Rapid adoption of battery electric vehicles means improving energy consumption is a top priority. Regenerative braking converts kinetic energy to electrical energy stored in the battery pack while the vehicle is decelerating. Coasting is an alternative strategy that minimizes energy consumption by decelerating the vehicle using only road load. This work refines a battery electric vehicle model to assess regen, coasting, and other deceleration strategies. A road load model based on public test data calculates tractive effort based on speed and acceleration. Bidirectional Willans lines are the basis of the powertrain model simulating battery energy consumption. Regen braking tractive and powertrain power are modeled backward from prescribed linear velocity curves, and the coasting trajectory is forward modeled given zero tractive power. Decel modes based on zero battery and motor power are also forward modeled. Multi-Mode decel (using a low power mode with regen) is presented as an intermediate strategy. An example vehicle is modeled in fixed-route simulations using these strategies and is scored based on travel time, energy consumption, and bias towards minimizing one of those metrics. Regen braking has the lowest travel time, and coasting the lowest energy consumption, but such bias increases overall cost. Multi-mode strategies lower overall cost by balancing reductions in travel time and energy consumption. The model is sensitive to grade and accessory load fluctuation, making this work adaptable to different vehicles and environments. This work demonstrates the utility of regen braking alternatives that could enhance connected and automated vehicle systems in battery electric vehicles. / Master of Science / As battery electric vehicle adoption accelerates, reducing energy consumption remains a priority. While regenerative braking saves energy by recharging the battery pack using kinetic energy, coasting (deceleration caused only by road load) has potential as well. This work focuses on refining a battery electric vehicle model and assessing various deceleration strategies. A road load model calculates wheel tractive effort, and Willans lines are used to model powertrain energy consumption. Coasting and other deceleration modes based on zero system power are modeled to produce speed trajectories, and regenerative braking power is modeled using prescribed linear velocity curves. Strategies that use multiple decel modes are also considered. An example battery electric vehicle is assessed using these strategies in fixed-route simulations. Vehicle performance is scored based on battery energy consumption and travel time. Regenerative braking has the lowest travel time, and coasting the lowest energy consumption, but those strategies also have the highest overall cost. Multi-mode strategies lower cost by balancing energy consumption and travel time. The strategies are sensitive to changes in road grade and accessory power, meaning the model can be used with different vehicles and environments. This work demonstrates the utility of alternatives to regenerative braking and how such strategies could enhance battery electric vehicles with autonomous capabilities.

Energy management strategies for charge sustaining hybrid electric vehicles reduce fuel power consumption from the engine and electric power consumption from the motor while meeting output power demand. The equivalent consumption minimization strategy is a real time control strategy which uses backward facing models and an equivalence ratio to calculate the lowest total fuel power consumption. The equivalence ratio quantifies the fuel power to battery power conversion process of the hybrid electric vehicle components and therefore quantifies electric power consumption in terms of fuel power consumption. The magnitude of the equivalence ratio determines when the hybrid electric vehicle commands a conventional, electric, or hybrid mode of operation. The equivalence ratio therefore influences the capability of the control strategy to meet charge sustaining performance. Willans line models quantify the input power to output power relationship for powertrain and drivetrain components with a linear relationship and a constant offset. The hybrid electric vehicle model performance is characterized using three Willans line models in the equivalent consumption minimization strategy. The slope of the Willans line models, or marginal efficiency, is used to generate a single equivalence ratio which quantifies the fuel to battery energy conversion process for the hybrid electric vehicle. The implementation of a Willans line based equivalent consumption minimization strategy reduces total fuel power consumption while achieving charge sustaining performance over mild and aggressive drive cycles. / Master of Science / The charge sustaining hybrid electric vehicle in this paper generates output power with an internal combustion engine powered by a fuel tank and an electric traction motor powered by a battery pack. Hybrid electric vehicle energy management strategies generate torque commands to meet output power demand based on the minimum total input power from both the fuel tank and battery pack. Willans line models simplify the energy management strategy by quantifying the output power to input power relationship, or efficiency, of each component with a linear slope and constant offset. The use of Willans line models quantifies the efficiency of the hybrid electric vehicle with three linear relationships. Energy management strategies also ensure the battery pack starts and ends at the same operating condition to maintain charge sustaining performance. Charge sustaining hybrid electric vehicles therefore use the battery pack as an energy buffer and do not need to be charged by an external power supply since all energy comes from fuel. The output to input power relationship of Willans line models quantifies the power conversion of the hybrid electric vehicle and coupled to a term which accounts for changes in the battery pack. The use of Willans line models in hybrid electric vehicles effectively generates torque commands to the engine and motor while improving fuel economy and maintaining charge sustaining performance.

