Collaborative Optimized Operation Model of Multi-Character Distribution Network Considering Multiple Uncertain Factors and Demand Response

As many new devices and factors, such as renewable energy sources, energy storage (ESs), electric vehicles (EVs), and demand response (DR), flood into the distribution network, the characteristics of the distribution network are becoming complicated and diversified. In this study, a two-layer collaborative optimized operation model for the multi-character distribution network considering multiple uncertain factors is proposed to achieve optimal dispatching of ES and EV and obtain the optimal grid structure of the distribution network. Based on basic device models of distribution network, the upper layer distribution network reconfiguration (DNR) model is established and solved by the particle swarm optimization (PSO) based on the Pareto optimality and the Prim algorithm. Then, the lower layer optimal dispatching model of ES and EV is established and solved by the binary PSO. The upper layer model and the lower layer model are integrated to form the collaborative optimized operation model for the multi-character distribution network and solved by iterating the upper and lower layers continuously. A case study is conducted on the IEEE 33-bus system. The simulation results show that the total network loss and the voltage deviation are decreased by 15.66% and 15.52%, respectively, after optimal dispatching of ES and EV. The total network loss and the voltage deviation are decreased by 28.39% and 44.46%, respectively, after the DNR with distributed generation (DG) and EV loads with little impact on the average reliability of the power supply. The total network loss and the voltage deviation are decreased by 26.54% and 27.04%, respectively, after the collaborative optimized operation of the multi-character distribution network. The collaborative optimized operation of the distribution network can effectively reduce the total cost by 114.45%, which makes the system change from paying to gaining.


Introduction
With the increasing access to ES, EV, and renewable energy generation devices such as wind turbines and photovoltaics, the distribution network is becoming a multi-character system. The access of these devices will bring a series of influences on the distribution network, including changing the power flows of the system, affecting the frequency and voltage of the network, and so on. Therefore, it is of great economic and safety benefit to analyze the characteristics and establish mathematical models of these devices to further study the optimal operation of the distribution network. The key technologies of the multicharacter distribution network are DNR and optimal dispatching of ES and EV. A large number of domestic and foreign scholars have already completed research on these aspects.
Several studies have been conducted on establishing the DNR model. The consumption of DG in the objective function in [1] is maximized as much as possible while satisfying (1) The optimal dispatching model for ES and EV is proposed to realize the cooperation of ES and EV. Compared with the existing studies that only use optimal dispatching strategies to solve other problems of distribution networks, the proposed model takes ES and EV as indispensable parts of the system, thus fully releasing the adjustable potential of them. (2) The DNR model is proposed to obtain the optimal grid structure of the distribution network. In the process of multi-objective optimization of existing studies, when a single objective deviates from its expectation greatly, other objectives are easily ignored. The proposed DNR model can measure the importance of each objective function reasonably. Compared with the existing intelligent algorithms with a wide search range which leads to slow convergence, the combination of the Prim algorithm and the Pareto optimality can obtain the optimal solution of the multi objective problem with high accuracy and fast speed while making sure the topology of the generated grid structure is radical. The rest of the paper is organized as follows. Section 2 presents the basic device models of the distribution networks, including the DG models, the ES model, the EV model, and the DR model. In Section 3, the lower layer optimal dispatching model of ES and EV is explained; in Section 4, the upper layer DNR model is explained; in Section 5, the collaborative optimized operation model is explained; in Section 6, the results of the case study on the IEEE 33-bus system are discussed, and the conclusion is provided in Section 7.

DG Output Model
The wind turbine output model [23] is shown in (1). The photovoltaic output model [24] is shown in (2) where P WT is the output power of wind turbine; P r−WT is the rated output power; v ci , v co and v r are the cut-in, cut-out, and rated wind speed; P PV is the output power of photovoltaic; n pv is the number of photovoltaic cells; P r−PV is the rated output power of a photovoltaic cell; R c and R r are the actual and rated light intensity; k is the power temperature coefficient; T c and T r are the actual and standard temperature.

