Basic Operation of AC Induction Motors (3)

Adjustable Frequency, Variable Speed Operation
For steady-state (as opposed to starting) operation, AC induction motors offer a reasonably linear torque per amp and high power factor characteristic. This is seen in Figure 5 as the part of the speed torque curve between “breakdown RPM” and “synchronous (no load) RPM.” It is this portion of the AC induction motor range of operation within which adjustable frequency drives function.

By varying both the frequency and voltage supplied to an AC motor, the controller can cause the motor to operate on a continuum of speed torque curves which allows operation in the “linear” region between breakdown and synchronous speeds (Figure 6).
This then allows the motor to operate near its optimal torque per amp or maximum efficiency point for a given load and speed.
As long as the motor flux is maintained constant while the frequency and voltage are varied, the basic “shape” of the speed torque curve will remain unchanged. The motor flux is proportional to the internal “counter-emf” divided by the frequency of that generated voltage. This can be described as:
where F is the motor flux,

Eg is the internally generated voltage due to motor rotation, f is the stator frequency, and k is a motor constant related to the winding turns, etc.
The flux paths for a four pole configuration are as seen in Figure 7 (for an instant in time). This pattern rotates at an effective speed given by Equation 1.
The motor counter-emf (Eg) can also be thought of as the voltage across the magnetizing reactance (Xm) in the equivalent circuit of Figure 3.
Maintaining constant flux while the speed (frequency) is varied can then be seen as requiring constant ratio of Eg / f (or constant Im).
Since Eg is a motor internal voltage, this needs to be related to the terminal voltage of the motor. From the AC motor equivalent circuit, it can been seen that the voltage drops across the stator resistance and leakage reactance represent the difference between Eg and the terminal voltage Vt.
If a controller were to maintain a constant ratio of TERMINAL voltage to frequency (Vt / f), rather than Eg / f, this would result in a noticeably decreasing flux level at lower speeds (frequencies).
The curves of Figure 8 demonstrate the effect of this failure to maintain the motor flux. It can be seen that the peak value of torque falls off at the reduced flux levels. In fact, the peak torque is approximately proportional to the square of the flux level, so the drop-off can be significant. The torque per amp is also (directly) proportional to the motor flux, so increased current draw for a given load (torque) will also result from reduced flux.
As a means to improve the system characteristics (beyond the curves of Figure 8), controllers often compensate for the difference between Vt and Eg in order to select the correct voltage for a given frequency. This compensation is often referred to as “voltage boost.” Since the major detrimental effect of constant Vt / f is at low voltages, low frequencies (low speeds), the voltage drop across the stator leakage reactance is usually ignored (as the impedance of an inductor is proportional to frequency). This leaves the drop across the stator resistance as the major source of a discrepancy between Vt and Eg at these low speeds.
Many controllers use a value of voltage boost which compensates for the IR drop of the stator at a current equal to the motor full load amps.

Vb is the per phase (line-to-neutral) voltage boost,
Rl is the per phase stator resistance,
IFL is the motor full load current.
This would result in a voltage versus frequency characteristic as shown in Figure 9. A weakness in this technique of boosting voltage is that the value of Vb is only “correct” for a single value of load current. If the full load current is used to set the voltage boost, then the motor will be overfluxed for lighter loads, and underfluxed for overload conditions. Depending on the low speed performance required by a given application, this may or may not be a problem.
It is now common to provide a “more intelligent” voltage boost function in many controllers. This can provide a closer to optimal operating condition at low speeds, resulting in better low speed torque delivery from the system.

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