Analysis of Charging Load Acceptance Capacity of Electric Vehicles in the Residential Distribution Network

Abstract

After large-scale electric vehicles (EVs) are connected to the residential distribution network, community charging has become one of the main bottlenecks at present, especially in old residential areas. Therefore, the current residential distribution network’s ability to accept charging load and when and how the distribution network needs to be transformed have become meaningful research points. Based on the characteristics of the EVs’ charging load of residential areas on a typical day and the size of the target annual charging load, this paper analyzes the acceptance capacity of the charging load of the distribution network on typical weekdays and weekends. By taking the charging load characteristics, the charging time of EVs, the voltage of each node of the distribution network, the line capacity, the transformation capacity of the distribution station as constraints, and the maximum capacity of the residential distribution network to accept the charging load as the objective function, the charging load capacity of the residential distribution network is analyzed. The particle swarm optimization algorithm is employed to solve the optimized mathematical model. The simulation uses an actual residential distribution network as an analysis example, and the partition optimization results prove the correctness and feasibility of this proposed method.

1. Introduction

Over the past three years, China’s new energy vehicle industry has achieved rapid development. The “New Energy Vehicle Industry Development Plan (2021–2035)” clearly states that the sales of new energy vehicles should reach 20% of the total sales of new vehicles, and it is proposed that pure EVs should be the main development target by 2025. The construction of basic charging facilities is the cornerstone of the development of new energy vehicles and has been listed as one of the key construction areas of “new infrastructure” [1]. As of July 2022, China’s EV charging infrastructure has reached 3.98 million units [2]. China will keep accelerating the development of EV charging infrastructure in the long term.

The impact of the charging behavior of large-scale EVs connected to the power grid through charging facilities on the distribution network, especially the distribution network in residential areas, cannot be ignored. The safe operation and reasonable planning of the distribution network are facing new challenges. These challenges are mainly manifested in: (1) the fact that the access of large-scale charging facilities to the distribution network lacks reasonable planning, guiding standards, and norms; and (2) the fact that community charging has become one of the main bottlenecks at present. Due to the limitations of facility land and line corridors in existing residential areas, it is difficult to increase the capacity of the distribution network [3]. Therefore, it is important to plan and construct charging facilities in residential areas to analyze the EV charging load acceptance capacity of the distribution network in residential areas according to the characteristics of the EV charging load.

At present, some studies have been carried out with an analysis of charging load acceptance capacities, mainly for urban regional distribution networks. Reference [4] divides the distribution network into different power supply areas according to the topology structure and network parameters of the urban distribution network, and distributes the EV charging load according to the divided power supply areas. The network power flow of the distribution network is calculated, and the capacity of the distribution network to accept the charging load is calculated based on the power flow calculation results. References [5,6] consider the interconnection between the EV charging network and the distribution network and establish a mathematical model of the distribution network’s maximum carrying capacity for EVs. References [7,8,9] take the operation risk of the urban distribution network as a quantitative index to evaluate the charging load acceptance capacity, and according to the optimization mechanism of the orderly charging of EVs, the analysis of the maximum acceptance capacity of the urban distribution network for the charging load of EVs is constructed. Reference [9] uses the entropy weight method to objectively improve the supervisor weight obtained by the AHP to evaluate the acceptance capacity of the distribution network. Reference [10] uses fuzzy theory to evaluate and analyze the acceptance capacity of EVs in the distribution network according to the charging load characteristics of EVs in different scenarios and proposes a distribution network reconfiguration method based on optimizing the charging load acceptance capacity. Reference [11] takes the distribution network in urban residential areas as the research and analysis object, considers the characteristics of EV charging load and conventional electricity load characteristics in residential areas, and proposes a method of accepting the charging load capacity of distribution network stations in residential areas. A large number of electric vehicles connected to the distribution network for charging will not only lead to a substantial increase in the load of the distribution network, but also bring about a large power loss and reduce the utilization rate of the equipment. More seriously, the reliability of the system will be seriously affected. Reference [12] investigates the sensitivity of the system reliability index to the access of different electric vehicles and makes a quantitative evaluation of the acceptance capacity of electric vehicles in the grid under different reliability levels. An evaluation method for the acceptance capacity of EVs is analyzed in the distribution network of two residential areas [13]. The results show that the location of EVs connected to the distribution network is different, and the acceptance capacity of EVs in the distribution network is very different. Reference [14] proposes an evaluation method for the acceptance capacity of charging posts in the distribution network through the coupling calculation of charging posts and charging loads and the constraints of distribution network operation risk indicators. To sum up, the publications mainly consider the capacity of the distribution network and the voltage deviation of nodes in the assessment of the acceptance capacity of the distribution network to accept the charging load of EVs. However, the different charging load characteristics caused by users’ travel habits, charging habits, and electric vehicle ownership have not been considered, especially in the residential distribution network.

