## 2 Materials and Methods
### Powertrain Model  
The work presented in this paper is motivated by the EcoCAR Mobility Challenge (MC) competition objectives and is designed to serve as the primary energy management  
Figure 1: Proposed EMS structure. system for the OSU competition vehicle. EcoCAR MC is a 4-year competition which challenges university students to apply advanced propulsion systems, electrification, SAE Level 2 automation, and vehicle connectivity to improve the energy efficiency, safety and consumer appeal of the competition-provided vehicle [19]. The vehicle in consideration is a 2019 Chevrolet Blazer with a through-the-road parallel hybrid architecture consisting of a General Motors (GM) 2.0 L turbocharged gasoline engine coupled with a DENSO 32 kW belted alternator-starter (BAS) for front powertrain propulsion and a 90 kW Parker Hannifin GVM210-100 electric machine mated to a BorgWarner eGearDrive rear-axle single speed gearbox to power the rear axle. A custom 3.5 kW-h Li-ion battery pack provided by Hybrid Design Services (HDS) serves as the electrical energy storage system (ESS). The vehicle powertrain architecture is highlighted in Figure 2.  
In this paper we assume SI units for all model parameters. For powertrain energy analysis, it is sufficient to model the vehicle as a point mass and express longitudinal dynamics as the equilibrium of forces acting on the vehicle. The equation of motion for a point mass can be derived from the equilibrium of forces acting on a vehicle:  
\[M_{veh}\frac{dv_{veh}}{dt}=\frac{T_{puct}-T_{brake}}{R_{wh}}-c_{roll}M_{veh}g \cos\delta-\frac{1}{2}\rho_{air}A_{f}C_{d}v_{veh}^{2}-M_{veh}g\sin\delta \tag{1}\]  
where \(M_{veh}\) is the effective vehicle mass, \(v_{veh}\) is the longitudinal vehicle velocity, \(\rho_{air}\) is the air density, \(A_{f}\) is the vehicle frontal area, \(C_{d}\) is the aerodynamic coefficient, \(g\) is the gravity acceleration, \(\delta\) is the road slope angle, \(c_{roll}\) is the rolling resistance coefficient, \(T_{puct}\) is the torque generated at the wheel shaft by the powertrain, \(T_{brake}\) is the braking torque, and \(R_{wh}\) is the wheel radius. Wheel speed is calculated using:  
\[\omega_{wh}=\frac{v_{veh}}{R_{wh}}. \tag{2}\]  
A simple transmission model is used which assumes a constant efficiency term:  
\[\omega_{t}=gt_{t}\omega_{wh} \tag{3}\]  
\[T_{t}= \begin{cases}\frac{\eta_{t}}{S_{t}}T_{wh}&\text{if }P_{wh}=T_{wh}\cdot \omega_{wh}\geq 0,\\ \frac{1}{\eta_{t}S_{t}}T_{wh}&\text{if }P_{wh}=T_{wh}\cdot\omega_{wh}<0\end{cases}  \tag{4}\]  
where \(\omega_{t}\) is the transmission speed, \(g_{t}\) is the transmission gear ratio, \(T_{t}\) is the transmission torque, \(\eta_{t}\) is the transmission efficiency, and \(T_{wh}\) is the wheel torque, which is equal to the force at the wheels multiplied by the wheel radius. A simple torque converter model is based on lookup tables created with experimental data for the pump and turbine torque ratio, capacity factor (\(K_{tc}\)), and speed ratio. The internal combustion engine model uses a static map-based approach which assumes that  
Figure 2: Vehicle architecture. the engine is a perfect actuator with no response delays. Fuel consumption is calculated using an engine fuel map which is a function of engine speed and torque:  
\[\dot{m_{f}}=f_{FE}(\omega_{ice},T_{ice}) \tag{5}\]  
where \(\dot{m_{f}}\) is the fuel flow rate, \(\omega_{ice}\) is the engine speed, and \(T_{ice}\) is the engine torque. The rear electric motor (REM) uses a static map model based on torque and efficiency maps. The REM is treated as a perfect actuator where transient effects are assumed to be captured by the map. The governing equations, in terms of power, for the REM model are as follows:  
\[P_{elec}= \begin{cases}\frac{1}{\eta_{rem}(\omega_{rem},P_{elec})}\omega_{rem} T_{rem}&\text{if $P_{elec}\geq 0$ (motoring mode)},\\ \eta_{rem}(\omega_{rem},P_{elec})\cdot\omega_{rem}T_{rem}&\text{if $P_{elec}<0$ ( generating mode)}\end{cases}