The plug-in hybrid vehicles (PHEV) technology can effectively address the issues of poor dynamics and higher energy consumption commonly found in traditional mining dump trucks. Meanwhile, plug-in hybrid electric trucks can achieve excellent fuel economy through efficient energy management strategies (EMS). Therefore, a series hybrid system is constructed based on a 100-ton mining dump truck in this paper. And inspired by the dynamic programming (DP) algorithm, a predictive equivalent consumption minimization strategy (P-ECMS) based on the DP optimization result is proposed. Based on the optimal control manifold and the SOC reference trajectory obtained by the DP algorithm, the P-ECMS strategy performs real-time stage parameter optimization to obtain the optimal equivalent factor (EF). Finally, applying the equivalent consumption minimization strategy (ECMS) realizes real-time control. The simulation results show that the equivalent fuel consumption of the P-ECMS strategy under the experimentally collected mining cycle conditions is 150.8 L/100 km, which is 10.9% less than that of the common CDCS strategy (169.3 L/100 km), and achieves 99.47% of the fuel saving effect of the DP strategy(150 L/100 km).
Recently, the energy consumption of conventional mining dump trucks has received increased attention as energy and environmental issues have become more prominent. Conventional large mining dump trucks are typically used in open-pit mining with electric drive. The trucks do not have power batteries. Therefore, they rely on the main brake and retarder for downhill braking. The mechanical energy generated during braking is usually converted to heat energy and dissipated, resulting in wasted energy. In addition, when going uphill with a full load, mining dump trucks must reduce speed to increase torque due to increased power demand, resulting in increased fuel consumption. Studies have shown that approximately 30% of all energy used in mining is consumed by the fuel consumption of mining dump trucks [
The energy management strategy (EMS) is essential for PHEVs to achieve fuel savings targets [
Optimization-based strategies aim to determine the best value for a control parameter of a constructed system model, by means of training or computation, in order to attain system optimization. These strategies can be categorized into two groups: those based on intelligent algorithms, and those based on optimization theory. Optimization methods used for optimization-based strategies can be divided into classical, metaheuristic, and dynamic optimization methods. Classical optimization methods are mainly based on mathematical theories and principles and are generally applicable to problems where the parameters of the problem are certain and well-defined. This approach relies on mathematical derivations and proofs and can usually provide an exact optimization solution, but often cannot be applied when the problem is complex or the parameters are not certain. Metaheuristic optimization methods are mainly derived from the concept of natural heuristics and have the advantage of being able to deal with problems with a large search space, the existence of local optimal solutions and complex constraints [
Intelligent algorithm-based optimization strategies obtain optimal or near-optimal solutions from model training results. Kong et al. [
The other approach is an optimization strategy based on optimal control theory, including global and transient optimization algorithms. One representative global optimization strategy is the DP algorithm, references [
Incorporating the PHEV-equipped hybrid power system into the mining dump truck’s structure, its multiple power sources can improve vehicle dynamics. The existence of the Rechargeable Energy Storage System (REESS) can replace the retarder for auxiliary braking and realize braking energy recovery, and this can also help the engine work for a longer time in the high efficiency zone, improving fuel utilization efficiency. The design of a reasonable and efficient EMS to further minimize fuel consumption and improve the fuel economy of mining dump trucks has become the focus of existing research. EMS applied to mining dump trucks must prioritize safety issues. Existing studies typically use EMS to passively constrain battery SOC and adjust it through a compensation mechanism when battery SOC exceeds upper and lower limits, which can have serious consequences in practical applications. For example, in the long downhill process, the vehicle performs the brake energy recovery according to the set process, and the SOC gradually increases to reach the set upper limit, at which time the compensation mechanism in the control strategy is triggered to adjust the battery SOC, but the vehicle is likely to be unable to continue the brake energy recovery because the battery is full, thus losing the auxiliary brake function, which is very dangerous in the long downhill process. To meet safety requirements, active control constraints on battery SOC are needed. Therefore, the EMS must be designed with global planning of battery SOC in advance as a strong constraint for the following optimization process, and real-time vehicle control in the final stage. Among the EMS discussed above, the intelligent algorithm-based EMS is still in the initial research stage, and its substantial computational burden makes practical applications difficult. The CDCS strategy, as a common EMS in mining dump trucks, often does not perform well in the face of special conditions (e.g., extreme weather); The ECMS algorithm, as a transient optimization strategy, selecting the appropriate EF can achieve near-optimal results. However, mining operating conditions vary greatly during the same work cycle (e.g., uphill and downhill, no load and full load), and achieving the desired performance with a fixed EF is difficult.
