Loop matrix coding-based distributed power supply-containing power distribution network fault recovery global optimization method

Abstract

The invention relates to a distributed power supply-containing power distribution network fault recovery global optimization method based on ring matrix coding, and the method comprises the steps: constructing a distributed power supply model, and obtaining a distributed power supply-containing power distribution network according to the distributed power supply model; the method comprises the following steps: establishing an ordered annular matrix according to a topological structure of a power distribution network, and performing integer coding on each loop in the ordered annular matrix to obtain an annular matrix code; constructing a power distribution network fault recovery model based on the load recovery rate, the network loss and the utilization rate of the distributed power supply; and generating an initial population according to the ring matrix coding, and performing optimization solution on the power distribution network fault recovery model by adopting an intelligent optimization algorithm to obtain a final fault recovery scheme. According to the method, ring matrix coding and a one-stage fault recovery strategy are combined, all solutions generated by utilizing the ring matrix coding are feasible solutions, and the feasibility of the final solution obtained by carrying out island division on the basis is also ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network fault recovery, and particularly to a global optimization method for distribution network fault recovery with distributed power sources based on loop matrix coding. Background Art

[0002] The wide deployment of distributed power sources has significantly changed the pattern of distribution networks. As more distributed power sources are connected to the distribution network, it has changed from a passive system to an active system, and its topological structure and operating characteristics have both changed. Traditional fault recovery methods designed for passive distribution network systems are no longer sufficient to handle the complex situations brought by distributed power sources. Therefore, it is crucial to implement innovative fault recovery methods to enhance the resilience of active distribution networks. This can ensure the safety and stability of the operation of the power system, especially in the event of system failures and power outages caused by emergencies such as natural disasters.

[0003] The core of distribution network fault recovery with distributed power sources lies in the recovery strategy and coding algorithm. Currently, domestic and foreign scholars have carried out a large amount of research work on how to solve the fault recovery problem. Among them, the fault recovery methods can be roughly divided into two categories: islanding-based methods and network reconfiguration-based methods. The islanding-based method refers to a method that uses the power supply of distributed power sources to ensure that some nodes disconnected from the main grid can continue to operate when a fault occurs in the distribution network. The islanding of the distribution network is of great significance for improving system reliability, ensuring power supply to loads, and realizing the utilization of distributed energy resources. The network reconfiguration-based method refers to a method that quickly isolates faults and restores power supply to the distribution network by adjusting the switch states and optimizing the recovery path when a fault occurs in the distribution network. The coding method of switches in network reconfiguration has an important impact on the solution results. The binary coding used in most current distribution network fault recovery algorithms will lead to problems such as a large search space, too many solution iteration times, and too slow solution speed. This greatly limits the practicality of the fault recovery algorithm.

[0004] Although existing research regards islanding and network reconfiguration as two key stages of distribution network fault recovery, these studies usually consider these two processes as relatively independent steps, resulting in limited coordination between them and failing to fully utilize the potential and advantages of distributed power sources. Therefore, how to effectively integrate these two stages of islanding and network reconfiguration, give full play to the power supply capacity of distributed power sources, and how to innovate the coding method to speed up the distribution network fault recovery speed and improve the practicality are the challenges that need to be solved currently. Summary of the Invention

[0005] The object of the present invention is to provide a global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding, so as to provide an optimal solution for fault restoration and solve problems such as large search space, excessive iteration times, and insufficient utilization of distributed power sources in intelligent optimization algorithms using traditional binary coding.

[0006] To achieve the above object, the present invention provides the following solution:

[0007] A global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding, comprising:

[0008] Construct a distributed power source model, and obtain a distribution network with distributed power sources according to the distributed power source model;

[0009] Establish an ordered loop matrix according to the topological structure of the distribution network, perform integer coding on each loop in the ordered loop matrix to obtain a loop matrix coding, wherein each row of the ordered loop matrix corresponds to a loop in the distribution network, and each non-zero element represents the number of a branch switch;

[0010] Construct a distribution network fault restoration model based on the load restoration rate, network loss, and distributed power source utilization rate;

[0011] Generate an initial population according to the loop matrix coding, and use an intelligent optimization algorithm to optimize and solve the distribution network fault restoration model to obtain a final fault restoration solution.

[0012] Optionally, obtaining the loop matrix coding includes:

[0013] Number the branch switches in the distribution network;

[0014] Establish a loop matrix according to the topological structure of the distribution network, remove the repeated branches in the loop matrix to obtain an ordered loop matrix, wherein each row in the loop matrix corresponds to a loop in the distribution network, and each element represents the number of a branch switch in the distribution network;

[0015] Re-integer code the non-0 elements in each row of the ordered loop matrix starting from 1 to obtain the loop matrix coding.

[0016] Optionally, constructing a distribution network fault restoration model based on the load restoration rate, network loss, and distributed power source utilization rate includes:

[0017] According to the load restoration rate objective function, network loss objective function, and distributed power source utilization rate objective function, obtain a comprehensive objective function and perform power constraint, power flow constraint, current constraint, voltage constraint, and radial network constraint to obtain the distribution network fault restoration model.

