A hybrid approach to optimal electric drive train design
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| Fig 3: Forces on vehicle
Vehicle has to work against different forces to move forward and these forces must be calculated to understand the power requirement of a vehicle. By calculation of these forces power required by vehicle is achieved under certain conditions. The major forces are as follows: Aerodynamic Resistance Tyre Rolling Resistance Power while climbing slopes Accelerating Power Above forces can be calculated to get the power requirement of vehicle at certain condition through which current is calculated which can be used to evaluate the range of vehicle. For range calculation of vehicle it is considered that the vehicle is running on a plane surface at constant rated speed. In this condition power for climbing slope and accelerating components will not come into picture. So in this paper only two forces are considered: Aerodynamic resistance Tyre rolling resistance Drag Force: The vehicle has to work against a force produced by air resistance (aerodynamic resistance), this force is called aerodynamic resistance. It is directly proportional to the air density, relative speed of vehicle, frontal area of vehicle and the drag coefficient which is a constant for a given vehicle design. The drag coefficient Cd is a dimensionless constant that attempts to capture, in one term, an object's resistance to flow. Cd can vary from as high as 1.2 for a bicycle with erect rider to 0.20 for a very aerodynamically-styled modern automobile. Although the equation used to determine the drag power is a simplification, it avoids complex air flow simulation while preserving the general behavior of the drag force with respect to velocity as for electric vehicles very high speeds are not considered. Drag Force Power = ½ * Pair * Cd * Af * v3 (2) Pair = density of air Cd = drag coefficient Af = frontal Area v = relative velocity of vehicle with respect to wind Typical value for air density is 1.23 kg/m3 and drag coefficient for electric scooter is 0.9 [1]. The frontal area can be measured for the scooter by projecting a bright light parallel to the front of the scooter and then measuring the area of the shadow on a wall behind. Here we will take the frontal area of 0.6 m2 for the vehicle[1]. 
Fig 4: Variation in drag force with speed The trend of drag power with speed is shown in the above graph. The graph shows that the rated speed will affect the range and the vehicle range will decrease with increase of speed. Tyre Rolling Resistance: Tyre rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface. It is caused by the deformation of the object, the deformation of the surface or both. Tyre Rolling Resistance Power = m * g * v * Crr (3) m = Total weight of vehicle including rider g = gravitational force v = velocity of vehicle Crr = Coefficient of tyre rolling The estimated value of Crr for electric scooter is 0.014 [1]. 
Fig 5: Rolling Resistance Power Vs Speed Variation in rolling resistance power with speed is shown in the Fig. 5. Total vehicle power = Drag force power + Tyre Rolling Resistance Power (4) 
Fig 6: Total Power of vehicle Vs Cruse speed The total Power variation with respect to varying speed and varying weight is shown in the Fig. 6 and 7 respectively. 
Fig 7: Total Power Vs Vehicle weight at 25km/h cruse speed The above equation can be used to calculate the required output power of vehicle to run at certain speed. Input power can be calculated by considering the efficiency factor of vehicle and than it can be divided by the input voltage to get the actual current consumed by the vehicle. Vehicle Current = (Total vehicle power * Efficiency factor) / Input Voltage (5)
IV. Motor The electric motor is the heart of any electric vehicle .Currently most of the electric vehicles use BLDC hub motor which gives more life and torque as compared to normal DC motor. BLDC is the most suitable option because it is easy to control as compared to the AC motors and have much longer life as compared to DC motors as the main failure in DC motors is due to brushless and it is brushless DC. The final performance of electric vehicle depends on motor performance, so the selection of right motor is very important. Following factors has to be considered to decide the specifications for motor: Rated speed Load caring capacity Ability to climb gradients Acceleration of vehicle The rated power of motor should be calculated as per the equation 4 for rated speed and rated load. The max power will be the sum of all the four forces given in section III. Acceleration power can be calculated from the kinetic energy of vehicle and gradient power can be calculated by evaluating the potential energy of vehicle. The equations already discussed in power requirements of vehicle can be used to evaluate power requirement of vehicle at different speeds and than it can be used to apply torque to the vehicle through dynamometer for motor testing. The % speed Vs % voltage curve is shown below and equation is achieved. 
Fig 8: Motor speed Vs voltage y = 5.338x – 431.4 y = % speed x = % voltage This relation is true when the battery voltage is lesser than the rated motor voltage. For voltage equal and above rated motor voltage, motor runs with rated speed. Controller takes care by PWM control that the motor runs with rated speed at voltage equal and above the rated motor voltage but as the voltage falls below the rated voltage, PWM is at it’s max duty cycle so the speed starts reducing with the reducing voltage. This relation is unique for the motors. V. Simulation 
Fig 9: Block Diagram for Simulation The equations for battery performance, motor speed response and vehicle current are already derived which can be used to realize the block as simulation model. It is a closed loop system which will calculate the speed and current which will be further used to calculate the distance travelled and AH consumed for small time interval. This calculated AH consumed will be again fed to the system to calculate the battery voltage and speed for the next cycle and these cycles will keep on going till rated full AH is consumed. AH consumption in a cycle = Vehicle current * Time / 60 (6)
Where time is in minutes Distance travelled = speed * time (7) It is assumed that the battery equation what have been achieved from one AH rating will work for all the ratings for the same type of batteries for same manufacturer. Different values of speed, battery voltage and battery AH can be tried and vehicle performance and range can be evaluated. 
Fig 10: Snap shot of my simulation model Below the simulated and practical results are given for the following system: Battery Voltage = 48V Battery Capacity = 33 AH Vehicle Speed = 25 km/h Vehicle total weight = 115kg vehicle weight + 70 kg rider Weight 
Fig 11: Simulated graph for vehicle speed Vs distance In the above graph the vehicle speed is 25km/h in starting as it is the max speed and limited by the PWM controller but after certain distance when battery voltage has dropped bellow certain limit the speed starts reducing. 
Fig 12: Actual Tested graph for vehicle speed Vs distance Range:
Actual: 123 km Above results shows that the simulated results are close to the actual tested results so the methodology we have used is validated and same can be used to build more complex simulation system for vehicles. In this model acceleration and deceleration is not considered nor in the actual testing. But the same technique and algorithms can be used to build the simulation model of specified acceleration and deceleration cycle. VI. Conclusion Equations are derived from experimental results and calculations to develop the algorithms for range and vehicle performance curve with dropping battery voltage. Simulation model based on these algorithms is also built which can be used to simulate the range and performance of vehicle with different battery voltage, battery capacity and vehicle loading conditions. The selection of the combination of motor and battery is also discussed and the mechanism to convert the vehicle specifications into motor specifications is explained. The simulation model based on the algorithms described is built and validated with practical results. The experimental results agree with the simulated results and verified the algorithms proposed. VII. References [1] Bruce Lin: “Conceptual design and modeling of a fuel cell Scooter for urban Asia”, Princeton University School of Engineering and Applied Sciences, Department of . [2] Aymeric Rousseau, Neeraj Shidore, Richard Carlson, Dominik Karbowski: “Impact of Battery Characteristics on PHEV Fuel Economy”, Argonne National Laboratory VIII. Biographies Download 0.8 Mb. Share with your friends:
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