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Assessment of power consumption of electric machinery in agricultural tasks for enhancing the route planning problem
Computers and Electronics in Agriculture 163 (2019) 104868
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Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Assessment of power consumption of electric machinery in agricultural tasks for enhancing the route planning problem Javier Romero Schmidt, Fernando Auat Cheein
T
⁎
Department of Electronics Engineering, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
A R T I C LE I N FO
A B S T R A C T
Keywords: Energy management Electric agricultural machinery Power assessment
In field operations, machinery is subject to resource restrictions that lead to a significant number of approaches to make it more efficient. Operational times, costs and manoeuvres, machinery effort, among others, are often considered for route planning strategies. In particular, the route planning problem (RPP) has been widely studied for both single and fleet of agricultural machinery performing a previously assigned task, considering the above constraints. However, such a study is limited to engine combustion of agricultural machinery. With electrically powered vehicles, it is yet to be determined how to estimate the power consumption and the power requirements for the route planning problem, to ensure that the vehicle will be able to complete the task. In electric machinery, the power is associated with the rolling resistance, the aerodynamic resistance of the vehicle, its mass, the terramechanic relationship between the wheel and the terrain, among other factors. In this work, it is analytically presented the estimation of the instantaneous power consumption (IPC) of an electric machinery in agricultural tasks, given a previously defined route, according to the nature of the terrain that it is traversing; and it is latter empirically validated in the field. The experiments performed in an avocado grove show a root mean square error of 60 kW in the estimation of the IPC, against 900 kW when using manufacturer information. The results shown herein can be used for further enhancing the route planning problem and the decision making process of the farmer, by adding power restriction (and thus, energy usage) of electric vehicles to the RPP.
1. Introduction As stated in Axema (2017), electrification is one of the major upcoming challenges in agricultural machinery industry. The opportunities for the manufacturer include, but they are not restricted to, the following: new technical functions, better performance during operations, decrease of production costs associated with fuel consumption, simple machine architecture and quick maintenance, increase of safety and better ergonomics for the user. In particular, being electrical and with the advances of the IoT (Internet of Things) and 5G communications, electrical agricultural machinery will be part of the communication and information technology, with the corresponding advantages in data collecting and data usage for decision processes (Kale and Sonavane, 2018; Sharma et al., 2018). Therefore, electrical machinery (EM) in agriculture is a push forward to smart farming (Axema, 2017; Mottaleb, 2018). However, when using EM in agricultural tasks, several issues arise, mainly related to energy management. The power consumption of any electric vehicle depends on both inner consumption, called auxiliaries,
⁎
and external factors (Cheon and Kang, 2017; Cauwer et al., 2015). Auxiliaries are related to, for example, lights of the vehicle, radio, air conditioning, sensors such as RTK (real time kinematics) and any other device powered by the vehicle’s batteries. External factors, on the other hand, constrain the power management by adding resistance to the vehicle’s motion (see Yano et al., 2014; Wang et al., 2017; Wu et al., 2015 for further reading). Among such resistances we can refer the most important ones: the inertia of the vehicle, the topology of the terrain, the aerodynamic constraints and the rolling resistance. Although it will be explained in detail in Section 2, the inertia of the vehicle, as a resistance, is associated with its acceleration and its mass (or load); the aerodynamic resistance is related to the vehicle’s speed; the rolling resistance is related to the mass of the vehicle and the rolling coefficient (strongly related to the terramechanic parameters of the terrain and the wheel); and the resistance given by the terrain topology: the effort of the engine is not the same when driving up a slope than driving it down. For the remainder of this work, auxiliaries will not be considered since their consumption can be easily modelled (Cauwer et al., 2015).
Corresponding author. E-mail address: [email protected] (F. Auat Cheein). URL: http://www.profesores.elo.utfsm.cl/~fauat/ (F. Auat Cheein).
https://doi.org/10.1016/j.compag.2019.104868 Received 18 December 2018; Received in revised form 21 June 2019; Accepted 22 June 2019 0168-1699/ © 2019 Elsevier B.V. All rights reserved.
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 1. Smart Farm and its main components.
2.1. Power assessment
The route planning problem (RPP) has been widely addressed in the literature (Mahmud et al., 2018; Spekken and de Bruin, 2013; ConesaMuñoz et al., 2016; Edwards et al., 2017; Jensen et al., 2015; Gracia et al., 2014) (and the references therein). Each strategy considers restriction factors such as the degrees of manoeuvrability of the machinery (or fleet) (Seyyedhasani and Dvorak, 2018; Conesa-Muñoz et al., 2016; Seyyedhasani and Dvorak, 2018; Seyyedhasani and Dvorak, 2017), the operation times to fulfil the task (Jiang et al., 2018; Seyyedhasani and Dvorak, 2018), how to enter or how to effectively leaves corridors in groves (Jensen et al., 2012; Bochtis and Sørensen, 2009; Hameed et al., 2010; Edwards et al., 2015), or how to automate the RPP process as a path planning algorithm for structured groves (Conesa-Muñoz et al., 2016). However, power or energy management in electric machinery in agriculture is a problem not yet addressed. Fig. 1 shows the general architecture of a smart farm and its main components (Kale and Sonavane, 2018). The machinery behaves as an IoT device, providing information to the Cloud which, after processing, delivers agricultural directives to the farmer. The farmer takes the decisions regarding the agricultural process and a route planning algorithm is generated for the EM. When route planning for agricultural operations, the above mentioned resistances constrain the operation times. If not properly planned, the EM could run out of energy in the middle of the process, thus contradicting the advantages of using this technology, mentioned in Axema (2017), if no preventive action is considered. This work is not focused on the RPP problem, but on assessing the instantaneous power consumption (IPC) of an EM, given a previously known route, from both analytical and empirical perspective, in a way to offer an estimation procedure to predict the required IPC before traversing a route, thus the farmer can take the corresponding decision.
