Fuel Efficiency Optimization of Input-Split Hybrid Electric Vehicle using DIRECT Algorithm Aishwarya Panday and Hari Om Bansal Department of Electrical and Electronics Engineering Birla Institute of Technology and Science, Pilani, India
[email protected] [email protected] Abstract—For cleaner and greener future, Hybrid vehicle has been accepted as best practical applications for transportation. The presence of two power sources, i.e. engine and battery in hybrid electric vehicles makes it necessary to intelligently split the power for lesser fuel consumption. An intelligent power management strategy is developed to fulfil on road power demand with good fuel economy. This article uses DIRECT method to control toggling between the engine and battery to reduce the overall liquid fuel consumption. The battery charge is utilized effectively without deteriorating its health. The control strategy is based on the optimization of vital parameters such as state of charge in the battery, engine idle speed, engine on duration and power demand. Numerous simulations are executed on the advanced vehicle simulator (ADVISOR) to authenticate the feasibility of the proposed controller. Keywords—Hybrid electric vehicle, power –split configuration, DIRECT algorithm, State of charge, Fuel economy, energy optimization.
I.
INTRODUCTION
Now a day, the world is moving toward cleaner and greener tomorrow. The transportation sector is wiping out the internal combustion engines (ICE) based vehicles because these vehicles use petroleum to propel it and emit toxic gases. As petroleum is a limited resource on the earth and depleting rapidly; an alternative mode of transportation, i.e. Hybrid Electric Vehicles (HEVs) is being hailed by all. This is capable of reducing the dependence on oil energy and cutting down toxic emissions level, hence protecting the environment and life on earth. The automobile industry consumed around 72% of global petroleum consumption in 2012. The fuel consumption rate in hybrid vehicles has been reduced by a greater amount due to its intelligent architectural layout. It consists of an ICE along with high power and efficient motor and generator. In HEV, to provide power to run the motor, a battery is also part of the architecture. The engine and motor in different manner assist the driver to fulfill the vehicle power demand. The rate of fuel consumption changes with the architectural layout adopted in the vehicle. The dominant architectures available in the literature are 1) series, 2) parallel and 3) power-split. The fuel economy and performance in power split architecture is found to be better
than series and parallel layout. In a power split configuration advantages of both parallel and series types are cherished and their disadvantages are removed. Toyota Hybrid System (THS) Prius was the first power split hybrid vehicle which had the capability of reducing the petroleum consumption as well as toxic emissions by using electrical energy stored in the battery [1]. Electric motor and engine of the same rating perform completely differently, as explained in figure 1. An electric motor produces high torque at zero speed while an ICE produces negative torque until some speed is achieved [2]. It is simple to judge, the engine and motor perform efficiently for a particular set of speed and torque ranges i.e. power ranges. If engine performs at its best efficient points, the fuel efficiency of HEV will improve. When the vehicle is 'on', the speed is very low and torque demand is high, start with the motor. When the speed and torque demand lies in the engine's fuel efficient region, turning the engine on is the more economical in terms of fuel saving.
Fig. 1. Engine and motor characteristic plot
During a trip, the vehicle utilizes two modes of operation for better utilizing the battery power and cut down the fuel consumption. In HEV, the battery gets charged
either through regenerative braking or engine, so it is desired to have a sufficiently charged battery at the end of the trip. Therefore, HEVs always follow the assumption of having initial charge is equal to final charge at the end of the trip. This is known as charge sustaining (CS) mode. In charge depleting (CD) mode, vehicle firstly utilizes the charge stored in battery to propel it. So battery depletes up to minimum allowable SOC value. After this the vehicle utilizes the charge sustaining mode (CS) and maintains the SOC level. During CD mode engine is not turned on and in CS mode battery SOC is maintained at the predefined threshold SOC. Figure 2 shows the component level architecture of Prius with series and parallel configuration and power flow directions. It consists of two motor generator set, MG1 and MG2, engine and planetary gear set (PGS). PGS is a speed coupler with three ports and two degrees of freedom and is responsible for transmitting power from/to motor, generator, engine and front wheels. Either engine or MG2 propel the vehicle to fulfil driver power demand. MG2 acts as a motor and gets the power from the battery pack. MG1 charges the battery and acts as a generator.
As, the driver has the prior knowledge of the trip through the GPS facility and other important information like battery SOC, state of health (SOH) through the battery management controller; so, considering all these, an energy management controller can be realized to optimally split the power for better fuel economy. In this paper, the research target is to improve fuel economy of an input split series-parallel HEV using DIRECT. DIRECT is applied to find the optimal values of parameters, under which the engine is turned off, i.e. no liquid fuel consumption and above which engine is on. It is targeted to operate the engine in its efficient region, hence good fuel economy is achieved. This method is efficient to perquisite the fuel economy all the way through the range of simulations. II.
