1.1. Motivation

Transportation electrification has received policy support from various countries to decrease the dependence on depleted fossil fuels and reduce greenhouse gas emissions, and become a research hotspot in recent years [1, 2]. In 2017, the UK government announced that new petrol and diesel car sales would be banned by 2040 [3]. Norway has seen the highest electric vehicle (EV) penetration in recent years, with EVs accounting for 48% of new car sales in the first quarter of 2019 [4]. The United States, particularly California, is actively developing incentives to promote EV growth and investment in charging infrastructure [5]. Several Asian countries, such as China and Japan, have also set ambitious market share targets for EVs [6, 7].

Unlike traditional vehicles, EVs have more diversified electricity sources, especially renewable energy generation, and their internal electrical systems are swifter and more controllable [8]. Furthermore, advanced communication technologies (e.g. 5G cellular networks) [9], GPS facilities, and intelligent metering infrastructures [10] make it possible for bidirectional data exchange between the power network, transportation network, and EV drivers. In this context, as dynamic loads and potential energy buffers, EVs enhance the coupling between power and transportation networks. Large numbers of EVs may reduce the stability of the grid, but if managed properly, they can actually increase the grid’s flexibility and boost renewable energy consumption [11]. By adopting reasonable charging strategies for EVs, the power network and transportation network are expected to make perfect cooperation, thereby achieving a win–win situation for the system operators, charging stations (CSs), and EV owners.

1.2. Literature Review

Various studies have explored practical and effective charging strategies for EVs. Among them, centralized strategies make scheduling decisions to coordinate the charging behavior of EVs from the system perspective [12]. The authors in [13] developed a centralized charging strategy for battery swapping stations (BSSs) using an improved population-based heuristic algorithm. It took into account the optimal charging priority and locations of EVs based on spot pricing and minimized the total charging cost and impacts on power quality. A centralized bilevel charging strategy for plug-in electric vehicles (PEVs) was presented in [14], aiming to coordinate the charging behavior from both spatial and temporal viewpoints. This strategy considered the benefits for the grid and EV users simultaneously. DeForest et al. studied the day-ahead centralized scheduling of an EV fleet participating in the wholesale electricity frequency regulation market, which involved optimizing EVs’ charging behavior, market bidding, and response to the grid system operator [15]. By contrast, decentralized strategies that allow individual EV owners to determine their charging patterns are also investigated [16]. Although decentralized approaches are inferior to centralized ones regarding uncertainty about system-level optimality and grid stability, they preserve individual privacy and authority and reduce computational and communication costs [17]. To evenly utilize available charging resources and avoid the excessive waiting time of EVs, a decentralized scheduling algorithm and a cooperative control policy were proposed in [18]. Zhou et al. developed an equilibrium model for coupled power and transportation networks, in which the spatial and temporal varied network flow solutions were obtained by a decentralized approach [19]. The authors in [20] established a decentralized control strategy for high penetration of PEVs, through which considerable charging load could be transferred to the night-time demand valley. In addition, the convergence of the adopted noncooperative games was proven under sufficient conditions. In [21], the EV aggregators and EV drivers considered two agent modes, namely the centralized protocol management mode and the decentralized one, were considered in the EV aggregator’s day-ahead bidding. The case study based on the Guangdong electricity market showed that EVs with the centralized agent mode were more sensitive to the electricity price.

Charging price can guide the charging behavior of EVs, which is one of the most critical factors affecting the efficiency of CSs and EVs [22]. However, in [12–21], the influence of charging price on EVs is not fully discussed.

