Sizing Methodology of Dynamic Wireless Charging Infrastructures for Electric Vehicles in Highways: An Italian Case Study

Abstract

The necessity of pushing the road mobility towards more sustainable solutions has become of undeniable importance in last years. For this reason, both research and industry are constantly investigating new technologies able to make the usage of battery electric vehicles(BEV) as accessible and usable as traditional internal combustion engine vehicles (ICEV). One of the most limiting issues concerns the short range of electric vehicles, which complicates their use for long distances, such as for highway travels. A promising solution seems to be the “charge-while-driving” approach, by exploiting the inductive dynamic wireless power transfer (DWPT) technology. Nevertheless, such systems show different issues, first of all, high investment and maintenance costs. Furthermore, it is not clear how extensive a potential dynamic wireless charging infrastructure needs to be to make a real advantage for electric vehicle drivers. As a consequence, the aim of this paper is to introduce a new methodology to estimate the number and length of wireless charging sections necessary to allow the maximum number of electric vehicles to travel a specific highway without the need to stop for a recharge at a service area. Specifically, the methodology is based on a algorithm that, starting by real traffic data, simulates vehicle flows and defines the basic layout of the wireless charging infrastructure. This simulator can provide a decision support tool for highway road operators.

1. Introduction

The necessity to reduce anthropogenic greenhouse gas emissions has become a central theme in political, social, and economic discussions. As reported in [1], global greenhouse gas emissions overcame 50 billion tons in 2022, with an almost exponential trend since the early 20th century. One of the main causes of these emissions, second only to energy generation processes, is the transportation sector [2]. In Europe, the situation appears particularly critical. In fact, in 2019, the transport sector in EU27 was responsible for 26% of greenhouse gas emissions (29% including international maritime traffic), a value undoubtedly higher than the global average of 19%, as reported in [3,4]. For this reason, the transport sector is receiving significant attention. Considering that 72% of that 29% comes from road transport [3], the need for intervention in the use of vehicles on our roads and highways becomes evident.

Net of all issues related to the battery lifecycle, electric mobility proves to be one of the most impactful solutions for achieving a significant reduction in climate-altering emissions from the road transport sector [5]. However, this approach requires a paradigm shift in the use of road vehicles, whether passenger or commercial ones. The main obstacle is the reduced range of battery electric vehicles (BEV) compared to traditional internal combustion engine vehicles (ICEV). This makes it difficult for electric vehicle drivers to have a highway driving experience similar to those using traditional vehicles. In particular, electric vehicle drivers will stop more frequently at service areas to recharge their vehicles. This could lead to serious issues on days with high traffic peaks, with unmanageable queues at charging stations [6]. These scenarios are further complicated by the so-called range anxiety, which is the fear of not having sufficient capacity to reach the destination [7], prompting people to recharge more than necessary. As a consequence, both research and industry have been working to explore solutions to overcome the range limitations of BEVs, thereby enabling greater adoption of electric mobility on highways. Firstly, highway operators and charging infrastructure operators are pushing to expand and make the charging infrastructure more extensive and widespread [8], in compliance with the European AFIR directive (Alternative Fuels Infrastructure Regulation) [9]. Other solutions involve the development of artificial intelligence algorithms that, through a vehicle-to-infrastructure (V2I) interaction approach, coordinate vehicle charging events on the network to minimize queues at charging stations, ensuring compliance with the minimum charge level requirements expected by EV drivers [6,10].

A different approach instead consists in implementing solutions that allow the vehicle to receive charging energy while in motion [11], thus reducing the need to stop for charging and avoiding the risk of running out of capacity. Among others, the most promising solution for implementing this approach seems to be the Dynamic Wireless Power Transfer (DWPT), proposed in literature in different variants [12]. In general, a DWPT system exploits primary coils integrated into the road pavement to transmit power to secondary coils installed on the vehicles [13].

The implementation of dynamic charging plants could lead to several benefits, such as the necessity of smaller traction batteries, the reduction of range anxiety and the increase of electric vehicles penetration on highways. In other words, by installing DWPT systems, highway infrastructure operators could promote the transition to electric mobility, initiating an increasingly virtuous circle of demand and supply.

