In this section both the total positive and negative wheel energy per cycle are calculated and divided by the cycle distance, in order to find the energy consumption for each of the concept cars.
Cycle energy per distance for the three concept cars can be seen in Figure 4.10. Over all, the consumption levels are similar for both Urban and Rural cycles, while they are somewhat higher for the Highway cycles. It is clear that the relative amount of braking energy is much larger for the Urban cycles, and rather limited for the Highway cycles. Furthermore, for the Urban cycles, acceleration and rolling resistance are the main causes of energy consumption, while the aerodynamic drag is rather small. Due to the somewhat higher speed levels in the Rural cycles, the aerodynamic drag becomes larger. Still for the Rural cycles the energy consumption seem to be relatively evenly chaired between the three sources. For the Highway cycles, the aerodynamic drag is the single largest cause of energy consumption, often followed by the rolling resistance. So, even though accel- eration is the main force to consider when studying peak power levels: when it comes to energy consumption it is not always the dominating cause, at least not according to the test cycles. For those cycles where acceleration is the main cause of energy consump- tion (Urban cycles in general, and NYCC, Artemis Urban and UC LA92 in particular), the braking energy is also larger compared to other cycles, thus there is a chance for recuperation.
Vehicles
energy consumption, while ECE has the lowest. This can be related to Table 3.2 to 3.7, where it can be seen that NYCC, Artemis Urban and ECE have relatively low maximum and average speed values, but ECE have much lower maximum acceleration and RPA value than NYCC and Artemis Urban. For the Rural cycles, UC LA92 has the highest consumption and NEDC the lowest. Both cycles have similar levels of average speed but the UC LA92 has a large time share spent at higher speed levels. It is also the UC LA92 that has the highest maximum acceleration amongst the Urban cycles, as well as the highest RPA value, while NEDC has the lowest. Finally the Artemis motorway cycles have the highest consumption between the Highway cycles, and HWFET the lowest. In this case it is not the cycle with the highest acceleration or RPA values that consume the most energy, but it is that cycle that has the highest average speed and spend the most time at high speed levels.
−150 −100 −50 0 50 100 150 200 250 80 89 91 93 100 101 118 123 95 100 101 103 120 91 127 137 147 147 155 −40 −50 −39 −41 −48 −48 −82 −83 −28 −26 −32 −21 −52 −8 −22 −14 −38 −18 −17 110 124 123 124 135 137 165 172 122 127 131 129 158 110 154 163 182 175 182 −57 −73 −58 −59 −70 −70 −117 −119 −41 −39 −48 −32 −76 −13 −34 −23 −58 −29 −28 135 148 148 150 161 163 194 201 149 153 157 157 187 136 184 193 214 206 214 −61 −75 −60 −62 −74 −74 −124 −127 −44 −41 −50 −34 −81 −14 −36 −24 −62 −31 −30
Positive and negative
wheel energy/ dist. (Wh/km) ECE WLTC Low jc08 FTP72 UDDS WLTC Middle SC03 NYCC Artemis URBAN NEDC WLTC High Artemis RURAL
EUDC UC LA92 HWFET REP05
WLTC Extra High US06
Artemis 130 Artemis 150
Urban Rural Highway
City − Aero. drag City − Roll. resist. City − Acc. Highway − Aero. drag Highway − Roll. resist. Highway − Acc. Sport − Aero. drag Sport − Roll. resist. Sport − Acc.
Figure 4.10 Positive and negative wheel energy per driven distance during Urban, Rural and High- way Test cycles, for all of the three concept cars, while acceleration is calculated using the described forward-backward method.
The positive and "negative" values of wheel energy consumption per driven distance, are also illustrated as a function of average running speed for each cycle and car, in Figure 4.11. As a frame of reference, the calculated wheel energy per driven distance while driving at constant speed levels are also included in the figure, i.e. while only considering aerodynamic and rolling resistance. As shown, the energy per distance when driving at constant speed increases with increasing speed, due to the speed dependency of the aerodynamic drag. The deviations between the positive cycle values and constant speed values of energy consumption represent the excess energy consumption due to the acceleration content in each cycle. At the same time, an equally large amount of "negative energy consumption" can potentially be regenerated with the electric powertrain, which would reduce the influence of acceleration on the net battery energy consumption.
