvector; p k represents the kth linearly independent eigenvector;

[0025] S24: determining the fault recovery status according to the number of connected components, that is, the number of linearly independent eigenvectors corresponding to zero eigenvalues;

[0026] When k=1, it indicates that G o The network is still connected, so the load loss caused by the fault can be effectively restored through the power transfer strategy;

[0027] When k>1, it means G o It has been divided into multiple independent connected components. At this time, the recovery of part of the load cannot rely on the transfer strategy. In this case, the reconstruction strategy can only restore the load connected to the power source. By finding the power source v s The corresponding independent connected components, that is, in p k Find v s The corresponding variable is a eigenvector of 1, and the load corresponding to the variable with a value of 1 in the eigenvector is the same as v s Connectivity;

[0028] S25: According to the analysis results of the connected components, determine the load that can be restored by reconstruction, which is recorded as R.

[0029] Furthermore, the specific operation steps of step S3 are as follows:

[0030] S31: Construct G through R o The subgraph of s ;

[0031] S32: Use the minimum ring set algorithm to obtain G s All the minimal ring sets in are denoted as C1,C2,…,C j ,…,C m ; among them C m represents the mth smallest ring, C mis a set of edges, that is, {e C,1 ,e C,2 ,…,e C,a}, e C,a Indicates C m The ath side of ;

[0032] S33: Find the intersection of two minimum ring sets, denoted as CI1, CI2,…, CI n ; Among them, CI n represents the nth smallest ring intersection, CI n ={e CI,1 ,e CI,2 ,…,e CI,b}, e CI,b Indicates CI n The b-th side of ;

[0033] S34: shuffle C1, C2, ..., C j ,…,C m The order of C is selected from each minimum ring by intervention to form different candidate solutions, thus forming a search space. The intervention method is: when C is extracted, m The edge of CI n When it appears, avoid CI when extracting the remaining minimum ring n edge;

[0034] The purpose of the candidate solution is to s Remove all the edges of the smallest ring, thereby untangling all the smallest rings, so that G S into a radial form.

[0035] Furthermore, the specific operation steps of step S4 are as follows:

[0036] S41: Combine the encoding strategy to generate N candidate solutions, each of which represents a hippopotamus, and record them as the initial population X, as shown below:

[0037]

[0038] Where: X N is the Nth candidate solution, x Nm is the mth variable of the Nth candidate solution;

[0039] S42: Phase 1 search: Update the location of male hippos and immature hippos in the river. The specific steps are as follows:

[0040] The formula for updating the position of male hippopotamus is:

[0041]

[0042]

[0043] Where: K is half of N; X D is the position of the dominant hippopotamus, x D,m is the mth variable of the dominant hippopotamus, X M,i is the position of the i-th male hippopotamus, X M,ij is the jth variable of the ith male hippopotamus; F is the fitness function; r1 is a random number in [0,1], rand is a random number in [0,1] generated for each judgment; [] is rounding, argmin() means finding the candidate solution with the smallest function value from all candidate solutions;

[0044] Immature hippopotamus position update formula:

[0045]

[0046] When τ≥0.6, X FB,i :x FB,ij =choice(y 1j ,y 2j ,…,y Kj ), for i=1,2,…,K, for j=1,2,…,m;

[0047] When τ<0.6, in C1, C2,…, C j ,…,C m Remove the current candidate solution X i The corresponding element, and according to the encoding strategy, regenerate a candidate solution as the immature hippopotamus X FB,i location;

[0048] Where: τ is the condition for immature hippos to leave the hippo group, T is the maximum number of iterations, t is the current number of iterations; sample(X,K) means randomly sampling K from X, choice() means randomly sampling 1 from the element; Y is the hippo group after sampling, Y i is the i-th candidate solution, y ij is the jth variable of the i-th candidate solution; X FB,i is the position of the i-th immature hippopotamus, x FB,ij is the jth variable of the i-th immature hippopotamus;

[0049] Update the candidate solution based on the positions of males and immature hippos in the hippo herd as follows:

[0050]

[0051] S43: The second phase of the search, the hippo defends against predators, the specific steps are as follows:

[0052] Combined with the encoding strategy, a candidate solution is generated as a predator, denoted as X P,i According to the coding strategy, the predator and the hippopotamus are in the same minimum ring. At this time, there are two paths for each variable of the hippopotamus and the predator, which are the shortest distance E s,i and the longest distance E l,i , as shown below:

[0053] E s,i =[e s,1 e s,2 …e s,o ]

[0054] E l,i =[e l,1 e l,2 …e l,u ]

[0055] Where: e s,o is the oth edge of the shortest path, e l,u is the u-th edge of the longest path;

[0056] When hippos face predators, they use two strategies to protect themselves: driving away and attacking, as shown below:

[0057]

[0058] Where: X R,i is the position of the i-th hippopotamus when facing the predator, x R,ij is the jth variable of the position of the i-th hippopotamus when facing the predator, x P,ij is the jth variable of the i-th predator; levy j is the Levy distribution value of the j-th variable, ζ is the long jump threshold, is an intermediate variable;

[0059] Update the candidate solution based on the hippopotamus's position when facing the predator as follows:

[0060]

[0061] S44: The third phase of the search, the hippo escapes from the predator. The specific steps are as follows:

[0062] When the hippopotamus cannot defend against predators, it will leave the current area and run to the nearest river to avoid being hurt by predators. Combined with the coding strategy, the safe location near the hippopotamus is represented by C1, C2, ..., C j ,…,C m Remove the current candidate solution X i The corresponding remaining elements are composed, and the range of the safe position decreases with the number of iterations, as shown below:

[0063]

[0064]

[0065] Where: X E,i Find a safe location for the i-th hippopotamus, x E,ij Find the jth variable of a safe location for the i-th hippopotamus; |C j | means C j The number of elements in Describe the set after sampling the jth minimum ring;

[0066] Update the candidate solution based on the safe position found by the hippopotamus, as shown below:

[0067]

[0068] Furthermore, the specific operation steps of step S5 are as follows:

[0069] S51: Establishing the objective function of distribution network fault reconstruction, taking into account the fault recovery objective: maximum load recovery rate objective f1, and network reconstruction objectives: minimum number of switching operations f2, minimum network loss f3, and minimum voltage deviation f4, as shown below:

[0070]

[0071] f2=min(|B|+|L|)

[0072]

[0073] Where: P v is the active load of vertex v; B is the set of sectional switches that need to be operated, L is the set of tie switches that need to be operated; I e is the current on edge e, r e is the resistance of edge e; U v is the voltage at vertex v, U N is the reference voltage;

[0074] S52: Combining the objective function and the constraint conditions, a constraint function for distribution network reconstruction after a fault is established, including:

[0075] a. Power flow constraints:

[0076]

[0077] Where: Q V is the reactive power of vertex v, P in,v is the active power flowing into vertex v, P out,v is the active power flowing out of vertex v, Qin,v is the reactive power flowing into vertex v, Q out,v is the reactive power flowing out of vertex v;

[0078] b. Voltage constraint:

[0079] U v,min ≤U v ≤U v,max

[0080] Where: U v,min is the lower limit of the voltage at vertex v, U v,max is the upper voltage limit of vertex v;

[0081] c. Branch current constraints:

[0082] I e ≤I e,max

[0083] Where: I e,max is the upper limit of the current of edge e;

[0084] d. Radial constraints:

[0085]

[0086] Where: G r is the graph after fault reconstruction, rank() represents the rank of the matrix, |V r | for G r The number of vertices, |E r | for G r The number of edges;

[0087] S53: Establishing a fitness function F for distribution network fault reconstruction;

[0088] Since the primary goal of a distribution network failure is to restore the load, all loads should be restored as much as possible. R has been determined from step S2, so each fault reconstruction strategy must restore R to ensure the primary goal. Therefore, the restored load remains unchanged. Therefore, f1 is not considered in the fitness function, and its fitness function is:

[0089] F=w2f2+w3f3+w4f4

[0090] Where: w2, w3 and w4 are weight coefficients;

[0091] When any constraint in step S52 is not satisfied, the fitness function is:

[0092] F=M

[0093] Where: M is the penalty coefficient;

[0094] S54: Use the improved Hippo optimization algorithm to solve F, and when t>T, output the optimal fault reconstruction strategy.

[0095] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0096] 1. The present invention uses connected components to perform fault recovery assessment and determines in advance the load that can be restored by reconstruction, thereby reducing the difficulty of problem solving.

[0097] 2. This paper proposes a coding strategy that can effectively increase the proportion of feasible solutions, thereby improving the solution efficiency of the Hippo optimization algorithm.

