*4.6. Calculating Total Driver Time*

It is important to calculate how much driver time is needed for the different charging strategies since the driver wage is a high cost in many countries. A driver is of course needed for the whole time that the bus is in motion, but also for the layover time, and for some, but not all, charging. Charging at the end stops between each trip is typically only a few minutes at a time, for which the driver will have to wait. In contrast, charging in the depot is completed while the bus is parked, hence, drivers do not need to be in duty during this type of charging. The extra charging at the end stops can sometimes be completed during a driver's break. This will not lead to any extra driver cost, but in this paper, we assume that a driver must be paid also during all the extra charging at the end stops. The total time drivers must be in duty during a day can be calculated as:

$$T\_{\text{Driver}} = \frac{T\_{\text{Driving}} + T\_{\text{LaysoverTotal}} + T\_{\text{ChgTotal}}}{k\_{\text{Driver}\,\text{UtilFactor}}} \,\text{}\tag{43}$$

where *k*DriverUtilFactor takes into account that it is not possible to plan driver schedules so that all of the driver's time is spent in active duty. In this example, it is assumed that 90% of the driver's time can be deemed as active duty. The same equation can be used for all types of buses, but the charging time will be different between them, and the driving time will differ due to different amount of driving to and from the depot. The time the buses drive is:

$$T\_{\text{Driving}} = T\_{\text{TripNetTotal}} + T\_{\text{PullInOut}} \tag{44}$$

where:

$$T\_{\text{TripNetTotal}} = N\_{\text{TripOfPeak}} \times T\_{\text{TripNetOfPeak}} + N\_{\text{TripPeak}} \times T\_{\text{TripNetPeak}} + N\_{\text{TripEvening}} \times \tag{45}$$
 
$$T\_{\text{TripNetEvening}} \text{-}$$

The charging time is different for the different types of buses. For EndStop1, it is:

$$\begin{array}{c} T\_{\text{ChgTotal}} = T\_{\text{ChargePeakEndStop1}} \times N\_{\text{TripPeak}} + T\_{\text{ChargeOfPeakEndStop1}} \times N\_{\text{TripOffset}} + \\ T\_{\text{ChargeForningEndStop1}} \times N\_{\text{TripEveng}} \end{array} \tag{46}$$

where the charging time per trip during different parts of the day for EndStop1, *T*ChargeXXXEndStop1, can be determined according to Equation (8).

For EndStop2, the corresponding value is:

$$\begin{array}{c} T\_{\text{ChgTotal}} = \\ T\_{\text{ClargęOiffPeakEndStep1}} \times N\_{\text{TripOffPeak}} + T\_{\text{ClargęEwinęEndStop1}} \times N\_{\text{TripEwening}} \\ + (N\_{\text{BusxTotal}} - N\_{\text{BusxPeak}}) \times T\_{\text{ClyzAstra2}} + \left( N\_{\text{BusMidday2}} - N\_{\text{BusMidday1}} \right) \times T\_{\text{ClyzAstra1}} \end{array} \tag{47}$$

where the first two terms represent the charging according to EndStop1, but only off-peak and in the evening. This charging is shown in red in Figures 8 and 9. The third part corresponds to the extra charging by the busses which are not in traffic during the midday period, and the fourth part is the charging by extra buses (if there are any).