Non-Dispatchable EV Load Model
The modes of EV access to the grid can be divided into two categories [25]: nondispatchable mode (EV only absorb electricity from the grid for charging) and dispatchable mode (both charging/discharging, acting in the same way as ES devices). We divided EV into three categories: buses, taxis, and private cars, which follow different normal distributions. The daily power consumption of non-dispatchable EV is related to the daily mileage, which follows a normal distribution [23] shown in (3). Then we use (3) to sample each EV to obtain the daily mileage, and afterward calculate the SOC (battery state of charge) of it. According to daily power consumption, the time required for charging each day can be obtained by (6).
where D EV is the daily mileage of EV; µ and σ are the mean value and standard deviation of and the normal distribution, E EV−consumption is the daily power consumption of EV; D EV,max is the maximum mileage; C EV is the battery capacity of EV; SOC EV is the remaining SOC of EV after driving D EV ; T EV−charge is the total charge time that EV requires in a day; P EV−charging is the charge power of EV.

Charge/Discharge Model of ES and Dispatchable EV
The dispatchable EV has the same effort as ES and can be viewed as a larger capacity battery, so they can be described by the same model. The balance equations of charge/discharge energy [26] are shown in (7) and (8). The constraints for SOC and the charge/discharge power are shown in (9)- (11).
P es−cmin ≤ P es−c ≤ P es−cmax (10) P es− f min ≤ P es− f ≤ P es− f max (11) where E es (t) is the energy stored in ES at moment t; η is the charge and discharge loss coefficient of ES; P es−c and P es− f are the charge and discharge power of ES. SOC max and SOC min are the upper and lower limits of SOC; P es−cmax and P es−cmin are the upper and lower limits of charge power; P es− f max and P es− f min are the upper and lower limits of discharge power.

DR Model
DR model considering electricity price and policy is shown in (12).
where P t Li is the per-unit load of node i at time t after DR; k ei and k pi are the demand elasticity coefficients of node i with respect to electricity price and policy; c t epc is the difference between electricity price and average electricity price at time t; a is the policy impact factor; P t Liz and P t Liz are the per-unit transferable load and per-unit non-transferable load of node i at time t.

Objective Functions
We optimize the charging/discharging strategy for ES and dispatchable EV in a day to make sure the total cost is minimized. The objective function is shown in (13).
where M is the total number of ES and EV. C i op is the cost of the number of charge/discharge operations, as there is an upper limit to the number of times a battery can be charged/discharged, so there is a cost for each charge/discharge operation. C i ep is the cost of charge/discharge power of the battery. The reason for this cost is that due to the peak and valley tariffs, the charge/discharge operation of the battery at different times will lead to an imbalance of revenue and expenditure. C i nw is the cost of wear and tear in a non-working state, which is due to the fact that the battery will age over time, even if it is not working. C i dp is the penalty cost after the battery enters the dead zone. The reason for this cost is that the battery can no longer charge/discharge after entering the dead zone, resulting in a decrease in the battery's regulation of power flow. C t nl is the cost of total network loss throughout the day.C t vd is the cost of voltage deviation.
C i dp = c dp T i dp (17) where n i op and N i op are the number of charge/discharge operations and the allowable number of charge/discharge operations of the ith device; C i battery is the battery cost of the ith device. c t ep is the electricity price at time t; P i,t battery is the charge/discharge power of the ith device at time t, whose value is positive when charging and negative when discharging. T i nw is the length of time that the ith device is not working; T i li f e is the total life of the ith device. c dp is the penalty cost per unit of time; T i dp is the total time that the ith device in the dead zone. P t loss is the active power loss of the network at time t; P t kj and Q t kj are the active and reactive power of line kj at time t; U t j is the voltage of node j at time t; r kj is the resistance of line kj. c dv is the cost factor of voltage deviation; ∆V t j is the amount of voltage deviation at node j at time t; J is the total number of nodes.

Constraint Conditions
The power balance constraints are shown in (20) and (21). The node voltage constraint is shown in (22). The line capacity constraint is shown in (23) The ES and EV constraints are shown in (9)- (11).
where P i and Q i are injected active and reactive power of node i; P DGi and Q DGi are the output active and reactive power from DG of node i; P Li and Q Li are the active and reactive loads of node i; P ESi and P EVi are the load of ES and EV of node i; G ij and B ij are the conductance and susceptance of line ij; θ ij is the difference of voltage phase angle between the two ends of line ij; U i and U N are the actual and rated voltage of node i; S ij max is the maximum capacity allowed for line ij.

