Electrical Vehicle Charging Load Mobility Analysis Based on a Spatial–Temporal Method in Urban Electrified-Transportation Networks

Abstract

Charging load mobility evaluation becomes one of the main concerns for charging services and power system stability due to the stochastic nature of electrical vehicles (EVs) and is critical for the robust scheduling of economic operations at different intervals. Therefore, the EV spatial–temporal approach for load mobility forecasting is presented in this article. Furthermore, the reliability indicators of large-scale EV distribution network penetration are analyzed. The Markov decision process (MDP) theory and Monte Carlo simulation are applied to efficiently forecast the charging load and stochastic path planning. A spatial–temporal model is established to robustly forecast the load demand, stochastic path planning, traffic conditions, and temperatures under different scenarios to evaluate the charging load mobility and EV drivers’ behavior. In addition, the distribution network performance indicators are explicitly evaluated. A Monte Carlo simulation is adopted to examine system stability considering various charging scenarios. Urban coupled traffic-distribution networks comprising 30-node transportation and 33-bus distribution networks are considered as a test case to illustrate the proposed study. The results analysis reveals that the proposed method can robustly estimate the charging load mobility. Furthermore, significant EV penetrations, weather, and traffic congestion further adversely affect the performance of the power system.

1. Introduction

Electrified transportation is becoming a prominent source of clean energy due to the emission of carbon dioxide and diesel and high gasoline cost concerns. The survey states that global EV deployments have reached more than 6 million in 2021 [1]. However, high EV penetration affects the optimal operation of transportation and power networks. Therefore, effectively forecasting the load demand as well as evaluating performance indicators of the power grid with a high penetration of EVs can maximize overall system benefits.

Several EV charging studies consider several aspects of capturing a traffic flow forecast, which may compromise the performance of the system. A Monte Carlo simulation was proposed to determine load demand, departure time, and range anxiety [2,3]. The charging load was analyzed considering electricity price and the EV driving behavior [4]. Based on the EV’s mobility on demand, a charging scheduling strategy was proposed for load demand forecasting in various regions [5]. The studies above established the load demand approaches and evaluated the stochasticity of EVs. However, most studies are incapable of efficiently capturing travel planning and disregarding mobility on demand.

Various studies have examined the nexuses of electrified transportation. The study provides a detailed analysis of coupled networks [6]. An origin–destination method was introduced to capture the load demand and the traffic flows [7]. A load control method for scheduling load mobility was proposed to optimize the system and reduce load curtailment [8]. A spatial–temporal approach considering EV travel routes and charging load forecasting was proposed based on the Dijkstra method [9]. A shortest-path algorithm-based EV spatial–temporal model was examined considering driving route selection [10].

The trip chain method is also widely considered to mitigate charging load forecasting constraints [11]. A travel chain approach was analyzed by developing a user equilibrium model considering EV path constraints and range anxiety [12]. The spatial–temporal technique for load scheduling in power-traffic networks was investigated [13]. Furthermore, the Monte Carlo simulation evaluates routing planning and driving patterns [14]. The allocation and sizing of charging stations and load demands were examined through a forecasting approach [15]. Nevertheless, traffic scenarios’ impact on charging load is underestimated. High congestion has a significant effect on charging performance, causing an additional burden during peak hours [16,17]. A spatial–temporal distribution strategy was presented to effectively capture the electric vehicle charging load mobility in coupled power-traffic networks. The charging load scheduling, stochastic path selection, and traffic flow scenarios through user equilibrium were explicitly analyzed [18]. Furthermore, spatial–temporal methods were analyzed to capture the traveling behavior and charging strategy as well as the influence of coupled power and transportation systems [19,20]. The studies evaluated traffic flow constraints, drivers’ demands, and charging uncertainty constraints. However, factors such as traffic congestion, weather, and drivers’ behaviors required further exploration of charging load mobility forecasting, which is susceptible to precisely capturing traffic states. Therefore, the load forecasting approaches consider the stochastic nature of EVs at an infancy stage.