[0098] 3. The present invention improves the Hippo optimization algorithm by modifying its continuous search process, thereby adapting it to discrete optimization problems. Furthermore, the improved Hippo optimization algorithm retains the advantages of the original Hippo optimization algorithm and outperforms the traditional Hippo optimization algorithm and other types of optimization algorithms in solving distribution network fault reconstruction problems.

[0099] In summary, this paper can effectively solve the distribution network fault reconstruction problem, thereby achieving rapid fault response and power restoration, reducing the impact on users and economic losses. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 Flowchart of the method of the present invention.

[0101] Figure 2 It is an IEEE 33-node standard network.

[0102] Figure 3 Flowchart for improving the Hippo optimization algorithm.

[0103] Figure 4 Schematic diagram of the different strategies a hippopotamus will adopt when facing a predator.

[0104] Figure 5 A comparison chart of the solution results of the improved Hippo optimization algorithm (IHO), Hippo optimization algorithm (HO), Grey Wolf optimization algorithm (GWO), Genetic algorithm (GA), Particle Swarm Optimization algorithm (PSO) and Energy Valley Optimization algorithm (EVO). DETAILED DESCRIPTION

[0105] The present invention will be further described below with reference to specific embodiments.

[0106] like Figure 1 As shown, this embodiment discloses a distribution network fault reconstruction method based on an improved Hippo optimization algorithm, which specifically includes the following steps:

[0107] 1) Construct an undirected graph model of the distribution network.

[0108] by Figure 2 Taking the distribution network of as an example, the loads and power sources of the distribution network are abstracted as the vertices V of the graph, and the lines between the loads are abstracted as the edges E of the graph, and an undirected graph model G(V,E) is constructed.

[0109] V and E are as follows:

[0110] V={v1,v2,v3,v4,v5,v6,v7,v8,v9,v 10 ,v 11 ,v 12 ,v 13 ,v 14 ,v 15 ,v 16 ,v 17 ,v 18 ,v 19 ,v 20 ,v 21 ,v 22 ,v 23 ,v 24 ,v 25 ,v 26 ,v 27 ,v 28 ,v 29 ,v 30 ,v 31 ,v 32 ,v 33}

[0111] E={e1,e2,e3,e4,e5,e6,e7,e8,e9,e 10 ,e 11 ,e 12 ,e 13 ,e 14 ,e 15 ,e 16 ,e 17 ,e 18 ,e 19 ,e 20 ,e 21 ,e 22 ,e 23 ,e 24 ,e 25 ,e 26 ,e 27 ,e 28 ,e 29 ,e 30 ,e 31 ,e 32 ,e 33 ,e 34 ,e 35 ,e36 ,e 37}

[0112] The specific parameters of the network are shown in the following table.

[0113] Table 1 IEEE33 node parameters

[0114]

[0115]

[0116] 2) Based on the constructed undirected graph model, perform fault recovery pre-assessment.

[0117] from Figure 2 It can be seen that line 4 is disconnected due to a fault. Then, the edge e corresponding to the faulty line is removed from G(V,E) o , where e o =e4. Thus, the distribution network model G after the fault is obtained o .

[0118] a. Solve for G o Independent connected components of G o The Laplace matrix L(G o ):

[0119] L(G o )=D(G o )-A(G o )

[0120] b. Solve L(G o ) of the homogeneous linear equations, thus obtaining G o Independent connected components:

[0121] L(G o )p=0

[0122] p=c1p1+c2p2+…+c k p k

[0123] L(G o ) has only one linearly independent eigenvector, k=1.

[0124] c, k=1 indicates G o It is still connected, so the load loss caused by the fault can be effectively restored through the power transfer strategy, that is, the load restored by reconstruction is R=V.

[0125] 3) Based on the load R that can be restored by reconstruction, a subgraph of the undirected graph model of the distribution network is constructed. The subgraph is then encoded using the minimal ring set of the subgraph. The encoding strategy is to take one edge from each minimal ring to form different candidate solutions, thus forming a search space. Through this encoding strategy, the solution space of the distribution network fault reconstruction problem is mapped to the search space of the algorithm.

