Simulation Study of Charging of

EV-Fleets in Underground Mining

Felix Gustavsson

Department of Physics

Umea University

A thesis submitted for the degree of

Master of Science in Engineering Physics

Spring 2020

Master’s Thesis in Engineering Physics, 30 ECTS

Felix Gustavsson, felixx.gustavsson@gmail.com

Supervisors: Susanne Schmitt, ABB Corporate Research Center, Germany

Dennis Janka, ABB Corporate Research Center, Germany

Andreas Nordenstrom, Dep. of Physics, Umea University

Examiner: Eddie Wadbro, Dep. of Computing Science, Umea University

Copyright © 2020. All Rights Reserved.

Department of PhysicsLinnaeus vag 20901 87 UmeaSwedenwww.physics.umu.se

Abstract

Due to an increasing concern of the introduction of greenhouse gas (GHG) regulations in

many jurisdictions, the underground mining industry is in high demand to tackle climate

change through innovative measures. In order to stay competitive, cope with rising energy

costs and GHG regulations, mining companies will have to consider the alternative to go

fully electric. As underground mines progress through time they are becoming deeper

and deeper, resulting in longer haulage distances and thus an increasing energy demand.

The research in this thesis was conducted to analyze and develop a simulation tool to

investigate the replacement of conventional diesel haulage trucks with battery electric

trucks that include a fast-charging capability in an underground mine environment. The

results show that there is a major difference in the achievable production rates depending

on the mine topography and a need for opportunity charging. Furthermore, the developed

tool could aid in decision making and provide a good frame of reference of the feasibility

of replacing an existing diesel operation by a battery electric one.

Acknowledgments

Firstly, I would like to thank Dr. Susanne Schmitt for giving me the opportunity to

perform the thesis at the ABB Corporate Research Center in Germany and for supervising

me in the first half. Secondly, I would like to thank Dr. Dennis Janka for supervising

the other half and everyone involved for the valuable input, resources, and great material

despite the ongoing COVID-19 pandemic. Conducting the thesis at the ABB Corporate

Research Center in Germany has been nothing but a positive, professional experience.

Finally, I would like to thank Eddie Wadbro at the Dep. of Computing Science, Umea

University, for being the examiner of this thesis.

Contents

1 Introduction 1

1.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 4

2.1 Mine Layout and Infrastructure . . . . . . . . . . . . . . . . . . . . . 4

2.2 Traction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 The forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Mechanical Traction . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Auxiliary Consumption Model . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Recuperation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.6 Charging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.7 Queuing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Methodology 16

3.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Model assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.1 Average speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.2 Topographies . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.3 Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.4 Queuing and Sampling . . . . . . . . . . . . . . . . . . . . . . 20

3.4 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4.1 Graph Representation . . . . . . . . . . . . . . . . . . . . . . 21

3.4.2 Implementation and Program Structure . . . . . . . . . . . . . 21

3.5 Software Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Results 24

4.1 Simulation runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Charging and queuing times . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Production rate and operational efficiency . . . . . . . . . . . . . . . 27

v

5 Discussion and conclusions 29

References 31

A Configuration file 33

B Algorithms 34

iv

1 Introduction

Mining has been essential to man’s existence since ancient times. In the broadest

sense, it is referred to as the extraction of all naturally occurring mineral substances

from the earth. In general, there are two types of mining: surface mining in which

the extraction of mineral takes place above earth; and underground mining, where

the minerals are extracted subterranean. For surface mining, one has to strip the

earth covering the near-surface ore to gain access to the ore deposit. Underground

mining consists of reaching ore deposits by digging tunnels or shafts into the earth.

When the depth of the ore body is reached the ore is then brought to the surface

through these. The basic production cycle for an underground mine can be split into

rock breakage and materials handling. Firstly rock breakage consists of drilling and

blasting, thereafter the material is loaded and hauled, and in some cases hoisted

vertically or inclined [1]. The loading is usually done by the Load-Haul-Dump

(LHD) machine. It moves blasted material from the face, where the mining work is

advancing, and loads it onto a haulage truck. The material is then hauled for longer

distances, either to the surface or a crusher.

Today, most underground mines are dependent on diesel-powered vehicles. The min-

ing industry will strive to become digitized, autonomous, and free of carbon dioxide

emissions. In order to both cut costs and reduce climate impact, transitioning to an

electric mine becomes the natural progression. With the continuous advancement

in battery technology, the question is not about whether going electric, the question

is how. Commercially the battery-electric trucks and buses have shown to be much

more efficient than their internal combustion engine counterparts. Being powered

by on-board batteries means free of infrastructure connecting the vehicle to over-

head powerlines. There are serious challenges introduced by battery electric vehicles

(BEVs) for the underground mining industry. One of them is how to handle the

charging infrastructure.

Charging the BEVs will not be an easy task. As opposed to diesel equipment, which

uses standardized fuel, it is not as simple as pouring liquid into the fuel tank. Battery

packs are rather complex and the charging process of the vehicles is not standardized

yet. In order for the mines to be designed electric, careful planning has to be made.

One has to understand the benefits of BEVs and to harness them while accounting

1

for the drawbacks. There is a great disparity between diesel vehicles and BEVs

when it comes to planning fuel distribution and the parking arrangement. Minimal

thought is needed regarding this for a mine consisting of diesel fleets in contrast to

one using BEVs. If not designed properly the consequence could easily be a cluster

of useless charging stations sitting around in the mine [2].

Physically experimenting with the replacement of diesel vehicles for BEVs in an

underground mine is highly impractical and unrealistic. Therefore it is more conve-

nient to study the system of BEVs by simulating it. A simulation is the resemblance

of a real-world process over time. This enables one to generate simulation data to

draw conclusions concerning the characteristics of the real system. By constructing

a simulation model the behavior of the system could be studied as it evolves over

time. The model could later be used, once validated, to answer a set of hypothetical

questions about the real system. Furthermore, simulation modeling could be used as

an analysis and design tool to predict changes and the performance of both existing

and new systems [3].

