A resilient self‐healing approach for active distribution networks considering dynamic microgrid formation

A large number of renewable distributed generation (DG) systems connect to the distribution network, affecting the structure of the traditional distribution network and forming an active distribution network (ADN). Although the accelerating grid penetration of DGs brings significant challenges to the distribution network operation, the islanded operation capability of DGs provides a flexible solution to the self‐healing of ADNs from faults. To ensure that ADN can quickly recover and reconfigure in the event of a fault and continue to maintain safe, economical, and reliable operation, this paper proposes a dynamic microgrid formation method for ADNs combined with the dynamic network reconfiguration and intentional islanding operation of DGs. An optimization model is designed to represent the proposed self‐healing method, maximizing the load restoration and minimizing the DG cost, line network loss, and voltage excursion simultaneously. A binary hybrid optimization solver is applied to pursue the optimal self‐healing schedules from the optimization model. The self‐healing method is evaluated on the Institute of Electrical and Electronics Engineers (IEEE) 33‐node system and the IEEE 123‐node system, which indicate its rationality and effectiveness fully verified. By optimizing the on and off states of the normally open switches and the on‐grid and off‐grid operation states of DGs, ADNs not only get healed with minimum load curtailment, but also achieve minimal DG generation cost, network loss, and node voltage deviation. In addition, compared with traditional solvers, the proposed solver has a slightly higher computational time than the corresponding solver.