To bridge the foregoing research gaps, this paper proposes a predictive equivalent consumption minimization strategy (P-ECMS), the core content of which includes global planning and stage parameter optimization, and the optimization results are used to realize the control of the vehicle using the ECMS algorithm, so that mining dump trucks can obtain the optimal EF under the current operating stage, and the EF can be changed with the change of working conditions, to meet the demand for energy saving and emission reduction, reduce fuel consumption. The details of the P-ECMS strategy are shown below:
The predictive equivalent consumption minimization strategy is proposed. The global planning is carried out for the cyclic conditions of the mine, and the optimal control manifold and the reference trajectory of the battery SOC are obtained by the DP algorithm. Apply the above SOC reference trajectory to guide the current SOC in the following real-time stage parameter optimization process and obtain the EF required by the ECMS algorithm in the current stage. Then the ECMS algorithm is used to achieve real-time control of mining dump trucks. The map information is used to construct the mining conditions for simulation experiments. The results show that the proposed P-ECMS strategy outperforms the common CDCS strategy in terms of fuel economy and is very close to the optimal solution under the DP strategy.
The rest of the article is organized as follows.
This paper focuses on a 100-ton mining dump truck and develops a series of hybrid systems to improve its power and fuel economy. The series hybrid structure is shown in
Symbol | Parameters | Values |
---|---|---|
Full vehicle mass | 100,000 kg | |
Vehicle windward area | 10.6 m^{2} | |
Tire rolling radius | 0.75 m | |
Air drag coefficient | 0.7 | |
Rolling resistance factor | 0.02 | |
The low calorific value of diesel fuel | 3.3 * 10^{7} J/L | |
Main reducer ratio | 17.8 | |
Transmission 1–4 gear ratios | [6.5 4.0 2.1 1] |
Without considering the dynamic characteristics of the engine, the engine model is simplified to a static model with fuel consumption rate and efficiency defined as
The engine power should be satisfied as
The main engine parameters are shown in
Parameters | Values |
---|---|
Engine displacement | 12.54 L |
Maximum power | 361 kW |
Rotational speed range | 1100–2100 rpm |
High-efficiency area power range | 160–270 kW |
This paper selects two permanent magnet synchronous motors to drive the vehicle in series, with their main performance parameters listed in
Parameters | Values |
---|---|
Rated power | 215 * 2 kW |
Maximum power | 270 * 2 kW |
Maximum speed | 3500 rpm |
Rated speed | 1500 rpm |
Parameters | Values |
---|---|
Rated power | 300 kW |
Maximum power | 375 kW |
Maximum speed | 2000 rpm |
Rated speed | 1500 rpm |
Lithium iron phosphate batteries, with their high power and energy density, safety, and long service life, are selected as the battery pack for the hybrid power system. A simple and effective internal resistance battery model is established [
In the formula:
SOC | Battery internal resistance |
---|---|
10% | 10.4 |
30% | 4.6 |
50% | 4.4 |
70% | 4.7 |
90% | 4.8 |
Parameters | Values |
---|---|
Battery pack capacity | 108 kWh |
Series and parallel form (S * P) | 168 * 10 |
Battery pack voltage | 621.6 V |
Battery efficiency | 0.95 |
The road resistance, air resistance, and acceleration resistance when the hybrid mining dump truck is running on a road with a slope with a full load are shown as
The driving force provided by the traction motor to the vehicle can be expressed as
The power balance equation is shown as
To provide a better comprehension of the P-ECMS strategy, this chapter explains two algorithms employed for it, the ECMS algorithm and the DP algorithm, in detail in the following two sections.
