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Sizing of a fuel cell electric vehicle: A pinch analysis-based approach
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Sizing of a fuel cell electric vehicle: A pinch analysis-based approach Shrihari D. Gaikwad a,b, Prakash C. Ghosh b,* a
Smt. Indira Gandhi College of Engineering, Navi Mumbai, India Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
b
highlights Component sizing of a fuel cell based electric vehicle. Pinch analysis optimisation methodology is adopted. Trade-off between of energy storage and fuel cell size. Complete system is simulated for optimized design.
article info
abstract
Article history:
Polymer electrolyte fuel cells are considered as a promising alternative to mitigate the CO2
Received 15 January 2019
emission in the transport sector. To achieve an efficient and cost-effective system,
Received in revised form
hybridisation of the energy storage system with a fuel cell is important. Efficient man-
19 September 2019
agement of energy is the key in order to achieve an efficient and cost-effective configu-
Accepted 17 January 2020
ration for fuel cell electric vehicle. Optimum sizing of the power source and energy storage
Available online xxx
system, which is capable of meeting the load requirement of the driving cycle is the key challenge for achieving efficient and cost-effective system. In this work, an alternative
Keywords:
methodology based on the principles of pinch analysis is proposed, for sizing the energy
Fuel cells
storage system and the fuel cell for fuel cell-based electric vehicle, and validated for the
Pinch analysis
Worldwide Harmonized Light Vehicle Test Cycle (WLTC) class-3 driving cycle.
Electric vehicles
© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Supercapacitors Batteries
Introduction The rapid depletion of fossil fuel and increasing environmental concern due to global warming motivates the researchers to develop cleaner and efficient drive systems. A fuel cell powered vehicle has the potential to reduce the emission by improving the conversion efficiency in the
transport sector. Among different types of fuel cells, Polymer Electrolyte Fuel Cell (PEFC) is considered to be the most promising candidate for automobile applications due to its low-temperature operation and higher efficiency. However, the high capital cost of PEFC is one of the major obstacles towards the commercial application, and the fuel cell needs to be optimally sized for automobile application to cater the energy requirements for a complete drive cycle. The load
* Corresponding author. E-mail address: [email protected] (P.C. Ghosh). https://doi.org/10.1016/j.ijhydene.2020.01.116 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Nomenclature r Cd Av v Mv g frr St g I Pfc fton
Air density (kg/m3) Aerodynamic drag coefficient Vehicle frontal surface area (m2) Vehicle speed (m/s) Vehicle mass (kg) Acceleration due to gravity (m/s2) Coefficient of rolling friction State of energy in ESS Generation form Fuel cell Load demand Fuel cell rated capacity Fraction of fuel cell rated capacity
Abbreviations FCEV Fuel cells electric vehicle PEMFC Polymer electrolytic fuel cells HESS Hybrid energy storage systems TDR Turndown ratio DoD Depth of discharge WLTC Worldwide harmonized Light vehicle Test Cycle
profile obtained from a drive cycle shows spiky nature and the fluctuation in the electrical demand can be catered by deploying an energy storage system (ESS), which will also be able to recover the energy during deceleration of the vehicle. An electrochemical ESS such as battery or supercapacitor can be used to take care of the fluctuation in the load profile. The lithium-ion battery is widely used in the electric vehicle due to its higher energy density and fast charging and discharging capabilities. Fuel cell hybrid electric vehicle (FCHEV) with a combination of the fuel cell and the battery has been studied by different research groups [1e4] and the components mainly the fuel cells and storage systems are sized by rule of thumb without following any sizing methodologies. FCHEV with a combination of fuel cell and supercapacitor has been explored by the researchers [3e6] to reduce the rated capacity of the fuel cells and the power demand during acceleration is met by the super capacitor. Fuel cell with the hybrid energy storage system (HESS) containing battery and supercapacitor is studied as an alternative option by different researchers [7e10] to reduce the size of the capacitor as well as the fuel cells to design a cost effective system. L. Wang et al. [7] sized the energy storage system by averaging the load profile which will lead to an non-optimal storage sizing. X. Hu et al., sized the battery and supercapacitor based HESS on the basis of life cycle cost analysis. Z. Song et al. [9] sized the energy storage system based on the driving ranges. Z. Yu et al. [10], sized battery, supercapacitor and fuel cells based on mass volume and the cost of the HESS. The performance of FCHEV depends on optimum energy management and optimum sizing of FCHEV components. In an FCHEV the fuel cell operates at constant power and the hybrid storage system will supply power to the vehicle when the demand is more than the generation from the fuel cells. At the same time, it will store braking energy and excess power generated by the fuel cell when generation is more than demand. Optimum sizing of
these components is necessary for better performance and fuel economy of the vehicle. Researchers studied different methods for sizing of storage system for FCHEV, J. Bauman et al. [11], used analytical solution [11], J. Lopes et al. [12] and used a simplified load profile, Y. Eren et al. [13] followed static optimisation technique for sizing of HESS [13]. Stochastic driving cycle based sizing optimisation [14]. Schaltz E. et al. [15], studied the effect of battery and supercapacitor sizing on a lifetime of battery Hegazy O et al. [16]studied particle swarm optimisation of sizing of fuel cell vehicle components, reported superiority over genetic algorithm optimisation. Xu L. et al. [17] studied multi-objective components sizing of fuel cell hybrid electric bus consisting fuel cell and battery, based on optimal energy management algorithm. Raga C. et al. [18] proposed sizing of HESS based on power and energy difference of fuel cell power and load demand as a function of fuel cell size. Liu C. et al. [19] studied optimal power source sizing of fuel cell hybrid vehicles based on Pontryagin’s minimum principle. He studied the effect of the fuel cell size and compared with the battery size, life and fuel economy. Gharibeh et al. [20]proposed the