Nevertheless, many difficulties remain regarding this type of system. The first is certainly the cost, both investment and maintenance [14]. Furthermore, there are no standardized practices yet concerning the integration of transmitting coils with road pavement and the consequent impact on maintenance procedures. In particular, the integration of specific materials with the asphalts, such as coils, casing and magnetic shields [15,16], still represent an open issue from the perspective of maintenance operations [17]. Last but not least, there is the need to quantify the actual benefit that a DWPT charging infrastructure can bring in terms of increasing electric mobility penetration in a given road network. Since the cost of each km of DWPT systems represent a huge investment, it results to be of extremely importance to correctly plan the layout of the infrastructure over the highway network.

Different models have been proposed in literature to define the right places and lengths of DWPT systems. In many cases, the focus is solely on buses. For example, in [18], the placement is optimized for a single vehicle, while in [19,20], an electric bus fleet is considered for planning. In other cases, methods are proposed with a focus on long-haul freight transportation only [21]. A more general approach is presented in [22], where an optimization model is proposed to minimize the number of plants in order to obtain the best integration with renewable energy sources.

Nevertheless, all these methodologies are based on complex and computationally demanding models. Their effectiveness on a complex and interconnected network, such as a highway network, has not been demonstrated, yet.

For this reason a new and simple methodology is proposed in the present paper for sizing DWPT infrastructures for passenger cars usage. In particular, a highway traffic flows simulator has been developed, which is able to evaluate the behavior of electric vehicles with DWPT plants. Starting from appropriate boundary conditions and assumptions that will be outlined later, the tool can define for a given highway the number, length, and position of DWPT sections necessary to support the flows of BEVs along the examined highway. The simulator can be exploited as Decision Support System (DSS) by highway network operators.

The paper is organized as follows. A detailed description of the methodology development is presented in Section 2. First, the main assumptions are enumerated in Section 2.1. Then, the procedures carried out to build the road network for simulations, the routing algorithms implemented and the BEVs population creation are described in Section 2.2, Section 2.3 and Section 2.4. The DWPT positioning algorithm is presented in Section 2.5. Therefore, a case study based on real data from Italian highways is presented in Section 3, with results description in Section 4. Finally, conclusions of the work and future perspectives are presented in Section 5.

2. DWPT Sizing Methodology

In this section, the proposed DWPT sizing methodology is described. Specifically, a simulator has been developed to deal with the highway network managed by Autostrade per l’Italia, which is the main Italian highway road operator. However, the simulator is highly flexible and can be adapted to all types of dense networks.

The considered network is represented in Figure 1.

From the figure it is possible to understand that the network is dense of nodes and interchanges between different highways. As a consequence, a model which has to deal with the whole network would require a high computational effort. For this reason, we developed a novel approach consisting into considering a single highway at a time, but without losing the contribution of vehicles that enter and/or exit on other highways, leveraging a routing algorithm able to evaluate flows passing through the highway interchanges.

Therefore, the methodology can be divided in two main parts. The first part consists of creating the discretized structure of the highway and the set of tours for the simulation. Each tour is characterized by information regarding the origin and destination stations, as well as other details related to the type of vehicle and travel capacity targets.

In Figure 2, a block diagram is shown representing the main steps of the first functional part of the methodology. GIS data of the highway network contain all the localization information of toll stations, interconnections, tunnels and bridges. Further, it is important to highlight here that real traffic data are used in the origin-destination matrix format.

The second part of the method consists of the simulator which, based on the the first part outputs, simulates the journeys of each tour, calculates the capacity variations, decides where to place possible DWPT charging sections, and evaluates various Key Performance Indicators (KPIs), defined in detail in the following sections. In Figure 3, a block diagram is shown that represents all the mentioned steps in a simplified manner.

All the blocks represented in Figure 2 and Figure 3 will be described in the following sections.

2.1. Assumptions

In this section, the main assumptions made in developing the sizing methodology are explained. In particular, different assumptions have been applied, regarding: DWPT constraints, DWPT operation and traffic flows. For the sake of simplicity, they are grouped and listed below:

• DWPT constraints:

  –

  only single-lane systems are considered;

  –

  DWPT systems cannot be located in correspondence with toll stations, tunnels, bridges and viaducts.

• DWPT operation:

  –

  the energy provided by the DWPT system is equal to the energy required by the single vehicle to travel that section. In other words, it is assumed that the system can supply the battery with the same energy that the latter is consuming, and therefore, the net energy consumption of the vehicle for each kilometer equipped with the DWPT system is zero;

  –

  each DWPT section is able to supply all vehicles transiting on it with the required power [14].

