Energy-Efficiency Improvement Potential of Electric Vehicles Considering Transmission Temperature

8th IFAC Symposium on Mechatronic Systems 8th IFAC Symposium on Mechatronic Systems Vienna, Sept. on 4-6, 2019 8th IFACAustria, Symposium Systems online at www.sciencedirect.com Vienna, Austria, Sept. 4-6,Mechatronic 2019 Available 8th IFACAustria, Symposium Systems Vienna, Sept. on 4-6,Mechatronic 2019 Vienna, Austria, Sept. 4-6, 2019

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IFAC PapersOnLine 52-15 (2019) 211–216

Energy-Efficiency Improvement Potential of Energy-Efficiency Improvement Potential of Energy-Efficiency Improvement Potential of Electric Vehicles Considering Transmission Energy-Efficiency Improvement Potential of Electric Vehicles Considering Transmission Electric Vehicles Considering Transmission Temperature Electric Vehicles Considering Transmission Temperature Temperature Temperature C. Wei, T. Hofman ∗∗ E. Ilhan Caarls, R. van Iperen ∗∗ ∗∗

C. Wei, T. Hofman ∗ E. Ilhan Caarls, R. van Iperen ∗∗ C. Wei, T. Hofman E. Ilhan Caarls, R. van Iperen ∗ C. Wei, T. Hofman ∗ E. Ilhan Caarls, R. van Iperen ∗∗ Engineering, Eindhoven University of ∗ Department of Mechanical of Mechanical Engineering, Eindhoven University of ∗ Department Technology, Netherlands (e-mail: [email protected], [email protected]). Department of Mechanical Engineering, Eindhoven University of ∗ Technology, Netherlands (e-mail: [email protected], [email protected]). ∗∗ Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands (e-mail: [email protected], [email protected]). Transmission Technology, Netherlands (e-mail: ∗∗ Bosch Bosch Transmission Technology, Netherlands (e-mail: ∗∗ Technology, Netherlands (e-mail: [email protected], [email protected]). [email protected], [email protected]) Bosch Transmission Technology, Netherlands (e-mail: [email protected], [email protected]) ∗∗ Bosch Transmission Technology, Netherlands (e-mail: [email protected], [email protected]) [email protected], [email protected]) Abstract: This study presents an integrated energy and transmission thermal management Abstract: This study presents an integrated energy and transmission thermal management system to quantify the presents impact ofana integrated cold-start on the energy consumption of electric vehicles Abstract: This study energy and transmission thermal management system to the impact of cold-start on the consumption of electric vehicles Abstract: This study presents energy and transmission thermal management system to quantify quantify the impact ofana a integrated cold-start on theit energy energy consumption of electric vehicles (EVs) from optimal control perspective. In addition, provides insights into reducing this cold providesconsumption (EVs) from optimal the control perspective. In addition, insights intoofreducing this cold system to quantify impact of a cold-start on theit electric vehicles effect from design point of view. The cold-start conditions in an EV refer to aareducing low transmission (EVs) from optimal control perspective. In addition, it energy provides insights into this cold effect from design point of view. The cold-start conditions in an EV refer to low transmission (EVs) fromdesign optimal control perspective. In addition, it provides into this temperature, which increases the power losses viscosity in cold the effect from point of view. Thefrictional cold-start conditions incaused an insights EVby refer to areducing loweffects transmission temperature, which increases the power lossesincaused viscosity effects in the effect from design point of are view. Thefrictional cold-start conditions an EVby refer to a low transmission transmission. These losses eventually compensated by the battery, leading to effects excess energy temperature, which increases the frictional power losses caused by viscosity in the transmission. These losses are eventually compensated by the battery, leading to excess temperature, which increases the frictional power losses caused viscosity in the transmission. These losses are especially eventually compensated by part the battery, leading to effects excess energy energy usage. A detailed EV model, the transmission withby transient thermodynamics usage. A detailed EV model, especially the transmission part with transient thermodynamics transmission. These losses are eventuallythe compensated by part the battery, leading tocontroller excess energy based on experiment data, is developed, and the integrated energy and thermal usage. A detailed EV model, especially transmission with transient thermodynamics based on experiment data, is developed, and transmission the integratedpart energy and thermalthermodynamics controller aims aims usage. A experiment detailed EVdata, model, especially the transient to maximize the energy efficiency. Numerical show that a with cold-start influences the energybased on is developed, and results the integrated energy and thermal controller aims to