sizing of the hybrid energy storage system (HESS)based on peak demand and peak regenerative power. Hu Z. et al. [21] studied the effect of battery size on the performance of FCHEV with battery. These methods are based on specific conditions or based on the analytical solution. However, a generalised methodology for sizing of HESS in an FCHEV is important. Pinch analysis is used in the chemical process for minimising energy consumption by arranging demand and supply. Kulkarni et al. [22] has explored this method for sizing the energy storage in a solar thermal system and Arun et al. [23] applied it for sizing photovoltaic-battery system. In the present work, a methodology for optimisation of energy storage requirement for FCHEV is developed using the principles of pinch analysis. Proposed methodology employs time series discreatisation of load demand, generated from known driving cycle. Energy balance is achieved by varying generation within its limits, and excess or shortage of energy is balanced by energy storage system. Storage sizing curve is obtained by varying the fuel cell. From design point it is desirable to determine entire range of fuel cell size and storage requirement for FCHEV. In this paper, the entire range of feasible system configuration is identified and presented as a design space. Generation of design space helps in optimising and selecting appropriate system configuration of the storage system. The proposed method is used for sizing the fuel cell, and supercapacitor optimally for a known driving cycle.
System description A typical four-passenger vehicle powered by polymer electrolyte membrane fuel cell, with an energy storage system is considered for the present study as shown in Fig. 1. It is assumed that the PEFC will generate the total energy demand of the electric drive from hydrogen stored onboard. When the power demand by the motor exceeds the nominal capacity of the fuel cell, the energy storage system will meet the deficit in the demand of electric motor. During regenerative braking
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Fig. 1 e Block diagram of a fuel cell electric vehicle. energy is stored in ESS whereas during acceleration ESS is brought into operation to meet the power demand. Energy management controller regulates the flow of energy from the fuel cell and ESS to maximise the fuel economy of the FCHEV. Performance of FCHEV depends on energy management strategy and also on component sizing. The mass and volume are crucial because they influence fuel efficiency. The size of the fuel cell and ESS are obtained using the principle of pinch analysis.
Pinch analysis methodology
An autonomous system implies that the energy level of storage at the beginning and end of a cycle must be equal, i.e., Stði¼0Þ ¼ Stði¼nÞ
Moreover, the maximum generation cannot exceed the rating of the fuel cell. gi gref ci
DSti ¼ gi Ii ci
(5)
The value of cumulative energy generation must be equal to or greater than the cumulative energy demand during the entire cycle can be expressed mathematically as, i X
The proposed system is modelled through the discretisation of power demand for the entire drive cycle of operation into ‘n’ equal time intervals. For the successive intervals, the cumulative energy demand is obtained and compared with the cumulative generation by varying the power of the fuel cells between minimum to maximum limits to minimise the storage capacity in the system. During deceleration, power demand is negative, indicating the opportunity of the regeneration of energy in the system. Fuel cell size is varied from the average power demand of the drive cycle to the peak power demand. The fuel cell generates power to meet load demand and can be zero to maximum capacity. The mismatch between the generation and demand mainly dictates the size of the ESS (St), and it can be estimated for the ith interval as follows,
(4)
0
gi
i X
Ii
(6)
0
The point at which the cumulative energy production meets the cumulative energy demand is referred to Pinch Point. The storage size is estimated as: (7) Sti jmax ; 0 i n
(1)
where the gi is the load demand, and li is the generation from the fuel cell. The state of the energy level in the ESS at the end of the ith interval is given by, Sti ¼ Sði1Þ þ DSti ci
(2)
The state of stored energy in ESS must always be a positive quantity and can be expressed mathematically, as follows: Sti 0ci
(3)
Fig. 2 e Illustrative representation of cumulative demand, cumulative generation and mismatch profile for the entire drive cycle.
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Fig. 2 shows the cumulative energy demand, generation and mismatch for the entire driving cycle for a fixed fuel cell size and load demand. It shows that the cumulative demand never exceeds the cumulative generation and it becomes equal to the cumulative generation at a point referred to pinch point. The cumulative demand decreases during regenerative braking due to negative load demand. The mismatch profile is minimum at the pinch point, and the difference of the maximum and minimum point in the mismatch profile refers to the size of the storage. By varying the fuel cell size from the peak demand to the average load demand, the storage requirement is calculated as represented graphically in Fig. 3. It shows if the fuel cell size is less than the average load demand, the net energy generated in a cycle is less than the total energy demand for the drive cycle. It also indicates that irrespective of the initial level of storage, the system can never ensure the autonomy in the system, as the final amount of the stored energy is always less than the initial value. Thus, the constraint given by Eq (4) can never be satisfied and is represented as infeasible region-I in Fig. 3. For the fuel cell size greater than the peak demand, the storage is unnecessary as the fuel cell is capable of meeting the power demand. For any fuel cell size between these two limits, energy storage is needed to ensure the autonomy of the system as illustrated by the region between feasible regions and infeasible region in Fig. 3. It can be seen that as fuel cell size increases, the storage size decreases. In the infeasible region-II, though enough energy can be generated by the fuel cell, the storage is insufficient to cater the mismatch in the system. It makes region-II also infeasible as far as the autonomy is concerned. For fuel cell size from average load demand to peak demand, storage is required for operation of the system with constraints mentioned above. The minimum size of storage as a function of the fuel cell is denoted by the blue line between infeasible region-II and feasible regions.