| INTRODUCTION
The introduction of microgrids (MGs) is aimed at addressing the emergence of high-penetration renewable energy in the distribution network, which has been further identified as a valuable alternative to centralized power generation and high-capacity transmission in power system operation and planning.However, the high permeability of renewable energy in the distribution network and the significant impact of events on the power system have led to the necessity of addressing the issue of distribution network elasticity.Resilience represents the ability of the power system to effectively withstand low-probability and high-impact events, while ensuring the minimum likelihood of power supply interruption and the ability to quickly recover and return to normal operating conditions.
As the direction of distribution network development, the core function and the most important feature of the distribution network with distributed generations (DGs) is the self-healing function. 1Because the distribution network has the characteristics of "closed-loop design, open-loop operation," when the power outage is caused by a permanent fault, the switch in the active distribution network (ADN) will automatically isolate the fault, and the distribution network will be divided into two parts, the outage area and the energized area. 2 If a fault occurs in the distribution network, the fault is located and isolated in a timely manner, and then through the reasonable allocation and operation of sectional and contact switches in the distribution network, 3 the load in the lost area is quickly restored in the fastest possible time with the optimal power supply strategy to achieve the ultimate goal of uninterrupted power supply. 4ith a large number of DG access to the distribution network, its own characteristics make the distribution network voltage, network loss, current distribution, network structure, and so forth show fluctuation and randomness, and other trends. 5If the relationship between DGs and the distribution network cannot be solved reasonably, it is not only difficult to play the advantages of DGs to a large extent, but it also makes the distribution network become extremely unstable and even causes the expansion of the area of the power loss area. 6,7For this reason, it is necessary to formulate appropriate and effective smart distribution network fault self-healing strategies to reasonably solve the impact of distributed power grid integration on the distribution network. 8istribution network fault self-healing is a multidimensional, multiobjective, multitemporal, multiconstraint nonlinear combinatorial optimization problem.Some research conducted in this area can be divided into two categories.The first type of solution proposes a method for switching and shaping MG under fault conditions, with different objectives, including reducing downtime and interruption loads, as well as switching time.Their purpose is to find the optimal MGs switch and formation when a fault occurs.Another type of method is to assume that the switching state and network configuration have been specified, which focus on the optimal operation of distributed switches.
A possible solution to the issue of distribution network elasticity is to use MGs functionality.With the development of communications, the installation of automatic control infrastructure, and smart devices, they play an important role in the management of distribution networks, especially by increasing self-healing capabilities.As one of the most important characteristics of an intelligent distribution network, self-healing ability improves the elasticity and flexibility of the network.
MG forming is an important tool that enables the use of the above resources for outage management in emergency situations to improve network resilience.By dividing the distribution system into multiple MGs, 9 the operation and reliability of the distribution network can be improved.After a fault occurs, the segment switch will separate the fault area, thus forming an MG.During outages, MGs can operate in island mode or gridconnected mode.MGs located downstream of the network will stop receiving service from the grid and act as an independent power source for their customers.In this mode, if the upper limit of MGs generation is less than instantaneous consumption, the distribution system operator will have the ability to perform direct load control procedures by using the communication infrastructure to maintain a real-time balance between generation and consumption.This process is known as distribution system restoration (DSR). 10Therefore, MG forming is one of the most important tools for optimizing DSR, which can have a significant impact on improving network resilience.However, these studies have some shortcomings when considering distribution network constraints, such as material cost constraints.
With the above in mind, finding the optimal DSR strategy under the infiltration of MGs and DG is a fundamental task.As a nonlinear problem, the DSR problem has many topological and operational constraints.To solve DSR problems, several methods have been introduced, such as expert systems, 11 mathematical programming, 12 multiagent systems, 13 fuzzy logic, 14 and heuristic search. 15,16ew of these studies have identified DSR strategies taking into account MGs capabilities.By dividing the distribution system into multiple MGs, Arefifar et al. 17 ZHAO ET AL.
| 231 introduced an optimization model to improve reliability.Sheng et al. 18 proposed an agent-based self-healing protection system paradigm with an expert system based on graph theory.Pham et al. 19 developed a new DSR program based on a graph model and a knapsack problem formula that uses decentralized generation availability.Liu et al. 20 propose a framework for analyzing the resilience of power grids with integrated MGs under extreme conditions.In Li et al., 21 a fully decentralized multiagent system is proposed to deal with complex DSR problems involving DG.However, the global optimization ability of this method is not strong, and it is easy to fall into local optima.
In Wang et al., 22,23 a multi-MGs scheduling framework is introduced by considering the self-healing mode.The main focus of these papers is MGs scheduling.The way the DSR strategy and distribution system is divided into multiple MGs in self-healing mode is predetermined, rather than dynamically formed.In Li et al., 24 an algorithm based on graph search is proposed for intelligent distribution network with MGs.In Romero et al., 25 Ding et al., 26 and Yuan et al., 27 a mathematical method is used to form an MG when a fault occurs.Due to a large number of binary and continuous decision variables in DSR problems, a method is proposed by Romero et al. 25 and Ding et al. 26 to reduce the problem space and thus the computational time of the problem.Yuan et al. 27 proposed a new and improved algorithm to determine the optimal distribution system recovery plan to improve grid resilience.An improved flexible switch pair operation is used to maintain the radial nature of the distribution system.Yan and Wu 28 propose a service recovery method based on the improved Deep Deterministic Policy Gradient algorithm to assist in the service recovery of isolated MGs.In the above research, when faced with distribution networks containing DGs, the commonly used method is to isolate the DGs when a fault occurs.This can prevent DGs from endangering circuit safety and damaging DGs devices.However, this cannot fully leverage the role of DGs in island operation.
Therefore, several studies conducted in this regard can be divided into two categories.The first group of papers proposed a method for switching and forming MG in the event of a fault, with different objectives, including reducing downtime and interruption loads, as well as switching times.The main focus of these papers is to find the optimal MGs switch and formation when faults occur.Other papers assume that the exchange state and network configuration have been specified and focused on the optimal operation of DGs.However, when a fault occurs, the predetermined configuration may not necessarily be the optimal configuration.The optimal configuration can be changed based on fault location, the power generation of DGs, and so forth.
In summary, there are still many problems in the current research.A unified security-constrained optimization model that considers network reconfiguration and islanding and includes the fault repair strategy is established to solve the ADN fault restoration strategy using a binary hybrid algorithm.Simulation results show that the proposed method can effectively improve the reliability of distribution network fault recovery.
To address the shortcomings of the above methods, this paper establishes a unified mathematical model that considers network reconfiguration and islanding and includes fault repair strategies and uses a binary hybrid algorithm to solve the ADN fault restoration strategy to achieve temporal fault reconfiguration.Specifically, the approach effectively integrates multiple factors (e.g., load restoration, DGs, network losses, and voltage offsets) in the modeling process.To further improve the convergence speed and global optimization ability of the model, we introduce a load priority model, which takes into account the importance of different loads and the operational safety of the distribution network, and incorporates them into the optimization objective function, and solves the model using a binary hybrid algorithm, and the simulation results show that the proposed method can effectively improve the reliability of fault restoration of the distribution network.
In summary, the innovations of this paper are listed as follows: (1) When establishing a unified fault recovery model, we fully considered various constraints, including easily overlooked material constraints, and proposed a dynamic MG structure with ADN fault recovery strategy to solve the landing fusion problem and achieve time fault reconstruction.(2) We introduce a troubleshooting strategy to optimize the troubleshooting time and sequence of the power grid by using DGs and switches when multiple line faults occur in the distribution network, and compare the accuracy and computational time of the proposed hybrid optimization solver with the Binary Quantum-behaved Particle Swarm Optimization (BQPSO) solver and Binary Fruit Fly Optimization Algorithm (BFOA) solver.(3) We evaluated our method on the Institute of Electrical and Electronics Engineers (IEEE) 33-node system and the IEEE 123-node system.Experimental results show that the proposed method can achieve optimal self-healing solutions based on the coordinated operation of switches and DGs.
The remaining sections of the article are divided into four parts: Section 2 contains the establishment of the objective function for the self-healing optimization of the distribution network; Section 3 contains the construction of the self-healing algorithm, which is solved using the hybrid binary algorithm; Section 4 contains the simulation case study, based on the IEEE 33-node network and the IEEE 123-node network; and Section 4 contains the conclusion.