Following the guidelines presented in Wong (2013), Jazar (2011) and Wu et al. (2015), the tractive effort of the EM can be modelled as:
ftractive = m ·a +
ρ CD·Af ·v 2 + frl ·m ·g ·cosθ + mg sinθ 2 R R Ra
rl
g
(1)
In Eq. (1), m is the mass of the EM, which can vary according to its load in agricultural applications; a is the translational acceleration of the vehicle; Ra the aerodynamic coefficient, which can be discarded when traversing at low speeds (see Yano et al., 2014 and the references therein), and ρ the air density, Af the vehicle frontal area, CD the drag coefficient and v the vehicle velocity. The wheel-terrain relationship is represented by the rolling resistance Rrl , where frl is the rolling coefficient and g the gravity acceleration. If the terrain presents an inclination, then there will be a grade resistance Rg being θ the terrain inclination. The dot represents scalar product. It is to be noted that Eq. (1) does not include the regenerative braking system. If Pf is the output power of the EM, then:
ρ Pf = ftractive ·v = ⎡m ·a + CD·Af ·v 2 + frl ·m ·g ·cosθ + m ·g ·sinθ⎤·v ⎢ ⎥ 2 ⎣ ⎦
(2)
Then, the input power can be calculated as Pf = ηP , where η is the engine efficiency expressed as:
η=
P − I 2·r P
(3)
where I is the current and r the resistance of all auxiliaries and copper in the EM. Then, the instantaneous power can be calculated as:
2. Materials and methods
P = I 2·r + ftractive ·v
As previously stated, the power estimation when using EM in agricultural tasks allows for a more efficient route and task planning. Knowing beforehand the power needed to accomplish a given task provides the farmer with more information for the decision making process. In this work, the EM is assumed to have mechanic heading and therefore only traction is electric and it is not considered regenerative braking system. The following sections introduce the mathematical formulation of the power assessment, the route planning and the experimental set-up.
(4)
Following the work of Wu et al. (2015), the tractive force ftractive is generated by the torque of the motor such as:
ftractive =
τ K ·Φ ·I = a d R R
where R is the wheel radius, τ is the motor torque, K a is the armature constant and Φd is the magnetic flux. Replacing K a. Φd by K in the above expression and merging with Eqs. (2)–(4), the instantaneous power can be rewritten as: 2
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
agricultural tasks, the trajectory tracking methodology previously presented by the authors in Cheein and Scaglia (2013) and Cheein (2016) was implemented for profiling velocity. As shown in Eq. (7), velocity is needed to estimate the power consumption. Thus, following (Cheein and Scaglia, 2013; Cheein, 2016), it was planned a path kinematically compatible with the EM holonomic restrictions. Then, each point of the path had a velocity associated with it. Therefore, the route and the velocities that the machinery should have at each way-point in the route are information previously known. 2.3. Experimental set-up The experimental set-up consists of an electric vehicle -a golf cartmechatronized at the GRAI-UTFSM, Valparaiso, Chile. The vehicle has a power (voltage and current) sensor measuring the instantaneous power directly from the batteries. The power sensor acquires 1000 readings per second. An RTK (real time kinematics) mounted at the top of the vehicle allows for geo-referencing the acquired data. The RTK acquires ten readings per second. In addition, the vehicle also has depth cameras, encoders on its rear wheels, and IMU (inertial measuring unit) incorporated, but not used for the purpose of this work. All sensors are connected to an on-board GPU (graphics processing unit) that processes all data in real time. Fig. 2 shows the golf cart (left) with all the equipment installed; the power sensors connected to the batteries (up, right) and the GPU (down, right). Table 1 summarizes the equipment used in this work and its more important specifications. The environment where the experimentation was carried out corresponds to an avocado Hass grove located at Valparaíso region, Chile. A ground view of the grove is shown in Fig. 3 (left) and a satellite view on the right. As can be seen, the terrain is flat but not level, hence disturbances are expected to occur during manoeuvring.
Fig. 2. Electric vehicle used in this work (left), with the RTK mounted at its chassis; power sensors connected to the vehicle’s batteries (top right); Jetson TX board used as core processor (down right).
