*Drivers of electric cars are often very sensitive to the issues of consumption and range of their vehicles.This is because combustion engines are still used as a benchmark against which electric vehicles must be compared. This is understandable from the user’s point of view, because no driver wants to accept major restrictions in everyday use. Since manufacturers’ information on range and consumption is often not useful information in practice, potential buyers often ask owners of electric vehicles what range and consumption are in their experience.*

The problems that arise when trying to provide meaningful information about the consumption and range of an electric car are due to the very strong dependence of these parameters on a wide variety of influences. While in vehicles with combustion engines the majority of the energy is converted into heat regardless of the operating conditions and thus the consumption for the drive fluctuates comparatively little, in electric vehicles any change in the operating conditions is very noticeable. In addition, in contrast to the tank of a combustion engine vehicle, the battery of an electric car should not be used completely for reasons of durability. The information on ranges therefore also depends on the actual battery utilization that is beneficial in continuous operation.

## Factors influencing consumption

The influences on consumption can be roughly divided into two categories. The first category includes all driving dynamics influences. These mainly include driving resistance and drive losses. Driving resistance is essentially made up of air and rolling resistance as well as the force required to overcome differences in altitude and to accelerate the vehicle. Drive losses occur in the mechanical and electrical drive train of the vehicle. When considering consumption, it should be noted that energy contributions from differences in altitude on the route are fundamentally reversible. Therefore, a consumption analysis only makes sense for a route with equal altitude. However, this condition can be met very easily by driving in a loop style or by driving back to the starting point. The kinetic energy stored in the driving speed is also partially reversible depending on the driving behavior and recuperation capabilities of

the vehicle. However, the energy loss that occurs here is a crucial part of the consumption analysis and must therefore be taken into account. All other driving dynamics influencing factors are irreversible and are converted into heat.

The second category includes influences that are largely independent of driving dynamics. This includes the energy requirements of the vehicle electronics and auxiliary units. The ambient temperature plays a key role here. However, the ambient brightness and humidity also have a small influence on energy consumption. The following equation 1 summarizes many of the influences mentioned for the total power drawn from the battery.

End customers as vehicle users generally do not have special equipment and measuring technology to be able to determine the consumption of their vehicle depending on all influencing factors. Therefore, the only method available to the end customer to determine vehicle parameters is the statistical evaluation of driving data collected in everyday use under real environmental conditions. But it is precisely these everyday trips under real conditions that provide the most useful parameters for the interested person, as they reflect typical behavior more realistically. Due to the large differences in consumption and range over the course of the year, individual values determined at specific times are unsuitable for use as characteristic values. Statistical certainty can only be achieved by appropriately summarizing

driving data. The formation of specific average values for consumption appears to be the most practical approach here. Specific average values can reflect representative parameters of a vehicle.

## Calculation of average consumption values

**Annual average**

A characteristic parameter of electric vehicles is the annual average consumption. Various methods are conceivable for calculating the average, but they lead to different results.

According to a first method, the procedure can consist of simply calculating the average value of all recorded individual consumption values 𝑉𝑖 per driving cycle. Equation 2 shows the calculation.

This method provides a reasonable average if each individual consumption value has the same weight (i.e. if all individual values are completely equal). However, this requirement is not met in everyday driving, as the individual consumption values occur at irregular intervals under different environmental conditions. Therefore, the average value calculated in this way is not very representative.

A second method for calculating the average consumption, according to equation 3, consists in dividing the individual driving energies 𝐸_{𝑖} accumulated over the entire observation period by the correspondingly accumulated individual driving distances 𝑠_{𝑖}.

This method provides the average value for the energy actually used in the year and the total distance driven. However, this method also does not take into account the different weighting of individual consumption. Therefore, even according to this calculation, no representative average value for the average annual consumption would be expected.

In order to effectively include the different weights of the individual values, a calculation according to a third method according to equation 4 is useful. This method calculates the area under the consumption vs. time curve and divides it by the time period under consideration.

This method can better take into account the unequal distribution and the corresponding weighting of individual consumption values over the course of the year.

A calculation comparison with the numerical examples of real driving data listed in Table 1 is intended to illustrate the different effects of the calculation methods.

