An Optimal Energy Management System for Battery Electric Vehicles

An Optimal Energy Management System for Battery Electric Vehicles

Engine and Powertrain Control, Simulation and Modeling Engine Powertrain Control, OH, Simulation August 23-26, 2015. on Columbus, USA and Modeling 4th...

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Engine and Powertrain Control, Simulation and Modeling Engine Powertrain Control, OH, Simulation August 23-26, 2015. on Columbus, USA and Modeling 4th IFACand Workshop August 23-26, 2015. Columbus, USA Engine and Powertrain Control, OH, Simulation and online Modeling Available at www.sciencedirect.com August 23-26, 2015. Columbus, OH, USA

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An Optimal Energy Management System for Battery Electric Vehicles An Optimal Energy Management System for Battery Electric Vehicles An Optimal Energy Management System for Battery Electric Vehicles B. Sakhdari*. N. L. Azad** B. Sakhdari*. N. L. Azad**   B. Sakhdari*. N. L. Azad** *Systems Design Engineering Department, University of Waterloo,  *Systems Design Engineering Department, University of Waterloo, Waterloo, ON, Canada (Tel: 226-929-3333; e-mail: [email protected]). Waterloo, ON, Canada (Tel: 226-929-3333; e-mail: [email protected]). *Systems Design Engineering Department, University ** (e-mail:[email protected]) of Waterloo, **(Tel: (e-mail:[email protected]) Waterloo, ON, Canada 226-929-3333; e-mail: [email protected]). ** (e-mail:[email protected]) Abstract: Environmental pollution and high fuel costs have increased demands for an alternative Abstract: Environmental pollution Battery and high fuel costs have (BEVs) increased forthe anattention alternative energy source for transportation. Electric Vehicles aredemands attracting of energy source for transportation. Battery Electric Vehicles (BEVs) are attracting the attention of Abstract: Environmental pollution and high fuel costs have increased demands for an alternative researchers of automotive engineering field to address these concerns because of their reputation for researchers of automotive engineering field to address these concerns because of their reputation for energy source for transportation. Battery Electric Vehicles (BEVs) are attracting the attention of being fully green as well as more efficient than Internal Combustion Engine Vehicles (ICEVs). being fullytwo green as problems well engineering as more Combustion Engine Vehicles (ICEVs). researchers of automotive fieldare tothan address thesedriving concerns because of their reputation for However, major with efficient BEVs theirInternal short range and the limited service life However, two major problems with BEVs are their short driving range and the limited service life being fully green as well as more efficient than Internal Combustion Engine Vehicles (ICEVs). of their costly batteries. Enhancing BEVs’ driving range and their batteries’ lifetime are possible of their costly batteries. Enhancing BEVs’ driving and their batteries’ lifetime possible However, two major problems with BEVs are their range short driving range and the limited service life through developing more effective energy management systems (EMSs) for them. are This study through developing more effective energy management systems (EMSs) for them.flow This study of their costly batteries. Enhancing driving range and batteries’ lifetime are possible proposes an optimal EMS for a BEV,BEVs’ the Toyota RAV4 EV, by their considering the power between proposes anconsumers optimal EMS for a BEV, the Toyota RAV4 EV,systems by considering the through developing more effective energy management (EMSs) forpower This study the energy inside the vehicle. Dynamic programming (DP) is used tothem. findflow an between optimal the energy consumers inside the vehicle. Dynamic programming (DP) is used to find an optimal proposes an optimal EMS for a BEV, the Toyota RAV4 EV, by considering the power flow between power distribution between the vehicle drivetrain and the heating system for a standard driving power distribution between drivetrain and the heating system for to atostandard driving the energy consumers insidethe the vehicle. Dynamic programming is used find an optimal cycle. A high-fidelity model of vehicle the vehicle in Autonomie is also(DP) employed demonstrate the cycle. A high-fidelity model of the vehicle in Autonomie is also employed to demonstrate power distribution between the vehicle drivetrain and the heating system for a standard driving effectiveness of the devised EMS. The results show that the proposed strategy can improve the the effectiveness ofofthe results that the strategy improve the cycle. Ahealth high-fidelity modelEMS. of BEV. theThe vehicle in show Autonomie is proposed also employed to can demonstrate battery the devised considered battery healthofofthe the devised considered BEV. effectiveness EMS. The results show that the proposed strategy can improve the Keywords: Battery Electric Vehicles, Energy Management System, Battery Health, Dynamic © 2015, IFAC (International Federation of Automatic HostingSystem, by Elsevier Ltd. AllHealth, rights reserved. battery health of the considered BEV. Keywords: Battery Electric Vehicles, Energy Control) Management Battery Dynamic Programming. Programming. Keywords: Battery Electric Vehicles, Energy Management System, Battery Health, Dynamic Programming. short operating range, and also, their expensive battery has a INTRODUCTION short operating and also, their expensive batterymarket has a INTRODUCTION limited service range, life, which restricts BEVs’ wide Global warming, limited fossil fuel resources, and the limited service life, which restricts BEVs’ wide market short operating range, and also, their expensive battery has a INTRODUCTION presence at the end. The development of an effective Energy Global warming, limited fossil fuel people resources, the presence increasing price of oil have encouraged to findand a clean, at the end. The development of an effective Energy limited service life, which restricts BEVs’ wide market Management System (EMS) for BEVs is critical to address the increasing price ofsolution oil havefor encouraged to itfind a clean, Global limited fossil fuelpeople resources, and the Management safe and warming, efficient their mobility, and seems that for BEVs isofcritical to address the System (EMS) presence at the end. The development an effective Energy issues. safe and efficient their and seems that above-mentioned increasing pricetransportation ofsolution oil havefor encouraged people to aHybrid clean, the electrified is themobility, right way toitfind go. above-mentioned issues. Management System (EMS) for BEVs is critical to address the the transportation themobility, right way toitlast go. Hybrid safeelectrified and Vehicles efficient solution for is their seems that Many EMSs haveissues. been developed for HEVs, and they have Electric (HEVs) were introduced inand the decade, above-mentioned Many EMSs have been developed for HEVs, and they have Electric Vehicles (HEVs) were introduced in the last decade, the electrified transportation is the right way to go. Hybrid caused a significant effect on reducing the vehicle’s energy and gained a lot of attention from research communities and caused a significant effect on reducing the vehicle’s energy Many EMSs have been developed for HEVs, and they have and gained a lot of attention from research and consumption and emissions (Sciarretta and Guzzella 2007, Electric Vehicles (HEVs) were introduced incommunities theengine last decade, car manufactures. They take advantage of an IC along consumption and Emadi emissions and Guzzella 2007, a significant effect2011). on(Sciarretta reducing energy car take advantage of anacommunities IC engine and manufactures. gained a lot motor/generator, ofThey attention from and research and caused Wirasingha and EMSs the forvehicle’s HEVs can be with an electric also battery asalong their Wirasingha and Emadi 2011). EMSs for HEVs can be consumption and emissions (Sciarretta and Guzzella 2007, with an electric motor/generator, and also a battery as their car manufactures. They take advantage of an IC engine along storage unit. This hybridization of the vehicle powertrain categorized into rule-based and model-based control categorized into rule-based and model-based control Wirasingha and Emadi 2011). EMSs for HEVs can be storage unit. This hybridization of the vehicle powertrain with an electric motor/generator, and also a battery as their makes the engine smaller and more efficient. The HEVs’ strategies. The rule-based strategies try to operate each vehicle strategies. Thesubsystem rule-based strategies operateateach vehicle categorized into rule-based andtry to model-based control makes smaller and more efficient. HEVs’ storage the unit. This hybridization of the vehicle powertrain (ICE or electric motor) its highest potentials inengine the efficiency enhancement, energyThe saving and powertrain’s powertrain’s subsystem (ICE or electric motor) at itsDu highest strategies. The rule-based strategies try to operate each vehicle potentials in the efficiency enhancement, energy saving and makes the engine smaller and more efficient. The HEVs’ efficiency points. In (Banvait, Anwar et al. 2009, Liu, et al. emission reductions have resulted in many successful efficiency points. In (Banvait, Anwar et al.motor) 2009,developed Liu, Du etfor al. powertrain’s subsystem (ICE or electric at its highest emission reductions have resulted in many successful potentials in the efficiency enhancement, energy saving and 2012), a deterministic rule-based EMS was commercial products. Later, Plug-in Hybrid Electric Vehicles 2012), a deterministic rule-based EMS was developed for efficiency points. In (Banvait, Anwar et al. 2009, Liu, Du et al. commercial products. Later, Electric Vehicles emission were reductions havetoPlug-in resulted in many successful (PHEVs) introduced the car Hybrid market as a bridge from PHEVs. This strategy does not require future knowledge of the PHEVs.aThis strategy does not require future knowledge the 2012), deterministic rule-based developed for (PHEVs) introduced the car Hybrid market They as a bridge from vehicle’s commercial products. Later,totransportation. Plug-in Electric Vehicles path, and it works based onEMS a set ofwas the rules thatofhave HEVs to were the full-electric use larger vehicle’s path, and it works based on a set of the rules that have PHEVs. This strategy does not require future knowledge of the HEVs to the full-electric transportation. They use larger (PHEVs) than wereconventional introduced toHEVs the carthat market as afully bridge from been set up before the actual operation. Fuzzy logic controllers batteries can be charged beenanother set up before actualbased operation. Fuzzy logic vehicle’s path, and itrule-based works on a with set ofless the rulescontrollers that have batteries HEVs thata can be fuel fully charged HEVs tothan the conventional full-electric transportation. They use larger are kind ofthe EMSs computational before starting off, which results in better economy are another kind of rule-based EMSs with less computational been set up before the actual operation. Fuzzy logic controllers before starting off, which results in a better fuel economy batteries than conventional HEVs that can be fully charged (Taghavipour, Vajedi et al. 2012). Although HEVs and burden, but they are only optimum for special predefined burden, butkind they are onlyLanglois optimum for Denis, special predefined are another rule-based EMSs2011, with less computational (Taghavipour, Vajedi et al. 2012). and driving before off,successful, which results in only aAlthough better fuelHEVs economy cycles. Inof (Xia and Dubois et al. PHEVsstarting have been they are an interim solution driving cycles. In (Xia and Langlois 2011, Denis, Dubois et al. burden, but they are only optimum for special predefined PHEVs have been successful, they are only an interim solution (Taghavipour, Vajedi et al. 2012). Although HEVs and 2015), an adaptive fuzzy logic controller was introduced, to reduce our ecological footprints. Due to the use of ICEs in 2015), adapts an adaptive fuzzy logic controller wasincreases introduced, driving cycles. In (Xia and Langlois 2011, Denis, Dubois et al. to reduce our ecological footprints. Due to the use of ICEs in PHEVs have been successful, they are only an interim solution to different driving cycles but the which HEV/PHEVs, they are not entirely green and zero-emission which adapts to different driving cycles but increases the 2015), an adaptive fuzzy logic controller was introduced, HEV/PHEVs, they are not entirely green and zero-emission to reduce our ecological footprints. Due to the use of ICEs in computational load. The rule-based controllers find the near level. On the other hand, full electric vehicles use on-board computational load. The rule-based controllers find the adapts to different driving cycles but increases the level. On energy the other hand, full electric vehicles usethe on-board HEV/PHEVs, they are notand entirely green and for zero-emission optimum working condition for each component of near the electrical storages electric motors energy which optimum working condition for each component of the computational load. The rule-based controllers find the near electrical energy storages and electric motors for the energy level. On the other vehicles use is on-board generation. BEVs arehand, fully full green because the battery used as vehicle’s powertrain, but not the global optimal point in the vehicle’s powertrain, but the optimal pointofin can the working condition forglobal eachcontrol component generation. BEVssource are fully green because the battery isare used as optimum electrical energy storages and electric motors for the energy general case. However, thenot model-based strategies the only energy of the vehicle, and also, they very general case. However, the model-based control strategies can vehicle’s powertrain, but not the global optimal point in the the only energy source of the vehicle, and also, they are very generation. BEVs are fully green because the battery is used as efficient due to the use of electric motors instead of ICEs. find a global optimal solution to the power distribution find a global optimal solution to the power distribution general case. However, the model-based control strategies can efficient due to the use of electric motors instead of ICEs. the only energy source of the vehicle, and also, they are very However, in comparison with ICEVs and HEVs, BEVs have a problem for every driving condition. (Piccolo, Ippolito et al. for every driving condition. (Piccolo, et al. find a global optimal solution to the powerIppolito distribution However, in comparison ICEVs motors and HEVs, BEVs efficient due to the use with of electric instead of have ICEs.a problem However, in comparison with ICEVs and HEVs, BEVs have a problem for every driving condition. (Piccolo, Ippolito et al.