• Traffic flows:

  –

  all BEVs are supposed to pass over DWPT plants;

  –

  only BEVs vehicles are considered and ICEVs flows neglected;

  –

  temporal phasing is neglected and the total daily number of vehicles for each section is considered. As a consequence, changes in traffic patterns are not taken into account;

  –

  a constant consumption model is applied to vehicles, based on WLTP homologation data [23]. In other words, changes in speed and/or road gradient are not taken into account and, as a consequence, the energy consumption per unit distance for each electric vehicle is considered constant along the entire traveled section.

2.2. Highway Discretization

The first step of the presented methodology consists into the selection of the highway for DWPT sizing and into discretizing it in a finite number of segments. The input for the procedure are GIS data available in Autostrade per l’Italia database. Since the minimum level of spatial resolution of such data is 100 m, the highway segmentation has been set with the same step. This spatial segmentation can be changed accordingly to the available data, in order to increase the accuracy of the algorithm.

Therefore, a procedure aimed to identify all the available segments for an hypothetical DWPT plant is carried out. As already highlighted before, it is assumed that DWPT can not be placed in correspondence of toll stations, tunnels and bridges. In

Table 1. Main features of highway network managed by Autostrade per l’Italia.

Highway	Length (km)	Toll Stations	Tunnels (Number)	Tunnels (km)	Bridges (Number)	Bridges (km)
A01	759.8	65	132	96.8	420	55.3
A04	93.5	16	0	0.0	50	3.3
A07	50.0	7	29	13.2	75	9.2
A08	67.6	8	9	3.7	49	5.1
A09	31.5	2	12	4.1	21	1.7
A10	45.5	9	94	29.3	106	15.8
A11	81.7	10	2	0.7	54	2.1
A12	114.1	12	71	48.6	49	8.9
A13	127.3	15	0	0.0	52	6.1
A14	743.4	60	76	43.1	359	44.0
A16	172.3	12	22	8.0	85	9.8
A23	101.2	5	35	43.3	130	27.1
A26	244.8	12	89	51.0	194	30.7
A27	82.2	9	18	17.2	66	20.9
A30	55.3	6	8	4.7	72	6.6

the list of highways of the Autostrade per l’Italia network is presented, along with the number of toll stations, tunnels and bridges. For tunnels and bridges, the total length is also shown. Concerning toll stations, it is possible to assume that the prohibited segments are 100 m before and after the station.

For example, let us consider the longest highway, namely A01. In this case, by considering previous assumptions, about 165 km, i.e., 22% of the total highway length, are note available for DWPT plants. A schematic representation of discretization and selection of available and prohibited segments is shown in Figure 4.

A specific situation that may arise on some highway sections is that of so-called branch roads. In this work, it is assumed that such branch roads are not eligible for DWPT installations, for their reduced length, if compared with main highways. Therefore, to account for the vehicular flows coming from or directed towards toll booths on the branch road, all such toll booths are collapsed into a single point on the main highway section, corresponding to the intersection between the main highway and the branch road. This procedure is schematically represented in Figure 5.

A similar approach will be used to take into account vehicle flows coming from or directed to intersecting highways, as explained in the following section.

2.3. OD Matrix Construction and Routing Algorithms

The starting traffic data is represented by the origin-destination (OD) matrices covering the whole Italian highway network managed by Autostrade per l’Italia. These matrices are obtained by collecting each vehicle entering or exiting the highway network, allowing the maximum possible accuracy for this kind of information. By averaging all matrices related to working days of year 2023, a single average OD matrix has been obtained and exploited for the study. The matrix is a $n-by-n$ square matrix, where n is the number of toll stations. As a consequence, the $ij$ cell contains the daily average number of vehicles which enter the highway through the station i and exit through the station j. The first step consists into filtering the OD matrix, i.e., to select only the cells whose rows and columns belong to the selected highway. The drawback of this approach is that only vehicles entering and exiting on the same highway are considered, neglecting all those that only pass through it via interchanges. For the sake of example, let us consider the OD matrix of a two highways network, namely $H_1$ and $H_2$, connected by an interchange $I_1$. A schematic representation with example data is shown in Figure 6.

By exploiting the above mentioned approach of selection, just the traffic flow related to the single highway, say $H_1$ will be taken into account, as shown in the upper-right matrix in Figure 6. Nevertheless, there are vehicles which needs to travel from a station belonging to $H_1$ to a station belonging to $H_2$. By assuming $I_1$ as the sole connection between the two highways, this passage must occur through the interconnection $I_1$. In order to take into account such vehicles in the total number of flows passing through highway $H_1$, sums of tours originating from $H_2$ and ending in $H_1$, and vice versa, will be inserted in the $H_1$ matrix as interchange contribution, as shown in the lower-right matrix in Figure 6.

