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The charging load of electric vehicles (EVs) is characterized by uncertainty and flexibility, which burdens the distribution network, especially when there is a high penetration of distributed generation (DG) in smart grids. Largescale EV mobility integration not only affects smart grid operation reliability but also the reliability of EV charging services. This paper aims at estimating the comprehensive impacts caused by spatialtemporal EV charging from the perspective of both electricity system reliability and EV charging service reliability. First, a comprehensive reliability index system, including two novel indexes quantifying EV charging service reliability, is proposed. Then, considering traffic constraints and users’ charging willingness, a spatialtemporal charging load model is introduced. In the coupled transportation and grid framework, the reliability impacts from plenty of operation factors are analyzed. Moreover, the electricity system reliability and EV charging service reliability correlated with DG integration are discussed. A coupled transportation grid system is adopted to demonstrate the effectiveness and practicability of the proposed method. The numerical results analyze reliability impacts from EV penetration level, trip chain, EV battery capacity, DG installation location, and capacity. The proposed studies reveal that when the EV capacity ratio to DG capacity is 3:1, the system reliability reaches the maximum level.
1) Impacts on reliability are studied from the perspective of both electricity system and EV charging service.
2) A spatialtemporal simulation strategy for mobile EV charging load is proposed.
3) A coupled transportation and grid framework is used for reliability assessment.
4) Reliability impacts from EV penetration level, trip chain, EV battery capacity, DG installation location and capacity are quantified.
The problems of carbon emissions and energy shortage have been increasingly serious nowadays, which has captured people’s attention on sustainable and clean energy. Thus, the application of electric vehicles (EVs) has attracted much attention recently (
The transportation network and distribution network are closely coupled and interacted due to EV charging and movement. An integrated trafficpower framework proposed in
As participants in both urban transportation networks and distribution networks, characteristics of EV mobile charging load are closely associated with users’ travel habits and traffic constraints. Furthermore, the larger the scale of EV integration, the tighter the correlation among different participants. On this basis, some scholars have studied how to model transportation characteristics accurately. In
The existing research evaluates the impacts of electric vehicle integration on system reliability which is generally analyzed in terms of electricity system reliability. In contrast, the reliability of EV charging services is rarely discussed. In
The impacts of distributed generation (DG) integration on urban distribution networks cannot be ignored for its intermittent and uncertain power characteristics
Considering insufficiency in these studies, the reliability impacts of largescale mobile EV integration on electricity systembased sequential Monte Carlo method are discussed in this paper. The main contributions of this paper are as follows:
1) A comprehensive reliability assessment method that quantifies both electricity system reliability and EV charging service reliability is proposed. Two novel indexes aiming to quantify EV charging power reliability are put forward to evaluate the curtailing extent of charging energy in each bus and analyze the charging energy not supplied from a holistic perspective.
2) A spatialtemporal mobile EV charging load model based on the vehicletransportationgrid trajectory is proposed considering EV traffic characteristics and users’ charging willingness. In the coupled transportation and grid framework, reliability impacts considering plenty of operation factors are comprehensively analyzed.
3) Reliability impacts of DG integration on the grid with largescale mobile EV deployment are quantified. The coordinated operation strategy of EVs and DG is discussed as well. DG installation locations can be selected to coordinate the reliability level of the distribution system and EV charging service. Moreover, the optimal DG capacity configuration, which brings the highest system reliability level, is provided.
The rest of this paper is organized as follows: in
As an uncertain load coupling transportation system and distribution system, EVs should be modeled spatially and temporally. In this section, EV mobile trajectory is formulated first based on a trip chain and Dijkstra algorithm. Then flexible charging of EV is modeled, including EV trip time, SOC consumption, charging mode selection, and users’ charging willingness.
EV charging load is different from conventional load due to its traffic characteristics. EV traveling starting point, destination, traveling distance, and users’ habits will influence the charging behavior. Considering transportation constraints, EV state of charge (SOC) is determined through its travel trajectory. As a result, transportation topology should be modeled first. In this paper, graph theory is employed for bidirectional transportation network modeling (
After transportation topology is obtained, EV mobile behavior should be modeled. The mobile behavior of EV users can be understood as a spatial and temporal interacting process, normally starting from one certain point and finally arriving at the destination, which can be simply categorized into three basic aspects: work, entertainment, and residence. A trip chain is usually utilized to reflect EV dynamic travel characteristics (
Assuming every trip starts at home, and after staying in several places, i.e., workplaces, EV users eventually return to home. Then trip chains are obtained to simulate EV users traveling behaviors depicted in
EV traveling trajectory with two types of trip chains.