According to the charging load characteristics of EVs in residential areas, the topology structure of the distribution network in residential areas, and the characteristics of conventional loads of residents, this paper analyzes the EV charging load acceptance capacity of the distribution network in residential areas. The second part introduces the general idea of calculating the charging load acceptance capacity of the distribution network in residential areas. The third part introduces the characteristic analysis and charging load forecast of EVs in residential areas. The fourth part introduces the charging load acceptance capacity of the distribution network in residential areas The mathematical model of the analysis. The fifth part is the simulation case analysis. The sixth part summarizes the full text.

2. Residential Area Distribution Network Charging Load Acceptance Capacity

The analysis process of charging load acceptance capacity of the residential distribution network is shown in Figure 1. First, the EV charging load characteristics are predicted based on the travel characteristics of residents, etc., and the EV ownership is predicted to obtain the charging load size in the past three years and the target year. Then, according to the structure of the distribution network in the residential area, the daily load characteristics of the residential area, and the geographical characteristics of the residential area, the distribution network in the residential area is divided into different regions, and the conventional electricity load of each area is calculated. At the same time, considering factors such as geographical factors and node capacity, the nodes in each partition are prioritized for charging facility planning. By taking the maximum capacity of the residential distribution network to accept the EV charging load as the objective function; taking the overall capacity of the residential distribution network system, the capacity of the residential distribution network node, the voltage offset degree of the distribution network node, and the power flow balance are the constraint conditions; and establishing a mathematical model for the analysis of the charging load capacity of EVs in the residential distribution network, the particle swarm optimization algorithm could be applied to solve the established mathematical model. Afterward, the simulation calculation is used to determine the distribution network’s acceptance capacity for electric vehicle charging load.

3. Analysis of Charging Load Characteristics of EVs in Residential Areas

The charging load characteristics of EVs in residential areas affect the capacity of the distribution network to accommodate EVs. The size of the charging load in the past three years and the target year are closely related to factors such as the increase in the number of EVs and the charging probability of EVs in residential areas.

3.1. Probability of EVs Charging in Residential Areas

Factors such as residents’ travel habits, charging facilities in residential areas, and characteristics of EVs all affect the charging load of EVs in residential areas.

3.1.1. Charging Start Time

On weekdays, private vehicles account for 79.25% and 20.75% of trips for work trips and social shopping trips, respectively, and the vehicle trip rate is 77%. The trip type of private vehicle on weekends is a social shopping trip, and the trip rate is 70.4% [15].

As shown in Figure 2, the categories at the end of two trips on weekdays have different probability distribution characteristics. Figure 2a shows the distribution of the end time of work trips on weekdays. Due to the limitation of working hours, the end times of trips are more concentrated before and after getting off work, showing a typical unimodal normal distribution. Figure 2b shows the distribution of the end time of social shopping trips on weekdays, which presents a bimodal normal distribution because the return time of social shopping trips is relatively free [16].