The uncertainty of EV charging also poses a massive threat regarding power system stability perspectives. Therefore, the distribution network stability with large clusters of EVs required further analysis. A charging load effect on the distribution network was evaluated by a decentralized algorithm to maximize the charging schedule constraints. EV clusters were investigated to forecast the load demand and network losses [21]. The charging approach with significant EV integration was presented to diminish the cost of EV aggregators and improve system constraints [22]. Furthermore, the EV charging stations’ proper allocation and load influence on power grid perspectives were explicitly analyzed considering charging scheduling, vehicle-to-grid, and various optimization method constraints [23]. The EV charging station placement and load impact on the power system survey was addressed by analyzing various optimization strategies [24]. Similarly, the EV charging stations’ operation and proper allocation constraints were explicitly analyzed based on the real-world scenario [25]. The preceding studies assess the influence of extensive EV integration on the grid without systematically evaluating the clusters’ influences. Consequently, the stochastic nature of EVs impacts the performance of the overall system. The impact of significant EV integration and state of charge on the power system was examined using a quasi-dynamic simulation approach [26]. However, most approaches underestimate the load mobility demand and power system stability induced by various factors.

Therefore, this study proposes a charging load demand method to analyze the above-mentioned constraints. First, the charging load mobility considering the stochastic path selection, traffic scenarios, and EV charging and drivers’ behavior and weather influence in various periods is evaluated. The method can be applied under different scenarios, such as working days, holidays, hot weather, and during peak demand days. Furthermore, a robust spatial–temporal strategy is developed through MDP and Monte Carlo simulation approaches. The influence of large-scale EV penetration load mobility and weather as well as congestion’s effect on the power system is explicitly analyzed. Finally, the different performance indicators are scrutinized to efficiently capture the stability of the power network.

The structure of this article is organized as follows: Section 2 analyzes the modeling framework considering spatial–temporal patterns and electricity calculation and drivers’ behavior procedure for evaluating charging demand. Then, Section 3 scrutinizes power system performance assessment under various factors. Section 4 describes the case study and results analysis. Section 5 concludes the proposed study and provides future research.

2. Modelling Framework

In this section, a spatial–temporal model is presented to determine the system constraints. The model adopted an amalgamation of travel combinations, a Markov decision process, as well as a Monte Carlo simulation to forecast the load demand.

2.1. Electrical Vehicles Travel Demand Model

Electric vehicle travel routes cover residence (R), work (W), shopping (S), leisure time (LT), and extra destinations (E) providing EV charging services. Travel combinations comprise various categories; the working days travel combinations in a journey are R•W, R•W•S/LT/E, and R•S/LT/E, and holidays travel combinations are R•S/LT/E, R•S/LT/E, and without a trip, respectively. The traveling time t_s corresponds to a normal distribution f(t_s) as [27]:

$$f(t_s)=\frac{1}{\sqrt{2\pi }{t}_d}{\mathrm{e}}^{(-\frac{{(t_s-t_v)}^2}{2t_d{}^2})}$$

(1)

where t_v and t_d values rely on the travel combination.

2.2. EV Stochastic Path Selection Model

The MDP is applied to capture the EV path selection. The quintuple parameters {T, S, A, P, R} are considered in this study as displayed in Figure 1 [28]. T denotes selection time in a travel chain and J sites, and t_j ∈ T is the time when the EV passes through j sites. S presents the scenario and L, s_j ∈ S specifies the EV position t_j. A presents the actions required at selection time. π represents the route in a travel chain signified by β = {β(s_j), j = 0, 1, 2, …, J − 1, s_j ∈ S} and EV route β signified by {$O_1^0$, $O_N^1$, $O_{N-1}^2$, $O_1^3$, …, $O_n^j$, $O_q^{j+1}$,…, $O_{N-1}^{J-2}$, $O_N^{J-1}$, $O_1^J$}, as depicted in Figure 1. N signifies the position once the EVs arrive at the jth site. To explicitly capture the EV mobility transition from one traffic node to another node, the transition ratio analysis is mandatory. Therefore, P presents the transition ratio to determine EV mobility during route choice at time t_j transition from state s_j to s_j+1:

$$p_{j,j+1}^a=P(S=s_{j+1}|S=s_j \cap \beta (s_j)=a)$$

(2)