Regenerative braking For a known load profile and fuel cell size, Eq (2), Eq (3), Eq (6) and Eq (7) facilitate estimating the storage size. Considering
the positive load of the drive cycle (ignoring the energy available due to the braking), the variation in the storage requirement versus fuel cell size is illustrated by the blue line in Fig. 3. In the case of FCHEV kinetic energy of vehicle can be converted to electricity during braking and negative road gradient. If this power generation is treated as negative load demand. During braking operation, the electric motor converts the kinetic energy of vehicle into electrical energy which can be stored in the energy storage system to improve the overall fuel efficiency. Also, this braking energy needs to be captured and stored in storage (regenerative braking). With this constraint, effective average load demand is lowered, resulting minimum fuel cell size for feasible operation is lowered. To capture braking energy requires minimum storage irrespective of fuel cell size. This is represented in Fig. 3 as a feasible region I. In the feasible region-I, the increase in the fuel cell size beyond certain value results in fixed storage requirement to utilize the braking energy. In this region braking energy will be wasted if the storage requirement is below minimum shown by a horizontal line.
Turndown ratio (TDR) constraint Fuel cell system efficiency is high for the partial load; however, below a certain value, the efficiency falls due to the parasitic loss in the system. It sets a limit on minimum output power from fuel cell for better efficiency. This characteristic of fuel cell puts another constraint of minimum generation on fuel cell and is termed as turndown ratio. Turn on ratio refers to the window of the operational range of the fuel cell and is defined as the ratio of the minimum output to the maximum capacity. Hence, the inclusion of the turndown ratio in the system can be expressed mathematically as follows: gi gmin ci
(8)
Here, the minimum value, gmin refers to the minimum power generation capability considering the turndown ratio, ftdr and is given by Eq (10), where Pfc refers to the rating of the fuel cell. gmin ¼
Pfc ftdr
(9)
The introduction of theTDRconstraint in the optimisation, with the storage requirement, is plotted in Fig. 3. It shows up to a certain value of fuel cell size, the value of minimum storage is same as before up to local minima for respective turn on the ratio. If fuel cell size further increased requirement of storage increases to store excess energy generated due to the constraint of the turndown ratio. In the feasible region-III, the excess energy will be generated by the fuel cell, which will be unutilised. Considering constraints of regenerative braking and fuel cell turn on the ratio, the design space is shown in Fig. 3.
Illustrative example
Fig. 3 e Schematic representation of design space for sizing storage and fuel cell.
In this section, the methodology of design space using Pinch Analysis is applied for sizing components of FCHEV. The Worldwide harmonized Light vehicles Test Cycles (WLTC-3) as shown in Fig. 4a is considered as a load profile.
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Table 1 e Vehicle parameters and constants. Parameter Vehicle mass (Mv) Vehicle frontal surface area (Av) Drag Coefficient (Cd) Air density (r) Gravitational constant (g) Road gradient ( fÞ
Value 700 2.6 0.3 1.204 9.8 0
Unit kg m2 kg/m3 m/s2 degree
Following dynamic vehicle equation is used to estimate the load demand from the driving cycle which is plotted in Fig. 4b. 1 dv Fv ¼ rCd Av v2 þ frr Mv cosf þ Mv þ Mv g sinf 2 dx
(10)
wherer is air density, Cd is aerodynamic drag coefficient, Avvehicle frontal surface area. v is vehicle speed in m/s, Mv is vehicle mass, g is gravity, and frr is coefficient of rolling friction, Parameters used for generating load profile are listed in Table 1.
Fig. 4 e (a) WLCTC-3 driving cycle, (b) Electrical power demand for WLCTC -3 driving cycle.
5
During regenerative braking, the load demand is considered to be negative. From the load profile, the peak power demand is found to be 25 kW, average power demand is 9.76 kW, and the duration of the complete driving cycle is 1800 s. Electric drive efficiency is assumed 90%, and storage system round trip efficiency is assumed 90%. Total driving cycle duration is divided into equal 900 samples. The optimisation model is created and solved using frontline solver with linear solver engine, by varying fuel cell size from average load demand to peak-load demand to get required storage. Variation in storage requirement for varying fuel cell size from average load demand to peak demand with and without regenerative braking is shown in Fig. 5a. It shows no storage is required if fuel cell capacity is the same as peak demand and regenerative braking is not explored. On the other hand, ESS capacity of 870 Wh, is required for a fuel cell of 4.76 kW (average load demand). If regenerative braking is used, the minimum storage requirement is 26.6 Wh, even though the fuel cell capacity is further increased to peak power which is due to the storage required for capturing the energy during
Fig. 5 e (a) Fuel cell Vs storage requirement with and without regenerative braking (b) Fuel cell size vs storage requirement with turndown ratio.
