Simulation Modeling of Energy Efficiency of Electric Dump Truck Use Depending on the Operating Cycle

Abstract

Open-pit mining involves the use of vehicles with high load capacity and satisfactory mobility. As experience shows, these requirements are fully met by pneumatic wheeled dump trucks, the traction drives of which can be made using thermal or electric machines. The latter are preferable due to their environmental friendliness. Unlike dump trucks with thermal engines, which require fuel to be injected into them, electric trucks can be powered by various options of a power supply: centralized, autonomous, and combined. This paper highlights the advantages and disadvantages of different power supply systems depending on their schematic solutions and the quarry parameters for all the variants of the power supply of the dumper. Each quantitative indicator of each factor was changed under conditions consistent with the others. The steepness of the road elevation in the quarry and its length were the factors under study. The studies conducted show that the energy consumption for dump truck movement for all variants of a power supply practically does not change. Another group of factors consisted of electric energy sources, which were accumulator batteries and double electric layer capacitors. The analysis of energy efficiency and the regenerative braking system reveals low efficiency of regeneration when lifting the load from the quarry. In the process of lifting from the lower horizons of the quarry to the dump and back, kinetic energy is converted into heat, reducing the efficiency of regeneration considering the technological cycle of works. Taking these circumstances into account, removing the regenerative braking systems of open-pit electric dump trucks hauling soil or solid minerals from an open pit upwards seems to be economically feasible. Eliminating the regenerative braking system will simplify the design, reduce the cost of a dump truck, and free up usable volume effectively utilized to increase the capacity of the battery packs, allowing for longer run times without recharging and improving overall system efficiency. The problem of considering the length of the path for energy consumption per given gradient of the motion profile was solved.

1. Introduction

One of the effective ways to solve environmental problems in open-pit mining is to replace pneumatic tire vehicles with drive motors based on heat machines with electric ones in the transportation link [1,2,3]. Such replacements reduce the emission of fuel combustion products into the atmosphere and prevent the accumulation of exhaust gases in the pit (Figure 1a).

The use of vehicles with heavy carrying capacity and high mobility is necessary in open-pit mining [4,5,6]. Pneumatic tire dump trucks are the best choice, as their traction drives can be implemented using thermal or electric motors. Electric machines are preferred because of their environmental friendliness compared to dump trucks with heat engines requiring fuel [7,8]. Electrically driven machines can be equipped with a centralized, autonomous, or combined power supply [9]. Each of these options has its advantages and disadvantages depending on the circuit design and parameters of an open pit [10,11].

The effectiveness of using pneumatic dump trucks in mining depends on various factors, including the steepness of the road rise in the quarry and its length. To assess the impact of these factors on the energy consumption of a dump truck, calculations were made for all the options for a power supply [12,13]. The factors studied were the steepness of the road rise in the quarry and its length [14]. Our calculations show that the energy consumption of a moving dump truck practically does not change with all the different options for a power supply. Therefore, the choice of the optimal power supply for pneumatic dump trucks can be based on other factors, such as cost, availability of resources, and environmental aspects [15,16].

The use of the centralized option with a power supply (Figure 1b) has its limitations, mainly related to the extension of the traction network as the section deepens and to the complexity of transporting it to the loading location [17,18].

The use of an autonomous source of electrical energy involves using charging stations in the power supply system, which can operate either with batteries without removal from the rolling stock (Figure 1c) or with a replaceable battery (Figure 1d).

The first scheme is less preferable since the charging time is quite significant and a dump truck is disconnected from the technological process of transportation for a long period [19].

This research directly contributes to several of the United Nations Sustainable Development Goals (SDGs). Primarily, it supports SDG 7 (Affordable and Clean Energy) by investigating the feasibility of electric vehicles in mining operations, aiming to reduce reliance on fossil fuels. Furthermore, the study addresses SDG 9 (Industry, Innovation, and Infrastructure) by promoting innovative electric drive systems in heavy machinery. By improving the energy efficiency of mining operations, the research indirectly impacts SDG 12 (Responsible Consumption and Production) by reducing resource depletion and minimizing waste. Lastly, transitioning to electric vehicles in mining contributes to SDG 13 (Climate Action) by lowering greenhouse gas emissions associated with fuel combustion [20]. Understanding the integration of electric vehicles and their impact on sustainable mining experience is crucial for achieving a sustainable future.

This research aims to investigate the effectiveness of regenerative braking systems in electric dump trucks, operating in steep mining environments, and to explore the economic and environmental feasibility of alternative energy management strategies, including the potential benefits of eliminating regenerative braking in certain operational scenarios.

A key novelty of this research lies in its detailed analysis of regenerative braking efficiency, specifically within the context of steep and uphill mining cycles. While regenerative braking is a well-established concept in electric vehicle technology, its performance under the unique operating conditions of open-pit mining, characterized by significant elevation changes and heavy loads, is less explored. Published papers [4,5,6,8,12,18] focus their attention on on-road electric vehicle applications with milder gradients, failing to capture the complex interplay of factors influencing regenerative braking in mining environments. Our simulation provides valuable insights into the limitations of regenerative braking under such conditions, revealing its reduced effectiveness due to energy losses during the ascent phase. This finding challenges the assumption that regenerative braking will automatically lead to significant energy savings in all-electric mining vehicle applications, highlighting the need for tailored energy management strategies. The focus is on regenerative braking in steep mining cycles, making our work different and contributing to a more nuanced understanding of electric vehicle performance in heavy industry settings.

