Essential Dynamics for Developing Models for Control of Connected and Automated Electried Vehicles: Part A - Powertrain

Connected and Automated Vehicles (CAV) technology presents signiﬁcant opportunities for energy saving in the transportation sector. CAV technology forecasts vehicle and powertrain power needs under various terrain, ambient, and trafﬁc conditions. Even though the CAV technology is applicable to both conventional and electriﬁed powertrains, the energy saving opportunities are more apparent when the CAVs are Hybrid Electric Vehicles (HEVs). This is because of the ﬂexibility in the vehicle powertrain and possibility of choosing optimum powertrain modes based on the predicted traction power needs. In this paper, the powertrain dynamics essential for developing powertrain controllers for a class of connected HEVs is presented. To this end, control-oriented powertrain dynamic models for a test vehicle consisting of full electric, hybrid, and conventional engine operating modes are developed. The resulting powertrain model can forecast vehicle traction torque and energy consumption for the speciﬁed prediction horizon of the test vehicle. The model considers different operating modes and associated energy penalty terms for mode switching. Thus, the vehicle controller can determine the optimum powertrain mode, torque, and speed for forecasted vehicle operation via utilizing connectivity data. The powertrain model is validated against the experimental data and shows prediction error of less than 5 % for predicting vehicle energy consumption.

complex system consisting of numerous sub-systems. To ensure good fuel economy and drivability, it is imperative to model and characterize the dynamic interactions among the components. To establish and understand these interactions, physical prototyping and testing prove to be too expensive [3], whereas modeling and simulation is considered cost-effective and time-saving for modeling and control of connected electrified powertrains [4]. Connectivity facilitates forecasting future tractive and thermal loads and power demands to the vehicle. This can be utilized for intelligent control and energy saving [1]. Even though CAV information is helpful for the energy-efficient operation of conventional vehicles, EVs, and HEVs, the energy saving opportunities are more apparent when the CAVs are HEV due to flexibility in selecting the vehicle powertrain operating modes. In this paper, the powertrain dynamics that should be modeled for developing powertrain controller for connected vehicles is presented, with emphasis on connected HEVs (CHEVs). The overview of the dynamics essential for energy-efficient CHEV controls is provided in Fig.1. These dynamics include powertrain dynamics, thermal dynamics, and vehicle dynamics. As shown in Fig.1, these three dynamics are not decoupled: each one has implications on the other two. For instance, the operation of engine during cold-start includes thermal dynamics and may also include inefficient powertrain operation due to incomplete engine combustion. Another example includes vehicle ve-locity profiling in CAVs' control that highly depends on powertrain capability and vehicle dynamics, but also affects cabin thermal management due to the effect of vehicle speed on convective heat transfer between ambient and the cabin [29]. The three areas in Fig.1 include a large number of important dynamics for CAV control. This paper (part A) focuses on powertrain dynamics, while our subsequent paper (part B) focuses on thermal dynamics and vehicle dynamics. In particular, part A is centered on the dynamics essential for developing control-oriented and computationally-efficient powertrain models, and covers mode switching dynamics (clutch and power split mechanisms), internal combustion engine (ICE) transient dynamics, and e-motor energy conversion efficiency.

Important Dynamics for Vehicle Controls to Enable Energy Saving in Hybrid Electric CAVs
Vehicle powertrain models can be classified as steady state, quasi-static, and dynamic. Steady state models (e.g., Autonomie [40] and ADVISOR [36]) and quasi-static models (e.g., powertrain system analysis toolkit (PSAT) [37]) typically use mapbased models of vehicle sub-systems. Their main advantage is quick computation time; however, since they do not consider system dynamics, they become inaccurate for transient operations.
Dynamic modeling approach typically uses dynamic physicsbased models for vehicle sub-components, to ensure better accuracy in transient conditions, compared to static/ quasi-static models. Vehicle models are further classified as forward-looking (driver driven) or backward-looking (vehicle driven) models, depending on the direction of power flow calculation [38]. The calculation proceeds in the forward direction of powertrain power flow using transmitted torque and reflected torque and driver needs for speed tracking. On the other hand, backward models initiates from the traction force request at the wheels to the primary energy sources and is generally made of quasi-static models. ADVISOR is one example of backward model [36].
A list of prior CAV studies, including powertrain models, is presented in Fig.2. Three classes of connected vehicles, grouped by powertrain type, can be seen in Fig. 2: i) Conventional engine-based connected vehicles (ECVs): In [10], the authors implemented Eco-Approach, Eco-Departure, and Eco-Cruise control algorithms on a 2018 Cadillac CT6 testbed, in a high-fidelity dynamic model, and reported that the scenario in which driver was informed of the preview data had an 11% fuel saving compared the baseline. In [11], the authors