Figure 3 shows the probability distribution of the end time of private vehicle trips on weekends in residential areas. The characteristics of the end time of weekends are similar to those of workdays, but the peak time of weekends is earlier than the end of workdays. This is because the social shopping time on weekends is mainly at noon, particularly in between lunch and dinner before returning to the place of residence [16].

3.1.2. SOC at Start of Charge

Due to the insufficient fast-charging equipment for EVs at this stage, and the high charging costs in public places and during the day, EV users are very anxious about electricity. According to survey statistics, the situation of EV users in residential areas divided by initial charging SOC is shown in Figure 4 [17].

According to statistics, the average travel distance of EV users under the scenarios of weekdays and weekends is 11.4 km and 13.2 km, and the standard deviations are 4.88 km and 5.23 km, respectively. The numbers are normally distributed [18]. Assuming that the expected SOC of EV users in residential areas for charging is 1, and that the cumulative number of trips before each charging obeys a uniform distribution, the SOC at the beginning of charging is

$${\mathrm{S}}_0=(1-{\displaystyle \sum _{f=1}^h\frac{d_f}{d_{\max }}})\times 100\%$$

(1)

where S₀ is the starting SOC of EV charging in residential areas; h is the number of trips available before charging after the EV user is anxious; d_f is the mileage of the f-th trip, in km; d_max is the maximum travelable mileage, in km.

3.1.3. Charging Duration

The charging starting SOC, the maximum battery capacity, and the charging power of an EV are the main factors affecting its charging duration. The charging duration of each EV is

$$t_{\mathrm{c}}=\frac{({1-\mathrm{S}}_0)E}{P_c}$$

(2)

where t_c is the charging duration required to charge the SOC of the EV to 1, in hours; E is the battery capacity of the EV, in kWh; P_c is the EV charging power provided by the residential area, in kW.

3.2. Forecasting of EV Ownership in Residential Areas

The Bass model, as a dynamic evolution model that can express the process of emerging durable goods being gradually accepted by potential users, is often used to predict the diffusion trend of emerging durable goods [19,20]. Electric vehicles represent a new type of durable good, and forecasting their quantity is similar to forecasting the quantity of new durable goods.

In the discrete time domain, the Bass model can be expressed as

$$g(t)=Mp[1-\frac{G(t)}{M}]+qG(t)[1-\frac{G(t)}{M}]$$

(3)

where g(t) is the number of new durable goods newly added at time t; M is the upper limit of the maximum capacity of the user group; p and q are the coefficients representing the degree of influence of external media publicity and internal word-of-mouth communication on the diffusion of emerging durable goods, respectively; G(t) is the overall quantity of emerging durable goods accumulated to time t.

According to the statistical research of various durable goods, the empirical values of p and q in the Bass model range from 0.01 to 0.03 and 0.3 to 0.7, respectively.

4. Mathematical Model for Analysis of Charging Load Acceptance Capacity

4.1. Load Carrying Capacity Objective Function

The objective function is to take the maximum EV receiving capacity of the distribution network in residential areas as the objective function:

$$\{\begin{array}{l}\max C_E={\displaystyle \sum _{i=1}^{24}{C}_E(i)}\\ C_E(i)={\displaystyle \sum _{k=1}^r{\displaystyle \sum _{j=1}^{n_k}{P}_j^k(i)}}\end{array}$$

(4)

where C_E is the EV charging load that can be accepted by the residential distribution network, in kW; C_E(i) is the EV charging load that the residential distribution network can accept at the time i, in kW; r is the power supply area of the residential distribution network; n_k is the total number of nodes in the k-th power supply area of the residential distribution network; P_j^k(i) is the EV charging load that the j-th node of the k-th power supply area can accept at time i, in kW.

4.2. Restrictions

The constraints are the system capacity of the residential distribution network, the capacity of each station, the voltage offset of each node of the distribution network, and the power flow balance of the distribution network.

