Energy Optimized Routing for E-Vehicles

David Suske

, Alexander Sohr and Eric Neidhardt

DLR Institute of Transport Systems, German Aerospace Center, Germany

Keywords: Navigation systems, Electric vehicles, Engine-efficiency.

Abstract: The demand for routing tailored to electric vehicles will increase in the future due to the increasing number

of users of electric vehicles. A growing number of people will face the same problem. What is the fastest

energy-optimized route for my electric car to my destination? This paper describes the factors that influence

the energy-optimized routing of electric vehicles. In particular, it shows how the influencing factors are used

in routing and how they can be mathematically combines to obtain a general description. The influencing

factors: topology of charging stations, energy consumption, topology of infrastructure, seasonal dependency

and individual driving behavior are described. Furthermore, this paper shows the interactions between the

factors. A new method for determining necessary edge weights is then presented mathematically in general.

This weighting function was developed in the DLR project "Vehicle Intelligence and Smart Gearing" using

empirical data analysis. The resulting equation can be applied iteratively to existing routing graphs to

determine qualified edge weights. Existing current methods for routing are using the manufacturer

information for the power consumption per 100 kilometers to generate a weight for their edges on the routing

graph. Since consumption is only measured by the distance travelled, the shortest distance is always the one

with the lowest energy consumption. Furthermore, in existing systems, the consumption is always constant

for the same distance. This does not correspond to reality, since the range or consumption can increase or

decrease with temperature differences. In addition, manufacturers of electric vehicles produce standardized

consumption values that are generated under laboratory conditions and cannot be reproduced in reality. This

paper shows how a single function can look like that mathematically combines different influencing factors.

This result can be applied to existing routing systems to generate new, more qualified edge weights for energy-

optimized routing.

1 INTRODUCTION

Rising sales of electric vehicles result in an increasing

number of routing requests. In addition to

conventional questions like the shortest and fastest

route, the focus here is also on the most energy-

efficient route (Rubel, 2018).

Figure 1 shows the half-year report on the

development of electric mobility presented by the

Center of Automotive Management (CAM) at the

Bergisch Gladbach University of Applied Sciences.

The experts around Prof. Dr. Stefan Bratzel analyse

and assess the sales trends in important global

automotive markets in the first half of 2018 and 2017.

Despite the increasing sales figures shown above and

the continuous improvement of the charging

infrastructure, the challenge of e-routing will remain

in the coming years. The characteristics of this route

and the associated challenges of electro-mobility are

far more complex than those of conventional

vehicles. Both the range of the vehicles and the

availability of possible charging stations are the

central questions of route selection (Rubel, 2018). But

there are other dependencies that influence the choice

of route. This report defines and describes factors

influencing the choice of route. Furthermore, it is

shown how these are to be considered in a routing.

Regional and seasonal differences as well as

individual driving behavior are taken into account in

order to create an energy-optimized route.

Suske, D., Sohr, A. and Neidhardt, E.

Energy Optimized Routing for E-Vehicles.

DOI: 10.5220/0011358000003355

In Proceedings of the 1st International Joint Conference on Energy and Environmental Engineering (CoEEE 2021), pages 62-67

ISBN: 978-989-758-599-9

Figure 1. Sales trends for electric cars in key markets 2018/18 Hbj.1 (Bratzel, 2018)

2 INFLUENCING FACTORS

This chapter describes influencing factors when

selecting a route for electric vehicles. Each of the

following paragraphs describes a criterion for the

range of electric vehicles.

2.1 Topology of Charging Stations

The range of an electric vehicle is arbitrarily large.

Insofar as the vehicle is ready for operation and a

charging station is within range. For longer journeys,

the distribution of the charging stations is therefore

very important for the choice of route. It is essential

to consider any side effects of the route selection. The

lack of charging infrastructure can be fatal, especially

for less experienced users. For example, a route to a

less serviced area can often be found at charging

stations and the routing request would then be

completed. However, the remaining state of charge of

the vehicle may no longer be sufficient to reach the

next charging station. In this case, the suggested route

should draw attention to the problem that no charging

station can be reached from the destination.

