Control algorithm and energy management strategy for extended range electric tractors

It is difficult to make full use of the electrical energy of the power battery for extended-range electric tractors because the battery’s state of charge may be relatively high at the end of the running mileage. To address this situation, this paper aimed to study the control parameter adjustment in relation to the power battery’s electrical consumption and the diesel engine’s fuel consumption energy management strategy. Based on the AVL-Cruise simulation platform, the vehicle model of the tractor was established, and the control module of AVL-Cruise was used to compile the energy management strategy. In order to verify the superiority of the proposed strategy, the contrast strategy was employed in terms of the diesel engine start and stop control plus fixed point energy management strategy (FPEMS). The applicability of the proposed strategy was tested through continuous transfer operation and the small area deep loosening operation. The simulation results show that the proposed strategy was of good applicability. Compared with the FPEMS, the fuel consumption reduced significantly, and the electrical consumption of the power battery increased obviously.

Therefore, it is of great significance to study ERET.
Electrical energy can be generated and converted from many types of energy sources like solar energy, wind energy and hydropower [14] .Electrical energy from the power grid is widely used in rural areas of China, so increasing the consumption of the battery's energy can reduce diesel consumption and get rid of the dependence on fossil fuel [15] .
The goals of energy management strategy in hybrid electric vehicles (HEVs) were to minimize fuel consumption and pollutant emissions.There are mainly two kinds of methods of energy management strategy in HEVs: optimization approach control and rule-based control [16,17] .Ansarey et al. [18] adopted multi-dimensional dynamic programming in optimal energy management for a dual-storage fuel-cell hybrid vehicle and obtained maximum reduction in fuel consumption between a single and a double buffer fuel-cell hybrid vehicle in various driving cycles.
However, there is a problem called the "curse of dimensionality" in multi-dimensional dynamic programming.Hou et al. [19] applied the approximate Pontryagin's Minimum Principle (A-PMP) algorithm to parallel plug-in hybrid electric vehicles, and fuel consumption was reduced by 6.96%, compared with the conventional "All-Electric, Charge-Sustaining" strategy.
However, A-PMP algorithm is improperly used in the real-time control, because the calculations of boundary conditions and variable derivations in Hamilton function are complex and difficult.Nuesch et al. [20] conducted equivalent consumption minimization strategy (ECMS) to minimize the fuel consumption of a diesel-electric hybrid vehicle.However, an appropriate formulation is a problem for ECMS.A genetic algorithm and quadratic programming [21] were used in plug-in hybrid electric vehicles to improve engine work efficiency and reduce fuel consumption.But it takes time for a genetic algorithm to deal with a series of operations consisting of crossover, mutation and elite selection, and quadratic programming requires knowledge of the driving conditions beforehand.Rule-based methods [22,23] , which are simpler, easier and more reliable than optimization approach control methods, have been widely used by vehicle manufacturers.Fuzzy Logic [24] was used in series hybrid electric vehicles to enhance engine operation efficiency and extend the battery life.But much work must be done to build the fuzzy logic table .Banvait et al. [25] conducted rule-based energy management for a plug-in hybrid electric vehicle.The engine efficiency and gas mileage increased significantly, compared with a parallel control strategy.But energy saving can be further improved, for the state of charge (SOC) of a battery may be relatively high at the end of running mileage.
To address the problem of the SOC at the end of running mileage [25] , an energy-management strategy was tractor model [10] .Table 1 shows the main parameters of the ERET powertrain.Figure 2 shows the power flow in pure electric drive mode.The tractor operates in this mode when the power battery's SOC is higher than its minimum threshold, based on the energy management strategy.
The electrical power of the power battery is transformed to mechanical power by the traction motor, and then it flows to the transmission.Part of the power is transmitted to the power take-off shaft for the tractor's work, and another part is transmitted to the main reducer.
After its deceleration effect, the mechanical power goes through the differential and wheel-side reducer, and finally gets to the driving wheel that is used for traction.The available capacity of the power battery in pure electric drive mode is expressed in Equation ( 1): where, Δc is the available capacity of the power battery, A•h; c 0 is the capacity of the power battery, A•h; SOC t is the SOC of the power battery when the proposed strategy is going to work, %; SOC L is the desired threshold of the SOC when the engine starts to work, %.
The available energy of the power battery in pure electric drive mode is expressed in Equation ( 2): where, q is the available energy of the power battery, kW⋅h; u 0 is its nominal voltage, V.
The energy distribution in pure electric drive mode is expressed in Equation (3): where, W is the energy consumption of the tractor when overcoming traction resistance, rolling resistance, acceleration resistance, and gradient resistance, J; η is the efficiency of energy utilization of the transmission system; W F is the energy consumption of the tractor's accessories, J.
The efficiency of energy utilization of the tractor transmission system is expressed in Equation ( 4): where, η b is the discharge efficiency of the power battery; η m is the efficiency of the traction motor; η c is the efficiency of the traction motor's controller; η t is the efficiency of the transmission system; δ is the slip efficiency of the driving wheel.
By analyzing the tractor's ploughing operation, the energy consumption of the tractor can be expressed as Equation ( 5): where, W 1 is the energy consumption during the uniform acceleration stage, J; W 2 is the energy consumption during the uniform velocity stage, J; W 3 is the energy consumption during the uniform deceleration stage, J; W 4 is the energy consumption during the turning stage, J; all of them exclude the energy consumption of accessories.
The energy consumption of the tractor at each stage is expressed in Equation ( 6): where, F a is the acceleration resistance, N; F T is the ploughing resistance, N; F f is the rolling resistance, N; Based on Equations ( 5) and ( 6), it is can be deduced as In order to illustrate easily, α is set as in Equation (7).
The ploughing resistance of the tractor is where, Z is the number of plowshares; b n is the width of a single plowshare, cm; k 0 is the soil-specific resistance, N/cm 2 ; h is the depth of ploughing, cm.The soil-specific resistance is assumed as constant value.
The working distances of the tractor's stages are Based on Equations ( 1)- (10), under the condition that the tractor absolutely works in pure electric drive mode, control model can be established by In order to illustrate easily, set β as in Equation (11).
In this paper, Z is equal to 5, b n is equal to 45 cm, k 0 is equal to 7.