2. Methodology

The methodology employed in this study involves a simulation-based approach to evaluate the energy efficiency of electric dump trucks in open-pit mining operations. The simulation model was developed using main Equations (1)–(13) to represent the various aspects of the dump truck’s operation, including its movement along different terrains, loading and unloading processes, and energy consumption/recuperation during different phases of the operating cycle.

2.1. Model Description

The simulation model involves several key parameters:

Truck parameters are load capacity, mass (empty and loaded), dimensions, wheel radius, and mechanical transmission efficiency.

Road parameters are the length of road segments, the inclination/slope of the road, and road surface conditions (rolling resistance).

Power system parameters are battery capacity, voltage, converter efficiency, and regenerative braking capabilities.

Operational parameters are loading and unloading times, average speed on different road segments, and the overall operating cycle.

The model calculates the tractive effort required at different stages of operation using Equations (5)–(7), incorporating such resistances as rolling resistance, aerodynamic drag, inertial forces, and gravitational forces due to road slope. Using Equations (8), (9), (11) and (12), the model estimates the total energy consumption by simulating the movement of a dump truck during a representative operating cycle. This includes the energy consumption during acceleration, constant speed operation, deceleration, and maneuvering.

Figure 2 illustrates the flow chart to estimate energy consumption and recuperation, considering such parameters as truck properties, road segment, and operational parameters.

2.2. Assumptions and Limitations

The simulation model is based on certain simplifying assumptions.

Constant parameters, such as the rolling resistance coefficient and aerodynamic drag coefficient, are assumed to be constant for a given road segment and truck type. In reality, these parameters may vary slightly due to changes in road surface conditions, weather, and other factors.

Simplified maneuvering means that the energy consumption during maneuvering (loading and unloading) is estimated using a simplified model, assuming constant power consumption during these phases. In reality, the power consumption may vary depending on the specific maneuvering strategy and operator skill.

A battery model used in the simulation involves using constant voltage and efficiency during charging and discharging. This is a simplification of the real-world behavior of batteries, which can exhibit voltage drops and efficiency losses at high charge/discharge rates. The model does not explicitly account for temperature effects or battery degradation over time.

Negligible auxiliary loads are not explicitly accounted for by the model for the energy consumption of auxiliary systems, such as air conditioning, lighting, and hydraulic systems. These loads are assumed to be small compared to the traction power and are therefore neglected.

Truck parameters are load capacity, mass (empty and loaded), dimensions, wheel radius, and mechanical transmission efficiency.

Road parameters are the length of road segments, the inclination/slope of the road, and road surface conditions (rolling resistance).

Power system parameters are battery capacity, voltage, converter efficiency, and regenerative braking capabilities.

Operational parameters are loading and unloading times, the average speed on different road segments, and the overall operating cycle.

These assumptions introduce certain limitations to the accuracy of the simulation results. However, they allow for a computationally efficient simulation, providing valuable insights into the energy efficiency of different electric dump truck configurations and operating strategies.

2.3. Validation

The simulation model was validated by comparing its predictions with the experimental data obtained during field tests of electric dump trucks in open-pit mines. The model predictions for energy consumption, speed, and battery state of charge were found to be in reasonable agreement with the experimental data with a maximum error of about 10%. This level of accuracy is considered acceptable for the purposes of this study. The next stage of our research will be compiling the software and database of mining electric dump trucks and track profiles.

3. Analysis of Power Supply Options for Mining Dump Trucks

A preliminary analysis of the options for the power supply of the rolling stock shows that a combined option is advisable. At the same time, in order to reduce energy consumption, the power circuits of the traction electric drive should provide the traction mode and the regenerative braking mode [21], where part of the electrical energy, previously consumed in the traction mode, returns to the battery, recharging it [22,23].

Regardless of the option with the power supply system and the parameters of the traction drive elements (Figure 3), a converter is used in the power circuits of a dump truck electric drive, whose loss of electrical energy (according to the experience of operating them on other vehicles) does not exceed 1–2%.

The structural diagram of the traction electric drive shown in Figure 3 includes an energy source (ES), a converter (Pr), an electromechanical converter (EMPR) (a traction electric motor), a mechanical transmission (MT), a propeller (a pneumatic wheel) (PPD), and a control system (CS).

Power semiconductor devices are used as converter elements, regulating the energy supply to the traction motor [24]. Regardless of the parameters of the quarry where minerals are extracted, the technological cycle of dump trucks includes a loading place, a road along which dump trucks move when descending into the quarry and leaving it, and an unloading place (Figure 4).

The length of the dumping and loading sections, even at the initial stage of the quarry formation, is many times inferior to the length of the road (l_dump ≈ l_loading << l) along which empty and loaded dump trucks move. Therefore, the energy spent on maneuvering dump trucks is incommensurate with the costs when driving on the road.

The value of the longitudinal slope of the road significantly depends on the design and carrying capacity of dump trucks [25,26]. For i_slope slopes of 8% and for i_slope slopes of 16%, dump trucks have a carrying capacity of 75 tons; for i_slope slopes of 24%, dump trucks with articulated frames have a payload capacity of 30–40 tons [27].

4. Calculation of Energy Consumption for Dump Truck Movement

The method for calculating the energy consumption for the movement of a dump truck with a traction electric drive in one cycle, consisting of lifting a loaded dump truck and lowering it empty into the quarry, is considered in the work [28].

In accordance with the provisions of the theory of electric traction [29], movement along a road section is divided into three components: starting from a standstill until reaching a given speed, movement at a constant speed, and a braking section to a complete stop [30]. When a dump truck is moving in any mode, it overcomes the resistance to movement, which includes external forces manifested in the rolling resistance of the wheels, and the forces of aerodynamic resistance of the air environment [31]. Rolling resistance forces largely depend on the condition of the surface and the material of the track structure [32].

