Integrated Optimization of Power Split, Engine Thermal Management, and Cabin Heating for Hybrid Electric Vehicles

The 3rd IEEE Conference on Control T echnology and Applications (CCT A) August 19–21, 2019, Hong Kong, China Integrated Optimization of P ower Split, Engine Thermal Management, and Cabin Heating f or Hybrid Electric V ehicles Xun Gong 1 , Hao W ang 1 , Mohammad Reza Amini 1 , Ilya K olmanovsk y 2 , and Jing Sun 1 Abstract — Cabin heating demand and engine efficiency degra- dation in cold weather lead to considerable increase in fuel consumption of hybrid electric vehicles (HEVs), especially in congested traffic conditions. This paper presents an integrated power and thermal management (i-PTM) scheme for the optimization of power split, engine thermal management, and cabin heating of HEVs. A control-oriented model of a power split HEV , including power and thermal loops, is developed and experimentally validated against data collected fr om a 2017 T oyota Prius HEV . Based on this model, the dynamic programming (DP) technique is adopted to derive a bench-mark for minimal fuel consumption, using 2-dimensional (power split and engine thermal management) and 3-dimensional (power split, engine thermal management, and cabin heating) formu- lations. Simulation results for a real-w orld congested driving cycle show that the engine thermal effect and the cabin heating requir ement can significantly influence the optimal behavior for the power management, and substantial potential on fuel saving can be achieved by the i-PTM optimization as compared to con ventional power and thermal management strategies. I . I N T R O D U C T I O N Concerns of en vironmental impact and tightened fuel econ- omy regulations hav e motivated numerous technical inno- vations for vehicles efficienc y improvement, along with the increasing penetration of hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (PHEVs). The HEV po wer management has been studied extensi vely and sev eral tech- niques, from rule-based/heuristic approaches to optimization- based approaches, have been in vestigated [1]–[5]. The previous studies have proven that substantial fuel econ- omy gain can be achieved via advanced power split control methods with the assumption that the combustion engine is operating at its nominal/ideal thermal condition. Howe ver , in cold weather, when the vehicle stops or the vehicle operates in the electric driv e mode with engine off, the cabin heating requirements may cause fast engine cool-down, leading to the loss of energy efficienc y or frequent engine start-stop. Although the impacts of the thermal effects on the fuel economy ha ve been studied, the inte grated power and thermal management in cold weather conditions is still an open topic. In [6], an integrated powertrain control was proposed for an HEV equipped with a natural gas engine, in which the *This work is supported by the United States Department of Energy (DOE), ARP A-E NEXTCAR programm under award NO. DE-AR0000797 1 X. Gong, H. W ang, M.R. Amini and J. Sun are with Department of Nav al Architecture & Marine Engineering, University of Michigan, Ann Ar- bor , MI, 48109, USA. Emails: { gongxun, autowang, mamini, jingsun@umich.edu } 2 I. Kolmanovsk y is with the Department of Aerospace Engineer- ing, University of Michigan, Ann Arbor, MI, 48109, USA. Email: ilya@umich.edu optimization of catalyst light-of f time and fuel economy was considered. In [7], an off-line nonlinear constrained optimization was inv estigated for a specific series hybrid solar vehicle considering engine thermal ef fects. In [8]– [10], globally optimized energy management solutions were in vestigated for PHEVs equipped with electric heaters using multiple resources for meeting the heating requirement, and the energy saving potentials were illustrated by comparing with conv entional strategies. Due to the difference in config- urations between PHEVs and HEVs, the results may not be generalized to HEVs. In this paper , we propose an integrated power and thermal management (i-PTM) optimization framework for a power split HEV , accounting for cabin heating requirement. The engine is assumed to be the only resource to provide the heating power to the cabin. W e first dev elop and experimen- tally