P =
r·R2 ⎡ m ·a + CD·Af ·v 2 + frl ·m ·g + m ·g ·sinθ⎤ + v ⎥ K2 ⎢ ⎣ ⎦ ·⎡m ·a + CD·Af ·v 2 + frl ·m ·g + m ·g ·sinθ⎤ ⎢ ⎥ ⎣ ⎦
(5)
Since in this work all experiments were conducted in flat terrain at low speeds – and thus discarding aerodynamic effects – then Eq. (5) can be reduced to:
P≈
r·R2 ⎡ m ·a + frl ·m ·g⎤ + v·⎡m ·a + frl ·m ·g⎤ ⎥ ⎥ ⎢ K2 ⎢ ⎦ ⎣ ⎦ ⎣
(6)
2.4. Power consumption modelling
Thus, Eq. (6) offers an estimate of the instantaneous power consumption of the EM as a function of its velocity, the terramechanics constraints and the mass of the vehicle. Furthermore, if the velocity changes in the vehicle are rather small compared to the sampling time of the system, then acceleration can be discarded and the instantaneous power consumption can be estimated as:
Pt ≈
r·R2 ⎡ frl ·m ·g⎤ + vt ·⎡frl ·m ·g⎤ ⎥ ⎥ ⎢ K2 ⎢ ⎦ ⎣ ⎦ ⎣
To model the instantaneous power consumption of the EM, 1000 trials at several different constant speeds were repeated in the terrain shown in Fig. 3 (left). The terrain was a composition of clay and gravel. Thus, tables as the ones provided in Jazar (2011) and Wong (2013) where the rolling resistance of determined wheels are tabulated, cannot be used since the terrain is not of uniform composition. In addition, the terrain was unlevelled and only partially flat.
(7)
Table 1 Characteristics of the system and sensors.
where suffix t in Eq. (7) represents the sampling time of the system. Eq. (7) will be used to assess the power consumption of the EM, for a perfect flat and level terrain and traversing at such a low and cruise speed – without cornering – that aerodynamics resistances are not observed. The aim of the previous analysis is to show that velocity will be considered as the sole input for IPC estimation. For the remaining of the work, r , R, g , m and K will be assumed as constants (see Cauwer et al., 2015 for further details). 2.2. Motion planning The route planning problem for agriculture machinery is still a field of study, as shown in Bochtis and Sørensen (2010) and Conesa-Muñoz et al. (2016) (and the references therein). For an efficient route planning, it is usually considered as constraints the time in performing the tasks, the manoeuvrability restrictions, the distances to be travelled and also the resources available –mainly for combustion engines, as shown in Lovarelli et al. (2018). Several solutions have already been proposed and tested in the field with certain success (Conesa-Muñoz et al., 2016). However, the power profile consumption of EM in agriculture is still under study, specially considering the terramechanic relationship between the wheels and the terrain. With the aim of testing the power consumption of EM when traversing through a grove performing
Name
Description
Cushman Hauler Pro Electric system Max. Speed Autonomy Weight frl , η and CD
58 V DC 45 km(h−1) 100 km 669 kg (769 kg Loaded) 0.0008, 0.95 and 0.4626 respectively
Navcom SF-3040 Accuracy RTK (<40 km) Data Rate Communication
Horizontal: 1 cm + 0.5 ppm Vertical: 2 cm + 1 ppm Selectable between 1 Hz, 5 Hz and 10 Hz Serial port through USB
Voltage and current sensor Voltage Range From 15 V to 80 V Current Range From −300 A to 300 A Precision 12 bits ADC Sampling Rate 800 Hz Average Communication Serial port through USB Nvidia Jetson TX2 GPU CPU Memory
3
NVIDIA Pascal™, 256 CUDA cores HMP Dual Denver 2/2 MB L2 + Quad ARM® A57/2 MB L2 8 GB 128 bit LPDDR4 59.7 GB/s
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 3. Ground (left) and satellite (right) view of the Avocado Hass grove where the experimentation was carried out.
to occur and the best fit might not be linear. Therefore, polynomial (solid yellow line) and linear (solid orange line) fittings were tested. As can be seen, the R2 factor for the polynomial fitting reaches up to 66%, whereas for the linear case, 6%. Thus, the polynomial fitting was used herein. It is to be noted that we tested polynomial fitting up to the fourth order, but the second order gave the best R2 . The linear regression equation used for predicting IPC as a function of the speed of the vehicle is then:
The starting velocity was zero and the maximum velocity reached was around 20 km(h)−1. The vehicle traversed a distance of approximately 100 meters each trial. Sensor readings associated with transient responses until reaching cruise velocity – at starting and stopping – were discarded from this analysis. During the trials, the mass of the vehicle was assumed constant. 3. Results
(8)
P = −0.0333·v 2 + 1.0701·v
Following, the instantaneous power consumption of the EM was measured using the current and voltage sensors, and a model for estimating it was obtained. Later, such model was validated in long trial traverses through the avocado Hass grove. The route planning strategy followed is a modification of the one presented in Conesa-Muñoz et al. (2016) (since it is not the core of this work), and the velocity profiling strategy is the one previously published by the authors in Cheein (2016). Thus, we have the path and the velocities for each way-point in the route.
where P in Eq. (8) is in kW and v in km(h) vehicle.
−1
, is the velocity of the
3.2. Instantaneous power estimation: route planning To validate the proposed methodology for estimating the IPC, we implemented a version of the route planning approach previously published in Conesa-Muñoz et al. (2016), with the velocity profiling technique published by the authors in Cheein (2016). The experiments were performed in the Hass avocado grove shown in Fig. 3. Fig. 5 shows the route planned among the avocado corridors with 10 locations selected to depict our estimated IPC approach. Fig. 6 shows the results obtained during the trial. Each sub-figure shows the IPC measured from the vehicle and the estimated IPC. For visualization purposes, the ten locations from Fig. 5 are shown in pairs. As can be seen, for all cases, the estimated IPC follows closely the actual IPC of the vehicle. Finally, Fig. 7 shows the IPC as measured from the vehicle for each location from Fig. 5. As can be seen, the behaviour of the IPC is rather stochastic due to the disturbances in the terrain and the wheel mainly. Although the previous figures depict the behaviour of the IPC, both
3.1. Instantaneous power consumption modelling Fig. 4 shows the average instantaneous power consumption per each trial and per each cruise velocity in blue circles. To perform the experimentation, a trajectory tracking controller, developed by the authors (Cheein and Scaglia, 2013), was previously implemented on the vehicle to ensure that the cruise velocity reaches the profiled one. As can be seen in Fig. 4, two regression methods were used. Eq. (7) shows a linear behaviour of the IPC, but the terrain used for experimentation does not fulfil the ideal situation of being perfectly flat and levelled. On the contrary, unmodelled characteristics of the terrain (among other factors, such as wheel deformation, slippage or skidding) are expected
Fig. 4. Analysis of the trials at different constant speeds, starting at 4 km(h)−1 and finishing near 18 km(h)−1.