Optimization Strategies and Improvements of Solving Algorithm
The PSO [27] consists of updating formulas of velocity and position, which converge the positions of the particles to the global optimal position through continuous iterations.
where Vel k i and X k i are the velocity and position vectors of the kth iteration of the ith particle; ρ is the inertia coefficient; X gbest is the global optimal position; X pbest,i is the individual optimal position of the ith particle; c 1 and c 2 are the learning factors; r 1 and r 2 are random numbers within [0, 1].
The effective SOC range of the battery is from 20% to 80%, and when SOC reaches the boundary, the battery enters the dead zone, resulting in a significant reduction in the battery's regulation of load. So, we adopted the dead time constraint strategy to limit the dead time, which is shown in (26). As the SOC approaches 80%, the velocity of the particle tends to be negative, and thus the position of the particle tends to be negative, increasing the discharging possibility of the device and reducing its SOC, and vice versa.
where f (Vel k−1 i , X gbest , X pbest,i , X k−1 i ) is the original updating formula of velocity shown in (24); r 3 and r 4 are random numbers; soc i is the SOC vector of the battery of the ith particle; β is a constant designed to prevent the denominator from reaching zero.
The role of ES and EV is to regulate the load and smooth power flow, so we proposed the charge/discharge power optimization strategy shown in (27) and (28) to improve the updating formula of velocity.
where f (Vel k−1 i , X gbest , X pbest,i , X k−1 i , soc i ) is the updating formula of velocity shown in (26); c 3 is the learning factor; r 5 is a random number within [0, 1]; P load,ave is the average load; P load is the daily load; P EV is the EV load; P DG is the output power of DG.
According to the strategies mentioned above, the solving process of the optimal dispatching model of ES and EV is shown in Figure 1. c is the learning factor; r5 is a random number within [0, 1]; , load ave P is the average load; load P is the daily load; EV P is the EV load; DG P is the output power of DG. According to the strategies mentioned above, the solving process of the optimal dispatching model of ES and EV is shown in Figure 1.
Sample the wind speed and light intensity to obtain the output power of wind turbine and PV according to (1) and (2) Calculate the curve of daily load according to (12) Sample each EV to get their driving mileage and charging period in a day, and then use them to formulate the curve of EV load in a day Generate random particle swarms and input algorithm parameters Update the velocity and position of the particle according to (25) and (27) Calculate the objective function shown in (13), check the constraints using (9)~ (11) and (20)

Objective Functions
where k is the branch number; B is the total number of branches; k P and k Q are the active and reactive power flows of branch k; k R is the resistance of branch k; k U is the voltage at the first end of branch k. i is the node number; J is the total number of nodes.

Objective Functions
f 1 is the economy function described by the network power losses shown in (29). f 2 is the security function characterized by voltage offsets shown in (30).
where k is the branch number; B is the total number of branches; P k and Q k are the active and reactive power flows of branch k; R k is the resistance of branch k; U k is the voltage at the first end of branch k. i is the node number; J is the total number of nodes.

Constraint Conditions
The power balance constraints [28] are shown in (31) and (32). The node voltage constraint and branch current constraint [29] are shown in (33) and (34). The reliability constraint of the network is shown in (35). The mathematical expression of network topology constraint [30] is shown in (36).
where P loss and Q loss are the active and reactive power losses of the network; P s and Q s are the active and reactive power injected into the distribution network by the root node. U imax and U imin are the upper and lower voltage limits of node i. i k is the current of branch k; I kmax is the maximum current allowed for branch k. ASAI is the average power supply availability; λ k is the fault rate of branch k; P k, f ault is the active power outage caused by the fault of branch k; t is the average outage duration; ASAI min is the lower limit of ASAI. n l and b l are the number of connected nodes and branches.

Solving Algorithm for Network Reconfiguration
We use a binary PSO based on the Prim algorithm [31] to solve the DNR model. The model is a multi-objective problem; therefore, the principle of Pareto optimality [32] is used to determine the optimal solution. Moreover, the Prim algorithm can make sure that the model generates a radial network structure, so there is no need to verify that the topology satisfies the open-loop condition.
The goal of network reconfiguration is to obtain the optimal grid structure. Each branch has two states, selected and unselected, which can be represented by the binary code 1 and 0, respectively. The position of a particle is a vector whose dimension equals the number of branches, and each dimension can only take on a value of 1 or 0. The updating equations of velocity and position are shown in (37)-(39).
where Vel k i and X k i are the velocity and position vectors of the ith particle in the kth iteration; P k i is the individual optimal position of the ith particle after the kth iteration; P k g is the global optimal position after the kth iteration; c 4 and c 5 are accelerating factors; V max and V min are the upper and lower limits of velocity in function S; x k id is the position of the dth dimension of the ith particle in the kth iteration; v k−1 id is the velocity of the dth dimension of the ith particle in the k − 1th iteration; r is a random number within [0, 1].
The solving process of the DNR model is shown in Figure 2. The solving process of the DNR model is shown in Figure 2.
Initialize each parameter of the algorithm. Input grid structure, grid parameters, daily load of each node, location and output power of DG and the number, location and daily load of EV Generate particle swarm randomly and each particle represents a structure of the network Update the particle velocity according to (37) Generating the radiation network using the Prim algorithm shown in (38)

