induction motormathvfd
If i had an Induction motor that runs on 460 volts ,35 amps , develops a power of 35 hp at a speed of ~1800 RPM ( data acquired from a nameplate )
How is it possible to calculate the same parameters if i wanted to run this motor at 50 hz instead ? what equations should i use ? , all i know is that power would decrease as well as RPM (obviously).
The RPM is determined by the frequency and does not directly effect the current. The current is more closely related to torque. Some useful relationships are:
Motor speed RPM = 120 X Frequency (Hz) / Number of motor poles (4 poles for the Tesla I think)
Input power to the motor, Watts = Volts X Amps X Square Root of 3 X Power Factor
Horsepower output = Torque (Ft-Lbs) X RPM / 5252
Input Power X Efficiency = Output Power
1 Horsepower = 746 Watts
The Tesla motor is very efficient, 0.95 or higher
For constant torque operation, the voltage applied to the motor is proportional to frequency.
The Tesla motor can provide constant torque up to some frequency limit. Above that, the voltage does not increase any more (or perhaps it increases at a slower rate). That allows the motor to provide constant power.
Re. Test Data
It appears that the voltage and current for the test data are battery voltage and current. The power at the battery is just watts = voltage X current. The inverter is between the battery and the motor. The Tesla inverter efficiency is also quite high, perhaps 0.95 or higher.
In the last 25 years there has been an enormous amount of evolution and technology that has gone into controlling 3 phase Variable Frequency Drives. Discussing any details around how to do it in a new method or better exceeds the scope of a forum such as this, but would be a good basis for a PHD thesis.
A good starting point in your study is Vector mode control, which is typically one of 3 standards modes to run an off the shelf VFD drive in.
Constant Torque is a standard mode in most VFDs - BUT if you are talking a 50 or 60 hz motor - why would you choose to run at 100 hz UNLESS you had a reduction in torque requirement in your 60 hz - 100 hz range. In my experience every 3 phase motor rated at a base speed of 60 hz has a reduction in torque capability for speeds above 60 hz.
You will also want to do some reading and study the Pull up torque curve which has been a staple in motor theory and motor manuals for 75 years. If you get a good grasp for how Vector control modes manipulate this Torque curve at various speeds - you will have a foundation to start with.
Best Answer
Motor torque is a direct function of the design ratio of voltage and frequency, or the V/Hz ratio. Anything within +-10% of the design V/Hz ratio will allow the motor to develop design torque without significant added heating.
480V is the DISTRIBUTION voltage in North America, the actual NEMA motor DESIGN voltage is 460V to allow for voltage drop. A motor labeled as 460V 60Hz is designed for a V/Hz ratio of 7.67:1 (460/60) and if you multiply that back into 50Hz, that's where you get the 383V. So giving it anywhere between 345 and 420V at 50Hz should be absolutely fine for that motor. It will develop full torque, but because of the frequency being 5/6ths, will run 17% slower. because the mechanical power (HP or kW) is a function of speed and torque and your torque remains the same, the power will also drop by 17%, so if it was rated for 35HP, that will be roughly 30HP or 22kW.
Given that 35HP was never a "standard" NEMA HP rating for an AC induction motor (standards are 30HP and 40HP), my guess is that your motor STARTED OUT life as a 22kW 380V 50Hz motor (which IS a standard size) and was re-rated for use in North America as "35HP" at 460V 60Hz. So if you want to go back to running it on a 380-415V 50Hz system again as a 22kW motor, have at it.