4.2.1. Residential Area Distribution Network System Capacity Constraints

After the EV charging load that can be accommodated by the distribution network in the residential area is superimposed with the conventional electricity load in the residential area, the overall electricity load of the distribution network cannot exceed the overall capacity of the distribution network system in the residential area. Therefore, the capacity constraints of the distribution network system of the EV acceptance capacity analysis model are:

$$C_E(i)+P_{norm}(i)\le C_{\max }$$

(5)

where P_norm(i) is the conventional electricity load of the residential area at the i-th moment, in kW; C_max is the upper limit of the capacity of the distribution network system in the residential area, in kW.

4.2.2. Station Capacity Constraints

After the EV charging load that can be accommodated by the nodes in each power supply area of the residential distribution network is added with the conventional electricity load of the residential distribution network nodes, the overall electricity load of the node cannot exceed the capacity of each node of the residential distribution network. Therefore, the capacity constraints of the distribution network node station area of the EV acceptance capacity analysis model are:

$$P_j^k(i)+P_{norm\_j}^k(i)\le C_{\max \_j}^k$$

(6)

where P^k_{norm_j}(i) is the conventional electricity load of the j-th node in the k-th power supply area at time i, in kW; C^k_{max_j} is the upper limit of the capacity of the j-th node in the k-th power supply area, in kW.

4.2.3. Voltage Constraints at Each Node of the Distribution Network

After the EVs connected to the distribution network in the residential area reach the upper limit of the receiving capacity, the node voltage deviation degree of each node does not exceed the upper and lower limit of the node voltage of the distribution network. Therefore, the voltage constraints of each node of the distribution network of the EV acceptance capacity analysis model are:

$$U_n^{\min }\le U_n\le U_n^{\max }\begin{array}{cc}& \end{array}(n=1,\cdots ,node)$$

(7)

where node is the number of nodes of the distribution network; U_n is the node voltage of the n-th node of the distribution network, in V; U_n^min is the lower limit of the node voltage of the n-th node of the distribution network, in V; U_n^max is the node voltage of the n-th node of the distribution network upper limit, in V.

4.2.4. Power Flow Balance Constraint

The distribution network in residential areas is generally a radial network, the head node is the power supply node, and the other nodes are PQ nodes. Therefore, the power flow balance constraint of the distribution network in the residential area of the EV acceptance capacity analysis model in the residential area is:

$$\{\begin{array}{l}{P}_{\alpha }=U_{\alpha }{\displaystyle \sum _{\beta =1}^{node}{U}_{\beta }(G_{\alpha \beta }\cos {\delta }_{\alpha \beta }+B_{\alpha \beta }\sin {\delta }_{\alpha \beta })}\hfill \\ Q_{\alpha }=U_{\alpha }{\displaystyle \sum _{\beta =1}^{node}{U}_{\beta }(G_{\alpha \beta }\sin {\delta }_{\alpha \beta }-B_{\alpha \beta }\cos {\delta }_{\alpha \beta })}\hfill \end{array}$$

(8)

where P_α is the active power of the α-th node of the distribution network, in kW; Q_α is the reactive power of the α-th node of the distribution network, in kVA; U_α is the node voltage of the α-th node of the distribution network, in kW; U_β is the node of the β-th node of the distribution network voltage, in kW; G_αβ and B_αβ represent the real part and imaginary part of the node admittance matrix of the distribution network system, respectively; δ_αβ = δ_α − δ_β is the phase-angle difference between α and β.

4.3. Calculation of the Acceptance Capacity of EVs

The acceptance capacity of EVs in the distribution network of residential areas is mainly related to the charging load and charging characteristics of EVs and the charging habits of users. Among them, the average charging time, charging power, and charging probability of EVs are the main influencing factors.

The distribution network of residential areas can accommodate EV trips expressed as

$$n_{ev}=\frac{E_{day}}{t_c^a{P}_c\lambda }$$

(9)

where n_ev is the number of EVs that can be accommodated by the distribution network in the residential area; E_day is the maximum daily charging power provided by the distribution network under the condition that the load acceptance capacity of the distribution network, in kW; t_c^a is met and the charging load characteristics are kept constant, in an hour; P_c is the average charging time of electric vehicles in residential areas, in kW; λ is the proportion of EVs that need to be charged every day.