PROBLEM FORMULATION AND POWER TRAIN ANALYSIS
The problem is formulated to reduce the fuel consumption over a trip; hence an objective function is formulated as (1) .
m ft
1
.
where
.
m ft is total fuel consumption in a driving cycle. m f
is time rate of fuel consumption and is written as .
mf =
Pe * g e (l / h) where Pe is engine power, ge is 1000* γ f
specific fuel consumption and kg/l.
γ f is
mass density of fuel
So total fuel consumption in a driving cycle is ∑ ∆ . Fuel consumption is inversely
Fig. 2. Power split hybrid architecture
proportional to battery power Pb . A greater battery power
Substantial research efforts have been made in the energy management of EV to reduce the fuel consumption and emissions [3]. Divide rectangle (DIRECT) is derivative free algorithm, i.e. do not rely on derivatives; hence work nicely even when the objective function is noisy, time-variant and discontinuous. DIRECT generally work for a large search space and provides a global optimal solution for the problem. For a parallel PHEV configuration, DIRECT is used to tune the controller for energy management using MATLAB. Simulation is performed over different driving cycles to analyze their robustness on different driving conditions [4]. The gradient-based and derivative-free algorithm for hybrid electric vehicle performance optimization are compared in [5]. Based on the observations made in [5], Rousseau et al. used the DIRECT to optimize the vehicle performance [6]. As, the DIRECT algorithm does not require the objective function be differential and continuous, hence is suitable for parametric optimization of HEV problems [7].
will cause the vehicle to consume lesser fuel and vice-versa.
Pb is directly proportional to battery SOC as follows .
where ,
is battery capacity,
SOC is the time rate of is the open circuit voltage
Rb internal resistance of battery which can be obtained using (2a) and (2b) [8]. I b is the battery current. and
2 2 MG1, MG2, engine and requested torques
,
,
,
and speeds , , , are can be related using following equations as in (3a), (3b), (3c) and (3d). R and ς are the gear ratio of PGS and the final drive ratio [9-10].
N ω 7 N If SOC is low, the engine may start immediately. As the required vehicle speed increases, the engine starts. ω is the motor speed.
3 1
T
3 3 3
, ,
,
,
,
,
, ,
,
,
where
,
, , ,
4 4 4 4 4 4 4
,
,
,
,
,
,
, ,
,
,
,
,
, ,
,
,
,
,
,
,
, and
are the minimum and maximum values of speed and torque considered as constraints range of engine, MG1, MG2 and SOC respectively. While solving the objective function numerically for HEV, we need to maintain the constraints given in 4(a), 4(b), 4(c) 4(d), 4(e),4(f) and4(g). A. Vehicle power demand and analysis With the prior knowledge of trip profile, tractive force required at the wheel is calculated as in (2). Consider a vehicle of mass M moving at the speed of V on with an angle of alpha. On the road, rolling resistance, aerodynamic drag and rolling resistance oppose its movement [10]. So the total force applied to a vehicle to move in the forward direction is ρA CD V VW Pf Mgsinα 5 F where A is vehicle frontal area, CD is aerodynamic drag that characterizes the shape of the vehicle body, is air density, is vehicle speed and V is component of wind speed with vehicle moving direction, f is the rolling resistance and is road angle. Torque on driven wheel transmitted from the power plant is as in (6). i i ηT 6 T where i is gear ratio of transmission, i is gear ratio of drive line, η is efficiency of driveline from power plant to the driven wheels and T is the torque output from the power plant. T might be the torque of the engine or motor or combination of both, depending upon the torque required at the wheel to propel the vehicle. B. Modes of operation 1) Mode 0 (Launch and backup): During key on and travelling at low speed MG2 provides the primary tractive force.
