| The other parameters of the electric vehicle is given below, |
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| Motor and Controller Parameters: |
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| Rated Armature voltage= 72 V |
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| Rated armature current= 400 A |
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| Ra= 0.5Ω, KΦ= 0.7 Volt second |
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| Chopper Switching frequency= 400 Hz |
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| The vehicle speed-torque characteristics are given by the below equation |
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| What is EV steady state speed if duty cycle is 70%? |
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Given values |
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Armature voltage= 72 V |
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Rated armature current= 400 A |
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Ra= 0.5Ω, KΦ= 0.7 Volt second |
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Chopper Switching frequency= 400 Hz |
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Vv = Battery Voltage (V) * Duty Cycle |
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Vv = 72 * 0.70 |
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Vehicle voltage = 50.4V |
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| Now, Equation for Vehicle torque is given by: - |
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`T_v= ((V_v- ω.K_∅ )*K_∅)/R_a` |
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Where; |
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`T_v`= Vehicle Torque (N-m) |
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`V_v` = Vehicle voltage (Volts) |
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`ω`= steady state speed of vehicle (rps) |
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`K_∅`= Motor constant |
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`R_a`= Armature Resistance |
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`T_v= ((50.04 - 0.7*ω)*0.7)/0.5` |
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`T_v=70.56-0.98*ω` |
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`T_v=24.7+0.0051*ω^2` |
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Solving these two equations, |
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`70.56-0.98*ω =24.7+0.0051*ω^2` |
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We get a quadratic equation: |
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`0.0051*ω^2+0.98*ω-46.94=0` |
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Since quadratic equation, we get two values of ; |
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`ω`= 38.85 rad/s and `ω` = -230.95 rad/s |
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We take the positive value; |
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Steady state speed of vehicle = = 38.85 rad/s |