The ECMS algorithm is a transient optimization algorithm that aims to minimize equivalent fuel consumption while satisfying the driver’s demand. The objective function as
Subject to the physical constraints of
In the formula:
The DP algorithm is based on the Bellman optimality principle. In solving the optimal control problem, the DP algorithm divides the control problem into several periods. In each period, the optimal solution in the current state is calculated by combining the optimal solution of the previous period to obtain the optimal control manifold.
The equation of state for an optimal control problem can be expressed as
Its cost function is
In the formula:
The optimal control problem is solved by controlling the variables u to minimize or maximize
The cumulative cost function at step
After the above backpropagation procedure, the optimal cost function of the whole trip
To obtain good fuel economy and solve the common problems of mining dump trucks, this paper proposes a predictive equivalent consumption minimization strategy based on the DP optimization results, P-ECMS, to improve fuel economy. Given the single repetition of the mining dump truck’s working cycle and the significant differences between stages, the process can be divided into different stages. The optimal EF for each stage can be calculated in real time to achieve global optimization.
First, geographic information data is collected through real vehicle tests and processed to construct the mining site map. Since mining dump trucks operate under single-repetition working conditions, the collected driving data can be used to create typical cycle working conditions corresponding to the map. Then, the optimal global results for these typical cycle working conditions are solved offline using the DP algorithm. Segmentation points are determined based on characteristic points of the typical cycle condition (such as speed, slope, and load change points). By performing the stage parameter optimization based on the map information and the current SOC, the current optimal EF is obtained and applied to the ECMS algorithm, the realization of real-time control based on this optimal EF. The P-ECMS flow chart is shown in
The P-ECMS strategy comprises global planning based on the DP algorithm, stage parameter optimization, and control implementation using the ECMS algorithm. This section describes global planning using the DP algorithm in the offline state to determine the optimal control manifold and the optimal reference trajectory of the battery SOC.
For the energy management problem of a series hybrid mining dump truck, the battery SOC is taken as the state variable, and the
In the formula:
The optimal control problem is expressed as
In the formula:
The DP algorithm is utilized to solve the above problem. First, time is discretized in 1-second steps, battery SOC in 1%, and generator set output power in 10 kW steps. The variable grid is obtained and solved in two steps in the next process. For the case where the state variables are not in the grid, it is generally solved by linear interpolation to finally obtain the optimal control manifold
The inverse derivation process in the DP algorithm is shown below:
(1) Initialization: The state variable battery SOC is discretized over time into
(2) Solve the optimization subproblem.
(3) If
The forward derivation process in the DP algorithm is shown below:
(1) Initialization: Initial value of battery SOC
(2) Apply the interpolation method to calculate the
(3) Calculate the
(4) Calculate the state variables at step
(5) If
This section divides the whole trip into stages and obtains the optimal EFs for each stage by optimizing stage parameters with the optimal control manifold and the optimal reference trajectory of the battery SOC obtained in the previous section.
In ECMS algorithm, operating condition changes can affect the EF’s optimization effects. To adaptively adjust the EF, commonly used methods include real-time feedback based on battery SOC, offline optimization coupled with online identification, and regulation based on predictive information.
The cycle conditions of mining dump truck operation are relatively fixed, and the road information is relatively unique. Therefore, typical mining cycle conditions established by condition information collected through multiple cycle operations can be used as the real global conditions for predicting vehicle operations. The cycle is segmented and each stage is optimized separately due to the large variability of working conditions at different stages within the cycle.
First, the global segmentation process is performed based on the working condition information and the segmentation points determined in the offline state, which is divided into
The stage parameter optimization algorithm follows the steps below:
(1) Initialization: Load the map information and load the optimal control manifold
(2) Coordinate transformation: Get the current coordinates
(3) Stage update: If
(4) Get the current battery SOC information, which is recorded as
(5) Determine the stage target power. According to the result of the DP algorithm, the stage target power
(6) Solve the stage parameter optimization subproblem.