0 20 40 60 80 100 −150 −100 −50 0 50 100 150 200 250
Cycle mean speed (km/h)
Positive and negative
wheel energy/dist. (Wh/km)
City − E
wheel, pos Test cycles City − E
wheel, neg Test cycles City − E
wheel, pos Const. speed Highway − E
wheel, pos Test cycles Highway − E
wheel, neg Test cycles Highway − E
wheel, pos Const. speed
Sport − E
wheel, pos Test cycles Sport − E
wheel, neg Test cycles Sport − E
wheel, pos Const. speed
Figure 4.11 Wheel energy per driven distance during Urban, Rural and Highway Test cycles, for all the three concept cars.
4.3.2.1 The problem with 1 Hz speed data and acceleration calculation
It should be noted that the energy consumption per driven distance is sensitive to the method which is used to estimate the acceleration from the reference speed trace. As mentioned, most drive cycles are defined by one speed value per second, hence the asso- ciated acceleration must be calculated by differentiating the speed over time. This differ- entiation may be done using different methods such as the Forward, Backward or Central difference methods, where the acceleration of the current time step is calculated using the change in speed and time between the next and current time step, the current and previous time step, or between the next and previous time step, respectively.
Due to the relatively low time resolution of the cycle speed compared to vehicle dy- namics, the resulting accelerations differ for the three methods. Both the Forward and Backward difference methods give exactly the same acceleration levels, but they are shifted one sample period in time and thus attributed to different speed levels. For pos- itive accelerations, the accelerations calculated with the Forward difference method are attributed to lower speed levels, and during braking they are attributed to higher speed levels, while it is the opposite for the Backward difference method. The Central differ- ence method gives the average acceleration between the other two methods at the current time step, and is here regarded as the least erroneous method and has been used through- out this thesis.
It can thus be expected that the Backward method often will over estimate the propul- sion power and energy, and under estimate the braking power and energy, compared to the Central method. The percent change in wheel energy consumption per driven distance due to using the Backward difference method compared to using the Central difference method, can be seen in Figure 4.12 for propulsion and braking with the City car. As ex- pected, all cycles show an increase in propulsion energy consumption and most cycles show a decrease in available braking energy per distance, while four cycles show an in- crease in braking energy (Artemis RURAL, HWFET, REP05, and ArtemisMW130). For most cycles the difference is around 1-6% in both propulsion and braking mode, while it is as much as 13% and 16% for the acceleration intense Artemis URBAN and NYCC in
Vehicles propulsion mode.
The large difference between the acceleration estimation methods is reduced (inverse linearly) when the time resolution is increased. By re-sampling the speed vector through linear interpolation, it was noted that, at 6 Hz the difference is 1% or smaller for all cycles except Artemis URBAN and NYCC, and at 15 Hz the difference is 1% or lower for all cycles. −10 0 10 20 5.8 6.4 5.0 5.7 4.2 6.0 15.7 12.8 2.5 2.3 5.1 1.1 2.4 5.9 0.8 3.9 0.7 5.0 1.8 −5.5−4.7 −0.6 −5.4 −3.3 −4.5 −6.4−5.9 −3.4−2.7 3.3 −1.0 −3.0 −4.7 0.9 3.7 −0.7−0.6 4.6
Wheel Energy/Dist. Relative change (%)
Backwards comp. Central method
ECE WLTC Low jc08 FTP72 UDDS WLTC Middle SC03 NYCC Artemis URBAN NEDC WLTC High Artemis RURAL
EUDC WLTC Cl.3 UC LA92 HWFET REP05 WLTC Extra High
US06 Artemis 130
Urban cycles Rural cycles Highway cycles
Prop. Brake
Figure 4.12 Change in wheel energy per distance due to Backwards method compared to Central difference method, during Propulsion and Braking of all Test cycles, for the City car.