At present, the large-scale access to electric vehicles (EVs) is exerting considerable pressure on the distribution network. Hence, it is particularly important to analyze the capacity of the distribution network to accommodate EVs. To this end, we propose a method for analyzing the EV capacity of the distribution network by considering the composition of the conventional load. First, the analysis and pretreatment methods for the distribution network architecture and conventional load are proposed. Second, the charging behavior of an EV is simulated by combining the Monte Carlo method and the trip chain theory. After obtaining the temporal and spatial distribution of the EV charging load, the method of distribution according to the proportion of the same type of conventional load among the nodes is adopted to integrate the EV charging load with the conventional load of the distribution network. By adjusting the EV ownership, the EV capacity in the distribution network is analyzed and solved on the basis of the following indices: node voltage, branch current, and transformer capacity. Finally, by considering the 10-kV distribution network in some areas of an actual city as an example, we show that the proposed analysis method can obtain a more reasonable number of EVs to be accommodated in the distribution network.
With the establishment and growing popularity of strategic objectives such as carbon peaking and carbon neutralization worldwide, as well as the proposal of relevant concepts such as green power grids and green energy consumption, intelligent and sustainable modes of transportation, including electric vehicles (EVs), are being actively promoted [
EV charging load forecasting is the basis for analyzing the EV charging capacity of the distribution network, and researchers have conducted numerous studies in this regard. By analyzing the characteristics of the temporal distribution of the EV charging load, a Monte Carlo simulation method was used to predict the EV charging load after fitting the probability distribution of the last trip end time and daily mileage of the EV [
The capacity of the distribution network to accommodate EVs depends on various factors, which have been studied from different perspectives in the existing literature. The influence of the EV charging load on the service life of the distribution network transformer has been discussed extensively [
Although the aforementioned studies have used various evaluation indicators to analyze the capacity of the distribution network to accommodate EVs, the following deficiencies persist in the prediction of the EV charging load and the integration of the charging load and conventional load: (1) EV trips are random in time and space, and their charging time and place are related to the journey. However, the aforementioned studies have not fully considered the space-time characteristics of the EV charging load in its prediction. (2) When dividing the distribution network into functional areas, the load category in the functional area is generally considered unique; however, in fact, the load categories in the functional area are diverse. If there is only one load category in the default functional area, the accuracy of the result will be affected. Therefore, the conventional load should be processed more finely.
In view of the aforementioned shortcomings, this paper proposes a method for analyzing the EV capacity of the distribution network by considering the composition of the conventional load. First, the power load units in the distribution network are classified according to the load characteristics. Then, the distribution network topology is established by dividing the network into multiple small power supply areas. By combining the trip chain theory and the Monte Carlo method, the temporal and spatial distribution of the EV charging load is predicted, and a distribution method based on the proportion of the same type of conventional load between each node is proposed to integrate the charging load prediction results with the conventional load of the distribution network. The EV capacity of the regional distribution network is analyzed on the basis of the following indices: node voltage, branch power, and transformer load capacity. Finally, by considering a regional 10-kV distribution network as an example, the capacity of the distribution network to accommodate EVs is analyzed.
Owing to the complex distribution network lines and numerous loads in reality, as well as the random specific charging locations for EVs, a method for power load unit classification is proposed to prepare for the subsequent EV charging load distribution to each node of the distribution network.
A power load unit refers to the load with an independent distribution room or transformer for the power supply. Common power load units include residential buildings, communities, villages, office buildings, schools, and industrial parks. According to the load characteristics, the power load units can be categorized into residential load, commercial load, and office load. For convenience of the subsequent discussion, they will be denoted by class a, class b, and class c, respectively. The specific definitions are as follows.
It refers to the load that maintains the normal operation of residential places: a = {communities, villages, nursing homes, etc.}.
It refers to the load for commercial activities, b = {hotels, clubs, scenic spots, office buildings, etc.}.
It refers to the load involved in office and production activities, c = {government organs, schools, industrial parks, etc.}.