[0126] a. Construct G through R o The subgraph of s Get G s The set of all minimal rings in :

[0127] C1={e2,e6,e7,e 18 ,e 19 ,e 20 ,e 22 ,e 23 ,e 24 ,e 25 ,e 26 ,e 27 ,e 28 ,e 33 ,e 37}

[0128] C2={e8,e9,e 10 ,e 11 ,e 21 ,e 33 ,e 35}

[0129] C3={e6,e7,e8,e 15 ,e 16 ,e 17 ,e 25 ,e 26 ,e 27 ,e 28 ,e 29 ,e 30 ,e 31 ,e 32 ,e 34 ,e 36}

[0130] C4={e9,e 10 ,e 11 ,e 12 ,e 13 ,e 14 ,e 34}

[0131] b. After obtaining the minimum ring set, find the intersection between the two minimum ring sets:

[0132] CI1={e 33}

[0133] CI2={e6,e7,e 25 ,e 26 ,e 27 ,e 28}

[0134] CI3={e8}

[0135] CI4={e9,e 10 ,e 11}

[0136] CI5={e 34}

[0137] c. Taking the above results as an example, the encoding strategy of the present invention is illustrated.

[0138] The first step is to disrupt the extraction order, such as: C2→C4→C1→C3.

[0139] The second step is to extract an edge from C2 in a shuffled order, such as e 33 Because, e 33 It is located in CI1, so the subsequent minimal rings C4, C1, and C3 cannot have edges in CI1.

[0140] The third step is to extract an edge from C4 in the shuffled order. Since there is no edge in CI1 in C4, it is not necessary to do too much to select an edge from C4, such as e 12 At this time, e 12 Not in CI n appears, go directly to the next step.

[0141] Step 4: Extract an edge from C1 in the shuffled order. Since C1 contains an edge from CI1, we need to remove the edge from CI1 in C1 and then randomly extract an edge, such as e 25 At this time, e 25 Appears in CI2, so the subsequent minimal ring C3 cannot have edges in CI2.

[0142] Step 5: Extract an edge from C3 in the shuffled order. Since there is an edge in CI2 in C3, we need to remove the edge in CI2 from C3 and then randomly extract an edge, such as e 32 .

[0143] According to the above process, a candidate solution is obtained, where the positions of the candidate solutions are still sorted in the original order, that is, C1→C2→C3→C4. The candidate solution is e 25 , e 33 , e 32 , e 12 , the candidate solution represents thes Remove these edges so that G s Restore radial shape.

[0144] d. Advantages of the encoding strategy proposed by the present invention.

[0145] At present, the common coding methods for distribution network fault reconstruction are: binary coding and decimal ring coding strategy. s For example, the search space of binary encoding strategy is 2 36 The search space of the decimal ring coding strategy is 11760, while the search space of the coding strategy proposed in the present invention is only 8633.

[0146] The number of valid solutions is G s The number of spanning trees is 7629. The effective solution ratio of the binary coding strategy is 0.00001%, the effective solution ratio of the decimal ring coding strategy is 64.87%, and the effective solution ratio of the coding strategy proposed in the present invention is 88.37%.

[0147] Obviously, the coding strategy proposed in the present invention can significantly increase the proportion of valid solutions. Therefore, the coding strategy proposed in the present invention is superior to the binary coding strategy and the decimal ring coding strategy.

[0148] 4) Establish a mathematical model for distribution network reconstruction, including the maximum load recovery rate target, minimum number of switching operations target, minimum active power loss target, minimum voltage offset target, flow constraints, voltage constraints, branch current constraints and radial constraints.

[0149] a. Establish the objective function for distribution network fault reconstruction, taking into account the fault recovery goal: maximum load recovery rate target f1, as well as the network reconstruction goals: minimum number of switching operations f2, minimum network loss f3, and minimum voltage offset f4. The specific functions are as follows:

[0150]

[0151] f2=min(|B|+|L|)

[0152]

[0153] Where: P v is the active load of vertex v; B is the set of sectional switches that need to be operated, L is the set of tie switches that need to be operated; I e is the current on edge e, r e is the resistance of edge e; U v is the voltage at vertex v, U N is the reference voltage.

[0154] b. Combine the objective function and constraints to establish the constraint function for distribution network reconstruction after a fault, including:

[0155] Power flow constraints:

[0156]

[0157] Where: Q V is the reactive power of vertex v, P in,v is the active power flowing into vertex v, P out,v is the active power flowing out of vertex v, Q in,v is the reactive power flowing into vertex v, Q out,v is the reactive power flowing out of vertex v;

[0158] Voltage Constraints:

[0159] U v,min ≤U v ≤U v,max

[0160] Where: U v,min is the lower limit of the voltage at vertex v, U v,max is the upper voltage limit of vertex v;

[0161] Branch current constraints:

[0162] I e ≤I e,max

[0163] Where: I e,max is the upper limit of the current of edge e;

[0164] Radial constraints:

[0165]

[0166] Where: G r is the graph after fault reconstruction, rank() represents the rank of the matrix, |V r | for G r The number of vertices, |E r | for G r c. Establish the appropriate function F for distribution network fault reconstruction

[0167] Since the primary goal of a distribution network failure is to restore load, it is crucial to restore all loads as much as possible. Since R has already been determined in step 2), each fault reconstruction strategy must restore R to ensure this primary goal. Based on R, the value of the f1 target is 1, indicating that all loads can be fully restored through reconstruction.