4.4. Particle Swarm Optimization Algorithm

The particle swarm optimization (PSO) algorithm applies to the extreme value problem of continuous functions for nonlinear problems with strong global search capability. Therefore, in this paper, the PSO algorithm is chosen to solve the analytical model for the objective function and constraints of the established residential distribution network EV acceptance capacity analytical model [21,22]. It has two core formulas, which are the particle velocity update formula and the particle position update formula. Among them, the particle velocity update formula of the PSO algorithm is:

$$\begin{array}{c}{v}_i=\omega \times v_i+c_1\times rand()\times (pbes{t}_i-x_i)\\ +c_2\times rand()\times (gbest-x_i)\end{array}$$

(10)

where ω is the inertia weight of the algorithm when the value of inertia weight is large, when the algorithm has strong global search ability, when the value of inertia weight is small, and when the algorithm has strong local search ability (this paper takes ω as 0.8); c₁ and c₂ are the learning factors of the algorithm, i.e., c₁ is the individual learning factor of the particle and c₂ is the social learning factor of the particle (this paper generally takes c₁ = c₂∈ [0, 4] and c₁ = c₂ = 1.5); rand() is a random number between 0 and 1; v_i is the moving speed of particle i; x_i is the current position of particle i; pbest_i is the individual extremum of particle i; gbest is the global extremum of the particle population.

The particle position update formula of the PSO algorithm is:

$$x_i=x_i+v_i$$

(11)

In this paper, the admittance capacity of each node is the particle, the node access priority is set to a total of n levels, and the number of populations is N. The sum of the admittance capacity of all nodes in the distribution network is used as the fitness value, and the specific calculation process is shown in Figure 5. This paper uses matlab 2017b to program and simulate the model.

5. Case Analysis

5.1. Residential Area Parameters

Taking a residential area in a Chinese city as a reference, it is assumed that the residential area has 4000 households and a total population of 12,000 in 2019, the occupancy rate is 1, and there are 4056 private vehicles. The saturation value of EV ownership in the residential area M is the private vehicles in the residential area. The saturation value is 70%, p is 0.3, and q is 0.38, and the parameters of charging facilities for EVs and residential areas are shown in

Table 1. Parameters of EVs and charging facilities.

EVs as a Proportion of Private Vehicles/%	Battery Capacity/kWh	Recharge Mileage/km	Charging Power/kW
2.05	40.62	305	7

. The historical quantity and growth rate of private vehicles in the city are shown in

Table 2. Private vehicle quantities and growth rates in a city in China.

Year	Private Vehicle Quantity/Thousands	Private Vehicle Growth Rate/%
2011	1033	32.8
2012	1277	23.6
2013	1572	23.1
2014	1933	23.0
2015	2241	15.9
2016	2564	14.4
2017	2853	15.0
2018	3158	10.7
2019	3499	10.8

.

The maximum active load carried by the distribution system is set to 20 MW, and the rated voltage of the system is set to 10 kV. The node capacity and active and reactive load power parameters of each node in the target year are shown in

Table A1. Load parameters of each node.

Node Number	Node Injected Active Load/kW	Node Injected Reactive Load/kVar	Node Capacity/kVA	Power Factor
1	0	0	-
2	0	0	0
3	0	0	0
4	100	30	200	0.958
5	350	60	800	0.986
6	250	60	630	0.972
7	300	75	800	0.970
8	300	75	800	0.970
9	0	0	0
10	300	75	800	0.970
11	300	75	800	0.970
12	0	0	0
13	300	75	800	0.970
14	300	75	800	0.970
15	300	75	800	0.970
16	300	75	800	0.970
17	300	75	800	0.970
18	300	75	800	0.970
19	0	0	0
20	350	85	800	0.972
21	0	0	0
22	250	60	630	0.972
23	300	75	800	0.970
24	200	50	500	0.970
25	0	0	0
26	250	60	630	0.972
27	300	75	800	0.970
28	300	75	630	0.970
29	300	75	800	0.970
30	350	85	630	0.972
31	300	75	800	0.970
32	250	60	630	0.972
33	0	0	0
34	200	50	500	0.970
35	400	100	1000	0.970
36	350	85	800	0.972
37	300	75	800	0.970
38	200	50	500	0.970

, and the line impedance is shown in

Table A2. Line parameters of distribution network.