1.1 Problem statement

The process of mapping conventional diesel haulage trucks to an electric process

will be investigated. Due to the specifics of the problem, custom software has to be

made to simulate the energy consumption of the haulage trucks based on real data

from existing mines.

Furthermore, examining the strategic placement of charging locations as well as

evaluating how different parameters and mine topographies affects the availability

and efficiency of the battery electric haulage truck is of interest.

1.2 Objective

The goal of the study was to develop software and simulate a fast-charging appli-

cation of battery-electric haulage trucks in underground mining and examine the

effects of different parameters. The study intends to meet the following objectives

• Develop a tool that can simulate the energy consumption of a battery electric

haulage truck in an underground mine environment

2

• Investigate the effects of different batteries, charger capabilities, queuing times,

fleet sizes and topographies

• Compare production rate to a conventional diesel haulage truck

1.3 Limitations

The scope of the project is mainly limited to examining battery electric haulage

trucks with a fast-charging capability.

3

2 Theory

In order to model the energy consumption of a vehicle a traction model has to be

established. This can be done by examining the main energy-consuming effects and

the equation that constitutes the longitudinal dynamics of the vehicle. Therefore,

this section aims to formulate the physical models used in order to simulate the

energy consumption of the BEV.

2.1 Mine Layout and Infrastructure

Different mining methods requires a different infrastructure underground. The min-

ing methods are adapted to rock conditions, strength and stability of the ore body,

dimensions etc. Infrastructure is key, and depending on the conditions different

transportation systems are being used. Historically the transportation of ore, waste,

workers, and material is most commonly done through vertical shafts, see Fig. 1,

but in newer mine designs a decline ramp may be used instead. These would then

give access to the main underground levels and act as the main passageway for any-

thing going up or down. The connection of stopes with ore passes, tramming levels,

and workshops is made by drifts, shaft stations, and ramps [4].

The haulage trucks often transport material for long distances from the face, where

the LHDs are loading trucks with blasted material, to the crusher. Sometimes the

material is hauled to the surface [5]. Depending on where the crusher is located,

relative to the face, the material will be hauled either uphill, flat or downwards.

The route topography is important because driving material uphill would require

more work and thus increase energy consumption. For a battery electric vehicle, this

would be far from optimal because it would not benefit from the extra mass during

regenerative braking, which is a concept that will be explained more thoroughly,

when driving back downhill.

As underground mines are expanding with time the haulage distances will increase.

This introduce difficulties when deciding upon location for the charging infrastruc-

ture in the mine. The placement would also be very mine specific but in general

it would seem logical to place charging infrastructure close to main ramp intersec-

tions, crushers and workshops since naturally there would be a higher flow of traffic

at these locations.

4

Currently there are a few mine companies that have electric haulage trucks in op-

eration. Compared to the diesel trucks they would be able to travel faster, have

lower operating costs and a significantly reduced ventilation need. The drawbacks

being mainly high initial costs due to the required infrastructure [6]. According to

Bloomberg New Energy Finance (BNEF) the lithium-ion batteries (LIB) were quite

pricey a decade ago, namely US$1,183 per kWh (kilowatt-hour) in 2010. In 2019

they were reported costing, at a market average, US$156/kWh which is a significant

decrease. The battery technology is continuously advancing each year through new

pack designs and reduced manufacturing capital expenditures [7].

There are different ways of powering electric haulage trucks. For example, they

could be powered by a trailing cable, batteries and overhead power lines [6]. Being

powered by batteries would offer the highest flexibility as you would not be limited

by overhead powerlines or a trailing cable.

Figure 1 – 3D Model of an underground mine [8].

5

2.2 Traction Model

It is possible to split the energy flow of a BEV into charging and driving. This can

be visualized in Fig. 2. In the charging process, energy is drawn from the socket and

stored in the battery. For the driving process, energy is flowing from the battery

and mainly converted into mechanical energy via the electric powertrain in order to

move forward. A smaller part is consumed by the auxiliary system [9].

Charger Inverter

Auxiliary system

M

AC energyDC energy

BatteryMotor Reduction

Wheel

Driveshaft

Charge PowerDrive Power

Regeneration

80% of nominalcapacity

Figure 2 – A simple energy flow diagram of the powertrain of a BEV.

Mechanical energy is produced from the propulsion system and temporarily stored

in the vehicle in the form of kinetic energy when the vehicle is accelerated and

potential energy when it gains altitude. It is then assumed that the resisting forces

acting against the vehicle is draining energy from this reservoir.

The longitudinal dynamics of a road vehicle can be described by using Newton’s

second law

mvd

dtv(t) = Ft(t)− (Fa(t) + Fr(t) + Fg(t) + Fd(t)), (1)

where on the left hand side we have the inertia force caused by the vehicle mass. On

the right hand side Fa is the aerodynamic friction force, Fr the force due to rolling

friction, Fg the force due to gravity acting on inclined roads and Fd a disturbance

force summarizing the other unspecified effects. Ft is the force needed by the prime

mover, the motor, to generate mechanical traction, minus the inertia force, the force

required to accelerate the rotating parts inside the vehicle, and minus the friction

losses in the powertrain. In Fig. (3) these forces are visualized.

6

v

Ft

Fr

Fa

Fd

Fg

mv · gα

Figure 3 – Free body diagram over the essential forces in play on the vehicle.

2.2.1 The forces

Aerodynamic friction

In general the force due to aerodynamic friction, Fa, could be modeled as

Fa =1

2· ρ · Af · cd · (v − vw)2, (2)

where ρ is the density of air, Af the frontal area of the vehicle, cd the drag coefficient,

v the vehicle speed, and vw the wind speed. It is important to note that the air

density could change depending on ambient temperature, air pressure, and humidity

[9, 10].

Furthermore, it is worth noting that since speed is the only physical quantity that

could make the aerodynamic friction force substantial, in this case, it would not

make a big contribution to the overall resistance due to low speed limits in the

mine. For obvious reasons, wind speed would not have to be corrected for.