[0168] Since f1 has been determined, f1 is not considered in the fitness function, and F is:

[0169] F=w2f2+w3f3+w4f4

[0170] At this time, the weights can be adjusted according to the needs. For example, if the fault line repair time is long, then the fault reconstruction will have to run for a long time. At this time, the voltage offset and network loss will become more important. The values ​​of w3 and w4 can be increased to ensure that the fault reconstruction solution has the smallest voltage offset and network loss.

[0171] When any of the constraints in b above is not met, the fitness function is:

[0172] F=M

[0173] If the value obtained is M, it means that no feasible fault reconstruction solution has been found. In this case, the maximum iteration parameter of the optimization algorithm needs to be adjusted to increase the search time and search range of the algorithm.

[0174] 5) Use the improved Hippo optimization algorithm to solve the mathematical model of distribution network fault reconstruction, so as to obtain the optimal distribution network fault reconstruction strategy. Among them, the improved Hippo optimization algorithm process is as follows Figure 3 As shown, the following specifically explains how to use the improved Hippo optimization algorithm to solve the mathematical model of distribution network fault reconstruction.

[0175] 5.1) Initialization settings.

[0176] Combined with the encoding strategy, N candidate solutions are generated, each candidate solution represents a hippopotamus, and recorded as the initial population X, as shown below:

[0177]

[0178] Where: X N is the Nth candidate solution, x Nm is the mth variable of the Nth candidate solution;

[0179] 5.2) Phase 1 Search: Update the location of male hippos and immature hippos in the river. The specific steps are as follows:

[0180] The formula for updating the position of male hippopotamus is:

[0181]

[0182]

[0183] Where: K is half of N; X D is the position of the dominant hippopotamus, x D,m is the mth variable of the dominant hippopotamus, X M,i is the position of the i-th male hippopotamus, X M,ijis the jth variable of the ith male hippopotamus; F is the fitness function; r1 is a random number in [0,1], rand is a random number in [0,1] generated for each judgment; [] is rounding, argmin() means finding the candidate solution with the smallest function value from all candidate solutions;

[0184] Immature hippopotamus position update formula:

[0185]

[0186] When τ≥0.6, X FB,i :x FB,ij =choice(y 1j ,y 2j ,…,y Kj ), for i=1,2,…,K, for j=1,2,…,m;

[0187] When τ<0.6, in C1, C2,…, C j ,…,C m Remove the current candidate solution X i The corresponding element, and according to the encoding strategy, regenerate a candidate solution as the immature hippopotamus X FB,i location;

[0188] Where: τ is the condition for immature hippos to leave the hippo group, T is the maximum number of iterations, t is the current number of iterations; sample(X,K) means randomly sampling K from X, choice() means randomly sampling 1 from the element; Y is the hippo group after sampling, Y i is the i-th candidate solution, y ij is the jth variable of the i-th candidate solution; X FB,i is the position of the i-th immature hippopotamus, x FB,ij is the jth variable of the i-th immature hippopotamus;

[0189] Update the candidate solution based on the positions of males and immature hippos in the hippo herd as follows:

[0190]

[0191] 5.3) In the second stage of search, the hippopotamus defends against predators, e.g. Figure 4 The specific steps are as follows:

[0192] Combined with the encoding strategy, a candidate solution is generated as a predator, denoted as X P,i According to the coding strategy, the predator and the hippopotamus are in the same minimum ring. At this time, there are two paths for each variable of the hippopotamus and the predator, which are the shortest distance E s,i and the longest distance E l,i, as shown below:

[0193] E s,i =[e s,1 e s,2 …e s,o ]

[0194] E l,i =[e l,1 e l,2 …e l,u ]

[0195] Where: e s,o is the oth edge of the shortest path, e l,u is the u-th edge of the longest path;

[0196] When hippos face predators, they use two strategies to protect themselves: driving away and attacking, as shown below:

[0197]

[0198] Where: X R,i is the position of the i-th hippopotamus when facing the predator, x R,ij is the jth variable of the position of the i-th hippopotamus when facing the predator, x P,ij is the jth variable of the i-th predator; levy j is the Lévy distribution value of the j-th variable, ζ is the long jump threshold, and Ξ is the intermediate variable;

[0199] Update the candidate solution based on the hippopotamus's position when facing the predator as follows:

[0200]

[0201] 5.4) The third phase of the search, in which the hippopotamus escapes from the predator, involves the following steps:

[0202] When the hippopotamus cannot defend against predators, it will leave the current area and run to the nearest river to avoid being hurt by predators. Combined with the coding strategy, the safe location near the hippopotamus is represented by C1, C2, ..., C m Remove the current candidate solution X i The corresponding remaining elements are composed, and the range of the safe position decreases with the number of iterations, as shown below:

[0203]

[0204]

[0205] Where: X E,i Find a safe location for the i-th hippopotamus, x E,ijFind the jth variable of a safe location for the i-th hippopotamus; |C j | means C j The number of elements in

[0206] Update the candidate solution based on the safe position found by the hippopotamus, as shown below:

[0207]

[0208] 5.5) Record the current optimal result. When t>T, output the global optimal result, that is, the optimal distribution network fault reconstruction strategy. Otherwise, return to step 5.2).

[0209] In order to verify the method proposed by the present invention, adopt improved Hippopotamus optimization algorithm (IHO), Hippopotamus optimization algorithm (HO), Gray Wolf optimization algorithm (GWO), genetic algorithm (GA), particle swarm optimization algorithm (PSO) and energy valley optimization algorithm (EVO) to carry out comparative experiment.Because the improved Hippopotamus optimization algorithm (IHO) proposed by the present invention is improved according to the coding strategy proposed by the present invention, so other optimization algorithm can not use same coding strategy.Therefore, Hippopotamus optimization algorithm (HO), Gray Wolf optimization algorithm (GWO), genetic algorithm (GA), particle swarm optimization algorithm (PSO) and energy valley optimization algorithm (EVO) all adopt decimal ring coding strategy to encode.

[0210] The above distribution network fault case is used, and the above constructed F is used as input. Then, the improved Hippo optimization algorithm (IHO), Hippo optimization algorithm (HO), Grey Wolf optimization algorithm (GWO), genetic algorithm (GA), particle swarm optimization algorithm (PSO) and energy valley optimization algorithm (EVO) are used to solve the problem. The solution results are shown as follows: Figure 5 shown.

[0211] Experimental conclusion: Figure 5 It can be seen that the Improved Hippopotamus Optimization Algorithm (IHO) outperforms the Hippopotamus Optimization Algorithm (HO), the Grey Wolf Optimization Algorithm (GWO), the Genetic Algorithm (GA), the Particle Swarm Optimization Algorithm (PSO), and the Energy Valley Optimization Algorithm (EVO). Compared to other algorithms, the Improved Hippopotamus Optimization Algorithm is able to find the global optimal solution in a very short number of iterations.