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2001, Delprat, Lauber et al. 2004) used offline optimization methods to solve the energy distribution problem in a given vehicle. Their proposed EMS can be useful for offline tunings of the energy flow in the design process, but cannot be employed in real-time applications. Stochastic dynamic programming (SDP) can be used to determine the optimal energy flow for a more general case in real-world driving scenarios. (Moura, Stein et al. 2013) used SDP to investigate trade-offs between the battery health and energy consumption of a given vehicle. Model predictive controllers (MPC) are also very popular for the real-time energy management of HEVs (Borhan, Vahidi et al. 2012). (Taghavipour, Vajedi et al. 2012) utilized the MPC theory for the optimal EMS design of a PHEV with four different cases of the knowledge of future trip information.

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introduced. Then, the proposed EMS and the applied DP method will be mentioned. After implementing the proposed strategy on the vehicle’s model, the results of the simulations will be presented, along with some discussions and concluding remarks. BEV SYSTEM MODEL The Autonomie software was used to create a high-fidelity model of the considered BEV. Autonomie is an automotive modeling and simulation package developed by the Argonne National Lab. In this study, we employed a modified version of the Autonomie’s default BEV model by incorporating known parameters of the baseline RAV4 EV. Figure 1 shows the considered high-fidelity model in the Simulink environment. The mechanical part of the model includes the longitudinal dynamics of the vehicle and the drivetrain system. The electrical portion of the model consists of high-voltage and low-voltage batteries, a DC/DC converter, and also, an electrical heater unit.