Assume that the state transition ratio considering EV stochastic route planning is s_j = $O_n^j$. In addition, suppose that $D_{j,n}^{j+1,q}$ and $V_{j,n}^{j+1,q}$ represent the distance and speed between $O_m^j$ and $O_s^{j+1}$ sites. The transition ratio is $P_{j,n}^{j+1,st}$ in case EV accomplishes the next site $O_{st}^{j+1}$ with the least duration, which is higher compared to other transition ratios in a similar state st ∈ {1, 2, …, N}. The ratio of transition $P_{j,m}^{j+1,st}$ is simplified based on the EV’s trip duration between $O_n^j$ and $O_q^{j+1}$. Therefore, this phenomenon demonstrates that a more extended trip duration leads to a lower transition ratio, and the ratio of transition is simplified based on the travel period, as follows:

$$\left\{\begin{array}{ll}{P}_{j,n}^{j+1,q}=1& N=1\\ P_{j,n}^{j+1,q}=\frac{(1-P_{j,n}^{j+1,st})D_{j,n}^{j+1,q}}{(1-P\_t_{\max })V_{j,n}^{j+1,q}}& N\ge 2, q\ne st\end{array}\right.$$

(3)

The higher reward means the shortest driving time. Assume R represents the driving time to examine the EV actions based on route selection. In case the itinerary is altered, $O_n^j$ to $O_q^{j+1}$ with transition ratio $P_{j,m}^{j+1,q}$, the process can be checked with the reward, as portrayed in Figure 1.

2.3. Electricity Consumption Model

The load mobility is influenced by the traffic scenario and route saturations of the urban transportation system. A traffic-flow model is introduced for capturing the EV speed [29]:

$$\left\{\begin{array}{l}{v}_t^{i,j}(x)=\frac{v_{{}_{\max }}^{i,j}}{1+{\tau }_t{}^{\mu }}\\ \mu ={\alpha }_1+{\alpha }_2·{\tau }_t{}^{{\alpha }_3}\\ {\tau }_t=\frac{l_t^{i,j}(x)}{T{c}^{{}_{i,j}}}\end{array}\right.$$

(4)

where α₁, α₂ and α₃ are constants; $l_t^{i,j}$(x) is the traffic movement; Tc^i,j signifies saturation; and τ_t designates the road saturation.

Furthermore, the power utilization at different temperature levels is calculated by utilizing the air conditioner (AC) K_pect, and the relative coefficient K_temp for evaluating power consumption under various temperature scenarios is considered as:

$$\left\{\begin{array}{l}{K}_{pect}=a_1{T}_{emp}^3+a_2{T}_{emp}^2+a_3{T}_{emp}+b_1\\ K_{temp}=a_4{(T_{emp}+b_2)}^2+b_3\end{array}\right.$$

(5)

where a₁~a₄ and b₁~b₃ are constant values; T_emp indicates the temperature; and K_pect signifies different temperatures. Additionally, the decision to alter the AC is examined. A random number k is adopted to uniform distribution considering the various temperature states.

Therefore, considering the influence of AC, power utilization is simplified as:

$$Q_t(x)=\left\{\begin{array}{ll}{K}_t^{temp}{Q}_t^{i,j}(x)& k\le K_{pect}\\ Q_t^{i,j}(x)& k>K_{pect}\end{array}\right.$$

(6)

Furthermore, the state of charge percentage is simplified:

$$S_{OC,x}=(S_{OC,init}-\frac{{\displaystyle \sum _0^{L^x}{Q}_t(x)}}{E_{EV}})\times 100\%$$

(7)

2.4. Charging Demand Modelling Based on Drivers’ Intent

Considering load demand, the charging behavior assumes the travelers prefer to charge randomly, as the state of charge cannot ensure the remaining mileage. Furthermore, the remaining charge is enough. However, as the driver is concerned about the next journey, the driver can charge at the destination. If anxiety ascends, the drivers have a choice of out-of-intent charging.