2.2 Energy Consumption

The consumption of electric vehicles is expressed in

standard values and is not uniquely defined for

manufacturer or type (Hiller, 2018). For reasons of

increased sales, it is conceivable that strongly

optimized boundary conditions will be used as the

basis for the calculations. For the small car Nissan

Leaf, for example, this is 15 kWh per 100 kilometers,

for the electric Golf VW gives 12.7 kWh (Hiller,

2018). These standard values often do not correspond

to the real consumption of these vehicles. The

following is an overview of the standard values for

the vehicles with the highest sales volume according

to the CAM study (Bratzel, 2018).

Table 1. Consumption of electric vehicles (Bratzel, 2018).

Vehicle

Manufacturer

Consumption / 100 km

Tesla Model S P90D 22 kWh

Ranault Zoe 14,6 kWh

Nissan Leaf 15 kWh

Mitsubishi-MiEV (FL) 13,5 kWh

BMW i3 12,9 kWh

E-Golf 12,7 kWh

Mercedes B-Class ED 16,6 kWh

Table 1 shows the values according to the

manufacturer's own specifications. In addition to

these figures, independent methods according to

WLTP and NEDC promise more precise figures for

actual consumption. Worldwidmonized Light(-Duty)

Energy Optimized Routing for E-Vehicles

Vehicles Test Procedure, WLTP for short, is the new

standard test procedure that is intended to provide

realistic data on the fuel consumption of electric

vehicles and other passenger cars. The NEDC (New

European Driving Cycle), which has been in force

since 1992 and is not very accurate, will be gradually

replaced by September 1, 2018. Germany is regarded

as a global pione Hareer in the changeover. The

source (Kammerer, 2018) shows the differences

between the test cycles and how the new WLTP value

will affect the future. The fact is that these

measurements and efforts will not be able to

withstand a real measured value and experience, as

further criteria influence consumption and the

associated range (Kammerer, 2018).

2.3 Topology of Infrastructure

The construction of the roads and their gradients also

result in considerable differences in the choice of

route. As can be seen from the publication

"Topographic maps for greater range of the ECar"

(Spanik, 2018). In the BMW i3, for example, the fuel

consumption values per 100 km are almost twice as

high when driving uphill (Spanik, 2018). It also

depends on the vehicle how much energy can be

recovered when driving downhill. The exact creation

of a database for the construction of the road network

is therefore essential for choosing the right route.

Especially with an energy-optimized routing, height

differences have to be considered.

2.4 Seasonal Dependency

The seasonal dependency of the route choice refers to

the different consumption of energy in the seasons.

The electrical consumption for comfort components

in the vehicle, such as air-conditioning systems, is

usually higher in seasons such as winter and summer.

Tesla models, such as the Model S, heat not only the

interior, but also the battery if necessary. If the battery

is cold, kilometers are lost that are more than the lost

heat output (Becker, 2018).

The ADAC tested the loss in winter on a

Mitsubishi i-MiEV as an example and came to the

following verdict (Butz, 2018):

At speeds around 100 km/h, the relative losses in

range are still comparatively low:

• At 20 degrees, the electric car can travel 91

kilometers.

• At 0 degrees, it can cover 82 kilometers.

• At minus 20 degrees it's still 70 kilometers.

A much higher loss of range, on the other hand,

can be seen at speeds of 30 km/h:

• At 20 degrees, the electric car covers 188

kilometers.

• At 0 degrees it achieves 93 kilometers.

• At minus 20 degrees it's still 68 kilometres.

Inner cities at 50 km/h are therefore likely to

suffer greater losses in range due to seasonal

influences than on the motorway. This in turn

influences the choice of route.

2.5 Individual Driving Behavior

The individual driving behavior of individuals also

affects the fuel consumption or range and the

associated route selection of an electric vehicle.