Rolling resistance force

The rolling resistance is modeled as

Fr = RR% ·mv · g, (3)

7

where RR% is the rolling resistance in percentage, mv the mass of the vehicle, and g

the gravitation. Often, for the rolling resistance, a value of 2.5 to 3.0% is considered

when modeling the energy consumption in the underground mining case and given

the vehicle is using rubber tires. The road resistance could easily change depending

on the weather conditions [2]. Gravity and the vehicle mass would make this term

have a greater impact on energy consumption than for example the aerodynamic

friction force. A comparison between the two forces could be seen in Fig. 4. It is

easy to see that, at relatively low speeds, the aerodynamic friction almost makes no

contribution when looking at the sum of them.

Uphill resistance

Driving on a road with a gradient gives rise to a conservative force which affects the

behavior of the vehicle. For the simulation it will be modeled as

Fg = mv · g · sin(α), (4)

where α is the slope of the road. Gravity could of course vary in magnitude depend-

ing on the altitude, latitude, depth etc. Just as the rolling resistance, this expression

would become rather large in magnitude as well due to the gravity and mass term.

Inertial forces

The rotating parts of the powertrain and the inertia of the vehicle will cause fictitious

forces, also known as d’Alembert forces. In Eqn. (1) the force on the left hand side

stems from the vehicle mass. However the rotating masses, mr, of the powertrain

(wheels and engine) need to be included as well. They can be computed as

mr =1

r2w·Θw +

γ2

r2w·Θe, (5)

where rw is the wheel radius, γ the constant gear ratio and Θw the inertia of all

wheels and the rotating parts on the wheel side of the reduction drive. Similarly,

Θe is the inertia of the motor and the rotating parts on the motor side.

By adding mr to the vehicle mass the inertial force making up the left hand side of

8

Eqn. (1) then becomes

Fi = (mv +mr) ·d

dtv. (6)

Acceleration

Mind that Eqn. (6) is the only force containing acceleration. A simple model for

computing the energy required for accelerating a vehicle on a horizontal road would

be using the corresponding kinetic energy required to accelerate up to the desired

speed. By multiplying Eqn. (6) with vdt and integrating gives

Eacc =

∫Fi · v dt = (mv +mr) ·

∫dv2 =

1

2· (mv +mr) · v2, (7)

which is the consumed energy when accelerating up to a speed v.

2.2.2 Mechanical Traction

The mechanical traction force, Ft, needed to move the vehicle forwards could be

obtained from Eqn. (1). By disregarding the disturbance forces and rearranging

terms gives the traction force

Ft = Fa + Fr + Fg + Fi. (8)

To get the energy as a function of distance it is only a matter of multiplying the

traction force, Eqn. (8), with v and integrating with respect to time,

Et(s) =

∫Ft · v dt = Ft · v ·

∫dt = Ft · v · t = Ft · s. (9)

This is now the energy required to drive an arbitrary stretch of road at a constant

speed [10]. However this expression needs to be updated containing the energy due

to acceleration, Eqn. (7), which then leads to

Et(s) = Ft · s+ Eacc. (10)

9

0 20 40 60 80 100

0

5

10

15

20

Speed [km/h]

For

ce[k

N]

Faer

Froll

Fsum

Figure 4 – Comparison between the aerodynamic friction force and the rolling

resistance force for a vehicle driving at various speeds, weighing 70,000 kg and RR%

set to 3%. The sum is plotted to see the combined effect. Cross-wind is not corrected

for.

2.3 Auxiliary Consumption Model

The auxiliary systems of the vehicle could include everything from lights to hy-

draulics. Many seem to choose to neglect the auxiliary consumption due to it being

very vehicle and scenario specific. However for an electric city bus [11] shows that

the consumption is considerable, Fig. 5.

The mining haulage trucks raise the bed with the help of hydraulics powered by a

hydraulic pump. It is possible to imagine the vehicle being in three different regimes:

idling, driving, and dumping.

When the vehicle is in the dumping state it would during short periods, when the

vehicle raises the bed, demand more energy. However, when the vehicle is in a

driving or idling state the system would not use as much.

As manufacturers of electric haulage trucks often tend to specify a separate aux-

iliary motor powering the hydraulics it leads to the idea of modeling the energy

10

consumption for this system by thinking each regime using a certain percentage of

the specified auxiliary motor power [12]. A simple model would be phrased, math-

ematically, as

Eaux = ηaux · Paux · t, (11)

where ηaux would be the percentage used by each regime from the auxiliary motor

power Paux during the time t.

0.03 Wh/km (3%)

0.11 Wh/km (10%)0.03 Wh/km (3%)

0.31 Wh/km (30%)

0.3 Wh/km (29%)

0.27 Wh/km (25%)

BatteryAeroBrakeTyresTransmissionAuxiliaries

Figure 5 – Distribution of energy losses from an electric bus for a city drive cycle.

2.4 Recuperation Model

In general, EVs utilizes a concept called regenerative braking which means that the

kinetic energy is converted back to electrical energy upon deceleration, or when going

downhill. In a conventional vehicle, the kinetic energy is dissipated as heat during

braking. To not dissipate the energy the motor acts as a generator and current

flows in reverse, back into the on-board battery, see Fig. 2. This means a couple

of advantages: the battery gains more charge and thus the range is extended, lower

energy consumption, battery sizes may be smaller and less heat is outputted into

the mine environment.

11

In underground mining, this feature is major and plays a big role in the energy

consumption of the vehicle. For example, if downhill ore haulage is possible, less

energy will be consumed. In some cases, the battery electric haulage truck might

even perform several shifts on a single charge because of this. However, many times

downhill ore movement is not feasible. Essentially this puts the BEV at a great

disadvantage, it will discharge faster and require a bigger battery in order not to.

A solution could be either selecting top-down mining methods or haul material to

a centralized point with a conveyor uphill in order to minimize uphill haulage [2].

To model this, imagine the vehicle being in two different states: traction mode or

in braking mode. When the vehicle is in traction mode it essentially means that

the tractive force is positive, Ft ≥ 0. However when the vehicle is operating in

braking mode the decrease in kinetic energy is covered by the aerodynamic and

rolling friction losses, therefore not requiring any mechanical energy during this

phase, Ft < 0. The rest of the energy would conventionally be dissipated as heat

but in this case, recovered by the energy recuperation device.