| A DYNAMIC SELF-HEALING APPROACH FOR ADNS BASED ON NETWORK RECONFIGURATION AND INTENTIONAL DG ISLANDING
2.1 | The model based on self-healing approach 2.1.1 | Concept for the self-healing of ADNs and its optimization model construction Enabling automatic fault detection, isolation, and power restoration is one of the characteristics of an ADN.Distribution network fault detection, isolation, and power supply restoration are roughly divided into three development stages: first, the manual fault restoration mode in the traditional distribution network; second, the automatic reclosing restoration mode based on time relays; and third, the self-healing mode based on distribution automation with centralized control.The minimum fault response time based on manual selfhealing mode is 15 min, during which the operator needs to complete the fault information confirmation and power supply decision-making process, and the selfhealing recovery cycle is longer.The recovery mode based on automatic reclosing needs to consider the matching problem of action time, and there are many times of reclosing, which is a big impact on the system.The fault processing of a centralized intelligent distribution automation system is more rapid, generally between 20 s and a few minutes can be completed.
Distribution network self-healing can be divided into on-connected self-healing and off-grid self-healing, as illustrated in Figure 1.Specifically, on-grid self-healing restores the power supply to the nonfault outage loads by closing the normally open switch.Off-grid self-healing restores the power supply to the off-grid loads via intentional DG islanding.
In this paper, using islanded operation capability, a framework for monitoring and controlling the network in the normal and self-healing modes is proposed as shown in Figure 2.
The self-healing optimization process in this paper is shown in Figure 3. First, the primary inputs to the selfhealing optimization scheme are distributed power limits, switching states, and network topology, 29 while other inputs include branch current limits and node voltage limits.Then, each load in the system is assigned a priority weight based on the proposed prioritization scheme.Further, the optimization is solved based on the objectives of maximizing the amount of load to be supplied by its priority restoration, minimizing the network losses and voltage deviations, and minimizing the system operating cost.Finally, the output of the optimization solution is the optimal network configuration and DG power output.

