Energy Consumption Model

Rating the efficiency of a vehicle can be a complex task. Usually, the type approval consumption is used as an indicator (Eskandarian,2012). The energy consumption of a vehicle is evaluated by the amount of energy per 100 km travelling distance. The energy consumption of an EV depends on a number of factors, such as energy consumption characteristics of the electrical motor, gear ratio, driven speed, vehicle resistance, road and traffic conditions. The motor power output is always equal to the resistance power plus the dynamic power for acceleration of the vehicle as follows (Ehsani et al., 2009):

Pmtr= v 1000(meq dv dt + 1 2ρaAfCDv 2_{+ m} eqgsin(θ) + µrrmeqgcos(θ)). (2.28)

After determination of the motor power by Equation (2.28), the total energy consump- tion (Ecns) within the total distance, s, at a constant cruising speed, v, is obtained

by Ecns = PmtrEG EMEE s v (2.29)

where EG is equivalent energy content per gallon of gasoline (kW h), EM is electrical

energy consumed per kilometre, and EE is electrical energy in kW h.

2.3.3.1 State of the art in Energy Consumption Models

The scientific methodology related to the energy consumption of passenger cars relies on simulation models validated by real-world tank-to-wheel emission and energy mea- surements performed in urban and motorway areas (Eskandarian, 2012). The term tank-to-wheel refers to the energy transfer chain from the on-board energy storage sys- tem, typically fuel tank, battery, or compressed hydrogen, to the wheels during vehicle operation (Eskandarian, 2012). A vehicle’s tank-to-wheel energy consumption is deter- mined by a defined driving cycle (e.g., New European Driving Cycle (NEDC)), which is carried out on a test bed at stringently monitored conditions (Eskandarian,2012). TheBEVis able to achieve an efficiency of about 70% in type approval scenarios, a much higher value compared to levels achievable by conventional vehicles in standard driving cycles (Eskandarian,2012). In the real-world scenario, the tank-to-wheel efficiency drops down to 35% in urban driving and to 60% at higher velocities (Eskandarian,2012). These values are strongly dependent on the efficiency of the electrical motor and the discharge efficiency of the battery. Additionally, the range of a BEV is very limited due to the battery capacity. In theNEDC, theBEVis able to achieve a range of more than 120 km. During real-world driving, the maximum range is reduced to 70 km (Eskandarian,2012). Few works of literature about full-range energy consumption models can be found for the EVs especially for the ADAS applications. The energy consumption model based on road topography information and traffic situation was considered by S. Yang et al. (2013), Jiquan Wang et al. (2015), and Graser et al. (2015). A quasi-static drivetrain energy consumption model for theSmart-EDwas introduced by Tim Schwickart, Voos, and Darouach (2014). A physical and statistical approach aiming to develop a systematic energy consumption estimation approach suitable for theEVwas introduced by R. Zhang et al. (2015). Power-based electric vehicle energy consumption model that computes the instantaneous energy consumption of an EV using second-by-second vehicle speed, acceleration and roadway grade data as input variables was introduced by Y. Li et al. (2015), Xinkai Wu et al. (2015), and Fiori et al. (2016).

2.3.3.2 Proposed Energy Consumption Model and Validation

The velocity and traction force have a significant influence on the energy consumption. The energy consumption during cruising at constant velocity is equitable to the resistive powers. This can be approximated through the curve-fit process with measurement data by a polynomial of velocity as:

fcruise(v) = b3v3+ b2v2+ b1v + b0 (2.30)

where b3 = 0, b2 = 0.02925, b1 = 0.257, and b0 = 1.821 for the Smart-ED. It is

noteworthy that the fcruise formulation is adapted from (M. A S Kamal et al., 2011).

The acceleration and deceleration of the Smart-ED considering only the regenerative energy zone in the hybrid brake system can be approximated by a similar curve-fit process with measurement data using a polynomial of the traction input as:

facl(u) = a2u2+ a1u + a0 (2.31)

where a2 = 0.01622, a1 = 0.244, and a0 = 1.129. Power-to-mass ratio is a performance

measurement index of a vehicle, with the power of powertrain output being divided by the mass of the vehicle which is independent of the vehicle’s size. Therefore, combining the fcruise(v) and the facl(u), can lead to a model of the power consumption Pmtr of

theSmart-ED. At any given velocity and control input, a linear relation of the traction power-to-mass ratio (ptrac/meq) of the vehicle can be expressed as:

˙

Ecns= Pmtr= facl(u)

ptrac

meq

+ fcruise(v). (2.32)

Figure 2.17 shows power consumption model of the Smart-EDbased on traction input and velocity. Each contour line represents the related power consumption (in kW ). At the higher traction input and velocity, the positive energy with the higher rate is consumed. In contrast, at regenerative braking zone at different velocity, a limited amount of energy can be recovered. This novel model is capable of representing the regenerative braking effect when u(t) < 0 for the full-range velocity and traction input. This way, the power consumption of the BEV can be estimated by modelling traction- velocity characteristics map of the electric machine. The proposed model for the energy consumption is approximated through the curve-fit process with 98.46% coefficient of determination (R-squared).

Velocity, v (m/s) 0 5 10 15 20 25 C o n tr o l In p u t, u (N / K g ) -5 -4 -3 -2 -1 0 1 2 3 -22.3346 -15.8252 -15.8252 -9.3157 -9.3157 -9.3157 -2.8062 -2.8062 _-2.8062 3.7032 3.7032 3.7032 10.2127 10.2127 10.2127 16.7222 16.7222 16.7222 23.2317 23.2317 29.7411 29.7411 36.2506 umax(v) = 1.523 − 1.491tanh(0.08751(v − 15.6)) umin(v) = −5

Figure 2.17: Power consumption of the Smart-ED