In reality the electric powertrain is of course not 100% efficient. The losses in the

powertrain when converting electrical energy to mechanical energy at the wheels,

and vice versa, introduce efficiency factors. The total efficiency from battery to

wheels could be around 73% whereas for a diesel vehicle it could be as low as 35%

[2]. Therefore, by using Eqn. (10), the energy consumed or recuperated by the

motor can be modeled as

Emot =

Et

ηp+ Eaux traction mode Et ≥ 0, (12)

Et · ηr + Eaux regen mode Et < 0, (13)

where Eaux is the auxiliary energy consumption provided in Eqn. (11), ηp and ηr

are the propulsion efficiency (battery to wheels) and recuperation efficiency (wheels

to battery) respectively [13].

2.5 Energy Storage System

The rechargeable battery is a central component in a BEV. It is composed of one or

more energy cells housing an electrolyte in which ions flow from the positive terminal

12

(anode) to the negative terminal (cathode) thus creating a current. A couple of

different rechargeable battery types are lead-acid, nickel-cadmium (NiCd), nickel-

metal-hydride (NiMH), nickel-zinc (NiZn), and lithium-ion (LIB). Out of these, the

latter has the highest reported energy density. This is important because it limits

the driving range of the vehicle. In the mining industry battery electric haulage

trucks will have a high energy demand due to the gross weight. The remaining

capacity of the battery is measured in a dimensionless parameter called the state of

charge (SoC) and is a percentage of the nominal capacity. It can be defined as

SoC(t) =Q(t)

Qn

, (14)

where Q(t) is the current capacity and Qn the nominal capacity.

A battery management system (BMS) makes sure the battery is operating efficiently

and safely. Among other things, it monitors the energy consumption, current, SoC,

battery health and temperature. Additionally, it takes care of the redirection of the

energy from the regenerative braking back to the battery.

Batteries degrade and lose performance over time. In order to maximize its lifetime

(measured in cycles), it needs to operate not only at an optimal temperature but also

within a certain SoC limit. If not, the consequence will be faster cell degradation and

reduced range. Often the battery cycles between a lower limit SoC and a maximum

limit SoC in order to not be drained and preserve its lifetime. Of course, this is a

compromise between lifetime and battery utilization [2, 14, 15].

2.6 Charging System

In order to successfully deploy a fleet of BEVs in an underground mine the charg-

ing infrastructure needs to be placed strategically throughout the mine. This could

indeed be a very difficult task especially if the mine is already designed with re-

spect to diesel vehicles. Such a design has often given little thought to the parking

arrangement of the vehicles.

There are several ways of charging a battery. One common method by the current

manufacturers of BEVs for the mining industry uses off-board charging of off-board

batteries, also called battery swapping. This method is based on that the battery

13

is removed after being discharged and replaced with a fully charged one. Another

method, which will be considered by this thesis, is off-board charging of on-board

batteries. This approach requires the design of the mine to take into account charg-

ing stations at which the BEVs will be parked while charging. Furthermore, it allows

for a fast-charging (high capacity chargers) application since the size and weight of

the charger do not matter [2].

As discussed earlier, for various reasons, it is far from optimal to charge the battery

fully. The charging time of the battery could be modeled by assuming a linear

relationship between charge time and the SoC. In Fig. 6 for a constant-current

constant-voltage (CC-CV) charging process, there is a linear profile of the SoC up

to roughly 80%. The time it takes depends on many factors, however, for this thesis

it will be modeled with respect to the C-rate (rate of charge) the battery is capable

of receiving as well as the power delivery of the charger.

M. Ye et al.: Research on the Battery Charging Strategy

current curves of each stage can be obtained according to theheat production and constraint conditions.

IV. RESULT AND DISCUSIONA series of battery charging experiments was conducted. Theproposed charging strategy was used to operate the experi-mental instruments. The battery optimal charge test platformis shown in Fig. 5. In this paper, we will use an Arbin testsystem, a thermal chamber, a host computer and tempera-ture measuring instrument. An Arbin instrument was usedfor battery recharge and discharge tests. The volume of thethermal chamber was approximately 0.5 cubic meters. Thetested batteries used in this study were LR1865SZ batteries,as shown in TABLE 1. The test equipment and measuringdevices utilized in this study are shown in Fig. 5.

FIGURE 5. Configuration of optimal charge test platform.

A. OPTIMAL CHARGE PARAMETERS1) DETERMINATION OF THE SOC RANGETo simultaneously reduce the charge time and increase thecharge capacity, two targets need to be optimized according tothe charging time and charging capacity. It is obvious that theefficiency of charge and discharge is higher when the SOC is90%, but the advantage is not obvious, as shown in TABLE 2.Moreover, a total time of 3376 s are required to charge 90%of the battery capacity, which is 544 s more than the timespent to charge the battery to 80% SOC; however, its chargetime is half the time required to charge the battery to 100%SOC, as shown in Fig. 6. From the above results, the value ofSOCend is set to 90% in Eq. (15).

2) DETERMINATION OF THE STAGEThe genetic algorithm is used to optimize the stages ofthe method. The calculation process is shown in Fig. 4.Because of the lower number of stages, the heating rate must

TABLE 2. Charge efficiency.

FIGURE 6. Charging time at different SOC.

be reduced and it will make charging current value reducedto guarantee the charging capacity, thereby prolonging thecharging time. Hence, it is desired to increase the number ofheating rates stages to reduce the charging time. Nevertheless,the charging time is negligibly reduced by the increasingnumber of stages when the number of stages reaches a certainvalue. Therefore, it is necessary to use the GA to find theappropriate stages to balance the charging time and difficultyof optimizing the charging strategy. The fitness function canbe obtained by Eq. (13), and the β is set as 0.5 which meansthe charging time and temperature rise are equally important.The result is shown in Fig. 7.

FIGURE 7. Charging time at different stages.