[0018] Optionally, the comprehensive objective function is:

[0019] F = max(ω2f2 + ω3f3 - ω1f1)

[0020]

[0021] where F is the comprehensive objective function, ω1, ω2, and ω3 respectively represent the weights of each objective function, f1 is the network loss objective function, f2 is the load restoration rate objective function, f3 is the distributed power utilization objective function, B is the set of branches in the island network; R l represents the resistance of branch l; P l,t and Q l,t respectively represent the active power and reactive power of branch l at time t; U l,t represents the voltage of the end node of branch l at time t; κ l,t represents the state of branch l at time t; L main represents the load quantity restored by the main grid; k represents the number of islands in the current distribution network; L i represents the load restored by island i; δ i is an indicator variable; L total represents the total load of all nodes in the distribution network, ∑ i∈island P i，t represents the total power demand of all nodes in the island; ∑ j∈DG P j，t represents the total power that all distributed power sources can provide.

[0022] Optionally, according to the circular matrix encoding, an initial population is generated, and an intelligent optimization algorithm is used to optimize and solve the distribution network fault restoration model, including:

[0023] S1. Determine the basic parameters of the intelligent optimization algorithm, where the basic parameters include a preset maximum number of iterations and population size;

[0024] S2. Select a branch switch in each loop to disconnect according to the circular matrix encoding, and obtain the initial population according to the population size, where each solution in the population corresponds to a distribution network without loops;

[0025] S3. Perform island division on each solution in the population, and store the island division results of each solution;

[0026] S4. Generate new solutions according to the intelligent optimization algorithm, perform island division on each new solution, and store the new solutions and the corresponding island division results;

[0027] S5. Calculate the fitness values of the new and old solutions, and select the solution with a higher fitness value for retention. If the preset maximum number of iterations is reached, output the final fault recovery plan. If the preset maximum number of iterations is not reached, return to S4.

[0028] Optionally, the island division for each solution in the population includes:

[0029] S31. Obtain the parameters of each branch, the node load data, and the parameters of distributed power sources in the distribution network;

[0030] S32. Select the k-th distributed power source according to the order of the distributed power source numbers. Disconnect the k-th distributed power source from the distribution network, classify all the power-off nodes in the current network into the fault node set, and determine whether the k-th distributed power source can form an island;

[0031] S33. If the output power of the k-th distributed power source is greater than the power required to restore power supply to the power-off nodes and the nodes connected to the k-th distributed power source, store the power-off nodes in the island node set of the distributed power source. If not satisfied, abandon the division of the island centered on the k-th distributed power source;

[0032] S34. If there are still distributed power sources not selected, return to S32 until all distributed power sources are selected;

[0033] S35. Check the island node set. If there are the same nodes in the island, or there are connections between the nodes in the island, merge the islands and update the island node set. Calculate the total output power of the distributed power sources after merging the islands, and re-number all the islands;

[0034] S36. Select the re-numbered islands, perform a breadth-first search centered on the node connected to the distributed power source with the largest output power in the selected island, and complete the division of the selected island;

[0035] S37. If all the islands have been divided, generate the final island division result. Otherwise, return to S36 until all the islands are divided.

[0036] Optionally, performing a breadth-first search centered on the node connected to the distributed power source with the largest output power in the selected island and completing the division of the selected island includes:

[0037] Add all the nodes that do not affect the connectivity of the main grid and are connected to the selected island in the current distribution network structure to the set of nodes to be restored. Select nodes from the set of nodes to be restored and add them to the selected island until the total load power of all nodes in the selected island exceeds the total power of all distributed power sources. Remove the last added node to complete the division of the selected island.

[0038] The beneficial effects of the present invention are as follows: The present invention proposes a global optimization method based on loop matrix coding for fault restoration of distribution networks with distributed power sources. This method first reduces the size of the search space through loop matrix coding, and then performs island division while reconstructing the network. The combination of the two effectively solves the problem of fault restoration and reconstruction of distribution networks with distributed power sources. Through the simulation calculation of the test cases, the present invention has achieved the following effects:

[0039] (1) The method based on loop matrix coding effectively solves the problems of excessive search space and too many infeasible solutions commonly found in traditional binary coding, and avoids affecting the algorithm performance due to the appearance of unreasonable solutions such as loops and de-energized nodes. This coding method makes the iterative process of the solution more accurate, significantly improves the iterative speed, and effectively avoids falling into the local optimal solution.

[0040] (2) The one-stage fault restoration strategy combining network reconstruction and island division effectively enhances the diversity of solutions, and avoids the situation where the optimal solution cannot be obtained due to premature island division in the network reconstruction stage. In addition, the one-stage fault restoration strategy can also maximize the use of the power supply capacity of distributed generation, thereby alleviating the power supply pressure on the main grid.

[0041] (3) The present invention combines loop matrix coding with the one-stage fault restoration strategy. The one-stage fault restoration strategy effectively solves the problem of fewer solution selections in loop matrix coding. By generating a large number of island division schemes after disconnecting the loop, the space of possible solutions is significantly enriched. At the same time, loop matrix coding avoids the problem of infeasible solutions that may occur in the one-stage fault restoration strategy. All solutions generated using loop matrix coding are feasible solutions, and the final solutions obtained by performing island division on this basis also ensure their feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0043] Figure 1It is a framework diagram of a global optimization method for distribution network fault recovery with distributed power sources based on loop matrix coding according to an embodiment of the present invention;

[0044] Figure 2 It is a distribution network diagram of the IEEE 33-node system according to an embodiment of the present invention;

[0045] Figure 3 It is a flowchart of a global optimization method for distribution network fault recovery with distributed power sources based on loop matrix coding according to an embodiment of the present invention;

[0046] Figure 4 It is a result diagram of static island division according to an embodiment of the present invention;

[0047] Figure 5 It is a curve graph of algorithm convergence when there is a single fault line according to an embodiment of the present invention;