validate a control-oriented model, including both power and thermal loops. T o provide a bench-mark performance target, the DP is adopted to minimize the fuel consump- tion by controlling the engine operating mode, power split, and heating power supplied to the cabin, while enforcing the system constraints and managing thermal responses. T o demonstrate the thermal impact on behaviors of the po wer management and the corresponding fuel saving potential, a realistic winter congested dri ving scenario is considered in the simulation case study in which the proposed i-PTM with 2-dimensional and 3-dimensional DP formulations are compared with the baseline controllers. The rest of the paper is organized as follows. Section II introduces the model and Section III describes the problem formulations and optimization approach for i-PTM system. Section IV presents the simulation results and fuel saving potentials. Section V summaries the main findings. I I . C O N T R O L - O R I E N T E D I - P T M S Y S T E M M O D E L I N G In this section, a physics-based HEV model is described according to the power split configuration of T oyota Hybrid System (THS [11], [12]), including the power and thermal loops, and validated against the experimental data collected from our 2017 Prius test vehicle. The overall schematic of the power split HEV for heating scenario is shown in Fig. 1. In the power loop, the battery provides the electric power for vehicle traction ( P bat,mg ) and auxiliary de vices ( P bat,aux ). The total demanded traction po wer ( P trac ) is provided via a power split device (PSD) that blends the engine output power ( P e ) and electric motor traction power . In the thermal loop, considering the cabin heating requirement in winter, the 1 engine is assumed to be the only resource to provide heat power ( ˙ Q heat ) to the cabin through the heat core. Another circulation loop via front radiator/fan will be activ ated to remov e heat ( ˙ Q rad ) from the engine only when the coolant temperature ( T cl ) is higher than a specific threshold value. In cold weather conditions, the heat loss via air conv ection ( ˙ Q air ) is significant in engine thermal loop. Fig. 1: Schematic of a power split HEV thermal and power loops for heating scenario. A. Battery Model The governing equation of the battery state of charge (SOC) is given by ˙ S O C = − U oc − p U 2 oc − 4 R int P bat 2 R int C bat , (1) where P bat is the battery power , C bat is the battery capacity . The open-circuit voltage U oc and the internal resistance R int are functions of the battery SOC which are calibrated based on experimental data. The power provided by the battery is giv en by P bat = P bat,mg + P bat,aux , (2) where P bat,mg and P bat,aux are the electric po wer for traction auxiliary devices, respectiv ely . B. Engine Thermal T ransients Model In this work, the engine coolant temperature represents of the ov erall engine thermal state v ariable and its dynamics can be expressed by ˙ T cl = 1 M eng C eng ( ˙ Q f uel − P e − ˙ Q exh − ˙ Q air − ˙ Q rad − ˙ Q heat ) , (3) where M eng , C eng and T cl are the mass, the equiv alent spe- cific heat capacity , and the coolant temperature of the engine respectiv ely , ˙ Q f uel is the heat released in the combustion of the fuel, P e is the engine mechanical output power , ˙ Q exh , ˙ Q air and ˙ Q rad are the heat rejected by exhaust gas via the con vection from the engine to the air and via radiator/fan respectiv ely , ˙ Q heat is the heat power deliv ered to the cabin. The heat released in combustion is calculated by: ˙ Q f uel = LH V · W f ( ω e , τ e , T cl ) , (4) where LH V is the low heating value of the gasoline, W f is the fuel rate calculated by: W f = f f uel,map ( ω e , τ e ) · f cl,map ( T cl ) , (5) where f f uel,map denotes the nominal fuel consumption char- acterized by a map with engine speed ω e and torque τ e as the inputs, and f cl,map ( T cl ) is the correction factor reflecting the cold coolant temperature impact on the fuel consumption map. The look-up table adopted from Autonomie simulation software library and calibrated by Argonne National Labo- ratory [12] is shown in Fig. 2. Fig. 2: Correction factor on fuel consumption reflecting the coolant temperature sensitivity . The heat rejected by engine exhaust gas is defined as ˙ Q exh = γ exh ( ˙ Q f uel − P e ) , (6) where γ exh is the exhaust heat coefficient. The heat rejected by the air conv ection can be calculated by ˙ Q air = ( T cl − T com ) A eng α eng , (7) where T com is the temperature of the engine compartment, A eng is the equiv alent heat transfer area and α eng is the specific heat transfer coefficient. As a simplification, the engine compartment temperature is approximately expressed by a static equation associated with ambient temperature T amb and engine coolant temperature T cl . The heat removed by the radiator/fan is calculated by ˙ Q rad = f map,rad ( T cl ) , (8) where the f map,rad is a map calibrated based on the simu- lation and testing data. The heating po wer ˙ Q heat deliv ered to cabin is modeled based on the vehicle test data described by the following equation: ˙ Q heat = f ( T ain , T cab,sp , W bl ) , (9) where T ain is the vent air temperature, T cab,sp is the cabin temperature set-point and W bl is air flow through the cabin blower . The developed battery SOC and engine coolant models are validated against the experimental data collected by driving the HEV test vehicle over real-world city driving cycle in Ann Arbor , Michigan, in January as sho wn in Fig. 3. It can be seen that the model ((1) and (3)) captures the dynamics well. C. Cabin Thermal Model T o ev aluate the cabin temperature changes and driver com- fort, a cabin thermal model is needed. A simplified cabin av erage temperature model is considered as follo ws, ˙ T cab = 1 M cab C cab ( ˙ Q heat + ˙ Q load + ˙ Q sun ) , (10) where M cab and C cab represent the equiv alent air mass and heat capacity in the cabin respectiv ely , ˙ Q sun represents the radiation heat from the sun and ˙ Q load represents the heat load by heat transmission/con vection. All the parameters of the cabin temperature model are obtained from Autonomie software. Fig. 3: Model validation on battery SOC, engine coolant tempera- ture, and fuel flow rate (city dri ving cycle in Ann Arbor, MI). I I I . D Y N A M I C O P T I M I Z ATI O N F O R I - P T M The objectiv e of the i-PTM is to obtain the optimal fuel economy while taking the engine thermal condition and cabin heating requirements into account. The i-PTM problem is a multi-state nonlinear constrained optimization problem whose decision variables include integer for engine mode se- lection, as well as continuous v ariables. DP can be adopted to find the optimal solution, b ut it is computationally demanding and it depends on a giv en dri ving cycle. Ne vertheless, it provides a benchmark and useful insight to de velop online strategies. Thus, DP forms a good framework for solving the i-PTM problem at this stage. A. Pr oblem F ormulation In this paper , the fuel saving potential of i-PTM formulations in volving different thermal states are discussed. The dis- cretized HEV model described in Section II can be expressed in a general form as x k +1 = f ( x k , u k ) , (11) where u k ∈ R l denotes the vector of control variables and x k ∈ R n denotes the vector of state v ariables. 1) 1-dimensional baseline DP: In a con ventional power management problem, battery SOC is the only state while battery power P bat and engine operation mode e mode are selected as control variables [1]. This one-state DP addresses fuel economy optimization without explicit consideration of engine thermal condition and the coolant temperature sensitivity on the fuel consumption ( f cl,map ≡ 1 ). The 1-dimensional DP is considered as the “Baseline-DP” for comparison in the simulation study in Section IV. 2) 2-dimensional DP: For i-PTM problem incorporating the engine thermal condition, we select the battery SOC ( S O C k ) and engine coolant temperature ( T cl,k ) as the state variables and the engine operation mode ( e mode,k ), battery power ( P bat,k ) as control variables. W e refer to this two- state optimization problem as “Thermal-DP” for power split and engine thermal management. Assuming that the vehicle speed profile and heating po wer demand ( ˙ Q heat,k = ˙ Q heat,d ) are given as kno wn inputs, the optimization problem is to find the control input, u k = [ e mode,k , P bat,k ] , to minimize the o verall fuel consumption of