Owing the large number of power load units in the distribution network, to simplify the distribution network and facilitate the calculation, the concept of small power supply areas is proposed. It is simply understood that the power load units that are located on the same line and are relatively close to each other constitute a small power supply area. By dividing the distribution network into small power supply areas, the power load units in a certain range are gathered into a load node. Owing to such division, the distribution network is simplified considerably, as shown in
According to the division method shown in
According to the description of an EV trip in the trip chain theory, the daily trip process of a single EV is determined by the trip characteristic quantities, such as the first trip time Ts,1, the trip time tx from the departure to the destination, the parking time tp of different trip destinations, and the trip mileage d per trip [
The characteristic quantity in the trip chain can be categorized into time and space;
A suitable probability distribution model is selected for fitting according to the data distribution characteristics. When the data distribution characteristics are different from the distribution characteristics of common probability models, a Gaussian mixture distribution can be used for fitting, and its probability density function can be described by the weight
The analysis of the trip data revealed that the first trip moment of the day for the EV users obeys a one-dimensional Gaussian mixture distribution
According to the aforementioned method, the fitting of the EV travel characteristic quantities is completed, and the probability distribution of each characteristic quantity is calculated subsequently. Finally, the complete EV travel chain is generated through Monte Carlo random simulation. Furthermore, the endurance capacity of the vehicle decreases continuously during driving; hence, the initial state of charge (SOC) of the EV is set to 1 to update the battery charge state during driving. The calculation formula is expressed as follows:
It is assumed that the EV is charged when
It should be noted that in the survey and statistical data of users' trips in this study, there is no distinction between EVs and fuel vehicles, i.e., EVs and fuel vehicles are assumed to have the same trip regularity. In addition, this study is mainly based on the development status of EVs in the northern cities of China. At this stage, private EVs account for the vast majority of the EV market, whereas other types of EVs such as electric taxis account for a small proportion; the error caused by ignoring them is negligible. Moreover, considering that the charging of electric buses is uniformly dispatched by the operation company, it involves good planning and can be regarded as the conventional load in the distribution network. Hence, it will not be considered.
The temporal and spatial distribution of the EV cluster charging load in
By superimposing the EV charging load and the conventional load, the total load of the node after connecting the EV charging load can be obtained as follows:
A schematic diagram of the allocation method is shown in
To analyze and evaluate the capacity of an urban distribution network to accommodate EVs, the objective function for the maximum number of EVs accommodated in the distribution network is established as follows:
According to the objective function, the EV capacity of the distribution network is limited by the topology of the distribution network and its conventional load. It should be noted that the aim of this study is to calculate the maximum number of EVs that can be accommodated in the distribution network, regardless of the limitation of the charging piles, i.e., the number of charging piles in the distribution network is assumed to be sufficient.
The backward/forward sweep power flow calculation method [
In this study, part of an actual distribution network is used for analysis. The area contains six 110/10 kV substations with a total of 34 outgoing lines. The specific structure is simplified as shown in
Here, node 1 is the superior system equivalent node, the impedance between node 1 and node 2 is the system short-circuit impedance, node 2 is the 110 kV busbar, and nodes 3, 14, 20, 25, 28, and 40 are the 10-kV substation busbar nodes.