[0048] Figure 6 It is a fault recovery strategy under a single fault line according to an embodiment of the present invention;

[0049] Figure 7 It is a curve graph of algorithm convergence when there are multiple fault lines according to an embodiment of the present invention;

[0050] Figure 8 It is a fault recovery strategy under multiple fault lines according to an embodiment of the present invention. Specific embodiments

[0051] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0052] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0053] With the continuous progress of new energy technologies, distributed power sources, especially photovoltaic and wind power generation, are integrating into the power system on an unprecedented scale. This integration has transformed the traditional single-radial distribution network into a complex system with multiple power sources and multiple endpoints. When a fault occurs in the distribution network, distributed power sources represented by photovoltaic and wind power have shown the potential to provide power restoration for fault nodes. Therefore, in view of the fact that existing distribution network fault restoration methods do not fully utilize the power supply capacity of distributed power sources, and the optimization performance and convergence performance of the solution algorithms are insufficient, this embodiment proposes a global optimization method for distribution network fault restoration with distributed power sources based on loop matrix coding. Specifically, based on the characteristic that there should be no loops in the distribution network under normal operating conditions, each loop in the distribution network is encoded. Each time, only one branch switch in each loop needs to be disconnected. If there is a fault branch in the loop, there is no need to disconnect it, ensuring that there are no loops in the distribution network and only one branch switch in each loop is disconnected. Through loop matrix coding, the search space of the algorithm is reduced and the solution speed of the algorithm is optimized. Subsequently, a fault restoration model is established, island division is carried out during the network reconstruction process, and finally an intelligent optimization algorithm is used for solution to obtain the final fault restoration plan.

[0054] This embodiment provides a global optimization method for distribution network fault restoration with distributed power sources based on loop matrix coding, including:

[0055] Combining distributed power sources with energy storage devices to construct a stable power supply distributed power source model, and obtaining a distribution network with distributed power sources according to the distributed power source model;

[0056] Establishing an ordered loop matrix according to the topological structure of the distribution network, performing integer coding on each loop in the ordered loop matrix to obtain loop matrix coding, where each row of the ordered loop matrix corresponds to a loop in the distribution network, and each non-zero element represents the number of the branch switch;

[0057] Constructing a distribution network fault restoration model based on the load restoration rate, network loss, and distributed power source utilization rate;

[0058] Generating an initial population according to the loop matrix coding, and using an intelligent optimization algorithm to optimize and solve the distribution network fault restoration model to obtain the final fault restoration plan.

[0059] Specifically, the overall framework of the method in this embodiment is as Figure 1As shown in the figure, it includes three parts: (1) Constructing a distributed power generation model: Considering the time-varying characteristics of renewable energy, in this embodiment, a distributed generation model of wind energy storage and photovoltaic energy storage systems is adopted. The wind power generation and photovoltaic power generation are combined with energy storage devices to form a photovoltaic energy storage and wind energy storage system, thereby reducing the impact of the uncertainty of distributed power generation on fault recovery and ensuring the stable supply of electricity during the fault recovery process of the distribution network. (2) Encoding processing of the distribution network: First, an ordered loop matrix is established according to the topology of the distribution network. Subsequently, an integer encoding strategy is adopted for each loop, and finally, the branch switches of the distribution network are divided into different loops. (3) Optimizing and solving the fault recovery model: First, a fault recovery model is established and optimized and solved through intelligent optimization algorithms to gradually restore the power supply of each node. Finally, the recovery of the entire distribution network is achieved. The fault recovery model of this embodiment can be optimized and solved using a variety of intelligent optimization algorithms, and finally, the same stable solution can be obtained relatively quickly. During the solution process, island division is carried out to give full play to the power supply capacity of distributed generation (DG).

[0060] I. Distributed power generation model:

[0061] Considering the randomness and volatility of wind power generation and photovoltaic power generation, combining wind power generation, photovoltaic power generation with energy storage devices to form a wind-solar-storage system can effectively suppress the impact of uncertain factors and ensure stable power supply of the distribution network during fault recovery.

[0062] 1.1 Charge and discharge model of energy storage device:

[0063] Considering the capacity limit, maximum charge and discharge power, and charge and discharge cycle process, the charge and discharge model of the energy storage device can be simplified into two linear models. These two models can be represented by formulas (1) and (2) respectively.

[0064] E t+1 =E t +η c P c,t T - δE t (1)

[0065] E t+1 =E t -η d P d，t T - δE t (2)

[0066] Among them, E t represents the remaining energy of the energy storage device at the end of the t period; η c and η d are the charge efficiency and discharge efficiency respectively; P c,t represents the charge power in the t period; P d,trepresents the discharge power during period t; T is the charge-discharge duration during period t; δE t represents the power loss caused by charge-discharge behavior or other factors during period t. The charge-discharge cycle process needs to satisfy three constraint conditions, as shown in formulas (3), (4), and (5). Among them, P c.max and P d.max represent the maximum charge and discharge powers of the energy storage device respectively; E max and E min represent the upper and lower limits of the remaining energy allowed under normal operation of the energy storage device respectively.

[0067] P c，t ≤P c，max (3)

[0068] P d，t ≤P d，max (4)

[0069] E min ≤E t ≤E max (5)

[0070] 1.2 Photovoltaic-storage system model:

[0071] The power output of the photovoltaic power generation system is mainly affected by three key factors: light intensity, light area, and photoelectric conversion efficiency. These factors together determine the power generation capacity of the photovoltaic system under specific conditions. The calculation formula is as shown in formula (6). Among them, P PV represents the output power of the photovoltaic; L represents the light intensity; A represents the light-receiving area; η represents the photoelectric conversion efficiency.