The temperature rise is not obviously variable at differentstages, as shown in Fig. 7. Therefore, the stage can be selectedaccording to the charging time. From Fig. 7, no apparentlydecrease of charging time is found after stage 3. Therefore,

VOLUME 6, 2018 64197

Figure 6 – Constant current constant voltage (CC-CV) charging process of a Li-ion

battery [16].

2.7 Queuing Model

Each charging station is only designed to handle a certain number of vehicles charg-

ing at the same time. Therefore, when the number of vehicles exceeds the number

14

of charging stations (given that the charging station will only handle one vehicle)

you can no longer guarantee that the charging station will be available upon arrival.

This is when queuing arises. To deal with this charging congestion a simple queuing

model has been developed to estimate the probability of availability.

Let X be a stochastic variable representing the number of vehicles waiting at a

charger. If all charging stations along a route are being utilized equally as much of

the time by each vehicle then the probability of it using a specific charging station

along the route can be expressed as p = u/n where u is the fraction of time utilized

and n charging stations. Assuming all vehicles behave independently and X follows

a binomial distribution then the probability that a charging station is available could

be expressed as

P (X = 0) = (1− p)k−1, (15)

where k ≥ 1 is the number of vehicles [17].

15

3 Methodology

This chapter aims to describe the study process, data, the algorithms and system

description of the constructed program. Furthermore, it gives the reader a clear

view of how the study was conducted.

3.1 Literature Review

The thesis started with an extensive literature review to become familiar with the

terms used in underground mining, its operation, transportation systems as well as

the simulation models used for regular EVs. Mainly books, dissertations, articles

and websites served as the sources for the literature used. There were also internal

ABB reports and program code which gave inspiration to some ideas. Continuously

throughout the thesis work, bi-weekly meetings were held with internal stakeholders

which gave highly valuable input with the development of the simulation program

and data.

3.2 Data Analysis

Data was obtained from an existing underground mine located in the north of Swe-

den. It consisted of an activity sheet, Tab. 1, which logged activities performed

by the various resources (LHDs, haulage trucks etc.) in the mine during 1 week.

More specifically, this activity sheet contained important information about how a

typical day shift was performed by the haulage trucks. Among other things the ac-

tivity sheet contained operating time, tonnage moved and the names of the locations

where the loading and dumping occurred. In order to extract the distance, or route,

between the loading and dumping locations a distance matrix was provided by the

mining company containing the distances between locations along the ramps as well

as the depths they were located at. Data regarding the vehicle operating weight,

frontal area, batteries etc. were based off of different manufacturers’ specification

sheets for current battery electric haulage trucks.

16

Table 1 – Extracted data from the activity sheet during one day for a specific

haulage truck.

ActivityID Room Activity Resource Tstart Tend Destination Tonnes

1 H1362 Transport Haulage truck 2 06:15 08:15 Crusher 175.49

2 J1334 Transport Haulage truck 2 08:15 10:45 Crusher 225.63

3 H1450 Transport Haulage truck 2 10:45 14:15 Crusher 426.19

From the data a work cycle was mapped out which resembled the route traveled by

one conventional diesel haulage truck during a typical shift in effectively 8 h, see

Fig. 7. This truck moved a total of 827.31 t this shift which means a production

rate of ∼103 t/h.

It can be seen that there is a charger placed at node E and G. At node E there is a

workshop that could be a potential place for a charging station due to it being more

spacious. The charging station placed at node G would also be a wise candidate

as all haulage trucks would need to visit this location when dumping material. As

seen in the graph, the crusher is located at a higher altitude than the three faces at

which the loading happens. This means uphill haulage for the haulage truck. Since

there could be cases in which material is hauled downwards or flat, the same work

cycle, Fig. 7, was categorized into three topographies:

• Uphill haulage;

• Flat haulage;

• Downhill haulage

This was done by adjusting the depths of all nodes in the work cycle such that the

magnitude of the gradient remained the same for both uphill and downhill haulage.

For the flat case, each node was set to the same depth.

17

A

E

C

G

A NodeInfo Task 3: Depth: 1450m (H) Blast site 3 Material: 426.19t

C NodeInfo Task2: Depth: 1334m (J) Blast site 2 Material: 225.63t

G NodeInfo: Depth: 810m Crusher Charger

D

FD NodeInfo: Depth: 1040m (SR-HR) SR-HR intersection

F NodeInfo: Depth: 815m (SR-HR) SR-HR intersection

E NodeInfo: Depth: 980m Workshop Charger

Simon ramp

2569m

476m

1321m88m

B

782m

2752m

B NodeInfo Task 1: Depth: 1362m (H) Blast site 1 Material: 175.49t

Main ramp

Figure 7 – Work cycle of an 8h shift consisting of 3 tasks represented as a graph

with node and edge attributes.

3.3 Model assumptions

3.3.1 Average speed

Firstly there was no data such as an altitude or speed profile for the drive cycle. It

would then be really hard to know when to account for accelerations. This was the

reason for using an average speed to simulate the haulage trucks and account for

accelerations where they were known to happen such as at the dumping, loading,

and charging locations.

The data was not too reliable. Sometimes there was data stating the haulage trucks

moved so much material during a shift it would not be realistic for them to haul that

amount within the reported time. It essentially means they would have to travel at

an average speed far from what would be realistic in an underground mine scenario.

For example, looking at ’Task 1’ in Fig. 7 which cycles between nodes B and G.

We see that there is 175.49 t to be moved, and the round trip distance between the

nodes being ∼9.3 km. Assuming the haulage truck would carry a 30 t payload it

would have to travel 6 cycles in order to move 175.49 t. The task is reported taking

2 h in Tab. 1 when looking at the 1st ActivityID. Driving 6 cycles each being 9.3

18

km means ∼56 km in 2 h which results in an average speed of ∼28 km/h. Although

assuming an average speed of ∼30 km/h might sound a bit high this is what needs to

be assumed for the hauled material reported in those times to make sense physically.

Because of using an average speed, there would not be any need to account for stops,

time-wise, during loading and dumping, at intersections etc., other than charging

and queuing. If wanted, the developed program has support for accounting for

loading and dumping times.