In the case of automobiles, the rolling resistance forces shall be calculated as the sum of the forces acting on each axle of the vehicle:

$$W_{\mathrm{move}}={\displaystyle \sum _{i=1}^n{W}_{\mathrm{move}i}}={\displaystyle \sum _{i=1}^n{f}_i{G}_i},$$

where p is the number of axles of the vehicle; f_i is the rolling resistance coefficient of the i-th axle; and G_i is the weight of the vehicle on the i-th axle.

The rolling resistance coefficient depends, firstly, on the structure of the track (asphalt, concrete, etc.) and, secondly, on the condition of the wheels (the degree of tread wear, the amount of compressed air pressure in the pneumatic tire, etc.). Since the spread of these factors is difficult to consider, the rolling resistance coefficient for all the wheels of the car and the condition of the wheels are usually assumed to be the same in the calculations [33]. Under these assumptions, the rolling resistance force is calculated as follows:

$$W_{\mathrm{move}}=f\cdot G_{\mathrm{RS}},$$

(1)

where G_RS is the weight of the rolling stock (a dump truck).

The value of the rolling resistance coefficient along the horizontal section of the track depends on the speed of the vehicle. The most common empirical expressions of this dependence are of the following form:

$$\mathrm{and} f=\left\{\begin{array}{ll}0.0165\hfill & \mathrm{when} v\le 15 \mathrm{m}/\mathrm{s}\hfill \\ 0.0165+3.6\cdot {10}^{-4}(v-15)\hfill & \mathrm{when} v>15 \mathrm{m}/\mathrm{s},\hfill \end{array}\right.$$

where f is the rolling resistance coefficient when driving at a speed of $v$ along the track.

The values of the rolling resistance coefficient for various coatings of track structures are given in

Table 1. Values of the rolling resistance coefficient for various coatings.

Type of Road	F
Cement or asphalt pavement in good condition	0.012–0.018
Asphalt or asphalt pavement in satisfactory condition	0.018–0.02
Crushed stone or gravel highway treated with organic binders	0.02–0.025
Crushed stone or gravel highway without treatment	0.03–0.04
Cobblestone pavement in good condition	0.023–0.03
Cobblestone pavement with potholes	0.035–0.05
Dirt roads after rain	0.05–0.15
Wet sand	0.08–0.15
Quicksand	0.15–0.3
Snowy roads rolled and cleared	0.03–0.05

[34].

The aerodynamic component of the forces resisting the movement manifests itself in the form of the appearance of zones of high and low air pressure, which contributes to the formation of turbulence. At the same time, the largest share of energy (up to 60%) when overcoming air resistance is spent on the formation of air vortices [35].

Based on aerodynamic studies of the motion of a body of invariable shape in the air at a constant velocity of movement, the drag force $W_{\mathrm{r}.\mathrm{air}}$ is established to be approximately proportional to the product of the square of the velocity by the $S_{cross}$ area of the transverse (midship) section of a dump truck. Considering the streamlining ${\mathsf{\alpha }}_{air}$ coefficient, the calculation formula for determining an aerodynamic drag takes the following form:

$$\begin{array}{l}{W}_{\mathrm{r}.\mathrm{air}}={\mathsf{\alpha }}_{air}{S}_{cross}{v}^2,\\ S_{cross}=B_{ov}{H}_{ov}\end{array}$$

(2)

where $S_{cross}$ is the track width of the car; $H_{ov}$ and $B_{ov}$ are its overall height and width, respectively; and ${\mathsf{\alpha }}_{air}=0.6\dots 0.7 \mathrm{N}·{\mathrm{s}}^2/{\mathrm{m}}^4$.

During acceleration, energy is also spent on overcoming the forces of inertia [36], which depend on the mass of a dump truck and the developed acceleration and can be calculated according to the expression

$$W_{in}=(1+\mathsf{\gamma }){\displaystyle \frac{G_{\mathrm{RS}}}{g}}{\displaystyle \frac{dv}{dt}},$$

(3)

where γ is the coefficient of rotating masses of the dump track; $(1+\mathsf{\gamma })=1.04+k_{\mathrm{d}.\mathrm{t}}{i}_{\mathrm{g}.\mathrm{r}}^2;$ k_d.t = 0.05–0.07; and I_g.r is the gear ratio of the gearbox.

Despite these forces, additional forces of resistance to movement also act on a dump truck while driving, whose first component is due to the presence of road slopes, and the second is due to turns [37].

The component of slopes is determined according to the expression

$$W_{\mathrm{slope}}=i_{\mathrm{slope}}{G}_{\mathrm{RS}}.$$

(4)

In the areas of fitting into curves, owing to the low speed of movement, the drag force can be neglected.

Therefore, the required tractive effort during the ascent at the time of acceleration is calculated according to the formula

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{move}+W_{r.air}+W_{in}+W_{slope},$$

(5)

and when moving at a constant speed

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{move}+W_{r.air}+W_{slope}.$$

(6)

During the uniform downhill movement, the tractive force of the drive decreases, since the movement of a dump truck is facilitated by the rolling force [38]. The calculated expression takes the following view:

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{move}+W_{r.air}-W_{slope}.$$

(7)

The useful work performed by the drive is determined by the expression

$$A=F_{\mathrm{tr}.\mathrm{eff}}l,$$

(8)

where l is the path traveled, and the energy consumed from the source amounts to

$$E=A/\mathsf{\eta },$$

(9)

where $\mathsf{\eta }={\mathsf{\eta }}_{\mathrm{mech}.\mathrm{tr}}\cdot {\mathsf{\eta }}_{conv}\cdot {\mathsf{\eta }}_{PSS};$ η_mech.tr = 0.93–0.95 is the efficiency of the mechanical transmission; η_conv = 0.98 is the efficiency of the converter; and η_PSS = 0.95–0.98 is the efficiency of the power supply system, accounting for losses at the traction substation and losses in the traction network in the case of the centralized power supply.

