White Paper:

Induction Motors -
Constant Frequency / Constant Voltage
Variable Frequency / Variable Voltage

| Abstract | Intro. | Terminology & Equivalent Circuits | Speed-Torque Curves | Efficiency & Losses | Adj. Freq. Variable Speed Op. | Field Oriented Control | Constant Power Op. | Non-Fundamental Voltages, Current | Additional Motor Losses | Heat Dissipation | Switched Voltage Waveforms | Noise | Oversizing-Derating | Conclusions |


As more AC induction motors are applied to variable speed applications, it is increasingly important to understand how these motors operate. The differences between operation on "sinewave" power and "static" power supplies can be quite significant.

This session will review the basics of constant frequency / constant voltage operation of ac induction motors. These principles of operation will then be extended to the case of operation from variable frequency / variable voltage power. Finally, the effects of the non-sinusoidal voltage and/or current waveshapes will be covered.


AC induction motors have for many years been reliable workhorses in converting electricity into rotating power. The last 20 years has seen increasing usage of these motors with adjustable frequency controls to add variable speed capability to AC motors. While AC motors were initially applied to relatively simple variable speed applications (such as varying the flow rate of a fan or pump), advances in AC motors and control technology have allowed their use in higher performance applications.

With these higher performance applications (and higher performance motors and controls) has come the need for "high performance" matching of the control, motor, and the application. This session will provide additional understanding of the adjustable-frequency, variable-speed operation of AC induction motors, with the intent of fostering "smarter" application and improved performance.

Constant Frequency , Constant Voltage Operation
Terminology and Equivalent Circuits

Before trying to understand the operation of AC induction motors on adjustable-frequency power (variable-speed), it will be useful to briefly review the basic fixed-frequency operation of AC induction motors. The fundamental electromagnetic components are the stator and rotor (Figure 1). In the most common configuration, the stator has three interconnected phase windings, and the rotor winding is a set of short circuited bars known as a "squirrel cage."

Typical AC Induction Motor Stator and Rotor Laminations
Figure 1

With balanced three phase voltages applied to the windings of the stator, balanced currents flow in the three interconnected phase windings. These currents produce a magnetic field which "rotates" within the stator at a speed given by Equation 1.

N1 = 120 x f /P (1)

N1 = rotational speed of stator magnetic field in RPM (synchronous speed)

f = frequency of the stator current flow in Hz

P = number of motor magnetic poles

For various numbers of motors poles, Table 1 shows the synchronous speeds based on 60 Hz and 50 Hz frequencies.

2 60 3600
2 50 3000
4 60 1800
4 50 1500
6 60 1200
6 50 1000
8 60 900
8 50 750
10 60 720
10 50 600
12 60 600
12 50 500

AC Motor Synchronous Speeds Table 1

The natural tendency is for the rotor to "follow" the rotating magnetic field, and at no-load the rotor will turn at a speed y equal to Nl. Any difference in the rotational speed of the magnetic field and the rotor will result in a voltage being induced in the rotor squirrel cage winding. The resultant rotor current interacts with the magnetic field to produce torque. The difference in rotor mechanical speed versus magnetic field rotational speed is what is known as "slip."

The equivalent circuit for an AC induction motor can help visualize some of the motor characteristics. Figure 2a shows separate circuits for the stator and rotor, with the interaction between them modeled as a "transformer." This transformer has the unique characteristic of also changing the frequency of the signal! While the current in the stator is at the applied frequency of the motor power source, the rotor current flows at a frequency based on the slip of the motor.

AC Induction Motor Equivalent Circuits
Figure 2

Rather than work with such a two part equivalent circuit having currents at different frequencies, the circuits of Figure 2a are typically modified to come up with a single circuit as shown in Figure 2b.

Speed / Torque Curves

As an AC induction motor is started, the values of resistance and reactance offered by the motor (or seen by the power source) will vary. At the instant of applying power to a stopped motor, the magnetic field is rotating much faster than the (stationary) rotor. This implies 100% slip, so r2/s is minimized. As a result, the current drawn at starting (locked rotor) conditions is quite high. Also it is common to design rotor slots which have dramatically different impedance at high slip (say 60 Hz for starting) versus at typically less than I2 Hz slip (normal running). This changes the values of both x2 and r2 from starting to running conditions.