The complexity increases with the addition of more highways and interchanges, complicating the network graph. In such circumstances, to determine the vehicles routs in the network graph and establish if they pass through the selected highway and which interchanges they cross, it is necessary to compute the path each vehicle takes from its origin to its destination through the whole network. It is reasonable to assume that each vehicle travels the shortest route possible to reach its destination. Therefore, the Dijkstra’s algorithm is applied to each origin-destination pairs, thereby defining the related path. In particular, a Dijkstra’s algorithm is able to find the optimum path in shortest-path search problems [24]. This allows understanding for each cell of the initial OD matrix whether it will be included in the final matrix and if so, which interchanges will be crossed. In this procedure, the distance travelled before reaching the interchange is also calculated and used as explained in the following section.

2.4. Tours Creation

In this section, the tour generation procedure is illustrated. The aim is to create a population of tours which is able to describe the traffic flows scenario, mainly dependent on the percentage assumed for BEVs penetration and the selected highway with its own origin-destination matrix. In particular, the creation of tours consists into assigning an electric vehicle (with all its features) to each route identified by the origin-destination pairs on the highway. Therefore, each tour will be described by an origin O and a destination D, along with the following features:

• battery capacity of the vehicle, C ($\mathrm{kWh}$);
• unit consumption of the vehicle, $\delta$ ($\mathrm{kWh}/100 \mathrm{km}$);
• battery capacity when entering the highway through the origin station $So{C}_{in}$ (%);
• minimum allowed battery capacity during the journey and at the exit station, $So{C}_{min}$ (%).

For all these features, specific distributions have been created and exploited to generate the tours populations. About battery capacities and unit consumption, all BEVs passenger cars available on the market as of December 2023 were considered [25]. Furthermore, since the presented methodology is primarily aimed at working with future scenarios characterized by high electric vehicle penetrations, it is reasonable to consider only the most recent models on the market, omitting those models that, due to aging or poor performance, are not representative of the scenarios intended to be depicted. Specifically, 362 different models of electric vehicles distinguished by size, battery capacity, and average consumption have been taken into account. It is also worth to highlight here that light and heavy-duty commercial electric vehicles are not taken into account in the present work and will be addressed in future investigations.

Distributions of battery capacities and consumption are represented in Figure 7a,b.

It is possible noting that the average battery capacity of electric vehicles on the market is about 71 kWh, and the average consumption is 19.5 kWh/100 km. The combination of these data implies an average range of approximately 360 km.

For the initial SoC the distribution is constructed by exploiting the assumption that people prefer entering the highway with high values of SoC, e.g., between $60\%$ and $100\%$. For this reason, the battery percentage of the vehicle entering the highway is assigned using a normal distribution with a mean of 80%, variance of 15%, and values ranging from 60% to 100%, as depicted in Figure 7c. The two peaks at $So{C}_{in}=60\%$ and $100\%$ are due to assumption just explained above.

Regarding the minimum SoC allowed for each tour, it has been necessary to consider different parameters, such as the range anxiety and the remaining distance to travel outside the highway. As described in [26], people are uncomfortable when the SoC is lower than 30%. For this reason, a normal distribution is used with a mean of 25%, variance of 2.5%, and minimum and maximum values of 20% and 30%, respectively. The $So{C}_{min}$ distribution is pictured in Figure 7d.

Finally, once the full population has been generated, a filter is applied in order to exclude all tours satisfying the following equation:

$$So{C}_{out}=So{C}_{in}-{\displaystyle \frac{\delta (D-O)}{C}}\ge So{C}_{min}$$

(1)

where $So{C}_{out}$ is the state of charge of the battery when the vehicle reaches the destination station, C is the maximum battery capacity, $\delta$ is the unit consumption, $D-O$ is the travelled distance from origin to destination, expressed in kilometers. In other words, if the vehicle state of charge when it exits the highway is greater than or equal to the minimum allowed SoC, it is possible to exclude the related tour from the simulation, because it is assumed that it does not need to charge the battery during the highway route. To better explain this condition, it is representative of all vehicles entering with a high $So{C}_{in}$, with a short distance to be travelled.

Furthermore, it is important to consider that some vehicles can enter the selected highway via interchanges with another highway, as already explained in the previous section. In these cases, the same rule for SoC assignment at the entry stations is applied. Then, by evaluating the consumption on the road segment between the entry station and the interchange, the SoC at the interchange, i.e., the effective SoC entering the highway under study, is calculated. This procedure leads to an overall shift of the distribution towards lower values of initial SoC.