*Table 1: Example values of real driving data for comparing different averaging methods*

cycle i | 𝑽_{𝒊} (kWh/100 km) | 𝑬_{𝒊} (kWh) | 𝒔_{𝒊} (km) | 𝒕_{𝒊} (Tage) | 𝑽_{𝒊} ∙ 𝒕_{𝒊} |

1 (Summer) | 13.0 | 15.1 | 116 | 0.9 | 12.1 |

2 (Summer) | 13.2 | 25.7 | 195 | 1.0 | 13.6 |

3 (Summer) | 13.1 | 9.8 | 75 | 0.9 | 12.0 |

4 (Summer) | 12.8 | 45.6 | 356 | 1.1 | 14.0 |

5 (Winter) | 18.7 | 32.5 | 174 | 3.3 | 61.0 |

Using the example values from Table 1, the following average consumption values are obtained using the three methods (units omitted, all consumption values in kWh/100 km).

*Table 2: Results of the different mean calculations*

Even if the differences between methods 1 and 2 are only apparent in the decimal places according to these example values, it is nevertheless clear that the calculation method is not without significance for the result. In particular, when looking at the mean value according to method 3, it becomes clear that individual values have different influences on the mean value.

The differences in the calculation methods come into play precisely when a driver covers significantly different distances at certain times of the year. For example, if the driver drives very little in winter but frequently in summer, the annual average consumption will be greatly distorted when methods 1 and 2 are applied. This is because in such driving profiles, the seasonal consumption is not weighted correctly. The third method according to equation 4, which includes a time weighting of the consumption, leads to the most representative result for the annual average consumption and is therefore generally recommended as a calculation method.

**Seasonal averages**

Consumption varies significantly with the seasons. To characterize the vehicle, it is therefore useful to classify consumption by season. This allows the seasonal differences to be represented and compared with each other. Here, too, averaging using method three (according to equation 4) is most suitable.

The seasonal periods can be formed according to the usual calendar classification as shown in Table 3.

*Table 3: Seasonal assignment of months to periods according to calendar seasons*

Season | Months |

Spring | March, April, May |

Summer | June, July, August |

Autumn | September, October, November |

Winter | December, January, February |

**Range information**

For potential buyers of electric vehicles, the range is the most frequently requested parameter. It should therefore be specified with due care and take into account the actual everyday driving experience. As already mentioned, manufacturer information on ranges is not very useful because it relates to driving behavior that is hardly feasible in practice. For example, 100 % battery usage in everyday driving is hardly possible and not desirable from a technical point of view. This is because regular highpercentage charging and discharging of the battery leads to rapid degradation and thus to undesirable loss of capacity. Furthermore, the behavior of electric vehicles at SoC values below 0 % is not regulated and therefore often undefined, which makes driving in this state (e.g. to get to the next charging station) an incalculable risk.

Realistic range values, which can also be specified for regular operation, should be based on vehicle use that is beneficial to the battery and driving practice. The basis for this could be a battery usage of around 70 % of the total capacity, which would correspond to a typical SoC range between 10 % and 80 % or 20 % and 90 %. This SoC range is easy to maintain in everyday driving and also corresponds to the operating practice frequently used by many electric car drivers.

This would make at least two range figures for an electric vehicle useful. However, these range figures must relate to the corresponding driving consumption. With the driving consumption figures for the annual average and the seasonal values introduced above, this ultimately results in a total of 10 range figures that can adequately characterize the vehicle in everyday driving for a potential buyer.

**Driving data determination**

A Volkswagen ID.3 was used to determine the driving data as an example. The following information in Table 4 shows the key technical data of the vehicle.

*Table 4: Technical data of the electric vehicle used*

Vehicle type | Volkswagen ID.3 |

Battery (gross) | 62 kWh |

Battery (net) | 58 kWh |

Battery (usable) | 54 kWh |

Motor | Permanentmagnet-Synchronmotor |

transmission | Single speed gearbox |

Continuous power | 70 kW |

peak power | 150 kW |

Peak torque | 310 Nm |

Empty weight | 1804 kg |

Frontal area | 2.36 m² |

drag coefficient | 0.267 |

wheel size | 215/55R18 |

used tire pressure | 2.5 bar |

Driving data was collected over 12 months in everyday use with this vehicle in order to obtain key figures on consumption and range. The operating conditions for determining the driving data can be found in Table 5.

*Table 5: Operating conditions for driving data acquisition*

Operating period | 12 Months |

Total mileage | 32126 km |

Route proportions (City/Country/Motorway) | 20 %/30 %/50 % |

Region | Greater area of Rostock |

Ø-speed | approx. 60 km/h |

Charging sessions (Driving cycles) | 286 |

For the evaluation, the parameters listed in Table 6 were recorded for each driving cycle. A driving cycle includes all drives between two charging processes.