Trip chain of EVs.





RW•WR  RW•WE•ER  RE•EW•WR  RR•RW•WR  
RR•RR  RW•WR•RR  RE•ER•RR  RR•RE•ER  
RE•ER  RW•WW•WR  RW•EE•ER  RR•RR•RR 
The Dijkstra algorithm proposed by Dijkstra in 1959 is a common algorithm to find the shortest path from a point to any other point in graph theory (
In this section, EV traveling state, including traveling time and SOC consumption is modeled. As a flexible charging load, users’ charging willingness and charging pattern are also discussed.
According to the statistics of the UK Ministry of Transport in 2016 (
Then EV parking time and restarting time can be calculated based on EV traveling speed:
If EV is charged during the trip, then
SOC of EV is dependent on users driving length. If SOC is lower than its threshold value after a driving distance, then EV should be charged to ensure the next trip ends successfully. Thus, making sure SOC be able to support the next trip for each period is essential. Assuming that SOC is decreased linearly with the increase of traveling distance, SOC at one certain point during the trip can be calculated as follows:
Before EV charging mode selection, users should decide whether EV should be charged first. Based on the current SOC, the EV traveling distance that can be supported before reaching the threshold is formulated as follows:
If the following formula is met, then the
Naturally, the duration for midway charging can be calculated as follows:
However, considering users charging willingness, sometimes EV will still be charged even though the current SOC can support the next trip. In this case, users will choose to charge or not based on business urgency, or their behavioral habits, etc. Consequently, a user charging demand model is adopted in this paper to describe the charging probability based on fuzzy theory (
Then, the membership function
After users decide to charge for EV, then the charging pattern should be discussed. EV users usually charge for EV at night when a fullday trip ended, as they should be prepared for the next day’s trip, and electricity price in the evening is generally lower than during the day. For the charging mode, a slowcharging mode is preferred at night when there is enough time for the charging since frequent fast charging may accelerate battery aging. For other situations, the charging pattern should be analyzed. If SOC cannot be charged to the full state through slowcharging mode during the parking time, the fastcharge mode should be adopted, which can be expressed as follows:
As the mobile EV charging load model proposed is timedependent and the system state is continuously changed, the sequential Monte Carlo simulation is adopted in this paper to evaluate electricity system reliability (
In this part, three common reliability indexes to capture interruption duration, frequency, and load curtailment are introduced. In addition, two novel indexes aiming at EV charging service reliability are proposed to complement the existing indexes. All indexes are calculated based on sequential Monte Carlo simulation.
For the distribution system, reliability indexes of SAIFI (system average interruption frequency index), SAIDI (system average interruption duration index), and EENS (expected energy not supplied) are adopted to perform reliability assessment, which can be calculated as
Components faults in the distribution network are relevant to environmental and operational factors. Different factors, such as service time, production defects, temperature, etc., can lead to component fault with a specified probability (
Assuming that the duration of components in each state obeys an exponential distribution, the random state of the system is obtained by combining the operation states of components. Additionally, the electricity system reliability index is calculated based on the optimal power flow (OPF) solved by MATPOWER. Specific steps of the reliability assessment based on sequential Monte Carlo are as follows:
1) Set up the initial system state and input the original data, including grid topology, power load, charging load, power generation, etc.
2) According to the failure rate and repair rate of components, the time series state of components is extracted, and the component state matrix is generated. The duration of down and upstate is obtained as follows:
3) According to the component state matrix, the optimal power flow is calculated when a component failure occurred. If part of the load is curtailed, the system is considered in a failure state. Based on the simulation results, the reliability indexes are calculated based on
4) In the process of sequential Monte Carlo evaluation, a stopping criterion is adopted when calculated parameters during the simulation are tended to be stable, which can be seen as
In this section, the overall framework of the proposed method is introduced. The coupled system frameworkbased spatialtemporal EV charging mobility is shown in
Coupled system framework based spatialtemporal mobile EV charging.
Solution steps of the proposed method are shown in
Flowchart of reliability evaluation considering spatialtemporal EV charging load.