3.3.2 Topographies

The original shift was an uphill haulage case with an average grade of ∼11%. It was

obtained by taking the average of the rise over run for each node pair in Fig. 7, for

each task. The following grades were considered for the three types of topographies

investigated:

• Uphill haulage: +11%;

• Flat haulage: 0%;

• Downhill haulage: −11%

3.3.3 Vehicle

Throughout the simulations two different sized haulage trucks, HT1 and HT2, were

used, see Tab. 2. The main difference between the two being the mass and payload.

As the HT1 haulage truck was considered being the smaller one it was also restricted

to using smaller batteries as the mass would be very affected by the size of them.

The high capacity chargers were simulated with 600 kW and 1 MW, the latter being

more futuristic. The drag coefficient needs to be decided by CFD simulations. There

is plenty of research done already, e.g. [18] showing that ∼0.6 being reasonable for

a haulage truck.

These two trucks were then simulated as a fleet of 3, 5 and 7 haulage trucks perform-

ing the shift. What this effectively does is splitting the amount of material moved

equally between the fleet size, meaning much less work per vehicle. This was done

mainly because of a single haulage truck not being able to perform the shift in an

uphill haulage setting alone in a reasonable time.

19

The details provided in the expression for the rotating masses in Eqn. (5) would be

difficult knowing exactly. Therefore the vehicle mass in the expression for computing

the energy due to acceleration, Eqn. (7), was increased by 5% instead.

Table 2 – Key specifications used to simulate two different sized haulage trucks

throughout the simulations.

Parameter HT1 HT2 Unit

Curb weight 15,000 25,000 kg

Payload 30,000 45,000 kg

Battery capcaity [250, 450] [250, 750] kWh

Charger [600, 1000] [600, 1000] kW

Cd 0.6 0.6 −Af 7.3 7.3 m2

ηp 80 80 %

ηr 80 80 %

maxLimSoC 80 80 %

lowLimSoC 30 30 %

Rolling resistance (RR) 3 3 %

Average speed 8.3 8.3 m/s

3.3.4 Queuing and Sampling

Whenever a charging station was in an occupied state an assumption was made that

the queuing time would be 50 % of the charging time and then added to the total

time taken.

Because of the randomness associated with the queuing model 100 samples were

generated for each simulation and the parameters were averaged. The generation

was done by naming the output data file in the configuration file, it appends a new

row for each time the simulation is run. The plotting in the configuration was turned

off and the program ran 100 times by a simple for-loop in the terminal.

20

3.4 System Description

Describing the software is important to get a better understanding of how the system

is operating to accomplish the simulation. Therefore, this part provides a more in-

depth explanation of the more central pieces of software used in the system.

3.4.1 Graph Representation

The work cycle described earlier, Fig. 7, was represented as a graph using the

NetworkX Python package which contains many standard graph algorithms and

data structures for graphs, digraphs, and multigraphs. This package also enables

one to add node and edge attributes [19]. In this way, it would then be possible to

traverse the graph in any direction with the built-in NetworkX functions, and while

doing so, compute the energy consumption along each edge.

3.4.2 Implementation and Program Structure

The underlying models presented in the theory section were implemented in Python

3.8. Structurally, in the top-level, the main module takes in a configuration file

reading all necessary parameters set by the user where the user also specifies an

input graph file in a .py extension. NetworkX offers a variety of read-support for

various graph extensions but none that seemed very user friendly. This was the

reason for the graphs being constructed with the built-in functions of the NetworkX

package, making it essentially a Python module.

The main module then calls the sub-modules which handle the computations re-

garding energy, forces, queuing, and charging, as shown in Fig. 8. These modules

are described briefly below.

energy.py − Implements the auxiliary consumption, Eqn. (11), the acceleration

provided in Eqn. (7) and computes the work done with the expression of the traction

energy, Eqn. (9), by calling forces.py. It then uses Eqn. (12) and (13) to include

the efficiencies depending on the sign of the computed energy.

forces.py − Computes the forces, as in Eqn. (8), resisting vehicle movement.

queuing.py − Handles the queuing congestion by computing the probability of

another vehicle being at a charging station with Eqn. (15).

21

charging.py − This module is called every time the vehicle needs to charge or

update its SoC by using Eqn. (14). It computes the time taken to fully charge the

vehicle to the set maximum limit SoC by using the idea of ”charge over power” due

to the linear relationship shown in Fig. 6.

Input: configuration file

Interface

main.py

energy.py forces.py queuing.py charging.py

settings.py

Top-level Modules

Output: - Energy vs. distance plot - SoC vs. time plot

- Data file with useful info

Figure 8 – A visual representation of the program structure.

Heuristics

A first approach was to implement a simple/naive heuristic, see Alg. 1 in Ap-

pendix B, in the main.py module which would achieve the goal of simulating the

haulage trucks. This heuristic computes the SoC over time for a given sequence

of routes/cycles until the SoC reaches the lower limit. Then it goes back to the

last possible charging opportunity and charges to the maximum allowed SoC set

by the user. This is repeated for all vehicles. Although this approach worked, the

big problem with it was it only decided to take action charging when it registered

a SoC less than the lower limit. Mind that the vehicle could be at any node at

this point, meaning if not being at the charging node then it had to consume more

energy visiting one, resulting in the SoC falling below the lower limit.

To prevent this from happening a more intelligent heuristic, see Alg. 2 in Appendix

B, was implemented in order to reduce the risk of running below the set lower

22

limit SoC. At each charging node it predicts the vehicle SoC if it were to go to its

destination and back to the same charging node again. If the SoC turned out to be

below the lower limit, the action taken was to charge at the current charging node.

3.5 Software Interface

The interface, the interaction between user and program, consists of a configuration

file containing all information necessary to run the simulation. For an example, see

Appendix A.