As a motor accelerates to speed from a standstill, the changing impedances result in a unique characteristic developed torque and current drawn during the time of acceleration. Depending on the design of the motor, a torque / current characteristic such as one of those shown in Figure 3 would typically result. The NEMA Design B motor is considered the most "general purpose" of these characteristic shapes, with Design C and D typically used for more "difficult to start" loads. Table 2 gives some ranges of characteristics for integral HP, 1200 and 1800 RPM motors.

10 - 125 HP

A N/A 1.0 - 1.65 2.0
B 5.3 - 5.9 1.0 - 1.65 2.0
C 5.3 - 5.9 2.0 - 2.5 1.9
D 5.3 - 5.9 2.75 N/A

Typical AC Induction Motor Speed/ Torque / Current Data
Table 2


Typical AC Induction Motor Speed / Torque / Current Curves
Figure 3

As can be seen from all of these speed/torque curves, the current drawn by an AC motor in accelerating a load up to speed can be dramatically higher than the nominal running current. At the same time, the developed torque (during acceleration) may in some cases be less than the rated full load torque. Various methods exist to control the starting current drawn by an AC motor but the torque per amp seen during starting is always much lower than at running conditions.

The nature of an AC induction motors acceleration to running speed is such that it can impose high stresses on the stator end turns and the rotor. The high current draw also stresses the upstream power system, including cabling, transformers, switchgear, etc. For this reason, there is often significant effort made to "control" AC motor starting and acceleration - both in terms of motor design as well as application.

Efficiency and Losses

Returning to the AC motor equivalent circuit of Figure 2b, we can identify three of the five basic component losses which exist in AC induction motors. The losses dissipated in the resistance of the stator and rotor windings, plus the core loss (eddy current and hysteresis losses in lamination steel) are modeled in the equivalent circuit. A fourth component loss is the friction and windage of the rotor, fan, bearings, etc. Finally, there is the "leftover’ category of stray load losses. These are losses which are a compilation of various less easily modeled losses, but are often a significant loss in highly efficient machines. The stray load losses include eddy current losses in the conductors, core losses due to flux distortion with load, etc.

Since the friction and windage and core losses are essentially independent of load, while the other losses vary as the square of load (current), the efficiency of an AC induction motor falls off precipitously at light loads (see Figure 4).

AC Induction Motor Efficiency vs. Load
Figure 4

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.

AC Induction Motor Speed Torque Curve
Figure 5

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.

AC Induction Motor Steady State Operation
Figure 6

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:

The motor counter-emf (Eg) can also be thought of as the voltage across the magnetizing reactance (xm) in the equivalent circuit of Figure 2b. Maintaining constant flux while the speed (frequency) is varied can then be seen as requiring constant ratio of Eg / f .

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 AL voltage to frequency (Vt / f), rather than Eg / f, this would result in a decreasing flux level at lower speeds (frequencies). The curves of Figure 7 demonstrate the effect of this failure to maintain the motor flux. It can be seen that the peak value of torque falls of 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 proportional to the motor flux, so increased current draw for a given load will also result from reduced flux.

Speed Torque with Contant Terminal V/Hz
Figure 7


As a means to improve the system characteristics (beyond the curves of Figure 7), controllers often compensate for the difference between Vt and Eg in order to select tile 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 =If1 x r1 (3)

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 8. 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.

Low Speed Voltage Boost
Figure 8

"Field Oriented" Control

In order to obtain better control of AC motor torque, adjustable frequency controls sometimes make use of a regulation scheme known as "field-oriented" or "vector" control. This technique is intended to control the motor flux, and thereby be able to decompose the AC motor current into "flux producing" and "torque producing" components. These current components can be treated separately (in the control), then recombined to create the actual motor phase currents. This results in a solution to the boost adjustment problem, plus provides much better control of the motor torque - which allows higher dynamic performance.

In order to accomplish field-oriented control, the controller needs to have an accurate model of the motor equivalent circuit. This model eliminates the need to set "volts-per-Hz" and "boost" as is done m scalar (non field-oriented) control schemes. The actual voltage seen at the motor is then a result of the motor equivalent circuit and the specific current being regulated by the controller.