For the first part, the spatialtemporal EV charging load is modeled. Firstly, EV traveling starting time and back time are obtained according to a normal distribution. Then, the EV traveling path is obtained through the trip chain and Dijkstra path search algorithm. Considering EV users’ charging willingness,
After EV charging load modeling, the total system load can be determined by combining the initial system load and EV charging load. The components are modeled as the Markovian components with two states, up and down. The optimal power flow (OPF) calculation is performed to obtain the system state with the minimum load shedding. If load curtailment occurs, the system state is identified as a failure. According to the OPF results, the reliability indexes are calculated. Repeat these steps until solutions are converged.
In this section, simulations based on the IEEE 57node test system and a coupled transportation system are performed. EV spatial and temporal characteristics are analyzed first. Then system reliability is deeply evaluated based on different EV penetration levels, trip chain, EV battery capacity, DG integrating location, and capacity.
The topology of coupled IEEE 57bus system and 59node transportation system is depicted in
Coupled system of distribution and transportation network.
For the parameters of EVs, the battery capacity of each EV is set to be 30 kWh, and the fastcharging power and lowcharging power are 20 and 6 kW, respectively. The whole generator capacity is 1976 MW in the 57bus system. It is defined that the penetration level of EV is the ratio of the fast charging power of the whole fleet to the total generator capacity. For example, a 10% penetration level means there are 9800 EVs in the coupled system (
The sequential Monte Carlo method is adopted in this paper, and the step size of the sequential simulation is set to 15 min. The failure rate of the feeder is set to 0.002, and the repair rate is 0.25. The failure of the generator is not considered. Virtual generators that have high generating and operation costs are connected to load buses to calculate load curtailment. The daily load profile data is obtained from
Charging load simulation for a working day and a resting day is performed in this section to evaluate the difference of charging load in different typical days. Assuming in a working day, simple trip chain accounts for 40%, and complex trip chain accounts for 60%. For resting day, 40% of people will choose to rest at home, and the complex and straightforward trip chain accounts for 50 and 10%, respectively. The charging load of 200 electric vehicles in working day and resting day are simulated, respectively, as shown in
Daily EV charging load in resting and working day.
It can be seen in
EV is charged movably and indeterminately due to its traffic characteristics. Six electric vehicles’ traveling trajectories and charging power are presented in
Description of EVs’ traveling trajectory and charging demand.
To draw EV spatialtemporal characteristics more clearly, a complex trip chain and a simple trip chain are extracted to be compared, as shown in
The spatialtemporal EV mobile trajectory and corresponding SOC variation.
From
In this section, reliability indexes based on different EV penetration and trip chains are simulated. Besides, effects on the coupled system reliability due to EV charging based on different EV battery capacities are also discussed. Reliability indexes are shown in
Reliability indexes based on different EV penetration.
Reliability index  EV penetration  

10%  20%  30%  40%  
SAIDI (h/year)  0.3050  0.3685  0.5633  0.7741 
SAIFI (f/year)  0.6415  0.7631  1.0508  1.3006 
EENS (MWh/year)  97.4986  119.7360  138.5801  191.2316 
CENS (MWh/year)  5.2232  12.1849  24.8158  56.0833 
Reliability index POCCE based different EV penetration.
From the data above, it is not difficult to find that all reliability indexes, including CENS and POCCE, worsen with EV penetration increasing. Moreover, it is noteworthy that there is a trend towards worsening POCCE value, which means that although the total EV charging power has been increased, the growth rate of curtailed charging power is more significant than before. As a result, a conclusion can be drawn that EV charging service reliability will be more seriously influenced by the growth of charging demand. Besides, there is a large capacity of charging power curtailment in buses 27, 32, 33, 35, 52, 53, and 54, which shows that the EV charging demand in the lower part of the network is more robust than the results obtained from
Loss of total energy and EV charging energy at each load bus in a year based on different EV penetration.
By comparing the two kinds of curves of “Loss of Total Energy” and “Loss of EV Charging Energy” in
EV traffic characteristics are much correlated to users’ behaviors. The reliability indexes based on different ratios of the trip chains are shown in
Reliability indexes based on a different ratio of trip chain.
