To properly control an inverter, a modulation technique is needed. Many different approaches could be done to control it. Nevertheless, some parameters such as DC-link voltage utilization, produced harmonics and the final implementation with a DSP (Digital Signal Processor), should be considered before choosing which one is the most suitable for any project.

Just to clarify, here is the topology of a simple inverter:

Three different methods are presented, but the selected one for the final project is the Space Vector Modulation.

## SPWM (Sine Pulse Width Modulation)

This modulation method synthesizes a sine wave (after filtering) by comparing a sine-shaped control signal with a triangle-shaped carrier wave, as seen in the next picture. The frequency of the former is the frequency of the output signal and the frequency of the latter wave is the switching frequency.

The amplitude modulation ratio ** ma** is known as:

Having that in the normal operating system the maximum value for * ma *is 1, the DC-link voltage utilization could be discovered as:

Where Van is the amplitude obtained in each phase, having Vd as the DC-link voltage level.

## THIPWM

Should the dc-link voltage utilization be higher, a variation of the SPWM modulation can be made. The third harmonic is injected into the control signal, and it will end with higher efficiency. Having into account that the load is going to be a three-phase motor, the third harmonic will be cancelled in the windings of the motor.

Here is a pic of the signals:

## SVPWM

The Space Vector Pulse Width Modulation considers the spatial sum of 3 balanced sine waves as a rotating vector with a constant magnitude, compared with the previous methods, which treats each leg of the inverter individually. Here the switches of each leg are operated in a complementary manner, to avoid shorting the DC source. From that, the switches can have eight different states, which produces eight different space vectors. The control signals look similar to the THIPWM:

The DC-link utilization is the same as in THIPWM. Finally, the winner will be the SVPWM, as it has a high DC utilization without injecting harmonics to the signals. Therefore, it has less THD at lower voltages than the others.

## SVPWM Strategy

Here is an animation from * SwitchCraft*. I encourage you to read it after this article, as it will help you better understand the strategy, as here we are only looking at it briefly before developing the code for the DSP.

To derive the space vectors, a balanced operation is assumed:

Where the voltages are the line-to-neutral of each phase. The space vectors in the *alpha-beta* domain can be represented as:

Then, a Clarke transformation is used to change the 3 phase voltage system into the alpha-beta domain:

Now, operating with the previous two equations, the expression for the SVM is obtained:

Finally, inserting the voltages for each space vector, a look-up table of voltages is done. (Where C is *close* and O *open* for each leg of the inverter):

For the calculation of the eight space vectors, it is important to know that any reference vector within the circle (First picture), can be represented by a calculation between the two nearest space vectors and one of the zero vectors in a given time interval. Only one of the space vectors is activated at a time, so the reference vector is synthesized by the sequence of these two former vectors and the zero vector. To obtain the implementation into the DSP, the dwell times should be calculated.

Finally, the duty cycles are obtained following the next matrix expression:

Where K is three times three matrix that depends on the sector.

**That's it!** We made it through some modulation techniques and we have selected one for our purpose. In the next chapter, we will see how to simulate and build an inverter in PLECs software, the best solution to simulate and test power electronics. We are closer to the end of the project!

Thanks for reading ;)

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