In terms of the interaction between charging pricing and EV charging decision, Yang et al. presented an optimal EV route model and compared the impact of three time-of-use (TOU) electricity price profiles on the performance of EV charging [23]. The authors in [11] investigated the impacts of three kinds of charging strategies on the stability of distribution systems and the efficiency of electrified transportation systems. Although the charging price adopted in the price-based strategy was referred to as “dynamic price”, it is a fixed TOU price. To further explore the role of electricity price, research on charging prices has transferred to dynamic pricing methodologies in recent years. A dynamic charging price demand function was proposed in [24] to guide EV users to strategically choose the fast-charging stations while considering multiple demands of EVs, CSs, and the distribution network. The authors in [25] built a hierarchical game model to jointly settle the problem of CSs pricing and EV charging decisions. In this work, a concept of time-based billing was proposed to avoid possible low utilization caused by a usage-based billing scheme. Dynamic pricing algorithm was also studied in [26] to simultaneously determine charging price and schedule EVs and energy storage, which was solved by applying Lyapunov optimization. The authors in [27] proposed a two-stage Stackelberg game model to handle the problem of CS pricing, as well as PEVs station selection. However, only two competing CSs were considered in this model, which was still far from practical application. Ding et al. assumed CSs and an EV aggregator as two noncooperative stakeholders, seeking the coordination of charging pricing and EV travel-route scheduling [28]. EVs in [28] are all price-responsive and subject to centralized regulation by the EV aggregator. To avoid the unacceptable queue waiting time during the peak load period, the authors in [29] proposed a scheduled pricing policy. Compared with the most general flat pricing policy, this method also improved the profit margins for the CS operators.

Several technical, environmental, and economic factors have been considered in previous studies in terms of charging behavior modeling [30]. The authors in [31] systematically investigated and analyzed the main factors that influence the charging behavior and driving pattern of EVs from three domains of transport, vehicle technology, and power system, among which charging infrastructure and battery performance were identified as two core factors. Xiong et al. designed a behavior model based on the Quantal Response Equilibrium model and the level-k thinking model to simulate the bounded rationality of EV drivers when they select CSs to charge [32]. The authors in [33] proposed an EV behavior simulator to simulate the EV driver behavior aspects, including the importance of charging price, the importance of each trip, the sensibility of the battery’s state, and other parameters. In [34], the charging mode selection of EVs was determined by both service fee and battery lifetime–related cost, and whether an EV left the CS before charging was influenced by waiting time. Sun et al. focused on the detour distance that affects the fast-charging station choice behavior of EV users [35]. The estimation results demonstrated that private and commercial users have heterogeneous detour willingness when they have charging needs on weekdays or weekends. Charging willingness can also be characterized by expenses that EV drivers should pay, including travel costs, waiting time, and charging costs [27].

In [23–29, 31–35], the relationship between charging pricing and EVs charging decision-making and the influence of EV charging behavior modeling on its own charging decision-making are discussed respectively. However, in real life, as a separate interest subject, there is also an interest interaction relationship between the power system and the charging pile. The adjustment of electric energy in the power system will also affect the charging pricing and the charging decision of EVs.

When EVs are connected to the power system, the planning and scheduling of EV become a multistakeholder problem, commonly modeled by game theory [9]. A bilevel optimization model was proposed for determining the optimal allocation of CSs in [36]. The upper level sought the least social cost, while the lower level established a complete information game by considering the charging behavior of EV drivers. The authors in [37] established a real-time dispatching framework for EV navigation, which considered both the reliability of the power grid and the profitability of CSs. Moreover, different CSs were regarded as noncooperative players who adjusted the electricity price to maximize their profits. Authors of [38] presented a rolling horizon scheduling method considering the uncertainty of EV charging behavior and electricity price, and the two stakeholders, distribution network operators and EV drivers, could benefit from this method simultaneously. In [39], information from power systems and intelligent-transport systems was combined to optimize the charging strategy for massive EVs. This method can not only relieve traffic congestion but also improve the safety and economy of the power grid. The authors in [40] developed a bilevel programming model to address the planning of CSs and the spatial and temporal coordination of EVs. The test in [40] revealed the interdependency between the distribution network and transportation network on CS issues. Li et al. proposed a bilevel scheduling approach for real-time pricing of EV BSSs, in which the dynamic supply–demand relationship between the isolated micro-grid and BSSs was considered [41]. A hybrid method combining the heuristic with analytical optimization was also designed to effectively coordinate BSSs to participate in the economic operation of micro-grid.