Electric Vehicles
Hybrid Electric Vehicles FIGURE 2: Prior studies including modeling powertrain for control of CAVs [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. utilized a dynamic model and implemented bang-singular-bang optimal control to make decisions on the periods of maximal acceleration, maximal braking, coasting, and constant speed cruising for an engine-based connected vehicle, while provided with the CAV data. The authors reported up to 35% fuel energy saving using their proposed controller. In [12], the authors described a rule-based powertrain controller using CAV information for a conventional vehicle that resulted in 17% energy saving compared to the baseline non-CAV operation. In addition, for an ECV, the transmission gear position can be optimized to adapt to anticipated future vehicle speed and power demand. In [13], the authors proposed a control strategy to optimize vehicle speed and gear position simultaneously for an ECV, while considering both fuel efficiency and drivability. The results showed a 16% fuel benefits compared to a baseline. In [14], an optimal gearshifting strategy is presented to minimize fuel consumption and number of gear shifts in the new European driving cycle (NEDC).
The results show a 4% reduction in fuel consumption using the CAV information compared with the baseline. The authors only considered using a quasi-static brake-specific fuel consumption (BSFC) map-based engine model without engine dynamic transients. In [15], the authors proposed a computationally efficient model for evaluating the fuel consumption during the NEDC for gear selection and energy consumption. The optimization leads to a reduction of 7.5% in BSFC.
ii) Hybrid electric connected vehicles (CHEVs): When the vehicle platform is HEV, the vehicle controllers will be more complex, but the controllers have more opportunities to save energy by using the CAV information. In [22], the authors assess real-world fuel economy of CHEVs with advanced cylinder deactivation and 48V mild hybridization, in the presence of some variability induced by route characteristics, traffic condition, and driver behavior. For the evaluated route, the authors reported a 15% to 19% reduction in fuel consumption, compared to a baseline vehicle, without cylinder deactivation and CAV information. In [23], the powertrain dynamics is modeled using physics-based ODEs and used for the purpose of an integrated dynamic programming optimization of multiple CHEVs' oper-ation, to achieve group-level energy efficiency. In [24], the authors present a fuel efficient and hierarchical Model Predictive Control (MPC) strategy based on Equivalent Consumption Minimization strategy (ECMS) for a group of CHEVs in urban road conditions, and report an overall 12% energy consumption reduction compared with the baseline. In [26], the authors presented a two-level control architecture for a CHEV to optimize the vehicle speed profile and powertrain efficiency simultaneously. The powertrain is modeled in Vehicle-Engine SIMulation (VESIM) environment, whereas VISSIM is also used for traffic modeling.
Improvements of fuel efficiency compared with the baseline scenarios, under different traffic conditions, range from 7% to 40%.
In [27], the authors present an optimal map-based mode selection and powertrain control for a multi-mode CHEV. The best mode map and the best operation maps for powertrain components are generated using ECMS to minimize equivalent fuel cost at each operating point. In [28], the authors studied a drive mode optimization problem on a Chevrolet Volt to enable optimal drive modes for fuel minimization based on trip information, using a multidimensional correlation powertrain model.
iii) Fully-electric connected vehicles (CEVs): In [17], the authors developed a map-based EV powertrain model to explore the effects of different velocity profiling methods on energy efficiency of simulated CEVs in a single-lane traffic stream. In [11], the authors used a simplified EV model to explore the effect of different control strategies on the energy consumption. In [18], the authors simulate rear wheel CEVs driven by two permanent magnet synchronous in-wheel motors (PMSM), and reported energy savings up to 6% for Urban Dynamometer Driving Schedule (UDDS) obtained through proposed control algorithms. In [19], a look-ahead model predictive controller (LA-MPC) is designed that calculates the required motor torque demand to meet the dual objectives of increased traction, and anti-jerk control of a CEV. The authors developed a high-fidelity powertrain model in MapleSim software, and then reduced the order of the model for real-time control. In [20], the authors developed a nonlinear model predictive (NMPC) low-jerk cruise controller for an electric vehicle. A high-fidelity longitudinal dynamics model was developed for the test vehicle. The performance of the controller on the jerk index of the vehicle was assessed in a HIL simulation using the high-fidelity vehicle model while following a US06 driving cycle. In [21], the authors utilized a correlation-based powertrain model to perform a dynamic programming optimization for charging decisions of a CEV. This paper builds upon our extensive study for CHEV modeling and control as part of the U.S Department of Energy ARPA-e NEXTCAR program. The main new contributions of this work are: i) presenting the essential dynamics, including the engine transients and operating mode switching energy penalties, needed for computationally efficient and real-time control-oriented powertrain modeling of a CHEV, ii) systematic low-order modeling and experimental validation of powertrain dynamics suitable for fast execution with low computational cost, iii) vehicle experimentation and characterization at the component-level and system-level for charge-depleting and charge-sustaining operating modes, and iv) assessment of energy distribution of the test vehicle by sub-component in the chargedepleting operation mode for three U.S drive cycles. It is noteworthy that in none of the studies mentioned previously, the authors explicitly stated that they have used engine fuel penalty terms in powertrain modeling.
The structure of this paper is as follows: in Section 2, the vehicle setup, instrumented sensor suites, and the CAN-based data acquisition procedure is discussed. In Section 3, the powertrain dynamics and the experimental model validation of various powertrain sub-systems are discussed. After each sub-system model description, validation of that sub-system for the US06 drive cycle is followed. Included in this Section are engine transient dynamic model, engine fuel penalty terms, mode switching energy penalty terms, modeling of e-motor, drive unit, and Li-ion battery. Section 4 investigates: i) interdependence of the powertrain operating mode and the efficiency ii) energy distribution analysis of the test vehicle at the sub-component level, and iii) the effect of hysteresis on the powertrain dynamics and efficiency. Section 5 summarizes the findings from this paper.