Finally, it is possible to evaluate the resulting capacity, consumption and SoC distributions of the filtered population, with interchanges contribution, as shown in Figure 7e–h. The above mentioned left-shift of starting SoC distribution can be appreciated in Figure 7g.

2.5. DWPT Infrastructure Sizing Procedure

In this section, the core part of the methodology is presented, namely, the DWPT infrastructure sizing procedure. As already mentioned in Section 1, the methodology aims to be as simple as possible, in order of being useful to highway road operators as decision support system. In particular, the tool evaluates the number, length and position of DWPT segments to be installed on a certain highway, in order to allow the maximum number of electric vehicles to travel the highway without the need to stop for a recharge at a service area. This information can be exploited by the road operator to plan the implementation of the dynamic charging infrastructure on its network.

The procedure is based on the evaluation of a control function that is used to decide whether to place the DWPT in a given segment. A flow chart representing the algorithm for control function evaluation is proposed in Figure 8.

As represented in the figure, each segment of the highway is considered at a time, by changing the position index p. Therefore, each tour is considered and, by comparing its origin and destination with the index p, it is evaluated if the tour is driving in the specific section. For each j-th tour and each p-th section, the State of Charge, $So{C}_{j,p}$ is evaluated and, if

$$So{C}_{j,p}<So{C}_{j,min}$$

(2)

it means that the j-th tour has reached its minimum allowed SoC level and it is to be considered unsatisfied. Therefore, for each position index, the control function value ($C{F}_p$) is evaluated as follows:

$$C{F}_p=g(N_p,U_p,f_{SoC,p})$$

(3)

where $N_p$ and $U_p$ are the number of tours and the number of unsatisfied tours on the section p, respectively, while $f_{SoC,p}$ is the SoC distribution in the section p. The function g can be customized according to specific needs to implement the desired positioning logic.

Ones the control function has been evaluated for each position index, a simple approach based on a threshold can be exploited for positioning DWPT sections. A flow chart representation is shown in Figure 9.

In particular, the algorithm takes the following input values:

• control function threshold;
• minimum length of DWPT segments ($L_{min}$);
• maximum length of DWPT segments ($L_{max}$);
• highway segments where it is not possible to install a system, identified in Section 2.2.

A new DWPT section can start only if the following condition, $\mathsf{\xi }$, is verified:

$$\mathsf{\xi }:\forall x\in [{\mathrm{km}}_p,{\mathrm{km}}_p+L_{min}],x\notin S$$

(4)

where S represents the set of positions of toll stations, bridges, and tunnels. This condition ensures that a new DWPT section can start only if the minimum length $L_{min}$ is guaranteed, without encountering prohibited segments.

Finally, each tour is simulated again considering the presence of the DWPT systems identified and positioned in the previous steps. In this case, the battery energy consumption of each vehicle is considered equal to zero in the segments equipped with DWPT, and the number of unsatisfied tours and the SoC distribution for each highway position index are recalculated.

It is also worth noting that the methodology can be applied to highways with two carriageways. In this case, two control functions are calculated separately for left and right sides of the road with the procedure described in Figure 8. Then, the two control functions obtained are averaged and normalized, and the resulting function is exploited in the DWPT positioning algorithm described in Figure 9. As discussed hereafter, once the control function has been determined, different simulations with different values of threshold can be carried out in order to evaluate the percentage of satisfied tours and the number of DWPT plants to be installed. The lower the control function threshold, the higher the number and lengths of DWPT sections that the algorithm identifies. Then, by comparing the simulations results, it is possible to choose the solution which gives the highest percentage of satisfied tours with the minimum number and length of plants. In other words, the control function threshold acts as a decision parameter for the sizing methodology. This approach will be used in the case study described in the next section.

3. Case Study

In order to demonstrate the functionalities of the proposed methodology, a case study is presented in this section. In particular, the Italian highway A1 managed by Autostrade per l’Italia is considered. The highway is shown on the map of Figure 10a, along with positions of stations and interchanges with other highways in Figure 10b.

