Drive Cycle Generation for Stochastic Optimization ... - Semantic Scholar
2010 IEEE International Conference on Control Applications Part of 2010 IEEE Multi-Conference on Systems and Control Yokohama, Japan, September 8-10, 2010
Drive Cycle Generation for Stochastic Optimization of Energy Management Controller for Hybrid Vehicles Volker Schwarzer, Reza Ghorbani and Richard Rocheleau Abstract— A methodology to generate drive cycles based on probabilistic driving profiles is presented in this paper. The described approach can be utilized for the stochastic optimization of an energy management controller (EMC) for hybrid electric vehicles (HEVs). It enables for an optimal design towards a probabilistic driving portfolio such as individual driving characteristics of the vehicle operator, location, traffic conditions, topography and environment. Hence, maximum fuel efficiency for the individual driver can be achieved. The introduced method is implemented in a drive cycle generation tool. The approach is validated using a model of a parallel HEV powered by fuel cells. Simulation results are presented and the advantage of the proposed method over conventional approaches is proven.
I. INTRODUCTION Hybrid electric vehicles are characterized by combining two or more power sources to achieve an improved fuel economy. In order to accomplish this, the energy storage systems (e.g., batteries) in HEVs are utilized for recapturing the kinetic energy of the moving vehicle during braking intervals through regenerative braking. This extra degree of freedom, which is the power distribution between the sources of energy and the energy storage system, must be optimally controlled to achieve the best possible fuel economy. A typical HEV in city can then reduce gasoline consumption by approximately 30% in comparison to a conventional vehicle. However, this reduction is tied with the HEV powertrain characteristics and topology, drive cycle and operating conditions. As HEVs are gaining more popularity in the market, the importance of the energy management controller is escalating. Various approaches for the design and optimization of EMCs for HEVs have been published in the literature. Early energy management controllers were based on heuristic considerations such as simple rules or maps. State-of-the-art control strategies for HEVs are classified and reviewed by Salmasi [1]. Fuzzy logic-based control of hybrid vehicles has been reported by Langari and Won [2]. Dynamic Programming methodologies have been employed to determine the optimal control trajectories for HEVs, which can then be used as a benchmark to design control rules [3]. The above mentioned strategies are typically optimized for a specific vehicle by applying one characteristic drive cycle This work was supported by the Hawaii Natural Energy Institute (HNEI). V. Schwarzer is with the Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, USA [email protected] R. Ghorbani is an Assistant Professor with the Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, USA
[email protected] R. Rocheleau is the director of the Hawaii Natural Energy Institute, School of Ocean And Earth Science And Technology, University of Hawaii at Manoa, Honolulu, USA [email protected]
978-1-4244-5363-4/10/$26.00 ©2010 IEEE
and assuming constant operating characteristics. However, Sciarretta et al. stated that the achievable improvement in fuel economy using heuristic methods strongly depends on the particular vehicle and the driving conditions [4]. A driving profile of a real-world vehicle cannot be represented by a single drive cycle and constant operating conditions. It is rather dependent on an individual set of properties, such as driving characteristics of the vehicle operator, location, traffic conditions, topography and environment. Thus, an energy management strategy that has been optimized for one average assumed drive cycle and driving conditions is not necessarily an optimal strategy for a driving portfolio. In order to design a near optimal EMC for an individual driving profile, it is necessary to probabilistically describe the driving properties and subsequently optimize the EMC stochastically. This methodology facilitates the capability to adapt and optimize the EMC towards the driving characteristics of the vehicle operator. The paper presents a methodology to create individually adaptive driving profiles. A drive cycle generation tool is introduced, which is capable of generating drive cycles for the stochastic optimization of EMCs towards a specific driving profile. The method is then tested using a fuel cell hybrid vehicle model. Simulation results show the advantage of the proposed method over conventional approaches. II. HEV MODEL
Fig. 1. System architecture and energy control setup of fuel cell powered HEV
A Matlab/Simulink model of a fuel cell powered hybrid electrical vehicle was used for this research. The system architecture of the HEV is presented in Fig. 1. The vehicle is powered by a fuel cell stack and a lithium-ion battery pack as a buffer. The energy generated by the fuel cell stack is distributed between the electric motor and the battery. Consequently, the battery pack is either charged by excess
536
TABLE I
voltage source is described by the following equation:
S PECIFICATIONS OF VEHICLE - AND POWERTRAIN SOFTWARE MODEL Parameters Base vehicle weight Fuel cell type Fuel cell stack power Number of cells Battery type Battery nominal voltage Battery capacity Gradient coefficient Drag coefficient Tire rolling resistance Front area
E = E0 − K
Value 1200kg PEMFC 36kW 180 Li-ion battery 200V 6.5Ah 0 0.29 0.013 2m2
Q ∗ Q i −K it + A · e−B·it Q − it Q − it
(1)
,where E is the no load voltage, E 0 is constant voltage, K a polarization constant, i ∗ low frequency current dynamics, i the battery current, it the extracted capacity, Q the maximum battery capacity, A an exponential voltage and B an exponential capacity. A detailed description of the model can be found in reference [10]. C. Vehicle Dynamics Model The vehicle dynamics model computes the external forces applied to the vehicle for each iteration of the simulation. The external forces are inertia force for acceleration (F acc ), projected normal force (F grav ), rolling resistance (F roll ) and aerodynamic drag (F drag ).