In the case of the autonomous power supply, there are no losses in the traction network, but there are losses due to the transportation of the battery as the weight of a dump truck with the battery increases [39]. In braking mode, part of the kinetic energy of a dump truck in the traction electric drive can be returned to the source due to recuperation [40]. Given that effective braking with maximum effort is depleted at speeds of v_end = 5–7 km/h, the amount of the energy returned should be determined by the formula

$$E_{\mathrm{rec}}={\displaystyle \frac{G_{\mathrm{RS}}}{2g}}(v_{\mathrm{start}}^2-v_{\mathrm{end}}^2)/\mathsf{\eta },$$

(10)

where v_start and v_end are the start and end speeds of the braking mode, respectively.

Analysis of expressions (1)–(10) shows that the energy consumption for movement depends on the speed and length of the path traveled by a dump truck. At the same time, the value of the speed in the quarry is determined by the conditions of safe operation, and the length of the track is determined by the parameters of the quarry (depth, area, and slope value). The total energy consumption during the performance of one cycle, including lifting a dump truck with a load from the pit, lowering an empty dump truck, and maneuvering at the loading and unloading sites, is described by the expression

$$E_{\Sigma }=(A_{\mathrm{asc}}+A_{\mathrm{des}}+2A_{\mathrm{man}})/\mathsf{\eta },$$

(11)

where A_man is the work performed during maneuvering in the quarry and for dumping.

Since shunting movements practically do not depend on either the speed of movement or the length of the track, they can be assumed as constant and not taken into account when determining the dependence of E(l,v, and i_slope). Then, the expression (9) will take the form

$$E_{\Sigma }=(A_{\mathrm{asc}}+A_{\mathrm{des}})/\mathsf{\eta }=\left[(F_{\mathrm{asc}}+F_{\mathrm{des}})l\right]/\mathsf{\eta },$$

(12)

where F_asc and F_des are, respectively, thrust forces during ascent and descent, determined by expressions (5) and (7). When determining the dependencies of energy expenditure [41] on each argument, we assume that the others are constants.

5. Numerical Simulation of Energy Characteristics of a Mining Dump Truck

As an example, the energy consumption of a Komatsu HD605-7 mining dump truck can be calculated. The Komatsu HD605-7 electric dump truck is equipped with DC electric motors, which are powered by the largest car battery, weighing 4.5 tons. The battery capacity in different versions ranges from 600 to 700 kWh. The electric dump truck has the following physical dimensions: the length is 9.4 m, the width is 4.2 m, and the height is 4.4 m (with the body raised, the height is 9 m). The rated payload of the dump truck is 181 tons; the weight of the dump truck without load is 146 tons. The maximum torque is 8199 N m, and the rated power of the drive axle engines is R_dr = 620 $\times$ 2 kW. The gear ratio of the gearbox is i_g.r = 35.2, the wheel diameter is D_wheel = 3 m. The length of the road is l = 1 km, the slope is 16%, and the speed during the stretch is v_str = 20 km/h.

For the mode of movement of the dump truck from the pit to the dump with a constant velocity, the forces of resistance to movement [42] according to expressions (1), (2) and (4) will be as follows:

$$W_{\mathrm{move}}=f{G}_{\mathrm{RS}}=55.7 \mathrm{kN};$$

$$W_{\mathrm{r}.\mathrm{air}}={\mathsf{\alpha }}_{\mathrm{air}}{S}_{\mathrm{cross}}{v}^2=116.8 \mathrm{N},$$

where ${\mathsf{\alpha }}_{\mathrm{air}}$= 0.7 N·s²/m⁴, $S_{\mathrm{cross}}=B_{ov}{H}_{ov}=31.6 {\mathrm{m}}^2;$

$$W_{\mathrm{slope}}=i_{\mathrm{slope}}{G}_{\mathrm{RS}}=52.3 \mathrm{kN}.$$

Since the forces of aerodynamic resistance to the movement of a dump truck [43] do not exceed 1% of the tractive effort when changing the speed from 10 to 50 km/h, they can be neglected from the standpoint of the permissible accuracy of engineering calculations. Then, the calculation Formulas (6) and (7) take the form

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{\mathrm{move}}+W_{\mathrm{slope}}, F_{\mathrm{tr}.\mathrm{eff}}=W_{\mathrm{move}}-W_{\mathrm{slope}},$$

And in order to overcome the forces of resistance to uphill movement, the traction drive of a dump truck must develop the following force:

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{\mathrm{move}}+W_{\mathit{slope}}=107.4 \mathrm{kN},$$

The torque developed by the engines on the wheel rim is equal to

$$M_{\mathrm{wheel}}=i_{\mathrm{g}.\mathrm{r}}{P}_{eng}/n_{eng}=874.4 \mathrm{kN}\cdot \mathrm{m},$$

where $n_{eng}$ = 3000 min⁻¹ = 50 s⁻¹ is the rated engine speed.

The truck traction on the wheel rim is

$$F_{\mathrm{tr}.\mathrm{wheel}}=2M_{wheel}/D_{wheel}=584.2 \mathrm{kN},$$

which is greater than the required value according to the conditions of the problem.

