### Assessment metrics

In this section, we use computer simulation to illustrate the impact of wireless dynamic charging roads on urban mobility. Our goal is to determine if a future with (1) only charging stations, or (2) a combination of charging stations and dynamic charging roads, will be more beneficial to EV drivers. Specifically, we focus on how those charging facilities can ease the range anxiety problem, enabling EV drivers to finish their trips with sufficient energy. Next, we aim to see which scenario adds the least extra charging time to drivers’ trips. To this end, we simulate the following two metrics:

### Metric 1

(Percentage of trips that detoured) It is the number of trips that have to detour from the shortest routes to find a charging facility (due to insufficient energy) divided by the total number of trips.

### Metric 2

(Percentage of extra time added to a trip) It is the percentage of the extra time added to a trip due to charging at a charging station. For example, if a trip takes 50 min and charging takes 10 min, then the percentage of added extra time is \(\frac{10}{50} * 100\% = 20\%\). Since wireless dynamic charging roads can power EVs while driving, no extra time is added to trips due to charging.

The first metric measures the impact of the charging infrastructure on the overall efficiency of travel routes. It helps to determine how well the charging network is integrated into the city and if it aligns with the natural flow of traffic. The second metric is critical to drivers of commercial electric vehicles such as delivery vans or taxis, as this metric directly relates to operational costs and customer experience. For example, for a taxi driver, a reduced added time implies that he or she can fit more trips in a day, generating more profit. The same metric for a delivery van driver means more orders can be fulfilled.

### Datasets

To reflect the actual traffic, we utilize a six-month trip record dataset of yellow taxis from July 2019 to December 2019 in New York City (NYC). Yellow taxis are a signature of NYC and are the only serviced vehicles allowed to take street hails from every city borough. The dataset contains over 33 million records and is made available online by the New York City Taxi and Limousine Commission (TLC)^{46}. In the dataset, NYC is divided into 263 zones corresponding to the NYC Department of City Planning’s Neighborhood Tabulation Areas. Then, the starting and ending points of each trip are documented based on those zones. Since the traveled routes are not provided to maintain privacy, we assume the shortest driving routes for all those trips. We choose NYC since the city has a rich and reliable dataset on historical trip records. However, our simulation and analysis can be easily extended to other metropolitan cities where relevant datasets are available. For the road networks of NYC, we rely on data supplied by OpenStreetMap^{47}.

### Methodology

To compare two scenarios of (1) only charging stations, and (2) a combination of charging stations and dynamic charging roads, we assume a baseline of fifty level-two charging stations, since those are much cheaper than DC fast chargers and are likely to scale faster than DC fast chargers in the near future. In addition, a baseline scenario with existing infrastructure provides a useful point of comparison to measure the impact of any additional investments in charging stations or dynamic charging roads. It is also representative of many current urban settings where initial investments in EV charging infrastructure have already been made. Then, we investigate two future scenarios. One is when the city is equipped with another fifty charging stations. The other is when the city adds certain kilometers of dynamic charging, as summarized in Table 2.

Charging stations and dynamic charging roads are typically distributed in cities based on the spatial patterns of population density and socio-economic activities. Previous research has shown that in modern metropolitan areas, both population and traffic densities are highest at the city center and decline with increasing distance from the center. This decline often follows a power-law function, denoted as \(g: {\mathbb {R}} \mapsto [0,1]\), expressed as:

$$\begin{aligned} g(r) = {\left\{ \begin{array}{ll} (\frac{\mid r \mid }{r_{\textrm{min}}})^{-\alpha } &{} \mid r \mid > r_{\textrm{min}}\\ 1 &{} \mid r \mid \le r_{\textrm{min}}, \end{array}\right. } \end{aligned}$$

(1)

where \(r_{\textrm{min}}>0\) is the minimum value of *r* at which the power law holds, and \(\alpha \) is a positive constant that describes the rate at which the population and traffic densities decrease^{48,49}.

In our simulations, we use the same power-law function to determine the location of charging stations and dynamic charging roads under different scenarios. Specifically, we employ Eq. (1) to calculate the likelihood that a particular street intersection will host a charging station or that a specific road segment will be equipped for dynamic charging. The proximity of a road or intersection to the city center influences this likelihood, with closer locations having a higher probability of receiving such infrastructure.

We set \(r_{\textrm{min}}\) at 200 m for the simulations. The value of \(\alpha \) is chosen such that it aligns with the expected densities of charging stations or lengths of charging roads as described in the scenarios in Table 2. For instance, in the baseline scenario, we select \(\alpha \) so that the total expected number of charging stations, summed across all intersections, matches the target value of 50. In a future scenario where we aim to install certain kilometers of dynamic charging roads in New York City, \(\alpha \) is determined through multiple simulations to ensure that the average total length of the dynamically charged roads approximates the proposed kilometers.

We assume that all taxis in the experiment are EVs and that all trips start with a battery level uniformly distributed between 10% and 20%. This range mimics a real-world scenario where taxis may not always start a shift fully charged but are not so low on charge that they cannot complete short trips. It also introduces a practical level of stress on the charging infrastructure and lets us focus on the impact of charging infrastructure on trips that require charging.