energy provided from the fuel cell stack or by regenerative breaking.
Facc = m · a Fgrav = m · g · sin θ
A. Fuel Cell System Model
(2) (3)
Froll = µ · m · g · cos θ (4) 1 (5) Fdrag = · ρair · v 2 · cd · Af ront 2 Here, m is the vehicle mass, a the acceleration, g the gravitational acceleration, θ the road angle, ρ air the density of air, v the velocity of the vehicle, c d the drag coefficient and Af ront the vehicle’s front area. The power demand of the vehicle is then calculated with the external forces and the incremental change of position between each iteration. D. Energy Management Controller
Fig. 2. Schematic diagram of fuel cell system including cooling and humidification setup
A schematic diagram of the fuel cell system (FCS) is illustrated in Fig. 2. The FCS consists of a 36kW proton exchange membrane fuel cell (PEMFC) stack, a humidifier, an air pump, and a cooling system. The fuel cell stack is fed with hydrogen from a hydrogen tank on the anode side and air is provided by the air pump on the cathode side. Dry atmospheric air is humidified before entering the stack using the wet exhaust of the fuel cell stack. A radiator is utilized to keep the operating temperature of the fuel cell stack at an approximate constant level of 350K. The stack voltage is computed as a function of pressure, temperature, reactant partial pressure and relative humidity [5]-[9]. B. Battery Model A simple controlled voltage source in series with a constant resistance is used to model the battery. The open voltage source is calculated with a non-linear equation based on the actual state-of-charge (SOC) of the battery. The controlled
A predictive EMC is implemented in the HEV simulation. Fig. 3 shows a schematic diagram of the EMC. The controller uses information about terrain, traffic and individual driving characteristics to generate an approximation of the expected drive cycle. The vehicle dynamics model utilizes this data to estimate the average power demand of the vehicle during city and highway phases. During operation of the vehicle, the EMC measures the average error of a 20 second period between the battery’s state-of-charge (SOC) and the expected SOC. The scaled error feeds back to the power demand input. An evolutionary algorithm is used to optimize two control parameters for each drive cycle. The first parameter adjusts the power demand approximation which is computed by a vehicle dynamics model (meta-model). The second parameter scales the average SOC error. The objective function of the parameter optimization is to minimize the overall fuel consumption. III. STOCHASTIC DRIVE CYCLE GENERATION A driving profile is the collectivity of all duty cycles performed by a vehicle during its lifetime. In order to create a stochastic representation of a driving profile, the common key elements of all possible drive cycles have to be identified. Any drive cycle can then be partitioned into sections according to the identified elements. The key elements used in this study are: overall drive cycle duration, acceleration in city,
537
Fig. 3.
Schematic Diagram of the EMC
deceleration in city, acceleration on highway, deceleration on highway, cruising speed in city, cruising duration in city, cruising speed on highway, cruising duration on highway and stop duration. This classification can be extended if necessary. Each element is mathematically described and a probability function is assigned. The probability functions of the elements can be determined if the driving profile is entirely known in advance. If not, another option is to extrapolate available data of the expected drive cycles to obtain an estimation of the probability functions. Table II provides an overview of the key elements and the parameters. TABLE II Fig. 4.