2) Mode 1 (Normal driving conditions): Under normal driving conditions, the engine's power is divided into two paths: a portion drives the wheel and another portion drives and are tooth number the MG1 to produce electricity. in the ring and the sun gear of PGS respectively. is torque provided by engine to drive the wheel. Tg generating torque is provided by the engine to charge the battery pack and the motoring torque. N T 8 T N N N T 9 T N N N T 10 T N T 0 11 3) Mode 2 (Full acceleration): In this mode, Engine along with MG2 propels the vehicle and supplies the demand. MG2 is supplemented by power from the battery. N is the tooth number in the gear. N T T 12 T N 4) Mode 3 (Deceleration or regenerative braking): Recovered energy from braking is stored in the battery pack as wheels drive the generator. The braking energy dissipated at high speed is recovered with low generator efficiency. At lower speeds the recovering the energy will be low because at low motor rotational speeds, motor electromotive forces are low. The modes of operations described here are used to analyze the fuel efficiency of the vehicle. In mode 0, i.e., to start the vehicle when speed is almost zero or very less, high torque is required. At lower speed, motor's horsepower is 2 to 3 times higher than the rated horsepower and engine's torque is very less. So, running of the motor is beneficial in this condition and hence no fuel consumption. After certain lower speed the engine starts up, charges the battery as well as powers the wheels. If the speeds and torques are chosen wisely the engine will be bound to work in its efficient region and hence the fuel consumption will be optimum. The charge level in the battery increases through MG1 as described (9). MG2 doesn't work in mode 1. In case of cruising, where engine and MG2 both works, motor and engine both will have good electrical and chemical efficiencies respectively. Supposedly trip requires long hours of cruising at higher speed, then the engine and motor continues to supply the demand power, the efficiency may get down, hence fuel economy will be less and battery will get depleted rapidly. Considering the different modes, three
different cases may arise so (6) can be extended as in (13), (14) and (15).
80 70 60
m V i i η 13 T 4pi where m is mean effective pressure, V is volumetric density. (13) uses the engine power and acts like conventional ICE based vehicles.
speed(mph)
Case 1:
40 30 20 10 0
Case 2: d θ dθ B 14 dt dt where T is load torque when mechanical load is applied, J is represents moment of inertia, B is viscous friction and rotation speed. (14) utilizes motor as power plant and this case utilizes the CD mode of operation. T
0
200
400
Case 3:
m V d θ dθ i i η T J B 15 T 4pi dt dt Case 3 is used in condition of cruising and (15) represents CS mode of operation. TRIP ORIENTED ENERGY MANAGEMENT OPTIMIZATION
The force and torque demand of the vehicle in a general trip can be obtained using the road profile on which vehicle is running. Numerous simulations are applied to validate the proposed strategy over the ECE_EUDC drive cycle as shown in figure 3 (a). Required torque on the wheel to move the vehicle is given by (5), the required torque is calculated using the force and is shown in figure 3 (b). Fig. 3 (a) shows the standard road profile over which the control strategy has been tested. Fig. 3 (b) shows the force and torque required with respect to the vehicle speed from fig. 3 (a). The +ve torque in the graph shows that the power is drawn from engine or motor by the vehicle to propel it. The –ve torque indicated that the power is being generated during vehicle propulsion by which the battery can get charged. A real time controller is implemented using DIRECT and simulation is performed in Advanced Vehicle SimulatOR (ADVISOR). The model considered here is valid for both the steady-state and dynamic response.
600 Time(sec)
800
1000
1200
(a)
J
200 F o rc e (N )
i i η
0
-200
0
200
400
600 Time (sec)
800
1000
1200
0
200
400
600 Time (sec)
800
1000
1200
50 T o rq u e (N m )
T
III.
50
0 -50
-100
(b) Fig. 3. (a) ECE_EUDC driving cycle, (b) Force and torque of ECE_EUDC drive cycle
IV.
SIMULATION RESULTS AND DISCUSSION
The simulation is realized in ADvance Vehicle SimulatOR (ADVISOR), a Matlab based high-level powerful vehicle simulator. It used backward-forward facing approach with the advantage of meeting desired trace and can calculate maximum trace [11]. DIRECT is sampling based algorithm and was developed by Donald to find a global minimum using no derivative. The algorithm starts with the hypercube search space. The function is then sampled at the center point. The hypercube is then divided into smaller hyper rectangles and center points of these rectangles are again sampled. DIRECT identifies sets of optimal rectangle in every iteration. DIRECT is the modification of Lipschitz approach which does not specify the Lipschitz constant. When Lipchitz constant is not used, all the possible searches are performed for a predefined number of iteration [7,12-13]. This article optimizes the cs_eng_on_soc, cs_min_pwr, cs_electric_launch_spd and cs_eng_min_spd. cs_eng_on_soc is the minimum value of SOC below which the engine must be on. cs_min_pwr is the minimum power
Using all the constraint engine 'on' threshold is calculated; the engine is made 'on' and fuel consumption is calculated. The summarized fuel consumption and optimum values calculated for different parameters are listed in the table 1. To set 1, the highest fuel economy is obtained for cs_min_pwr. It is also observed that in set 1, for individual parameters the fuel economy is better that set 2, set 3 and set 4 parameters. This clearly depicts the impact of parameters over each other.