(7) Output the optimal EF
This section utilizes the optimum EF, which was obtained from the stage parameter optimization algorithm discussed earlier, to implement the ECMS algorithm. The aim is to achieve the best power distribution between the genset and the batteries and to obtain optimal fuel economy.
The objective function of the series hybrid system when applying the ECMS algorithm can be expressed as
In the formula:
In the formula:
In the formula:
The EF determines the performance of the ECMS algorithm. By applying the optimal EF
In this paper, an open-pit mining was selected as the test site, and the line-cycle test method was chosen for geographic data collection, considering the cost, cycle time, test conditions, and representativeness of geographic information. During the test, the driver was required to drive skillfully along a pre-planned test route, following the traffic flow during the working day for data collection and driving smoothly without overtaking or deliberately slowing down.
The driving condition of a mining dump truck in a mining are relatively fixed. After loading in the mining area, it travels uphill at a slower speed, then during the unloading area at a higher speed on flat roads, and finally returns empty to complete a cycle. In summary, the driving conditions of a mining dump truck mainly consist of four processes: full-load uphill, full-load flat road, empty-load downhill, and empty-load flat road.
To verify the proposed P-ECMS, using the above cycle conditions, simulations were conducted using ADVISOR and Matlab based on the system model established in
The diagram shows that during the empty-load flat road phase before the downhill phase, the truck operates in the electric mode, and the generator set is inactive. During the empty-load downhill phase, the generator set remains off, the truck recovers braking energy, and the traction motor reverses to recharge the battery pack. After the downhill stage, the truck is loaded, and in the full-load flat road phase, it is again driven in the electric mode, only the battery pack providing power to the traction motor. As the truck enters the full-load uphill phase, the power demand increases and the generator set is activated. During this stage, the generator set provides power to the traction motor and charges the battery pack. After the climb, the truck’s power demand decreases, and it is driven in the electric mode during the full-load flat road phase. During the full-load uphill phase, the engine cannot operate efficiently for long periods, as seen from the generator set output, resulting in more fuel being consumed.
For the cycle conditions of the mining, the DP strategy results are shown in
The DP results show that the battery SOC should be high before the mining truck goes uphill. This allows the engine operating point to be adjusted to work in the high efficiency zone while meeting the power demand, thus reducing fuel consumption.
Based on information about working conditions, such as mining site slope changes, vehicle load changes, and vehicle speed, the working conditions can be divided into 16 stages. Simulation results under the P-ECMS strategy when operating in CS mode are shown in
The EF for each stage is obtained using the stage parameter optimization algorithm. Combined with the change of this factor and considering the whole power demand, the truck can reach the desired target SOC as much as possible when operating in different stages, achieving optimal power allocation in each stage. For the whole range of conditions, the truck operation mode under the P-ECMS strategy is similar to that under the DP strategy, the generator set operating during the empty-load flat road phase and the full-load flat road phase to maintain a higher battery SOC enables the battery pack to provide sufficient power during uphill. However, compared to the DP strategy, during uphill operation, the generator set output power is lower, and the battery pack output power is higher, the engine operating time in the high efficiency zone is shorter compared to the operating time in the DP strategy, resulting in slightly higher fuel consumption.
When sufficient charging time is available, the plug-in hybrid mining dump trucks can operate in Charge-Depleting (CD) mode for improved fuel economy. Assuming a 12-hour operation in CD mode, we set the initial SOC at 0.8 and the minimum SOC throughout the operation at 0.3. The changes in fuel consumption and battery SOC during the operation under the P-ECMS strategy are shown in
The results of the CDCS strategy, the DP strategy, and the P-ECMS strategy are shown in
Parameter | CDCS | DP | P-ECMS (CS) | P-ECMS (CD) |
---|---|---|---|---|
Battery SOC at the moment of start moment | 0.58 | 0.58 | 0.58 | 0.8 |
Battery SOC at the moment of termination | 0.561 | 0.582 | 0.582 | 0.3 |
Fuel consumption (average) (L/100 km) | 168.7 | 150.1 | 150.9 | 143 |
Equivalent fuel consumption (L/100 km) | 169.3 | 150 | 150.8 | – |
Although both in the DP strategy and in the P-ECMS strategy, the generator set operates during the empty-load flat road phase and the full-load flat road phase, the fuel consumption results are lower than those of the electric mode under the CDCS strategy. Under the P-ECMS strategy, the equivalent fuel consumption is 150.8 L/100 km, 10.9% lower than the CDCS strategy (169.3 L/100 km) and 0.53% higher than the DP strategy(150 L/100 km). The battery SOC of the P-ECMS strategy under typical mining cycle conditions compared to the DP strategy is shown in
In summary, the P-ECMS strategy designed in this paper can more reasonably allocate power between the generator set and battery pack through real-time control, enabling the engine to operate more efficiently and reduce fuel consumption. It also has good power maintenance characteristics, reducing the frequency of stopping and charging for hybrid mining dump trucks, which improves transportation efficiency.