Collaborative Optimized Operation Model of Multi-Character Distribution Network
In this section, we combine the upper layer DNR model shown in Section 4 and the lower layer optimal dispatching model of ES and EV shown in Section 3 into a collaborative optimized operation model. The optimal solution can be obtained through continuous iteration between the upper and lower layers. The procedure of the algorithm is de-

Collaborative Optimized Operation Model of Multi-Character Distribution Network
In this section, we combine the upper layer DNR model shown in Section 4 and the lower layer optimal dispatching model of ES and EV shown in Section 3 into a collaborative optimized operation model. The optimal solution can be obtained through continuous iteration between the upper and lower layers. The procedure of the algorithm is described below.
(1) Initialize all the parameters. Input the load, power output of DG, parameters of EV, ES, and dispatchable EV, and grid information of each node for 24 h. (2) Calculate the injected power of each node, including the load, power output of DG, EV load, and charge/discharge power of ES and dispatchable EV. (3) Solve the upper layer DNR model using the binary PSO based on the Prim algorithm and output the optimal solution which represents the optimal grid structure when the condition of the Pareto optimal solution is met. (4) Pass the optimal grid structure of the upper layer to the lower layer optimization model.  (2); if yes, turn to step (7). (7) Output the charge/discharge dispatching schemes of ES and EV of 24 h and the optimal grid structure.
The solving process of collaborative optimized operation model of multi-character distribution network is shown in Figure 3. The solving process of collaborative optimized operation model of multi-character distribution network is shown in Figure 3.

Initialization parameters, input load of each node, power output of distributed generation, parameters of EV, ES and dispatchable EV and grid information
Output optimal grid structure and the all-day optimal dispatching schemes of ES and EV

Basic Information of Example System
The proposed approach is implemented in MATLAB and tested on the IEEE 33-bus [33] system shown in Figure 4. The whole year is divided into four scenarios: spring, summer, autumn, and winter. The relevant system parameters are shown in Appendix A. The total active and reactive load of the system is 3.715 MW and 2.3 Mvar, respectively. The rated voltage is 12.66 kV.

Basic Information of Example System
The proposed approach is implemented in MATLAB and tested on the IEEE 33-bus [33] system shown in Figure 4. The whole year is divided into four scenarios: spring, summer, autumn, and winter. The relevant system parameters are shown in Appendix A. The total active and reactive load of the system is 3.715 MW and 2.3 Mvar, respectively. The rated voltage is 12.66 kV.
The proposed approach is implemented in MATLAB and tested on th [33] system shown in Figure 4. The whole year is divided into four scenarios mer, autumn, and winter. The relevant system parameters are shown in Ap total active and reactive load of the system is 3.715 MW and 2.3 Mvar, res rated voltage is 12.66 kV.

Optimal Dispatching of ES and EV
We use the optimal dispatching model of ES and EV to obtain the opti ing schemes for four scenarios. The SOC results of ES and EV after the optim in a day are shown in Figure 5.

Optimal Dispatching of ES and EV
We use the optimal dispatching model of ES and EV to obtain the optimal dispatching schemes for four scenarios. The SOC results of ES and EV after the optimal dispatching in a day are shown in Figure 5. network.

Basic Information of Example System
The proposed approach is implemented in MATLAB and tested on the IEEE 33-bus [33] system shown in Figure 4. The whole year is divided into four scenarios: spring, summer, autumn, and winter. The relevant system parameters are shown in Appendix A. The total active and reactive load of the system is 3.715 MW and 2.3 Mvar, respectively. The rated voltage is 12.66 kV.