K EY VARIABLES FOR THE STOCHASTIC GENERATION OF DRIVE CYCLES Variable Overall drive cycle duration (s) Acceleration in city (ms−2 ) Deceleration in city (ms−2 ) Acceleration on highway (ms−2 ) Deceleration on highway (ms−2 ) Cruising duration in city (s) Cruising duration on highway (s) Cruising speed in city (ms−2 ) Cruising speed on highway (ms−2 ) Full stop duration (s)
µ 1800 1.3 -1.4 1.3 -1.4 25 400 9 25 10
σ 0.4 0.4 0.2 0.4 0.2 0.8 0.8 0.4 0.4 0.4
min 400 0.5 -1.9 1 -1.9 0 50 0 10 2
max 3000 1.9 -1 1.9 -1 200 1000 18 30 80
In this study, a stochastic driving profile based on an extended Urban Dynamometer Driving Schedule (UDDS) duty cycle is implemented in a software tool. The UDDS schedule is typically used for light duty vehicle testing in large metropolitan area. To simplify matters, Gaussian distributions are applied as probability functions, 2 1 x−µ 1 f (x; µ, σ) = √ exp − 2 σ σ 2π
(6)
Modular principle of the drive cycle generation tool
generated according to the implemented probability functions. First of all, the overall drive cycle length is determined. Corresponding to this result, the tool then creates values for the quantity, order and duration of city and highway driving phases. Next, parameters are generated for the sub-elements of these phases (acceleration, speed, duration, deceleration and quantity). The elements are then joined to form the drivecycle. Finally, velocity noise is added to the cruising phases of the cycle. Velocity noise is caused by traffic, road topology or unintentional driving maneuvers. Summation of sinusoidal functions (Eqn. 7) proves to be a good mathematical approach to model these noises; probability functions can be applied to the parameters of the function without a high sensitivity towards changing the characteristics of the noise. The parameters of the sinusoidal functions and the probability functions are determined via curve-fitting. Values presented in Table III have been derived based on the UDDS duty cycle.
where f (x; µ, σ) is a probability density function, σ 2 the variance, σ the standard deviation and µ the mean. The software tool is capable of generating an unlimited number of drive cycles. The modular principle of the tool is illustrated in Fig. 4. All parameters of the elements are
538
f (a1 ..an , b1 ..bn , c1 ..cn ) =
n i=1
(ai · sin (bi + ci ))
(7)
TABLE III PARAMETERS FOR MODELING VELOCITY NOISE (E QN . 7) DETERMINED BY CURVE FITTING FROM THE
Variable i 1 2 3 4 5
City ai 1.98 0.92 1.07 0.25 0.32
bi 0.07 0.38 0.47 0.26 0.65
ci 4.26 1.20 0.57 -0.49 -3.85
UDDS DUTY CYCLE Highway ai bi 1.28 0.02 1.30 0.09 0.57 0.18 0.73 0.13 0.73 0.25
ci 2.60 -1.01 0.95 -2.33 1.81
IV. RESULTS A. Drive Cycle Generation Figure 5 shows three different drive cycles generated by the drive cycle tool. All three cycles distinguish each other by different parameters, such as overall drive cycle duration, ratio between highway and city driving or cruising time. However, all cycles share the key characteristics of a specific driving profile that was based on the UDDS driving schedule, which represents driving in a busy city with numerous stopand-go periods and busy highway driving.
inefficiencies due to internal losses, as well as increased power demand by auxiliary components. It is evident that the battery is optimally utilized as a buffer to compensate for short-term deviations of the average power during a driving phase and the actual power demand . The variation of SOC is significantly low with ±7% over the entire length of the drive cycle. Furthermore, the SOC at the end of the cycle is at a similar level of 50% as its initial value. The overall efficiency of the system during the drive cycle is computed to be 32.11% based on the ratio of the upper heating value ∆HC0 of the consumed hydrogen to the energy used to power the vehicle. To investigate the efficiency of the above controller setup for a driving profile, the same EMC controller setup is now used for a drive cycle created by the tool. The created cycle shares similar characteristics to the UDDS drive cycle. The drive cycle and simulation results are presented in Fig. 7. The parameter tuning is no longer ideal for this drive cycle despite similar characteristics of the drive cycle to the UDDS profile. In addition, the fuel cell is not flawlessly operating in a quasi-static mode during city driving and generates more energy than needed during highway cycles. The excess energy is charged to the battery pack. As a consequence, the battery’s SOC at the end of the drive cycle is roughly 20% higher than its initial SOC. The overall efficiency of the system simulation based on the upper heating value of the consumed hydrogen is 30.18%, approximately 2% lower than before. Despite the fact that the applied control strategy was based on the characteristics of the UDDS drive cycle, it is not necessarily as efficient for probabilistic cycles derived by those characteristics. The proposed controller setup is not ideal for this cycle. C. Controller Efficiency
Fig. 5.