The transformer model and rated capacity of each substation are listed in
Number of nodes of the substation | Transformer model | Transformer capacity configuration (MVA) |
---|---|---|
3 | SFPZ7-50000/110 | 50 * 2 |
14 | SFZ7-10000/110 | 10 * 2 |
20 | SFZ7-12500/110 | 12.5 * 2 |
25 | SFZL7-6300/110 | 6.3 * 2 |
28 | SFZ7-40000/110 | 40 * 2 |
40 | SFPZ7-50000/110 | 50 * 2 |
The distribution network node conventional load and line impedance parameters are summarized in
Without considering the EV charging load connected to the distribution network, the power flow calculation is performed on the original distribution network. The node voltage distribution is obtained as shown in
As can be seen from the calculation results in
The National Household Trip Survey (NHTS) dataset [
The NHTS trip dataset contains 19 common trip purposes of the residents as well as the statistical analysis of the trip data of the vehicles within the city. The six trip purposes and trip frequencies of the residents with the highest frequency of driving on weekdays and weekends are summarized in
Trip frequency (%) | Go home | Shopping | Go to work | Entertainment | Pick up | Eat | Total |
---|---|---|---|---|---|---|---|
Weekdays | 32.48 | 16.86 | 16.30 | 8.63 | 7.50 | 7.19 | 88.96 |
Weekends | 36.93 | 20.34 | 3.98 | 13.76 | 4.08 | 11.70 | 90.79 |
In the calculation of the EV charging demand, the six trip destinations were classified into three categories: residential, office, and commercial. The charging demand generated at shopping and entertainment trip destinations was considered as commercial. Furthermore, charging was considered not to be performed when the stay at dining and pick-up trip destinations was too short.
The daily first trip times obeyed a three-peak mixed Gaussian distribution. The fitting results are shown in
Parameters | |||||||||
---|---|---|---|---|---|---|---|---|---|
Weekdays | 0.35 | 7.42 | 0.92 | 0.44 | 8.56 | 2.01 | 0.21 | 13.07 | 3.20 |
Weekends | 0.80 | 9.51 | 1.89 | 0.09 | 14.39 | 1.52 | 0.11 | 17.19 | 1.76 |
The trip duration of departure and destination follows a log-normal distribution
The mean and variance of the driving distance show a power function relationship with the driving duration. The fitting results are shown in
Trip day | ||||
---|---|---|---|---|
Weekdays | 0.19 | 1.34 | 0.09 | 1.37 |
Weekends | 0.12 | 1.49 | 0.07 | 1.50 |
The parking duration of vehicles at different destinations was analyzed, and only the shorter time was considered for vehicles whose destination was home; the case of returning home and not going out again was not considered. The vehicle parking times at different destinations show a large difference. The fitting results obtained using the log-normal and Gaussian mixture distribution are shown in
Trip purpose | Distribution type | Weekdays | Weekends | |
---|---|---|---|---|
Go home (min) | Log-normal distribution | 4.36 | 4.47 | |
1.15 | 1.16 | |||
Shopping (min) | Log-normal distribution | 3.08 | 3.21 | |
0.86 | 0.85 | |||
Go to work (h) | 3-peak mixed Gaussian distribution | 0.1 | 0.12 | |
0.64 | 0.40 | |||
0.45 | 0.27 | |||
0.43 | 0.38 | |||
3.84 | 3.74 | |||
1.38 | 1.48 | |||
0.47 | 0.49 | |||
8.97 | 8.34 | |||
1.36 | 1.92 | |||
Entertainment (min) | Log-normal distribution | 4.57 | 4.65 | |
1.02 | 0.94 | |||
Pick up (min) | Log-normal distribution | 1.64 | 1.91 | |
1.12 | 1.15 | |||
Eat (h) | Bimodal mixed Gaussian distribution | 0.38 | 0.62 | |
0.15 | 0.60 | |||
0.08 | 0.43 | |||
0.62 | 0.38 | |||
0.93 | 1.44 | |||
0.55 | 0.65 |
Dividing a day into 24 periods and considering the difference between going home for a short period of time and going home at the end of the trip, the size of the trip purpose shift matrix is 24 × 6 × 7. The trip shift probability between 17:00 and 18:00 on weekdays is shown in
The top five EVs in terms of the market share in the United States were selected for simulation. The specific parameters are listed in
Car model | Proportion | Battery capacity (kWh) | Power consumption per 100 km (kWh/100 km) |
---|---|---|---|
Tesla model 3 | 63% | 75 | 16 |
Tesla model X | 11.2% | 100 | 24 |
Tesla model S | 11% | 100 | 15.4 |
Chevrolet bolt | 8.1% | 66 | 17.2 |
Nissan leaf | 6.7% | 30 | 21.2 |
Considering the battery life and the impact on the distribution network, slow charging (5 kW) is preferred for EVs; however, fast charging (50 kW) is chosen when the slow charging mode cannot complete the charging task to support the next trip within the parking time. To improve the simulation accuracy, the EV trip and charging behavior were simulated continuously for 3 weeks with a simulation accuracy of 1 min. To exclude the error caused by the SOC in the starting phase, the charging load demand on Monday and Sunday of the second week in each charging area was chosen for analysis, as shown in
From
The analysis of charging loads connected to residential areas shows that the general trends of EV charging loads on weekdays and weekends are the same; however, between 12:00 and 20:00 on weekends, the EV charging loads are slightly higher than those at the same time on weekdays because more users are at home during the weekends and therefore have more opportunities to choose to charge their EVs at their place of residence.