Fig. 5. Route planned in the avocado grove with 10 locations selected to show the IPC estimation. 4
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 6. Measured and estimated IPC. (a)–(e) The IPC results for locations 1–2 to 9–10, respectively.
Fig. 7. Instantaneous power consumption vs. time, for the ten trials shown in Fig. 5.
Fig. 8. Energy usage for the ten locations shown in Fig. 5, considering also the energy usage given by the manufacturer, for comparison purposes.
measured and estimated, it still remains open its usability for the route planning problem. Therefore, an energy usage analysis is performed following.
Section 2.3; the red bar is the energy usage according to our knowledge about the terrain and the estimation made using Eq. (8). It is important to note that v in Eq. (8) corresponds to the velocity profiled during the route planning and not the actual velocity of the vehicle. Otherwise IPC estimation will be pointless for the route planning problem. For comparison purposes, we included the energy usage provided by the electric vehicle manufacturer: 10 kW at 10 km(h)−1 as sole estimation, represented by yellow bars in Fig. 8 (to obtain the energy, we used the sampling time of the system for the three cases). As can be seen, our
3.3. Energy usage The advantages of the presented methodology for estimating the IPC in electric vehicles in agriculture can be seen in Fig. 8, which shows the energy usage (in Joules) for the ten locations from Fig. 5. The blue bar represents the energy measured using our power sensors presented in 5
Computers and Electronics in Agriculture 163 (2019) 104868
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Fig. 9. Total energy required to complete the trial shown in Fig. 5.
approach estimates closely the actual energy of the vehicle. Fig. 9 shows the total energy required to perform the trial shown in Fig. 5. Clearly, using our approach the route planning problem will be able to have, beforehand, an estimated idea of how much energy would require to traverse a given path. Finally, ten different trials of similar length were repeated, obtaining an rmse (root mean square error) of approximated 60 kW, between the actual IPC and the estimated one. When using the power consumption provided by the manufacturer, the rmse increases up to 900 kW, approximately. 4. Conclusion In this brief it was presented a methodology for analytically and empirically assessing the instantaneous power consumption of an electric vehicle in agricultural scenarios. The problem was motivated by the need of having energy usage estimation for solving the route planning problem more efficiently. First, we showed that it is possible to obtain an analytical model of the power consumption related only to the terrain characteristics. Then, using previously published route planning algorithms and velocity profiling approaches, we showed that our approach can efficiently estimate the power consumption (and therefore, the energy usage) of the vehicle given a previous route. The information was later compared to the one given by the vehicle manufacturer. Our field tests have shown an rmse of approximately 60 kW, compared to the actual power consumed by the vehicle, against 900 kW (approximately), using the information provided by the manufacturer. Such encouraging results are aimed at providing the route planning solution with an estimation of the energy and power required to perform a given task, before executing it. Acknowledgements This research was founded by CONICYT Fondecyt grant 1171431, CONICYT FB0008 and CONICYT-PFCHA/MagísterNacional/201822170689. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.compag.2019.104868. References Axema, 2017. ELECTRIFICATION IN AGRICULTURAL MACHINERY (Accessed December, 2018). < http://www.axema.fr/agroequipements/Lists/Lesarticlespubliques/ Attachments/289/Road%20Map%20%C3%A9lectrification.pdf > . Bochtis, D., Sørensen, C., 2009. The vehicle routing problem in field logistics part i. Biosyst. Eng. 104 (4), 447–457. https://doi.org/10.1016/j.biosystemseng.2009.09. 003.. Bochtis, D., Sørensen, C., 2010. The vehicle routing problem in field logistics: Part ii.
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Wu, X., Freese, D., Cabrera, A., Kitch, W.A., 2015. Electric vehicles’ energy consumption measurement and estimation. Transport. Res. Part D: Transport Environ. 34, 52–67. https://doi.org/10.1016/j.trd.2014.10.007.. Yano, J., Nishimura, S., Fukunaga, K., Nakajima, M., Yamada, H., Moriguchi, M., 2014. Estimation of ev power consumption and route planning using probe data. SEI Tech. Rev. (78), 29–34.
1007/s11119-012-9290-5. Wang, J.bo, Liu, K., Yamamoto, T., Morikawa, T., 2017. Improving estimation accuracy for electric vehicle energy consumption considering the effects of ambient temperature, Energy Proc. 105, 2904–2909 (8th International Conference on Applied Energy, ICAE2016, 8–11 October 2016, Beijing, China). doi:https://doi.org/10.1016/j. egypro.2017.03.655. < http://www.sciencedirect.com/science/article/pii/ S1876610217307099 > . Wong, J., 2013. Terramechanics and Off-Road Vehicle’s Engineering. Elsevier.