[0212] The above-described embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, any changes made based on the shape and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A distribution network fault reconstruction method based on an improved Hippo optimization algorithm is characterized by: The following steps are involved: S1: Abstract the power source and load as the vertices of the graph, and the lines and tie switches between the loads as the edges of the graph to construct an undirected graph model of the distribution network; S2: Remove the edges corresponding to the faulty line in the undirected graph model and use the connected components to perform fault recovery assessment to determine the load that can be restored through reconstruction. The operation steps are as follows: S21: Remove the edge e corresponding to the fault line in the undirected graph model G(V,E) o , thus obtaining the distribution network model G after the fault o ; S22: Solving for G o The Laplace matrix L(G o ): L(G o )=D(G o )-A(G o ) Where: D(G o ) is G o The degree matrix of A(G o ) is G o The adjacency matrix of S23: Determine the number of independent connected components: o ) eigenvalues, the number of zero eigenvalues ​​is equal to the number of independent connected components, and the zero eigenvalue corresponds to k linearly independent eigenvectors, each representing an independent connected component. Therefore, solving L(G o ) can be used to obtain independent connected components: L(G o )p=0 p=c1p1+c2p2+…+c k p k Where: p is the characteristic vector; c k represents the coefficient of the kth linearly independent eigenvector; p k represents the kth linearly independent eigenvector; S24: determining the fault recovery status according to the number of connected components, that is, the number of linearly independent eigenvectors corresponding to zero eigenvalues; When k=1, it indicates that G o The network is still connected, so the load loss caused by the fault can be effectively restored through the power transfer strategy; When k>1, it means G o It has been divided into multiple independent connected components. At this time, the recovery of part of the load cannot rely on the transfer strategy. In this case, the reconstruction strategy can only restore the load connected to the power source. By finding the power source v s The corresponding independent connected components, that is, in p k Find v s The corresponding variable is a eigenvector of 1, and the load corresponding to the variable with a value of 1 in the eigenvector is the same as v s Connectivity; S25: According to the analysis results of the connected components, determine the load that can be restored by reconstruction, which is recorded as R; S3: Based on the loads that can be restored through reconstruction, a subgraph of the undirected graph model of the distribution network is constructed. The subgraph is then encoded using the minimal cycle set of the subgraph. The encoding strategy is to extract one edge from each minimal cycle to form different candidate solutions, thus forming a search space. This encoding strategy maps the solution space of the distribution network fault reconstruction problem to the search space of the algorithm. The steps are as follows: S31: Construct G through R o The subgraph of s ; S32: Use the minimum ring set algorithm to obtain G s All the minimal ring sets in are denoted as C1,C2,…,C j ,…,C m ; among them C m represents the mth smallest ring, C m is a set of edges, that is, {e C,1 ,e C,2 ,…,e C,a }, e C,a Indicates C m The ath side of ; S33: Find the intersection of the two smallest ring sets, denoted as CI1, CI2,…, CI n ; Among them, CI n represents the nth smallest ring intersection, CI n ={e CI,1 ,e CI,2 ,…,e CI,b }, e CI,b Indicates CI n The b-th side of ; S34: shuffle C1, C2, ..., C j ,…,C m The order of C is selected from each minimum ring by intervention to form different candidate solutions, thus forming a search space. The intervention method is: when C is extracted, m The edge of CI n When it appears, avoid CI when extracting the remaining minimum ring n edge; The purpose of the candidate solution is to s Remove all the edges of the smallest ring, thereby untangling all the smallest rings, so that G S into a radial form; S4: Combine the proposed encoding strategy to generate the initial population of the Hippo optimization algorithm. Then, based on the characteristics of the candidate solutions obtained by the encoding strategy, the continuous search process of the Hippo optimization algorithm is improved through crossover and circular search methods, so that the Hippo optimization algorithm can be adapted to discrete optimization problems. The operation steps are as follows: S41: Combine the encoding strategy to generate N candidate solutions, each of which represents a hippopotamus, and record them as the initial population X, as shown below: Where: X N is the Nth candidate solution, x Nm is the mth variable of the Nth candidate solution; S42: Phase 1 search: Update the location of male hippos and immature hippos in the river. The specific steps are as follows: The formula for updating the position of male hippopotamus is: Where: K is half of N; X D is the position of the dominant hippopotamus, x D,m is the mth variable of the dominant hippopotamus, X M,i is the position of the i-th male hippopotamus, X M,ij is the jth variable of the ith male hippopotamus; F is the fitness function; r1 is a random number in [0,1], rand is a random number in [0,1] generated for each judgment; [] is rounding, argmin() means finding the candidate solution with the smallest function value from all candidate solutions; Immature hippopotamus position update formula: When τ ≥ 0.6, X FB,i : x FB,ij = choice(y 1j , y 2j , …, y Kj ), for i = 1, 2, …, K, for j = 1, 2, …, m; When τ<0.6, in C1, C2,…, C j ,…,C m Remove the current candidate solution X i The corresponding element, and according to the encoding strategy, regenerate a candidate solution as the immature hippopotamus X FB,i location; Where: τ is the condition for immature hippos to leave the hippo group, T is the maximum number of iterations, t is the current number of iterations; sample(X,K) means randomly sampling K from X, choice() means randomly sampling 1 from the element; Y is the hippo group after sampling, Y i is the i-th candidate solution, y ij is the jth variable of the i-th candidate solution; X FB,i is the position of the i-th immature hippopotamus, x FB,ij is the jth variable of the i-th immature hippopotamus; Update the candidate solution based on the positions of males and immature hippos in the hippo herd as follows: S43: The second phase of the search, the hippo defends against predators, the specific steps are as follows: Combined with the encoding strategy, a candidate solution is generated as a predator, denoted as X P,i According to the coding strategy, the predator and the hippopotamus are in the same minimum ring. At this time, there are two paths for each variable of the hippopotamus and the predator, which are the shortest distance E s,i and the longest distance E l,i , as shown below: AND s,i =[and s,1 And s,2 …And s,o ] AND l,i =[and l,1 And l,2 …And l,u ] Where: e s,o is the oth edge of the shortest path, e l,u is the u-th edge of the longest path; When hippos face predators, they use two strategies to protect themselves: driving away and attacking, as shown below: Where: X R,i is the position of the i-th hippopotamus when facing the predator, x R,ij is the jth variable of the position of the i-th hippopotamus when facing the predator, x P,ij is the jth variable of the i-th predator; levy j is the Levy distribution value of the j-th variable, ζ is the long jump threshold, is an intermediate variable; Update the candidate solution based on the hippopotamus's position when facing the predator as follows: S44: The third phase of the search, the hippo escapes from the predator. The specific steps are as follows: When the hippopotamus cannot defend against predators, it will leave the current area and run to the nearest river to avoid being hurt by predators. Combined with the coding strategy, the safe location near the hippopotamus is represented by C1, C2, ..., C j ,…,C m Remove the current candidate solution X i The corresponding remaining elements are composed, and the range of the safe position decreases with the number of iterations, as shown below: Where: X E,i Find a safe location for the i-th hippopotamus, x E,ij Find the jth variable of a safe location for the i-th hippopotamus; |C j | means C j The number of elements in Describe the set after sampling the jth minimum ring; Update the candidate solution based on the safe position found by the hippopotamus, as shown below: S5: Construct a mathematical model for distribution network fault reconstruction, including the maximum load recovery rate target, minimum number of switching operations target, minimum active power loss target, minimum voltage offset target, flow constraints, voltage constraints, branch current constraints and radial constraints. Use the improved Hippo optimization algorithm to solve the mathematical model of distribution network fault reconstruction, and thus obtain the optimal distribution network fault reconstruction strategy.