| The optimization objectives of the self-healing process
Before modeling the research question, the control variables employed, the constraint problem, and the objective function must be described.In the process of distribution network self-healing optimization, certain operation constraints and self-healing optimization objectives need to be met.Generally, the distribution network structure must be reasonable so as to recover as much load as possible in the process of self-healing, minimize the loss of the system after self-healing, 30 and minimize the deviation between the voltage after recovery and the voltage before recovery.In the process of self-healing, the line load, node voltage, and branch current should not be greater than the rated value.
Since the focus of this paper is on ADN restoration, it is necessary to consider parameters that are not normally applicable when dealing with traditional DSR problems.To achieve the above goals, this paper mainly uses the following indicators to measure the advantages and disadvantages of the scheme.
(1) Load recovery quantity F 1 : At the time of failure (or before), each load in the system is assigned a priority weight because the main goal of recovery is to recover as many affected loads as possible while prioritizing higher-priority loads.According to the priority weight, the normal power consumption of users can be guaranteed to the maximum extent.
  where LW k is the priority weight of load k, for load importance levels 1-3, their corresponding LW k values are 10, 2, and 0.1, respectively; N T is the total number of time intervals during the grid restoration period; μ k is the state quantity of load k, and L is all the nodes on the line.
If the goal is simply to maximize load recovery, the priority weights can be replaced with one.(2) The operation cost F 2 of distributed power supply is assumed to be linearly related to its power supply, so the output power of the power supply should be kept as low as possible during normal operation.
  where P DG,k is the active power output of the kth DG in the distribution network, P k DG, is the rated output of the kth DG.
(3) The network loss F 3 after self-recovery ensures that the network loss during fault recovery is as small as possible.
where n is the number of branches; x i is the state of the ith switch node; R i is the resistance of branch i; I i F I G U R E 2 Proposed operation and self-healing strategy by islanded operation.DG, distributed generation; DLC, direct load control; ESS, energy storage system; IED, intelligent electronic device; MMG, Multi-Microgrid.
is the current flowing through branch i; N i is the number of branches; P TX,norm is the rated power of distribution transformers.(4) Ensure that the voltage offset F 4 after self-healing is minimized.
where V m and V 0 are the actual voltage value and the rated voltage value of point z, respectively; N z is the number of buses.
When different control variables are used, the selfhealing optimization problem is a multiobjective optimization problem.Therefore, these objective functions need to be weighted linearly and finally combined to form an objective function.The multiobjective function is as follows: where f is a multiobjective optimization function; λ 1 , λ 2 , λ 3 , and λ 4 are the weight coefficients.Considering this goal, the first thing to ensure is to recover as much load as possible, so the Load recovery quantity has the highest weight in the objective function.The second is to ensure the minimum voltage offset and reduce voltage loss, so its weight ranks second.On the basis of the above two categories, the minimum network loss and operation cost will be considered, so its weight is the smallest, their values are 0.6, 0.1, 0.1, and 0.2.

| The optimization constraints of the self-healing process
To ensure the acquired self-healing solution is feasible, the power balance, network security, DG capacity, and fault repair constraints are integrated into the optimization process.Each of the considered constraints will be discussed in the following.
(1) Power flow constraint The power flow constraints indicate that for any time instance, the power demand of node t should be equal to the difference between the inflow power and the outflow power: where are the total inflow power and the total outflow power of node t; P t is the power demand of node t. where is the imaginary part of the current, U k re and U k im the real and imaginary parts of the voltage; P DG,k and Q DG,k are the active and reactive power of distributed power supply k.
(2) Kirchhoff constraint The Kirchhoff current equation of node k is as follows:     where The radiality constraint is based on the following characteristics of the spanning tree 31 : By introducing the binary variable γ, the distribution network topology can be ensured to correspond to the spanning tree connected to the main substation.Every node except the root node (substation node) has only one parent node, which can be expressed by the following equation: ZHAO ET AL.
where γ is a binary variable, Γ B /Γ SW is a branch set with the disconnected branch removed.Γ sub is the set of substation nodes of the system; Γ N /Γ sub is the set of system nodes with substation nodes removed, and s(k) is the set of all nodes connected to node k. (4) Branch current constraint That is, the branch current cannot exceed the maximum allowed branch current.

I I
, where I i and I ma are the current flowing through branch i and the maximum allowable current of branch i, respectively.( 5) Node voltage constraint The node voltage must be kept within the minimum and maximum allowable voltage values of the node.
where U i is the voltage value of node z; U z min and U z max are the allowable minimum voltage and maximum voltage of node z, respectively.( 6) Feeder capacity constraint The branch power cannot exceed the maximum power allowed by the branch.

S S
, where S i and S i max are the power and maximum allowable power of branch i, respectively.(7) Transformer overload constraint The power-bearing capacity of the transformer cannot exceed the allowable maximum power value.

S S
, where S j and S j max are, respectively, the power and allowable maximum power of transformer j.