Vehicle Test Setup
The test vehicle of this study is a Chevy Volt II generation, a light-duty plug-in HEV with two motor-generator units and an engine for propulsion. The test vehicle could be run in pure electric, hybrid electric, and conventional engine operations. This allows to determine vehicle powertrain dynamics for varying elec- nodes) could be stored for analysis. In addition to the signals available from the CAN bus, the test vehicle was instrumented with a suite of sensors including accelerometers, gyroscopes, an anemometer, GPS, radar, and Lidar, as shown in Fig. 4(a). The data logger setup utilized MicroAutoBox dSPACE ® embedded PC, placed at the trunk of the test vehicle, as shown in Fig. 4(b).

The vehicle was tested at Michigan Tech's Advanced Power
Systems Research Center (APSRC). In addition, extensive vehicle test data was provided by the Argonne National laboratory (ANL) through chassis dynamometer tests for different drive cycles.

Powertrain Dynamics and Modeling
In this Section, the major powertrain dynamics for control of a CHEV are presented and modeled for the test vehicle in this work. Fig. 3 shows the overall structure of the vehicle powertrain model and its dependencies on the vehicle dynamics, driver torque request, and HEV supervisory controller. A control-oriented model is developed for the vehicle powertrain to assist CHEV model-based real-time controllers. The model uses dynamic equations and experimental map data. In the following, modeling major powertrain dynamics is discussed.