Optimal Dispatching of ES and EV
We use the optimal dispatching model of ES and EV to obtain the optimal dispatching schemes for four scenarios. The SOC results of ES and EV after the optimal dispatching in a day are shown in Figure 5. The load curve before and after optimal dispatching of ES and EV are shown in Figure 6. It can be seen from Figure 6 that the load after dispatching is significantly smoother than that before dispatching, and the peak-valley difference is significantly reduced. It is obvious that ES and dispatchable EV can smooth the load and reduce the peak-valley difference of load. This is due to the fact that when operating in the dispatchable mode, EVs can both absorb electricity from the grid and release electricity to the grid, acting in the same way as ES devices. ES devices can regulate the load, smooth the load and reduce power flow fluctuations through planned charge and discharge behavior, so the load after the dispatching of ES and EV is much smoother than before.  (1) and (2) of daily load according to (12) iod in a day, and then use them to formulate the curve of EV load i swarms and input algorithm parameters on of the particle according to (25) and (27)  The load curve before and after optimal dispatching of ES and EV are shown in Figure 6. It can be seen from Figure 6 that the load after dispatching is significantly smoother than that before dispatching, and the peak-valley difference is significantly reduced. It is obvious that ES and dispatchable EV can smooth the load and reduce the peak-valley difference of load. This is due to the fact that when operating in the dispatchable mode, EVs can both absorb electricity from the grid and release electricity to the grid, acting in the same way as ES devices. ES devices can regulate the load, smooth the load and reduce power flow fluctuations through planned charge and discharge behavior, so the load after the dispatching of ES and EV is much smoother than before. obvious that ES and dispatchable EV can smooth the load and reduce the peak-valley ference of load. This is due to the fact that when operating in the dispatchable mode, E can both absorb electricity from the grid and release electricity to the grid, acting in same way as ES devices. ES devices can regulate the load, smooth the load and red power flow fluctuations through planned charge and discharge behavior, so the load a the dispatching of ES and EV is much smoother than before. In order to further illustrate the importance of ES and dispatchable EV, we remo all the ES and dispatchable EV and solve the dispatching problem again. The compari of results with and without ES and dispatchable EV are shown in Figure 7. The percent of decrease in the total network loss and voltage deviation with ES and dispatchable is shown in Table 1. In all scenarios, the access of ES and dispatchable EV reduces the t network loss and voltage deviation. In spring, the comparison of the results with  (1) and (2) of daily load according to (12) iod in a day, and then use them to formulate the curve of EV load i swarms and input algorithm parameters on of the particle according to (25) and (27) 13), check the constraints using (9) In order to further illustrate the importance of ES and dispatchable EV, we removed all the ES and dispatchable EV and solve the dispatching problem again. The comparison of results with and without ES and dispatchable EV are shown in Figure 7. The percentage of decrease in the total network loss and voltage deviation with ES and dispatchable EV is shown in Table 1. In all scenarios, the access of ES and dispatchable EV reduces the total network loss and voltage deviation. In spring, the comparison of the results with and without ES and dispatchable EV is the most obvious of the four scenarios. The total network loss is reduced by 23.58% and the voltage deviation is reduced by 50.56% in spring. After optimal dispatching of ES and EV, the percentage of decrease in the total network loss within the year is 15.66%, and the percentage of decrease in voltage deviation within the year is 15.52%. In summary, the optimal dispatching model of ES and EV can smooth the load, reduce network power loss, and increase voltage quality. without ES and dispatchable EV is the most obvious of the four scenarios. The total network loss is reduced by 23.58% and the voltage deviation is reduced by 50.56% in spring. After optimal dispatching of ES and EV, the percentage of decrease in the total network loss within the year is 15.66%, and the percentage of decrease in voltage deviation within the year is 15.52%. In summary, the optimal dispatching model of ES and EV can smooth the load, reduce network power loss, and increase voltage quality.    In order to verify the effectiveness of the dead time constraint strategy and the charge/discharge power optimization strategy proposed in Section 3.3, Table 2 shows the comparisons of the dispatching results of the spring scenario with or without each strategy. According to Table 2, when there is no dead time constraint, the total time the battery is in the dead zone and the total non-working time of the battery are significantly increased, which is nearly six times that when there is a dead time constraint. The decrease in the regulation effect of the battery leads to the weakening of effects of ES and dispatchable EV, resulting in an increase in total network loss and total voltage deviation for the whole day. Figure 8 is the comparison of the load curve with and without the charge/discharge power optimization strategy. Combining Figure 8 with Table 2, when there is no charge/ discharge power optimization strategy, the total load increases sharply, which is because the large charge/discharge power of ES and dispatchable EV is very large. At this time, the system cannot regulate load well and the battery is more likely to enter the dead zone and nonworking state.