Compared with the extensive literature on the EMS design for HEV/PHEVs, there are only a few studies on the energy management of pure EVs, which could be because of their simpler powertrain architectures and limited degrees of freedom for the energy distribution. Many studies have investigated an optimum power distribution between ultracapacitors and batteries for EVs hybridized with ultracapacitors, which will increase the vehicle’s driving range and the lifecycle of its energy storage system (Romaus, Gathmann et al. 2010, Trovao, Santos et al. 2013). There are more limitations in terms of the EMS enhancement in BEVs because they have only batteries as their energy sources. In (Kachroudi, Grossard et al. 2012), the authors used the particle swarm optimization (PSO) method to optimally control the energy flow between the powertrain and the other vehicle’s auxiliaries for a given BEV. They tried to decrease the vehicle’s energy consumption, and at the same time maintain the comfort of the passengers, by providing some suggestions to the driver. (Masjosthusmann, Kohler et al. 2012) took advantage of the heating system’s power control, and (Roscher, Leidholdt et al. 2012) used the cooling system’s power control to reduce the overall energy consumption and increase the battery health of BEVs. They developed a rule-based method that turned off the vehicle’s HVAC system in high drivetrain power demands, and turned it on again in the low driving power demands so the resulting battery current peaks diminished. These methods cannot guarantee finding optimum power distributions in different conditions to maintain the comfort and increase the fuel economy. Also, they cannot be adjusted by the driver to choose different operating modes, such as the comfort or fuel economy.

Figure 1. Autonomie-based BEV model The longitudinal dynamics model is based on the external forces applied to the vehicle, as shown in Figure 2: 𝑎𝑎𝑥𝑥 =

1 ∗ (𝐹𝐹𝑝𝑝 − 𝐹𝐹𝑎𝑎 − 𝐹𝐹𝑟𝑟𝑟𝑟 − 𝐹𝐹𝑔𝑔 ) 𝑚𝑚𝑣𝑣

(1)

where 𝑎𝑎𝑥𝑥 is the vehicle’s acceleration, 𝑚𝑚𝑣𝑣 is the vehicle’s equivalent mass, 𝐹𝐹𝑝𝑝 is the propulsion force form both vehicle’s driving wheels, 𝐹𝐹𝑎𝑎 is the aerodynamic resistance force, 𝐹𝐹𝑟𝑟𝑟𝑟 is the friction force due to the rolling resistance of the wheels, and 𝐹𝐹𝑔𝑔 is the gravity force due to the road slope:

In this study, the authors develop an optimal EMS for a BEV, the Toyota RAV EV, to increase the battery’s service life. The drivetrain and heating system as the two major energy consumers are considered, and then, DP is applied to find an optimal power distribution between them. The optimal power distribution means smoother current demands from the battery with reduced current peaks. This will result in less sudden heat generations and temperature gradients inside the battery which cause shortening the battery life (Savoye, Venet et al. 2012). The proposed strategy is simulated using an Autonomie-based model of the vehicle in the FTP driving cycle.

Figure 2. Vehicle’s longitudinal dynamics model 𝐹𝐹𝑝𝑝 = 𝐹𝐹𝑎𝑎 =

In what follows, first, the modeling of the vehicle’s longitudinal dynamics and the cabin’s thermal model are 87

𝜏𝜏𝑅𝑅𝑅𝑅 + 𝜏𝜏𝐿𝐿𝐿𝐿 − 𝜏𝜏𝑏𝑏𝑏𝑏 𝑟𝑟𝑤𝑤

1 𝜌𝜌. 𝐴𝐴𝑣𝑣 . 𝑐𝑐𝑎𝑎 . 𝑣𝑣 2 . 𝑠𝑠𝑠𝑠𝑠𝑠(𝑣𝑣) 2

(2) (3)

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𝐹𝐹𝑟𝑟𝑟𝑟 = 𝑚𝑚𝑣𝑣 . 𝑔𝑔. 𝑐𝑐𝑟𝑟𝑟𝑟 . 𝑐𝑐𝑐𝑐𝑐𝑐(𝜃𝜃) . 𝑠𝑠𝑠𝑠𝑠𝑠(𝑣𝑣)

(4)

𝐹𝐹𝑔𝑔 = 𝑚𝑚𝑣𝑣 . 𝑔𝑔. 𝑠𝑠𝑠𝑠𝑠𝑠(𝜃𝜃)

(5)

route. 𝑃𝑃𝐿𝐿 is the power of low-voltage energy consumers which receive their power through the DC/DC converter. The DC/DC converter was modeled with a constant efficiency: 𝑃𝑃𝐿𝐿 = 𝜂𝜂𝐷𝐷𝐷𝐷/𝐷𝐷𝐷𝐷 . 𝑃𝑃ℎ

where 𝜏𝜏𝑅𝑅𝑅𝑅 , 𝜏𝜏𝐿𝐿𝐿𝐿 𝑎𝑎𝑎𝑎𝑎𝑎 𝜏𝜏𝑏𝑏𝑏𝑏 are the right and left wheel’s driving torques and braking torque, respectively, 𝑟𝑟𝑤𝑤 is the wheel radius, 𝜌𝜌 is the air density, 𝐴𝐴𝑣𝑣 is the vehicle’s frontal area, 𝑐𝑐𝑎𝑎 is the aerodynamic coefficient, 𝑣𝑣 is the vehicle’s velocity, 𝑐𝑐𝑟𝑟𝑟𝑟 is the rolling resistance coefficient, and 𝜃𝜃 is the road slope.