A set of 50 drive cycles is created to investigate a possible efficiency gain of a stochastic controller designed for an entire driving profile compared to a conventional controller. The HEV system simulation is then executed for all drive cycles and both controller strategies. The overall fuel consumption of the 50 cycle driving profile is measured for both controllers and compared. The optimal control parameters of the average assumed UDDS cycle are applied for the conventional control setup. For the stochastic controller, the genetic optimization algorithm determines the optimal EMC parameters for each drive cycle. The stochastic controller exceeds the performance of the conventional non-stochastic setup by approximately 1% in respect of fuel efficiency. An improvement of 2% is obtained for a driving profile of 50 cycles with larger deviations towards the average drive cycle. This is significant since only a software modification for EMS is implemented.
Three random drive cycles created by the drive cycle generator
B. EMC Optimization The result of the EMC strategy optimization for the UDDS drive cycle is presented in Fig. 6. Optimal controller tuning was achieved with a genetic optimization algorithm minimizing overall fuel consumption. The fuel cell stack is mostly operated in quasi-static mode in order to avoid dynamic
V. CONCLUSION AND FUTURE WORKS A drive cycle generation tool based on probabilistic driving profiles has been developed for the stochastic optimization of EMC strategies for HEVs. The necessity to stochastically optimize energy management systems has been exposed
539
FC Stack Power Demand (kW)
Battery SOC (%)
Vehicle Power (kW)
Drive Cycle (m/s)
30 20 10 0 4 2 0 −2 60 50 40 10 5 0
0
200
400
Fig. 6.
600
800
1000 Time (s)
1200
1400
1600
1800
UDDS drive dycle: System simulation after EMC parameter optimization
FC Stack Power Demand (kW)
Battery SOC (%)
Vehicle Power (kW)
Drive Cycle (m/s)
40 20 0 5 0 −5 70 60 50 40 15 10 5 0
0
500
1000
1500
2000
2500
Time (s)
Fig. 7.
Generated random drive cycle: Non ideal energy management when UDDS EMC strategy applied
when HEVs are used for a variety of driving conditions rather than just one driving schedule in a fixed environment. The optimization of an EMC strategy based on just one drive cycle does not necessarily guarantee highest fuel efficiency for a probabilistic driving profile. Therefore, the development of a stochastic optimization tool for heuristic EMCs is proposed in order to capture the stochastic sensitivity of EMCs towards a driving profile. VI. ACKNOWLEDGMENTS The authors gratefully acknowledge the contribution of the Hawaii Natural Energy Institute, the Gottlieb Daimler and Carl Benz Foundation and reviewers’ comments. R EFERENCES [1] F. R. Salmasi, ”Control Strategies for hybrid electric vehicles: evolution, classification, comparison, and future trends”, IEEE Transactions on Vehicular Technology, vol. 56, issue 5, part 1, 2007, pp. 2393-2404. [2] H. D. Won and R. Langari, ”Fuzzy torque distribution control for a parallel hybrid vehicle”, Int. J. Knowl. Eng. Neural Netw., vol. 19, 2002, pp. 4-10.
[3] L. Johannesson and B. Egardt, ”Approximate dynamic programming applied to parallel hybrid powertrains”, Proceedings of the 17th World Congress IFAC, 2008, pp. 3373-3379. [4] A. Sciarretta and L. Guzzella, ”Control of hybrid electric vehicles”, IEEE Control Systems Magazine, vol. 27(2), 2007, pp. 60-70. [5] S. Yerramalla, A. Davari, A. Feliachi and T. Biswas, ”Modeling and simulation of the dynamic behavior of a polymer electrolyte membrane fuel cell”, Journal of Power Sources, vol. 124, 2003, pp. 104-113. [6] J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge, ”Performance modeling of the ballard mark iv solid polymer electrolyte fuel cell”, Journal of the Electrochemical Society, vol. 142, 1995, pp. 1-8. [7] T. E. Springer, T. A. Zawodzinski, and S. Gottesfeld, ”Polymer electrolyte fuel cell model”, Journal of the Electrochemical Society, vol. 138(8), 1991, pp. 2334-2342. [8] T. V. Nguyen and R. E. White, ”A water and heat management model for proton-exchange membrane fuel cells”, Journal of the Electrochemical Society, vol. 140(8), 1993, pp. 2178-2186. [9] J. T. Pukrushpan, H. Peng, and A. G. Stefanopoulou, ”Controloriented modeling and analysis for automotive fuel cell systems”, Journal of Dynamic Systems, Measurement and Control, vol. 126, 2004, pp. 1425. [10] O. Tremblay, L. A. Dessaint and A. I. Dekkiche, ”A generic battery model for the dynamic simulation of hybrid electric vehicles”, Vehicle Power and Propulsion Conference, 2007, pp. 284-289.