Starting Node	End Node	Resistance/Ω	Reactance/Ω	Distance/km
1	2	0.0264	0.0714	0.2
2	3	0.264	0.714	2
3	4	0.27	0.335	1
3	5	0.27	0.335	1
5	6	0.27	0.335	1
5	7	0.27	0.335	1
5	8	0.27	0.335	1
2	9	0.264	0.714	2
9	10	0.27	0.335	1
9	11	0.27	0.335	1
9	12	0.27	0.335	1
12	13	0.27	0.335	1
12	14	0.27	0.335	1
12	15	0.27	0.335	1
12	16	0.27	0.335	1
12	17	0.27	0.335	1
12	18	0.27	0.335	1
2	19	0.066	0.1785	0.5
19	20	0.27	0.335	1
19	21	0.132	0.357	1
21	22	0.27	0.335	1
21	23	0.27	0.335	1
21	24	0.27	0.335	1
21	25	0.27	0.335	1
25	26	0.27	0.335	1
25	27	0.27	0.335	1
21	28	0.27	0.335	1
28	29	0.27	0.335	1
29	30	0.27	0.335	1
30	31	0.27	0.335	1
31	32	0.27	0.335	1
2	33	0.33	0.8925	2.5
33	34	0.54	0.67	2
33	35	0.27	0.335	1
33	36	0.27	0.335	1
33	37	0.27	0.335	1
33	38	0.27	0.335	1

. Node 1 of the power distribution system in the calculation example is a balanced node and its per-unit value of the node voltage is 1.05, and the other nodes are PQ nodes. Unit reactance X = 0.357 Ω/km; branch line model: LGJ-120, unit resistance R = 0.27 Ω/km, unit reactance X = 0.335 Ω/km. The per-unit value of the node voltage of all nodes in the power distribution system can range from 0.93 to 1.05.

5.2. EV Access Node Prioritization

The distribution network is divided into different power supply areas according to the topology of the distribution network in the residential area and the conventional electricity load. In this paper, we take the distribution system of a residential area in China as an example, and divide the distribution network into four power supply zones, as shown in Figure 6.

The distribution system is a radiating distribution network. When the charging facility is connected to the node near the end of the distribution network for charging, the node voltage offset and network loss will increase. When the node at the terminal is charged, the degree of node voltage offset and network loss will be reduced. Therefore, when planning and constructing EV charging facilities in residential areas, charging facilities should be constructed at the head-end of the distribution network.

5.3. Simulation Conditions

By analyzing the conventional electricity load data of the residential area, the conventional electricity load data of the residential area is processed per unit, and the per unit value of the conventional electricity load at each moment of the typical weekdays and weekends in summer is obtained respectively, as shown in Figure 7.

In this paper, considering factors such as geographical location, node capacity, and line impedance, and the priority of EV access nodes in each power supply zone is divided, as shown in

Table 3. Priority of EV access nodes in each power distribution area.

Power Distribution Area	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8	Level 9	Level 10	Level 11
Area I	5	7	8	6	4	-	-	-	-	-	-
Area II	13	18	17	14	15	16	10	11	-	-	-
Area III	20	28	29	30	27	23	26	22	31	32	24
Area IV	35	36	37	34	38	-	-	-	-	-	-

.

5.4. Simulation Results

Fitting the private vehicles growth rate data in Table 2, the fitting result can be expressed as

$$f(t)=a{\mathrm{e}}^{-{(\frac{t-b}{c})}^2}$$

(12)

where a, b, and c are the fitting curve parameters for a = 0.4652, b = 2003, and c = 12.51, respectively.