Energy management strategy
To reduce fuel consumption, an energy management strategy was proposed for the control parameter adjustment (EMSCPA) in an ERET in this paper.In order to test the proposed strategy, the FPEMS is set as the contrast.

Diesel engine start and stop control plus fixed point energy management strategy
For diesel engine start and stop control, the diesel engine starts when the power battery's SOC is lower than the minimum threshold SOC L and it shuts down when the power battery's SOC is higher than its maximum threshold SOC H .When the power battery's SOC is between the maximum and minimum thresholds, the diesel engine stays in current state.The diesel engine start and stop control is shown in Figure 5.For the fixed point energy management strategy, the diesel engine works at constant power after the diesel engine starts.
After theoretical analysis and simulation test, the proportional, the integral and the differential of the PID controller used in this case are respectively set as 20, 0.0002 and 0.0025.where, P T is the power required to drive a tractor, kW; P bT is the discharge power of the power battery in the case of consuming its own energy, kW; P eT is the power of the range extender, kW; ϕ(t) is the state of the diesel engine.The diesel engine works when ϕ(t) is equal to one, and it shuts down when ϕ(t) is equal to zero.
The start and stop control of the diesel engine is expressed in Equation ( 13): where, SOC H is a constant.SOC L depends on the algorithm of the control parameter adjustment.
Based on Equation (11), when SOC L is set to zero, the following expression can be obtained: where, A is set to represent the right part of Equation ( 14), that is, t 0 0 0.1852 0 Based on Equation ( 11), when SOC L is set to 15%, it can be obtained that ( ) where, B is set to represent the right part of Equation ( 15 Based on the previous research [10] , the simulation model of the ERET is established.The simulation model is shown in Figure 7.

Working condition
To verify the applicability of the EMSCPA, two conditions are set, which are the continuous transfer operation and the small area deep loosening operation.
The ETET's running diagrams about continuous transfer

Simulation results and analysis
Two working conditions were designed to compare the performances of FPEMS and EMSCPA.
For the continuous transfer operation, Figure 11 shows the simulation results of fuel consumption rate and cumulative fuel consumption controlled by the FPEMS and EMSCPA respectively.In Figure 11   The simulation results of the power battery's discharge power controlled by the FPEMS and EMSCPA are shown in Figure 13 and Figure 14 respectively.And it is can be known that the power battery's discharge is steady.In Figure 13, the power battery's discharge power decreases obviously after 7838 s.And the time is 16 567 s in Figure 14.  Figure 17 shows the simulation results of the discharge power of the power battery with the FPEMS.

Figure 1
Figure 1 shows the structure of the powertrain of an ERET.The power battery, diesel engine-generator, traction motor, transmission, main reducer, differential, and wheel-side reducer constitute the basic components of the powertrain.The power battery, diesel engine-generator, and traction motor are connected to electricity.The traction motor, transmission, main reducer, differential, and wheel-side reducer are connected mechanically.At the same time, the controller is linked with the diesel engine-generator, power battery, and traction motor by a control link.The design of this powertrain is based on that of a YTO 1804

Figure 1
Figure 1 Structure of the powertrain of ERET

2. 2
Power flow of ERET powertrain An ERET powertrain has two energy sources.One is the power battery; the other is an extended range device consisting of a diesel engine-generator.Multiple energy sources provide the possibility for multiple operating modes.The ERET powertrain has three operating modes, consisting of the pure electric drive, extended-range, and parking charging modes.