In addition to EVs, the installed capacity of renewable energy, such as PV and wind turbines, has experienced rapid growth worldwide in recent years. Distributed energy resources (DERs) are gradually becoming a rising force in the power market [42]. The CSs are expected to obtain economic and clean electricity from DERs, while EVs can obtain more flexible charging time and price. As for DERs, EVs’ charging and discharging behaviors can promote their consumption and help realize mobile energy storage [43]. Therefore, considering the DERs in the synergetic planning and scheduling among distribution networks, EVs and CSs can benefit multiple stakeholders. The authors in [44] proposed a framework for peer-to-peer energy trading between CSs and a business entity equipped with PV panels. Compared with the energy trading directly with the grid, this framework significantly reduced the cost of prosumers and increased the self-consumption rate of PV power. Luo et al. regarded the transportation agency, city manager, and power agency as stakeholders and carried out the joint optimization of the locating and sizing of the CSs and the PV stations as well as the time-varying charging price of the CSs [45]. This work can guide the planning and scheduling of the integrated transportation and power system. A bilevel planning model for CSs considering wind, solar power, and energy storage is established in [46], which comprehensively considers the energy cost and environmental benefits. The result of the case study revealed that the access of renewable energy is profitable to the whole system.

The research results in [42–46] show that the access of renewable energy is beneficial to the whole power system. Considering DERs, EVs and CSs in collaborative planning and scheduling between distribution networks can benefit multiple stakeholders. Therefore, it is of great significance to study the interaction between EVs and active distribution networks.

1.3. Contribution

However, most of the existing studies have neglected various factors affecting charging behavior, especially in centralized scheduling, which fails to preserve the decision-making authority of EV individuals. In addition, more research is needed on the interaction of pricing strategies between power and transportation systems, as well as the impact of pricing strategies on renewable energy consumption. Otherwise, it is difficult to provide practical guidance in planning and scheduling scenarios where power and transportation systems are more closely coupled in the future.

1.4. Organization

The remainder of this paper is organized as follows. Section 2 introduces the modeling of the traffic network, and Section 3 describes the bilevel pricing methodology for power distribution and transportation networks. The solving methods of the upper and lower models are presented in Section 4. Section 5 verifies the proposed methodology through the Dublin area–based testbed. In Sections 6 and 7, the discussion and conclusion are given, respectively.

2.1. System Construction

Highway traffic flow can be predicted by machine learning methods based on collected historical data. In this paper, an artificial neural network (ANN) model is adopted to forecast the hourly traffic flow [49]. The hourly data of EVs on the road can then be calculated by multiplying the market share of EVs. At the beginning of time t, the initial position, destination, and battery state of each EV are randomly generated on the road segments.

2.2. EV Characteristics

2.3. CS Operation

To evaluate the performance of the proposed methodology in promoting renewable energy consumption, CSs are divided into three categories: CSs located near wind farms, CSs located near PV stations, and ordinary ones with neither wind farm nor PV station nearby. The power output of wind farms and PV stations is also predicted using ANN.

The relationship between CSs is a noncooperative game. When their pricing reaches a Nash equilibrium, they will uniformly broadcast their charging price to all EVs on the road at each period t. EV drivers can then book charging services to the CSs with high willingness value, and CSs will receive the booking requests from the EV drivers if they have free charging slots.

3.1. Bilevel Dynamic Pricing Methodology

Figure 1 demonstrates the detailed workflow of the proposed pricing mechanism.

The upper power grid aims to minimize the total cost of power generation and transmission. The optimal economic dispatch strategy is determined based on the electricity demand fed back by the lower CSs and power generation information of their nearby wind farms or PV stations. Each CS’s LMP is determined by a power flow trace method and then passed to the lower level as input.