Parameters
Set 1
cs_eng_on_soc cs_min_pwr cs_electric_launch_spd cs_eng_min_spd cs_min_pwr and cs_electric_launch_spd cs_eng_on_soc and cs_eng_min_spd cs_eng_on_soc and cs_min_pwr cs_eng_on_soc and cs_electric_launch_spd cs_min_pwr and cs_eng_min_spd cs_electric_launch_spd and cs_eng_min_spd cs_eng_on_soc, cs_min_pwr and cs_electric_launch_spd cs_eng_on_soc, cs_min_pwr and cs_eng_min_spd cs_eng_on_soc, cs_electric_launch_spd and cs_eng_min_spd cs_min_pwr, cs_electric_launch_spd and cs_eng_min_spd cs_min_pwr, cs_electric_launch_spd, cs_eng_min_spd and cs_eng_on_soc
Set 3
Set 4
70 65
Fuel economy (mpgge*) 44.61 45.41 43.43 44.61 43.54 42.59 42.59 42.56 43.43 43.39 43.28 43.35
60 55
50 45
FUEL ECONOMY WITH DIFFERENT PARAMETERS
Set
Set 2
75
40
200
400
600 800 Time (sec)
1000
1200
1400
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
42.19
0.2
43.35
0.1
42.89
0
cs_min_pwr shows the highest fuel economy in all the cases considered. The different plots are gathered to verify the authenticity of the proposed discussion. The initial charge on battery cs_init_soc=70% and minimum allowable range up to which the battery can be depleted is 30%. The variation of SOC over the entire trip is shown in figure 4 (a). Figure 4 (b) shows the engine off/on status with respect to varying SOC as shown in figure 4 (a). Analyzing figure 4 (a) and (b) together, clarify that whenever the engine is
0
(a)
e n g in e o f f s t a t u s
TABLE I.
off, the SOC is decreasing, i.e. propulsion power is provided by a motor. Similarly, when the engine is on, SOC level is either increasing or held constant, i.e., the battery is getting charged either through regenerative braking or by engine. Figure 4 (c) represents the fuel consumption for the trip. It can easily be observed that the motor is on for zero fuel consumption case only. After 100 seconds the engine gets on and recharges the battery up to 70% to make the charge available for the next trip. Figure 4 (d) and (e) show the engine and motor characteristics according to the speed and torque values which have been used during vehicle propulsion over the trip.
S O C (% )
commanded of the engine. cs_electric_launch_spd is the vehicle speed threshold; below this speed, the engine is turned off. cs_eng_min_spd is the speed below which engine will be on but does not utilize the fuel. Parameters individually or/and under the influence of each other and affects the performance of the vehicle. To analyze this, parameters are grouped in different sets, i.e., Set 1, set 2, set 3 and set 4. Set 1 contains the individual parameters considered, set 2 contains group of two parameters, set 3 contains a group of 3 parameters and set 4 contains group of four parameters. Sets and the contained parameters are shown in table 1. Value selection of these parameters affects the engine on/off status; hence have an impact on fuel consumption. DIRECT has been used here to find the optimal values of parameters to maximize the fuel economy as well as supply the road power demand.
0
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600 800 Time (sec)
(b)
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1400
V.
0.7
The HEVS are occupying a larger space in the transport sector. Maximization of fuel efficiency in HEVs is of utmost importance. The main purpose of this paper is to propose DIRECT strategy to control hybrid vehicles in optimality. The DIRECT algorithm can be used for realtime optimal control. The various vital parameters are optimized here for maximizing the fuel economy and the results of different combinations are tabulated. Detailed analysis is performed to check the impact of these considered parameters over each other and variation in fuel consumption is observed.
0.6
F u e l u s e (lit e rs )
0.5 0.4 0.3 0.2 0.1 0
CONCLUSION
REFERENCES 0
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[1]
(c)
500
Torque versus speed
400
[2]
E n g in e s p e e d
[3]
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[4]
0 150
Speed versus torque
[5] 100 50
[6]
0 0
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(d)
[7] [8]
Torque versus speed
400
[9]
M o to r s p e e d
350 300
[10]
250 200
[11]
150 100
Speed versus torque
[12]
50
[13]
0 -50 150
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-50
0 50 Motor torque
100
(e) Fig. 4. (a) SOC variation over entire trip (b) Fuel consumption over entire trip, (c) Engine speed torque characteristics, (d) Motor speed torque characteristics.
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