Experience

We in India have 4 year course for doing bachelors in engineering. And in 4 years we have 8 semesters. So I think as an electrical engineer electrical machine was included as a main subject in electrical engineering. So we had electrical machine-1(Includes DC machine theory), Electrical machine-II (Includes AC machine and transformer theory), Electrical machine-III (Includes Electromagnetic circuit calculations as per practical networks), Electrical AC drives, Electrical machine design-I and finally electrical machine design-II.
Be sure when talking to your prospective variable frequency drives suppliers that both of you are on the same page. The VFD is usually rated for some max continuous current, with a corresponding short-time peak (measured at a few minutes and at a few seconds). There's a BIG difference in current for a 27000 HP machine at 13800V vs one at 690V!
Source current cannot damage the load, the only safety need is Overload protection, for example you are not using VFD but a DOL starter the basic type to run your motor, the only protection it have is Thermal Overload protection, that you select as per your motor max current so that in event of stall or mechanical overload the TOL shall trip. You may have a 1000KVA transformer in your factory and using 1KW motor as load it doesn't mean that high power source will damage small loads.
Having a higher rated Variable Frequency Drive (VFD) will not damage a motor as long as it is within the control range of the VFD. The VFD is rated in amperes and nor motor horsepower. The current technology force vector VFDs will train to the motor if the motor ratings are input and it is within the parameters of the VFD. If the VFD is grossly oversized it will not auto tune, however.
A motor is also a heater and requires cooling. If run at low speeds for too long it will overheat. The low range of operation in a VFD is really only to provide a soft start when/if needed. If you are running a motor at 20% a lot, it's too big for the job. Use two smaller ones to provide a wider range of operation.
Some VFD vendors have dedicated simulation software available which can help get right solution with above mentioned inputs. Simulation Software can also show the voltage spike trends at drive output and motor input to make sure that motor is safe with the solution voltage spikes are below motor CIV value all time.
AC Motor shall be selected according to the type of Load & Application with the kind of cooling for the motor needed and after selecting the motor & identifying the application requirement in terms of torque, you can select various VFD available in the market for specific applications pertaining to your requirement in different brands.
If the motor is not sized properly, ie over-sized as they often are, then a VFD will offer savings even at fixed speed and load ie A motor running under loaded will be inefficient regardless of its rated efficiency and this can be corrected by use of a VFD (or a better motor sizing).
Regulating the speed of the pump by using of either a variable frequency drive controls the motor, or a mechanical fluid coupling. According to the experience of both the mechanical fluid coupling method and the VFD method.
If it is a centrifugal compressor with consistent gas density (mole weight), the load is quadratic and you can size the variable frequency drive based on the motor hp (as long as you don't require over-speed, which needs more detailed review).
If you are selecting a VFD for a squared torque application, then you could select a lightly duty variable frequency drive. But remember you are then not supposed to increase the speed beyond the designed fan/motor speed.
In high performance applications we've used Closed Loop Vector with Resolver Feedback with great success in special applications at Ultra High speeds in excess of 20K RPM for SPM. In our variable torque applications using IPM we utilize Sensorless FOC with a special algorithm that provides motor efficiencies unachievable before the modifications that are required by our customers.
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