Each CS at the lower level broadcasts its charging price and operating status in real time. Thus, the EVs to be charged on the road determine their charging willingness based on the charging price, detour distance, charging level, and operational status of each CS, and book charging service to the intended CS. The charging demands of each CS can then be calculated. Based on this charging willingness determination method, a noncooperative game model is established at the lower level solved by the greedy algorithm: each CS aims to maximize its own profit and adjusts its own charging price to seek Nash equilibrium.

The upper power grid updates the optimal economic dispatch strategy according to the charging demand of each CS fed back by the lower traffic network. The iteration is repeated until the iteration termination condition is met.

According to the above procedure, the LMP of the distribution network and the charging price of the CSs (hereinafter referred to as the dynamic price of the game, DPG) are obtained hour by hour.

3.2. Upper Level Subproblem

3.3. Lower Level Subproblem

4.1. Upper-Level Power Grid

4.2. Lower-Level Traffic Network

The Nash equilibrium is often used to describe the market state, but the network constraints will induce market separation and greatly influence the Nash equilibrium [59, 60]. Since the noncooperative game in this paper has high complexity to formulate a more realistic environment and is an NP-Hard problem, the existence and uniqueness of the Nash equilibrium are difficult to be mathematically proved [61, 62].

To find the approximate Nash equilibrium, we propose an equivalent definition of the generalized Nash equilibrium, which serves as a termination condition in the iterative solution process of Algorithm 2.

5.1. Testbed Establishment

To verify the effectiveness of the proposed bilevel pricing model, an integrated traffic and power distribution network testbed is established based on the actual traffic network topology in Dublin. The topology of the studied distribution network is based on the IEEE 33-node test system. The specific topology of the integrated testbed is shown in Figure 2.

Based on our previous research on pricing strategy in this area [47], 13 CSs are assumed to be located in the Dublin area. Their charging patterns and available charging slots are given in Table 1.

It is assumed that C4 and C6 are located near offshore wind farms, C14 is also within an onshore wind-rich area, and C3, C8, and C14 are located near PV stations. The other CSs are considered ordinary ones. Based on historical data collected from a wind and solar power generation project in Ireland, the predicted hourly output curves of surplus wind and solar power in a typical day are shown in Figure 3. And the following analysis on the renewable energy consumption only focuses on the surplus renewable energy.

The traffic flow information is predicted based on historical traffic data of the Dublin Traffic Agency, and the charging demands of EVs are generated following Inverse Gaussian distribution [66]. Figure 4 presents the hourly traffic flow data on the seven highways in Dublin.

In addition to the DPG proposed in this paper, two comparative pricing mechanisms are set up, namely TOU tariff and flat rate, as shown in Table 2.

5.2. Algorithm Performance

The bilevel pricing model judges whether the problem’s solution reaches the generalized Nash equilibrium according to the equivalent function F(p_t) defined above.

According to the MATLAB memory profiler tool, the execution time of the Case study is 292.15 s, and the highest computer resource value is 127,792 kB, which is lightweight and could run with low computational resource demand. As demonstrated in Figure 5, all 24 time periods in a day can reach the generalized Nash equilibrium within 4 iterations.

To verify the pure strategy Nash equilibrium, 100 groups of test are carried out. For different time periods, the DPG of different CSs is adjusted respectively, and the results obtained are compared with those of the DPG. Three groups of results are shown in Figure 6. It can be seen that no CS can increase its profits by raising or lowering its own DPG in these cases.

5.3. LMP Analysis

Figure 7 shows the LMP of each CS obtained by the upper-level decision under the Nash equilibrium at 5 typical time slots.

It can be found that no matter the morning rush hour (8:00–9:00), evening rush hour (16:00–17:00), or other time slots (13:00–14:00, 20:00–21:00), the value of the LMP is mainly related to the power loss. The LMP of CSs near the head point of the distribution network is low, such as the nearest C2, C3, and C4, while the LMP of CSs far from the head point is high, such as the most far C14.