Reliability index  Ratio of simple trip chain to complex trip chain  

1:9  3:7  5:5  7:3  9:1  
SAIDI (h/year)  0.5596  0.4245  0.3926  0.3635  0.3543 
SAIFI (f/year)  1.0611  0.8594  0.7550  0.7592  0.7208 
EENS (MWh/year)  142.6823  138.8306  125.3006  119.4343  108.0768 
CENS (MWh/year)  25.1174  23.6312  23.4708  23.0626  22.4251 
The reliability index POCCE based on a different ratio of trip chain.
It can be noticed that with the decreasing of the complex trip chain proportion, the value of all reliability indexes is basically on a downward trend, which means system reliability has been improved. This is because, for the complex trip chain, the EV traveling trajectory is more complex. Therefore, the charging demand becomes more robust. As the proportion of the complex trip chain decreased, the system is less burdensome, and the reliability level is significantly improved. To see the difference further intuitively, the interruption frequency and duration in each load busbased trip chain of 1:9 and 9:1 are shown in
Interruption frequency and duration based trip chain of 1:9 and 9:1.
From
However, the above simulations are based on the constant capacity of each electric vehicle. In reality, different EV models may have various battery capacities. Thus, analyzing the effect of EV operation with different capacities is mandatory and practical. Keep the total EV capacity constant, i.e., the penetration level is the same as the data in
Reliability indexes with increased battery EV capacity based on different EV penetration.
Reliability index  EV penetration  

10%  20%  30%  40%  
SAIDI (h/year)  0.3157  0.4927  0.8462  1.5880 
SAIFI (f/year)  0.6329  0.7454  0.9752  1.1992 
EENS (MWh/year)  96.0692  113.0622  122.7943  148.2297 
CENS (MWh/year)  5.3000  15.9867  37.2476  109.8706 
To compare the data in
Change rate of reliability index with increased EV battery capacity based on different EV penetration.
It can be seen that the change rates of index “SAIDI” and “CENS” are greater than zero with penetration 10–40%, while the change rates of index “SAIFI” and “EENS” are less than zero. It means that after increasing EV battery capacity, “SAIDI” and “CENS” are increased and “SAIFI” and “EENS” are decreased, and as EV penetration increases, the change becomes more obvious. It may because EV users will have more unsatisfactory charging requirements in the event of a power outage when the capacity of the EV battery increases. Additionally, it may lead to a large amount of charging load at a certain moment, making the system burden much heavier. Consequently, the system becomes more complex to maintain steadystate operation. Hence, the Index “SAIDI” is increased. Since the total EV capacity is constant, the increase of EV charging power at certain moments leads to the charging power decrease at other moments. As a result, the frequency failure of the system and the amount of load curtailment are diminished.
Due to the development of green energy and the requirements of national policies, the amount of DG in smart grids has been considerably increased. EV and DG are both characterized by their power uncertainty. Hence, system operation will be significantly influenced when they are jointly integrated into grids. This part describes the effect of DG integration on both EV charging service and distribution system reliability considering EV charging. Among all types of uncertain resources, the photovoltaic (PV) power characteristics differ greatly from charging load characteristics, as its power supply is cut off at night while EV is mainly charged at that time. In this case, PV is chosen to represent the uncertainty of DG.
In this section, two PVs with different capacities are integrated into the coupled system to evaluate its operation on system reliability. Considering the topology of the distribution system and traffic density, different PV installation locations may result in different reliability impacts. The PV installation location is determined based on the coupled system reliability. Aiming at improving EV charging service reliability, locations can be obtained by selecting buses with the two most considerable values based on
Based on the two formulas above, bus 27 and bus 35 are selected for PV installation locations based on EV charging service reliability, and bus 31 and bus 33 for distribution system reliability. The daily timevarying output of PV can be seen from
Reliability indexes with PV integration.