maximize the energy efficiency. Numerical results show that a cold-start influences the energybased on experiment is Through developed, and results the energy and thermal controller aims saving potential, up todata, 2.9%. analysis of integrated temperature-dependent transmission to maximize the energy efficiency. Numerical show that a cold-start influences thebehavior energysaving potential, up to 2.9%. Through analysis of transmission behavior to the energy efficiency. Numerical results show that athe cold-start influences energysaving potential, up analysis of temperature-dependent temperature-dependent transmission behavior andmaximize energy losses of to the2.9%. EV, Through design considerations of reducing cold impact, thusthe improving and energy lossesup of to the2.9%. EV, Through design considerations of reducing the cold impact, thus improving saving potential, analysis of temperature-dependent transmission behavior energy efficiency, be derived. and energy losses can of the design considerations of reducing the cold impact, thus improving energy efficiency, can be EV, derived. and energy losses of the EV, design considerations of reducing the cold impact, thus improving energy efficiency, can be derived. © 2019,efficiency, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. energy can be derived. Keywords: Keywords: Electric Electric vehicles, vehicles, Energy Energy efficiency, efficiency, Cold-start, Cold-start, Transmission Transmission temperature, temperature, Optimal Optimal control. Keywords: Electric vehicles, Energy efficiency, Cold-start, Transmission temperature, Optimal control. Keywords: Electric vehicles, Energy efficiency, Cold-start, Transmission temperature, Optimal control. control. 1. INTRODUCTION which has not been addressed in literature from opti1. which has been in from opti1. INTRODUCTION INTRODUCTION which has not not been addressed addressed in literature literature fromenergy optimal control viewpoint. To that end, an integrated mal control viewpoint. To that end, an integrated energy 1. INTRODUCTION which has not been addressed in literature from optimal control viewpoint. To management that end, an system integrated energy and transmission thermal containing Faced with stringent emissions regulations and energy and transmission thermal containing mal control viewpoint. To management that end,transmission an system integrated energy and transmission thermal management system containing Faced with stringent emissions regulations and energy detailed component models with transient detailed component models with transmission transient Faced withpowertrain stringent emissions regulations and energy shortage, electrification has proven to be and transmission thermal management systemcombustion containing detailed component models with transmission transient shortage, powertrain electrification has proven to be thermodynamics is necessary. Unlike internal Faced withsolution. stringent emissions regulations and vehicles energy shortage, powertrain electrification has proven to be the right Admittedly, hybrid electric thermodynamics is necessary. Unlike internal combustion detailed component models with transmission transient the right solution. Admittedly, hybrid electric vehicles is necessary. Unlike internal combustion engine vehicles, where the engine produces a large amount shortage, powertrain electrification haselectric proven be thermodynamics the righttaking solution. Admittedly, hybrid (HEVs), advantage of hybridization, madevehicles atosubengine vehicles, where the engine produces aa large amount thermodynamics is Canova necessary. Unlike internal combustion engine vehicles, where the engine produces large amount (HEVs), taking advantage of hybridization, made a subof heat, Laboe and (2012), to warm up, e.g., cabin the right solution. Admittedly, hybrid electric vehicles of heat, Laboe and Canova (2012), to warm up, e.g., cabin (HEVs), taking advantage of hybridization, made ainsubstantial contribution to reducing fuel consumption the engine vehicles, where the engine produces a large amount of heat, Laboe and Canova (2012), to warm up, e.g., cabin stantial contribution to reducing fuel consumption in the and lubrication oils, EVs are lack of heat, posing challenges (HEVs), taking advantage of hybridization, made a(EVs) and lubrication oils, EVs are lack of heat, posing challenges stantial contribution to to reducing fuel consumption insubthe of last decade. Compared HEVs, electric vehicles Laboe and Canova (2012), warm up, e.g., cabin lubrication oils, EVs are lack of to heat, posing challenges last decade. Compared HEVs, electric vehicles (EVs) forheat, transmission warm-up. Therefore, apart from quantifystantial contribution to to reducing fuel consumption in the and last decade. Compared to HEVs,impact electric vehicles (EVs) even have an increased positive on environment, for transmission warm-up. Therefore, apart from quantifyand lubrication oils, EVs are lack