Features such as time and driving style play a role

here. If, for example, a restrained driver drives to

work with a prudent driving style, it will consume less

electricity than a notorious speedster that accelerates

a lot. Furthermore, a prudent driver can also become

a high consumer if he is under time stress and wants

to reach his destination quickly. Similar rules apply

here as with conventional combustion engines in

order to increase the range: (Greenfinder, 2018)

• Quiet and prudent driving

• Drive in anticipation

• Avoid strong accelerations

• The lower the speed, the lower the energy

consumption

This behavior is still encouraged by some

manufacturers. With different driving modes, such as

Comfort, EcoPro and EcoPro+, as is possible with the

BMW i3, for example. In electric cars, the so-called

recuperation effect takes effect. This means that some

of the energy generated by the braking effect of the

engine is fed back into the battery. The energy

recovered in this way extends the range of the electric

car. If, on the other hand, you step too hard on the

brake, energy is also generated, but in this case, as

with combustion engines, it is released more in the

form of warmth and can no longer be used as well

(Greenfinder, 2018).

3 ENERGY-OPTIMIZED ROUTES

In this chapter, the previously described

dependencies for energy-optimized routing for e-

vehicles are put into context. It also describes how

influencing factors can influence each other.

Furthermore, the procedure for implementing an

energy-optimized routing is described.

3.1 Interactions

CoEEE 2021 - International Joint Conference on Energy and Environmental Engineering

In order to find the best possible energy-optimized

route, it is not sufficient to optimize the criteria for

route enquiries in terms of range mentioned in

Chapter 2. The topology of the charging stations does

not initially play a role in energy-optimized routing,

as this does not influence energy consumption.

However, if this criterion is not met in sufficient

numbers within the start/finish relationship, no

routing is possible. Therefore, the existence of a

charging infrastructure is absolutely necessary for the

consideration of an energy-optimized route.

The data on energy consumption could also not be

used for energy-optimized routing. As Section 2.2

shows, the data on the standard values of the

individual vehicles are not very accurate. If these

values were used to determine a low-consumption

route, the shortest route would always be found.

Sections 2.3 to 2.5 show that the shortest route does

not have to be the most energy efficient.

Nor can it be generalized that, as shown in section

2.3, a flat straight route is more energy efficient than

a winding route. On a very twisty route that has no

vertical meters, section 2.5 may be more effective

than section 2.3. The topology of the network

therefore requires the driver to be slower, more

prudent and more forward-looking. Furthermore,

section 2.4 shows that the weather can also influence

the most energy efficient route.

3.2 Procedure

The theoretical implementation of an energy-

optimized routing for electric vehicles is only

possible with a sensible weighting of the influencing

factors. The following influencing factors can be

derived from the literature: (Bratzel, 2018)

(Kammerer, 2018) (Spanik, 2018) (Becker, 2018)

(Butz, 2018) (Greenfinder, 2018)

• Existence of charging infrastructure

• Travel speed

• Structure of the road network (angle of

vertical meters, angle between edges)

• Outside temperatures

• Driving behavior

• Energy consumption of comfort

components

The weighting of the influencing factors is based

on a percentage distribution of the empirical values

described in the literature and is not supported by

empirical data. Table 2 below shows the weighting

ratio for the influencing factors.

Table 2. Weighted influencing factors.

Influencing factor Influence in percent (%)

Existence of charging

infrastructure

Travel speed 30

Construction of the road

network

Outdoor temperatures 20

Driving behavior 15

Comfort components 5

A routable graph is created according to this

model. The graph evaluates a node and edge topology

according to the following algorithm. This applies to

all edges (n) in a routable graph. The individual

weight of the influencing factors is determined with

points from 0 to 100. The points are then weighted in

percent based on their influence. The lower the score

of the individual influencing factors, the lower the

resulting edge weight for routing. Thus the value 0 is

to be understood as optimal and 100 as worst value

for the individual evaluation.

1. The velocity on the edge (n) is linearly assigned

to the point values from 0 to 100, where applies:

𝑓

(

𝑥

)

=

x if 0≤𝑥≤100

100 𝑥>100

{ x ∈ N ∪ {0}}

(1)

2. Slope of the edge (n) in f(x)=

 ()

 ()

∗

100 %

(2)

Linear equation for the determination of points:

y = m*x +n





(3)

n = 50

(4)

x =





(



)



(



)

∗ 100



(5)

(

)



0 x<−100





∗





(



)



(



)

∗ 100



+ 50 if −100≤x≤100

100 x>100

(6)

The result of this equation is that at a gradient of

45 degrees or 100 percent, the maximum worst

value is assumed to be 100, while at a gradient of

45 degrees, the maximum best value is assumed

to be 0.