23

4 Results

4.1 Simulation runs

The HT2 haulage trucks were simulated as a fleet of 3 vehicles. The outputted

SoC and energy consumption could be seen for three different topographies: Uphill

haulage in Fig. 9; flat haulage in Fig. 10 and downhill haulage in Fig. 11. The

results show that for this configuration it would take roughly 7 h in an uphill haulage

scenario, 4 h for a flat haulage profile and only ∼2.5 h for a downhill haulage case per

vehicle. Worth noting is that the SoC falls very close to 20 % in the uphill haulage

scenario, Fig. 9.

The vehicle connects 13 times to a charging station in the uphill haulage case, only

three times for the flat case and it never has to charge in the downhill haulage

topography. We also see that the energy consumed uphill, Fig. 9, is about 3 times

more than for flat haulage in Fig. 10. For the downhill case, the vehicle actually

generated more energy than it consumed and did not need to charge at all.

0 2 4 60.2

0.4

0.6

0.8

Time [h]

SoC

[%]

0 20 40 60 80

0

200

400

600

800

1,000

Distance [km]

Ener

gy[k

Wh]

Figure 9 – Direct output from the developed simulation. SoC of the HT2 vehicle

and the corresponding energy consumption. Uphill topography with battery size of

250 kWh.

24

0 1 2 30.3

0.4

0.5

0.6

0.7

0.8

Time [h]

SoC

[%]

0 20 40 60 80

0

100

200

300

Distance [km]

Ener

gy[k

Wh

]Figure 10 – Direct output from the developed simulation. SoC of the HT2 vehicle

and the corresponding energy consumption. Flat topography with battery size of

250 kWh.

0 0.5 1 1.5 2 2.5

0.4

0.5

0.6

0.7

0.8

Time [h]

SoC

[%]

0 20 40 60 80

−150

−100

−50

0

Distance [km]

Ener

gy[k

Wh]

Figure 11 – Direct output from the developed simulation. SoC of the HT2 vehicle

and the corresponding energy consumption. Downhill topography with battery size

of 250 kWh.

4.2 Charging and queuing times

Both the HT1 and HT2 haulage truck types were simulated for the uphill haulage

case using different battery capacities with a different C-rate for two chargers. For

three different fleet sizes the charging time was investigated. The results are shown

25

in Fig. 12. They show that having a bigger fleet, bigger battery and a more capable

charger keeps the total time of the task spent on charging much lower. Having a

bigger sized truck in combination with a big fleet seem to give the lowest charging

time. Interestingly for the HT1 haulage trucks, a fleet of 7 vehicles and 350 kWh

battery gives the same, and the lowest, charging time for both the 600 kW and 1 MW

charger. However, for the HT2 haulage truck, the 1 MW charger in combination

with a 750 kWh battery and a fleet of 7 vehicles gives the lowest charging time alone

in this category of trucks.

In Tab. 3 the mean total queuing times, per vehicle, for different fleet sizes and

battery capacities for the HT1 uphill haulage case are shown. We notice that for

each battery size the queuing time remains roughly the same across the fleet sizes.

The mean queuing time decreases with increasing battery capacity. For example, at

150 kWh there is 95 minutes of average total queue time for a 3-fleet but for a 250

kWh battery it drops to 39 minutes for the same fleet. We find a similar behavior

for the HT2 case in Tab. 4.

150 200 250 300 350

50

60

70

Battery capacity [kWh]

Char

ging

tim

e[%

]

600kW 3F600kW 5F600kW 7F1MW 3F1MW 5F1MW 7F

400 500 600 700

40

50

60

70

Battery capacity [kWh]

Char

ging

tim

e[%

]

600kW 3F600kW 5F600kW 7F1MW 3F1MW 5F1MW 7F

Figure 12 – Time spent on charging of the total time taken to perform the shift

for the HT1 trucks on the left and HT2 on the right. The batteries using the 600

kW charger have a C-rate of 1.33 whereas with the 1 MW charger the C-rate was

set to 1. Fleet sizes are indicated with the F suffix.

26

Table 3 – Mean total queuing times per vehicle, in minutes, over various battery

sizes for the HT1 haulage trucks in the uphill haulage case. {chargePower, Crate}= {600 kW, 1.33 1/h}

HT1: UPHILL HAULAGE

Battery size\Fleet size 3F 5F 7F

150 kWh 95 min 95 min 105 min

250 kWh 39 min 45 min 47 min

350 kWh 27 min 31 min 24 min

Table 4 – Mean total queuing times per vehicle, in minutes, over various battery

sizes for the HT2 haulage trucks in the uphill haulage case. {chargePower, Crate}= {600 kW, 1.33 1/h}

HT2: UPHILL HAULAGE

Battery size\Fleet size 3F 5F 7F

350 kWh 72 min 62 min 69 min

550 kWh 25 min 27 min 24 min

750 kWh 15 min 21 min 14 min

4.3 Production rate and operational efficiency

In Fig. 13 it is possible to see the production rate per vehicle for each topography

for the HT2 haulage trucks simulated as a fleet of 3 vehicles performing the shift.

In the downhill case, the vehicles are on par regarding the production rate with

the conventional diesel vehicle, ∼103 t/h, for all investigated battery capacities. For

the flat case, the productivity seems to be 80 t/h with a 250 kWh battery but is

rising up closer to 90 t/h with a 450 kWh battery. In the uphill case, which was the

original, the battery electric fleet only manages to haul 40 t/h per vehicle for a 250

kWh battery, then decreasing the production rate a bit with a 350 kWh battery but

increases closer to 50 t/h with a 450 kWh battery size.

In Fig. 14 the results for the operational efficiency (the time spent moving of the

total time taken) for different fleet sizes with the chargers set to 600 kW. For the

smaller HT1 trucks there were no major difference in the operational efficiency for a

27

fleet size of 3 and 5 vehicles. However, for a 7 fleet there is a bump in the efficiency

from ∼45 % for a 150 kWh to ∼55 % for a 350 kWh battery. Furthermore, we notice

that a fleet size of 7 vehicles seem to be twice as efficient per vehicle than a fleet size

of 3 vehicles. We notice pretty much the same behavior of the HT2 vehicles. The

difference to the HT1 trucks being only slight.