Internal Combustion Engine Model
A dynamic model of a 1.5 liter 4-cylinder naturally aspirated DI SI engine is developed based on the principles outlined in [32][33][34] to predict the engine torque, speed, and instantaneous fuel consumption and fuel penalty terms for moving from one engine speed and torque condition to another operating point during transient engine operation. The model schematic is shown in Fig. 5  This air-EGR mixture enters the engine cylinder during the intake process and the amount of fuel injected is determined in the DI fuel injection sub-system. The ECU considers extra fuel (i.e., fuel penalty) based on engine coolant and three-way catalyst (TWC) temperatures. This is to ensure air-fuel mixture is combustible during cold start and also minimize TWC light-off time via catalyst heating to minimize vehicle tailpipe emissions.
Engine torque is determined as a function of spark timing, AFR, in-cylinder air mass flow rate, and engine speed. Finally, the engine speed is determined in the rotational dynamics sub-system. Engine speed and torque are the outputs of the engine model being fed to the drive unit/ transmission sub-system. From a control perspective, besides satisfying the drivetrain dynamics to control the longitudinal speed or acceleration of the vehicle, engine control system objectives of the ECU include: i) To maintain air-fuel ratio at a desired value, ii) To maintain engine-out emission below required threshold, and iii) To heat up TWC during cold start by adjusting spark timing, engine speed, AFR, and fuel injection amount and timing [33,34]. The governing equations to represent important engine dynamics are summarized as x 13 (t) = f 6 (x 6 , x 7 , u 1 , u 4 ) Where, T ind is the engine indicated torque, T load is the ex- L th is the stoichiometric air/fuel mass ratio for gasoline fuel and λ is the air/fuel equivalence ratio. The term T f represents the hydrodynamic and pumping friction losses represented in terms of a loss torque. Hydrodynamic or fluid-film friction is the principal component of mechanical friction losses in the engine [34]. a 0 , a 1 , a 2 , b 0 , and b 1 are parameters that are determined by experimental engine testing to calculate the friction torque. θ is the throttle angle, A(u 1 ) = A(θ )= A T is the throttle angledependent area,ṁ at is the throttle air flow rate,ṁ EGR is the EGR flow rate,ṁ ac is the in-cylinder air flow rate, V man is the intake manifold volume, T man is the manifold temperature, R u is the universal gas constant, η vol is the volumetric efficiency, ρ a,m is the air density, N is the engine speed, k 1 = C D .γ 0.5 √ R.T 0 , k 2 = 2×γ γ−1 , and K 3 , K 4 , K 5 , and K 6 are regression constants. C D is the discharge coefficient of valves, P 0 and T 0 are the ambient pressure and temperature values, respectively, ω eng is the angular speed of engine crankshaft in rad/sec, T br is the engine brake troque (N.m), p r is ratio of intake manifold pressure to ambient pressure, and γ is specific heat ratio. Volumetric efficiency (η vol ) depends on the manifold pressure and the engine speed, and is estimated using regression of experimental engine data.

Engine Startup Fuel Penalty Engine and
three-way catalyst (TWC) thermal conditions and temperatures play important roles in ECU strategies to adjust fuel injections.
These affect the engine fuel flow rate and should be considered in the engine dynamic modeling to improve vehicle fuel consumption prediction. Three categories of fuel penalty, depending on the engine startup status are considered in this work, shown in Fig. 6: i) Engine cold-start fuel penalty: Engine cold-start leads to increased fuel consumption because of the need to inject more fuel since low cylinder wall temperature and cold air result in poor combustibility of injected fuel [43]. In addition, high viscosity of the lubricant between piston and the liner interface results in increased friction losses [43], ii) TWC light-off fuel penalty: ECU commands to run the engine at high speed to quickly heat up TWC which leads to higher fuel consumption. For the TWC temperature below 300 • C, the TWC conversion efficiency is less than 50%, leading to high CO, HC, and NOx tailpipe emissions [33], and iii) Cranking fuel penalty: Cranking happens between the time of start of the engine crankshaft rotation from the rest position until the engine achieves stable idling speed (e.g., 600-700 RPM). During the cranking transient engine operation, ECU commands appropriate fuel injections to initiate first engine combustion cycles until the engine reaches sustainable combustion status.
These three fuel penalties were quantified by analysing the test vehicle data under cold and normal conditions. Finally, these three penalties were determined based on engine coolant temperature (e.g., T coolant < 0 • C) and TWC temperature (e.g., T TWC < 300 • C). The results, shown in Fig. 6-(a), indicate that the coolant light-off fuel penalty is very substantial; thus, CAV controller should minimize the need for TWC heating by monitoring the TWC temperature . The second significant fuel penalty is the engine col-start and finally, the cranking fuel penalty is the least significant. These penalty factors need to be taken into account in the CAV controller.