(8) Capacity constraint of DGs
The output of the DG cannot exceed the maximum capacity of the access DG.
To cope with natural disasters and large line breakage faults, the grid side needs to recover each line fault sequentially and needs to find the optimal order of repairment during the fault hours.The way to optimize the fault repair strategy is to add a series of new constraints on the switch state variables during network reconfiguration and islanding and to integrate them into the model of unified fault recovery between reconfiguration and islanding.The disconnection of the line is guaranteed while the fault still exists.At most h faulted lines can be recovered at the same time.The constraints on the opening and closing states of the faulted lines in the model to indicate the fault repair strategy are as follows: where F is the set of vectors composed of all faulty line start nodes and end nodes; α i j t , represents the switching state of the branch with node i as the start and node j as the end in the fault recovery time period t, which is a 0-1 variable; h is the number of lines that can be overhauled simultaneously at most in a time period; and T f is the time consumed for repairing a faulty line.Before fault removal, the faulty line open state variable (verified expression) is forced to be 0. Equation (20) describes the initial state of fault occurrence, where the faulty lines are all in the disconnected state, and Equation ( 22) ensures that at most h faulty lines can be serviced in each time slot during fault recovery.(10)

Material constraint
In the process of troubleshooting power distribution networks, the materials that need to be used are usually divided into three categories, among which Class A materials are metal materials, such as copper, aluminum, and so forth.Class B materials are insulation materials, such as rubber, plastic, and so forth.Class C substances are usually low-value and consumable substances, such as welding rods, welding wires, and so forth.The material cost for distribution network troubleshooting is as follows: where sf i t , is the operating state of the faulty line i at time t (0 is open, 1 is closed), with a total of IL faulty lines.ma i , mb i , and mc i are the quantities of three types of materials required for a single maintenance period of faulty line i.ma, mb, and mc are the upper limit of the quantity that can be called up by the three types of material units during the maintenance period (3, 4, and 5, respectively).

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Solving procedure for the selfhealing model based on a binary hybrid optimization solver

| A binary hybrid optimization solver
In this paper, we combine the particle swarm algorithm with the fruit fly algorithm and utilize a binary hybrid algorithm for the solution.
(A) Binary Quantum-behaved Particle Swarm Optimization The switch state values used for smart distribution network fault self-healing optimization are a set of discrete variables, so to solve the problem of discrete variables, a BQPSO algorithm based on binary coding can be used to optimize the operation of the process, 32 which represents the switch states in binary.
First, in the BQPSO algorithm, binary codes 0 and 1 are used to represent the position information of particles, and the Hamming distance is used to represent the distance between particles.For example, the Hamming distance between particles X i and X j is shown as follows: where d H is the Hamming distance function, whose value is equal to the number of corresponding bits with different values in the binary coded position information string of two particles.
Then, the average optimal position m best (t) of the population is obtained according to all individual optimal position strings encoded by binary in the population.To improve the performance of the algorithm, the value of random point S id (t) is calculated according to the single point crossing method in the genetic algorithm, which can avoid the particles falling into the local optimal solution.In general, one of the two values y 1 and y 2 generated by the single-point crossover operation can be chosen as P id (t) at will so that the value of P id (t) can be obtained.
Finally, it is necessary to calculate the particle position update equation, as shown below: where the left side of the formula can be regarded as the Hamming distance between X id (t + 1) and s id (t), and its value must be an integer, so it can be rewritten as where the [*] symbol on the right is the integer operator, the value of X id (t + 1) can be deduced from the value on the right and the value of s id (t).The steps of BQPSO algorithm are as follows: (1) Initialization: The initial position of each particle is represented by a string of binary numbers.(2) Calculate the current fitness function value of each particle and compare it with the fitness value of the individual's optimal position at the previous moment, so that P i (t) = X i (t), if the current value is smaller, otherwise P i (t) = P i (t − 1).(3) Calculate the m best value of the average optimal position of the population.(4) Calculate the current global optimal position and compare it with the fitness value of the global optimal position at the last time.If the current value is smaller, set P g (t) = P g (t), otherwise P g (t) = P g (t − 1).( 5) The local attraction factor S i (t) was calculated by the single point crossing method to generate a new population.( 6) Judge whether the maximum number of iterations or termination condition is reached; if not, go to step (2); otherwise, the algorithm ends.