A fuzzy theory is applied and the power satisfaction F_sat is utilized to formulate the intent of drivers:

$$F_{sat}=\frac{S_{OC,x}{E}_{EV}}{{\displaystyle \sum _0^{L_{next}}{Q}_t(x)}}$$

(8)

L_next indicates the mileage of the EV’s next trip.

Assume R_fuz represents the charging load and R_fuz(F_sat) is adopted to evaluate the charging behavior, which can be formulated as [19]:

$$R_{fuz}(F_{sat})=\left\{\begin{array}{ll}1& F_{sat}<F_{{}_{sat}}^{\min }\\ \gamma & F_{{}_{sat}}^{\min }\le F_{sat}<F_{{}_{sat}}^{\max }\\ 0& F_f\ge F_{{}_{sat}}^{\max }\end{array}\right.$$

(9)

$$\gamma =\sin [\frac{\pi }{4}(1+\frac{F_{{}_{sat}}^{\min }}{2}(\frac{F_{{}_{sat}}^{\max }-2F_{sat}+F_{{}_{sat}}^{\min }}{F_{{}_{sat}}^{\max }-F_{{}_{sat}}^{\min }}))]$$

(10)

where R_fuz(F_sat) specifies the EV driver charging ratio and analyzes the range concern regarding the journey. F_sat < $F_{sat}^{\min }$ indicates that there must be charging demand due to the remaining power in case the EVs cannot satisfy the remaining journey. Moreover, a charging ratio deteriorates to zero since the EV has sufficient charge to accomplish the route with F_sat ≥ $F_{sat}^{\max }$.

The EV drivers must decide on the charging mode, either slow or fast charging, considering the charging choice:

$$\frac{P_{slow}{T}_{{}_p}^i}{E_{EV}}+S_{OC,init}^i<S_{OC,\exp }$$

(11)

Further, charging time T_char is determined and $X_{par}^{mid}$ and T_char are expressed as:

$$\left\{\begin{array}{l}{\displaystyle \sum _0^{L_{{}^{thr}}}{Q}_t(x)}=E_{EV}(S_{OC,init}-S_{OC,thr})\\ {\displaystyle \sum _{n=1}^{n_c}{L}_r<L_{{}^{thr}},n_c\in \{1, 2, \dots , J\}}\\ X_{par}^{mid}=f(n_c)\end{array}\right.$$

(12)

$$\left\{\begin{array}{l}{L}_{mid}={\displaystyle \sum _{n=1}^{n_c}{L}_n}\\ T_{Char}=\frac{{\displaystyle \sum _0^{L_{mid}}{Q}_t(x)-}{S}_{OC,init}{E}_{EV}}{(p_{fast} || p_{slow})}\end{array}\right.$$

(13)

where L_thr specifies the traveling distance S_OC,ini to S_OC,thr; ∑L_r is the travel time to a threshold and the nth charging station; and n_c is the total amount of units transited by drivers once the state of charge declines, S_OC,thr.

2.5. Probabilistic Effect on Load Demand

The probabilistic effect can alter the traveling route outcomes. Therefore, the evaluation of the load demand covering various zones comprising a residential zone (RZ), commercial zone (CZ), and working zone (WZ) is simplified as:

$$F_{DCP}^d=\frac{{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{z^d}^{M_z^d}{(P_z^d(t)-P_z^{avr})}^2}}}{{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{z^d}^{M_z^{all}}{P}_z^d(t)}}}$$

(14)

$$P_w^{avr}=\frac{{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{w^l}^{N_w^{all}}(P_w^l(t))}}}{N_w^{all}T}$$

(15)

where $M_z^d$ signifies traffic nodes of zone d; the charging load of TNN is signified by $P_z^d$(t), z^d; $M_z^{all}$ is the traffic nodes covering the corresponding zones; and $P_z^{avr}$ indicates the zone load demand.