540
Drive Cycle Generation for Stochastic Optimization of Energy Management Controller for Hybrid Vehicles Volker Schwarzer, Reza Ghorbani and Richard Rocheleau Abstract— A methodology to generate drive cycles based on probabilistic driving profiles is presented in this paper. The described approach can be utilized for the stochastic optimization of an energy management controller (EMC) for hybrid electric vehicles (HEVs). It enables for an optimal design towards a probabilistic driving portfolio such as individual driving characteristics of the vehicle operator, location, traffic conditions, topography and environment. Hence, maximum fuel efficiency for the individual driver can be achieved. The introduced method is implemented in a drive cycle generation tool. The approach is validated using a model of a parallel HEV powered by fuel cells. Simulation results are presented and the advantage of the proposed method over conventional approaches is proven.
I. INTRODUCTION Hybrid electric vehicles are characterized by combining two or more power sources to achieve an improved fuel economy. In order to accomplish this, the energy storage systems (e.g., batteries) in HEVs are utilized for recapturing the kinetic energy of the moving vehicle during braking intervals through regenerative braking. This extra degree of freedom, which is the power distribution between the sources of energy and the energy storage system, must be optimally controlled to achieve the best possible fuel economy. A typical HEV in city can then reduce gasoline consumption by approximately 30% in comparison to a conventional vehicle. However, this reduction is tied with the HEV powertrain characteristics and topology, drive cycle and operating conditions. As HEVs are gaining more popularity in the market, the importance of the energy management controller is escalating. Various approaches for the design and optimization of EMCs for HEVs have been published in the literature. Early energy management controllers were based on heuristic considerations such as simple rules or maps. State-of-the-art control strategies for HEVs are classified and reviewed by Salmasi [1]. Fuzzy logic-based control of hybrid vehicles has been reported by Langari and Won [2]. Dynamic Programming methodologies have been employed to determine the optimal control trajectories for HEVs, which can then be used as a benchmark to design control rules [3]. The above mentioned strategies are typically optimized for a specific vehicle by applying one characteristic drive cycle This work was supported by the Hawaii Natural Energy Institute (HNEI). V. Schwarzer is with the Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, USA [email protected] R. Ghorbani is an Assistant Professor with the Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, USA
[email protected] R. Rocheleau is the director of the Hawaii Natural Energy Institute, School of Ocean And Earth Science And Technology, University of Hawaii at Manoa, Honolulu, USA [email protected]
978-1-4244-5363-4/10/$26.00 ©2010 IEEE
and assuming constant operating characteristics. However, Sciarretta et al. stated that the achievable improvement in fuel economy using heuristic methods strongly depends on the particular vehicle and the driving conditions [4]. A driving profile of a real-world vehicle cannot be represented by a single drive cycle and constant operating conditions. It is rather dependent on an individual set of properties, such as driving characteristics of the vehicle operator, location, traffic conditions, topography and environment. Thus, an energy management strategy that has been optimized for one average assumed drive cycle and driving conditions is not necessarily an optimal strategy for a driving portfolio. In order to design a near optimal EMC for an individual driving profile, it is necessary to probabilistically describe the driving properties and subsequently optimize the EMC stochastically. This methodology facilitates the capability to adapt and optimize the EMC towards the driving characteristics of the vehicle operator. The paper presents a methodology to create individually adaptive driving profiles. A drive cycle generation tool is introduced, which is capable of generating drive cycles for the stochastic optimization of EMCs towards a specific driving profile. The method is then tested using a fuel cell hybrid vehicle model. Simulation results show the advantage of the proposed method over conventional approaches. II. HEV MODEL
Fig. 1. System architecture and energy control setup of fuel cell powered HEV
A Matlab/Simulink model of a fuel cell powered hybrid electrical vehicle was used for this research. The system architecture of the HEV is presented in Fig. 1. The vehicle is powered by a fuel cell stack and a lithium-ion battery pack as a buffer. The energy generated by the fuel cell stack is distributed between the electric motor and the battery. Consequently, the battery pack is either charged by excess
536
TABLE I
voltage source is described by the following equation:
S PECIFICATIONS OF VEHICLE - AND POWERTRAIN SOFTWARE MODEL Parameters Base vehicle weight Fuel cell type Fuel cell stack power Number of cells Battery type Battery nominal voltage Battery capacity Gradient coefficient Drag coefficient Tire rolling resistance Front area
E = E0 − K
Value 1200kg PEMFC 36kW 180 Li-ion battery 200V 6.5Ah 0 0.29 0.013 2m2
Q ∗ Q i −K it + A · e−B·it Q − it Q − it
(1)
,where E is the no load voltage, E 0 is constant voltage, K a polarization constant, i ∗ low frequency current dynamics, i the battery current, it the extracted capacity, Q the maximum battery capacity, A an exponential voltage and B an exponential capacity. A detailed description of the model can be found in reference [10]. C. Vehicle Dynamics Model The vehicle dynamics model computes the external forces applied to the vehicle for each iteration of the simulation. The external forces are inertia force for acceleration (F acc ), projected normal force (F grav ), rolling resistance (F roll ) and aerodynamic drag (F drag ).