the HEV , while enforcing the state constraints and vehicle operating constraints. Thus, with a given driving cycle being discretized by N sampling instants, the optimal energy efficient operation deri ved by “Thermal-DP” can be obtained by minimizing the following cost function: min : J ( x k , u k , N ) = N X k =0 W f ,k ( x k , u k ) + Φ( x N ) , (12) where Φ( x N ) is the terminal cost on the states x N = [ S O C N , T cl,N ] . The constraints on control v ariables and state variables are imposed by: S O C min ≤ S O C k ≤ S O C max , T cl,min ≤ T cl,k ≤ T cl,max , P bat,min ≤ P bat,k ≤ P bat,max . (13) Moreov er , the vehicle should satisfy the operation constraints according to dif ferent operation modes of the engine e mode ∈ { 1 , 2 , 3 } , i.e, (i) Engine off: e mode = 1 , P e,k = 0 , ω e,k = 0 , W f ,k = 0 ; (ii) Engine idling: e mode = 2 , P e,k = 0 , ω e 6 = 0 , W f ,k = W idle , where W idle is the fuel rate in idling mode; (iii) Engine on: e mode = 3 , P e,k > 0 , ω e,k 6 = 0 , W f ,k = f f uel,map ( ω e,k , T e,k ) · f cl,map ( T cl,k ) . It should be noted that when e mode = 3 , to reduce the computational load of DP , we assume that (I) the engine operates on the optimal operation line which has been extracted from the experimental data, and (II) the fuel consumption is corrected to reflect the effect of cold temperatures. 3) 3-dimensional DP: Next, we explore the fuel saving potential via cabin temperature management by coordinating the heating power supply to the cabin. In such a case, we assume that the given heating power demand can be relaxed as long as the cabin temperature is maintained within the desired range. The cost function (12) can be further extended with the state of the cabin temperature ( T cab,k ) and the additional control variable of heating power ( ˙ Q heat,k ). The control input ˙ Q heat,k can be conv erted to physical control variables based on model (9). W e refer to this three-state optimization problem as “Thermal-Cabin-DP” for power split, engine thermal management, as well as cabin heating. The corresponding cost function is as follows: min : J ( x cab k , u cab k , N ) = N X k =0 W f ,k ( x cab k , u cab k ) + Φ( x cab N ) , (14) where x cab k = [ S O C k , T cl,k , T cab,k ] is the expanded state vector and u cab k = [ e mode,k , P bat,k , ˙ Q heat,k ] is the expanded control vector . Additional constraints on cabin temperature and heating power are also considered: T LB cab ≤ T cab,k ≤ T U B cab , ˙ Q heat,min ≤ ˙ Q heat,k ≤ ˙ Q heat,max , (15) where T LB cab and T U B cab denote the predefined lower and upper boundary of the cabin temperature. The different DP formulations mentioned above, in terms of state and control v ariables, are summarized in T able I. The corresponding simulation comparison results and the fuel saving potentials will be discussed in Section IV. T ABLE I: DP Formulations for i-PTM Controller State Control input Baseline-DP S O C e mode , P bat Thermal-DP S O C, T cl e mode , P bat Thermal-Cabin-DP S O C, T cl , T cab e mode , P bat , ˙ Q heat B. Quantization Effects DP problems of Section III-A are solved numerically using quantization and interpolation with the sampling time for model (11) chosen as T s = 1 sec . Considering the “curse of dimensionality” associated with DP , the grid size should be selected carefully . Since the 3-dimensional “Thermal-Cabin- DP” becomes intractable with small grids, we limit the grid size to a certain level as shown in T able II to balance the computational load and numerical accuracy . T ABLE II: Quantization of state and control variables V ariables Grids S O C S O C min : 0 . 01 : S O C max T cl T cl,min : 1 C o : T cl,max T cab T LB cab : 1 C o : T U B cab P bat P bat,min : 0 . 5 kW : P bat,max e mode 1 : 1 : 3 ˙ Q heat ˙ Q heat,min : 0 . 