2.6. Distribution Network Charging Load Modeling

The interdependence across TNN and DNN based on data information is accumulated, and the load demand is simplified as:

$$P_z(t)={\displaystyle \sum _{m=1}^{M_{EV}}{P}_z^n(t)}$$

(16)

And the power system load is calculated as:

$$P_{DN}(t)={\displaystyle \sum _{z=1}^{N_z}{p}_z}(t)$$

(17)

The P_DN(t) supply in Z for stopping criterion, and the simulation is ended in case y₁ achieves the extreme value W₁; otherwise, repeat the charging load demand.

$$\max \{|A_n^{Z_b}-A_{n-1}^{Z_b}|\}\le {\delta }_1$$

(18)

where Z_b represents the column vector in matrix Z; $A_n^{Zb}$ is the average value; and δ₁ denotes computation precision.

3. Distribution Network Performance Analysis

Considering various realistic factors, load forecasting has a high forecasting accuracy, which was briefly discussed earlier. This section mainly analyzes and forecasts the influence of charging load from distribution networks performance perspectives considering EV high penetrations, hot weather, and high congestion constraints.

3.1. Distribution Network Performance Assessment Indexes

The performance indexes considering per unit value (PUV), fast voltage stability index (FVSI), losses of load probability (LOLP), system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), and expected energy not supplied (EENS) are adopted for power grid performance evaluation [30]:

$$F_{PUV}=\frac{V_i-V_i^{ra}}{V_i^{ra}}\times 100\%$$

(19)

$$F_{FVSI}=\frac{4{(Z_{ij})}^2{Q}_j}{{(V_i)}^2{X}_{ij}}$$

(20)

$$F_{LOLP}=\frac{1}{T_{total}}{\displaystyle \sum _{n_b=1}^{N_b}{T}_{bre}^{n_b}}$$

(21)

$$F_{SAIFI}=\frac{{\displaystyle \sum _{n_b=1}^{N_b}{\displaystyle \sum _z^{N_z}{T}_{n_b}^z}}}{N_R{N}_z}$$

(22)

$$F_{SAIDI}=\frac{{\displaystyle \sum _{n_b=1}^{N_b}{\displaystyle \sum _z^{N_z}{T}_{bre}^{n_b,z}}}}{N_R{N}_z}$$

(23)

$$F_{EENS}=\frac{1}{N_R}{\displaystyle \sum _{n_b=1}^{N_b}{\displaystyle \sum _{z=1}^{N_z}{P}_{n_b}^z}}$$

(24)

where $V_i^{ra}$ and V_i represent the nominal and actual voltage; Z_ij and X_ij signify the resistance of power transmission; N_b denotes the total amount of simulations; N_R is the performance evaluation duration; $T_{n_b}^z$ indicates the disruption at distribution network nodes z; and $P_{n_b}^z$ indicates system losses.

3.2. Distribution Network Performance Analysis through Monte Carlo Simulation

A Monte Carlo simulation is applied to determine components in a distribution network. The failure and repair rates of components are specified as η, σ. An interval of components under different scenarios corresponding to exponential distribution is simplified as [31]:

$$\left\{\begin{array}{l}G(\eta )=\eta e^{-\eta {\upsilon }_1}\\ {\upsilon }_1=\frac{1}{\eta }\ln {\phi }_1\\ G(\sigma )=\sigma e^{-\sigma {\upsilon }_2}\\ {\upsilon }_2=\frac{1}{\sigma }\ln {\phi }_2\end{array}\right.$$

(25)

where φ₁ and φ₂ are a sequence of random numbers between 0 and 1.

The setup process can be obtained through the state sequence and the duration of the components. The reliability index is estimated based on (19)–(24). The exact computation steps are as follows: first, initialize the information and sample the state series as well as the duration to determine the process conditions. Determine whether the setup is faulty or meets the requirements.

Check if the number of simulation times y₂ ranges the maximum value W₂. If yes, the process is accomplished:

$$\xi =\frac{\sqrt{F({\nu }_{Zi})}}{U[{\nu }_{Zi}]}\le {\delta }_2$$

(26)

where ξ, F represents the variance coefficient; U describes an expectation value; ν_Zi represents the Zi performance index during simulations; and δ₂ specifies the convergence accuracy.