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Contents lists available at ScienceDirect
Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Assessment of power consumption of electric machinery in agricultural tasks for enhancing the route planning problem Javier Romero Schmidt, Fernando Auat Cheein
T
⁎
Department of Electronics Engineering, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
A R T I C LE I N FO
A B S T R A C T
Keywords: Energy management Electric agricultural machinery Power assessment
In field operations, machinery is subject to resource restrictions that lead to a significant number of approaches to make it more efficient. Operational times, costs and manoeuvres, machinery effort, among others, are often considered for route planning strategies. In particular, the route planning problem (RPP) has been widely studied for both single and fleet of agricultural machinery performing a previously assigned task, considering the above constraints. However, such a study is limited to engine combustion of agricultural machinery. With electrically powered vehicles, it is yet to be determined how to estimate the power consumption and the power requirements for the route planning problem, to ensure that the vehicle will be able to complete the task. In electric machinery, the power is associated with the rolling resistance, the aerodynamic resistance of the vehicle, its mass, the terramechanic relationship between the wheel and the terrain, among other factors. In this work, it is analytically presented the estimation of the instantaneous power consumption (IPC) of an electric machinery in agricultural tasks, given a previously defined route, according to the nature of the terrain that it is traversing; and it is latter empirically validated in the field. The experiments performed in an avocado grove show a root mean square error of 60 kW in the estimation of the IPC, against 900 kW when using manufacturer information. The results shown herein can be used for further enhancing the route planning problem and the decision making process of the farmer, by adding power restriction (and thus, energy usage) of electric vehicles to the RPP.
1. Introduction As stated in Axema (2017), electrification is one of the major upcoming challenges in agricultural machinery industry. The opportunities for the manufacturer include, but they are not restricted to, the following: new technical functions, better performance during operations, decrease of production costs associated with fuel consumption, simple machine architecture and quick maintenance, increase of safety and better ergonomics for the user. In particular, being electrical and with the advances of the IoT (Internet of Things) and 5G communications, electrical agricultural machinery will be part of the communication and information technology, with the corresponding advantages in data collecting and data usage for decision processes (Kale and Sonavane, 2018; Sharma et al., 2018). Therefore, electrical machinery (EM) in agriculture is a push forward to smart farming (Axema, 2017; Mottaleb, 2018). However, when using EM in agricultural tasks, several issues arise, mainly related to energy management. The power consumption of any electric vehicle depends on both inner consumption, called auxiliaries,
⁎
and external factors (Cheon and Kang, 2017; Cauwer et al., 2015). Auxiliaries are related to, for example, lights of the vehicle, radio, air conditioning, sensors such as RTK (real time kinematics) and any other device powered by the vehicle’s batteries. External factors, on the other hand, constrain the power management by adding resistance to the vehicle’s motion (see Yano et al., 2014; Wang et al., 2017; Wu et al., 2015 for further reading). Among such resistances we can refer the most important ones: the inertia of the vehicle, the topology of the terrain, the aerodynamic constraints and the rolling resistance. Although it will be explained in detail in Section 2, the inertia of the vehicle, as a resistance, is associated with its acceleration and its mass (or load); the aerodynamic resistance is related to the vehicle’s speed; the rolling resistance is related to the mass of the vehicle and the rolling coefficient (strongly related to the terramechanic parameters of the terrain and the wheel); and the resistance given by the terrain topology: the effort of the engine is not the same when driving up a slope than driving it down. For the remainder of this work, auxiliaries will not be considered since their consumption can be easily modelled (Cauwer et al., 2015).
Corresponding author. E-mail address: [email protected] (F. Auat Cheein). URL: http://www.profesores.elo.utfsm.cl/~fauat/ (F. Auat Cheein).
https://doi.org/10.1016/j.compag.2019.104868 Received 18 December 2018; Received in revised form 21 June 2019; Accepted 22 June 2019 0168-1699/ © 2019 Elsevier B.V. All rights reserved.
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 1. Smart Farm and its main components.
2.1. Power assessment
The route planning problem (RPP) has been widely addressed in the literature (Mahmud et al., 2018; Spekken and de Bruin, 2013; ConesaMuñoz et al., 2016; Edwards et al., 2017; Jensen et al., 2015; Gracia et al., 2014) (and the references therein). Each strategy considers restriction factors such as the degrees of manoeuvrability of the machinery (or fleet) (Seyyedhasani and Dvorak, 2018; Conesa-Muñoz et al., 2016; Seyyedhasani and Dvorak, 2018; Seyyedhasani and Dvorak, 2017), the operation times to fulfil the task (Jiang et al., 2018; Seyyedhasani and Dvorak, 2018), how to enter or how to effectively leaves corridors in groves (Jensen et al., 2012; Bochtis and Sørensen, 2009; Hameed et al., 2010; Edwards et al., 2015), or how to automate the RPP process as a path planning algorithm for structured groves (Conesa-Muñoz et al., 2016). However, power or energy management in electric machinery in agriculture is a problem not yet addressed. Fig. 1 shows the general architecture of a smart farm and its main components (Kale and Sonavane, 2018). The machinery behaves as an IoT device, providing information to the Cloud which, after processing, delivers agricultural directives to the farmer. The farmer takes the decisions regarding the agricultural process and a route planning algorithm is generated for the EM. When route planning for agricultural operations, the above mentioned resistances constrain the operation times. If not properly planned, the EM could run out of energy in the middle of the process, thus contradicting the advantages of using this technology, mentioned in Axema (2017), if no preventive action is considered. This work is not focused on the RPP problem, but on assessing the instantaneous power consumption (IPC) of an EM, given a previously known route, from both analytical and empirical perspective, in a way to offer an estimation procedure to predict the required IPC before traversing a route, thus the farmer can take the corresponding decision.