Energy Optimized Routing for E-Vehicles

3. The outside temperature is assumed to be optimal

at 20 degrees. Values left and right of x = 20

worsen the scoring again. With less than minus

20 degrees and more than +60 degrees the

maximum worst value of 100 is reached (Butz,

2018).

(

)

=

100 x< −20

0,05 ∗ (x − 20)² if −20≤x≤60

100 x>60

(7)

The function corresponds to the illustration of a

parabola shifted by 20 on the X axis and

compressed by 0.05.

4. The driving behavior is classified into 5 levels,

which are shown in table 3:

Table 3. Driving behavior point table.

Behavior Points

Looking foresighted 0

Less foresighted 25

Average 50

Less aggressive 75

Aggressive 100

The driving behavior must be defined by the user

himself before routing. In the case of larger

amounts of data, a mechanical evaluation using

"Deep Learnin" is conceivable. For this purpose,

the individual driving behavior is classified by a

neural network.

5. The use of comfort components is listed in table

4 and the totals of the points are then added.

Table 4. Points for comfort components.

Comfort components Points

Air conditioning 50

Seat heating 30

Light 15

Radio 5

The comfort components used must be specified

during routing. The selection is implemented via

a check box, the sum of which is the weight for

this influencing factor.

6. The last influencing factor is the presence of a

charging infrastructure during and after the

journey. For this purpose, the energy

consumption described in Chapter 2.2 according

to WLTP, if not available according to NEDC or

as a last possibility the manufacturer's data, is

taken to 100 km. Due to the inaccuracy, the value

is increased by 20 percent. The algorithm

determines the consumption after each edge and

searches for a charging station if the vehicle has

only 20 percent of its load left. In addition, at

least 10 percent of the load must still be present

at the destination so that the driver can safely

leave the destination again. If these criteria

cannot be met. Then the lack of the charging

infrastructure is to be regarded as a KO criterion

and no route to the destination can be found.

On the basis of the points to be determined for

each influence criterion, the weight for the edge is to

be determined by means of the following weighting

function. For a = speed, b = structure of the road

network, c = outside temperatures, d = driving

behavior and e = comfort components.

(

)

(

a∗0,3

)

(

b∗0,3

)

(

c∗0,2

)

(

d∗

0,15

)

(

e ∗ 0,05

)

(8)

Each influencing factor can only take values

between 0 best and 100 worst. Thus, the weight of the

edge is defined in the closed interval from 0 to 100.

The new weight of the edge is taken into

consideration during routing and results in the most

energy-optimal route.

4 CONCLUSION

The demand for energy-optimized routes for e-

vehicles increases with the number of vehicles sold.

Conventional questions about the fastest or shortest

route are more sufficient for the user. Especially

because of the often still short range of electric

vehicles, the question of the lowest possible

consumption is at the forefront of the considerations.

Optimizing fuel consumption means increasing the

range.

Chapter 2 describes dependency factors for this

question. Each criterion is decisive for the choice of

route. The necessity of the inclusion is explained in

the respective sections. This shows that it is not only

the infrastructure that can influence the most energy-

efficient route. Environmental influences and

individual factors also play a role.

Chapter 3 compares the dependencies between the

influencing factors. For example, bad weather

influences one's own driving behavior towards a

quieter driving style. This in turn has a positive effect

on the choice of route. It also shows that not all

influencing variables may be weighted equally. For

example, the difference in altitude of a route from

start to finish has a greater influence on the most

energy-efficient route than driving with or without air

conditioning.

Section 3.2 describes the weighting for the

influencing factors as well as the functions for

determining the point values for each criterion. The

CoEEE 2021 - International Joint Conference on Energy and Environmental Engineering

algorithm described in this chapter can be applied to

a routable graph to demonstrate energy optimized

routing for an electric vehicle.

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Energy Optimized Routing for E-Vehicles