In general, users stay in commercial areas for a short time, which is not sufficient to complete charging. Hence, the charging load of EVs entering commercial areas on weekdays and weekends is low; however, people are more accustomed to visiting commercial areas on weekends, making the charging load on weekends slightly higher than that on weekdays.
Combined with the aforementioned analysis of the charging loads in each region, the prediction results of this study for the spatial and temporal distribution of the EV charging loads are consistent with the actual situation and have high accuracy.
Taking Monday of the second week as an example, the EV capacity of the distribution network is analyzed according to the process shown in
From
Line branch | 11 | 12 | 13 |
---|---|---|---|
Conventional load (kVA) | 2764.3+393.7i | 2468.9+351.6i | 937.6+133.5i |
Total (kVA) | 6170.8+878.8i |
Number of nodes | Class a load | Class b load | Class c load |
---|---|---|---|
11 | 6.09% | 3.98% | 0.23% |
12 | 4.00% | 13.09% | 0% |
13 | 1.05% | 7.61% | 0% |
First, the analysis is done from the perspective of the conventional load on the line where node 11 is located. When EV charging load is not considered, the conventional load on the line is shown in
The aforementioned analysis shows that under the existing distribution grid structure, the number of EVs that can be accommodated in the distribution grid in the region is around 22973, considering the spatial and temporal characteristics of the EV trip and charging behavior.
The proposed method allocates the charging load in proportion to the conventional load of the same category among the nodes, which offers the following advantages:
The manner of division of the distribution network into functional areas is improved. Previously, the functional area was large in scope and had a single conventional load category. However, in fact, the functional area may also contain other categories of the conventional load during the division. For example, the office area includes not only schools, party and government agencies, and factories and other loads but also residential and commercial loads of a certain scale. The division of the electric load unit classification and electronic supply area in this study overcomes this drawback.
The accuracy of the charging load allocation is improved. If the spatial characteristics of the charging load are not considered, i.e., if the charging load in each area is not distinguished, and the total charging load is directly distributed according to the total conventional load of each node, there will be a large deviation in the distribution result, as shown in
Distribution mode | Distribution results (kW) | Total (kW) | ||
---|---|---|---|---|
Spatial characteristics are considered | Class a | Class b | Class c | 1245.1 |
1123.6 | 119.0 | 2.5 | ||
Spatial characteristics are not considered | 788.5 | 788.5 |
As can be seen from
Considering that the increasing EV charging load due to large-scale access to EVs will affect the safe and stable operation of the distribution network, this paper proposed a method for analyzing the EV charging capacity of the distribution network. First, the topology the of distribution network was simplified by analyzing and preprocessing the distribution network model. Second, by combining the trip chain theory and Monte Carlo simulation method, the driving trip and charging behavior of urban residents was analyzed, and the temporal and spatial distribution of the EV charging demand was predicted. Considering the diversity of the conventional load composition categories of the actual distribution network nodes, a distribution method based on the proportion of the conventional load of the same category among nodes was proposed to integrate the charging load with the conventional load of the distribution network. Finally, the EV charging capacity of the distribution network was solved via power flow calculation. In this study, specifically, a feasible EV charging load distribution method was proposed on the basis of the characteristics of the space-time distribution of the EV charging load and the composition characteristics of the node conventional load. Compared with the traditional method of dividing the distribution network into functional areas, this study made a more refined classification of the power load units in the power supply area. The proposed EV charging load distribution method was shown to effectively reduce the error caused by a single load category in the traditional method, ensure reasonable distribution of the charging power to each node, and improve the reliability of the results. The findings presented herein can provide not only a reference to power grid operators for relevant decisions but also significant guidance to the government for planning the development of EVs.