Following the guidelines presented in Wong (2013), Jazar (2011) and Wu et al. (2015), the tractive effort of the EM can be modelled as:
ftractive = m ·a +
ρ CD·Af ·v 2 + frl ·m ·g ·cosθ + mg sinθ 2 R R Ra
rl
g
(1)
In Eq. (1), m is the mass of the EM, which can vary according to its load in agricultural applications; a is the translational acceleration of the vehicle; Ra the aerodynamic coefficient, which can be discarded when traversing at low speeds (see Yano et al., 2014 and the references therein), and ρ the air density, Af the vehicle frontal area, CD the drag coefficient and v the vehicle velocity. The wheel-terrain relationship is represented by the rolling resistance Rrl , where frl is the rolling coefficient and g the gravity acceleration. If the terrain presents an inclination, then there will be a grade resistance Rg being θ the terrain inclination. The dot represents scalar product. It is to be noted that Eq. (1) does not include the regenerative braking system. If Pf is the output power of the EM, then:
ρ Pf = ftractive ·v = ⎡m ·a + CD·Af ·v 2 + frl ·m ·g ·cosθ + m ·g ·sinθ⎤·v ⎢ ⎥ 2 ⎣ ⎦
(2)
Then, the input power can be calculated as Pf = ηP , where η is the engine efficiency expressed as:
η=
P − I 2·r P
(3)
where I is the current and r the resistance of all auxiliaries and copper in the EM. Then, the instantaneous power can be calculated as:
2. Materials and methods
P = I 2·r + ftractive ·v
As previously stated, the power estimation when using EM in agricultural tasks allows for a more efficient route and task planning. Knowing beforehand the power needed to accomplish a given task provides the farmer with more information for the decision making process. In this work, the EM is assumed to have mechanic heading and therefore only traction is electric and it is not considered regenerative braking system. The following sections introduce the mathematical formulation of the power assessment, the route planning and the experimental set-up.
(4)
Following the work of Wu et al. (2015), the tractive force ftractive is generated by the torque of the motor such as:
ftractive =
τ K ·Φ ·I = a d R R
where R is the wheel radius, τ is the motor torque, K a is the armature constant and Φd is the magnetic flux. Replacing K a. Φd by K in the above expression and merging with Eqs. (2)–(4), the instantaneous power can be rewritten as: 2
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
agricultural tasks, the trajectory tracking methodology previously presented by the authors in Cheein and Scaglia (2013) and Cheein (2016) was implemented for profiling velocity. As shown in Eq. (7), velocity is needed to estimate the power consumption. Thus, following (Cheein and Scaglia, 2013; Cheein, 2016), it was planned a path kinematically compatible with the EM holonomic restrictions. Then, each point of the path had a velocity associated with it. Therefore, the route and the velocities that the machinery should have at each way-point in the route are information previously known. 2.3. Experimental set-up The experimental set-up consists of an electric vehicle -a golf cartmechatronized at the GRAI-UTFSM, Valparaiso, Chile. The vehicle has a power (voltage and current) sensor measuring the instantaneous power directly from the batteries. The power sensor acquires 1000 readings per second. An RTK (real time kinematics) mounted at the top of the vehicle allows for geo-referencing the acquired data. The RTK acquires ten readings per second. In addition, the vehicle also has depth cameras, encoders on its rear wheels, and IMU (inertial measuring unit) incorporated, but not used for the purpose of this work. All sensors are connected to an on-board GPU (graphics processing unit) that processes all data in real time. Fig. 2 shows the golf cart (left) with all the equipment installed; the power sensors connected to the batteries (up, right) and the GPU (down, right). Table 1 summarizes the equipment used in this work and its more important specifications. The environment where the experimentation was carried out corresponds to an avocado Hass grove located at Valparaíso region, Chile. A ground view of the grove is shown in Fig. 3 (left) and a satellite view on the right. As can be seen, the terrain is flat but not level, hence disturbances are expected to occur during manoeuvring.
Fig. 2. Electric vehicle used in this work (left), with the RTK mounted at its chassis; power sensors connected to the vehicle’s batteries (top right); Jetson TX board used as core processor (down right).