energy provided from the fuel cell stack or by regenerative breaking.
Facc = m · a Fgrav = m · g · sin θ
A. Fuel Cell System Model
(2) (3)
Froll = µ · m · g · cos θ (4) 1 (5) Fdrag = · ρair · v 2 · cd · Af ront 2 Here, m is the vehicle mass, a the acceleration, g the gravitational acceleration, θ the road angle, ρ air the density of air, v the velocity of the vehicle, c d the drag coefficient and Af ront the vehicle’s front area. The power demand of the vehicle is then calculated with the external forces and the incremental change of position between each iteration. D. Energy Management Controller
Fig. 2. Schematic diagram of fuel cell system including cooling and humidification setup
A schematic diagram of the fuel cell system (FCS) is illustrated in Fig. 2. The FCS consists of a 36kW proton exchange membrane fuel cell (PEMFC) stack, a humidifier, an air pump, and a cooling system. The fuel cell stack is fed with hydrogen from a hydrogen tank on the anode side and air is provided by the air pump on the cathode side. Dry atmospheric air is humidified before entering the stack using the wet exhaust of the fuel cell stack. A radiator is utilized to keep the operating temperature of the fuel cell stack at an approximate constant level of 350K. The stack voltage is computed as a function of pressure, temperature, reactant partial pressure and relative humidity [5]-[9]. B. Battery Model A simple controlled voltage source in series with a constant resistance is used to model the battery. The open voltage source is calculated with a non-linear equation based on the actual state-of-charge (SOC) of the battery. The controlled
A predictive EMC is implemented in the HEV simulation. Fig. 3 shows a schematic diagram of the EMC. The controller uses information about terrain, traffic and individual driving characteristics to generate an approximation of the expected drive cycle. The vehicle dynamics model utilizes this data to estimate the average power demand of the vehicle during city and highway phases. During operation of the vehicle, the EMC measures the average error of a 20 second period between the battery’s state-of-charge (SOC) and the expected SOC. The scaled error feeds back to the power demand input. An evolutionary algorithm is used to optimize two control parameters for each drive cycle. The first parameter adjusts the power demand approximation which is computed by a vehicle dynamics model (meta-model). The second parameter scales the average SOC error. The objective function of the parameter optimization is to minimize the overall fuel consumption. III. STOCHASTIC DRIVE CYCLE GENERATION A driving profile is the collectivity of all duty cycles performed by a vehicle during its lifetime. In order to create a stochastic representation of a driving profile, the common key elements of all possible drive cycles have to be identified. Any drive cycle can then be partitioned into sections according to the identified elements. The key elements used in this study are: overall drive cycle duration, acceleration in city,
537
Fig. 3.
Schematic Diagram of the EMC
deceleration in city, acceleration on highway, deceleration on highway, cruising speed in city, cruising duration in city, cruising speed on highway, cruising duration on highway and stop duration. This classification can be extended if necessary. Each element is mathematically described and a probability function is assigned. The probability functions of the elements can be determined if the driving profile is entirely known in advance. If not, another option is to extrapolate available data of the expected drive cycles to obtain an estimation of the probability functions. Table II provides an overview of the key elements and the parameters. TABLE II Fig. 4.