The removal of the cargo will require spending energy in accordance with (8)

$$E=F_{\mathrm{tr}.\mathrm{eff}}l=107.4\mathrm{MJ}.$$

The calculations are based on the condition of uniform traffic along the entire road. However, in reality, at the initial stage, a dump truck accelerates up to a speed of 20 km/h, braking at the end of the journey, lowering the speed up to 5 km/h with regenerative braking.

The value of the energy recovered during recovery according to (10) will be

$$E_{\mathrm{rec}}={\displaystyle \frac{G_{\mathrm{RS}}}{2g}}(v_{\mathrm{start}}^2-v_{\mathrm{end}}^2)\mathsf{\eta }=\mathrm{kJ},$$

and when accelerating to a speed of v_str, the energy is consumed in the amount of

$$E_{\mathrm{start}}={\displaystyle \frac{G_{\mathrm{RS}}}{g}}{\displaystyle \frac{v_{\mathrm{str}}^2}{2}}/\mathsf{\eta }=581.3 \mathrm{kJ}.$$

The calculations show insignificant values of the recuperation and start-up energy compared to the energy consumed when moving along the haul. Therefore, they can be neglected in further calculations. The energy consumed in shunting modes is also negligible [44].

The energy costs for the movement of an empty dump truck during the descent into the quarry are determined according to expression (7), and the values of the resistance forces included in the expression when moving at the lifting speed will be the same:

$$F_{\mathrm{tr}.\mathrm{eff}}=W_{move}-W_{slope}=2.7 \mathrm{kN}.$$

The energy consumed from the power supply at the launch of the truck into the pit is calculated according to (8)

$$E_{down}=F_{\mathrm{tr}.\mathrm{eff}}l=2.6\cdot 1000=2.8 \mathrm{MJ}.$$

Therefore, the total energy consumption for one shuttle flight according to (12) will be

$$E_{\Sigma }=\left[(F_{\mathrm{asc}}+F_{\mathrm{des}})l\right]/\mathsf{\eta }=124.6 \mathrm{MJ}.$$

The indices of the total energy expenditure as a function of the length of the road l in the quarry when driving at a speed of v = 20 km/h along a slope with a slope of i_slope = 16% are summarized in

Table 2. Indicators of the total energy consumption in functions of the road length.

l, km	0.5	1.0	1.5	2.0	2.5	3.0
Eσ, MJ	61.2	122.4	183.6	224.8	286	367.2

.

Table 2, containing the results of the calculations, confirms the effect of the length of the haul on the energy consumption at a given gradient.

The proposed method can be used to calculate the energy for a given slope value. The results of calculating the energy consumption in MJ for the movement of a dump truck at speeds v from 10 to 50 km/h with gradients of i_slope = 7, 14, and 21% and road lengths of l = 0.5–3 km are summarized in

Table 3. The results of the calculation of energy consumption during the movement of a dump truck.

		l, km	1	1.5	2	2.5	3.0	3.5
	Eσ, MJ
Islope = 7%	EΣ		62	123.3	187.2	247.7	306.7	369.9
Islope = 14%	EΣ		63	123.7	184.5	247.9	304	366.8
Islope = 21%	EΣ		62	123.2	183.4	247.3	306.7	369.4

.

The required tractive effort when climbing an 8% gradient will be F_tr.eff.asc/7 = 79.75 kN and F_tr.eff.des/7 = 28.25 kN when descending.

The required tractive effort when descending a slope of 24% will be F _{tr.eff.asc/21} = 131.25 kN and F_{tr.eff.des/21} = −23.25 kN when descending. The minus sign indicates that when descending a road with such a slope, it is necessary to apply braking or use the regenerative braking mode. In this case, the amount of recuperation energy is calculated using the formula

$$E_{\mathrm{rec}}=F_{\mathrm{tr}.\mathrm{eff}.\mathrm{des}/24}l,$$

and the total electricity consumption is found according to

$$E_{\Sigma }=\left[(F_{\mathrm{tr}.\mathrm{eff}.\mathrm{asc}/24}-F_{\mathrm{tr}.\mathrm{eff}.\mathrm{des}/24})l\right]/\mathsf{\eta }.$$

Analysis of the results obtained shows that the energy consumption of the traction drive of a dump truck practically does not depend on the slope of the quarry road and the speed of movement along it. At the same time, in the case of a small slope, energy is consumed during the removal of minerals and when a dump truck goes into the quarry. In the case of a large gradient, the energy consumption during the ascent increases, which is partially compensated by recovery during the descent into the quarry.

The use of the regenerative braking mode requires an energy storage device in the power supply system scheme [45], in which it is advisable to use a storage battery. In the case of the centralized power supply, it must be installed at the traction substation [46]. At the same time, even with the centralized power supply, it is necessary to place a storage device on a dump truck to power the traction motors in shunting modes, since it is impossible to place supports for the traction network in the loading area [47].

The parameters of the accumulator [48] in the centralized power supply scheme are determined based on the duration of the working day of a dump truck t_work at the maximum depth of the quarry. This is the duration of one cycle, consisting of the periods of lifting t and lowering t, the time of loading t_loading, and unloading t_unloading:

$$t_{\mathrm{work}}=n_{\mathrm{cycle}}(t_{\mathrm{asc}}+t_{\mathrm{des}}+t_{\mathrm{loading}}+t_{\mathrm{unloading}}).$$

The terms included in the formula change as the quarry deepens. Therefore, it is advisable to operate with weighted average values.