P =
r·R2 ⎡ m ·a + CD·Af ·v 2 + frl ·m ·g + m ·g ·sinθ⎤ + v ⎥ K2 ⎢ ⎣ ⎦ ·⎡m ·a + CD·Af ·v 2 + frl ·m ·g + m ·g ·sinθ⎤ ⎢ ⎥ ⎣ ⎦
(5)
Since in this work all experiments were conducted in flat terrain at low speeds – and thus discarding aerodynamic effects – then Eq. (5) can be reduced to:
P≈
r·R2 ⎡ m ·a + frl ·m ·g⎤ + v·⎡m ·a + frl ·m ·g⎤ ⎥ ⎥ ⎢ K2 ⎢ ⎦ ⎣ ⎦ ⎣
(6)
2.4. Power consumption modelling
Thus, Eq. (6) offers an estimate of the instantaneous power consumption of the EM as a function of its velocity, the terramechanics constraints and the mass of the vehicle. Furthermore, if the velocity changes in the vehicle are rather small compared to the sampling time of the system, then acceleration can be discarded and the instantaneous power consumption can be estimated as:
Pt ≈
r·R2 ⎡ frl ·m ·g⎤ + vt ·⎡frl ·m ·g⎤ ⎥ ⎥ ⎢ K2 ⎢ ⎦ ⎣ ⎦ ⎣
To model the instantaneous power consumption of the EM, 1000 trials at several different constant speeds were repeated in the terrain shown in Fig. 3 (left). The terrain was a composition of clay and gravel. Thus, tables as the ones provided in Jazar (2011) and Wong (2013) where the rolling resistance of determined wheels are tabulated, cannot be used since the terrain is not of uniform composition. In addition, the terrain was unlevelled and only partially flat.
(7)
Table 1 Characteristics of the system and sensors.
where suffix t in Eq. (7) represents the sampling time of the system. Eq. (7) will be used to assess the power consumption of the EM, for a perfect flat and level terrain and traversing at such a low and cruise speed – without cornering – that aerodynamics resistances are not observed. The aim of the previous analysis is to show that velocity will be considered as the sole input for IPC estimation. For the remaining of the work, r , R, g , m and K will be assumed as constants (see Cauwer et al., 2015 for further details). 2.2. Motion planning The route planning problem for agriculture machinery is still a field of study, as shown in Bochtis and Sørensen (2010) and Conesa-Muñoz et al. (2016) (and the references therein). For an efficient route planning, it is usually considered as constraints the time in performing the tasks, the manoeuvrability restrictions, the distances to be travelled and also the resources available –mainly for combustion engines, as shown in Lovarelli et al. (2018). Several solutions have already been proposed and tested in the field with certain success (Conesa-Muñoz et al., 2016). However, the power profile consumption of EM in agriculture is still under study, specially considering the terramechanic relationship between the wheels and the terrain. With the aim of testing the power consumption of EM when traversing through a grove performing
Name
Description
Cushman Hauler Pro Electric system Max. Speed Autonomy Weight frl , η and CD
58 V DC 45 km(h−1) 100 km 669 kg (769 kg Loaded) 0.0008, 0.95 and 0.4626 respectively
Navcom SF-3040 Accuracy RTK (<40 km) Data Rate Communication
Horizontal: 1 cm + 0.5 ppm Vertical: 2 cm + 1 ppm Selectable between 1 Hz, 5 Hz and 10 Hz Serial port through USB
Voltage and current sensor Voltage Range From 15 V to 80 V Current Range From −300 A to 300 A Precision 12 bits ADC Sampling Rate 800 Hz Average Communication Serial port through USB Nvidia Jetson TX2 GPU CPU Memory
3
NVIDIA Pascal™, 256 CUDA cores HMP Dual Denver 2/2 MB L2 + Quad ARM® A57/2 MB L2 8 GB 128 bit LPDDR4 59.7 GB/s
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 3. Ground (left) and satellite (right) view of the Avocado Hass grove where the experimentation was carried out.
to occur and the best fit might not be linear. Therefore, polynomial (solid yellow line) and linear (solid orange line) fittings were tested. As can be seen, the R2 factor for the polynomial fitting reaches up to 66%, whereas for the linear case, 6%. Thus, the polynomial fitting was used herein. It is to be noted that we tested polynomial fitting up to the fourth order, but the second order gave the best R2 . The linear regression equation used for predicting IPC as a function of the speed of the vehicle is then:
The starting velocity was zero and the maximum velocity reached was around 20 km(h)−1. The vehicle traversed a distance of approximately 100 meters each trial. Sensor readings associated with transient responses until reaching cruise velocity – at starting and stopping – were discarded from this analysis. During the trials, the mass of the vehicle was assumed constant. 3. Results
(8)
P = −0.0333·v 2 + 1.0701·v
Following, the instantaneous power consumption of the EM was measured using the current and voltage sensors, and a model for estimating it was obtained. Later, such model was validated in long trial traverses through the avocado Hass grove. The route planning strategy followed is a modification of the one presented in Conesa-Muñoz et al. (2016) (since it is not the core of this work), and the velocity profiling strategy is the one previously published by the authors in Cheein (2016). Thus, we have the path and the velocities for each way-point in the route.
where P in Eq. (8) is in kW and v in km(h) vehicle.
−1
, is the velocity of the
3.2. Instantaneous power estimation: route planning To validate the proposed methodology for estimating the IPC, we implemented a version of the route planning approach previously published in Conesa-Muñoz et al. (2016), with the velocity profiling technique published by the authors in Cheein (2016). The experiments were performed in the Hass avocado grove shown in Fig. 3. Fig. 5 shows the route planned among the avocado corridors with 10 locations selected to depict our estimated IPC approach. Fig. 6 shows the results obtained during the trial. Each sub-figure shows the IPC measured from the vehicle and the estimated IPC. For visualization purposes, the ten locations from Fig. 5 are shown in pairs. As can be seen, for all cases, the estimated IPC follows closely the actual IPC of the vehicle. Finally, Fig. 7 shows the IPC as measured from the vehicle for each location from Fig. 5. As can be seen, the behaviour of the IPC is rather stochastic due to the disturbances in the terrain and the wheel mainly. Although the previous figures depict the behaviour of the IPC, both
3.1. Instantaneous power consumption modelling Fig. 4 shows the average instantaneous power consumption per each trial and per each cruise velocity in blue circles. To perform the experimentation, a trajectory tracking controller, developed by the authors (Cheein and Scaglia, 2013), was previously implemented on the vehicle to ensure that the cruise velocity reaches the profiled one. As can be seen in Fig. 4, two regression methods were used. Eq. (7) shows a linear behaviour of the IPC, but the terrain used for experimentation does not fulfil the ideal situation of being perfectly flat and levelled. On the contrary, unmodelled characteristics of the terrain (among other factors, such as wheel deformation, slippage or skidding) are expected
Fig. 4. Analysis of the trials at different constant speeds, starting at 4 km(h)−1 and finishing near 18 km(h)−1.