of heat, posing challenges even have an increased positive impact on environment, warm-up. Therefore, apart fromtoquantifying transmission the energy-saving potential, it is imperative come up last decade. HEVs,impact electric (EVs) for even have anCompared increased positive onvehicles environment, which accelerates their to resurgence. In order to reduce ing the energy-saving potential, it is come up for transmission warm-up. Therefore, apart fromto quantifying the energy-saving potential, it point is imperative imperative to come up which accelerates their resurgence. In order to reduce with viable solutions from design of view improve even have an increased positive impact on environment, with viable solutions from design point of view to improve which their resurgence. order focused to reduce energy accelerates consumption, previous studiesInmainly on ing the energy-saving potential, it is imperative to come up with viable solutions from design point of view improve energy consumption, previous studies mainly focused on energy efficiency with cold-start conditions, thus bridging to which accelerates their resurgence. Inmainly order focused to reduce energy efficiency withfrom cold-start conditions, thus bridging energy consumption, previous studies on with design and control of EVs from energy perspective, Hofviable solutions designand point of view to bridging improve design and control of EVs from energy perspective, Hofenergy efficiency with cold-start conditions, thus the gap between a cold-start a warm-start. These energy consumption, studies focusedHofon design and control of previous EVset energymainly perspective, man Dai (2010); Dib al. De Cauwer al. gap between aa cold-start and aa warm-start. These energy with cold-start conditions, thus bridging man and and Dai (2010); Dib etfrom al. (2014); (2014); De Cauwer et etHofal. the the gapefficiency between cold-start and warm-start. These solutions help improve the performance and durability of a design and control of EVs energy perspective, man and Dai (2010); Dib etfrom al. (2014); De Cauwer al. solutions (2015), e.g., taking into account of mechanical and et elechelp improve the performance and durability of the gap between a cold-start and a to warm-start. These solutions help improve the performance and durability of a a (2015), e.g., taking into account of mechanical and electransmission, eventually contributing energy efficiency man and Dai (2010); Dib et al. (2014); De Cauwer et al. transmission, eventually contributing to energy efficiency (2015), e.g., taking into thermal account domain, of mechanical andwhich elec- solutions help improve the performance and durability of a trical energy flows. The however, transmission, eventually contributing to energy efficiency trical energy flows. The thermal domain, however, which improvement. It requires a deep understanding of trans(2015), e.g., taking into account domain, of mechanical andwhich elec- improvement. It requires a deep understanding of transtrical plays crucial role determining the consumption thermal however, transmission, eventually contributing to energy efficiency plays a aenergy crucialflows. role in inThe determining the energy energy consumption It requires a deep understanding of transmission temperature dynamics during heating interval and trical energy flows. The thermal domain, however, which improvement. plays a crucial role in determining the energy consumption of an EV, has not been fully investigated yet. mission temperature dynamics during heating interval and improvement. It requires a deep understanding of transof an EV, has not been fully investigated yet. mission temperature dynamics during heating interval and energy analysis of the EV at system level. plays a crucial role in determining the energy consumption of an EV, has not been fully investigated yet. energy of EV missionanalysis temperature duringlevel. heating interval and energy analysis of the thedynamics EV at at system system level. Many researchers assume the transmission of an EV, has not been fully yet.is Many researchers assume theinvestigated transmission is already already at at energy Motivated by the above discussion, this paper originally analysis of the EVdiscussion, at system level. Many researchers assume the transmission is already at Motivated its efficient operating temperature at the beginning of the by the above this the aboveenergy discussion, this paper paper originally originally its efficient operating temperature at beginning of proposes anbyintegrated and transmission thermal Many researchers assume transmission is already at Motivated its efficient operating temperature at the theWu beginning of the the driving mission, that is, a the warm-start, et al. (2013); proposes an integrated energy and transmission thermal Motivated byintegrated the above discussion, this paper originally proposes an energy and transmission thermal driving mission, that is, a warm-start, Wu et