As known in Figure 2, the power loss from C2 to head point is relatively less than that from C8 to head point, and the LMP of C2 is slightly lower than that of C8 from 3:00 to 4:00. However, in the other three time slots, the LMP of C2 is greater than that of C8, which is marked in red circle in Figure 7. This is owing to the allocation of transmission cost considered in the power flow trace method. The charging demand of C2 is lower than that of C8 from 3:00 to 4:00, but the situation is the opposite in the other three time slots, which can be seen in Figure 8 in Section 5.4.2.

5.4. Economic Analysis of CSs

5.4.1. DPG

The temporal and spatial distribution of the DPG of the CSs in the lower level is shown in Figure 9, and the DPG of different CSs at different periods is distinguished by the color depth of the color blocks. It can be seen that the DPG varies between 9.42 and 24.23 ¢/kWh. For reference, the charging fees of local CSs in Ireland vary depending on the type of charger. According to the ESB Networks Ireland, the charging price of standard AC chargers (up to 22 kW) varies between 12 and 43 ¢/kWh, while that of DC fast chargers is about 43 ¢/kWh [67].

Compared with other CSs, C4, C6, and C14 in wind-rich areas have more blue color blocks, which means that their charging prices are generally lower, while C9, C10, and C11 have brighter yellow color blocks, which represents that their charging prices are generally higher. The specific reasons will be analyzed later.

5.4.2. Charging Demand and Profit Distribution

Considering the detour distance and charging price, each EV owner will subscribe to the CS with the highest charging willingness. Then, the spatial and temporal distribution of the charging demand of all CSs is generated, as shown in Figure 8.

Figure 10 presents the spatial and temporal distribution of the profits of all CSs, which are calculated according to the optimization results of LMP in the upper level and DPG in the lower level.

Since the daily profits of the CSs under the TOU or flat rate are greatly affected by the set charging price, only the trends of daily profits under the three pricing mechanisms are compared in this paper, which can be seen in Figure 11.

The profitability of each CS is influenced by its geological location, the presence of renewable energy nearby, and the output of renewable energy. Apart from the two well-located ordinary CSs, C9 and C10, the daily profits of renewable energy-rich C3, C6, C8, and C13 are significantly higher than other ordinary ones under the three pricing mechanisms. Since these CSs have priority to use nearby free wind or solar power, their cost of purchasing electricity from the upper grid can be reduced. However, the daily profits of C4 and C14, located near wind farms, are lower than others. On the one hand, the installed capacities of the wind power near these two CSs are relatively small, and the morning rush hour coincides with the valley of the wind turbine output, which results in the limited utilization of wind power. On the other hand, C4 sits on a road with sparse traffic, while C14 is far from the center of Dublin. Their poor geographical location is not attractive for EV drivers regarding detour distance.

A horizontal comparison shows that when the proposed DPG is adopted, daily profits of C4, C6, and C14 in wind-rich areas are distinctly improved compared to the other two pricing mechanisms. When a fixed charging price is adopted, EV owners’ charging willingness will only be affected by the detour distance, and the CSs located on light roads have no advantage in attracting EV owners. In particular, C14 is located at the end of the distribution network, resulting in higher power transmission costs, so its daily profit will be even less than other CSs. By contrast, the DPG balances the profits of all CSs to a certain extent by allowing them to adjust their charging price, especially to improve the profits of CSs with poor locations near wind farms. Consistent with Figure 9, C4, C6, and C14 all reduce their charging price to increase EV owners’ charging willingness to them, and then their daily profits can be improved. It can also be seen from Figure 11 that, compared to TOU and flat rate, the profit of C4 has increased by 19.72% and 18.77%, C6 has increased by 6.17% and 5.45%, and C14 has increased by 26.75% and 26.88%, respectively. Meanwhile, the fluctuation of the daily profits of other CSs is within the acceptable range, which shows that the DPG can improve the profits of these CSs without excessively reducing that of the others.