One result of field-oriented control is that by virtue of the motor flux being maintained, the motor torque-per-amp can be held constant down to zero speed. An additional advantage results from the improved control (predictability) of motor output torque - that is, higher "dynamic" performance. This allows AC drives to serve applications requiring high "velocity loop bandwidth," such as servos.

Constant Power Operation

The discussions above regarding voltage boost and field oriented control as a means to maintain motor flux have been presented in regard to "constant torque" operation. This can also he thought of as operation "below base speed" (Figure 9).

AC Motor Speed Ranges
Figure 9

Above the speed at which the output voltage of the controller is maximum, the controller can no longer maintain constant flux as speed is increased further. This is equivalent to where a DC motor begins to be "field weakened" to achieve higher speeds. Both for AC as well as DC machines, voltage (armature voltage for DC) remains constant, so for constant load current, constant output power is available.

As the frequency supplied to an AC induction motor is increased (with voltage held constant), the "field weakening" causes a reduction in the motor peak torque capability as seen in Figure 10. This family of curves can alternatively be drawn as speed - power, rather than speed - torque curves (Figure 1). The fact that the peak power decreases as speed is increased by field weakening is the most "inherent" limitation to the "constant power speed range" of an AC drive.

AC Motor Speed/Torque Curves Basd on Field Weakening by Increasing Frequency with Constant Voltage
Figure 10

AC Motor Speed/Power Curves Basd on Field Weakening by Increasing Frequency with Constant Voltage
Figure 11

Non-Fundamental Voltages Current

Up to this point, we’ve talked about varying the voltage and frequency applied to an AC induction motor as if the voltages and currents were still sinusoidal in shape. In fact, depending on the type of adjustable frequency controller, various nonfundamental voltage and current components will exist (Figure 12).

Typical Adjustable Frequency Controller Voltage and Current Waveforms
Figure 12

The waveforms in Figure 12 are often looked at in the frequency domain (Laplace or Fourier transform). In the waveforms of Figure 12 a, b, c, d, the higher frequency components (non-fundamental components) are "harmonics’ of the fundamental frequency. That is they occur at frequencies equal to integer multiples of the fundamental frequency. For the PWM waveforms of Figure 12 e, f, the switching (carrier) frequency is usually not synchronized to the fundamental frequency. This leads to a set of non-fundamental frequency components which are not true harmonics of the fundamental frequency.

Whether or not the non-fundamental current components are harmonics of the fundamental, they do not contribute to the normal production of torque. They can, in fact, produce pulsating (ripple) torque’s which lead to other problems. The nonfundamental voltages similarly do not provide fundamental flux for the development of torque.

Additional Motor Losses

While these non-fundamental components do not provide basic torque, they do cause motor losses. Since the stator winding carries the total current (fundamental and non-fundamental components), the RMS value of the total current produces the stator winding 12R loss. The RMS value of the non-fundamental currents can range from I % of the fundamental to over 10%, depending on the controller and motor combination, as well as the operating point.

The non-fundamental components in the stator can also be "transferred" to the rotor by transformer action (induction). Depending on the specific motor design, including rotor slot details, the rotor may "see" a significant increase in its non-fundamental (non-slip frequency) current. This will then result in added rotor I2R losses.

The non-fundamental voltage harmonics will produce flux variations which are not adding to motor torque, but which do cause eddy current and hysteresis losses in the motor magnetic laminations. Again, the specific combination of controller and motor will strongly influence the magnitude of these additional losses.

Heat Dissipation

Adding to the motor heating caused by the additional losses discussed above, a "self-ventilated’ (e.g. DPG, TEFC) motor WM have less ability to dissipate these losses at lower speeds (Figure 13). For this reason, it is often appropriate to use a motor with ventilation which is speed-independent (TENV, DPFV, TEBC) when operating across a wide range of speeds. As can be discerned from Figure 13, the desirability of speed-independent cooling is typically more pronounced for larger machines.