[0072] P PV =LAη (6)

[0073] According to the outputs of the photovoltaic and energy storage at each moment, the output of the post-fault photovoltaic-storage power generation system can be obtained from formula (7), where P p，t represents the combined output of the photovoltaic-storage system during period t, and P PV，t represents the photovoltaic output during period t.

[0074] P p，t =P PV，t +P c，t (7)

[0075] 1.3 Wind-storage system model:

[0076] The output power of the wind power is directly determined by the wind speed, as defined in formula (8). Among them, P r represents the rated power of the wind turbine; v c represents the cut-in wind speed; v r represents the rated wind speed; v fIndicates the cut-out wind speed. Then, the output power of the wind-storage system is defined by Equation (9). Where, P w,t represents the combined output of the wind-storage system at time t; P WT,t represents the wind power output at time t.

[0077]

[0078] P w,t = P WT,t + P c,t (9)

[0079] II. Loop matrix encoding:

[0080] Obtaining the loop matrix encoding includes:

[0081] Numbering the branch switches in the distribution network;

[0082] Based on the topological structure of the distribution network, a loop matrix is established, and the duplicate branches in the loop matrix are removed to obtain an ordered loop matrix, where each row in the loop matrix corresponds to a loop in the distribution network, and each element represents the number of a branch switch in the distribution network. Removing the duplicate branches in the matrix aims to ensure that each branch switch appears only once in the entire matrix;

[0083] Re-encoding the non-zero elements in each row of the ordered loop matrix starting from 1 to obtain the loop matrix encoding.

[0084] Based on the characteristic that there are no loops in the normally operating distribution network, in this embodiment, a loop matrix-based encoding method is used to encode the distribution network. This method can effectively avoid generating solutions containing loops by disconnecting one branch in each loop, thereby improving the iteration efficiency of the algorithm and accelerating the solution speed. This encoding method first constructs an ordered loop matrix according to the topological structure of the distribution network, and then performs integer encoding on each loop in the loop matrix.

[0085] Taking the IEEE 33-node distribution network as an example. All sectionalizing switches and tie switches in the distribution network are closed and numbered one by one, thus constructing a distribution network topological graph as shown in Figure 2 . In this network, there are a total of 5 closed loops, where S i (i = 1, 2,..., 37) represents the numbers of each branch switch. By removing the redundant branches in the loops, the generation of invalid solutions is reduced, thereby effectively reducing the computational complexity of the algorithm. The finally obtained ordered loop matrix is shown in Equation (10). Where each row corresponds to a loop in the distribution network, and each non-zero element represents the number of a branch switch.

[0086]

[0087] Each row in the ordered circular matrix is integer - encoded starting from 1, obtaining the integer - encoding strategy based on the ordered circular matrix as shown in Table 1, where R1 to R5 respectively correspond to a loop in the distribution network.

[0088] Table 1

[0089]

[0090] After adopting the integer - encoding method, only one branch switch needs to be selected and disconnected in each loop, thus reducing the search space of the distribution network fault - recovery problem. Compared with the traditional binary - encoding method, its search space is reduced from 2 37 to 10×4×6×8×8 / b n , where b n represents the maximum number in the loop where the fault line is located. When the fault branch switch is S 10 , the value of b n is 6.

[0091] III. Intelligent algorithm optimization:

[0092] In this embodiment, by combining two fault - recovery methods of network reconfiguration and islanding division of the distribution network, a fault - recovery model is established, and an intelligent optimization algorithm is used to iteratively solve this model, finally obtaining a fault - recovery scheme. This fault - recovery model can be iteratively solved using a variety of intelligent optimization algorithms, such as genetic algorithm (GA), particle swarm optimization algorithm (PSO), teaching - learning - based optimization algorithm (TLBO), and a hybrid algorithm based on teaching - learning - based optimization algorithm and tabu search algorithm (TLBO - TS). And using these algorithms to solve can quickly obtain a stable solution in the end.

[0093] 3.1 Fault - recovery model:

[0094] Constructing a distribution - network fault - recovery model based on load recovery rate, network loss, and distributed - power - source utilization rate includes:

[0095] According to the load - recovery - rate objective function, network - loss objective function, and distributed - power - source - utilization - rate objective function, obtain the comprehensive objective function and perform power constraint, power - flow constraint, current constraint, voltage constraint, and radial - network constraint to obtain the distribution - network fault - recovery model.

[0096] Specifically, in the key stage of distribution - network fault recovery, the primary consideration is to ensure the maximum restoration of power supply to the load. Secondly, the efficient utilization of distributed energy resources needs to be concerned. The present invention realizes the effective fault recovery of the distribution network by constructing a multi - objective optimization model. This model takes network loss, load recovery rate, and distributed - power - source utilization rate as key indicators to comprehensively evaluate the recovery performance after the distribution - network fault and formulate recovery strategies. The network - loss objective function f1 is defined as shown in formula (11).

[0097]

[0098] Among them, B is the set of branches in the island network; R l represents the resistance of branch l; P l，t and Q l，t respectively represent the active power and reactive power of branch l at time t; U l，t represents the voltage at the end node of branch l at time t; κ l.t represents the state of branch l at time t, κ l，t =1 and κ l，t =0 respectively indicate whether branch l is powered on. The load restoration rate objective function f2 is defined as shown in formula (12).