The charging behavior of EV drivers, e.g., choosing when, for how long, and at which station to charge, in practice, is complicated and may depend on several factors such as personal schedules, charging prices, and station availability and accessibility^{50}. In this case study, we assume a general behavior that an EV driver will stop to charge for 20 min if there is a charging station on their routes and the EV battery level is under 10%. This assumption allows all drivers to act uniformly, making it easier to model and interpret the behavior across a fleet of taxis. Another option could be to assume that a driver will charge until the battery reaches a sufficient level for the trip. However, since we are particularly interested in the extra added time to a trip due to charging, i.e., Metric 2, a fixed 20-min charge would lead to more frequent stops as the number of stations increases, providing a clearer mechanism to study the impact of the increased number of charging stations on this metric. In the model where the driver charges “until sufficient,” adding more charging stations might not substantially change the “extra added time” because drivers would simply fill up as needed, regardless of the number of stations. A fixed 20-min charge also better reflects the operational constraints of a taxi service, where time off the road directly translates to lost revenue.

Since our experiment aims to find the aggregated impact over millions of trips, we assume an average driving speed inside NYC of 20 km/h and a constant energy consumption model, i.e., the amount of energy that an EV consumes equals a fixed rate times the traveled distance. To be specific, in the simulation, we assume an energy consumption rate of 0.186 kWh/km, which is close to the EPA-estimated energy consumption rate of the Nissan Leaf and the Chevrolet Bolt (two of the best-selling EVs models in the US). In addition, for charging facilities, we assume an output power of 6 kW for all level two charging stations and 20 kW for dynamic charging roads based on surveys of popular charging stations and dynamic charging systems^{38,51}. We also assume a constant charging model, i.e., the amount of energy charged equals the time that the EV is plugged in or is traveling on dynamic charging roads times the output power of the charging facility. In reality, the energy consumption and charging rates will depend on several determinants such as weather conditions and driving behaviors. However, since the simulation is performed on a large number of trips spanning an extended period of time, we adopt a simple assumption of constant energy consumption and charging models.

Using the road network dataset from OpenStreetMap, we simulate each scenario from Table 2. For the baseline and scenario 1, 50 and 100 charging stations are generated based on the probability in Eq. (1), respectively. For scenario 2, we investigate the cases when 5%, 3%, 1%, 0.3%, 0.1%, and 0.02% of the roads in NYC are equipped with dynamic charging systems, corresponding to 1226, 822, 385, 118, 57, and 25 km of charging roads, respectively.

### Empirical results

We analyze yellow taxi trip data to assess two key performance metrics under varying scenarios. The first metric, i.e., Metric 1, measures the percentage of trips that must detour to recharge before reaching their destination. These detours occur because the vehicle exhausts its battery before completing the shortest path. Figure 3 shows the percentage of trips that detour according to the varying numbers of kilometers of dynamic charging roads. We observe that implementing 25 km of dynamic charging roads has a slightly greater impact in reducing detours than installing 50 level-2 charging stations. Specifically, both scenarios cut the detour rate by approximately 0.1% compared to the baseline scenario. Calculating the relative differences, the addition of 50 charging stations reduces the detour rate by \(\frac{0.75-0.68}{0.75} * 100\% = 9.3\%\), while 25 km of dynamic roads result in a \(\frac{0.75-0.66}{0.75} * 100\% = 12\%\) reduction.

While the costs of constructing charging stations and charging roads will vary by city due to factors such as land and construction costs, our results serve as a general guide to their potential benefits. Thus, specific cost considerations are left to local urban planners and policymakers in individual cities.

Table 3 presents how increasing the length of dynamic charging roads correlates with reductions in Metric 1. Importantly, this relationship is positive but non-linear with a diminishing return, indicating that while the initial expansion of dynamic charging infrastructure significantly mitigates Metric 1, the effectiveness of further expansion lessens with scale. For instance, early enhancements, such as increasing from 25 to 57 km, significantly improve the reduction factor from 1 to 1.6. However, extensive expansions, from 822 to 1226 km, yield a minimal increase in the reduction factor from 6.8 to 6.9, despite a substantial investment in infrastructure. This pattern suggests that, while costs remain high, it may be more cost-effective to install dynamic charging systems on a limited number of high-traffic routes. However, as the technology matures and costs decline, broader implementation may become viable. Urban planners and policymakers should weigh these considerations carefully when deliberating on the expansion of charging infrastructure.

In Fig. 4, we present the percentage of extra time added to a trip due to charging, i.e., Metric 2. One can see that when another 50 charging stations are introduced, i.e., future scenario 1, the trips see a significant 41% surge in added charging time. In contrast, the integration of dynamic charging roads leads to a decrease in this added charging time. This discrepancy can be understood in conjunction with the findings from Fig. 3, which demonstrates that both added charging stations and charging roads reduce the necessity for detours. Specifically, with the increased availability of charging stations, the detour rate diminishes as EV drivers have more access points to recharge. Consequently, they spend longer periods charging, ensuring their vehicles have enough energy to complete their journeys. This situation presents an intriguing trade-off, i.e., the advantage of fewer detours is offset by the extended charging durations.

Conversely, dynamic charging roads offer a dual advantage, i.e., they reduce both the detour rate and the charging duration. When 25, 57, 118, 385, 822, and 1226 km of NYC roads are embedded with dynamic charging systems, the extra charging time drops by 18.4%, 25.7%, 37.9%, 54.8%, 68.4%, and 69.6%, respectively, compared to the baseline. However, the introduction of charging stations leads to a 41.4% increase in this metric. It implies that dynamic charging roads have a clear advantage over traditional charging stations in efficiency and user convenience.

The insights from our study are invaluable for urban planners and policymakers. As cities consider resource allocation for EV infrastructure, our findings suggest that, in the long run, dynamic charging roads might offer more tangible benefits compared to conventional charging stations. Moreover, our results could be leveraged to drive EV adoption rates. Assurances of minimized detours and reduced charging times could make EVs an even more appealing proposition for the modern commuters.