K EY VARIABLES FOR THE STOCHASTIC GENERATION OF DRIVE CYCLES Variable Overall drive cycle duration (s) Acceleration in city (ms−2 ) Deceleration in city (ms−2 ) Acceleration on highway (ms−2 ) Deceleration on highway (ms−2 ) Cruising duration in city (s) Cruising duration on highway (s) Cruising speed in city (ms−2 ) Cruising speed on highway (ms−2 ) Full stop duration (s)
µ 1800 1.3 -1.4 1.3 -1.4 25 400 9 25 10
σ 0.4 0.4 0.2 0.4 0.2 0.8 0.8 0.4 0.4 0.4
min 400 0.5 -1.9 1 -1.9 0 50 0 10 2
max 3000 1.9 -1 1.9 -1 200 1000 18 30 80
In this study, a stochastic driving profile based on an extended Urban Dynamometer Driving Schedule (UDDS) duty cycle is implemented in a software tool. The UDDS schedule is typically used for light duty vehicle testing in large metropolitan area. To simplify matters, Gaussian distributions are applied as probability functions, 2 1 x−µ 1 f (x; µ, σ) = √ exp − 2 σ σ 2π
(6)
Modular principle of the drive cycle generation tool
generated according to the implemented probability functions. First of all, the overall drive cycle length is determined. Corresponding to this result, the tool then creates values for the quantity, order and duration of city and highway driving phases. Next, parameters are generated for the sub-elements of these phases (acceleration, speed, duration, deceleration and quantity). The elements are then joined to form the drivecycle. Finally, velocity noise is added to the cruising phases of the cycle. Velocity noise is caused by traffic, road topology or unintentional driving maneuvers. Summation of sinusoidal functions (Eqn. 7) proves to be a good mathematical approach to model these noises; probability functions can be applied to the parameters of the function without a high sensitivity towards changing the characteristics of the noise. The parameters of the sinusoidal functions and the probability functions are determined via curve-fitting. Values presented in Table III have been derived based on the UDDS duty cycle.
where f (x; µ, σ) is a probability density function, σ 2 the variance, σ the standard deviation and µ the mean. The software tool is capable of generating an unlimited number of drive cycles. The modular principle of the tool is illustrated in Fig. 4. All parameters of the elements are
538
f (a1 ..an , b1 ..bn , c1 ..cn ) =
n i=1
(ai · sin (bi + ci ))
(7)
TABLE III PARAMETERS FOR MODELING VELOCITY NOISE (E QN . 7) DETERMINED BY CURVE FITTING FROM THE
Variable i 1 2 3 4 5
City ai 1.98 0.92 1.07 0.25 0.32
bi 0.07 0.38 0.47 0.26 0.65
ci 4.26 1.20 0.57 -0.49 -3.85
UDDS DUTY CYCLE Highway ai bi 1.28 0.02 1.30 0.09 0.57 0.18 0.73 0.13 0.73 0.25
ci 2.60 -1.01 0.95 -2.33 1.81
IV. RESULTS A. Drive Cycle Generation Figure 5 shows three different drive cycles generated by the drive cycle tool. All three cycles distinguish each other by different parameters, such as overall drive cycle duration, ratio between highway and city driving or cruising time. However, all cycles share the key characteristics of a specific driving profile that was based on the UDDS driving schedule, which represents driving in a busy city with numerous stopand-go periods and busy highway driving.
inefficiencies due to internal losses, as well as increased power demand by auxiliary components. It is evident that the battery is optimally utilized as a buffer to compensate for short-term deviations of the average power during a driving phase and the actual power demand . The variation of SOC is significantly low with ±7% over the entire length of the drive cycle. Furthermore, the SOC at the end of the cycle is at a similar level of 50% as its initial value. The overall efficiency of the system during the drive cycle is computed to be 32.11% based on the ratio of the upper heating value ∆HC0 of the consumed hydrogen to the energy used to power the vehicle. To investigate the efficiency of the above controller setup for a driving profile, the same EMC controller setup is now used for a drive cycle created by the tool. The created cycle shares similar characteristics to the UDDS drive cycle. The drive cycle and simulation results are presented in Fig. 7. The parameter tuning is no longer ideal for this drive cycle despite similar characteristics of the drive cycle to the UDDS profile. In addition, the fuel cell is not flawlessly operating in a quasi-static mode during city driving and generates more energy than needed during highway cycles. The excess energy is charged to the battery pack. As a consequence, the battery’s SOC at the end of the drive cycle is roughly 20% higher than its initial SOC. The overall efficiency of the system simulation based on the upper heating value of the consumed hydrogen is 30.18%, approximately 2% lower than before. Despite the fact that the applied control strategy was based on the characteristics of the UDDS drive cycle, it is not necessarily as efficient for probabilistic cycles derived by those characteristics. The proposed controller setup is not ideal for this cycle. C. Controller Efficiency
Fig. 5.
