2.1.6 Space Vector Pulse Width Modulation

The Space Vector Pulse Width Modulation (SVPWM) is a conventional technique to drive a two-level voltage source inverter. It provides the following advantages:

  • It improves the harmonic content of the phase voltages
  • It increases the DC bus utilization range by about 15%

The following section describes the theory behind the SVPWM.

Each of the inverter phase outputs can be in any one of the two states: zero when it is connected to the negative rail, and one when it is connected to the positive rail. Therefore, a three-phase inverter can have 23 = 8 possible states as shown in the following figure.

Figure 2-7. Space Vector Modulation

Each state represents a space vector with a magnitude and phase angle as provided in the following table:

Table 2-1. Magnitude and Phase Angle
IndexStateSpace Vector
00000
1100Umej0
2110Umejπ/3
3010Umej2π/3
4011Umejπ
5001Umej4π/3
6101Umej5π/3
71110

The states with index zero and seven are null states, because there is no line-to-line voltage across any of the phases in these states. All the states other than the null states are active states and represent a phase with a magnitude, and a phase in the space vector plane. The following figure shows these space vectors.

Figure 2-8. Space Vector Modulation

The SVPWM technique generates any space vector with a specified magnitude and angle by modulating between the two adjacent active vectors, between which the desired vector lies and the null vectors. The transitions between different states are carried out, hence only one power switch transition happens between state transition.

Equation 2-3. Desired Space Vector Calculation
UOUT=1Ts(Tk Umejkπ/3+ TlUmejlπ/3+ Tz2U0+Tz2U7)
Ts=Tk+Tl+Tz

Where:

  • Um is the maximum AC peak voltage
  • Ts is the PWM period
  • Tk and Tl are the time for which adjacent active vectors are imposed
  • U0 and U7 are null vectors for zero and seven states respectively
  • Tz is the time for which the null vectors are imposed