(B) Fruit Fly Optimization Algorithm with Binary Coding
BFOA with Binary Coding (BFOA) uses binary coding to represent the switching state with binary numbers 0 and 1. 33 The position of Drosophila individual can be expressed as

X t x t x t x t ( ) = [ ( ), ( ), …, ( )],
where t is the number of iterations, i is the ith fruit fly, and m is the dimension of the space.
According to the idea that the Sigmoid function is used to map the value of speed to the interval [0, 1] to represent the probability of binary bit taking 1 by speed in binary particle swarm optimization algorithm, the step can also be mapped to the interval [0, 1] to realize the conversion of its binary encoding.Its function expression is shown in (30): ( ) = 0, other, where rand() is a random number within the interval [0, 1]; Sigmoid(step) is the probability that the value of position x ij takes 1.Although this binary encoding method makes the global search ability of the algorithm enhanced, with the execution of iteration, the algorithm has strong randomness, and the lack of local search ability, and the convergence is very poor.Therefore, another binary encoding method is proposed to discretize the velocity value in PSO.According to this method, it is transformed into binary encoding, as shown below: When step ≤ 0:
When step > 0: In other words, this binary encoding method enhances the local search ability of the algorithm, and the convergence speed is fast, but the corresponding global search ability is very poor.
Therefore, in this section, the two encoding methods are combined, and a selection control factor δ is introduced to determine when and which encoding method is adopted for operation, so as to obtain a hybrid binary encoding method to achieve the purpose of complementary advantages.
The basic steps of the BFOA algorithm are as follows: (1) Initialization: Set the population number n and the maximum iteration number max_T.Select control factor δ, the initial position of the fruit fly population X i , and so forth, and binary coding of the initial position of the fruit fly population.(2) With the iteration number T = 0, flies searched and approached the food source by olfaction, and set the random direction and distance for each fly to approach the food source.3) and ( 4) to determine whether the current maximum flavor concentration value is higher than that of the last iteration.If so, skip stepping (5).( 8) Determine whether the maximum number of iterations is reached.If T = max_T, then perform step (6).
When the number of iterations T = max_T, the algorithm ends.
In the paper, considering that the BQPSO algorithm is prone to premature and the BFOA algorithm is prone to fall into local optimal solutions, a binary hybrid BQPF algorithm is obtained by combining the BQPSO algorithm and BFOA algorithm using a two-population evolution strategy and information interaction mechanism.The algorithm first USES double population evolution strategy to the whole population groups are divided into two parts, respectively, for the DP 1 and DP 2 , then use BQPSO algorithm and BFOA algorithm, respectively, at the same time to the initial values for the two parts of the calculation, and then compare these two kinds of algorithm to get the optimal solution, and select the smaller the population as a whole group of optimal solutions, And enter the next iteration calculation, until the stop condition is met, the algorithm is finished.The basic flow of the BQPF binary hybrid algorithm is shown in Figure 4. model In this paper, BQPF binary hybrid algorithm is selected to optimize the fault self-healing of an intelligent distribution network with DG, and the optimal recovery strategy is found to meet the conditions with the goal of load balancing and optimal operation benefit.The whole algorithm process is shown in Figure 5, and the specific steps are as follows: (1) Input the network parameters and relevant information of the faulty line, and set the corresponding switch status on the faulty line to zero.(2) Simplify the network topology of the smart distribution network.| 239 (3) Find out whether there is DG in the power loss area, use DG to recover the important load, and use BQPF binary hybrid algorithm to recover the load in the power loss area.(4) Initialize the relevant parameters of the BQPF binary hybrid algorithm, and execute the algorithm to recover the load in the power loss area.(5) Output the optimal solution, namely, the optimal power supply restoration scheme.

