*2.2. Energy Density, Trip Structures and Modeling of Battery Levels*

The energy density of electric batteries is known to be low relative to that of diesel fuel. Furthermore, the time required to transfer a certain amount of energy by charging its batteries, either conductively or inductively, is large compared to the time required to pump diesel fuel into the tank of a comparable vehicle with a combustion engine. Finally, an electric battery is not only expensive but also heavy due to its relatively low energy density. For all those reasons, the decision about the capacity of the battery of an electric vehicle is delicate from both the economic and the operational perspective: Very large batteries are not only expensive, but their transportation as part of the moving vehicle itself also consumes energy. On the other hand, small batteries require frequent re-charging and need to have ample spatially distributed charging facilities, again either for conductive or inductive charging.

For those reasons, many researchers studying dynamic inductive charging infrastructure design problems decided to model allocation decisions for ITUs together with battery size decisions for vehicles. The typical assumption is that a vehicle, say, a passenger bus serving an urban bus line, starts with a full battery at some initial location A, travels along a pre-defined route while serving a sequence of bus stations, and ends the tour at some final destination B. The charging infrastructure has to be allocated in such a way that the vehicle is never confronted with an empty battery while on its trip. To this end, the State of Charge (SOC) of the battery is tracked meticulously, considering both phases of de-charging and phases of charging (while passing ITU-equipped segments of the road system). An underlying assumption is that if the bus reaches the end of its tour, all that is needed is a battery that is not empty and that the battery will be fully charged before the bus begins its next trip. Examples of those modeling approaches can be found in Ko and Jang [17], Hwang et al. [18] and Ko et al. [19]. An important result of those studies is that the optimal structure of the charging infrastructure depends on the number of vehicles using it. Suppose only a small number of vehicles use the charging structure. In that case, it is beneficial to equip those few vehicles with large (and expensive) batteries to need only a few charging segments along the route the vehicles will travel. It is, however, not attractive to have a very large number of those vehicles equipped with large and expensive batteries. In this case, it is economically advisable to have a larger fraction of the road segments

equipped with ITUs and to be able to operate with smaller (and, hence, less costly) battery sizes in many vehicles.

When considering the question of how to allocate the ITUs and PSUs within the road network of an airport apron, it turns out that the spatial structure as well the nature of the trips driven by, say, passenger buses, differs substantially from those found in urban mass transportation by public buses.

Figure 2 presents as an example a selected part of Vienna Airport. On the airport apron, a road network connects the aircraft parking positions, equipment service areas, vehicle depots and terminal buildings adjacent to the airport apron. The parking positions for aircraft can be distinguished between gate positions and outside positions (Mensen [20]). Passengers can reach an aircraft parked at a gate position via a boarding bridge, while apron buses are used for transportation to the outside parking positions.

**Figure 2.** Selected part of the apron at Vienna Airport. Source: Vienna Airport [online], 48◦07003.3900 N 16◦33052.7500 E, Height 785 m, Google Earth © GeoBasis-DE/BKG 2009, URL: http://www.google. com/earth on 19 April 2022.

ITU PSU

The layout of the terminal buildings determines the location of gate parking positions and the passenger gates. There are different terminal layout concepts, such as the pier, the satellite and the linear design. Figure 2 shows that these three layout concepts co-exist at Vienna airport.

At each terminal, several gates are available. Some gates are used exclusively to let passengers (un-)board their aircraft via a passenger bridge or to use passenger buses to transport the passengers to or from an outside aircraft parking position. In contrast, other gates can operate both with passenger bridges or passenger transportation buses.

During the turnaround of an aircraft, apron vehicles travel to and from the specific parking position, as well as gates or depots. A passenger bus, the exemplary type of vehicle considered in this paper, could pick up passengers at an aircraft and transport them to a terminal gate. Afterward, the bus could travel to another gate to pick up passengers and transport them from that gate to the parking position of their respective aircraft.

If we compare the operational elements of trips driven by passenger buses on airport aprons to those in urban public transport, we see three important differences:


Due to the third point, it seems impractical to follow the very detailed modeling approach introduced in Ko and Jang [17] and track at a very fine-grained resolution the SOC for the potentially extremely large number of conceivable service requests.

For this reason, we decided in this paper, as in Helber et al. [7] and Broihan et al. [8], to use a fundamentally different modeling approach. We require that the energy intake must be higher than the energy consumption for every service request. Therefore, the battery charge level at the end of a service request cannot be lower than at the beginning. As a result of that modeling decision, we do not need to model the SOC of the vehicles' battery in detail.