Fig. 5. Route planned in the avocado grove with 10 locations selected to show the IPC estimation. 4
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Fig. 6. Measured and estimated IPC. (a)–(e) The IPC results for locations 1–2 to 9–10, respectively.
Fig. 7. Instantaneous power consumption vs. time, for the ten trials shown in Fig. 5.
Fig. 8. Energy usage for the ten locations shown in Fig. 5, considering also the energy usage given by the manufacturer, for comparison purposes.
measured and estimated, it still remains open its usability for the route planning problem. Therefore, an energy usage analysis is performed following.
Section 2.3; the red bar is the energy usage according to our knowledge about the terrain and the estimation made using Eq. (8). It is important to note that v in Eq. (8) corresponds to the velocity profiled during the route planning and not the actual velocity of the vehicle. Otherwise IPC estimation will be pointless for the route planning problem. For comparison purposes, we included the energy usage provided by the electric vehicle manufacturer: 10 kW at 10 km(h)−1 as sole estimation, represented by yellow bars in Fig. 8 (to obtain the energy, we used the sampling time of the system for the three cases). As can be seen, our
3.3. Energy usage The advantages of the presented methodology for estimating the IPC in electric vehicles in agriculture can be seen in Fig. 8, which shows the energy usage (in Joules) for the ten locations from Fig. 5. The blue bar represents the energy measured using our power sensors presented in 5
Computers and Electronics in Agriculture 163 (2019) 104868
J. Romero Schmidt and F. Auat Cheein
Biosyst. Eng. 105 (2), 180–188. https://doi.org/10.1016/j.biosystemseng.2009.10. 006.
Fig. 9. Total energy required to complete the trial shown in Fig. 5.
approach estimates closely the actual energy of the vehicle. Fig. 9 shows the total energy required to perform the trial shown in Fig. 5. Clearly, using our approach the route planning problem will be able to have, beforehand, an estimated idea of how much energy would require to traverse a given path. Finally, ten different trials of similar length were repeated, obtaining an rmse (root mean square error) of approximated 60 kW, between the actual IPC and the estimated one. When using the power consumption provided by the manufacturer, the rmse increases up to 900 kW, approximately. 4. Conclusion In this brief it was presented a methodology for analytically and empirically assessing the instantaneous power consumption of an electric vehicle in agricultural scenarios. The problem was motivated by the need of having energy usage estimation for solving the route planning problem more efficiently. First, we showed that it is possible to obtain an analytical model of the power consumption related only to the terrain characteristics. Then, using previously published route planning algorithms and velocity profiling approaches, we showed that our approach can efficiently estimate the power consumption (and therefore, the energy usage) of the vehicle given a previous route. The information was later compared to the one given by the vehicle manufacturer. Our field tests have shown an rmse of approximately 60 kW, compared to the actual power consumed by the vehicle, against 900 kW (approximately), using the information provided by the manufacturer. Such encouraging results are aimed at providing the route planning solution with an estimation of the energy and power required to perform a given task, before executing it. Acknowledgements This research was founded by CONICYT Fondecyt grant 1171431, CONICYT FB0008 and CONICYT-PFCHA/MagísterNacional/201822170689. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.compag.2019.104868. References Axema, 2017. ELECTRIFICATION IN AGRICULTURAL MACHINERY (Accessed December, 2018). < http://www.axema.fr/agroequipements/Lists/Lesarticlespubliques/ Attachments/289/Road%20Map%20%C3%A9lectrification.pdf > . Bochtis, D., Sørensen, C., 2009. The vehicle routing problem in field logistics part i. Biosyst. Eng. 104 (4), 447–457. https://doi.org/10.1016/j.biosystemseng.2009.09. 003.
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Wu, X., Freese, D., Cabrera, A., Kitch, W.A., 2015. Electric vehicles’ energy consumption measurement and estimation. Transport. Res. Part D: Transport Environ. 34, 52–67. https://doi.org/10.1016/j.trd.2014.10.007.
1007/s11119-012-9290-5. Wang, J.bo, Liu, K., Yamamoto, T., Morikawa, T., 2017. Improving estimation accuracy for electric vehicle energy consumption considering the effects of ambient temperature, Energy Proc. 105, 2904–2909 (8th International Conference on Applied Energy, ICAE2016, 8–11 October 2016, Beijing, China). doi:https://doi.org/10.1016/j. egypro.2017.03.655. < http://www.sciencedirect.com/science/article/pii/ S1876610217307099 > . Wong, J., 2013. Terramechanics and Off-Road Vehicle’s Engineering. Elsevier.
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