al. (2013); management system to quantify the energy-efficiency imits efficient operating temperature at the beginning of the management system to quantify the energy-efficiency imdriving mission, that is, a warm-start, Wu et al. (2013); Hofman and Janssen (2017). This may not hold, however, proposes an integrated energy and transmission thermal management system to quantify the energy-efficiency imHofman and Janssen (2017). This may not hold, however, provement potential of EVs with cold-start conditions. driving mission, that is,been a warm-start, Wu ethours, al.however, (2013); Hofman and Janssen (2017). This may not hold, for example, the car has parked for a few which provement potential of EVs with cold-start conditions. management system to quantify thecold-start energy-efficiency imfor example, the car has been parked for not a few hours, which provement of EVs with The systempotential contains a detailed vehicle model,conditions. in particHofman and the Janssen (2017). This may hold, however, for example, carinhas been parked for a few hours, which The is not uncommon our daily life, namely, a cold-start. system contains aa detailed vehicle model, in particprovement potential of EVs with cold-start conditions. The system contains detailed vehicle model, in particis not uncommon in our daily life, namely, a cold-start. ular the transmission part including thermodynamics on for example, the carinconditions has been parked few transmission hours, which ular the transmission part including thermodynamics on is uncommon our daily life, for namely, a cold-start. In not EVs, cold-start reflect a alow The system contains apart detailed vehicle model, in control particular the transmission including thermodynamics on In EVs, cold-start conditions reflect a low transmission the basis of measurement data, and the resulting is not uncommon our dailyfrictional life, namely, a dissipation cold-start. the basis of measurement data, and the resulting control In EVs, cold-start reflect a power low transmission temperature, whichinconditions increases ular the transmission including thermodynamics on the basis of solved measurement data, and the resulting control temperature, which increases frictional dissipation problem is by part using optimal control technique. In EVs, ofcold-start conditions reflect a power low effects. transmission temperature, which increases frictional power dissipation because increased hydrodynamic viscosity These problem is solved by using optimal control technique. the basis of measurement data, and the resulting control because of increased hydrodynamic viscosity effects. These problem is solved using optimal control Furthermore, from by design perspective, feasibletechnique. solutions temperature, which hydrodynamic increases frictional dissipation because increased effects. These Furthermore, losses areofultimately compensated byviscosity thepower battery, resulting from design perspective, feasible solutions problem is solved by using optimal control technique. Furthermore, from design perspective, feasible solutions losses are ultimately compensated by the battery, resulting are presented to improve energy efficiency of EVs under because of increased hydrodynamic viscosity effects. These losses are energy ultimately compensated by the battery,inresulting in extra consumption. The difference energy are presented to improve efficiency of EVs under Furthermore, from design energy perspective, feasible solutions are presented to improve energy efficiency of EVs under in extra energy consumption. The difference in energy a cold-start via analyzing the influence of transmission losses are energy ultimately compensated by and the battery, a cold-start via analyzing the influence of transmission in extra consumption. The difference inresulting energy consumption between a cold-start a warm-start is are presentedvia improve efficiency EVs under atemperature cold-start analyzing the influence ofoftransmission consumption between a cold-start and a warm-start is ontothe energyenergy consumption and energy balin extra energy consumption. The difference in energy consumption between a cold-start and a warm-start is considered as the energy-efficiency improvement potential, temperature on the energy consumption and energy a cold-start via analyzing the influence of transmission considered as the energy-efficiency improvement potential, temperature on the energy consumption and energy balbalconsumption between a cold-start and a warm-start is considered as the energy-efficiency improvement potential, temperature on the energy consumption and energy balconsidered theIFAC energy-efficiency improvement potential, 2405-8963 © as 2019, (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Copyright © 2019 IFAC 614 Copyright © under 2019 IFAC 614 Control. Peer review responsibility of International Federation of Automatic Copyright © 2019 IFAC 614 10.1016/j.ifacol.2019.11.676 Copyright © 2019 IFAC 614