We are grateful to our professors for their patient guidance as well as our laboratory associates for their assistance. We also thank Zhangjiakou Power Supply Company for their support. We would like to acknowledge TopEdit
First node number | End node number | Branch impedance ( |
Active power of end node (kW) | Reactive power of end node (kVar) |
---|---|---|---|---|
1 | 2 | 0.0000+0.0278i | 0.0000 | 0.0000 |
2 | 3 | 0.0048+0.1176i | 0.0000 | 0.0000 |
3 | 4 | 0.1602+0.2896i | 3920.4000 | 558.3600 |
3 | 5 | 0.0582+0.1097i | 2257.2000 | 321.4800 |
5 | 6 | 0.0582+0.1097i | 856.5000 | 121.9864 |
6 | 7 | 0.0582+0.1097i | 1982.5700 | 282.3660 |
7 | 8 | 0.0582+0.1097i | 500.9400 | 71.3460 |
3 | 9 | 0.2232+0.4345i | 3165.5250 | 450.8475 |
3 | 10 | 0.5412+0.9335i | 3752.1000 | 534.3900 |
3 | 11 | 0.1038+0.1940i | 2764.3030 | 393.7038 |
11 | 12 | 0.1038+0.1940i | 2468.9610 | 351.6399 |
12 | 13 | 0.1038+0.1940i | 937.6290 | 133.5411 |
2 | 14 | 0.0327+0.5834i | 0.0000 | 0.0000 |
14 | 15 | 0.6257+1.0442i | 1447.8750 | 206.2125 |
15 | 16 | 0.6257+1.0442i | 1311.7500 | 186.8250 |
16 | 17 | 0.6257+1.0442i | 1034.5500 | 147.3450 |
17 | 18 | 0.6257+1.0442i | 826.6500 | 117.7350 |
14 | 19 | 2.3556+4.4434i | 1480.0500 | 210.7950 |
2 | 20 | 0.0245+0.4667i | 0.0000 | 0.0000 |
20 | 21 | 0.4950+0.8280i | 1527.0750 | 217.4925 |
20 | 22 | 0.3997+0.7736i | 3848.6250 | 548.1375 |
22 | 23 | 0.3997+0.7736i | 1022.1750 | 145.5825 |
20 | 24 | 1.4786+2.7731i | 1227.6000 | 174.8400 |
2 | 25 | 0.0574+0.9261i | 0.0000 | 0.0000 |
25 | 26 | 0.2621+0.3103i | 3153.1500 | 449.0850 |
26 | 27 | 0.2621+0.3103i | 638.5500 | 90.9450 |
2 | 28 | 0.0060+0.1458i | 0.0000 | 0.0000 |
28 | 29 | 0.0161+0.0198i | 2363.6250 | 336.6375 |
28 | 30 | 0.0876+0.2488i | 3437.7750 | 489.6225 |
28 | 31 | 0.1872+0.3110i | 950.2500 | 135.3386 |
31 | 32 | 0.1872+0.3110i | 4044.1500 | 575.9850 |
32 | 33 | 0.1872+0.3110i | 1025.6400 | 146.0760 |
28 | 34 | 0.4238+0.7056i | 3507.0750 | 499.4925 |
28 | 35 | 0.0585+0.1116i | 1722.6000 | 245.3400 |
35 | 36 | 0.0585+0.1116i | 1366.2000 | 194.5800 |
36 | 37 | 0.0585+0.1116i | 1289.4750 | 183.6525 |
37 | 38 | 0.0585+0.1116i | 1027.1250 | 146.2875 |
28 | 39 | 0.6190+0.8384i | 2504.7000 | 356.7300 |
2 | 40 | 0.0048+0.1176i | 0.0000 | 0.0000 |