The most important low-voltage consumer is the HVAC system. In this work, we are considering the cabin’s heater as the only low-voltage consumer. 𝑃𝑃ℎ is the required power for heating the vehicle’s cabin. It mostly depends on the ambient temperature, available sunlight, number of the passengers, and their desired cabin’s temperature. The cabin`s air temperature differs with respect to the amount of heat transferred from and to the vehicle’s cabin, as given below:

The drivetrain of the vehicle is modeled by mapping an efficiency factor relating the mechanical power and the electrical power from the energy supply of the vehicle: 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚ℎ = 𝜂𝜂𝑒𝑒𝑒𝑒 (𝜏𝜏, 𝑁𝑁) ∗ 𝑃𝑃𝑏𝑏

𝑇𝑇̇ =

(6)

𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚ℎ = 𝜏𝜏𝜏𝜏

(7)

𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 𝜂𝜂𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝜏𝜏, 𝑁𝑁) ∗ 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚ℎ

(8)

𝑄𝑄̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝜌𝜌𝑎𝑎 𝑣𝑣𝑎𝑎 𝑐𝑐𝑎𝑎

𝑄𝑄̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑄𝑄̇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑄𝑄̇𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑄𝑄̇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝑃𝑃ℎ 𝑄𝑄̇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐾𝐾𝑐𝑐 . ∆𝑇𝑇

A battery model similar to (Dib, Chasse et al. 2012) has been employed, in which the battery’s open circuit voltage and the resistance 𝑉𝑉𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑎𝑎 𝑅𝑅𝑏𝑏 are related to the state of charge or SOC. Due to the internal resistance of the battery, the final voltage of the battery will be less than the open circuit voltage, and also, a higher battery current will cause a lower final voltage. Figure 3 shows a simple circuit-based model of the vehicle’s battery. The battery current can be calculated from the total power, as follows:

𝑄𝑄̇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 100. 𝑁𝑁𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

(13) (14) (15)

The conduction trough the vehicle’s body is related to the difference between the cabin and ambient temperature with a conduction constant 𝐾𝐾𝑐𝑐 . 𝑄𝑄̇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is the heat dissipation by each passenger, which is known to be around 100 W for each person. The radiation can be neglected for low temperature situations. The driver tries to follow the predefined speed trajectory, and applies the required driving or braking torques to the wheels:

(9)

𝜏𝜏 ∗ = (𝑣𝑣 ∗ (𝑠𝑠) − 𝑣𝑣(𝑠𝑠)) ∗ 𝐺𝐺𝑑𝑑𝑑𝑑𝑑𝑑 (𝑠𝑠)

where 𝑅𝑅𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎 𝑉𝑉𝑜𝑜𝑜𝑜 depend on the battery’s SOC.

(16)

where 𝐺𝐺𝑑𝑑𝑑𝑑𝑑𝑑 is the driver’s model, 𝑣𝑣 ∗ is the desired speed, 𝑣𝑣 is the vehicle’s actual speed, and 𝜏𝜏 ∗ is the driver`s desired torque in frequency domain.

Figure 4. Battery’s equivalent circuit model 𝑃𝑃𝑏𝑏 is the total system’s power, and two most important consumers of it are the drivetrain and the vehicle’s accessories: 𝑃𝑃𝑏𝑏 = 𝑃𝑃𝑑𝑑 + 𝑃𝑃𝐿𝐿

(12)

where 𝑄𝑄̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is the total heat flow into and from the vehicle’s cabin. This quantity consists of the heat conduction, radiation, passengers’ heat dissipation, and the HVAC system’s power. 𝜌𝜌𝑎𝑎 is the air density, 𝑣𝑣𝑎𝑎 is the volume of the cabin’s air, and 𝑐𝑐𝑎𝑎 is the specific heat capacity of air. The passenger specifies the desired temperature, and the HVAC unit tries to maintain the temperature in a region near the desired value:

where 𝜏𝜏 and 𝑁𝑁 are the torque and angular velocity of the vehicle’s wheel. 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎 𝐼𝐼𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 are the battery’s charging and discharging voltage and current. Because of the mechanical frictions and also limitations in the regenerative braking, the efficiency in the regenerative mode is different from the electrical to mechanical power efficiency amount defined previously for the propulsion mode:

𝑉𝑉𝑜𝑜𝑜𝑜 − √(𝑉𝑉𝑜𝑜𝑜𝑜2 − 4𝑅𝑅𝑏𝑏 𝑃𝑃𝑏𝑏 ) 𝐼𝐼𝑏𝑏 = 2𝑅𝑅𝑏𝑏

(11)

(10)

𝑃𝑃𝑑𝑑 is the summation of power demand from the drivetrain and the generated power by regenerative braking with considering efficiencies. The drivetrain’s power is a function of the vehicle’s speed and the motor torque. The speed and torque trajectories of the vehicle can be predicted using the data received from GPS, GIS and ITS technologies for a given

Figure 3. Proposed architecture of BEV’s EMS

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this study, we want to change this simple strategy with considering the vehicle’s future power demands for the drivetrain component, and also, find an optimal trajectory for the electrical heater’s power. This can be formulated as an optimal control problem which will be solved to obtain the optimum heater’s power trajectory, as shown later.