In Figure 11a, the Origin-Destination matrix is presented, derived from average daily traffic data on working days in 2023. For convenience, the stations have been renamed S, while the interconnections are referred to as I. In particular, the cell $ij$ represents the daily average number of vehicles entering the highway from the station (interconnection) $S_i$ ($I_i$) and exiting the highway from the station (interconnection) $S_j$ ($I_j$). As can be seen, by utilizing the routing algorithms described in Section 2.3, it is possible to describe the vehicular flows using an OD matrix with 48 toll stations and 13 interconnections with other highways. Assuming a 100% penetration of BEVs, the matrix represents all electric traffic flows through the A1 on a typical working day. Obviously, this assumption represents the most complex case and can be considered realistic for future penetration scenarios, expected for 2050 [27]. From this matrix, a reduced matrix can be obtained, considering only the tours that require to charge during the journey, i.e., tours not satisfying the condition expressed in Equation (1). This reduced matrix is shown in Figure 11b, illustrating the urgency of DWPT infrastructure for the given scenario. As expected, most tours near the diagonal of the OD matrix, i.e., those with shorter travel distances, do not need recharging and can reach their destination with the available capacity.

It is important to note that, by analyzing the reduced OD matrix, it is possible to calculate that the daily average number of tours that would require recharging on the highway on a working day is approximately equal to 56,000 vehicles.

By exploiting the procedure described in Figure 8 it is possible to evaluate all the input values for the control function calculation and the control function itself. In Figure 12, number of vehicles and SoC distributions are represented with respect to the highway positions, both for right and left carriageways. In particular, total number of tours and unsatisfied tours for each position are plotted in Figure 12a,b. More in detail, the total number of vehicles for each highway position (blue curves), along with the number of vehicles with $SoC<So{C}_{min}$ (red curves), are represented. On the other hand, Figure 12c,d show the SoC distributions for each position, where green triangles represent average values, orange horizontal lines medians and black circles represent the outliers. The distributions are constructed by calculating the values of SoC for each vehicle in the specific highway position.

As already described in Section 2.5, the Equation (3) can be customized according to the specific positioning logic to be implemented. By observing results shown in Figure 12, the following approach can be carried out:

• DWPT must be placed at points with high number of daily tours;
• DWPT must be placed at points with high number of vehicles with $SoC<So{C}_{min}$;
• DWPT must be placed where the variance of the SoC distribution is low.

The latter condition is useful to reduce the effect of alteration in the SoC distribution due to highway entries and exits. Specifically, entries and exits lead to an increase in the average value of the SoC distribution, which does not accurately represent the tours that were already on the highway in previous positions. Consequently, the variance increases at the stations. The idea is to guide the algorithm to place the DWPT plants where the variance is low, meaning where the effect of entries and exits on the distribution is also low. As a consequence, the function in the highway position p takes the following form:

$$C{F}_p=a{\displaystyle \frac{U_p}{N_p}}+b\left(1-{\displaystyle \frac{iq{r}_p}{max\left(iq{r}_p\right)}}\right)+c{\displaystyle \frac{N_p}{max\left(N_p\right)}}$$

(5)

where $iqr$ is the interquartile range, used instead of variance due to the high number of outliers in the distributions, $N_p$ and $U_p$ are the number of tours and the number of unsatisfied tours, respectively. a, b and c are weights that can be chosen for obtaining the desired function. In particular, the control function has been calculated for all possible combinations of a, b, and c in the interval [0.2,0.8], with step of 0.1, by considering only set of parameters with sum equal to 1. Therefore, the smoothness S of each curve has been evaluated according to the following equation [28]:

$$S={\int }_p{\left(C{F}^{″}\left(x\right)\right)}^{2}dx$$

(6)

where the integral is calculated over the highway positions p. Calculated values of smoothness are represented in Figure 13 for each combination $C1$–$C15$.

In this case, since the method involves positioning the DWPT only where the control function exceeds a certain threshold, it is essential that the control function is as non-smooth as possible. This ensures high sensitivity to changes in the threshold and prevents the algorithm from over-positioning events. For this reason, the combination 5 with $a=0.2$, $b=0.6$, $c=0.2$ is chosen and the resulting control function is represented in Figure 14, for right and left carriageways and for the resulting normalized average.

4. Results

In this section, main results of case study are presented. In particular, by exploiting the control function calculated in previous section, simulations at different values of threshold have been carried out. Moreover, four different combinations of $L_{min}$ and $L_{max}$ have been tested, namely:

• $L_{min}=1$ km, $L_{max}=2$ km
• $L_{min}=1$ km, $L_{max}=5$ km
• $L_{min}=1$ km, $L_{max}=10$ km
• $L_{min}=2$ km, $L_{max}=5$ km

For each simulation, the following KPIs have been evaluated and shown in

Table 2. Comparison of sizing algorithm results for different DWPT layouts with 100% BEV penetration on highway A1.