Since the energy is consumed by a dump truck drive from the battery only during shunting periods [49], knowing the number of cycles per shift, as well as the energy consumption in the E_man shunting modes, the required amount of energy E_shift consumed per shift is determined by the following expression:

$$E_{\mathrm{shift}}=n_{\mathrm{cycle}}{A}_{man}/({\mathsf{\eta }}_{\mathrm{conv}}\cdot {\mathsf{\eta }}_{\mathrm{mech}.\mathrm{tr}}).$$

(13)

The loading time is t_loading = 10 min, t_unloading = 3 min, and t_man = 5 min at a speed of v_man = 5 km/h; the length of the road is l = 3000 m; the speed of movement along the road is v_road = 20 km/h; and the voltage of the traction battery is U_tr.b = 400 V. Assuming the above-mentioned, we can calculate the parameters of the storage battery.

The number of cycles per shift is determined by the formula

$$n_{\mathrm{cycle}}={\displaystyle \frac{t_{\mathrm{work}}}{t_{\mathrm{loading}}+t_{\mathrm{unloading}}+2l/v_{\mathrm{road}}+2t_{\mathrm{man}}}}=4.$$

A single-cycle maneuvering operation is

$$A_{\mathrm{man}}=(F_{\mathrm{asc}}+F_{\mathrm{des}})v_{\mathrm{man}}{t}_{\mathrm{man}}=26.4 \mathrm{MJ},$$

and during the shift, the energy expenditure according to (13) will be

$$E_{\mathrm{shift}}=4\cdot 25.8/(0.98\cdot 0.95)=112.3 \mathrm{MJ}.$$

With a voltage of 400 V on the traction battery, its capacity should be 77 Ah. In the case of the autonomous power supply, the capacity of the battery increases up to 1046 Ah.

As the battery is discharged, its output voltage decreases [50], which deteriorates the dynamic characteristics of the drive. In order to eliminate this phenomenon and to extend the service life of the battery, it is advisable to limit its discharge to 80% of the nominal value. In this case, the capacity of the battery should be raised to 5200 Ah.

An alternative solution to a battery-type storage device is a capacitor storage device [51,52], which has a number of advantages:

Its charging process is almost instantaneous since it is not associated with the chemical reactions characteristic of any type of battery.

The value of charge and discharge currents does not depend on internal electrical resistance and is determined only by the parameters of charging circuits and consumer circuits.

A decrease in temperature is known to decrease the rate of chemical reactions in galvanic cells with their complete cessation at air temperatures below −30… −40 °C [53]. This requires thermostats to be installed on the rolling stock, which complicates the design of a power supply, and high temperatures (in summer) require cooling.

Capacitors connected in series and parallel, like galvanic cells in a storage battery, do not require the use of special measures to balance the currents, flowing in them, and the voltage applied to them due to the slight difference in their electrical parameters. The charge and discharge currents of each cell in a storage battery formed by a multitude of elements with a significant range of parameters must be regulated. This significantly complicates the circuit of the storage device power circuits [54].

At the same time, the capacitor storage device also has a significant drawback due to the requirement for stability of the voltage on its terminals, feeding the traction drive [55]. To clarify this point, the experimentally obtained output characteristic of the battery U_bat(I_,bat) must be referred to (Figure 5).

It is known from the theory of the development of electric machines that the deviation in the voltage, supplying the motor with power from the nominal value, changes its characteristics [56,57]. In particular, a decrease in voltage decreases tractive effort, which is undesirable.

During operation, the value of the supply voltage varies from U_max to U_min. In the absence of battery recharging, the working zone of dependence U_bat (I_bat) lies within the shaded area in the figure. Therefore, the value of the battery charge Q_bat, expressed in ampere-hours, can be calculated according to [58]

$$E_{\mathrm{bat}}=U_{\mathrm{bat}}{Q}_{\mathrm{bat}},\mathrm{where} Q_{\mathrm{bat}}=E_{\mathrm{bat}}/U_{bat}.$$

In cases where the recuperation current of a braking dump truck should be limited by the value of the accumulator permissible according to the passport data, a capacitor accumulator should be connected to the vehicle in parallel with the accumulator [59]. To determine the value of the capacitor capacitance, we set the condition that it is inadmissible to reduce the voltage value below 15% of the rated (U_min = 0.15 U). Then, the required capacitance of the capacitor for receiving the recuperation energy [60], suggesting that the minimum voltage is retained on it, will be determined as

$$C={\displaystyle \frac{2E_{\mathrm{rec}}}{U_{\mathrm{nom}}^2-U_{\min }^2}}.$$

It is known from the theory of electric traction that when the voltage on the motor decreases, the power and speed developed by it decrease, and energy consumption increases [61]. A graphic representation of this effect by the example of a DC traction motor of series excitation is shown in Figure 5. When the value of the supply voltage changes during movement from U_max to U_min, the speed of the rolling stock increases along the curve U_var. Such a curve is typical when using a battery, since when discharging, the voltage on it changes within the shaded zone, reflecting the change in the value of the charge accumulated in it and the decrease in the output voltage in this regard. The experimentally obtained curve is characteristic of the battery, because when discharging, the voltage on it changes within the shaded area, reflecting the change in the accumulated charge value in it and the decrease, in this respect, of the output voltage value (Figure 6).

When using a capacitor, the U_var curve starting at the point U_max of the maximum voltage at the endpoint will have a lower velocity value. In view of this, to “raise” the characteristic to coincide with the curve of the battery source, it is necessary to increase the capacitance of the capacitor or ultimately increase its mass.