PROPOSED EMS CONCEPT The goal of the vehicle’s EMS is to decrease the energy consumption and increase the battery life through an optimal distribution of the power. Figure 4 illustrates the proposed architecture of the EMS unit. The devised EMS determines an optimal energy flow for the electrical components to achieve the reference speed, by considering the driver’s demand and the vehicle environment’s information. The EMS outputs can be suggested to the driver on a monitor, or it can be implemented to operate automatically as part of a supervisory control unit. In this study, we are just considering the power distribution to the electrical heater for a preliminary investigation of the proposed concept.

The objectives of the optimal control problem are to minimize failures in maintaining the cabin’s temperature close to the desired value as well as the fluctuations in the battery current with a minimum of the total consumed energy. A cost function is defined with the three above-mentioned goals, as follows: 1-The temperature needs to be maintained close to the desired value so the following term should be minimized: 𝑡𝑡𝑓𝑓

𝑓𝑓1 = 𝑅𝑅𝑡𝑡 ∗ ∑(𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 − 𝑇𝑇𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 )2

As mentioned before, a higher amount of the battery current may result in a higher voltage drop, which, in turn, requires more current for a specific power demand. The higher battery current amount means more power loss, producing more heat inside the battery, which also requires more power for cooling it down again; therefore, high peaks in the battery current should be avoided. The battery current fluctuates due to the changes of power demands of the vehicle’s drivetrain and electrical components during a specific trip. If we assume that the current fluctuates with a sinusoidal form, then: 𝐼𝐼𝑏𝑏 = 𝐼𝐼̅𝑏𝑏 + 𝐼𝐼̃𝑏𝑏 sin(𝜔𝜔𝜔𝜔)

(17)

2 𝐸𝐸𝑏𝑏 = ∫ 𝑃𝑃𝑏𝑏 . 𝑑𝑑𝑑𝑑 = ∫ 𝑉𝑉𝑜𝑜𝑜𝑜 . 𝐼𝐼𝑏𝑏 . 𝑑𝑑𝑑𝑑 = (𝑅𝑅𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝑅𝑅𝑏𝑏 ). 𝐼𝐼̅̅̅̅ 𝑏𝑏

(18)

𝐸𝐸𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

1 2 = 𝑅𝑅𝑏𝑏 . 𝐼𝐼̅𝑏𝑏 + 𝑅𝑅𝑏𝑏 . 𝐼𝐼̃𝑏𝑏 2 2

(20)

𝑡𝑡=0

where 𝑅𝑅𝑡𝑡 is a weighting coefficient. 2- The main objective is to achieve a smoother battery current, which, in turn, means a smoother overall power demand profile. Minimizing the term below gives us a smoother power demand sequence: 𝑡𝑡𝑓𝑓

𝑓𝑓2 = 𝑅𝑅𝑝𝑝 ∗ ∑(𝑃𝑃𝑏𝑏 − 𝑃𝑃̅𝑏𝑏 )2

(21)

𝑡𝑡=0

where 𝐼𝐼 ̅ is the mean current value, and 𝐼𝐼̃ is the amplitude of the sinusoidal current fluctuations. With this formulation of the current, the total consumed battery energy 𝐸𝐸𝑏𝑏 and the total produced heat inside the battery 𝐸𝐸𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 for a fluctuation period will be:

∫ 𝑅𝑅𝑏𝑏 . 𝐼𝐼𝑏𝑏2 . 𝑑𝑑𝑑𝑑

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where 𝑅𝑅𝑝𝑝 is a weighting coefficient, and 𝑃𝑃̅𝑏𝑏 is the expected mean power demand for a given trip. 𝑃𝑃̅𝑏𝑏 is calculated by averaging the expected powers of the drivetrain and a conventional heating system for a given driving cycle and ambient temperature. 3- The last objective is to minimize the total consumed energy: 𝑡𝑡=𝑡𝑡𝑓𝑓

𝑓𝑓3 = 𝑅𝑅𝑒𝑒 ∗ ∑ 𝑃𝑃𝑏𝑏2

(19)

(22)

𝑡𝑡=0

where 𝑉𝑉𝑏𝑏 , 𝐼𝐼𝑏𝑏 , and 𝑅𝑅𝑏𝑏 are the battery`s voltage, current, and internal resistance, respectively. The energy loss inside the battery is related to the square of mean current and current fluctuations. By reducing the fluctuations of the battery current, the energy loss decreases for the same final power demand. The vehicle’s EMS can smoothen the battery current and reduce the current peaks by distributing the demanded power wisely to the vehicle’s components. During the acceleration or when the vehicle is moving on a high slope road, EMS will put the heater in a low power mode. When the drivetrain’s power demand decreases, EMS returns the heater to a high power mode. In this way, EMS acts as a virtual capacitor that uses the thermal capacity of the vehicle’s cabin to achieve a smoother power demand profile.