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Cycles (WLTC), which represents the real-world driving behavior, are selected. Moreover, cold-start conditions are required for these driving cycles.

Paux Electrical

2.2 Longitudinal dynamics

Batt

Taking into account of aerodynamic drag force, rolling resistance and inertia force, the speed wwh (k) and torque Twh (k) demanded at the wheels to follow the driving cycle can be expressed as follows: vveh (k) wwh (k) = , (5) rwh

PE

Thermal Electrical Mechanical EM TR

Fig. 1. Integrated energy and transmission thermal management system for a CVT-based electric vehicle.

1 2 (k) Twh (k) = ( · ρair · cd · Af · vveh 2 + cr · mveh · g · sign(vveh (k)) Jwh + (mveh + 4 · 2 ) · aveh (k)) · rwh . rwh

ance of the EV. The rest of this paper is structured as follows. System modeling is given in Section 2. Section 3 describes the optimization problem. Simulation results are demonstrated in Section 4. Finally, conclusions are drawn in Section 5.

where ρair represents the air density, cd the aerodynamic drag coefficient, Af the frontal area of the vehicle, cr the rolling resistance coefficient, mveh the total vehicle mass, g the gravitational acceleration, Jwh the wheel inertia and rwh the effective wheel radius.

Ptr,th Chemical

Mechanical

2. SYSTEM MODELING

(6)

2.3 CVT

The vehicle under consideration is shown in Fig. 1. The transmission employed in this study is a push-belt type continuous variable transmission (CVT). Thermal energy as represented by the red-dashed line is added to conventional mechanical and electrical energy flows. A backward facing model comprising both energy dynamics and thermodynamics with a time step of one second, which is sufficient for the optimal controller design, is created in this research. It is assumed that, except the transmission, all heat sources are in thermal equilibrium with ambient, and once the transmission operating temperature is reached, this target temperature is maintained afterwards. The transmission temperature model is built by using a lumped approach, based on first-order principles. The integrated system can be written as x(k + 1) = f (x(k), u(k), w(k)). (1) where k is the time index. The state vector consists of the state of charge (SOC) of the battery and the transmission temperature, given by x(k) = [ξ(k), θtr (k)]T . (2) The control variable is the variator ratio of the CVT, giving, u(k) = γvar (k). (3) The disturbance vector contains the vehicle speed and acceleration, which are given by the driving profile, i.e., w(k) = [vveh (k), aveh (k)]T . (4) 2.1 Driving cycle Since the system requires the disturbance known a priori, a mix of official and real-world driving cycles are used. Specifically, the New European Driving Cycle (NEDC), which is widely used to certify fuel consumption measurements, and the Worldwide Harmonized Light Vehicles Test 615

The CVT consists of four major parts: variator, pump, DNR (drive, neutral and reverse) and final drive. The CVT provides a continuous variable speed ratio γvar between the primary pulley and the secondary pulley to optimize the operating point of the power source. It should be noted that the pump operates above 1000 rpm. Assuming the ratio between the secondary pulley and the wheel is a constant γf d , the speed and rotational acceleration of the final drive are computed by wf d (k) = wwh (k) · γf d , (7) (8) ∆wf d (k) = ∆wwh (k) · γf d . The torque of the final drive is calculated by  Twh (k)   , if Twh (k) > 0,  γ f d · ηf d (9) Tf d (k) = Twh (k) · ηf d   , if Twh (k) ≤ 0.  γf d where ηf d is the efficiency of the final drive. The torque loss of the final drive is given by Twh (k) Tf d,loss (k) = Tf d (k) − . (10) γf d The power dissipation in the final drive is obtained by Pf d,loss (k) = Tf d,loss (k) · wf d (k). (11) The speed and rotational acceleration of the primary pulley are calculated by wpri (k) = γvar (k) · wf d (k), (12) (13) ∆wpri (k) = γvar (k) · ∆wf d (k). Considering inertia effects Jvar,i and Jvar,o , the torque of the primary pulley is given by Tf d (k) + Jvar,o · ∆wf d (k) Tpri (k) = + Jvar,i · ∆wpri (k). γvar (k) (14)

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Therefore, the total torque demand can be calculated by Ttot (k) = Tpri (k) + Tvdp,loss (wpri (k), Tpri (k), γvar (k)). (15) where Tvdp,loss (wpri , Tpri , γvar ) denotes the torque loss in the variator, DNR and pump. Detailed loss maps are employed for the calculation. The corresponding power losses of these components can also be computed. Constraints on the variator ratio and primary pulley torque are (16) γvar (k) ∈ [γ var , γ var ], Tpri (k) ∈ [T pri , T pri ]. (17) Hence, with warm-start conditions, the power dissipation in the CVT can be expressed as w (k) = Pvdp,loss (wpri (k), Tpri (k), γvar (k)) Ptr,loss

+ Pf d,loss (k).