[0099]

[0100] Among them, L main represents the load quantity restored by the main grid; k represents the number of islands in the current distribution network; L i represents the load restored by island i; δ i is an indicator variable, δ i =1 and δ i =0 respectively indicate whether island i is available; L total represents the total load of all nodes in the distribution network. The distributed power utilization rate objective function is defined as shown in formula (13).

[0101]

[0102] Among them, ∑ i∈island P i，t represents the total power demand of all nodes in the island; ∑ j∈DG P j，t represents the total power that all distributed power sources can provide. Based on the above three objective functions, the comprehensive objective function F is obtained, and its definition is shown in formula (14).

[0103] F = max(ω2f2 + ω3f3 - ω1f1) (14)

[0104] Among them, ω1, ω2 and ω3 respectively represent the weights of each objective function, which are set to 0.4, 0.4 and 0.2; before incorporating f1 into formula (13) for comprehensive calculation, f1 should be normalized. In addition, the fault recovery model should satisfy 5 constraint conditions, as defined in formulas (15)-(19).

[0105] C1: Island power balance constraint. The constraint condition is defined as shown in formula (15). Among them, P eq，trepresents the total output power of all distributed power sources within the island during period t; L represents the set of all nodes within the island; P i，t represents the power demand required to restore power supply to node i during period t; P loss，t represents the network loss during period t.

[0106] P eq，t ≥∑ i∈L P i，t +P loss，t (15)

[0107] C2: Power flow constraint. The constraint condition is defined as shown in formula (16). Among them, P i.t and Q i.t respectively represent the active power and reactive power of node i during period t; N i represents the set of nodes connected to node i; G ij and B ij respectively represent the conductance and susceptance of branch ij; θ ij，t represents the voltage phase angle difference of branch ij during period t.

[0108]

[0109] C3: Current constraint. The constraint condition is defined as shown in formula (17). Among them, I ij，t represents the current flowing through branch ij during period t; I ij.max is the maximum current allowed to flow through branch ij.

[0110] I ij.t ≤I ij.max (17)

[0111] C4: Voltage constraint. The constraint condition is defined as shown in formula (18). Among them, U i，t is the voltage of node i during period t; U i.max and U i.min respectively represent the upper and lower limits of the voltage of node i.

[0112] U i.min ≤U i.t ≤U i.max (18)

[0113] C5: Topological constraint. The constraint condition is defined as shown in formula (19). Among them, g represents the current topological structure of the distribution network, and G represents the set of network topological structures of the distribution network.

[0114] g ∈ G (19)

[0115] 3.2 Island division:

[0116] The islanding division process in this embodiment occurs during the iterative solution process of the intelligent optimization algorithm. Each new solution generated by the intelligent algorithm during iteration corresponds to a distribution network without any loops and all nodes are connected to the main network. The islanding division is performed on the generated new solution.

[0117] The solution process includes the following steps:

[0118] (1). Configure the basic parameters of the intelligent optimization algorithm, including the number of iterations, population size, etc.

[0119] (2). Select a branch switch to disconnect in each loop according to the loop matrix coding, and initialize the population according to the population size. Each solution in the population corresponds to a distribution network without loops. Then, perform the islanding division strategy on each solution in the population. Store the islanding division scheme of each solution for subsequent fitness calculation.

[0120] (3). Generate new solutions according to the iteration rules of the algorithm, and then perform the islanding division operation on each new solution. Store the new solutions and their corresponding islanding division results for subsequent calculation and comparison. Among them, the iterative optimization of the solutions is also carried out in the search space provided by the loop matrix coding.

[0121] (4). Calculate the fitness values of the old and new solutions after islanding division, compare their fitness values, and select the solution with a higher fitness value to be retained for subsequent iterative optimization.

[0122] (5). When the algorithm reaches the specified maximum number of iterations, generate the final fault recovery method. Otherwise, return to step (3) to continue the iteration.

[0123] The specific steps of the islanding division operation during the solution process are as follows.

[0124] (1). Read the parameters of each branch, the load data of each node, the parameters of distributed power sources, and other relevant information in the distribution network.

[0125] (2). Select the kth distributed power source in the order of distributed power source numbers and disconnect it from the distribution network. Then, classify all the power-off nodes in the current network into the fault node set N loss where a power-off node refers to a node whose power supply is interrupted due to a distribution network fault or a line disconnection. At the same time, calculate the power required for all power-off nodes to restore power supply and the power required for the nodes connected to the kth distributed power source to restore power supply, and add them up to obtain the total power demand P load to determine whether this distributed power source can form an island.

[0126] (3). Compare the total power demand P loadand the output power of the selected distributed power source. If the output power of the selected distributed power source is greater than the total power demand P load , then all these power-loss nodes are included in the island node set island k of this distributed power source. Otherwise, the division of the island centered on the k-th distributed power source is abandoned.

[0127] (4) Confirm whether all distributed power sources have been selected. If there are still distributed power sources not selected, return to step (2) and continue to process the remaining distributed power sources until all distributed power sources have been selected.

[0128] (5) Check each island node set. If there are the same nodes in some islands, or there are connections between the nodes in two islands, then merge these islands and update the island node set. Subsequently, calculate the total output power of the distributed power sources after the connected islands are merged. Finally, re-number all the islands.

[0129] (6) According to the numbering of the islands in step (5), select an island. Conduct a breadth-first search centered on the node connected to the distributed power source with the largest output power in this island, including: adding all the nodes that do not affect the connectivity of the main grid and are directly connected to the currently selected island to the set R load of nodes to be restored. Then randomly select nodes from these nodes to join the island. If R load is empty, then re-select all the nodes that do not affect the connectivity of the main grid and are directly connected to the island to join R load . Until the total load power of all the nodes in the island exceeds the total power of all the distributed power sources in this island. Finally, remove the last added node to complete the division of this island.