𝑃𝑃𝑏𝑏 is the summation of the drivetrain and heating system’s powers. The required drivetrain’s power is known for a specified speed trajectory based on the vehicle’s model. The heating power is the system’s input, and the temperature is the state of the system. The relation between the heating power and the cabin’s temperature provides the plant model. This results in the optimization problem below: min 𝐽𝐽(𝑃𝑃𝑏𝑏 , 𝑇𝑇) = 𝑓𝑓1 + 𝑓𝑓2 + 𝑓𝑓3 𝑃𝑃ℎ

𝑃𝑃𝑏𝑏 = 𝑃𝑃ℎ + 𝑃𝑃𝑑𝑑 𝑇𝑇𝑘𝑘+1 = 𝑇𝑇𝑘𝑘 +

(23)

𝑃𝑃ℎ + 𝑄𝑄̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ∗ ∆𝑡𝑡 𝜌𝜌𝑎𝑎 𝑣𝑣𝑎𝑎 𝑐𝑐𝑎𝑎

0 ≤ 𝑃𝑃ℎ ≤ 4000 [𝑊𝑊]

OPTIMUM EMS DESIGN PROCESS A typical heating system in BEVs increases the temperature to the driver’s demanded value, and then tries to maintain the temperature in a region close to it. So, when the temperature reaches the higher limit, the heater will be turned off or brought to a lower power mode, and when the temperature reaches the lower limit, the heater will be turned on again. In

0 ≤ 𝑇𝑇 ≤ 30

[℃]

DP was used to solve the optimal control problem through considering the heating power 𝑃𝑃ℎ as a discretized input from 0 to 4000 W, and the cabin’s temperature was discretized from 89

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0 to be 30° 𝐶𝐶. This algorithm tries to find an optimal trajectory for 𝑃𝑃ℎ by minimizing 𝐽𝐽(𝑃𝑃𝑏𝑏 , 𝑇𝑇) and using the state equation to determine the cabin’s temperature resulting from different 𝑃𝑃ℎ sequences.

power demand profile, an optimal heating power trajectory to minimize the defined cost function was found. Figure 6 illustrates the resulting optimal trajectory for the heater’s power and the cabin’s temperature variations during the FTP driving cycle. The driver’s desired temperature was assumed to be 22° 𝐶𝐶, and the ambient temperature was fixed at −10 ℃. Also, the passenger compartment’s initial temperature was 0℃ and the maximum heating power was set at 4000 W.

SIMULATION RESULTS We chose the FTP-75 driving cycle to evaluate the performance of the proposed EMS. The vehicle’s high-fidelity model was simulated with the knowledge of FTP-75 speed trajectory. Considering the efficiencies of the drivetrain, converter and actuators, the total driving power demand of the vehicle was calculated from a forward simulation. This power demand was then used as a known input for the defined DP problem. Figure 5 shows the speed trajectory, and the driving power demand resulting from the vehicle’s model simulation.

4

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Figure 7. Total power demand with and without the proposed EMS

x 10

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Figure 5. FTP-75 driving cycle and the resulting power demand ( Wh )

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Figure 8. Battery’s SOC variations and the heat loss inside the battery during the FTP-75 driving cycle

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Ph (W)

For the non-optimal heating scenario, the heater starts with the maximum power until the cabin’s temperature reaches the desired value, and after that point, the heater is switched to a lower power mode that maintains a constant cabin’s temperature. With the proposed EMS, as shown in Figure 6, the heater tries to increase the cabin’s temperature to the desired value, but at the same time prevents high peaks in the total power demand. Thus, the initial heating takes longer than the non-optimum strategy, and after that, the temperature will fluctuate within a bound near the desired value to avoid high power demand peaks. Figure 7 depicts the power demand of the vehicle with the optimal and non-optimal strategies for a

2000

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ba t

E los s

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-2

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Figure 6. Cabin’s temperature and the required heating power for the optimum and non-optimum strategies The maximum driving power demand is about 60 kW, and the total driving energy demand for the whole cycle is about 4.79 kWh with considering the regenerative braking. With this 90

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part of the FTP cycle. The devised EMS algorithm has resulted in smaller peaks in the battery power demand by properly regulating the heater’s power. This effect, in turn, improves the battery service life.

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Moreover, the presented results are for using fixed weighting coefficients in the defined cost function. These weighting coefficients can be varied for a certain driving mode specified by the driver to introduce a trade-off between the comfort and drivability of the vehicle.