(18)

Under a cold-start, however, due to higher frictional losses caused by hydrodynamic viscosity effects, the transmission losses are higher. To mimic the real situation, a transmission cold factor, which is a function of the transmission temperature, is introduced to adjust the nominal power w (k). In this work, models associated dissipation Ptr,loss with the transmission thermodynamics are developed on the basis of, van Berkel (2013), where experiments were performed for transmission temperatures ranging from 30◦ C to 80◦ C. The transmission cold factor is given by    1 + ctr,1 · (θtr − θtr (k))    c c(θtr (k)) = if θtr (k) < θtr , ·e tr,2 ·(θtr −θtr (k)) ,    1, if θtr (k) = θtr . (19) where ctr,1 and ctr,2 are constant coefficients. θtr is the operating temperature, from which the cold effect on the transmission losses becomes negligible. The temperaturedependent power dissipation in the transmission is computed by c w (k) = c(θtr (k)) · Ptr,loss (k). (20) Ptr,loss The heat production in the transmission can thus be calculated as c (k) − Ptr,amb (k). (21) Ptr,th (k) = Ptr,loss The power lost to the ambient air is given by (22) Ptr,amb (k) = ctr,amb · Atr · (θtr (k) − θamb ). where ctr,amb represents the heat transfer coefficient to the ambient and Atr is the heat exchange area. As a result, the transmission temperature can be derived as follows:  Ptr,th (k)  θtr (k) + ∆t, if θtr (k) < θtr , θtr (k+1) = ctr,h · ctr · mtr  θtr (k), if θtr (k) = θtr . (23) where ctr,h is a heating coefficient, which compensates for the slower heating of the metal parts than that of the lubrication oil. ctr is the transmission specific heat and mtr its mass. 2.4 Integrated motor-generator Given the total torque demand, the torque supplied by the EM at the torque-split location (in consideration of mechanical braking) is given by 616

213

if Ttot (k) > 0 ∨ 1000 · π Ttot (k) < 0 ∧ wpri (k) ≥ . (24) 30 The additional torque provided by the mechanical braking is defined as (25) Tbr (k) = Ttot (k) − Tem,ts (k), if Ttot (k) < 0. The speed and rotational acceleration of the EM are computed by 1000 · π wem (k) = max(wpri (k), ), if wpri (k) > 0, (26) 30 ∆wem (k) = ∆wpri (k). (27) Taking into account of the EM inertia Jem , the torque of the EM is caculated by Tem (k) = Tem,ts (k) + Jem · ∆wem (k). (28) The power loss of the EM including power electronics (PE) Pem,loss is described by a look-up table. Hence, the electric power supplied to/by the EM is obtained by Tem,ts (k) = Ttot (k),

Pem,elec (k) = wem (k) · Tem (k)

+ Pem,loss (Tem (k), wem (k)). Constraints imposing on the EM are wem (k) ∈ [wem , wem ], Tem (k) ∈ [T em (wem (k)), T em (wem (k)].

(29) (30) (31)

2.5 Battery The battery is modeled by using an equivalent circuit approach, a voltage source in series with an internal resistance. The electric power provided by the battery and its current are computed by Pbatt (k) = Pem,elec (k) + Paux . (32)  2 (k) − 4 · P Voc (k) − Voc batt (k) · Rint (k) Ibatt (k) = . 2Rint (k) (33) where Paux is the auxiliary power, a constant. Voc represents the open circuit voltage of the battery and Rint is the battery internal resistance. Consequently, the SOC is governed by Ibatt (k) · ηbatt (Ibatt (k)) ξ(k + 1) = ξ(k) − ∆t. (34) 3600 · Qbatt where ηbatt is the battery charging efficiency and Qbatt is the battery capacity. The battery current is bounded by (35) Ibatt (k) ∈ [I batt , I batt ]. 3. OPTIMIZATION PROBLEM In this work, the cold factor works as a penalty on the system, and the additional power dissipation is eventually compensated by the battery, leading to excess energy consumption. Hence, the system aims to find not only an optimal SOC trajectory but also an ideal warm-up profile of the transmission to minimize the energy consumption. In view of the model complexity, which is highly non-linear and non-convex, and has many constraints, the optimization problem is solved by using dynamic programming (DP). Although DP is computationally expensive, it is a widely used optimization algorithm to find global optimal solution. Furthermore, it provides insights into design of

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online controllers, e.g., by establishing relationships between DP, Pontryagin’s minimum principle (PMP) and equivalent consumption minimization strategy (ECMS). Given the driving cycle, DP, Bertsekas (2005); Sundstr¨om and Guzzella (2009), is applied to obtain an optimal control law represented by the variator ratio γvar to minimize the battery usage Pbatt , i.e.,  min : J (x(k), k) =

u(k)∈U

Pbatt (((ξ(k), θtr (k)), γvar (k)) | (vveh (k), aveh (k))) .