[0130] (7) Check whether all the islands have been divided. If all the islands have been divided, then generate the final island division plan; otherwise, return to step (6) and continue to process the remaining islands until all the islands have been divided.

[0131] In steps 2 and 3 of the above island division, first disconnect the distributed power source from the distribution network, and then judge whether this distributed power source can form an island. The purpose of this approach is to ensure that there will be no power-loss nodes due to island division, to ensure that as many nodes as possible are powered while giving full play to the power supply capacity of the distributed power source. In step 6, by randomly selecting nodes from the set R load of nodes to be restored and deciding whether to add them to the island, the diversity of the solution is improved, which helps to find the optimal solution.

[0132] IV. Fault recovery algorithm flow:

[0133] The fault recovery method adopted in this embodiment mainly consists of three parts: reading the data of the distribution network, applying the loop matrix coding method, and using an intelligent optimization algorithm for iterative solution. The flowchart is as shown in Figure 3 and the specific steps are as follows.

[0134] (1) Read the network topology, characteristic information, fault location of the distribution network, and the power output data of the wind-solar-storage system, providing the basic data for the subsequent fault recovery algorithm.

[0135] (2) Construct a loop matrix according to the topology of the distribution network. Each element in the matrix represents the switch number of a branch in the distribution network, and each row corresponds to a loop in the distribution network, containing the switch numbers of all branches in the loop. In this way, the complex topology of the distribution network is represented in the form of a matrix, facilitating subsequent algorithm processing.

[0136] (3) Process the loop matrix generated in step (2), remove duplicate branches, and ensure that each branch switch appears only once in the entire matrix. Then perform integer coding on the switches in each loop to accurately represent each loop. The purpose of this step is to simplify the matrix structure and assign a unique code to each loop, facilitating subsequent algorithm operations and identification.

[0137] (4) Configure the basic parameters of the algorithm, such as the number of iterations and population size.

[0138] (5) Initialize the population and execute the island division strategy for each solution in the population. Store the island division scheme of each solution for subsequent fitness calculation. The island division strategy is to make full use of the power supply capacity of distributed power sources to ensure that as much power as possible is supplied to the load during the fault recovery process.

[0139] (6) Generate new solutions according to the iteration rules of the selected intelligent optimization algorithm, and then perform island division operations on each generated new solution. Store the new solutions and their corresponding island division results for subsequent calculations and comparisons. By continuously generating new solutions through iteration and performing corresponding processing, a better fault recovery scheme is gradually searched.

[0140] (7) Calculate the fitness values of the old and new solutions after dividing the islands, compare their fitness sizes, and select the solution with better fitness to be retained for subsequent iterative optimization.

[0141] (8) When the algorithm reaches the specified maximum number of iterations, output the final fault recovery scheme. Otherwise, return to step (6) to continue iterating to further optimize the solution.

[0142] During the iterative solution process of the intelligent optimization algorithm, the solution obtained in each iteration corresponds to a connected and acyclic structure of the distribution network. By performing island division on all the solutions generated during the iteration process and combining the island division strategy adopted in this embodiment, the power supply capacity of distributed power sources can be fully utilized, and the occurrence of power outage nodes can be effectively avoided, thereby ensuring the load recovery rate of the final fault recovery strategy.

[0143] Next, experimental verification is carried out for the fault recovery method provided in this embodiment. The data set, experimental settings, and experimental results of this embodiment are analyzed below.

[0144] Data set:

[0145] This embodiment uses the IEEE 33-node system with distributed power sources as shown in Figure 2 as a test case to verify the effectiveness of the method. The three-phase power base value of this distribution network is 10 MVA, the network base voltage is 12.66 kV, the active power is 5084.26 kVA, and the reactive power is 2547.32 kVA. The distribution network includes wind power and photovoltaic energy storage systems. The positions, types, and capacities of DGs are shown in Table 2.

[0146] Table 2

[0147]

[0148] Experimental design:

[0149] To evaluate the effectiveness of the fault recovery strategy proposed in this embodiment, four different fault recovery schemes are designed, and their fault recovery performances are compared.

[0150] (1). Scheme 1: The method proposed in the present invention is adopted. The topological structure of the distribution network is encoded based on the ring matrix encoding method. A fault recovery algorithm that integrates island division and network reconstruction into one stage is used.

[0151] (2). Scheme 2: This scheme uses the traditional binary coding technology to encode the switch branches of the distribution network. And island division and network reconstruction are integrated into one stage.

[0152] (3). Scheme 3: This scheme uses the ring matrix encoding method proposed in this embodiment. After encoding, a two-stage distribution network recovery method is adopted, that is, island division is first performed, and then network reconstruction is performed on the remaining nodes.

[0153] (4). Scheme 4: This scheme uses the traditional binary coding technology to encode the switch branches of the distribution network and adopts a two-stage distribution network recovery strategy.

[0154] Both Scheme 3 and Scheme 4 belong to the static islanding division method, that is, the process of dividing the system into several relatively independent island areas according to preset fixed conditions and parameters. This method less considers the changes in the real-time operating state of the system. The scale and quantity of each island are determined by the initial state and remain unchanged during the optimization process. The islanding division results of Scheme 3 and Scheme 4 are as Figure 4 shown.

[0155] To verify the feasibility of this embodiment in solving single-branch fault and multi-branch fault problems, the following two scenarios are designed.