Network Reconfiguration with DG and EV Loads
We use the DNR model to conduct simulations on each scenario. Optimize structures for each scenario are shown in Figure 9.

Network Reconfiguration with DG and EV Loads
We use the DNR model to conduct simulations on each scenario. Optimized grid structures for each scenario are shown in Figure 9.
Comparisons of results before and after reconfiguration are shown in Figure 10. The percentage of decrease in total network loss, voltage deviation, and average reliability of power supply after reconfiguration is shown in Table 3. It can be seen from Figure 10 and Table 3 that the total network loss and total voltage deviation after reconfiguration are reduced, and the reduction in voltage deviation is more obvious. After reconfiguration, the percentage of decrease in the total network loss within the year is 28.39%, and the percentage of decrease in voltage deviation within the year is 44.46%. In summer, the comparison of the results before and after the reconfiguration is the most obvious of the four scenarios. The total network loss is reduced by 38.96% and the total voltage deviation is reduced by 59.50% in summer.

Figure 8.
Comparison of load curve with and without charge/discharge power optimization strategy.

Network Reconfiguration with DG and EV Loads
We use the DNR model to conduct simulations on each scenario. Optimized grid structures for each scenario are shown in Figure 9. Comparisons of results before and after reconfiguration are shown in Figure 10. The percentage of decrease in total network loss, voltage deviation, and average reliability of power supply after reconfiguration is shown in Table 3. It can be seen from Figure 10 and Table 3 that the total network loss and total voltage deviation after reconfiguration are reduced, and the reduction in voltage deviation is more obvious. After reconfiguration, the percentage of decrease in the total network loss within the year is 28.39%, and the percentage of decrease in voltage deviation within the year is 44.46%. In summer, the comparison of the results before and after the reconfiguration is the most obvious of the four scenarios. The total network loss is reduced by 38.96% and the total voltage deviation is reduced by 59.50% in summer. Comparisons of results before and after reconfiguration are shown in Figure 10. The percentage of decrease in total network loss, voltage deviation, and average reliability of power supply after reconfiguration is shown in Table 3. It can be seen from Figure 10 and Table 3 that the total network loss and total voltage deviation after reconfiguration are reduced, and the reduction in voltage deviation is more obvious. After reconfiguration, the percentage of decrease in the total network loss within the year is 28.39%, and the percentage of decrease in voltage deviation within the year is 44.46%. In summer, the comparison of the results before and after the reconfiguration is the most obvious of the four scenarios. The total network loss is reduced by 38.96% and the total voltage deviation is reduced by 59.50% in summer.  The percentage of decrease in average reliability of power supply within the year is 0.01% in Table 2, which means the average reliability of power supply is not much different, that is because before and after reconfiguration, the topology of the distribution network is radial and the power supply mode is open-loop single power supply, so the reconfiguration has little impact on the reliability of power supply.  The percentage of decrease in average reliability of power supply within the year is 0.01% in Table 2, which means the average reliability of power supply is not much different, that is because before and after reconfiguration, the topology of the distribution network is radial and the power supply mode is open-loop single power supply, so the reconfiguration has little impact on the reliability of power supply.

Collaborative Optimized Operation of Multi-Character Distribution Network
This section analyzes the collaborative optimization operation model of the multicharacter distribution network of four seasons. A comparison of results between the optimized dispatching model and collaborative optimized operation model is shown in Figure 11. The percentage of decrease in the total network loss, voltage deviation, and total cost of collaborative optimized operation model of distribution network compared to optimal dispatching model for ES and EV is shown in Table 4.
Average reliability of power supply 0.02% 0.01% −0.03% 0.02% 0.01% The percentage of decrease in average reliability of power supply within the year is 0.01% in Table 2, which means the average reliability of power supply is not much different, that is because before and after reconfiguration, the topology of the distribution network is radial and the power supply mode is open-loop single power supply, so the reconfiguration has little impact on the reliability of power supply.