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Fig. 6 e Variation in the cumulative demand, cumulative generation and storage requirement (pinch point) with 5 TDR and variable fuel cell size. (a) fuel cell 8.17 kW, (b) fuel cell 12.25 kW (c) Fuel cell 16.34 kW.
Fig. 7 e Sizing of fuel cell and energy storage system using pinch analysis for the WLCTC-3 drive cycle.
braking. Regenerative braking resulted in a reduction of minimum (average load demand) fuel cell size by 0.3 kW. For better fuel economy the fuel cell should be operated above the minimum load. Fig. 5b represents the variation in storage requirement if fuel cell capacity increased from average load demand with different turndown ratio (TDR) constraint. The requirement of storage decreases until some point, i.e., local minima, and if further fuel cell capacity increased, the storage requirement is increased to store excess energy generated due to TDR constraint. Local minima are found to be at different fuel cell capacity for different turn on ratio and are higher for a higher turndown ratio. Points a,b and c correspond to pinch points at different fuel cell sizes. Fig. 6aec show the variation in the cumulative demand, the cumulative generation and the pinch points corresponding to the fuel cell size. Fig. 7 shows a variation in the storage requirement for the selected load profile for variable fuel cell size with no TDR and TDR 5. For no TDR condition, the minimum storage requirement
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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the higher efficiency of the fuel cell at partial load. A higher fuel cell makes possible to operate always at partial load near high efficiency. Further, the increase in the fuel cell size beyond optimum value improves the overall energy efficiency, however, give rise costing storage requirement which increases mass and volume of the power train.
Energy management
Fig. 8 e Variation in the drive cycle efficiency with FC capacity.
is 26 Wh, and this storage is required for storing the energy obtained from regenerative braking. For TDR 5, a minimum storage capacity of 352 Wh is required along with a fuel cell of capacity 12.25 kW. Fuel cell size is 45% of peak load,i.e., 12.25 kW. Fig. 8 shows the variation in system efficiency for different fuel cell size with no TDR and TDR 5, the efficiency of the system increases with higher fuel cell capacity; this is due to
Optimisation of FCHEV components sizing with pinch analysis involves the certain generation pattern from the fuel cell. Results of component sizing using pinch analysis are validated by developing an energy management algorithm. Fuel cell capacity is considered to be 12.25 kW, and storage size is considered to be 652 Wh. Flowchart of the energy management algorithm is presented in Fig. 9. If load demand is less than the fuel cell minimum output, the fuel cell operates at its minimum power, in this mode excess energy is used to charge storage device. If demand is more than fuel cell rated power, the fuel cell is operated at maximum capacity and storage device will supply the energy demand to meet the energy deficit in the system. If the power demand lies between the minimum and maximum power of the fuel cell capacity, the fuel cell operating mode is decided by state of charge of the storage system. Simulation result of energy management is shown in Fig. 10. Initial SOC of the storage system is assumed to be 50%, it deviated by 0.25% at the end of the cycle.
Fig. 9 e Flowchart for the energy management algorithm.
Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Fig. 10 e Fuel Cell generation pattern from energy management algorithm, power sheared by HESS and variation in the state of charge of HESS.
Conclusion In this paper, a design space method based on Pinch is applied successfully to size the components of FCHEV based on aWLTC-3 driving cycle. In this analysis, the fuel cell meets the onboard power required for FCHEV. Energy storage system supports the fuel cell to match the load profile. FCHEV power system is studied, and a mathematical formulation is done considering various constraints involved in sizing such a system. It is studied that for a given load profile, the size of the fuel cell must be at least equal to the average load demand. Moreover, the size of the storage decreases monotonously with the increase in the fuel cell size, and no storage is required if fuel cell capacity is equal to peak demand if the energy from regenerative braking is not stored. If regenerative braking is to be used, minimum storage is required to store energy available during the deceleration of the vehicle. To maximise the system efficiency, the constraint for TDR is applied to the fuel cell. Pinch analysis is used to obtain the design space for FCHEV with a known driving profile. The storage sizes are determined by varying the fuel cell size from average load to peak load estimated from the driving cycle. This design space can be used further for optimisation of fuel cell and storage device. Beyond local optima, the storage requirement increases with increase in fuel cell size to accommodate excess energy generated due to the constraint of TDR. During extra high power requirements of driving cycle from 1480 to 1720 s, maximum energy is required and whatever is shortage, should be supplied by storage system. Size of storage device is influenced by the load in this part of the profile. Results of sizing FCHEV components using pinch analysis are validated by simulating proposed energy management algorithm for the WLCDC-3 driving cycle. Energy
management controller needs to operate fuel cell always above its TDR factor (0.2 in this case), due to this constraint fuel cell operates at its peak capacity only if required by load profile and keeps room in energy storage device at the same time maximises the efficiency.