This paper proposes a predictive equivalent consumption minimization strategy based on the DP optimization results, P-ECMS. Based on a 100-ton conventional mining dump truck, a series hybrid system is constructed. Then, the collected driving data can be used to create typical cycle working conditions. We use the DP algorithm offline to perform global planning for the mining site cycle working conditions to obtain the optimal control manifold and the SOC reference trajectory. The SOC reference trajectory is then applied to guide the battery SOC in the subsequent real-time stage parameter optimization process to obtain the EF in the current stage and applied to the ECMS algorithm, the realization of real-time control based on this optimal EF.
(1) The CDCS strategy prioritizes driving the truck in electric mode, which results in a lower battery SOC when the mining truck is driving uphill. This increases the power output of the generator set. In contrast, although the engine block of the mining dump truck under the P-ECMS strategy is always in operation during the empty-load flat road phase and the full-load flat road phase, the output power is lower, and it keeps the battery SOC higher when starting to uphill, which the battery can provide enough power to regulate the engine operating range, reduce fuel consumption.
(2) Compared to the DP strategy, the P-ECMS strategy achieves near-optimal fuel economy. It also has the capability of real-time online control.
(3) Under mining conditions, the equivalent fuel consumption of the P-ECMS strategy is 150.8 L/100 km, which is 10.9% lower than the CDCS strategy (169.3 L/100 km). It is 99.47% of the fuel-saving effect of the DP strategy (150 L/100 km), achieving near-optimal fuel savings.
(4) The DP and P-ECMS strategies can distribute the power of the generator set and the power battery more rationally than the CDCS strategy, so the engine works more in its high efficiency zone and reduces fuel consumption.
(5) The P-ECMS strategy can enhance the fuel economy of plug-in hybrid mining dump trucks when running in CD mode, but only if there is sufficient time for charging and adequate charging equipment.
In view of the effectiveness of the P-ECMS strategy, the following research focuses on considering robustness, e.g., changes in gradient, temperature, etc., to improve the fuel economy of the strategy further.
Engine torque, engine speed, engine efficiency
Fuel consumption rate
Battery pack efficiency
Generator set output power
Engine output power
Traction motor demand power
Battery pack output power
Battery open circuit voltage
Battery pack capacity
Gravitational acceleration
Vehicle speed
Coefficient of inertia
Vehicle acceleration
Traction motor torque
Drive shaft and gearbox transmission efficiency
Main reducer ratio
Tire rolling radius
Vehicle demand power
Traction motor output power
Road resistance power consumption
Air resistance power consumption
Acceleration resistance power consumption
Battery voltage
Battery resistance
Engine fuel consumption
Battery equivalent fuel consumption
Equivalent factor
Thanks are due to the editors and reviewers for their valuable opinions, which are of great help to improve the quality of this paper.
The author received no specific funding for this study.
Study conception and design: Yu Yixuan, Wang Yulin; data collection: Yu Yixuan, Li Qingcheng; analysis and interpretation of results: Yu Yixuan, Wang Yulin, Jiao Bowen; draft manuscript preparation: Yu Yixuan. All authors reviewed the results and approved the final version of the manuscript.
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
The authors declare that they have no conflicts of interest to report regarding the present study.