The fitting result of (12) is used to predict the number of private vehicles in the residential area to obtain its saturation value, and the Bass model is used to predict the number of EVs. The predicted results of the number of private vehicles and electric vehicles are shown in Figure 8.

The Monte Carlo method is used to sample and simulate the travel of EVs in the residential area, and the distribution probability of the EV charging time in the residential area on weekdays and weekends is obtained, as shown in Figure 9.

The average charging time of EVs in residential areas is shown in

Table 4. Average charging time of EVs in residential areas.

Type of Trip	Work Trips on Weekdays	Social Shopping Trips on Weekdays	Social Shopping Trips on Weekends
Average charging time/hours	2.36	2.38	2.38

. The calculation results show that the proportions λ of EVs that need to be charged on weekdays and weekends are 37.53% and 34.99%, respectively.

According to the power supply partition and node access priority of the residential distribution network, the particle swarm algorithm is used to solve the analysis model of the EV reception capacity of the residential distribution network in the target year based on the power flow calculation, and the weekdays are then obtained. The spatial and temporal distribution of EV charging load acceptance capacity in residential distribution networks on weekends and weekends is shown in Figure 10. The EV charging load accepted by the distribution network in residential areas on weekdays is distributed from 1:00 to 12:00 in time; the EV charging load accepted by the distribution network in residential areas on weekends is distributed in time from 1:00 until 10:00.

When the time constraints of EV charging behavior in residential areas are not considered, the maximum EV charging load that can be connected to each power supply partition of the power distribution system is shown in Figure 11. Due to the relatively large capacity of nodes 31, 32, and 24 of the 9th, 10th, and 11th nodes at the end of the load priority end of the EV in the power distribution system, the power distribution system has no overload and operation risks, leading to the power supply on weekends. The reception capacity of Zone II at 24:00 sharply increases.

Figure 12 shows the node voltage when the output power of the head-end node of the distribution network is the largest. When the output power of the head-end node of the distribution network is the largest, the voltage of nodes 14, 15, 16, 17, and 18 is the lowest but does not exceed the allowable range of the 10 kV line voltage offset.

Nodes 5, 13, 20, and 35 are located in the power supply area’s first-level charging nodes. The acceptable charging load is calculated within the allowable range of the acceptance capacity while keeping the charging load characteristics unchanged, and the comparison between the load characteristics and the acceptance capacity is shown in Figure 13 (taking node 5 as an example). For each node in the target year, the daily serviceable number of vehicles and the charging capacity is shown in

Table 5. Priority of EV access nodes in each power supply area.

Node	5	13	20	35
All-day charging capacity (weekdays)/kWh	1339	1421	1339	1736
The number of charging EVs throughout the day (weekdays)/vehicles	202	215	202	262
Number of EVs that can be accommodated (weekdays)/vehicles	538	573	538	698
All-day charging capacity (weekends)/kWh	2355	2557	2355	3095
The number of charging EVs throughout the day (weekends)/vehicles	353	383	353	464
Number of EVs that can be accommodated (weekdays)/vehicles	1009	1095	1009	1326

.

6. Conclusions

According to the topology structure of the distribution network in the residential area, the daily load, and the characteristics of the charging load of the residential distribution network, this paper establishes an optimized mathematical model to calculate the maximum acceptance capacity of the EV charging load in the residential distribution network. The main conclusions are as follows:

(1) The proposed calculation method for the acceptance capacity of the EV charging load in the residential distribution network can be extended to other residential distribution network with any topology.

(2) Through the different charging load characteristics of EVs in the distribution network on typical weekdays and weekends and the predicted charging load size in the next five years, the capacity margin of the residential distribution network and whether it needs to be transformed in the next five years can be analyzed. In addition, due to the more balanced distribution of charging probability on weekends, the number of charging EVs that can be accommodated on weekends is about 1.87 times that of workdays.