05 kW : ˙ Q heat,max I V . D P S I M U L A T I O N R E S U L T S A N D D I S C U S S I O N A. Real-W orld Congested Driving Cycle The simulation is conducted in MA TLAB/Simulink environ- ment with the model as described in Section II. In this work, we focus on the congested city dri ving cycle. T o construct the realistic congested driving profile, a representati ve real-world congested driving cycle (16 mins) is recorded and extracted in Ann Arbor, Michigan. V ehicle speed and demanded trac- tion power are shown in Fig. 4. The ambient temperature of T amb = − 10 C o is assumed, which is common during the winter days in Ann Arbor . Fig. 4: The profile of the real-world congested city driving cycle: (a) vehicle speed, (b) driving power demand. B. DP Optimization Results 1) Thermal DP v .s Rule-based Contr oller: W e first compare the proposed “Thermal-DP” with a rule-based controller that is based on a load lev eling logic with well tuned parameters, see [13]. In this case, we assume the heating power is giv en as a constant ˙ Q heat = 1500 W . T o prev ent the engine tem- perature from dropping too lo w , the rule-based controller will start the engine with idling status e ven there is no traction power requirement when T cl < 40 C o [14]. Compared with rule-based controller, “Thermal DP” uses the engine more often b ut in a relatively lower load lev el as sho wn in Fig. 5 (c) and Fig. 6 (a) which leads to higher coolant temperature and SOC. As the coolant temperature drops do wn, the rule-based controller turns on the engine with idle mode to enforce thermal constraint, while the “Thermal-DP” suggests to start the engine in charging mode at vehicle stops (820 s - 900 s) to keep the coolant temperature warm while charging the battery . The fuel saving by DP is nearly 6%. 2) Baseline DP v .s Thermal DP: In order to further illustrate the impact of engine thermal ef fect on the optimized power management of the HEV , the results of “Thermal DP” are compared against the “Baseline DP” which does not consider the engine coolant temperature as a state and its effect on fuel consumption in optimization. The comparison results Fig. 5: Comparison results of Rule-based controller v .s Thermal- DP: (a) battery SOC, (b) engine coolant temperature, (c) engine power (d) battery traction power . ˙ Q heat = 1500 W . Fig. 6: Comparison results of Rule-based controller v .s Thermal- DP: (a) engine mode of rule-based controller, (b) engine mode of thermal-DP , (c) fuel consumption. ˙ Q heat = 1500 W . are sho wn in Fig. 7. Compared with the “Baseline DP”, the “Thermal DP” makes the engine work harder at the beginning of the trip when the engine coolant temperature is relativ ely high. By doing this, more electric energy is stored into the battery (Fig. 7 (a)) and thermal energy is stored in coolant as reflected by the higher coolant temperature (Fig. 7 (b)). In contrast, towards the end of the trip, the “Thermal DP” releases the stored electric energy into traction po wer which av oids much engine operation at high load when the coolant temperature is low . From Fig. 8 (a), it can be seen that the engine start-stop timing is almost the same, howe ver , the po wer split ratio is totally different. The “electric and thermal storage concept” leads to 2 . 7% fuel saving potential. 3) Thermal-Cabin-DP: The results of i-PTM optimization which applies the “Thermal-Cabin-DP” are presented in Fig. 9. In this case, the heating power ˙ Q heat is allowed to Fig. 7: Comparison results of Baseline DP v .s Thermal-DP: (a) battery SOC, (b) engine coolant temperature, (c) engine power (d) battery traction po wer . ˙ Q heat = 1500 W . Fig. 8: Comparison results of Baseline DP v .s Thermal-DP: (a) engine mode, (b) fuel consumption. ˙ Q heat = 1500 W . vary in the range of 1200 W − 1800 W . T o manage the cabin the temperature, the terminal value of the cabin temperature T cab,N is set as the same as the case of ˙ Q heat = 1500 W and the lower bound of the cabin temperature T LB cab is pre- defined. As shown in Fig. 9 (a) and (b), to minimize the fuel consumption, DP suggests the driv er to compromise the cabin thermal comfort by manipulating the heating power and make the cabin temperature to follo w the predefined lower bound trajectory for further fuel savings. Note that the power split strategy of “Thermal-Cabin-DP” is almost the same with “Thermal-DP”, ho wever , by slowing down the warm-up period and slightly reducing the steady-state temperature, the average cabin temperature is reduced by 0 . 5 C o while nearly 1% fuel can be sav ed. Fig. 10 summaries the overall fuel consumptions of the HEV with different strategies. Up to 6 . 