Acknowledgments This paper is based on the work proposed under the project entitled “Development of Compressed Hydrogen-Fuel Cell Integrated System Suitable for Light Duty Vehicles” funded by Govt. of India through the Department of Science and Technology (DST/TMD/HFC/2K18/42)
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Sizing of a fuel cell electric vehicle: A pinch analysis-based approach Shrihari D. Gaikwad a,b, Prakash C. Ghosh b,* a
Smt. Indira Gandhi College of Engineering, Navi Mumbai, India Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
b
highlights Component sizing of a fuel cell based electric vehicle. Pinch analysis optimisation methodology is adopted. Trade-off between of energy storage and fuel cell size. Complete system is simulated for optimized design.
article info
abstract
Article history:
Polymer electrolyte fuel cells are considered as a promising alternative to mitigate the CO2
Received 15 January 2019
emission in the transport sector. To achieve an efficient and cost-effective system,
Received in revised form
hybridisation of the energy storage system with a fuel cell is important. Efficient man-
19 September 2019
agement of energy is the key in order to achieve an efficient and cost-effective configu-
Accepted 17 January 2020
ration for fuel cell electric vehicle. Optimum sizing of the power source and energy storage
Available online xxx
system, which is capable of meeting the load requirement of the driving cycle is the key challenge for achieving efficient and cost-effective system. In this work, an alternative
Keywords:
methodology based on the principles of pinch analysis is proposed, for sizing the energy
Fuel cells
storage system and the fuel cell for fuel cell-based electric vehicle, and validated for the
Pinch analysis
Worldwide Harmonized Light Vehicle Test Cycle (WLTC) class-3 driving cycle.
Electric vehicles
© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Supercapacitors Batteries
Introduction The rapid depletion of fossil fuel and increasing environmental concern due to global warming motivates the researchers to develop cleaner and efficient drive systems. A fuel cell powered vehicle has the potential to reduce the emission by improving the conversion efficiency in the
transport sector. Among different types of fuel cells, Polymer Electrolyte Fuel Cell (PEFC) is considered to be the most promising candidate for automobile applications due to its low-temperature operation and higher efficiency. However, the high capital cost of PEFC is one of the major obstacles towards the commercial application, and the fuel cell needs to be optimally sized for automobile application to cater the energy requirements for a complete drive cycle. The load
* Corresponding author. E-mail address: [email protected] (P.C. Ghosh). https://doi.org/10.1016/j.ijhydene.2020.01.116 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Gaikwad SD, Ghosh PC, Sizing of a fuel cell electric vehicle: A pinch analysis-based approach, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.116
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Nomenclature r Cd Av v Mv g frr St g I Pfc fton
Air density (kg/m3) Aerodynamic drag coefficient Vehicle frontal surface area (m2) Vehicle speed (m/s) Vehicle mass (kg) Acceleration due to gravity (m/s2) Coefficient of rolling friction State of energy in ESS Generation form Fuel cell Load demand Fuel cell rated capacity Fraction of fuel cell rated capacity
Abbreviations FCEV Fuel cells electric vehicle PEMFC Polymer electrolytic fuel cells HESS Hybrid energy storage systems TDR Turndown ratio DoD Depth of discharge WLTC Worldwide harmonized Light vehicle Test Cycle
profile obtained from a drive cycle shows spiky nature and the fluctuation in the electrical demand can be catered by deploying an energy storage system (ESS), which will also be able to recover the energy during deceleration of the vehicle. An electrochemical ESS such as battery or supercapacitor can be used to take care of the fluctuation in the load profile. The lithium-ion battery is widely used in the electric vehicle due to its higher energy density and fast charging and discharging capabilities. Fuel cell hybrid electric vehicle (FCHEV) with a combination of the fuel cell and the battery has been studied by different research groups [1e4] and the components mainly the fuel cells and storage systems are sized by rule of thumb without following any sizing methodologies. FCHEV with a combination of fuel cell and supercapacitor has been explored by the researchers [3e6] to reduce the rated capacity of the fuel cells and the power demand during acceleration is met by the super capacitor. Fuel cell with the hybrid energy storage system (HESS) containing battery and supercapacitor is studied as an alternative option by different researchers [7e10] to reduce the size of the capacitor as well as the fuel cells to design a cost effective system. L. Wang et al. [7] sized the energy storage system by averaging the load profile which will lead to an non-optimal storage sizing. X. Hu et al., sized the battery and supercapacitor based HESS on the basis of life cycle cost analysis. Z. Song et al. [9] sized the energy storage system based on the driving ranges. Z. Yu et al. [10], sized battery, supercapacitor and fuel cells based on mass volume and the cost of the HESS. The performance of FCHEV depends on optimum energy management and optimum sizing of FCHEV components. In an FCHEV the fuel cell operates at constant power and the hybrid storage system will supply power to the vehicle when the demand is more than the generation from the fuel cells. At the same time, it will store braking energy and excess power generated by the fuel cell when generation is more than demand. Optimum sizing of
these components is necessary for better performance and fuel economy of the vehicle. Researchers studied different methods for sizing of storage system for FCHEV, J. Bauman et al. [11], used analytical solution [11], J. Lopes et al. [12] and used a simplified load profile, Y. Eren et al. [13] followed static optimisation technique for sizing of HESS [13]. Stochastic driving cycle based sizing optimisation [14]. Schaltz E. et al. [15], studied the effect of battery and supercapacitor sizing on a lifetime of battery Hegazy O et al. [16]studied particle swarm optimisation of sizing of fuel cell vehicle components, reported superiority over genetic algorithm optimisation. Xu L. et al. [17] studied multi-objective components sizing of fuel cell hybrid electric bus consisting fuel cell and battery, based on optimal energy management algorithm. Raga C. et al. [18] proposed sizing of HESS based on power and energy difference of fuel cell power and load demand as a function of fuel cell size. Liu C. et al. [19] studied optimal power source sizing of fuel cell hybrid vehicles