Model Validation
The engine model was implemented in MATLAB/ Simulink ® and was experimentally validated with extensive vehicle test data. Validation of engine torque, fuel flow, and air flow are shown in Fig. 7 for US06 drive cycle. The validation results show the developed dynamic engine model can predict engine torque and instantaneous fuel consumption with RMSE of 4.7 N.m and 0.7 g/sec, respectively, during the transient engine operation.

Fuel Penalty Mapping for Engine Transients
Depending on the HEV operating mode, the engine operation could involve substantial engine transients. Fig. 8 shows the engine operating points for three standard US drive cycles. These

Electric Motor-Generator Model
The test vehicle has two permanent magnet electric motorgenerators (MG) for propulsion and regeneration, denoted by are considered as states of the dynamics system. The methodology described in [8] was used for the mathematical modeling of x 2 (t) = g(u 1 , u 2 ) (23) x 4 (t) = u 1 K PM (25) x 5 (t) = K PM .u 2 (26)   [42] for voltage and current trace replication. In this method, the electrical dynamics of the battery pack is modeled by using two circuits, one modeling the long-term, and the other modeling the short-term dynamics of the battery pack. As shown in Fig.11, a separate thermal sub-model provides the electrical sub-model with the battery pack temperature information that highly affects the battery electrical dynamics.

Li-ion Battery Model
The battery electrical model developed in this work is summarized by following equations: y 3 (t) = y 1 .u 1 (38) where, R T S , C T S and V CT S represent the resistance, capacitance, and voltage drop in the shorter time constant RC circuit, respectively; R T L , C T L , and R CT L represent the resistance, capacitance, and voltage drop in the longer time constant RC circuit, respectively; R s is the series resistance, V OCV is the open circuit voltage (OCV), Q is the battery capacity, I batt is the battery current, and SOC i is the initial state of charge of the battery. All these parameters are dependent on the temperature and SOC.
The battery model was validated against vehicle experimental data. Validation of SOC for US06 drive cycle is shown in can estimate SOC with RMSE of less than 0.4 %.
Other methods of battery modeling such as online cell parameter estimation [45] or recursive neural networks [45] can be used to improve model accuracy and manage aging, however these methods need extensive sensor instrumentation inside the battery pack, or large operating data sets.

Drivetrain Model and Operating Modes
Chevy Volt Gen II has five operating modes, mechanized using two planetary gear sets and three clutches, depending on the vehicle speed and traction torque requirements. Fig. 13 shows these five modes including i) one motor EV (1EV), ii) two motor EV (2EV), iii) low extended-range (LER), iv) fixed gear (FG), and v) high extended-range (HER).

One Way
Where, I MGA is inertia of MGA. F 1 is internal force acting between the gears of planetary gear 1 (PG1) and, T MGA is torque generated by MGA. S 1 and R 1 are radii of sun and ring gear for planetary gear 1 (PG1).ω MGA is angular acceleration of MGA. In addition, P 1 = S 1 + R 1 and P 2 = S 2 + R 2 .