${\mathit{L}}_{\mathbf{min}}$ (km)	${\mathit{L}}_{\mathbf{max}}$ (km)	Threshold	Number of Plants per Carriageway	DWPT Total Length per Carriageway (km)	% of BEV with $\mathit{SoC}\ge {\mathit{SoC}}_{\mathit{min}}$	Total Energy Demand (MWh/day)
1	2	0.2	221	401.30	51.95	1829.63
1	2	0.3	213	386.90	49.31	1768.09
1	2	0.4	182	328.00	40.53	1562.06
1	2	0.5	133	243.90	30.50	1211.73
1	2	0.6	97	176.30	12.82	861.21
1	2	0.7	74	134.30	4.28	619.27
1	2	0.8	57	101.40	1.98	468.73
1	5	0.2	150	430.80	55.78	1919.81
1	5	0.3	146	416.10	53.14	1858.67
1	5	0.4	123	352.20	43.86	1641.39
1	5	0.5	87	259.90	32.62	1263.62
1	5	0.6	63	186.80	14.25	893.59
1	5	0.7	48	140.00	4.56	632.12
1	5	0.8	33	103.60	1.90	466.85
1	10	0.2	138	437.30	56.80	1944.88
1	10	0.3	135	422.70	54.18	1884.53
1	10	0.4	115	358.50	44.81	1667.25
1	10	0.5	80	266.00	33.54	1289.03
1	10	0.6	58	191.60	14.90	912.98
1	10	0.7	45	144.20	5.16	649.96
1	10	0.8	31	106.90	2.19	481.37
2	5	0.2	100	358.10	44.07	1612.09
2	5	0.3	96	342.50	41.49	1547.10
2	5	0.4	81	292.10	34.07	1373.01
2	5	0.5	62	223.60	27.45	1097.45
2	5	0.6	41	154.40	10.49	747.78
2	5	0.7	29	110.70	2.56	500.99
2	5	0.8	24	91.10	1.34	415.05

:

• number of DWPT plants per carriageway;
• total length of DWPT sections per carriageway;
• percentage of satisfied tours;
• total daily energy demand (MWh/day).

The third one represents the percentage of BEVs using DWPT that are able to reach the exit station with a residual capacity greater than the minimum allowed, i.e., the percentage of vehicles that would not need to stop for charging in a service area, thanks to the usage of the DWPT infrastructure. The latter KPI refers to the total energy delivered to all tours each day, both satisfied and unsatisfied.

The values considered for the threshold are 0.2 to 0.8 with a 0.1 step.

For the sake of example of simulations results, the curves representing the total number of vehicles and number of unsatisfied vehicles with respect to the highway positions are shown in Figure 15, for all $L_{min}$ $L_{max}$ combinations and for 0.2 and 0.6 threshold values.

It is possible to note that by increasing the threshold, differences between $L_{min}$ $L_{max}$ combinations decrease. Moreover, the best combination in terms of percentage of satisfied tours results to be $L_{min}=1$ km $L_{max}=10$ km. This is confirmed in Figure 16, where a plot representing the percentage of satisfied tours with respect to threshold values and length combinations is shown. Furthermore, number and total length of plants are described by markers color and size, respectively. The total energy demand is represented through transparency of markers.

It is important to highlight that the methodology results are strongly dependent on the specific highway considered for sizing. In the case of highway A1, characterized by high numbers of bridges and tunnels, the more flexible the combination of $L_{min}$ $L_{max}$, the better the result in terms of percentage of satisfaction. The worst combinations result to be $L_{min}=1$ km $L_{max}=2$ km and $L_{min}=2$ km $L_{max}=5$ km. In the former case, the constraint to set small length plants, implies an increase in number of plants. This layout would cause an increase in complexity and cost of the system, due to its high fragmentation. In the latter case, all plants smaller than 2 km are excluded, with a consequent decrease in the percentage of satisfied tours. On the contrary, best combinations are $L_{min}=1$ km $L_{max}=5$ km and $L_{min}=1$ km $L_{max}=10$ km, which guarantee a higher decision flexibility to the algorithm.