| RESULTS
In this paper, we analyze the fault recovery strategy optimization scheme on a modified IEEE 33-node network with its single-line diagram illustrated in Figure 6.The distribution network has three photovoltaic (PV) systems connected and services loads of various importance levels (as in Table 1).The considered permanent faults are in the form of line outages, resulting in the de-energization of all sections downstream of the fault.The faulty sections are lines 2-19, 6-7, 12-13, 21-22, 24-25, 26-27, and 32-33.The simulation is performed on an Intel Core i7-8850H with a 2.6 GHz central processing unit, 32 GB random-access memory, and 64-bit operating system personal computer.
Figure 7 shows the changes in the load size of each node during a day.Overall, there are two peak periods for the power of each load node, which are from 8:00 to 11:00 and from 15:00 to 18:00.
Figure 8 presents the variation curve of PV in a day, the size of PV varies with factors, such as sunlight intensity from 6:00 to 20:00.
In this paper, we establish a unified model of dynamic fault reconstruction and islanding with temporal sequencing, and solve the dynamic fault recovery strategy using a binary hybrid algorithm.
Using the dynamic fault recovery model formulated in this paper, from 8:00 to 9:00, the power system malfunctioned, and the location of the fault point is shown in Figure 9, the topology for different fault periods is shown in Figures 10-14.
As shown in Figure 9, from 8:00 to 9:00, the system experienced seven faults.To reduce the impact of the faults on the overall system, S 1 , S 2 , S 3 , and S 4 on the interconnection line are closed, and the affected load nodes formed islands with PV and interconnection lines.
In Figure 10, from 9:00 to 10:00, the fault between 26 and 27 was repaired.At this time, S 5 was closed, and the load node originally located on the island was reconnected to the main network.At this time, only one island (12, 13, and 14) remained.
As shown in Figure 11, from 10:00 to 11:00, the faults located from 24 to 25, 11 to 12, and 14 to 15 were repaired.The interconnection lines where S 1 and S 5 are located do not need to continue providing power transfer functions, so their switches were disconnected.At this point, all load nodes in the system are connected to the main network, but some nodes rely on interconnection lines to connect to the main network, so further maintenance and reconstruction are needed.F I G U R E 9 Breakdown phase (8:00-9:00).PV, photovoltaic.
F I G U R E 14 Breakdown phase (13:00-14:00).PV, photovoltaic.Figure 12 shows that the faults located between 2 and 19 are repaired from 11:00 to 12:00, and S 3 can be disconnected at this time.
Then, in Figure 13, we can observe that the faults located between 21 and 22 are repaired from 12:00 to 13:00, and S 4 can be disconnected at this time.
Finally, from 12:00 to 13:00, the faults located between 32 and 33 are repaired that are shown in Figure 14.S 2 can be disconnected at this time.At this point, all communication lines are disconnected, all faults are restored, and the system is restored to the state before the fault occurred.The strategy proposed in this article reduces the impact of the fault.
The distribution network voltage profiles and power curtailments at different network reconfiguration stages are illustrated in Figures 15 and 16.
It can be seen that as the fault recovery progresses, the grid voltage profiles and the power supply conditions get improved, reflected in an overall reduction in the volatility of the distribution grid voltage and the decreasing power curtailment.In the initial stage of the fault, the voltage of some load nodes reached around 1.04 pu, and the power curtailments reached 30 kW.With the reconstruction and recovery of the system, the voltage stabilized at 0.98-1.00pu, and the power curtailments decreased to 0 kW.
The expected total load versus actual total load comparison curve for the distribution system is shown in Figure 17.In the early stage, when the fault has just occurred, it can be seen that there is a large deviation between the expected total load and the actual total load, while with the system reconfiguration and fault recovery, the load of each node of the distribution network gradually recovers, and the deviation between the expected total load and the actual total load is gradually narrowed down, which verifies the feasibility and validity of the dynamic fault recovery strategy in this paper.
To evaluate the performance of the proposed hybrid optimization solver, a comparison of the accuracy and computational time is performed on the test case, with the comparison results given in Table 2.It turns out that the proposed hybrid optimization solver achieves the lowest power curtailment during service restoration and the lowest total power losses as opposed to the BQPSO solver and the BFOA solver.For all three solvers, bus voltages are maintained within the security limits (i.e., 0.95-1.05pu).The computational time of the proposed solver is slightly higher than its counterparts.
To further demonstrate the scalability of the proposed self-healing approach, an extra case study is performed on a modified IEEE 123-node test network with its single-line diagram.For the selected test network, three PV systems are grid-connected, aiming at providing active islanding during the service restoration process.The aggregate load profile and PV profiles are shown in Figure 18.The permanent faults occur at lines 13-18, 35-36, 50-51, 67-97, and 93-94.By following the modeling and solving procedure of the self-healing approach in Section 2, the operational states of all seven switches at each restoration stage are tabulated in Table 3 and the circuit diagram for each recovery phase is shown in Figures 19-21.
The total power curtailment is shown in Figure 22.After the fault occurs, the actual total power of the system decreases.As the system reconstruction progresses, the load affected by the fault gradually resumes operation and the fault is also repaired.Therefore, the difference between the actual total power of the system and the expected total power is reduced.
The computational performance of the proposed hybrid optimization solver is again validated on the extra test case, with the results listed in Table 4.The proposed optimization solver can bring a self-healing solution with lower power curtailment.