6. Discussion

In order to estimate the percentage increase in capacitance, and, consequently, the mass of the capacitor, and to achieve the coincidence of characteristics, we will use the following ratios:

• The energy consumed by the movement of a vehicle with a battery

  $$\begin{array}{l}E=U_{\mathrm{bat} \mathrm{nom}}{Q}_{\max }-U_{\mathrm{bat} \min }{Q}_{\min }=(1-k_U{k}_Q)U_{\mathrm{bat} nom}{Q}_{\max }\\ \hspace{1em}=(1-0.85\cdot 0.25)U_{bat nom}{Q}_{\max }=0.7875U_{bat nom}{Q}_{\max },\end{array}$$

where k_U = U _{bat min}/U_{bat nom} is the voltage drop factor (usually k_U = 0.85 − 0.87; k_Q = Q_min/Q_max; Q_min = 0.25 Q_max);

• The value of the capacitor energy consumed for the movement of the vehicle

  $$E={\displaystyle \frac{C_{\mathrm{cap}}{U}_{bat nom}^2}{2}}-{\displaystyle \frac{C_{\mathrm{cap}}{U}_{bat \min }^2}{2}}=0.7875U_{bat nom}{Q}_{\max },$$

where

$$C_{\mathrm{cap}}={\displaystyle \frac{5.67Q_{\max }}{U_{\mathrm{bat} nom}}}.$$

When using the full energy of the capacitor (discharge to zero), the required value of its capacitance is ${C^{\prime }}_{\mathrm{cap}}$

$${C^{\prime }}_{\mathrm{cap}}={\displaystyle \frac{2E}{U_{\mathrm{bat} nom}^2}}={\displaystyle \frac{2Q_{\max }}{U_{\mathrm{bat}\mathrm{nom}}}}.$$

As a result, to ensure the operation of a drive with a capacitor energy source in terms of characteristics identical to those of an accumulator, it is necessary to increase the capacitor capacity as follows:

$$C_{\mathrm{cap}}/C_{\mathrm{cap}}^{\prime }={\displaystyle \frac{5.67Q_{\max }}{U_{\mathrm{bat}\mathrm{nom}}}}/{\displaystyle \frac{2Q_{\max }}{U_{\mathrm{bat}\mathrm{nom}}}}=2.84 times$$

Accordingly, the analysis of the energy efficiency of electrically driven heavy-duty mining dump trucks used in open-pit mining showed the comparability of energy consumption when using three different power supply schemes: centralized, autonomous, and combined. The obtained calculated data, which demonstrate almost identical energy consumption in all three options, indicate the need for a comprehensive economic analysis to substantiate the choice of the optimal scheme [62,63]. It is noteworthy that neither the length of the transport route (the distance from the loading point to the dump) nor the angle of ascent significantly influences the total energy consumption. The average daily energy consumption per dump truck was approximately 110 MJ.

A more in-depth study of the autonomous power supply, using either batteries or double electric layer capacitors (supercapacitors), has demonstrated the advantages of using batteries in terms of weight and size characteristics. However, the use of batteries increases the weight of a dump truck and significantly depends on the duration of operation without recharging. The charging mode must be optimized after each production and transport cycle. After several hours of operation or at the end of a shift, the mode requires additional research and simulation, taking real operating conditions into consideration. As an alternative solution, the prompt replacement of a discharged battery with a charged one is considered, which allows the continuous operation of the equipment to be ensured. Compared to rechargeable batteries, a larger capacity is required to provide similar performance with supercapacitors. This significantly complicates and increases the cost of the design [64].

Analysis of the energy efficiency and the regenerative braking system [65] reveals low efficiency of recuperation when lifting cargo from the quarry. In the process of lifting from the lower horizons of the pit to the dump and back, kinetic energy is converted into heat, reducing the efficiency of recovery accounting for the technological cycle of the operation. In these circumstances, the rejection of the regenerative braking system in open-pit electric dump trucks removing soil or solid minerals from the open-pit mine to the top seems to be economically feasible. Eliminating the recuperation system will simplify the design, reduce the cost of the truck, and free up usable volume effectively used to increase battery capacity, resulting in longer battery life and improved overall system efficiency. Consequently, the optimization of the power supply system must consider energy consumption, economic factors, and technological features of the operation of mining dump trucks.

However, while this study suggests abandoning regenerative braking in certain uphill mining scenarios, several potential drawbacks must be considered. The elimination of regenerative braking may have implications for vehicle safety, particularly during downhill operations. The primary braking system will need to be adequately sized to handle the full kinetic energy of a loaded dump truck, which could increase the risk of brake overheating and reduce braking performance in emergencies. The effect of this has not been fully addressed in our study and requires additional analysis. This might necessitate more frequent brake maintenance and replacement, increasing operational costs and downtime. Further investigation into the specific braking performance requirements and the implementation of other safety measures, such as enhanced auxiliary braking systems, would be necessary to mitigate these risks. Furthermore, the absence of regenerative braking could affect the durability of the electric motor and other components in the long run. The regenerative braking system can reduce wear and tear of the main braking system; hence, its removal may increase the frequency of its maintenance. This area needs further exploration to fully assess the impact of the proposed approach on the system’s operational reliability.

When comparing battery and supercapacitor options for the autonomous power supply, beyond mass and volume characteristics, a comprehensive Lifecycle Assessment (LCA) is crucial for addressing environmental concerns. LCA considers the entire environmental impact of a technology, starting from raw material extraction and manufacturing, through its operational lifetime, up to end-of-life management (recycling or disposal).

Batteries, while offering high energy density, often have LCA challenges. The extraction of raw materials like lithium, cobalt, and nickel can have significant environmental and social impacts. Manufacturing processes are energy-intensive, and the end-of-life management of batteries poses a considerable challenge due to the presence of hazardous materials. Recycling technologies for lithium-ion batteries are still developing, and improper disposal can lead to soil and water contamination.