A set of 50 drive cycles is created to investigate a possible efficiency gain of a stochastic controller designed for an entire driving profile compared to a conventional controller. The HEV system simulation is then executed for all drive cycles and both controller strategies. The overall fuel consumption of the 50 cycle driving profile is measured for both controllers and compared. The optimal control parameters of the average assumed UDDS cycle are applied for the conventional control setup. For the stochastic controller, the genetic optimization algorithm determines the optimal EMC parameters for each drive cycle. The stochastic controller exceeds the performance of the conventional non-stochastic setup by approximately 1% in respect of fuel efficiency. An improvement of 2% is obtained for a driving profile of 50 cycles with larger deviations towards the average drive cycle. This is significant since only a software modification for EMS is implemented.
Three random drive cycles created by the drive cycle generator
B. EMC Optimization The result of the EMC strategy optimization for the UDDS drive cycle is presented in Fig. 6. Optimal controller tuning was achieved with a genetic optimization algorithm minimizing overall fuel consumption. The fuel cell stack is mostly operated in quasi-static mode in order to avoid dynamic
V. CONCLUSION AND FUTURE WORKS A drive cycle generation tool based on probabilistic driving profiles has been developed for the stochastic optimization of EMC strategies for HEVs. The necessity to stochastically optimize energy management systems has been exposed
539
FC Stack Power Demand (kW)
Battery SOC (%)
Vehicle Power (kW)
Drive Cycle (m/s)
30 20 10 0 4 2 0 −2 60 50 40 10 5 0
0
200
400
Fig. 6.
600
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UDDS drive dycle: System simulation after EMC parameter optimization
FC Stack Power Demand (kW)
Battery SOC (%)
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40 20 0 5 0 −5 70 60 50 40 15 10 5 0
0
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Fig. 7.
Generated random drive cycle: Non ideal energy management when UDDS EMC strategy applied
when HEVs are used for a variety of driving conditions rather than just one driving schedule in a fixed environment. The optimization of an EMC strategy based on just one drive cycle does not necessarily guarantee highest fuel efficiency for a probabilistic driving profile. Therefore, the development of a stochastic optimization tool for heuristic EMCs is proposed in order to capture the stochastic sensitivity of EMCs towards a driving profile. VI. ACKNOWLEDGMENTS The authors gratefully acknowledge the contribution of the Hawaii Natural Energy Institute, the Gottlieb Daimler and Carl Benz Foundation and reviewers’ comments. R EFERENCES [1] F. R. Salmasi, ”Control Strategies for hybrid electric vehicles: evolution, classification, comparison, and future trends”, IEEE Transactions on Vehicular Technology, vol. 56, issue 5, part 1, 2007, pp. 2393-2404. [2] H. D. Won and R. Langari, ”Fuzzy torque distribution control for a parallel hybrid vehicle”, Int. J. Knowl. Eng. Neural Netw., vol. 19, 2002, pp. 4-10.
[3] L. Johannesson and B. Egardt, ”Approximate dynamic programming applied to parallel hybrid powertrains”, Proceedings of the 17th World Congress IFAC, 2008, pp. 3373-3379. [4] A. Sciarretta and L. Guzzella, ”Control of hybrid electric vehicles”, IEEE Control Systems Magazine, vol. 27(2), 2007, pp. 60-70. [5] S. Yerramalla, A. Davari, A. Feliachi and T. Biswas, ”Modeling and simulation of the dynamic behavior of a polymer electrolyte membrane fuel cell”, Journal of Power Sources, vol. 124, 2003, pp. 104-113. [6] J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge, ”Performance modeling of the ballard mark iv solid polymer electrolyte fuel cell”, Journal of the Electrochemical Society, vol. 142, 1995, pp. 1-8. [7] T. E. Springer, T. A. Zawodzinski, and S. Gottesfeld, ”Polymer electrolyte fuel cell model”, Journal of the Electrochemical Society, vol. 138(8), 1991, pp. 2334-2342. [8] T. V. Nguyen and R. E. White, ”A water and heat management model for proton-exchange membrane fuel cells”, Journal of the Electrochemical Society, vol. 140(8), 1993, pp. 2178-2186. [9] J. T. Pukrushpan, H. Peng, and A. G. Stefanopoulou, ”Controloriented modeling and analysis for automotive fuel cell systems”, Journal of Dynamic Systems, Measurement and Control, vol. 126, 2004, pp. 1425. [10] O. Tremblay, L. A. Dessaint and A. I. Dekkiche, ”A generic battery model for the dynamic simulation of hybrid electric vehicles”, Vehicle Power and Propulsion Conference, 2007, pp. 284-289.
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