based on Pontryagin’s minimum principle. He studied the effect of the fuel cell size and compared with the battery size, life and fuel economy. Gharibeh et al. [20]proposed the sizing of the hybrid energy storage system (HESS)based on peak demand and peak regenerative power. Hu Z. et al. [21] studied the effect of battery size on the performance of FCHEV with battery. These methods are based on specific conditions or based on the analytical solution. However, a generalised methodology for sizing of HESS in an FCHEV is important. Pinch analysis is used in the chemical process for minimising energy consumption by arranging demand and supply. Kulkarni et al. [22] has explored this method for sizing the energy storage in a solar thermal system and Arun et al. [23] applied it for sizing photovoltaic-battery system. In the present work, a methodology for optimisation of energy storage requirement for FCHEV is developed using the principles of pinch analysis. Proposed methodology employs time series discreatisation of load demand, generated from known driving cycle. Energy balance is achieved by varying generation within its limits, and excess or shortage of energy is balanced by energy storage system. Storage sizing curve is obtained by varying the fuel cell. From design point it is desirable to determine entire range of fuel cell size and storage requirement for FCHEV. In this paper, the entire range of feasible system configuration is identified and presented as a design space. Generation of design space helps in optimising and selecting appropriate system configuration of the storage system. The proposed method is used for sizing the fuel cell, and supercapacitor optimally for a known driving cycle.
System description A typical four-passenger vehicle powered by polymer electrolyte membrane fuel cell, with an energy storage system is considered for the present study as shown in Fig. 1. It is assumed that the PEFC will generate the total energy demand of the electric drive from hydrogen stored onboard. When the power demand by the motor exceeds the nominal capacity of the fuel cell, the energy storage system will meet the deficit in the demand of electric motor. During regenerative braking
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Fig. 1 e Block diagram of a fuel cell electric vehicle. energy is stored in ESS whereas during acceleration ESS is brought into operation to meet the power demand. Energy management controller regulates the flow of energy from the fuel cell and ESS to maximise the fuel economy of the FCHEV. Performance of FCHEV depends on energy management strategy and also on component sizing. The mass and volume are crucial because they influence fuel efficiency. The size of the fuel cell and ESS are obtained using the principle of pinch analysis.
Pinch analysis methodology
An autonomous system implies that the energy level of storage at the beginning and end of a cycle must be equal, i.e., Stði¼0Þ ¼ Stði¼nÞ
Moreover, the maximum generation cannot exceed the rating of the fuel cell. gi gref ci
DSti ¼ gi Ii ci
(5)
The value of cumulative energy generation must be equal to or greater than the cumulative energy demand during the entire cycle can be expressed mathematically as, i X
The proposed system is modelled through the discretisation of power demand for the entire drive cycle of operation into ‘n’ equal time intervals. For the successive intervals, the cumulative energy demand is obtained and compared with the cumulative generation by varying the power of the fuel cells between minimum to maximum limits to minimise the storage capacity in the system. During deceleration, power demand is negative, indicating the opportunity of the regeneration of energy in the system. Fuel cell size is varied from the average power demand of the drive cycle to the peak power demand. The fuel cell generates power to meet load demand and can be zero to maximum capacity. The mismatch between the generation and demand mainly dictates the size of the ESS (St), and it can be estimated for the ith interval as follows,
(4)
0
gi
i X
Ii
(6)
0
The point at which the cumulative energy production meets the cumulative energy demand is referred to Pinch Point. The storage size is estimated as: (7) Sti jmax ; 0 i n
(1)
where the gi is the load demand, and li is the generation from the fuel cell. The state of the energy level in the ESS at the end of the ith interval is given by, Sti ¼ Sði1Þ þ DSti ci
(2)
The state of stored energy in ESS must always be a positive quantity and can be expressed mathematically, as follows: Sti 0ci
(3)
Fig. 2 e Illustrative representation of cumulative demand, cumulative generation and mismatch profile for the entire drive cycle.
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Fig. 2 shows the cumulative energy demand, generation and mismatch for the entire driving cycle for a fixed fuel cell size and load demand. It shows that the cumulative demand never exceeds the cumulative generation and it becomes equal to the cumulative generation at a point referred to pinch point. The cumulative demand decreases during regenerative braking due to negative load demand. The mismatch profile is minimum at the pinch point, and the difference of the maximum and minimum point in the mismatch profile refers to the size of the storage. By varying the fuel cell size from the peak demand to the average load demand, the storage requirement is calculated as represented graphically in Fig. 3. It shows if the fuel cell size is less than the average load demand, the net energy generated in a cycle is less than the total energy demand for the drive cycle. It also indicates that irrespective of the initial level of storage, the system can never ensure the autonomy in the system, as the final amount of the stored energy is always less than the initial value. Thus, the constraint given by Eq (4) can never be satisfied and is represented as infeasible region-I in Fig. 3. For the fuel cell size greater than the peak demand, the storage is unnecessary as the fuel cell is capable of meeting the power demand. For any fuel cell size between these two limits, energy storage is needed to ensure the autonomy of the system as illustrated by the region between feasible regions and infeasible region in Fig. 3. It can be seen that as fuel cell size increases, the storage size decreases. In the infeasible region-II, though enough energy can be generated by the fuel cell, the storage is insufficient to cater the mismatch in the system. It makes region-II also infeasible as far as the autonomy is concerned. For fuel cell size from average load demand to peak demand, storage is required for operation of the system with constraints mentioned above. The minimum size of storage as a function of the fuel cell is denoted by the blue line between infeasible region-II and feasible regions.