4. Case Study

4.1. Parameter Settings

This section further explores the features of the proposed study through case studies. An urban transportation network is adopted as an example, and the charging load of an EV in various zones is simulated. The various zones in the transportation network correspond to different nodes, such as RZ (1–16), CZ (24–30), and WZ (17–23), respectively. The transportation network contains 30 nodes and 52 routes corresponding to the main routes. Regarding the distribution network, the IEEE 33 busbar system is applied. The 12,000 population of EVs are considered in the case study. The electrified transportation network nodes’ configuration, capacity, and length of the routes and related parameters are provided in Tables S1–S3 as Supplementary Materials.

4.2. Results and Discussion

The charging demand simulations for working days and holidays are exhibited in Figure 2. It can be noted that for a working day, the demand of WZ is mostly concentrated between 08:30 and 12:30, and RZ and CZ between 18:00 and 23:00. Moreover, the loads of the three zones remain constant at different time intervals. On the other hand, the charging demand in WZ is nearly zero during holidays, while the other two regions have higher charging demand between 08:00 and 24:00. The peak time on working days and holidays in all zones occurs approximately 2 to 3 h behind the prescribed travel time. Furthermore, jet lag is caused by transportation networks in various locations. Moreover, the typical working day charging load peak demand is almost two times higher than the holidays. This is because 35% of the total EV fleets are not utilized for transportation on holidays, which diminishes the peak demand.

Figure 2. EV charging demand: (a) working days; (b) holidays.

Figure 2. EV charging demand: (a) working days; (b) holidays.

The load demand on hot and congested days is calculated as portrayed in Figure 3. Apart from traveling behavior and hot weather factors, the constraints for both days are similar to the working days. The charging demand on a hot day is similar to a working day. However, the magnitude rises sharply, by about 81.23%, on a hot day. This event happened due to transportation electricity consumption, and additional electricity consumption for AC can increase the charging demand during a hot day. The charging load on a highly congested day is 54.5%, which is higher than a working day. Also, a delay event occurred at RZ and CZ due to the high congestion, causing EV clusters to consume extra traveling time.

Furthermore, the comparative estimation of working day load demand through a stochastic method and the shortest route scheduling through the Dijkstra method is analyzed as shown in Figure 4a. It can be observed that the charging demand of CZ and WZ is significantly less compared to the MDP analysis shown previously. Additionally, the demand concentrated on RZ later at 18:00. Therefore, the proportion was greatly lowered, and the load demand through Dijkstra was 28.43% lower compared to MDP due to the power dissipation brought through the Dijkstra being less than MDP, which can be fulfilled by the initial state of charge. Thus, the charging load during the daytime is reduced. Some drivers charge at RZ once they are back home after a journey. Therefore, charging load regardless of the drivers’ intent is shown in Figure 4b. A spatial–temporal pattern is comparable to the driver’s charging intent case and the load demand also concentrated at RZ during 18:00–24:00. However, load demand with drivers’ intent dropped significantly, and showed a higher demand of approximately 14.23%, indicating that the driver’s behavior significantly affects the load forecasting.

The CZ has a more substantial proportion of fast charging compared to RZ and WZ due to charging time in CZ being scarce and unable to satisfy the load demand. Furthermore, analyzing CZ fast-charging time under four different scenarios can also optimize the operational benefits of the charging system displayed in Figure 5. Fast-charging time on a working day is concentrated between 18:00 and 21:00 during working hours. Moreover, the charging is relatively scattered during holidays between 12:00 and 20:00. The simulation results during highly congested and hot days are similar to the working days. However, the load demand of both days increased intensely due to peak charging demand.

A coefficient disparity is introduced to explicitly analyze the probabilistic effect on the load demand described in Figure 6. As the probabilistic effect increased, there was an overall reduction in RZ and CZ. A contrary event occurred in WZ; the disparity describes that the RZ and CZ demand steadily shifted towards WZ. However, the disparity of corresponding zones was still below zero. Therefore, the dimension of the disparity stipulates that the probabilistic influence on the load partially replicates the forecasting approach.