Mode-switching Energy Penalty
Vehicle components require extra energy to perform mode transition. If this energy penalty information is known, intelli-gent strategies can be incorporated in the supervisory controller to minimize those energy penalties and optimize energy consumption. There is an energy penalty associated with the mode switching in the test vehicle, depending which modes are involved. For instance, for switching from 2EV to LER mode requires the engine to start. As explained previously in Section 3.1, depending on the engine coolant temperature and TWC temperature, fuel penalties are induced and should be considered. Fig. 6-(a) shows the mode switching penalty as a result of engine startup.
The vehicle transmission unit includes a pump, an auxiliary pump, and a transmission. The pump pressurizes transmission oil when an engine is operating; however, when the engine is not operating, the auxiliary pump coupled to the pump in parallel pressurizes the transmission oil. During mode transitions, the test data of the test vehicle's auxiliary pump showed an instant increase (i.e., spike) in auxiliary pump power consumption for a few seconds. This spike in power should be considered as part of the mode switch penalty. A data-driven auxiliary pump model is developed and validated to estimate the energy consumption by the auxiliary pump. As shown in Fig. 6-(b), the energy penalties associated with mode switching in transmission unit auxiliary pump results in energy penalties over 1 kJ (for FG to HER mode switch). This is because of the higher vehicle speed and tractive effort in the HER mode, which tolls the transmission unit auxiliary pump.

Discussion
The developed powertrain model from Section 3 can be used for analysis, optimization, and design of control strategies for The powertrain operation and CHEV energy consumption highly depends on the vehicle mode of operation. Fig. 14   The developed model from Section 3 is used to analyze powertrain operation during the three drive cycles in Fig. 14 Vehicle operation in the charge depleting mode is analyzed using the developed powertrain model and part of the results is shown in Fig.17. The results indicate that: i) MGB consumes the majority of the energy in all three drive cycles. Since the UDDS cycle has frequent start-stop events and low driving speeds, MGA assists total requirements but its contribution is about 1% of the total. For the high speed drive cycles of HWFET and US06, MGA is used negligibly, too. ii) The auxiliary pump losses are much higher in the UDDS drive cycle at 8% of total   Fig. 18. The developed model from Section 3 is used to determine the minimum switching time to avoid hysteresis energy penalty for mode switching (Fig. 19). The results from Fig. 19 can be directly used in CHEV supervisory controller to minimize vehicle energy consumption. The developed dynamic powertrain model is embedded inside a model predictive control framework to select the optimum In another study [27], the authors used the powertrain model described in this paper to optimally select the vehicle operating mode in conjunction with a speed planning algorithm. The authors used an equivalent consumption minimization strategy (ECMS) to minimize the equivalent fuel cost at each operating point. The authors did not provide the energy saving percentage but in the reported optimal operation, the engine operation is constrained to the best BSFC region only. In [31], the authors utilized the powertrain model developed in this work as part of a combined motion planning and powertrain control algorithm to reduce vehicle energy consumption by avoiding wasteful driving maneuvers implemented by an automatic control and dynamic optimization (ACADO) toolkit for real-time execution. The reported energy savings range from 1.4% to 9.4% on a real-world driving cycle.

Summary and Conclusions
This paper presented the essential powertrain dynamics that are important to consider for modeling a CHEV, using the Chevy Volt gen II testbed. Dynamic powertrain models were developed and experimental validated for the powertrain sub-systems, including the engine, electric motor-generators, battery, and drivetrain. These include computationally efficient powertrain models for control of CHEVs. The developed dynamic powertrain model can predict the vehicle energy consumption with an overall prediction error of less than 5%.
For the engine, startup fuel penalty terms (i.e., cold-start, catalyst light-off, and cranking fuel penalties) were considered.
In addition, an engine speed-torque map was created to determine the fuel penalty for the engine transients. Furthermore, mode-switching energy penalty terms related to transmission unit auxiliary pump were quantified, helping the vehicle controller to make intelligent decisions to minimize energy penalty during mode switching. The vehicle operating modes for three U.S drive cycles were presented. The energy distribution analysis carried out in the discussion provided the share of each energy source/ sink for the three federal drive cycles which showed the MGB has a share above 80% for all three drive cycles.
The developed dynamic powertrain model can be utilized within a model-based CHEV controller to optimally select powertrain modes based on forecasted traction power needs. This paper presented the use of the developed powertrain model to avoid hysteresis during acceleration and deceleration scenarios. The results of using the developed powertrain model within CHEV controllers in our studies [25,27,[29][30][31] show the energy saving up to 9.4% oratory for providing Chevy Volt II chassis dynamometer test data.