Regenerative braking For a known load profile and fuel cell size, Eq (2), Eq (3), Eq (6) and Eq (7) facilitate estimating the storage size. Considering
the positive load of the drive cycle (ignoring the energy available due to the braking), the variation in the storage requirement versus fuel cell size is illustrated by the blue line in Fig. 3. In the case of FCHEV kinetic energy of vehicle can be converted to electricity during braking and negative road gradient. If this power generation is treated as negative load demand. During braking operation, the electric motor converts the kinetic energy of vehicle into electrical energy which can be stored in the energy storage system to improve the overall fuel efficiency. Also, this braking energy needs to be captured and stored in storage (regenerative braking). With this constraint, effective average load demand is lowered, resulting minimum fuel cell size for feasible operation is lowered. To capture braking energy requires minimum storage irrespective of fuel cell size. This is represented in Fig. 3 as a feasible region I. In the feasible region-I, the increase in the fuel cell size beyond certain value results in fixed storage requirement to utilize the braking energy. In this region braking energy will be wasted if the storage requirement is below minimum shown by a horizontal line.
Turndown ratio (TDR) constraint Fuel cell system efficiency is high for the partial load; however, below a certain value, the efficiency falls due to the parasitic loss in the system. It sets a limit on minimum output power from fuel cell for better efficiency. This characteristic of fuel cell puts another constraint of minimum generation on fuel cell and is termed as turndown ratio. Turn on ratio refers to the window of the operational range of the fuel cell and is defined as the ratio of the minimum output to the maximum capacity. Hence, the inclusion of the turndown ratio in the system can be expressed mathematically as follows: gi gmin ci
(8)
Here, the minimum value, gmin refers to the minimum power generation capability considering the turndown ratio, ftdr and is given by Eq (10), where Pfc refers to the rating of the fuel cell. gmin ¼
Pfc ftdr
(9)
The introduction of theTDRconstraint in the optimisation, with the storage requirement, is plotted in Fig. 3. It shows up to a certain value of fuel cell size, the value of minimum storage is same as before up to local minima for respective turn on the ratio. If fuel cell size further increased requirement of storage increases to store excess energy generated due to the constraint of the turndown ratio. In the feasible region-III, the excess energy will be generated by the fuel cell, which will be unutilised. Considering constraints of regenerative braking and fuel cell turn on the ratio, the design space is shown in Fig. 3.
Illustrative example
Fig. 3 e Schematic representation of design space for sizing storage and fuel cell.
In this section, the methodology of design space using Pinch Analysis is applied for sizing components of FCHEV. The Worldwide harmonized Light vehicles Test Cycles (WLTC-3) as shown in Fig. 4a is considered as a load profile.
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Table 1 e Vehicle parameters and constants. Parameter Vehicle mass (Mv) Vehicle frontal surface area (Av) Drag Coefficient (Cd) Air density (r) Gravitational constant (g) Road gradient ( fÞ
Value 700 2.6 0.3 1.204 9.8 0
Unit kg m2 kg/m3 m/s2 degree
Following dynamic vehicle equation is used to estimate the load demand from the driving cycle which is plotted in Fig. 4b. 1 dv Fv ¼ rCd Av v2 þ frr Mv cosf þ Mv þ Mv g sinf 2 dx
(10)
wherer is air density, Cd is aerodynamic drag coefficient, Avvehicle frontal surface area. v is vehicle speed in m/s, Mv is vehicle mass, g is gravity, and frr is coefficient of rolling friction, Parameters used for generating load profile are listed in Table 1.
Fig. 4 e (a) WLCTC-3 driving cycle, (b) Electrical power demand for WLCTC -3 driving cycle.
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During regenerative braking, the load demand is considered to be negative. From the load profile, the peak power demand is found to be 25 kW, average power demand is 9.76 kW, and the duration of the complete driving cycle is 1800 s. Electric drive efficiency is assumed 90%, and storage system round trip efficiency is assumed 90%. Total driving cycle duration is divided into equal 900 samples. The optimisation model is created and solved using frontline solver with linear solver engine, by varying fuel cell size from average load demand to peak-load demand to get required storage. Variation in storage requirement for varying fuel cell size from average load demand to peak demand with and without regenerative braking is shown in Fig. 5a. It shows no storage is required if fuel cell capacity is the same as peak demand and regenerative braking is not explored. On the other hand, ESS capacity of 870 Wh, is required for a fuel cell of 4.76 kW (average load demand). If regenerative braking is used, the minimum storage requirement is 26.6 Wh, even though the fuel cell capacity is further increased to peak power which is due to the storage required for capturing the energy during
Fig. 5 e (a) Fuel cell Vs storage requirement with and without regenerative braking (b) Fuel cell size vs storage requirement with turndown ratio.