40 | 41 | 0.5783+1.1401i | 2868.5250 | 408.5475 |
41 | 42 | 0.5783+1.1401i | 2640.8250 | 376.1175 |
40 | 43 | 0.4004+0.7530i | 2217.6000 | 315.8400 |
43 | 44 | 0.4004+0.7530i | 712.8000 | 101.5200 |
44 | 45 | 0.4004+0.7530i | 2460.1500 | 350.3850 |
40 | 46 | 0.0618+0.1095i | 1220.1750 | 173.7825 |
46 | 47 | 0.0618+0.1095i | 390.9260 | 55.6773 |
47 | 48 | 0.0618+0.1095i | 1931.8610 | 275.1438 |
48 | 49 | 0.0618+0.1095i | 1393.9200 | 198.5280 |
49 | 50 | 0.0618+0.1095i | 1193.5400 | 169.9890 |
40 | 51 | 0.0592+0.0903i | 2138.4000 | 304.5600 |
40 | 52 | 0.6885+1.2236i | 1628.5500 | 231.9450 |
40 | 53 | 0.2990+0.5777i | 992.4750 | 141.3525 |
53 | 54 | 0.2990+0.5777i | 1282.0500 | 182.5950 |
40 | 55 | 0.1521+0.2808i | 1103.8500 | 157.2150 |
55 | 56 | 0.1521+0.2808i | 746.2100 | 106.2784 |
56 | 57 | 0.1521+0.2808i | 2148.3000 | 305.9700 |
57 | 58 | 0.1521+0.2808i | 1425.6000 | 203.0400 |
Trip time | Last trip | This trip | |||||
---|---|---|---|---|---|---|---|
Go home | Shopping | Go to work | Entertainment | Pick up | Eat | ||
Weekdays |
Go home | (2.76,1.05) | (2.36,0.72) | (2.94,0.73) | (2.85,0.86) | (2.41,0.73) | (2.39,0.68) |
Shopping | (2.45,0.73) | (2.21,0.77) | (2.46, 0.8) | (3.24,0.96) | (2.18,0.94) | (2.28,0.77) | |
Go to work | (3.01,0.78) | (2.68,0.82) | (2.79,0.88) | (2.94,0.84) | (2.85,0.78) | (2.38,0.73) | |
Entertain-ment | (2.89,0.80) | (2.61,0.85) | (2.20,0.83) | (2.83,0.86) | (3.11,0.94) | (2.70,0.79) | |
Pick up | (2.34,0.73) | (2.46,0.80) | (2.73,0.76) | (3.22,0.82) | (2.25,0.79) | (2.35,0.73) | |
Eat | (2.5, 0.74) | (2.31,0.85) | (2.33,0.69) | (2.93,1.12) | (2.76,1.04) | (2.49,0.92) | |
Weekends |
Go home | (3.05,1.31) | (2.46,0.70) | (2.75,0.76) | (3.09,0.90) | (2.56,0.87) | (2.62,0.80) |
Shopping | (2.48,0.70) | (2.21,0.70) | (2.04,0.46) | (2.66,0.56) | (2.65,0.89) | (2.39,0.96) | |
Go to work | (2.81,0.77) | (2.67,0.79) | (2.54,0.87) | (3.32,0.24) | (2.95,0.79) | (2.51,0.88) | |
Entertain-ment | (3.07,0.87) | (2.75,0.78) | (2.25,1.15) | (3.15,0.98) | (2.97,0.93) | (2.95,0.90) | |
Pick up | (2.56,0.93) | (2.81,1.01) | (3.13,1.04) | (3.61,0.79) | (2.87,0.98) | (2.96,0.86) | |
Eat | (2.69,0.82) | (2.69,0.86) | (2.40,0.97) | (2.83,1.03) | (3.18,0.79) | (2.51,0.89) |