Collaborative Optimized Operation of Multi-Character Distribution Network
This section analyzes the collaborative optimization operation model of the multicharacter distribution network of four seasons. A comparison of results between the optimized dispatching model and collaborative optimized operation model is shown in Figure 11. The percentage of decrease in the total network loss, voltage deviation, and total cost of collaborative optimized operation model of distribution network compared to optimal dispatching model for ES and EV is shown in Table 4.  We can observe through Figure 11 and Table 4 that the results of the collaborative optimized operation model are better than that of the optimal dispatching model for almost all scenarios, with the most obvious difference in the results in summer. Compared with the optimal dispatching model, the total network loss calculated by the collaborative optimized operation model is reduced by 37.32%, the total voltage deviation is reduced by 45% and the total cost is reduced by 452.42%. Although the voltage deviation calculated by the collaborative optimized operation model at spring is slightly higher than that calculated by the optimal dispatching model, the total cost calculated by the collaborative optimized operation model is lower than that calculated by the optimal dispatching model, which is 35.16% lower.
In Table 4, the percentage of decrease in the total network loss within the year is 26.54%, the percentage of decrease in voltage deviation within the year is 27.04% and the percentage of decrease in total cost within the year is 114.45%. In summary, the collaborative optimized operation model can significantly reduce the total cost and improve the economy and safety of the distribution network compared with the optimal dispatching model of ES and EV.

Conclusions
This paper established a collaborative optimized operation model of a multi-character distribution network and solved it by the binary PSO. The collaborative optimized operation problem of the multi-character distribution network is decomposed into the optimal dispatching subproblem and the network configuration subproblem. The main conclusions are as follows: (1) Taking ES and EV into consideration, the optimal dispatching model can reduce the total network loss and the voltage deviation by 15.66% and 15.52%, respectively. The dead time constraint strategy can reduce the total time that the battery is in the dead zone and the total non-working time of the battery, thus reducing the total cost of the network. The charge/discharge power optimization strategy plays a role in smoothing the load. With these strategies, the optimal dispatching model can achieve optimal operation of the distribution network with ES and EV. (2) The DNR model can change the power flow by obtaining the optimal grid structure using the binary PSO and the Prim algorithm. This model can reduce the total network loss and the voltage deviation by 28.39% and 44.46%, respectively. The average reliability of power supply after DNR only decrease by 0.01%. In summary, the DNR has positive effects on total network loss and voltage deviation with little negative impact on the reliability of the power supply. Moreover, the Prim algorithm can make sure the topology of the generated grid structure is radial and the Pareto optimality is extremely effective in dealing with multi-objective optimization problems. (3) The two-layer collaborative optimized operation model of the multi-character distribution network, as a combination of the optimal dispatching model of ES and EV and the DNR model, takes all components of the distribution network into consideration and can effectively optimize the grid structure and obtain optimal dispatching scheme. This model can reduce the total network loss and voltage deviation by 26.54% and 27.04%, respectively. The total cost of the system is reduced by 114.45% after the collaborative optimized operation of the distribution network, which makes the system change from paying to gaining.
In this paper, we proposed the collaborative optimized operation model of the multicharacter distribution network, but there is still room for improvements in our study. Future research can be developed in the following aspects: (1) The DG output model in the distribution network and other component models can be modified more accurately. Methods of data sampling under each scenario more scientifically in the future are to be studied. (2) The proposed DNR model is a static model, which can be replaced by a dynamic DNR to achieve higher accuracy in future research. The core idea of the dynamic reconstruction is to divide the whole time period into several discrete time periods, and then perform static reconfiguration within each discrete time period.

Parameters Parameter Values
Rated capacity 2 MW Upper limit of charge and discharge power ( P es−cmax , P es− f max ) 0.25 MW Lower limit of charge and discharge power ( P es−cmin , P es− f min ) 0 MW Upper limit of SOC ( SOC max ) 0.9 Upper limit of SOC ( SOC min ) 0.    Table A6. Parameters of algorithm, objective function, and constraints in mathematical models.

Value Parameter Value
Demand elasticity coefficient with respect to electricity price ( k ei ) −0.5 Policy impact factor ( a) 0.2 Demand elasticity coefficient with respect to policy ( k pi ) 0. Accelerating factors ( 4 c , 5 c ) 2 Iteration times 50 Cost factor of voltage deviation ( dv c ) 10 Penalty cost per unit of time ( dp c ) 0.5 Table A7. Parameters of demand response model.