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Fig. 6 e Variation in the cumulative demand, cumulative generation and storage requirement (pinch point) with 5 TDR and variable fuel cell size. (a) fuel cell 8.17 kW, (b) fuel cell 12.25 kW (c) Fuel cell 16.34 kW.
Fig. 7 e Sizing of fuel cell and energy storage system using pinch analysis for the WLCTC-3 drive cycle.
braking. Regenerative braking resulted in a reduction of minimum (average load demand) fuel cell size by 0.3 kW. For better fuel economy the fuel cell should be operated above the minimum load. Fig. 5b represents the variation in storage requirement if fuel cell capacity increased from average load demand with different turndown ratio (TDR) constraint. The requirement of storage decreases until some point, i.e., local minima, and if further fuel cell capacity increased, the storage requirement is increased to store excess energy generated due to TDR constraint. Local minima are found to be at different fuel cell capacity for different turn on ratio and are higher for a higher turndown ratio. Points a,b and c correspond to pinch points at different fuel cell sizes. Fig. 6aec show the variation in the cumulative demand, the cumulative generation and the pinch points corresponding to the fuel cell size. Fig. 7 shows a variation in the storage requirement for the selected load profile for variable fuel cell size with no TDR and TDR 5. For no TDR condition, the minimum storage requirement
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the higher efficiency of the fuel cell at partial load. A higher fuel cell makes possible to operate always at partial load near high efficiency. Further, the increase in the fuel cell size beyond optimum value improves the overall energy efficiency, however, give rise costing storage requirement which increases mass and volume of the power train.
Energy management
Fig. 8 e Variation in the drive cycle efficiency with FC capacity.
is 26 Wh, and this storage is required for storing the energy obtained from regenerative braking. For TDR 5, a minimum storage capacity of 352 Wh is required along with a fuel cell of capacity 12.25 kW. Fuel cell size is 45% of peak load,i.e., 12.25 kW. Fig. 8 shows the variation in system efficiency for different fuel cell size with no TDR and TDR 5, the efficiency of the system increases with higher fuel cell capacity; this is due to
Optimisation of FCHEV components sizing with pinch analysis involves the certain generation pattern from the fuel cell. Results of component sizing using pinch analysis are validated by developing an energy management algorithm. Fuel cell capacity is considered to be 12.25 kW, and storage size is considered to be 652 Wh. Flowchart of the energy management algorithm is presented in Fig. 9. If load demand is less than the fuel cell minimum output, the fuel cell operates at its minimum power, in this mode excess energy is used to charge storage device. If demand is more than fuel cell rated power, the fuel cell is operated at maximum capacity and storage device will supply the energy demand to meet the energy deficit in the system. If the power demand lies between the minimum and maximum power of the fuel cell capacity, the fuel cell operating mode is decided by state of charge of the storage system. Simulation result of energy management is shown in Fig. 10. Initial SOC of the storage system is assumed to be 50%, it deviated by 0.25% at the end of the cycle.
Fig. 9 e Flowchart for the energy management algorithm.
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Fig. 10 e Fuel Cell generation pattern from energy management algorithm, power sheared by HESS and variation in the state of charge of HESS.
Conclusion In this paper, a design space method based on Pinch is applied successfully to size the components of FCHEV based on aWLTC-3 driving cycle. In this analysis, the fuel cell meets the onboard power required for FCHEV. Energy storage system supports the fuel cell to match the load profile. FCHEV power system is studied, and a mathematical formulation is done considering various constraints involved in sizing such a system. It is studied that for a given load profile, the size of the fuel cell must be at least equal to the average load demand. Moreover, the size of the storage decreases monotonously with the increase in the fuel cell size, and no storage is required if fuel cell capacity is equal to peak demand if the energy from regenerative braking is not stored. If regenerative braking is to be used, minimum storage is required to store energy available during the deceleration of the vehicle. To maximise the system efficiency, the constraint for TDR is applied to the fuel cell. Pinch analysis is used to obtain the design space for FCHEV with a known driving profile. The storage sizes are determined by varying the fuel cell size from average load to peak load estimated from the driving cycle. This design space can be used further for optimisation of fuel cell and storage device. Beyond local optima, the storage requirement increases with increase in fuel cell size to accommodate excess energy generated due to the constraint of TDR. During extra high power requirements of driving cycle from 1480 to 1720 s, maximum energy is required and whatever is shortage, should be supplied by storage system. Size of storage device is influenced by the load in this part of the profile. Results of sizing FCHEV components using pinch analysis are validated by simulating proposed energy management algorithm for the WLCDC-3 driving cycle. Energy
management controller needs to operate fuel cell always above its TDR factor (0.2 in this case), due to this constraint fuel cell operates at its peak capacity only if required by load profile and keeps room in energy storage device at the same time maximises the efficiency.
Acknowledgments This paper is based on the work proposed under the project entitled “Development of Compressed Hydrogen-Fuel Cell Integrated System Suitable for Light Duty Vehicles” funded by Govt. of India through the Department of Science and Technology (DST/TMD/HFC/2K18/42)
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