# How does carrier frequency and pulse width modulation in a VFD work together to control AC motor speed?

There is a lot of online information about this but there is also a lot of contradictory information. What is carrier frequency exactly and does it stay the same or does it vary? I understand the concept of PWM but if carrier frequency stays constant, then how does an AC motor see varying degrees of pulse width in order to operate on a simulated AC signal? I'm just trying to find the truth, in detail, about the relationship between carrier frequency, the speed reference signal, and PWM in order to control an AC motor.

• Initially as you are trying to gain understanding, ignore carrier frequency. It does not need to be varied to control the motor, and some VFD's do not vary carrier frequency. The essence of it is that the EFFECTIVE voltage applied, say from L1 to L2 of the motor, is Vpeak * D, where Vpeak is the amplitude of the voltage, and D is the duty cycle. Vpeak will be relatively constant (but may be either positive or negative) and duty cycle will be varied to achieve EFFECTIVE sinusoidal control. Or some approximation of sinusoidal. – mkeith Aug 19 '18 at 5:59
• Bear with me as I stumble through this. As you suggest, I will ignore carrier frequency for the time being. I follow everything you are saying but I'm looking for specifics as to how this is all done. Vpeak is your DC bus voltage, correct? How are the duty cycle variations achieved? Is there a direct correlation between duty cycle and the rate of IGBT switching? – Mike Aug 19 '18 at 6:11
• So L1 is connected to a half-bridge. And L2 is connected to a half bridge. During the time that the L1 to L2 voltage is positive, L2 will be pinned to GND by its bridge (low side IGBT on). Meanwhile, the L1 bridge will be varied between high and low. The percentage of time that L1 is high is the duty cycle, D. It starts off low, eventually reaches close to 100% at the peak of the sinusoid, and then starts tapering down toward zero again. When it crosses zero, the situation reverses. L1 will be pinned to GND and L2 will be duty cycled to achieve control. This is over-simplified version. – mkeith Aug 19 '18 at 6:20
• @Mike, look into Class D amplifiers, which share a lot of principles with VFDs. – Nick Alexeev Aug 19 '18 at 6:21
• Thank you, gentlemen, for your swift responses. I need a little time to digest what you have given me to look over. I am an electrician by trade, but my electronics memory is a little rusty. – Mike Aug 19 '18 at 6:46

## 1 Answer

In a VFD, the carrier frequency is the frequency of switching the power devices. To start with a simple example, consider the H bridge circuit shown below. The four transistors can be switched sequentially to produce a crude approximation of a sine wave. There are two on/off switching cycles required to produce one cycle of the output waveform, so the switching frequency is twice the output frequency. If the output frequency changes the carrier frequency must change proportionally.

To control an induction motor, the voltage must be controlled to maintain a relatively constant ratio of voltage to frequency. To do that with pulse width modulation (PWM), one or more switching events must be added to the scheme as shown below. Adding PWM to control the voltage with this scheme makes the switching frequency six times the output frequency. The switching frequency is usually selected to be much more than six times the output frequency to reduce the harmonic content and provide a better quality effective output waveform. Various manufacturers describe their control schemes in different ways. In one way or another, the waveform required to produce the desired motor performance is calculated and the devices are switched accordingly within limits that the design has put on the switching frequency.

It is possible to use a higher number of modulated pulses at lower output frequencies in comparison to the number used at higher output frequencies. In that case, the switching frequency as a multiple of output frequency could rise and fall as the output frequency increases rather than just rising in proportion to output frequency. There are other factors in the overall control scheme and VFD design that add further complexity to the relationship between output frequency and switching frequency.

The following diagrams shows two possible PWM designs based on a triangle carrier wave intercepting a sinusoid reverence wave. These show how a variable frequency with proportional variable voltage PWM sine wave simulation can be implemented with either a carrier frequency that is a multiple pf the sine frequency or with a constant carrier frequency.

Note that the switching rate is only the count of on/off and off/on transitions per second. The "on" duration and "off" duration can be adjusted over a wide range without changing the switching frequency.

Various aspects of the “triangulation method” pulse width modulation schemes for VFDs are described in:

J. Zubek, A. Abbondanti and C. J. Norby, "Pulsewidth Modulated Inverter Motor Drives with Improved Modulation," in IEEE Transactions on Industry Applications, vol. IA-11, no. 6, pp. 695-703, Nov. 1975. doi: 10.1109/TIA.1975.349357

That paper cites:

K. Heintze et al., “Pulse width modulating static inverters for the speed control of induction motors,” Siemens-Z., vol. 45 (3), pp. 154-161, 1971.

and:

A. Schonung and H. Stemmler, "Static frequency changers with subharmonic control in conjunction with reversible variable speed ac drives," Brown-Boveri Review, pp. 555-577, Aug./Sept. 1964.

The triangulation method may have been used to some extent before microprocessors were used in VFDs. In many discussions, the triangle carrier wave is used to illustrate the basic principle rather than to describe the detailed implementation. With microprocessor control, it is possible to simulate sine waves with variable voltage and frequency in many ways with a fixed or variable switching frequency. Many schemes have been described and used. It is difficult to determine which schemes are popular today.

There may be schemes that, in effect, change the both the number and width of PWM pulses for every cycle of output waveform that is produced. In most modern VFD designs, the processor constantly recalculates the required output voltage and frequency.

• Charles, thank you for the thorough explanation. During my research on this, many sites made it sound as though carrier frequency always stayed constant. This confused me because I could not understand how PWM could take place if the power switching devices are always switching at the same rate all the time. It sounds like your explanation defies this and makes sense to me. Or am I missing something? – Mike Aug 22 '18 at 9:10
• Here is a link that I found to be very good. However, there is an image with carrier frequency shown to be steady in time and amplitude. This is where I get stumped. If carrier frequency is the frequency of the power switching devices, which sends the DC pulses to the motor, how is the sine wave simulated if the carrier frequency is shown to be constant like it is shown in the link? I have seen an image similar to this at several different websites. machinedesign.com/motorsdrives/… – Mike Aug 24 '18 at 6:01
• Deleted comments and added to answer. – Charles Cowie Aug 26 '18 at 14:29