The presented results can give an idea of the effectiveness of dynamic wireless power transfer on an important highway, like the Italian A1. First, it is worth nothing that in any of the studied combinations it is possible to reach a percentage of satisfaction equal to 100%. Instead, a maximum percentage of 56.8% is obtained with $L_{min}=1$ km $L_{max}=10$ km and threshold equal to 0.2, with DWPT sections covering about the 58% of each carriageway of the A1 highway. As a consequence, it can be evaluated that, by exploiting this DWPT layout, the total daily number of vehicles yet impelled to stop for charging in service areas would be equal to about 24,000 vehicles, i.e., the 43.2% of 56,000 vehicles using DWPT each working day (Section 3). This means obviously that the dynamic charging infrastructure can not replace the standard conductive static infrastructure, that must be consequently further empowered in next years.

Finally, important considerations can be carried out about the energy demand to by supplied through DWPT. As shown in Table 2, in order to achieve a percentage of satisfaction greater than 25%, an energy demand higher than 1 GWh per day must be supplied. Conversely, a plant coverage of at least 35% of the highway would be necessary, with a daily electricity demand greater than 1.2 GWh, in order to satisfy at least 30% of the vehicles in transit. Furthermore, the maximum value of energy demand, leading to the maximum percentage of satisfaction identified above, is equal to 1.9 GWh per day.

5. Conclusions and Future Perspectives

A novel methodology for sizing a Dynamic Wireless Power Transfer (DWPT) infrastructure on highways has been presented and discussed in this work. The procedure begins with the collection and analysis of GIS and traffic data from the highway road network. Data from network managed by Autostrade per l’Italia, the largest highway operator in Italy, have been used in this study. However, this methodology is flexible and can be adapted to any other highway network. By leveraging a well-known routing algorithm, a comprehensive dataset of tours to be simulated is generated. The positions and lengths of DWPT segments on a specific highway are then identified through simple logic. Essentially, the algorithm calculates a control function for each highway position and, based on a predetermined threshold value, decides if the location is suitable for DWPT installation. The algorithm’s outputs include the number and length of the plants, the total daily energy demand and the percentage of tours that reach their destination with a State of Charge greater than the minimum allowed capacity.

A detailed case study was also conducted to apply the sizing methodology to the main Italian highway, the A1. Real traffic data were exploited, and a scenario assuming full penetration of battery electric vehicles was considered. Various layout combinations were tested by varying the minimum and maximum lengths of DWPT segments ($L_{min}$ and $L_{max}$), along with the control function threshold. Among the different configurations, the combination of $L_{min}=1$ km and $L_{max}=10$ km proved to be the most effective, resulting in a maximum percentage of satisfied tours around 57%. This was achieved with 138 plants, each contributing to a total length of approximately 437 km per carriageway. The total energy demand for this scenario was estimated to be about 1.9 GWh per day, illustrating the significant energy requirements for sustaining such an infrastructure.

Results of the methodology helped to highlight the huge technical complexity of all possible layouts identified for a hypothetical DWPT infrastructure designed for full BEV penetration of passenger cars on the main Italian highway. This complexity impacts both the road network and the energy network. Another interesting remark regards the importance of considering DWPT as a complementary technology to stationary conductive charging. Indeed, it is evident that the DWPT infrastructure alone cannot fully satisfy the charging needs of all vehicles in future scenarios, highlighting the need for a mixed approach.

Finally, this study paves the way for future investigations. For the sake of example, different levels of electric vehicle penetration can be compared in order to estimate the necessary growth rate of a potential DWPT infrastructure. The impact and requirements of both light and heavy-duty commercial vehicles can be also addressed in a specific study. Additionally, the methodology could be further refined by integrating the role of traditional conductive stationary charging stations located in service areas, creating a more comprehensive and holistic approach to planning highway charging infrastructure. This integration would ensure a more resilient and flexible charging network capable of satisfying various types of vehicles and usage patterns. An additional area of investigation, necessary to understand potential issues on the energy infrastructure side, is to include hourly traffic profiles for different vehicles in order to calculate the power requirements for each charging lane.

Moreover, by exploiting the hourly traffic profiles and more accurate battery consumption models, further evaluations will be conducted to assess the performance of the DWPT infrastructure in extreme situations characterized by increased volume of traffic. For the sake of example, such situations occur at the beginning or at the end of summer holidays in Italy, when traffic jams and incidents severely challenge the highway network.

Finally, future investigations could explore the economic aspects of deploying, maintaining and operating DWPT infrastructures sized using the present methodology. While the high investment cost of such systems can be easily estimated, specific considerations must also be carried out on the user side, by investigating the willingness to pay for this type of mobility service. This would help in understanding the economic feasibility of such a complex system, which can enable the charging-by-drive paradigm and push the transition to a more sustainable and electrified transportation system.