5.5. Renewable Energy Consumption

Figure 12 presents the hourly wind and solar power consumption of CSs in renewable energy-rich areas.

According to Figure 12(a), from 0:00 to 7:00, the wind power output is in a valley period, and there are few EVs to be charged on the road, so the wind power consumption rates of C4, C6, and C14 are low. When the morning rush period (7:00 to 9:00) comes, the wind power consumption rates all rise and sometimes even reach 100%. Subsequently, as the wind power output increases and traffic flow decreases, the consumption rates decline. Wind power consumption slightly increases during the evening rush hours (16:00 to 18:00). After that, the traffic flow rapidly decreases, and the wind power output shows a downward trend, so the wind power consumption rates further decrease.

Figure 12(b) shows no solar consumption after sunset. In the morning and evening rush hours, the solar power consumption of C3, C8, and C13 can all reach 100%. Although 9:00 to 16:00 is the peak period of solar power output, the consumption rates are limited due to the small number of EVs to be charged on the road. Among them, C13 shows an overall higher consumption rate than the other two CSs for its relatively small installed capacity of wind turbines.

As can be seen in Table 3, under the proposed DPG, the overall consumption of renewable energy is better than the other two pricing mechanisms. CSs in wind-rich or solar-rich areas can exploit free renewable energy generation to attract more EV owners by adjusting their charging prices, and then renewable energy consumption can be promoted.

5.6. Usage of Charging Facilities

Table 4 presents the average utilization rate of charging facilities in renewable energy-rich CSs under the three pricing mechanisms. It can be seen that under the DPG, the utilization rate of CSs in wind-rich areas has increased overall, while that of CSs in solar-rich areas has declined. Under the other two pricing mechanisms, the solar power-related CSs have better performance in charging facilities usage for their location advantages, while the utilization rates of wind power-related ones are much lower. By adjusting charging prices, the DPG can promote renewable energy consumption and balance the utilization rate of CSs in wind-rich and solar-rich areas.

It should be pointed out that the comparison of the utilization rates of all CSs in this region is meaningless because the total charging demand is determined. When more EVs are attracted to the CSs near wind farms or PV stations, the number of EVs to be charged at other CSs will decrease, resulting in a reduction in the utilization rate of their charging facilities.

5.6.1. Influence on Traffic Flow

Figure 13 takes the typical time periods of morning peak (8:00–9:00), evening peak (16:00–17:00), and other time periods (5:00–6:00, 20:00–21:00) as examples to intuitively show the selection results of EV owners under three pricing mechanisms.

When fixed pricing mechanisms for CSs are adopted, the lower-level model is no longer an optimization problem, and the charging willingness of EV owners will be determined by the fixed charging price and detour distance. Therefore, EVs on heavy roads tend to choose the nearest CSs, which will intensify the busyness of these CSs and degree of road congestion, and result in poor usage and profits of CSs on light roads. As can be seen from Figure 13, regardless of the morning and evening peak hours or other periods, under the two fixed pricing mechanisms, C3, C8, C9, C10, and C11 have become the choice of the majority of EVs for their location advantages. Although the solar power consumption of PV stations near C3 and C8 is promoted to a certain extent, the congestion of heavy roads such as M3, M4, and M7 is also increased.

However, when the DPG is adopted, the price adjustment of each CS can balance not only the daily profits but also the charging demand of EVs. It can be seen that under the DPG, wind power consumption near C4, C6, and C14 is promoted, and the utilization rates of CSs in remote areas such as C5 and C7 are all increased. The result reflects that the proposed DPG can disperse the traffic flow to some extent by influencing the charging willingness of EV drivers. Compared with Figures 13(a) and 13(d), the dispersion effect of DPG in Figures 13(b) and 13(c) is more prominent because the charging demand of EVs during off-peak hours is much less than that in rush hours.