Influence of Speed on Heat Dissipation
Figure 13

In addition to the problem of loss of dissipation at lower speeds, the use of a TEFC or DPG motor for operation at high speeds can result in large windage losses, as well as acoustic noise problems.

Switched Voltage Wavefronts

The use of semiconductor switching devices to create the adjustable frequency input to AC induction motors can result in some effects beyond the "non-fundamental components" issues. The waveforms seen in Figure 14 are expanded views of the PWM voltage of Figure 12 e. As power transistors have evolved, their ability to "turn on" quickly has also improved dramatically. This implies a high level of "dV/dt" as defined in Figure 14 b. Both this high dV/dt as well as the higher peak voltages seen by a motor applied with this type of controller need to be considered in designing motors for these applications.

Adjustable Frequency Controller Output Voltage Waveforms
Figure 14

The higher peak voltages seen at the motor terminals provide a higher dielectric stress on the motor insulation system. These peaks occur at each transition (carrier frequency for a PWM controller) on each of the motor phases. Due to the repetitive nature of this voltage, an inadequate motor insulation system (from a dielectric standpoint) will often fall in a rather short period of time (days to months).

The high dV/dt of these switched wavefronts contributes to the overshoot and ringing of the voltage at the motor terminals, but also has an interesting effect of its own. Based on Equation 4, a high dV/dt can cause a high current flow in a capacitive circuit.

I = C x dV/dt (4)

While motors are often not thought of as having a characteristic capacitance, there are both phase to ground as well as phase to phase capacitances associated with AC induction motors. This capacitive effect is "distributed’ in that the windings have various "Positions" relative to the stator core, as well as to the other phases. This causes the capacitively-coupled current flow to also be (unequally) distributed. These currents, while very short in duration, also occur at every transition (dV/dt) and can cause failure of an inadequately insulated motor in a short time.

Another result of these capacitively-coupled currents is that if a ground connection is not provided (from the motor frame), significant psuedo-square wave voltages will occur on the motor frame which can be a hazard to personnel. A proper ground connection will eliminate these voltages, but there will be fairly high frequency currents flowing to ground.

The leads connecting the controller to the motor also will experience some of the same capacitively coupled currents as the motor (phase to phase and phase to ground).


Another effect of the non-fundamental waveforms of Figure 12 on AC induction motors is the possibility to produce acoustic noise. Beyond noise due to "windage" effects, the majority of motor noise is due to components deforming in a manner which can pump air in the audible frequency range.

While all structures have characteristic sets of natural frequencies and corresponding mode shapes, some of these are of more concern. If any of the non-fundamental waveform frequencies are closely aligned with motor natural frequencies, the forces produces by these voltages and currents may excite mode shapes which could result in high audible noise at a specific frequency.

The use of motor designs which have as "sparse" as possible a set of (potentially noise producing) natural frequencies is a good starting point to reduce opportunities for noise problems. By appropriate design of the electromagnetic structure, the force distribution of the higher frequencies can also be mitigated.

Oversizing / Derating

An approach to applying AC induction motors to adjustable-h-frequency, variable-speed operation can be to oversize or derate motors for the application. This is an approach which may in simple applications be successful, but a number of potential hazards exist.

Whether or not a motor is derated / oversized will not be of any help if the insulation system is inadequate for the switched voltage wavefronts from the controller. A motor loaded to less dm full load can fail just as quickly as one fully utilized if the insulation dielectric capability is lacking.

A motor which is derated will have lower reactances, which in a CSI application may be fine, but can cause excessive current ripple in a PWM environment. This high ripple can cause IIET trips of the controller, overheating of the controller transistors, or motor overheating. Also a derated motor will have low damping as a result of the its low slip, which can cause instability problems in open loop drives, or modeling problems in a field-oriented controller.

Since AC induction motors can have a significant level of no load (magnetizing) current compared to full load current, a derated motor will often operate at a reduced power factor at the application load. This can result in higher full load current which may exceed the continuous rated current of the controller.


AC induction motors are likely to continue to be reliable sources of fixed speed rotating power. Their successful use in variable speed applications is increasing. In order to avoid unsuccessful applications, the users, controller and motor manufacturers need to communicate well. This will allow appropriate matching of the load, motor, and controller.

Document B-7097-2