250 300 350 400 450

40

60

80

100

Battery capacity [kWh]

Pro

duct

ivit

y[t

/h]

Uphill: +11% gradeFlat: 0% gradeDownhill: -11% grade

Figure 13 – Fleet size of 3 HT2 haulage trucks hauling material in different to-

pographies. The batteries received the full capacity of two 600kW chargers.

150 kWh 250 kWh 350 kWh0

10

20

30

40

50

Oper

atio

nal e

fficie

ncy

[%] 600kW 3F

600kW 5F600kW 7F

350 kWh 550 kWh 750 kWh0

10

20

30

40

50

60

Oper

atio

nal e

fficie

ncy

[%] 600kW 3F

600kW 5F600kW 7F

Figure 14 – The operational efficiency for both the HT1, on the left, and HT2

haulage trucks to the right. {chargePower, chargeRate} = {600 kW, 1.33 1/h}.Fleet sizes are noted with the suffix F.

28

5 Discussion and conclusions

The results mainly confirm that, with this simulation setup, the uphill haulage

shift is not in favor of battery electric haulage trucks. There is simply too much

energy required to move a vehicle of that weight uphill for this shift. Replacing the

conventional diesel vehicle would at least require a fleet of 3 HT2 trucks having a

250 kWh battery, they would then finish the shift in just about 8 h according to

the left SoC plot in Fig. 9. A flat haulage profile, Fig. 10, gives more promising

results as the same fleet and specifications would finish the shift twice as fast and

thus resulting in twice the production rate, Fig. 13. Although a flat haulage profile

would not be too common in an underground mining scenario it still is an interesting

case because then mining companies could examine ideas such as putting a conveyor

to a level closer to the crusher and haul material from there which would level out

the haulage profile. The downhill haulage case, Fig. 11, was the only case that could

match the diesel vehicle in terms of the production rate of ∼103 t/h per vehicle for

all examined battery capacities. Even though the fleet size was 3 vehicles it only

took just over 2.5 h per vehicle to perform the shift. This means you could replace

the diesel vehicle with just one battery electric vehicle given the haulage profile was

downhill.

For the uphill case the production rate seemed to be very low for the HT2 trucks,

this obviously has to do with the massive energy consumption and the time spent

on charging. In the productivity plot, Fig. 13, there is a small dip in the production

rate from 250 kWh to 350 kWh which might seem odd, but the reason is most likely

that in the 250 kWh simulation there was a lower SoC registered which meant it

could utilize the battery more and bump up the productivity. The productivity

does not really seem to depend too much on the battery capacity although it surely

increases. As with everything there is an economic aspect that would most likely

tell which option would be the most economically viable as batteries have shown to

be rather expensive. However, that is not in the scope of this thesis.

Not too surprisingly, considering the energy consumption, the battery electric trucks

spend a considerable amount of the time charging for the uphill haulage scenario, see

Fig. 12. For the HT1 haulage trucks, they often spend more than 50 % of the time

charging for all battery capacities with two exceptions just below 50 %. The same

29

goes for the HT2 trucks except for the 750 kWh battery size where most fleets spend

less than 50 % of the total time charging. This means there would definitely be a

need for opportunity charging if considering a fast-charging application for battery

electric haulage trucks.

The queuing model showed expected results regarding the average total time spent

on queuing per vehicle across increasing battery capacity for each fleet size. It

decreased because you could survive longer on a charge with a bigger battery and

therefore not having to charge as often. For the same battery size, the total time

spent on queuing seemed to generally increase with increasing fleet size. This is

also what one would expect since more vehicles would increase the probability of a

charging station being occupied. A flaw with the model is that it does not take into

account that there could be multiple vehicles in the queue. However, the purpose of

the model was to somewhat account for queuing rather than completely ignoring it

since it would become a potential problem with more vehicles than charging stations.

The operational efficiency increases with a growing fleet size for each battery ca-

pacity, Fig. 14, which is to be expected. However, it did not grow as much with

increased battery capacity. A reason could be, for example, if having twice the

battery capacity, then since the logic implemented in Alg. 1 is to charge whenever

the SoC falls below the set lower limit it just means it would take double the time

charging instead.

Although the simulation program is very simple in its foundation and in need of fu-

ture work such as validation towards other software etc. it could still be a useful tool

for getting a rough idea of how different parameters affect the energy consumption

along a given route for a battery electric vehicle.

30

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Mining BEV GMG-WG-v02-r01.pdf, 2018. Accessed 2020-06-30.

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Simulation, 5th New Internatinal Edition. Pearson Education, 2010.

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University of Technology, 2012.

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32

A Configuration file

Table 5 – Example of a configuration file.

Model Parameter Value Unit

Graph graphFile uphillGraph −Data fileName DATA uphill.csv −

plotting 1 −numberOfVehicles 1 −mass 25000 kg

load 45000 kg

Cd 0.6 −Af 7.3 m2

speed 8.3 m/s

e driv 80 %

Vehicle e recup 80 %

dumpTime 0 s

loadTime 0 s

auxPower 125 kW

aux idle con 10 %

aux driv con 20 %

aux dump con 90 %

battCap 550 kWh

Battery chargeRate 1 1/h

maxLimSoC 80 %

lowLimSoC 30 %

id 0 −Vehicle Task sourceNode B −

targetNode G −material 175490 kg

Charger chargePower 600 kW

chargerUsage 26 %

rho 1.2 kg/m3

Environment g 9.81 m/s2

RR 3 %

33

B Algorithms

Algorithm 1 Naive logic for simulating an EV

1: procedure drive(...)

2: for each vehicle do

3: Compute SoC(t) for a given work cycle

4: if SoC(t) < SoCmin then

5: Go back to last possible charging opportunity

6: Charge to SoCmax

7: end if

8: end for

9: end procedure

Algorithm 2 Intelligent charging logic

1: procedure hypothetical charging(...)

2: if at charging node then

3: Compute hypothetical SoChyp the next time the vehicle visits this node

4: if SoChyp < SoCmin then

5: Charge to SoCmax

6: end if

7: end if

8: end procedure

34