AC Motor torque simulation

Question

I am trying to do a simulation on the start up speed to a system powered by an AC motor.

As part of this I am trying to find a mathematical torque/speed curve that I can use.

I expect a curve that looks something like this.

I have used the equations HERE as reference for the below calculations.

My general process is

• Determine motor resistance & inductance based on published data for full load conditions
• Use this to plot a curve of the motors torque speed relationship

However the curve I am getting looks nothing like the published curve at low speeds. Have I done anything wrong, or is there a more accurate model I can use.

I am using a WEG motor as a reference with the following published data

• Frame: 315H/G
• Output: 185 kW
• Frequency: 50 Hz
• Poles: 6
• Full load speed: 988
• Slip: 1.20 %
• Voltage: 415 V
• Rated current: 328 A
• Locked rotor current: 2000 A
• Locked rotor current (Il/In): 6.1
• No load current: 119 A
• Full load torque: 1789 Nm
• Locked rotor torque: 190 %
• Breakdown torque: 210 %

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Update

The best I can fit based on Charles Cowie's Answer

• Rth = 0.03424
• Xth = 1E-9
• R2 = 0.0020499
• X = 1E-8

This still looks nothing like the published curve I am going to give up and go with just taking samples from number of motor curves. But I would still like to get a solution to this.

Answer 1

There are a few things you have wrong. First, 1789 Nm is the rated ("full load") torque, not the maximum torque. The maximum torque is usually called the "breakdown torque" and according to your data, it is 210% of the full load torque. This puts the maximum torque at 3756.9 Nm. The locked rotor torque also isn't 42.93 Nm, but rather 190% of the full load torque. This puts the locked rotor torque at 3399.1 Nm.

Try fixing those things. Also notice that the graph provided plots the speed, torque, and current as a ratio of the rated values.

Answer 2

I think that the problem may be that you don't have sufficient information about the motor. What is the basis for your calculation of K?

The information presented here seems to follow the methods used in the texts that I have and the presentations of the material that I have seen.

Edit 1 To get good results, you really need good values for all of the equivalent circuit parameters. I found a paper entitled "Estimation of induction motor equivalent circuit parameters from nameplate data" by Keun Lee, Div. of Eng., Colorado Sch. of Mines, Golden, CO, USA; Frank, S. ; Sen, P.K. ; Polese, L.G. ; Alahmad, M. ; Waters, C. I will try to get a copy.