[0156] (1) Scenario 1: The faulty branch is between Node 9 and Node 10.

[0157] (2) Scenario 2: The faulty branches are between Node 3 and Node 4, and between Node 9 and Node 10.

[0158] Experimental analysis:

[0159] After the fault occurs, first isolate the faulty node, and then execute the four proposed fault recovery schemes and conduct research and comparison. To implement the four proposed strategies in different scenarios, this embodiment adopts four intelligent optimization algorithms, namely genetic algorithm, particle swarm optimization algorithm, teaching optimization algorithm, and a hybrid algorithm based on teaching optimization algorithm and tabu search algorithm. Table 3 shows the distribution network recovery results of the four schemes in Scenario 1, and Table 4 shows the recovery results of the four schemes in Scenario 2.

[0160] Table 3

[0161]

[0162]

[0163] As shown in Table 3, all four algorithms in Scheme 1 can restore power to all nodes in the distribution network, and the network loss converges to a stable value, with its network loss level only slightly higher than that of Scheme 2. The utilization rates of distributed power sources of the four intelligent optimization algorithms have reached the optimal level, making full use of the power supply capacity of distributed power sources. The fitness of the four algorithms in Scheme 1 is 0.52, which is the highest among all schemes. Generally speaking, the present invention can effectively solve the single-branch fault problem. In Scheme 2, the dynamic island division under binary coding causes the originally connected distribution network to be disconnected, generating a large number of power-off nodes. Since the nodes in these areas are not connected to the power source, the network loss is very low. This causes the algorithm to fall into a local optimum and obtain an infeasible solution. In Scheme 3, due to the prior island division, multiple loops in the loop matrix are eliminated. Only two loops remain in the entire distribution network, and the search space is too small to obtain the optimal solution. Therefore, the final loss of the network is relatively large. In Scheme 4, all algorithms except the particle swarm optimization algorithm can supply power to all nodes in the distribution network. However, the network loss of Scheme 4 is the highest among all schemes. Both Scheme 3 and Scheme 4 adopt a two-stage restoration strategy, that is, island division is carried out first, and then network reconstruction is carried out. And Scheme 3 adopts loop matrix coding, with lower network loss and a larger final value of the objective function, which strongly proves that loop matrix coding is superior to traditional binary coding.

[0164] Table 4

[0165]

[0166]

[0167] Compared with Scenario 1, the branch between nodes 3 and 4 in the distribution network in Scenario 2 is also disconnected, resulting in the inability to implement the best fault recovery scheme in Scenario 1. Therefore, in Scenario 2, the fitness of Scheme 1 decreases compared with Scenario 1. However, as can be seen from Table 4, despite this change, the fitness of Scheme 1 is still the highest among all schemes. Generally speaking, the present invention still shows high effectiveness in solving multi-fault problems. To further verify the effectiveness of the method proposed by the present invention in optimizing intelligent algorithms to solve the distribution network fault recovery problem, a comprehensive performance analysis was carried out on the four intelligent algorithms in Scheme 1, which is the method used in the present invention. The specific fault recovery performances of the four algorithms in Scenario 1 are shown in Table 5 and Figure 5 , while the detailed fault recovery performances of the four algorithms in Scenario 2 are shown in Table 6 and Figure 7 . The population size of all algorithms is set to 20.

[0168] Table 5

[0169]

[0170] According to Table 5 and Figure 5 the results, during the optimization process, the four algorithms adopted in the proposed solution of the present invention can all converge the lowest network loss to a stable value, showing strong stability and reliability, and verifying the adaptability and consistency of the algorithms under boundary constraint conditions. In addition, there is a significant difference between the highest network loss and the lowest network loss, and all four algorithms can quickly reduce the network loss of the optimal solution within a small number of iterations, showing obvious convergence. In summary, the solution of this embodiment not only improves the convergence ability of the algorithms, but also ensures the stability of the algorithms.

[0171] After the branch between node 9 and node 10 is disconnected, only four closed loops of R1, R2, R4, and R5 remain in the distribution network. At this time, the size of the search space is 2560. Subsequently, one branch is selected from each loop to be disconnected, so that the distribution network forms a radial topology structure, and island division is carried out on this basis. As Figure 6 shown, the final distribution network is successfully divided into four islands, and the island utilization rate reaches 85%, effectively exerting the power supply capacity of the islands and significantly reducing the burden on the main network power supply.

[0172] Table 6

[0173]

[0174] To further explore the effectiveness of this method in solving the problem of multiple faulty lines, Table 6 and Figure 7 show the specific performance of the four intelligent algorithms after applying the solution of this embodiment in Scenario 2. From the results, it can be seen that all four algorithms converge to a stable value after 5 to 6 iterations. Compared with Scenario 1, the iteration speed of the algorithms has been improved to varying degrees. In addition, the average network loss of all solutions is also closer to the final network loss. In summary, the solution of this embodiment shows higher efficiency and better overall optimization performance when solving the problem of multiple faulty lines.

[0175] After the branches between node 9 to node 10 and between node 3 to node 4 are disconnected, only three closed loops of R2, R4, and R5 remain in the distribution network. At this time, the scale of the search space is 256. Then, after disconnecting the remaining three loops, island division of the distribution network is carried out. Since the branch between node 3 and node 4 fails, the main network current can only be transmitted from node 6 to nodes 4, 5, 24, 25, 26, 27, 28. Therefore, if all the branches around node 6 are disconnected, DG1 cannot meet the power supply requirements of all the de-energized nodes, and thus does not meet the conditions for island division. To ensure that all nodes can resume power supply, it is decided not to divide the island centered on DG1, but to reconnect the just-disconnected branches. As Figure 8 shown, finally three islands are formed, and the island utilization rate is 69%.

