Inverters, PWM and AC Voltage Controllers

An inverter turns DC into AC of adjustable voltage and frequency, as needed for motor drives, UPS and solar systems. AC voltage controllers change only the RMS voltage.

Single-phase inverters

Half bridge (output ±V_dc/2) and full bridge (output ±V_dc).

For a full-bridge square-wave output of amplitude V_dc:

• Fundamental peak = 4V_dc/π; fundamental RMS = 4V_dc/(π√2) = 0.9 V_dc.
• Only odd harmonics; the nth harmonic has amplitude 4V_dc/(nπ).
• Quasi-square (phase-shift) control with pulse width 2d: V_n = (4V_dc/(nπ)) sin(n d). The 3rd harmonic is eliminated with a pulse width of 120°.

Three-phase bridge inverter

• 180° conduction: each switch conducts for half a cycle, three switches on at a time. Line voltage RMS = 0.816 V_dc; phase voltage is a six-step wave.
• 120° conduction: two switches on at a time.
• Triplen harmonics are absent from the line voltages.

Pulse-width modulation

• Sinusoidal PWM: compare a sine reference with a triangular carrier.
• Modulation index m_a = V_ref,peak/V_carrier,peak. For m_a ≤ 1 (linear region), single-phase full-bridge fundamental peak = m_a V_dc; three-phase line-to-line RMS fundamental = 0.612 m_a V_dc.
• Frequency modulation ratio m_f = f_carrier/f_ref; harmonics appear around multiples of m_f, so a high carrier frequency makes them easy to filter.
• Space vector PWM uses the DC bus about 15% better.

Current and voltage source inverters

VSI (stiff DC voltage, capacitor) is most common; CSI (stiff DC current, large inductor) suits some large drives.

AC voltage controllers and cycloconverters

• Phase control of an AC supply with back-to-back SCRs or a TRIAC (lamp dimmers, fan regulators). Resistive load RMS output: V_o = V_s √((1/π)(π − α + sin 2α/2)).
• Integral cycle control: on for n cycles out of m: V_o = V_s √(n/m) (heaters).
• Cycloconverters convert AC directly to lower-frequency AC (large slow motors).

Worked example

A full-bridge inverter has V_dc = 200 V with square-wave output.

• Fundamental RMS = 4 × 200/(π√2) = 180.1 V.

Practice