(36) where U represents the admissible controls and G(x(kn ), kn ) represents the terminal cost. The intermediate cost can be calculated by  J (x(k), k) = min

u(k)∈U

J (x(k + 1), k + 1)+

 (37)

Pbatt (((ξ(k), θtr (k)), γvar (k)) | (vveh (k), aveh (k))) .

In addition to the constraints described in Section 2, extra constraints on the system are (38) ξ(k) ∈ [ξ, ξ],

θtr (k) ∈ [θtr , θtr ]. (39) The optimal control problem given by (36) is solved for two simulation settings so as to achieve the goal of this research, which are described as follows.

S0 : The transmission is at its operating temperature at the outset, which indicates that there is no cold effect. The optimal controller tries to find an ideal SOC trajectory. This is an ideal scenario. S1 : A cold-start of the transmission is considered. It consists of two continuous dynamic states, ξ and θtr . The optimization strategy aims to generate an ideal SOC profile and a warm-up trajectory of the transmission simultaneously. This is common in reality. The energy-saving potential can be identified, by comparing the battery energy consumption (in kWh/100km) between S0 and S1 , which shows the upper limit of what can be expected in reality, i.e., ECS1 − ECS0 (40) ∆ES = ECS1 where ECS0 and ECS1 are the energy consumption of the corresponding simulation setting. 4. SIMULATION RESULTS Through post analysis, it is found that the difference in the SOC trajectory between the two settings is very small. It means that the cold impact on the integrated energy and thermal controller is not significant. It should be noted that the same goes to using the control from S0 to the augmented model including thermodynamics. In this case, the battery energy consumption cannot be produced because it is not integrated at vehicle level, which is not considered for comparison later on. The reason of the small difference is that, from optimization perspective, the 617

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Fig. 2. SOC profiles and driving modes of the electric vehicle for S1 on the NEDC (top) and WLTC (bottom). integrated energy and thermal management system tries to maximize the efficiency of the power source independent of simulation settings. Thus, only the SOC trace for S1 is depicted, as shown in Fig. 2. The considered EV has two driving modes, electric vehicle (EV) mode and brake energy recuperation (BER) mode. The general trend is as expected. As evident by Fig. 3, compared with NEDC, the transmission temperature in WLTC increases faster, which reduces the cold effect remarkably. The NEDC is best characterized by an urban part, [0, 780] s, which indicates low driving demand, leading to a slow rise of the transmission temperature, and a highway portion, [780, 1180] s, which represents high driving load, resulting in a rapid rise of the temperature. Two distinguishing slopes of the temperature profile are visible. Note that the slope less than zero is mainly due to convection to the ambient during standstill. The transmission temperature at the end of the NEDC is still far lower than the operating temperature. Since the efficiency of the power source is maximized as explained before, another factor that affects the temperature increase is the driving profile. Even for the more demanding WLTC, which has higher average speed, longer driving length and shorter stop duration, the operating temperature is reached at 1766 s, almost the end of the driving mission. Compared with the WLTC, the slower temperature increase in the NEDC leads to a slower decrease in the cold factor, resulting in a higher penalty on the energy consumption, as ultimately this extra power dissipation

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Fig. 3. Energy dynamics and thermodynamics of the EV with CVT for the NEDC and WLTC using two simulation settings. (Top to bottom) Vehicle velocity (vveh ), driving demand (Pdem ), transmission temperature (θtr ), transmission cold factor (ctr ), battery energy (Ebatt ). is compensated by the battery. As a result, cold-start conditions have an impact on the energy consumption, and the energy-saving potential is identified to be 2.9% on the NEDC and 1.7% on the WLTC. It should be noted that the 2.9% energy-saving potential is obtained assuming the initial transmission temperature is 30◦ C. In reality, depending on how long the car has been parked, the energy-saving potential may differ. Because of the cold effect, it is clear that the energy consumption decreases while increasing the initial transmission temperature. The energy-efficiency improvement rate can be defined as   EC  − ECθtr (k0 ) θtr (k0 )=30◦ C  . (41) ∆ESθtr (k0 ) =  EC  ◦ θtr (k0 )=30 C

618

where θtr (k0 ) ∈ [30◦ C, 80◦ C] represents the initial transmission temperature. The relationship between the energyefficiency improvement rate and the initial transmission temperature is shown in Fig. 4, which can be approximated by a quadratic fit as 2 (k0 ) + c1 · θtr (k0 ) + c0 . (42) ∆ESθtr (k0 ) = c2 · θtr

with c0 = −1.1929, c1 = 0.0361 and c2 = 1.7857e−4 . As expected, the energy efficiency increases while increasing the initial transmission temperature due to the cold effect. For a given transmission temperature, neglecting the term Ptr,amb , the demanded thermal budget that the system should allocate to bring the transmission to its desired thermal energy level is described by (43) Etr,th = ctr,h · ctr · mtr · (θtr − θtr (k0 )). where Etr,th is a constant value, independent of driving cycles. As long as the system can provide the heating

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Fig. 5. Energy balance of the electric vehicle on the NEDC.