Furthermore, charging sizing requirements for working days are scrutinized, as depicted in Figure 7. It can be noted that the data are consumption-based, and each unit facilitates a single EV throughout the charging duration, which means the data captures the total numbers being charged simultaneously. Analysis indicates that required charging points are sporadically dispersed, and the quantity of charging units in WZ is twice as many compared to CZ and RZ between 09:00 and 17:00, which also explicates the phenomenon of higher load demand in WZ compared to RZ and CZ during weekdays, as analyzed earlier in Figure 3a. The charging unit demand of RZ and CZ is similar during 17:00–24:00. However, the overall demand in RZ is relatively more significant than in CZ.

The hot day and highly congested day caused higher charging load demand, as analyzed in Figure 3. The EV high penetrations, high congestion, and weather impact on distribution network performance indicators are quantified as shown in Figure 8 and

Table 1. Performance indicators of the power system under different charging states.

Scenarios	LOLP (Year)	SAIFI (t/Year)	SAIDI (h/Year)	IEENS (MWh/Year)
With 70% penetration during working day	0.004252	13.5853	4.5835	37.1596
With 85% penetration during working day	0.004371	13.9235	4.8358	40.4833
With 100% penetration during working day	0.004401	14.6854	5.2136	45.1584
Highly congested day	0.004477	14.9158	5.3234	51.7656
Hot day	0.004512	14.9647	5.3743	54.8174

, respectively. The high penetrations caused more significant numbers, and indexes of hot days and highly congested days are more extensive than working days. This suggests that the peak load demand led to more fragile distribution stability. The load losses of distribution network nodes are portrayed in Figure 8. The results reveal that higher penetration, hot weather, and high congestion caused greater losses and a rapidly increased load demand. Likewise, the losses diminished in nodes 15–18 and 27–30. However, if the system infrastructure is well established with relevant emergency demand responses, the system’s performance can be optimized, lending additional support to the power system.

Finally, load demand influence for power system performance perspectives is explicitly quantified through PUV and FVSI. Figure 9 and Figure 10 show the values of distribution network nodes, demonstrating that higher FVSI values caused higher losses in the distribution network. From Figure 9a,b, it can be observed that the five charging scenarios have similar voltage drop events during 7:00–12:00 and 17:00–23:00. Therefore, during this period, the distribution network relies on nodes 7–18 and 27–33 because of severe voltage drops. The continued deterioration of PUVs happens due to massive EV penetration and increased high temperature and congestion constraints. Likewise, the overall upward event occurred to the FVSI, as shown in Figure 10a,b. The higher FVSI leads to intensifying EV penetration as well as emergencies of hot days and high congestion, thus deteriorating overall system performance. Consequently, lower FVSI leads to optimal performance of the system.

5. Conclusions and Future Work

The ambiguity of electrical vehicles charging load affects the coupled power and transportation networks’ performance. A spatial–temporal forecasting strategy of EV charging demand and performance assessment of the power systems perspectives is analyzed in this paper. The EVs’ load mobility as well as stochastic path selection are captured through the proposed model. Additionally, the performance assessment method of the distribution system effectively determines the load effect under various states considering the numerous indexes. The case studies revealed that the proposed model can robustly capture the charging schedule. Furthermore, load forecasting analysis demonstrates the real-world scenario by explicitly evaluating factors including load mobility, path selection, traffic flow, drivers’ behavior, and hot weather. Also, the travel chain mechanisms and driving behavior caused significant differences in load distributions in various scenarios. The hot weather and high congestion caused significant load demands, and the charging delay happened during a highly congested day. The significant EV integration, traffic congestion, and hot weather lead to higher load losses, which may compromise the performance and safe operation of the coupled power-transportation networks. In our future work, the proposed study can be further expanded to explicitly analyze optimal charging sitting and sizing to reduce the charging delay during peak demand. Furthermore, determines the coupled power and transportation networks’ price mechanisms and dynamic power and traffic flow constraints under various scenarios.