# The Fundamental Theory Behind Space Vector Pulse Width Modulation

### Key Takeaways

• Space vector pulse width modulation (SV PWM) is a digital modulation technique used to generate PWM load line voltages that are equal to the reference load line voltage.

• The concept of SV PWM is that three functions of time, whose algebraic sum equals zero at any instant, can be represented in a 2-D space.

• Some advantages of SV PWM are increased fundamental output voltage, good utilization of DC input voltage, and improved harmonic performance and reduced THD values. Industrial use three-phase inverters

Three-phase inverters are abundantly used in industries for high-power and medium voltage applications. These inverters efficiently generate sinusoidal voltages from discrete voltage levels. Various switching frequency methods are employed in three-phase inverters to achieve sinusoidal output with low switching power loss, low total harmonic distortion (THD), and less computation time. Given the merits of low current ripple, reduced switching frequency, and better utilization of DC bus voltage, space vector pulse width modulation (SV PWM) is in high demand.

## Defining Space Vector Pulse Width Modulation

Pulse width modulation techniques significantly improve the performance of three-phase inverters. Generally, regular PWM techniques consider three-phase inverters as three separate stages working independently to generate a three-phase voltage. Among the various PWM techniques, space vector pulse width modulation works differently for a few reasons:

• SV PWM treats three-phase inverters as a single unit.

• SV PWM provides a digital modulation technique to generate PWM load line voltages that are typically equal to the reference load line voltage.

SV PWM integrates eight unique switching states in the three-phase inverter, and modulation is all about switching from one state to another. The switching states and switching period in SV PWM is selected using space vector transformation.

## How Does Space Vector Pulse Width Modulation Work?

SV PWM is the most widely used PWM technique in multilevel inverters. The concept of SV PWM is that three functions of time, whose algebraic sum is equal to zero at any instant, can be represented in a 2-D space. Space vector transformation converts three-phase components into 2-phase components or space vectors. The space vectors defined in the complex plane are used to implement SV PWM in the 2-D plane.

A three-phase system can be vectorially represented using the following transformation, where ax, ay, and az are the three-phase components that are analogous to phase voltages in a three-phase system: A𝛼 and A𝛽 are the space vectors that form the orthogonal 2-phase system which can be given by a rotating vector as: The three-phase system can be represented by the same rotating vector, where  By comparing the last two equations above, you can conclude that a 3-phase system is converted into a complex plane. This 3-phase to 2-phase conversion helps in the analysis of 3-phase systems as a single unit, instead of one phase at a time.

The reverse transformation from 2-phase to 3-phase is possible, demonstrated by following the equations: where ## The Advantages of SV PWM

Compared to sinusoidal PWM, space vector pulse width modulation is a much better technique because of the following advantages:

1. Increased fundamental output voltage

2. Good utilization of DC input voltage

3. Improved harmonic performance and reduced THD values

4. Easy to implement using digital processors

5. Less computation time required

Three-phase inverters will continue to be used to achieve maximum three-phase voltages with low THD, low switching loss, low current ripple, and good utilization of DC input voltage. The space vector pulse width modulation technique provides a wonderful solution. Whenever working on three-phase inverters in photovoltaic systems or electric drives, try switching from regular SPWM to SV PWM.