Week-6 Challenge: EV Drivetrain

OBJECTIVE - 2:

TO CALCULATE STEADY STATE SPEED OF THE EV AT A DUTY CYCLE OF 70%:

• Given data:
  • An Electric Vehicle's powertrain with 72V battery pack is shown in the diagram below. The duty ratio for acceleration operation is 'd1' and for the braking operation the duty ratio is 'd2'.
  • Rated Armature Voltage = 72 V
  • Rated Armature Current = 400 A
  • Armature Resistance R_a = 0.5 ohm
  • K*Phi = 0.7 Volt Second
  • Chopper Switching Frequency = 400 Hz
  • Duty Cycle = 70%

  • The vehicle speed-torque characteristics are given by the equation below:

    

• Let us consider the above Torque equation as equation 1.

• `T_v = 24.7 + (0.0051)omega^2`........................................................ (1)

• The relation between Speed and Torque is:
• `omega = V_t/(Kphi) - (R_a)/(Kphi)^2*T_v`
• Also,
• `T_v = (V_t*Kphi)/(R_a) - (Kphi)^2/(R_a)*omega`
• `V_t = V_s *`Duty Cycle
• V_t = 72 * 0.7 = 50.4 V

• Now Solving the Torque equation:
• `T_v = (50.4*0.7)/0.5 - (0.7)^2/0.5*omega`

• `T_v = 70.56 - 0.98*omega` ...............................................................(2)

• Equating both the equations we get:

• `24.7 + (0.0051)*omega^2 = 70.56 - 0.98*omega`
• `(0.0051)*omega^2 + 0.98*omega - 45.86 = 0` ..................................(3)

• The above equation is a Quadratic Equation and is in the form of ax^2 + by + c = 0.
• To find the solutions:

• D = b^2 - 4*a*c
• D = 0.98^2 - 4*0.0051*(-45.86)
• D = 0.9604 + 0.935544
• D = 1.895944
• `root_D = 1.377`

• `alpha = (-b + root_D)/(2*a)`
• alpha = (-0.98 + 1.377) / (2*0.0051)
• alpha = 38.92

• `beta = (-b - root_D) / (2*a)`
• beta = (-0.98 - 1.377) / (2*0.0051)
• beta = -231.07

• By solving the above equation we got speed as 38.92 rad/sec and -231.07 rad/sec.
• Since we know the duty cycle is 70% which implies that more amount of voltage is supplied to the motor by the battery and the vehicle is in accelerating condition so, we will consider the positive value of the speed that is 38.92.
• Therefore, the steady state speed of the vehicle at 70% duty cycle is 38.92 rad/sec.

OBJECTIVE - 3:

TO DEVELOPE THE MATHEMATICAL MODEL OF SPEED VS TORQUE CHARACTERISTICS OF A DC MOTOR USING SIMULINK:

• The relation between Speed and Torque of a DC motor is:
  • `omega = V_t/(Kphi) - (R_a)/(Kphi)^2*T_v`
• Creating a Simulink model to evaluate the above equation:

PLOTS:

SCOPE: (SPEED VS TIME):

SPEED VS TORQUE GRAPH:

OBJECTIVE - 4:

INDUCTION VS DC BRUSHLESS MOTOR BY WALLY RIPPEL, TESLA

• In his blog he wants to discuss Electric vehicles and the Motors used in it.
• At the beginning he discussed that there is no best engine which will fit all the requirements and demands of all the people, rather there are different types of engines to suit personal requirements, such as price and performance. This is also true for electric vehicle drives.
• Then he discusses how different technologies are getting replaced by the upcoming new technologies like Lead has been replaced by lithium and DC by either DC brushless or induction and starts discussing the brushless DC motor and Induction motor.
• With brushless machines, the rotor includes two or more permanent magnets that generate a DC magnetic field (as seen from the vantage point of the rotor). In turn, this magnetic field enters the stator core (a core made up of thin, stacked laminations) and interacts with currents flowing within the windings to produce a torque interaction between the rotor and stator. As the rotor rotates, it is necessary that the magnitude and polarity of the stator currents be continuously varied – and in just the right way - such that the torque remains constant and the conversion of electrical to mechanical energy is optimally efficient. The device that provides this current control is called an inverter. Without it, brushless motors are useless motors.
• Unlike the DC brushless rotor, the induction rotor has no magnets – just stacked steel laminations with buried peripheral conductors that form a “shorted structure.” Currents flowing in the stator windings produce a rotating magnetic field that enters the rotor. In turn, the frequency of this magnetic field as “seen” by the rotor is equal to the difference between the applied electrical frequency and the rotational “frequency” of the rotor itself. Accordingly, an induced voltage exists across the shorted structure that is proportionate to this speed difference between the rotor and electrical frequency. In response to this voltage, currents are produced within the rotor conductors that are approximately proportionate to the voltage, hence the speed difference. Finally, these currents interact with the original magnetic field to produce forces – a component of which is the desired rotor torque.
• When a 3-phase induction motor is connected to utility type 3-phase power, torque is produced at the outset; the motor has the ability to start under load. No inverter is needed. (Were an inverter needed, Tesla’s invention would have been useless until sometime in the 1960s.) The fact that induction motors are directly compatible with conventional utility power is the main reason for their success. In contrast, a brushless DC motor produces no starting torque when directly connected to fixed frequency utility power. They really need the aid of an inverter whose “phase” is maintained in step with the angular position of the rotor.
• While 3-phase induction motors have great utility, they also have some severe limitations. They cannot operate from DC; AC is a must. Shaft speed is proportionate to line frequency. Hence, when used with utility power, they are constant speed machines. Finally, when operated from utility power, they have limited starting torque and somewhat limited running peak torque capabilities, when compared to DC type machines.
• Add an inverter (without any feedback control) and it becomes possible to power an induction machine from a battery or other DC source; variable speed also becomes possible simply by adjusting the inverter frequency. Still, torque performance is low compared with DC machines. Add some feedback loops such that the inverter produces the exact frequency that the motor “desires,” and the induction motor is now capable of competing with DC and DC brushless for vehicle applications.
• Both DC brushless and induction drives use motors having similar stators. Both drives use 3-phase modulating inverters. The only differences are the rotors and the inverter controls. And with digital controllers, the only control differences are with control code. (DC brushless drives require an absolute position sensor, while induction drives require only a speed sensor; these differences are relatively small.)
• One of the main differences is that much less rotor heat is generated with the DC brushless drive. Rotor cooling is easier and peak point efficiency is generally higher for this drive. The DC brushless drive can also operate at unity power factor, whereas the best power factor for the induction drive is about 85 percent. This means that the peak point energy efficiency for a DC brushless drive will typically be a few percentage points higher than for an induction drive.
• In an ideal brushless drive, the strength of the magnetic field produced by the permanent magnets would be adjustable. When maximum torque is required, especially at low speeds, the magnetic field strength (B) should be maximum – so that inverter and motor currents are maintained at their lowest possible values. This minimizes the I² R (current² resistance) losses and thereby optimizes efficiency. Likewise, when torque levels are low, the B field should be reduced such that eddy and hysteresis losses due to B are also reduced. Ideally, B should be adjusted such that the sum of the eddy, hysteresis, and I² losses is minimized. Unfortunately, there is no easy way of changing B with permanent magnets.
• In contrast, induction machines have no magnets and B fields are “adjustable,” since B is proportionate to V/f (voltage to frequency). This means that at light loads the inverter can reduce voltage such that magnetic losses are reduced and efficiency is maximized. Thus, the induction machine when operated with a smart inverter has an advantage over a DC brushless machine – magnetic and conduction losses can be traded such that efficiency is optimized. This advantage becomes increasingly important as performance is increased. With DC brushless, as machine size grows, the magnetic losses increase proportionately and part load efficiency drops. With induction, as machine size grows, losses do not necessarily grow. Thus, induction drives may be the favored approach where high-performance is desired; peak efficiency will be a little less than with DC brushless, but average efficiency may actually be better.
• Permanent magnets are expensive – something like $50 per kilogram. Permanent magnet (PM) rotors are also difficult to handle due to very large forces that come into play when anything ferromagnetic gets close to them. This means that induction motors will likely retain a cost advantage over PM machines. Also, due to the field weakening capabilities of induction machines, inverter ratings and costs appear to be lower, especially for high performance drives. Since spinning induction machines produce little or no voltage when de-excited, they are easier to protect.
• Induction machines are more difficult to control. The control laws are more complex and difficult to understand. Achieving stability over the entire torque-speed range and over temperature is more difficult with induction than with DC brushless. This means added development costs, but likely little or no recurring costs.

• In his blog he explained about the DC brushless motor and the Induction motor and its advantages and disadvantages over each other.
• The author's perspective was there is no clear winner among them as both of the motors will be used for different purposes.
• DC brushless drives will likely continue to dominate in the hybrid and coming plug-in hybrid markets, and that induction drives will likely maintain dominance for the high-performance pure electrics.
• He has a thought that when the EVs and HEVs become more electrically intensive and as their performance levels increase then as they have a lot of hardware is common in both drives then both the DC and the Induction motor can work side by side in the coming golden era.

CONCLUSION:

• In the above assignment we learnt about different power converters used in Hybrid Electric Vehicles and Electric Vehicles and saw their applications.
• We calculated the steady state speed of the Electric vehicle at a Duty cycle of 70% with the given other parameters.
• We developed a mathematical model in the Simulink to represent the Torque Speed characteristics equation and plotted the speed vs torque graph.
• We also explained in detail about the author's perspective regarding the Brushless DC motor and the Induction motor.