Figure 2 Figure 4 .
Figure 2 Power flow in pure electric drive mode Figure 3 shows the power flow in extended-range mode.The tractor works in this mode when the power battery's SOC is lower than its minimum threshold, based on the energy management strategy.The diesel engine's mechanical power is transformed into electrical power by the generator, and it then flows to the power battery.The other power flow is the same as the power flow in pure electric drive mode.Power flow in parking charging mode is shown inFigure 4. The power battery is charged by a charging pile when the tractor is not working and the power battery's SOC is relatively low.The charging pile's electrical power is transmitted to the power battery.

Figure 3 Figure 4
Figure 3 Power flow in extended-range mode F i is the gradient resistance, N; d 1 is the distances of the uniform acceleration stage, m; d 2 is the distances of the uniform velocity stage, m; d 3 is the distances of the uniform deceleration stage, m; d 4 is the distances of the turning stage, m.
constants d m0 are the single-way distances of the tractor's stages, m; (d 10 is the single-way distances of the uniform acceleration stage, d 30 is the single-way distances of the uniform deceleration stage, and d 40 is the single-way distances of the turning stage); S is the operation area of the tractor, mu, (1 mu=666.7 m 2 ); l is the farmland length, m.The working distance of the tractor'

Figure 5
Figure 5 Control of engine start-stop 4.2 Energy management strategy of control parameter adjustment The EMSCPA proposed in this paper is based on the FPEMS.It is simple and easy to use in practice.Based on the improvement of the FPEMS, the utilization of electrical energy of the battery was improved, and the working time of the diesel engine decreased.The diesel engine worked at constant power after the diesel engine started.The control of the diesel engine was the same as the diesel engine start and stop control plus fixed point energy management strategy.The power distribution strategy is expressed in Equation (12): bT T eT bT , () 0 ( ) , () 1 P t P P P t η ϕ η ϕ = ⎧ = ⎨ + = ⎩ (12)

Figure 6
Figure 6 Control flow diagram of control parameter adjustment

Figure 7
Figure 7 Simulation model of ERET

Figure 8 Figure 9
Figure 8 Running diagram of ERET , it can be found that, the diesel engine outputting constant power continued for 7838 sec under the FPEMS.When it enters extended-range mode, the diesel engine's fuel consumption rate reaches 22.328 L/h.When the time reaches 21 108 s, the diesel engine's cumulative fuel consumption runs up to 82.307 L. Under the EMSCPA, the diesel engine starts and works at a constant power at the time of 16 567 s, and when the ERET enters extended-range mode, its fuel consumption rate is around 22.328 L/h.At 21 108 s, the diesel engine's cumulative fuel consumption comes to 28.166 L.

Figure 12 shows
Figure12shows the simulation results of the SOC of power battery and the electrical consumption using the FPEMS and EMSCPA respectively.Under the FPEMS, the power battery's initial SOC value is 80%.At 7838 s the SOC goes down to 50%, and later it goes down, following a lower slope.At 21 108 s the power battery's SOC decreases to 31.36% and the electrical consumption reaches 398.036 kW⋅h.Under the

Figure 11 Figure 12
Figure 11 Fuel consumption rates and cumulative fuel consumptions of the two strategies under the continuous transfer operation

Figure 13
Figure 13 Discharge power of power battery using FPEMS under the continuous transfer operation

Figure 14
Figure 14 Discharge power of power battery adopting EMSCPA under the continuous transfer operation The above simulation results show that under the continuous transfer operation, the cumulative fuel consumption using the EMSCPA is 34.22% of the cumulative fuel consumption employing the FPEMS.The electrical consumption adopting the FPEMS is 70.83% of the electrical consumption conducting the EMSCPA.For the small area deep loosening operation, Figure 15 shows the simulation results of fuel consumption rate and cumulative fuel consumption employing the FPEMS.Under the FPEMS, the diesel engine starts and works at a constant power at the time of 4061 s, and the diesel engine's fuel consumption rate is around 22.328 L/h.At 9346 s, the diesel engine's cumulative fuel consumption reaches 32.781 L. The simulation results of the power battery's SOC and the electrical consumption controlled by the FPEMS and EMSCPA respectively are shown in Figure 16.Under the FPEMS, the power battery's initial SOC value is 70%.The SOC decreases to 50% when the time reaches 4061 s.Later it goes down, following a lower slope.And at 9346 s, the power battery's SOC decreases to 38.30% and electrical consumption increases to 247.638 kW⋅h.Under the EMSCPA, the power battery's initial SOC value is 70%, and the tractor operates in pure electric drive mode on the whole course.When the time reaches 9346 s, the power battery's SOC value reduces to 23.02%, and the electrical consumption adds up to 346.868 kW⋅h.

Figure 18
Figure18shows the simulation results of the discharge power of the power battery with the EMSCPA.It is can be found from Figures17 and 18that the power battery's discharge is steady.In Figure17, the power battery's discharge power decreases obviously after 4061 s.

Figure 15 FuelFigure 16 Figure 17 6 Conclusions
Figure 15 Fuel consumption rate and cumulative fuel consumption of FPEMS under the small area deep loosening operation