The use of devised EMS causes a smoother power demand, and as a result, a smoother battery current. As discussed before, a smoother battery current generates less heat loss in the battery’s internal resistance. Figure 8 illustrates the total energy loss by the battery’s internal resistance and the battery’s state of charge during the simulation.

CONCLUSIONS Growing concerns about the global warming and limited energy sources have caused global demands to explore more efficient and green ways of transportation. HEVs were introduced in the last decades as a temporary alternative to these problems, and now, BEVs are finding their way into our every day’s transportation. An optimal EMS controller can improve the both battery life and energy economy of a BEV by finding the most optimum energy flow within the vehicle. This paper proposed an EMS that controls the power distribution between the energy consumers inside a single source electric vehicle. A high-fidelity model of BEVs in Autonomie was revised slightly to represent the Toyota RAV4 EV, and also, simulated to calculate the vehicle’s power demand during the FTP driving cycle. The proposed EMS employed DP to determine an optimum heating power profile which resulted in smaller battery current peaks and smoother power demand sequence for it. In summary, the simulation results shows that the proposed EMS can decrease the energy loss inside the battery and increase the battery lifetime of the considered BEV.

As it can be seen, the proposed EMS results in a smaller total energy loss in the battery’s resistance, however, it does not have a significant effect on SOC. DISCUSSIONS The proposed EMS uses DP to find an optimal heater’s power trajectory for a specific driving cycle. Figure 5 shows the FTP75 driving cycle, which is a standard city driving pattern designed for measuring the fuel consumption of passenger cars. The optimized heating causes a fluctuation in the passenger compartment’s temperature, as shown in Figure 6. It takes longer to reach the desired temperature with this strategy because the driving power demand’s peaks cause the EMS controller to put the heater in a lower power mode. EMS uses the heating capacity of the passenger compartment as a virtual capacitor to minimize fluctuations in the battery current. As it can be seen in Figure 7, the proposed EMS has decreased the power demand peaks of the battery by an optimal control of the heater. In summary, during the high propulsion power demand situations, EMS puts the heater in a low power mode, and for the low driving power demands, returns it back to a higher power mode. The weightings in the cost function can be changed to have different driving modes. Increasing 𝑅𝑅𝑡𝑡 will improve the comfort by minimizing the temperature peaks and overshoots, but it means less emphasis on the consumed energy.

REFERENCES Banvait, H., S. Anwar and C. Yaobin (2009). A rule-based energy management strategy for Plug-in Hybrid Electric Vehicle (PHEV). American Control Conference, 2009. ACC '09. Borhan, H., A. Vahidi, A. M. Phillips, M. L. Kuang, I. V. Kolmanovsky and S. Di Cairano (2012). "MPC-Based Energy Management of a Power-Split Hybrid Electric Vehicle." Control Systems Technology, IEEE Transactions on 20(3): 593-603. Delprat, S., J. Lauber, T. M. Guerra and J. Rimaux (2004). "Control of a parallel hybrid powertrain: optimal control." Vehicular Technology, IEEE Transactions on 53(3): 872-881. Denis, N., M. R. Dubois and A. Desrochers (2015). "Fuzzybased blended control for the energy management of a parallel plug-in hybrid electric vehicle." Intelligent Transport Systems, IET 9(1): 30-37. Dib, W., A. Chasse, D. Di Domenico, P. Moulin and A. Sciarretta (2012). "Evaluation of the Energy Efficiency of a Fleet of Electric Vehicle for Eco-Driving Application." Oil & Gas Science and Technology-Revue D Ifp Energies Nouvelles 67(4): 589-599. Kachroudi, S., M. Grossard and N. Abroug (2012). "Predictive Driving Guidance of Full Electric Vehicles Using Particle Swarm Optimization." Vehicular Technology, IEEE Transactions on 61(9): 3909-3919. Liu, S., C. Du, F. Yan, J. Wang, Z. Li and Y. Luo (2012). A Rule-Based Energy Management Strategy for a New BSG Hybrid Electric Vehicle. Intelligent Systems (GCIS), 2012 Third Global Congress on. Masjosthusmann, C., U. Kohler, N. Decius and U. Buker (2012). A vehicle energy management system for a Battery

The smoother power demand profiles and currents of the battery lead to less heat loss as well as a longer lifetime for it, which is critical for a BEV. Figure 8 shows SOC and the total energy loss in the battery’s resistance. With the devised EMS controller, the energy loss in the battery has decreased by about 13% at the end of the simulated driving cycle. However, this strategy does not have a significant effect on the battery’s final SOC because, for an efficient low resistance battery, the losses are generally very small, as compared to the high power demands of the vehicle’s drivetrain for propulsion. Also, the proposed EMS does not aim at decreasing the mean current demand but reducing the fluctuations of the battery current. However, by considering other sources of power loss in the vehicle for the EMS design, such as the DC/DC converter, air conditioner, seat heaters, entertainment systems, and necessary cooling power for the battery, the final SOC and the driving range of the vehicle can be improved.

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