Three-phase sinusoidal PWM inverter

A three-phase sinusoidal PWM (SPWM) inverter is a six-switch bridge whose switching instants are fixed by comparing three sinusoidal reference waves (120° apart) with a common high-frequency triangular carrier. The output line voltages are pulse trains whose fundamental is sinusoidal and adjustable in both magnitude and frequency.

Circuit

      +----+--------+--------+
      |    |        |        |
 Vdc/2   S1 D1    S3 D3    S5 D5
  ---  |    |        |        |
  O    +-a  +--b     +--c     |
  ---  |    |        |        |
 Vdc/2   S4 D4    S6 D6    S2 D2
      |    |        |        |
      +----+--------+--------+
        a, b, c -> 3-phase load

Each leg (S1–S4, S3–S6, S5–S2) is switched in a complementary way (with a small dead time). Diodes carry reactive current back to the source.

Principle of operation

1. Three references $v_{ra}, v_{rb}, v_{rc}$ of amplitude $A_r$ and frequency $f_r$ (desired output frequency), displaced by 120°.
2. One triangular carrier $v_c$ of amplitude $A_c$ and frequency $f_c \gg f_r$.
3. Leg a: if $v_{ra} > v_c$, S1 is ON and $v_{aO} = +V_{dc}/2$; if $v_{ra} < v_c$, S4 is ON and $v_{aO} = -V_{dc}/2$. Legs b and c work the same way with $v_{rb}$, $v_{rc}$.
4. Line voltage $v_{ab} = v_{aO} - v_{bO}$ takes values $+V_{dc}$, 0, $-V_{dc}$.

 vc /\/\/\/\/\/\/\/\/\/\/\/\/   carrier
 vra  .-''-.          .-''-
     /      \        /       ref a
 ---'--------\------/--------
               '-..-'
 vaO +Vdc/2 |-| |--| |---| |--|
     -Vdc/2 | |_|  |_|   |_|
          (wide pulses near
           +peak of vra)
 vab  +Vdc  |||| ||||
         0 -------------------
      -Vdc         |||| ||||

Key quantities

• Amplitude modulation index $m_a = A_r/A_c$. For $m_a \le 1$ (linear range):

$$\begin{aligned} \hat V_{aO1} &= m_a\frac{V_{dc}}{2} \\ V_{L1,rms} &= \frac{\sqrt3}{2\sqrt2}\,m_a V_{dc} = 0.612\,m_a V_{dc} \end{aligned}$$

• Frequency modulation ratio $m_f = f_c/f_r$. It is chosen odd and a multiple of 3, so that the three phases have identical waveforms and triplen carrier harmonics cancel in the line voltages.
• Output frequency is changed by changing $f_r$; output voltage by changing $m_a$.

Harmonics

• Harmonics appear as side-bands around $m_f$, $2m_f$, $3m_f$, … (e.g. $m_f \pm 2$, $2m_f \pm 1$).
• Low-order harmonics are almost absent, so a small filter (or the load inductance itself) gives near-sinusoidal current.
• Overmodulation ($m_a > 1$): output rises less than linearly and low-order harmonics (5th, 7th) appear; at very large $m_a$ the inverter becomes a six-step (square-wave) inverter.

Advantages, drawback and uses

• Voltage and frequency control within the inverter (no variable dc link needed).
• Low harmonic distortion, small filter.
• Drawback: higher switching losses than six-step operation.
• Used in variable-speed induction motor drives (V/f control), UPS and grid-tie inverters.