[0176] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding, characterized in that, Including: Construct a distributed power source model, and obtain a distribution network with distributed power sources according to the distributed power source model; Establish an ordered loop matrix based on the topological structure of the distribution network, perform integer coding on each loop in the ordered loop matrix to obtain a loop matrix code, where each row of the ordered loop matrix corresponds to a loop in the distribution network, and each non-zero element represents the number of a branch switch; Construct a distribution network fault recovery model based on the load recovery rate, network loss, and distributed power source utilization rate; Generate an initial population according to the loop matrix code, and use an intelligent optimization algorithm to optimize and solve the distribution network fault recovery model to obtain a final fault recovery solution.

2. The global optimization method for fault restoration of a distribution network with distributed power sources based on ring matrix coding according to claim 1, wherein Obtaining the loop matrix code includes: Number the branch switches in the distribution network; Establish a loop matrix according to the topological structure of the distribution network, remove the repeated branches in the loop matrix to obtain an ordered loop matrix, where each row in the loop matrix corresponds to a loop in the distribution network, and each element represents the number of a branch switch in the distribution network; Re-integer code the non-0 elements in each row of the ordered loop matrix starting from 1 to obtain the loop matrix code.

3. The global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding according to claim 1, characterized in that Constructing a distribution network fault recovery model based on the load recovery rate, network loss, and distributed power source utilization rate includes: According to the load recovery rate objective function, network loss objective function, and distributed power source utilization rate objective function, obtain a comprehensive objective function and perform power constraint, power flow constraint, current constraint, voltage constraint, and radial network constraint to obtain the distribution network fault recovery model.

4. The global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding according to claim 3, wherein, The comprehensive objective function is: F = max(ω2f2 + ω3f3 - ω1f1) Among them, F is the comprehensive objective function, ω1, ω2, and ω3 respectively represent the weights of each objective function, f1 is the network loss objective function, f2 is the load restoration rate objective function, f3 is the distributed power utilization objective function, and B is the set of branches in the island network; R l represents the resistance of branch l; P l，t and Q l，t respectively represent the active power and reactive power of branch l at time t; U l，t represents the voltage of the end node of branch l at time t; κ l.t represents the state of branch l at time t; L main represents the amount of load restored by the main grid; k represents the number of islands in the current distribution network; L i represents the load restored by island i; δ i is an indicator variable; L total represents the total load of all nodes in the distribution network, ∑ i∈island P i，t represents the total power demand of all nodes within the island; ∑ j∈DG P j，t represents the total power that all distributed power sources can provide.

5. The global optimization method for fault restoration of a distribution network with distributed power sources based on ring matrix coding according to claim 1, characterized in that, Generating an initial population according to the loop matrix code and using an intelligent optimization algorithm to optimize and solve the distribution network fault recovery model includes: S1. Determine the basic parameters of the intelligent optimization algorithm, where the basic parameters include a preset maximum number of iterations and population size; S2. Select a branch switch in each loop to disconnect according to the loop matrix code, and obtain the initial population according to the population size, where each solution in the population corresponds to a distribution network without loops; S3. Perform island division on each solution in the population and store the island division results of each solution; S4. Generate new solutions according to the intelligent optimization algorithm, perform island division on each new solution, and store the new solutions and the corresponding island division results; S5. Calculate the fitness values of the old and new solutions, and select the solutions with high fitness values to be retained. If the preset maximum number of iterations is reached, output the final fault recovery solution. If the preset maximum number of iterations is not reached, return to S4.

6. The global optimization method for fault restoration of a distribution network with distributed power sources based on ring matrix coding according to claim 5, characterized in that, Performing island division on each solution in the population includes: S31. Obtain the parameters of each branch, node load data, and parameters of distributed power sources in the distribution network; S32. Select the kth distributed power source in ascending order of the distributed power source numbers, disconnect the kth distributed power source from the distribution network, classify all the power-off nodes in the current network into the fault node set, and determine whether the kth distributed power source can form an island; S33. If the output power of the k-th distributed power source is greater than the power required to restore power supply to the power outage node and the nodes connected to the k-th distributed power source, then store the power outage node in the island node set of the distributed power source; otherwise, abandon the division of the island centered on the k-th distributed power source. S34. If there is a distributed power source that has not been selected, then return to S32 until all distributed power sources have been selected. S35. Check the island node set. If there are identical nodes in the islands or there are connections between the nodes in the islands, then merge the islands and update the island node set, calculate the total output power of the distributed power sources after merging the islands, and re-number all the islands. S36. Select the re-numbered islands, perform a breadth-first search centered on the node connected to the distributed power source with the largest output power in the selected island, and complete the division of the selected island. S37. If all the islands have been divided, then generate the final island division result; otherwise, return to S36 until all the islands are divided.

7. The global optimization method for fault restoration of a distribution network with distributed power sources based on loop matrix coding according to claim 6, characterized in that Performing a breadth-first search centered on the node connected to the distributed power source with the largest output power in the selected island and completing the division of the selected island includes: Adding all the nodes that do not affect the connectivity of the main grid and are connected to the selected island in the current distribution network structure to the set of nodes to be restored, selecting nodes from the set of nodes to be restored and adding them to the selected island until the total load power of all the nodes in the selected island exceeds the total power of all the distributed power sources, removing the last added node, and completing the division of the selected island.

Images