Fig. 4. Influence of transmission temperature on the NEDC. power required to heat the transmission, the impact of cold-start conditions can be mitigated. Therefore, in order to bridge the gap between S0 and S1 , thus improving energy efficiency, it is imperative to come up with feasible solutions. As reported in, Jarrier et al. (2000), the average distance travelled in Europe is around 10 km, which is similar to the length of the NEDC. Hence, the NEDC is used for analysis. Observing the energy balance of the NEDC, energy losses of each component, as illustrated in Fig. 5, it can be seen that the waste heat from the PE and EM (PEEM) is significant, which seems to be the major heat source of the EV. More importantly, the amount of waste heat available in the PEEM is even higher than the thermal budget needed for the transmission heating. It can be envisioned that the cold effect can be reduced substantially by using the waste heat from the PEEM, which provides insights into design of the waste heat recovery technology. Furthermore, though the convection term Ptr,amb is widely ignored in literature, via post calculation, it is actually not negligible and accounts for a considerable part of the total power loss in the transmission. This suggests that a certain degree of transmission encapsulation can be considered, which increases the lifetime and performance of the transmission, and provides fast warm-up for the next cold-start, eventually improving energy efficiency. 5. CONCLUSION An integrated energy and transmission thermal management system is proposed to investigate the impact of a cold-start on the energy-saving potential of an EV and to derive design considerations of reducing this cold effect. Optimal control is applied to a detailed EV model including transmission thermodynamics, to maximize energy efficiency. It can be concluded that cold-start conditions affect the energy consumption, up to 2.9%, yet have a small influence on the optimal controller. Additionally, the transmission temperature dynamics during heating period and the energy losses of the EV are thoroughly analyzed. From design viewpoint, transmission encapsulation and utilizing waste heat from PEEM to heat transmission are 619

presented as viable means to reduce the cold effect, thus achieving better energy saving. A combined design and control approach to determine the ultimate energy saving is recommended for future work. REFERENCES Bertsekas, D. (2005). Dynamic Programming and Optimal Control. Athena Scientific, Belmont, MA, USA. De Cauwer, C., Van Mierlo, J., and Coosemans, T. (2015). Energy consumption prediction for electric vehicles based on real-world data. Energies, 8, 8573–8593. Dib, W., Chasse, A., Moulin, P., Sciarretta, A., and Corde, G. (2014). Optimal energy management for an electric vehicle in eco-driving applications. Control Engineering Practice, 29, 299–307. Hofman, T. and Dai, C. (2010). Energy efficiency analysis and comparison of transmission technologies for an electric vehicle. Proceedings of the 2010 IEEE Vehicle Power and Propulsion Conference, 1–6. Hofman, T. and Janssen, N. (2017). Integrated design optimization of the transmission system and vehicle control for electric vehicles. Proceedings of the 20th IFAC World Congress, 50, 10072–10077. Jarrier, L., Champoussin, J.C., Yu, R., and Gentile, D. (2000). Warm-up of a d.i. diesel engine: Experiment and modeling. Proceedings of the SAE 2000 World Congress. Laboe, K. and Canova, M. (2012). Powertrain waste heat recovery: A systems approach to maximize drivetrain efficiency. Proceedings of the ASME 2012 Internal Combustion Engine Division Spring Technical Conference, 985–992. Sundstr¨ om, O. and Guzzella, L. (2009). A generic dynamic programming matlab function. Proceedings of the 2009 IEEE Control Applications, (CCA) Intelligent Control, (ISIC), 1625–1630. van Berkel, K. (2013). Control of a mechanical hybrid powertrain. PhD thesis, Eindhoven University of Technology. Wu, G., Zhang, X., and Dong, Z. (2013). Impacts of two-speed gearbox on electric vehicle’s fuel economy and performance. Proceedings of the SAE 2013 World Congress and Exhibition.