Supercapacitors, on the other hand, generally have a more benign LCA profile. They typically utilize more abundant and less toxic materials like carbon. The manufacturing processes are often less energy-intensive than battery production processes. Supercapacitors also boast a longer lifespan and better recyclability compared to those of batteries. However, the higher volume and weight required for a supercapacitor system to match the energy storage capacity of a battery can indirectly increase the vehicle’s energy consumption during operation. This must be factored in the LCA.

A comprehensive LCA should consider the following:

Material extraction involves the environmental and social impacts of mining and processing raw materials.

Manufacturing deals with energy consumption, water usage, and emissions during component and system assembly.

Transportation includes energy used to transport materials and components.

Operation considers energy efficiency and emissions during the operational lifetime of a dump truck.

End-of-life concerns recycling potential, disposal methods, and associated environmental impacts.

This area needs further exploration to fully assess the impact of battery or supercapacitor choice on the system’s operational reliability and carbon footprint.

Therefore, while supercapacitors may appear less attractive due to their size and cost, a holistic LCA perspective may reveal a lower overall environmental impact compared to batteries, making them a more sustainable option for certain mining applications. Our future work should focus on conducting a detailed LCA to compare these energy storage technologies within the specific context of electric mining dump truck operations.

A comparison of the weight and size indicators of the energy source in the autonomous power supply (a battery or double-layer electric capacitor) indicates the feasibility of using a battery. A detailed Lifecycle Assessment is needed to accurately determine the environmental impact. The use of a battery increases the weight of a dump truck and significantly depends on the drive power time. At the same time, various options for its recharging are possible (after one excavation cycle or after operating for several hours or shifts). Determining the optimal option requires additional research.

Future research directions are built upon the findings of this study, and several options for future research emerge.

Optimization of charging protocols means investigating advanced charging protocols (e.g., fast charging and opportunity charging) to minimize downtime and maximize battery lifespan in mining environments. The research should explore the impact of different charging profiles on battery degradation and overall system efficiency. This study should include the integration of smart charging algorithms and adapting to real-time operating conditions.

The integration of renewable energy sources implies exploring the integration of on-site renewable energy sources, such as solar or wind power, to charge electric dump trucks. This would reduce the reliance on grid electricity and further minimize the environmental footprint of mining operations. Research should focus on designing optimal hybrid power systems, combining renewable energy with battery storage.

Advanced battery technologies provide evaluating the performance of emerging battery technologies, such as solid-state batteries or lithium–sulfur batteries, in mining applications. These technologies offer the potential for higher energy density, improved safety, and longer lifespan compared to conventional lithium-ion batteries.

Enhanced regenerative braking systems involve researching advanced control strategies for regenerative braking systems to maximize energy recovery and improve braking performance. This could include exploring the use of supercapacitors as a buffer to capture and release energy during regenerative braking, especially in steep downhill sections. Further study should be undertaken to determine the longevity of braking systems.

Real-world data validation suggests conducting more extensive field tests of electric dump trucks in various mining environments to validate the simulation results and gather real-world data on energy consumption, battery performance, and maintenance requirements. Fleet management and optimization include developing fleet management tools and optimizing the scheduling and routing of electric dump trucks based on real-time energy consumption, charging availability, and operating conditions.

High-energy density batteries, dealing with advancements in lithium-ion battery chemistry, such as using silicon anodes and nickel-rich cathodes, significantly increase energy density [64]. Solid-state batteries, which replace the liquid electrolyte with a solid material, offer the potential for improved safety, higher energy density, and longer lifespan. Regenerative braking control involves advanced control algorithms for regenerative braking, being developed to improve energy recovery and minimize wear of friction brakes. Battery management systems (BMSs) suggest improved BMS algorithms, enhancing battery performance and lifespan by optimizing charging and discharging profiles, monitoring cell health, and preventing overcharging and deep discharging [64]. Wireless charging provides the possibility of easy charging capabilities and optimization [65].

7. Conclusions

Studying the energy efficiency of using pneumatic tire vehicles with an electric drive in open-pit mining allows determining, when using heavy-duty dump trucks in quarrying, their power supply provided by three different circuit solutions: centralized, autonomous, and combined. Energy consumption, as calculations show, is commensurate in all the cases. Therefore, the determination of the preferred option requires a detailed economic justification.

The energy consumption for each of the three power supply options is practically not affected by the length of the arm from the loading point to the dump and by the steepness of the ascent. During the shift, the energy consumption per mining dump truck is about 110 MJ. The comparison of the mass and size indicators of the energy source with the autonomous power supply (an accumulator or double electric layer capacitor) indicates the expediency of using the battery. The use of the battery increases the weight of a dump truck and is significantly dependent on the power supply time of the drive. At the same time, various options for recharging it are possible (after one cycle of removal, after operating for several hours, or shifting). Determining the best option requires additional research. In addition, the option of replacing a discharged battery with a charged one can be used. To ensure the operation of the drive with a capacitor energy source in terms of characteristics identical to the battery, it is necessary to increase the capacitor capacity almost 2.84 times. The efficiency of energy use and the recuperation system are substantiated to be directly dependent on the operating modes of a mining dump truck. When it transports coal or waste rock from the depths of the pit to the top and then transports it to the dump site, the use of recovery energy is almost reduced. Therefore, it is not necessary to install the recuperation system on mining electric dump trucks, simplifying and reducing the cost of the design of a dump truck and the useful geometry of the freed-up space can be used to increase the capacity of batteries.

The results of this study can be used at the following stages: design of machines and energy sources; justification of energy-efficient solutions; evaluation of operating modes; and design of control systems for electric quarry dump trucks.