*Table 6: Recorded driving data per driving cycle*

Parameter (unit) | Explanation |

Charging start (date, time) | Date and time of start of battery charging |

Charging time (hours) | Net charging time (i.e. minus idle time) |

Charging energy (kWh) | Amount of energy measured by the charging device at the end of charging |

mileage (km) | mileage according to vehicle display |

Start-SoC (%) | state of charge at the start of charging |

End-SoC (%) | state of charge at the end of charging |

speed (km/h) | average speed for the driving cycle according to the vehicle display |

consumption (kWh/100 km) | Average consumption for the driving cycle according to vehicle display |

Temperature (°C) | Average ambient temperature for the driving cycle |

Many other parameters can be calculated from the parameters of the collected driving data. The following overview shows a selection.

Parameter (unit) | Explanation |

Charging stroke (%) | Difference between end SoC and start SoC |

Discharging stroke (%) | Difference between predecessor end SoC and start SoC |

Driving energy (kWh) | the energy taken from the battery during the driving cycle |

Charging loss (%) | percentage difference between driving and charging energy |

Driving distance (km) | Difference between previous mileage and current mileage |

Charging consumption (kWh/100 km) | Consumption related to charging energy |

Cycle time (days) | Time difference between two charging sessions |

Range (km) | theoretical range at respective cycle consumption |

The diagram in Figure 1 shows the vehicle’s fuel consumption and the average ambient temperature per driving cycle over the course of the year. The significant differences in fuel consumption between the colder and warmer seasons are clearly visible.

*Figure 1: Time course of energy consumption and ambient temperature per driving cycle*

Complementary to this is the range based on the respective cycle consumption shown in Figure 2 at 100 % and 70 % utilization of the available battery capacity. This diagram also shows the clear dependence on the time of year.

*Figure 2: Time course of the extrapolated range at 70 % and 100 % battery usage and respective cycle consumption*

The consumption and range curves shown make it clear that individual values have little significance. In order to bring statistical certainty to the data, average values for consumption are calculated as described above in order to obtain representative parameters for the vehicle.

**Results**

The driving data were summarized as annual and seasonal values as shown above. Table 7 shows the numerical values in an overview.

*Table 7: Numerical values of the average consumption and range values for the different periods*

Period | temp. (°C) | mileage (km) | driving energy (kWh) | speed (km/h) | consumption (kWh/100 km) | 70 %-range (km) | remain. range (km) |

Year | 10.6 | 32126 | 4814 | 60 | 15.1 | 235 | 101 |

Spring | 9.0 | 9798 | 1559 | 63 | 15.7 | 221 | 95 |

Summer | 19.8 | 7141 | 952 | 56 | 13.3 | 264 | 113 |

Autumn | 10.6 | 9279 | 1288 | 62 | 13.8 | 254 | 109 |

Winter | 2.7 | 5908 | 1014 | 57 | 17.5 | 205 | 88 |

The diagrams in Figure 3 and Figure 4 show the driving consumption and ranges in a corresponding graphical representation.

*Figure 3: Driving consumption of the electric vehicle per season over the course of a year*

*Figure 4: Course of seasonal ranges for 70 % battery usage and the respective remaining ranges*

**Discussion and conclusion**

The individual seasonal values show a balanced result in terms of the average speeds driven. The seasonal consumption values can therefore be compared quite well with one another. The different seasonal mileages, however, show that it makes sense to use weighted average calculations to determine consumption figures. The additional consumption between summer and winter is expected to be large and amounts to 4.2 kWh/100 km (+32 %). This additional consumption leads to a loss of range (70 % value) between summer and winter of 59 km (-22.4 %).

How can the question posed at the beginning about the consumption and range of an electric vehicle be answered? The answer can only be: “It depends…”. Although this answer is unsatisfactory, it correctly reflects the situation. One way out is to provide seasonal averages under everyday driving conditions and documented driving conditions. This approach was followed in the current series of tests. The information under the documented operating conditions can therefore be considered to be sufficiently statistically reliable.

**Author**

Prof. Dr.-Ing. Ansgar Wego

Faculty of Engineering

Hochschule Wismar

University of Applied Sciences Technology, Business and Design

Philipp-Müller-Straße 14

23966 Wismar