Torque-Speed characteristic of induction machine
This post aims to explain the famous torque-speed characteristics of asynchronous (induction) motor. We try to make it simple and understandable. First we thought to put without mathematics into the title. Well, we might write 2-3 formulas, but keep it as simple as possible. Promised!
Importance of Torque-Speed characteristic
Torque-speed characteristic is a key diagram defining the performance of the electric motor. Many people make the obvious error that they just focus on rated power. Equally or more important is the torque profile. The situation may slightly change in case of VFD driven motor where the machine is operated within a very narrow slip range. However, for a fix speed machine operated direct on-line the torque-speed characteristic is crucial.
Asynchronous motor without (too many) equations
At the university I had an excellent teacher for Electric drives and Automatic control in electric drives. He always wanted us to understand the things rather than memorizing them. One his quote that I ‘ll never forget was:
If you (fresh graduate of electrical engineering) can analytically solve complex integrals but do not understand how induction motor works, you will be seen as a dummy by your senior colleagues.
Of course, we have used many equations, formulas and mathematical models, but one day as preparations for the finals he gave an explanation “asynchronous motor without equations”. Let’s try to convey his message!
Torque-Speed characteristic of asynchronous machine
The goal here is to abbreviate the famous shape of a torque-speed curve of an asynchronous machine (motor or generator). In addition, it is useful to display the stator current-speed curve in the same diagram. The high starting current for across the line starting of asynchronous machine is a well known issue and such diagram nicely illustrates where it comes from.
There are obviously multiple approaches how to analyze or identify the torque-speed curve of the machine.
- Analytical approach with set of equations (mathematical model based on ECD)
- Simulation approach (mathematical model based on ECD or FEM)
- Geometrical representation using Heyland-Osanna circle
- Simplified abbreviation using engineering opinion
* ECD = Equivalent circuit diagram
** FEM = Finite element model
The mathematial description of asynchronous machine based on equivalent circuit diagram is known and does not need to be described here in detail. Just as a remark, there are multiple ECDs used in the literature to describe an asynchronous machine. The difference is usually in the level of detail. The full ECD is required for modelling a dynamic (fast transient) behavior of the machine. For other purpose certain simplifications can usually be done without hurting the results significantly. The starting of asynchronous machine is neither a steady state nor a fast transient. Slight simplification of the full ECD is acceptable, especially when analyzing the torque-speed characteristic qualitatively. For example, you may transfer a paramater from stator to rotor side or merge two parameters into one.
Simulation models are also mathematical models. The software programme usually includes the machine model as a ready-made block where the user just need to enter the project data. That is of course very convenient. However, most users see the model as a black box. While the simulation probably helps you to solve your task it is not necessarily helping you to understand the working principle of asynchronous machine. I remember a scientific conference where the presenter was discussing with a committee member whether a machine with resistance-free rotor can produce torque or not. The argument of the presenter was: “Well, I saw it in the simulation…” This is dangerous and also a bit embarrassing, isn’t it? You shall be the master and the simulation is just your design aid.
Heyland-Osanna circle (also called just circle diagram) is a great complementary way to abbreviate the characteristic of asynchronous machine. I don’t see it being much used which is a pity. It is a powerful method that tells you a lot about the asynchronous machine and the relationship between the quantities. You see the stator and rotor current, its active and reactive components, torque, mechanical power, overloadability etc. Once I got the circle diagram of asynchronous machine constructed right for the first time I was really proud of myself. The best thing is that you can create the circle diagram just using the nameplate values of the machine combined with few qualified estimations. If measured values (no-load and short-circuit condition) are available, a more accurate diagram can be constructed.
The last option mentioned here is the use of engineering judgement. With minimum laws of physics we can abbreviate the shape of the torque-speed curve. Of course, it does not provide you with the exact figures when seeking for the quantitative values. However, it helps you to create your own opinion and develop your own understanding of the asynchronous machine and its behavior. In fact, you should ideally start with this approach before using simulations or some ready-made programs written by others. With the right engineering judgement you are able to justify whether the simulation results make sense or whether something is wrong. You can avoid situations where you present obviously wrong results.
The abbreviation of the torque-speed characteristic based on engineering judgement is quite easy. In fact, you just need an elementary knowledge of R-L circuit and the Faraday’s law of induction.
Physical explanation
For the purpose of our analysis we divide the torque-speed characteristic into three sections I, II and III as shown in figure below:
Remark:
You may have torque on the x-axis and speed on the y-axis or vice versa. Choose whatever you are used to. Besides the rotational speed mark also the slip on the same axis.
Rotor impedance
In order to explain the torque-speed characteristic and current-speed characteristic it is useful to make following consideration…
Summary
Knowledge of torque-speed characteristic of asynchronous machine is essential for most engineering tasks related to this type of motor. While there are ready-made models and programs available, we encourage each engineer to develop own understanding of this characteristic and be able to explain its shape as well as to know the impact of specific factors (e.g. rotor resistance, stator voltage).
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References
[1] Motor basics: Power, speed and torque, https://mb-drive-services.com/power-speed-and-torque/
[2] ABB Motors and Generators, https://new.abb.com/motors-generators