2. The distribution network fault reconstruction method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: In step S1, the power source and the load are abstracted as the vertices V of the graph, and the lines and tie switches between the loads are abstracted as the edges E of the graph, and an undirected graph model G(V,E) is constructed.

3. The distribution network fault reconstruction method based on the improved Hippo optimization algorithm according to claim 2 is characterized in that: The specific operation steps of step S5 are as follows: S51: Establishing the objective function of distribution network fault reconstruction, taking into account the fault recovery objective: maximum load recovery rate objective f1, and network reconstruction objectives: minimum number of switching operations f2, minimum network loss f3, and minimum voltage deviation f4, as shown below: f2=min(|B|+|L|) Where: P v is the active load of vertex v; B is the set of sectional switches that need to be operated, L is the set of tie switches that need to be operated; I e is the current on edge e, r e is the resistance of edge e; U v is the voltage at vertex v, U N is the reference voltage; S52: Combining the objective function and the constraint conditions, a constraint function for distribution network reconstruction after a fault is established, including: a. Power flow constraints: Where: Q V is the reactive power of vertex v, P in,v is the active power flowing into vertex v, P out,v is the active power flowing out of vertex v, Q in,v is the reactive power flowing into vertex v, Q out,v is the reactive power flowing out of vertex v; b. Voltage constraint: IN v,min ≤U v ≤U v,max Where: U v,min is the lower limit of the voltage at vertex v, U v,max is the upper voltage limit of vertex v; c. Branch current constraints: I e ≤I e,max Where: I e,max is the upper limit of the current of edge e; d. Radial constraints: Where: G r is the graph after fault reconstruction, rank() represents the rank of the matrix, |V r | for G r The number of vertices, |E r | for G r The number of edges; S53: Establishing a fitness function F for distribution network fault reconstruction; Since the primary goal of a distribution network failure is to restore the load, all loads should be restored as much as possible. R has been determined from step S2, so each fault reconstruction strategy must restore R to ensure the primary goal. Therefore, the restored load remains unchanged. Therefore, f1 is not considered in the fitness function, and its fitness function is: F=w2f2+w3f3+w4f4 Where: w2, w3 and w4 are weight coefficients; When any constraint in step S52 is not satisfied, the fitness function is: F=M Where: M is the penalty coefficient; S54: Use the improved Hippo optimization algorithm to solve F, and when t>T, output the optimal fault reconstruction strategy.

Images