Reliability index  Total PV capacity  

100 MW  200 MW  300 MW  400 MW  
Bus with PV integration  27.35  31.33  27.35  31.33  27.35  31.33  27.35  31.33 
SAIDI (h/year)  0.2106  0.1564  0.1972  0.1589  0.3722  0.2459  0.7849  0.6005 
SAIFI (f/year)  0.4320  0.3292  0.4395  0.3775  0.6320  0.4839  1.4952  1.2065 
EENS (MWh/year)  70.4218  48.5267  55.2075  41.7842  72.0103  47.5085  171.1702  114.5682 
CENS (MWh/year)  7.7053  7.7334  6.4259  6.4825  12.7411  10.8313  50.3606  38.3109 
CENS/EENS  0.1094  0.1594  0.1164  0.1551  0.1769  0.2280  0.2942  0.3344 
Besides, it can be noticed that with the increase of PV integration capacity, both distribution system reliability and EV charging reliability are improved first and then decreased. To see trends more visually, select bus 31 and 33 as the integration locations, and the reliability indexes with PV capacity from 100 to 450 MW are shown in
Reliability indexes with PV integrationbased capacity from 100 to 450 MW.
When PV capacity is from 100 to 170 MW, the indexes are all on a downward trend, which means as PV penetration increases, the electricity system reliability level is improved. Consequently, the optimal PV capacity leading to the highest reliability is about 170 MW. As PV is integrated into the system, the operation of the distribution network is changed from a single power supply mode by the main power grid to a more flexible multiterminal power supply mode by both the power main grid and PV. EV can be supplied by DG, which alleviates the system burden to a great extent. Besides, the basic power supply can be ensured by PV output in some areas when there is a system failure occurred. It means that when the ratio of EV capacity to DG capacity is 3:1, the coordinated optimal operation strategy is obtained. However, when PV capacity exceeds 200MW, the electricity system reliability level starts to decline. It is noteworthy that when PV capacity is increased by more than 370 MW, the reliability index starts to keep proliferating. Furthermore, when PV capacity reaches 400 MW, the system reliability level is even lower than the initial reliability level without PV integration. PV cannot undertake the main load for its intermittency and uncertainty, especially when there are numerous flexible EV charging loads.
Reliability impacts of largescale mobile EV integration on both electricity system and EV charging service system in a coupled transportation and grid framework are explored in this paper. The case study results indicate the following:
• With the increase in EV penetration level and proportion of the complex trip chain, the reliability level for both the electricity system and EV charging service shows a downward trend. EV charging service reliability will be more severely affected by the growth of charging demand.
• Through increasing EV battery capacity, indexes “SAIDI” and “CENS” are increased while “SAIFI” and “EENS” are decreased. As EV penetration increases, the change becomes more obvious. The results implicate that both distribution network reliability and EV charging service reliability can be improved significantly by increasing EV battery capacity if there is enough backup power during the peak period.
• DG installation locations can be determined to coordinate the reliability level of the distribution system and EV charging service. Appropriate DG capacity can improve system reliability, but once a certain threshold is exceeded, the system will rapidly collapse. When DG capacity is about 170 MW, i.e., the ratio of EV capacity to DG capacity is 3:1, the highest system reliability level is reached. However, when DG capacity exceeds 370 MW, system reliability starts to deteriorate rapidly.
The original contributions presented in the study are included in the article/
PX, YX: Conceptualization, methodology; PX: Writing—original draft preparation; YX, JL: Supervision; JG, WX, WS, ZJ, SJ, HZ: Writing—reviewing and editing.
This work was supported by the National Natural Science Foundation of China (51807127, 52111530067), the Sichuan Science and Technology Program (2020YFSY0037).
Authors JG and WX were employed by company State Grid Sichuan Economic Research Institute. Author ZJ was employed by company State Grid Chongqing Shiqu Power Supply Company.
The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The Supplementary Material for this article can be found online at:
traveling duration in a trip
nodes number that a trip includes
road length
traveling speed
point of parking time
point of traveling starting time
staying duration in the destination
midway charging duration
SOC after arriving at a destination
initial SOC
traveling distance
power consumption per mileage
EV battery capacity
slowcharging power
fuzzy coefficient
elastic coefficient
traveling distance before reaching SOC threshold
SOC threshold value
number of distribution system load buses
charging power based charging mode selection
load shedding in bus
vectors of active and reactive power injections
vectors of corresponding active and reactive load curtailment
vectors of active and reactive power loads
vectors of active and reactive generating power
vectors of active power limits
vectors of reactive power limits
vector of bus voltage magnitude
vectors of bus voltage limits
number of simulated cycles
outage period
number of the outage periods
simulation year
number of users in load bus
interruption frequency of bus
load curtailment of node
EV charging load in bus j
curtailment of EV charging load in node
repair state
failure state
a random number evenly distributed between 0 and 1
variation coefficient