| CONCLUSIONS AND FUTURE WORK
The article proposes a dynamic MG formation method for ADNs based on the network reconfiguration and the intentional DG islanding.
(1) A specialized optimization model was constructed to simulate the self-healing process, taking into account network security, fault repair constraints, and materials.(2) To pursue an optimal self-healing solution, a binary hybrid algorithm is proposed to solve the mathematical model.service restoration and the lowest total power losses as opposed to the BQPSO solver and the BFOA solver.
For future work, our proposed self-healing model will take into account other practical factors (e.g., the labor force required for the repairing work) that can affect the effectiveness of the self-healing process. 34Besides, other impacts of uncertain DG power outputs will also be further merged and optimized for our method.| 247

3 )
d k , im and I d k , re are the imaginary and real parts of the load current of the outflow node k, respectively; are the imaginary part and the real part of the current of the distributed power supply of the flow person node k; I mk im and I mk re are the imaginary and real parts of the branch current of branch km, respectively.(The radiality constraint

( 3 )
Calculate the fitness function value of each individual Drosophila, namely, the taste concentration determination value.(4) The individual with the highest flavor concentration in the Drosophila population was identified, and its flavor concentration value and location were recorded.(5) Flies to the location with the highest flavor concentration.(6) Generate a random number rand() and encode the position in binary, and then update the binary string representing the position information of Drosophila to generate a new Drosophila population with n population.(7) Perform steps (

F I G U R E 4
Basic flow of binary hybrid algorithm.BFOA, Binary Fruit Fly Optimization Algorithm; BQPSO, Binary Quantum-behaved Particle Swarm Optimization.F I G U R E 5 Model solution of fault self-healing method of intelligent distribution network with DG.DG, distributed generation.F I G U R E 6 IEEE 33-node topology with distributed power supply.IEEE, Institute of Electrical and Electronics Engineers.

F
I G U R E 15 Voltage profiles at different network reconfiguration stages.F I G U R E 16 Power curtailments at different network reconfiguration stages.

FF
I G U R E 19 IEEE 123-node test network and fault recovery phase 1 circuit diagram.(A) Normal state and (B) fault recovery state 1.PV, photovoltaic.I G U R E 20 Fault recovery phases 2 and 3 circuit diagram.(A) Fault recovery state 2 and (B) fault recovery state 3. PV, photovoltaic.
IE t and OE t are the set of edges of inflow and outflow node t, respectively;  S t ∈ Importance levels for all loads.
F I G U R E 7 Load profiles applied to the IEEE 33-node network.IEEE, Institute of Electrical and Electronics Engineers.
17 Expected aggregate load profile versus actual aggregate load profile.Comparison of accuracy and computational time among different optimization solvers (for IEEE 33-node test network).Aggregate load profile and PV profiles for the IEEE 123-node test network.IEEE, Institute of Electrical and Electronics Engineers; PV, photovoltaic.
Abbreviations: BFOA, Binary Fruit Fly Optimization Algorithm; BQPSO, Binary Quantum-behaved Particle Swarm Optimization; IEEE, Institute of Electrical and Electronics Engineers.F I G U R E 18 T A B L E 3 Switch state at different fault recovery stages.
By optimizing the on and off states of the normally open switches and the on-grid and off-grid operation states of DGs, ADNs not only get healed with minimum load curtailment, but also achieve minimal DG generation, network loss, and node voltage deviation.It has been proven that the proposed hybrid optimization solver has advantages in accuracy compared with the BQPSO solver and BFOA solver.(3) Case studies were carried out on a modified IEEE 33-node network and IEEE 123-node network, and the simulation results proved that the proposed selfhealing method can effectively restore the faulty ADN to its normal operation state with minimum effort.Moreover, the proposed hybrid optimization solver achieves the lowest power curtailment during I G U R E 21 Fault recovery phases 4 and 5 circuit diagram.(A) Fault recovery state 4 and (B) fault recovery state 5. PV, photovoltaic.F I G U R E 22 Comparison of aggregate load profile between normal state and fault recovery state for the IEEE 123-node test network.IEEE, Institute of Electrical and Electronics Engineers. F T A B L E 4 Comparison of accuracy and computational performance among different optimization solvers (for IEEE 123-node test network).: BFOA, Binary Fruit Fly Optimization Algorithm; BQPSO, Binary Quantum-behaved Particle Swarm Optimization; IEEE, Institute of Electrical and Electronics Engineers.ZHAO ET AL. Abbreviations