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Energy Balances for the Electric Vehicle
Figure 3–11 Change in resistance with discharge.
Change in Resistance (milliohms)
16 14
12
10 8
6
4
2
0
4 10 20 30 40 50 60 70 80 90 98 % DOD
0-10 W/kg 10-79 W/kg 79-50 W/kg 50-20 W/kg
Identical to the VRLA battery, a 90-Ahr NiMH battery undergoes a similar change in the battery resistance. The discharge variation is the worst-case resistance calculated for the performance of the battery pack when the EV goes from a cruising speed of approximately 30mph (20A) to a hard acceleration of 60mph (170A). Figure 3–12 illustrates a change in the battery resistance for a regenerative charge applied during the driving at 15W/kg and 60W/kg, respectively.
ENERGY BALANCES FOR THE ELECTRIC VEHICLE
Several factors influence the EV energy balance. The energy removed from the traction batteries, defined as a positive power gain is expressed in kilowatts (kW). The energy consumption during the time interval is calculated as the total power loss multiplied by the time increment and is termed as a negative power gain expressed in kilowatts (kW).
The factors influencing the energy balance of the EV include:
• Aerodynamic drag losses • Rolling resistance losses
Change in Resistance (milliohms)
15 14 13 12 11 10 9 8 7 6
4 0 812162024283236404448525660646872768084
% DOD
City Driving Discharge Charge at 15W/kg Charge at 60W/kg
• Road inclination • Power required for vehicle acceleration • Transmission inefficiencies • Power losses due to system controller (engine) inefficiencies • Parasitic losses • Power gained from regenerative braking • Power from heat engine
The drag losses are associated with the EV body design. The power loss due to the aerodynamic drag, represented by a variable Paero (watts) is expressed by the equation
Paero = Afrontal ¥ Cdrag ¥ V3 ¥rair/2 where Afrontal is the frontal vehicle area (m2), Cdrag is the drag coefficient of the EV, V is the velocity of the EV (m/s), and rair is the atmospheric density (kg/m3).
Rolling Resistance Losses
The rolling resistance is associated with the force necessary to overcome the friction of EV tires. The rolling energy loss equation required to overcome rolling resistance, expressed as Proll is
Proll = MGr.Veh. ¥ g (R0 + R1 ¥ V + R2 ¥ V2 + R3V3) ¥ V
where MGr.Veh. is the gross vehicle mass (kg), g is the acceleration due to gravity (m/s2), and R0, R1, R2, and R3 are rolling resistance coefficients.
Road Inclination Losses
The following equation calculates the power loss associated with the road inclination. Expressed in watts, the road inclination loss (Pincl) is represented by the equation
Pincl = MGr.Veh. ¥ g ¥ V ¥ sin (bincl ¥ π/180)
where bincl is the road inclination angle expressed in degrees with respect to the horizontal and converted to radians in the equation.
Vehicle Acceleration Power Losses
The following equation calculates the power requirements associated with the EV acceleration. Expressed in watts, the acceleration power loss Paccel is represented by the equation
Paccel = Vave ¥ MGr.Veh. ¥ a
where Vave is the average velocity (m/s) expressed as Vave = 1/2(V2 + V1) and a is the acceleration expressed as DV/Dt (m/s2).
Transmission Inefficiencies
The power loss associated with the transmission inefficiencies is estimated by dividing the power required to put the EV into motion. It is expressed as the ratio of the sum of the power losses due to aerodynamic drag, rolling resistance, road inclination, and acceleration by the EV transmission efficiency. The transmission efficiency is determined from the drive train efficiency data and the torque data. The torque converter speed output is expressed by the equation
Torque converter speed = V ¥ G/π ¥ d and
Torque converter torque (t) = Pmove/G ¥w
where d is the EV tire diameter (m), G is the transmission gear ratio, and w is the wheel rotation rate (RPM).
The torque (t) and the converter speed are calculated using the above expressions. Next, the torque data input table (output torque as a function of the output speed) is interpolated to determine the speed ratio corresponding to the output speed—torque combination. The drive train efficiency is interpolated from the drive train efficiency table as a function of the speed ratio.
The engine efficiency is defined as the ratio of the engine power to the energy consumed by the EV. The amount of traction battery energy consumed by the vehicle at any time is inversely proportional to the controller’s efficiency. The engine efficiency model is currently interpolated or extrapolated using a table of the controller’s efficiency with respect to percent rated controller power. The efficiency is plotted as a function of the rated controller power, based on the fuel economy data (Figure 3–13).
Figure 3–13 Engine efficiency with respect to % rated controller power.
Power from Regenerative Braking
As the energy gained due to braking the wheels of an EV is returned back to the traction battery pack, there is a fractional gain of power. The regenerative braking gained is expressed as
Pregen =-eregen ¥ MGr.Veh. ¥ a ¥ V
where a is the acceleration (m/s2), eregen is the regenerative braking efficiency.
Power from a System Controller/Engine
The energy consumed by the conventional combustion engine may be determined using the equation
Fuel = Pengin ¥ Dt/(Hfuel ¥rfuel ¥ eengine ¥ ealternator)
where eengine is the engine efficiency and ealternator is alternator efficiency.
In case of a conventional vehicle, the power from the engine (Pengine) is equal to the sum of all power losses. The loss Pengine is expressed by the equation
Pengin = Pmove + Pparasitic + Fuel energy consumed
In case of an EV, the power from the engine may be determined using the equation
Pengine = Pparasitic + Pmove + Pregen = Pparasitic + (Paero + Pincl + Prolling)/etrans + Pregen
where Pparasitic is the parasitic losses, Pmove is the total power to move the EV, Paero is the aerodynamic drag loss, Pincl is the inclination loss, Prolling is the rolling resistance loss, and etrans is the transmission efficiency.
In case of a hybrid vehicle, there are additional losses associated including the energy storage system and regenerative braking system. The energy is estimated as the integral of power and time. The energy losses and the energy gains are added to the SOC of the traction battery system. The engine power level is adjusted using the Auxiliary Power Unit (APU) control file.