Due to increased urgency regarding environmental concerns within the transportation industry, sustainable solutions for combating climate change are in high demand. One solution is a widespread transition from internal combustion engine vehicles (ICEVs) to battery electric vehicles (BEVs). To facilitate this transition, reliable energy consumption modeling is desired for providing quick, high-level estimations for a BEV without requiring extensive vehicle and computational resources. Therefore, the goal of this paper is to create a simple, yet reliable vehicle model, that can estimate the energy consumption of most, if not all, electric vehicles on the market by using parameter normalization techniques. These vehicle parameters include the vehicle test weight and performance to obtain a unified net Willans line to describe the input/output power through a linear relationship. A base model and three normalized models are developed by fitting the UDDS and HWFET energy consumption test data published by the EPA for all BEVs in the U.S. market. Out of the models analyzed, the normalization with weight performs best with the lowest RMSE values at 0.384 kW, 0.747 kW, and 0.988 kW for predicting the UDDS, HWY, and US06 data points, respectively, and 0.653 kW for all three data sets combined. Consideration of accessory loads at 0.5 kW improves the model normalized by weight and performance by a reduction of over 20% in RMSE for predictions with all data sets combined. Removing outliers in addition to consideration of accessory loads improves the model normalized by weight and performance by a reduction of over 36% in RMSE for predictions with all data sets combined. Overall, results suggest that a unified net Willans line is largely achievable with accessible energy consumption data on U.S. regulatory cycles. / Master of Science / Due to increased urgency regarding environmental concerns within the transportation industry, sustainable solutions for combating climate change are in high demand. One solution is a widespread transition from conventional internal combustion engine vehicles (ICEVs) to battery electric vehicles (BEVs). To facilitate this transition, reliable energy consumption modeling is desired to support quick, high-level analyses for BEVs without requiring expensive resources. Therefore, the goal of this paper is to create a simple vehicle model that can estimate the energy consumption of most, if not all, electric vehicles by scaling the data using vehicle parameters. These parameters include the vehicle test weight and performance to obtain a unified net Willans line model describing the input/output power through a linear relationship. The UDDS (city) and HWFET (highway) energy consumption data points used to develop the model are easily accessible from published EPA data. Out of the models analyzed, the normalization with test weight performs best with the lowest error values at 0.384 kW, 0.747 kW, and 0.988 kW for predicting the UDDS, HWFET, and US06 (aggressive city/highway cycle) data points, respectively, and 0.653 kW for all three data sets combined. Consideration of accessory loads at 0.5 kW improves the model normalized by weight and performance by a reduction of over 20% in error for predictions with all data sets combined. Removing outliers in addition to consideration of accessory loads improves the model normalized by weight and performance by a reduction of over 36% in error for predictions with all data sets combined. Overall, results suggest that a unified net Willans line is largely achievable with accessible energy consumption data on U.S. regulatory cycles.

With electric vehicles becoming increasingly prevalent in the automotive market consumers are becoming more conscientious of total driving range. In light of this trend, reliable and accurate modeling methods are necessary to aid the development of more energy efficient vehicles with greater drivable range. Many methods exist for evaluating energy consumption of current and future vehicle designs over the US certification drive cycles. This work focuses on utilizing the well-established Willans line approximation and proposes a simplified modeling method to determine electric vehicle energy consumption and powertrain efficiency. First, a backwards physics-based model is applied to determine tractive effort at the wheel to meet US certification drive cycle demand. Second, the Willans line approximation then augments the tractive effort model and parameterizes the vehicle powertrain to establish a bi-directional power flow method. This bi-directional approach separates propel and brake phases of the vehicle over the certification City and Highway drive cycles to successfully isolate the vehicle powertrain from non-intrinsic losses, such as parasitic accessory loads. The proposed method of bi-directional modeling and parameter tuning provides significant insight to the efficiency, losses, and energy consumption of a modeled electric vehicle strictly using publicly available test data. Results are presented for eight electric vehicles with production years varying from 2016 to 2021. These electric vehicles are chosen to encapsulate the electric vehicle market as performance electric vehicles to smaller commuter electric vehicles are selected. All vehicles are modeled with an accessory load constrained between 300 and 850 W and a regenerative braking ("regen") low-speed cutoff of 5 mph with six of the eight vehicles modeled with a regenerative braking fraction of 94%. The bi-directional Willans line is then tuned to reach agreement with the net EPA energy consumption test data for each vehicle with the results presented as representative of the chosen vehicle. Lastly, a transfer function relating major model inputs to the output is derived and lends considerable insight for the sensitivity of the modeling method. Sensitivity of the proposed modeling method is conducted for a 2017 BMW i3 with the model deemed reasonably resilient to changes in input parameters. The model is most sensitive to changes in powertrain marginal efficiency with a 6% decrease of marginal efficiency leading to a 0.404 kW and 0.793 kW cycle average net battery power increase for the City and Highway drive cycles respectively. Additionally, the model is also sensitive to changes in vehicle accessory load with a direct relationship between increases of vehicle accessory load to increases of cycle average net battery power for the City and Highway cycles. The sensitivity results justify the use of the proposed model as a method for evaluating vehicle energy consumption and powertrain efficiency solely using publicly available test data. / Master of Science / Developing robust and accurate methods for analyzing electric vehicle energy consumption and powertrain efficiency is of great interest. For the purposes of this paper, powertrain refers to a motor / inverter pair which is coupled to a simple gear reduction for torque multiplication. Many vehicles are designed with motors of varying power and torque capabilities which can present challenges when attempting to effectively compare electric vehicles from different manufacturers. The proposed modeling method presented in this work utilizes public test data to derive detailed vehicle and powertrain information. Vehicle energy consumption is also modeled and compared to net EPA test data. Eight electric vehicles are modeled with each vehicle representing a specific segment of the current electric vehicle market. A bi-directional Willans line is applied to model the propel and brake phases of each electric vehicle over the US certification drive cycles. The bi-directional approach effectively isolates the vehicle powertrain from non-intrinsic losses. From the derived powertrain parameters and modeled energy consumption, the proposed method is deemed accurate and highly useful for translating public test data to detailed vehicle information. Lastly, a sensitivity analysis is presented with the proposed method deemed reasonably resilient to changes in input parameters. The modeling method is most sensitive to changes of powertrain marginal efficiency and vehicle accessory load but constraining these inputs to reasonable ranges for electric vehicles proves sufficient.