85% fuel saving can be achiev ed compared with the rule-based controller . Note that the computation time of the “Thermal-DP” and “Thermal- Cabin-DP” are approximate 1 hour and 40 hours respectively on a computer with Intel Core i7 @ 2.6GHz CPU. Fig. 9: Results of Thermal-Cabin-DP: (a) cabin temperature, (b) heating power . Fig. 10: Results of fuel saving applying different strategies. V . C O N C L U S I O N S This paper presents the integrated po wer and thermal man- agement for a power split HEV during cold winter days in congested city driving scenario. The objecti ve is to optimize the fuel efficiency while accounting for the engine thermal condition and cabin heating requirements. The dynamic pro- gramming technique is adopted to find the optimal solution based on an experimentally validated model of the po wer- split HEV that includes power and thermal loops. The simulation results of a real-world congested driving cycle show that the optimal power management, as well as the fuel consumption, change significantly when the engine thermal condition is incorporated. Up to 6.85% fuel saving potential is demonstrated by integrated power and thermal optimiza- tion compared with a well-calibrated rule-based controller . R E F E R E N C E S [1] A. Sciarretta and L. Guzzella, “Control of hybrid electric vehicles, ” IEEE Contr ol Systems , vol. 27, no. 2, pp. 60–70, 2007. [2] E. Silvas, T . Hofman, N. Murgovski, L. F . P . Etman, and M. Steinbuch, “Revie w of Optimization Strategies for System-Level Design in Hy- brid Electric V ehicles, ” IEEE T ransactions on V ehicular T echnology , vol. 66, no. 1, pp. 57–70, 2017. [3] C. Sun, S. J. Moura, X. Hu, J. K. Hedrick, and F . Sun, “Dynamic T raffic Feedback Data Enabled Energy Management in Plug-in Hybrid Electric V ehicles, ” IEEE T ransactions on Control Systems T echnology , vol. 23, no. 3, pp. 1075–1086, 2015. [4] C. Marina Martinez, X. Hu, D. Cao, E. V elenis, B. Gao, and M. W ellers, “Energy Management in Plug-in Hybrid Electric V ehi- cles: Recent Progress and a Connected V ehicles Perspective, ” IEEE T ransactions on V ehicular T echnology , vol. 66, no. 6, pp. 4534–4549, 2016. [5] H. W ang, I. Kolmano vsky , M. R. Amini, and J. Sun, “Model Predicti ve Climate Control of Connected and Automated V ehicles for Improved Energy Ef ficiency, ” Pr oceedings of American Control Confer ence , pp. 828–833, 2018. [6] J. Kessel, D. Foster , and W . Bleuanus, “T owards integrated powertrain control: thermal management of NG heated catalyst system, ” in Pr oc of the International Confer ence on Advances in Hybrid P owertrains , pp. 1–6, 2008. [7] I. Arsie, G. Rizzo, and M. Sorrentino, “Effects of engine thermal transients on the energy management of series hybrid solar vehicles, ” Contr ol Engineering Practice , vol. 18, no. 11, pp. 1231–1238, 2010. [8] J. Gissing, P . Themann, S. Baltzer , T . Lichius, and L. Eckstein, “Op- timal Control of Series Plug-In Hybrid Electric V ehicles Considering the Cabin Heat Demand, ” IEEE T ransactions on Contr ol Systems T echnology , vol. 24, no. 3, pp. 1126–1133, 2016. [9] M. Shams-Zahraei, A. Z. K ouzani, S. Kutter , and B. B ¨ aker , “Integrated thermal and energy management of plug-in hybrid electric vehicles, ” Journal of P ower Sources , vol. 216, pp. 237–248, 2012. [10] L. Engbroks, D. Gorke, S. Schmiedler, J. Strenkert, and B. Geringer, “ Applying forward dynamic programming to combined energy and thermal management optimization of hybrid electric vehicles, ” 5th IF AC Confer ence on Engine and P owertrain Control Simulation and Modeling , pp. 416–422, 2018. [11] J. Liu and H. Peng, “Modeling and Control of a Power-Split Hybrid V ehicle, ” IEEE T ransactions on Control Systems T echnology , vol. 16, no. 6, pp. 1242–1251, 2008. [12] N. Kim, A. Rousseau, D. Lee, and H. Lohse-busch, “Thermal model dev elopment and validation for 2010 T oyota Prius, ” SAE T echnical P aper , no. 2014-01-1784, pp. 1–10, 2014. [13] J. Liu, H. Peng, and Z. Filipi, “Modeling and Analysis of the T oyota Hybrid System, ” Pr oceedings of the American Contr ol Confer ence , pp. 24–28, 2005. [14] T . T ashiro, “Power Management of a Hybrid Electric V ehicle During W arm-up Period Considering Ener gy Consumption of Cabin Heat Components, ” 8th IF AC Symposium on Advances in Automotive Con- tr ol , vol. 49, no. 11, pp. 393–398, 2016.