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MC-E2 · Inverter drive basics

The Inverter and PWM Drive

An inverter makes AC of any magnitude and frequency from a single DC source. Pin down how adjusting the on-time fraction of fast switching makes the average a sine wave.

Vary the on-time fraction sinusoidally — the average voltage is…

An inverter ties the output terminal to +Vdc or -Vdc, switching very fast. Left raw it is a coarse square wave, but the switching is so fast that the motor’s inductance filters out the high frequency and leaves only the average. Use the modulation-index slider to vary the on-time fraction sinusoidally. What shape is the average (gold) threading through the coarse pulses?

Modulation index mm = 0.80
Slide for continuous modulation index. Copper is the switched output, gold is the average (fundamental).
Fundamental voltage and V/f
V1 = m·(Vdc/2) = 0.40 Vdc · V/f ∝ m/f
The average is not a square wave. The square wave is the raw, unfiltered switching output. What we are after is the smooth curve those pulses trace on average.
Average of sinusoidal duty?
Misaligned

The inverter switches DC into AC

A three-phase inverter ties semiconductor switches to a DC bus in two-per-leg, three legs. Each leg ties the output to +Vdc when its upper switch is on and -Vdc when the lower is on. Running the three legs 120° apart gives three-phase AC. Switched just once each it would be a coarse square wave, but in practice it switches very fast, at several kilohertz. The inductance of the motor winding filters out this high switching-frequency component, so only the average remains in the current.

ObserveVout = ×Vdc
The inverter output is either +Vdc or -Vdc.
ChooseVavg = (2d - 1) ?
The average voltage is set by the duty.

PWM averages into a sine

The fraction of a switching period the output stays at +Vdc is the duty. A duty of one half averages to zero; a larger duty averages toward +, a smaller toward -. Varying this duty sinusoidally over one output period makes the average voltage trace a sine. The way to set the duty is pulse-width modulation (PWM), usually made by comparing a reference sine to a fast triangular carrier. The reference sine’s amplitude is the modulation index m and sets the output voltage; its frequency sets the output frequency. The two are independent, so voltage and frequency are held separately.

Fill inV1 = m ?
The output voltage magnitude is set by the modulation index.
On your ownVf const → m ?
To keep the flux, make the modulation index proportional to frequency.

One inverter runs every machine

The V/f control of an induction machine is making the modulation index m proportional to the output frequency to keep the flux constant; the variable speed of synchronous machines and servos and the electronic commutation of BLDC are all this inverter shaping voltage and frequency to a command or the rotor position. Fast switching brings switching loss and harmonics, but these are tamed by raising the carrier frequency and refining the modulation, such as space-vector PWM. What the DC machine’s commutator did with a mechanical contact, the inverter generalizes with semiconductor switches. Every machine of this subject, begun at the magnetic circuit, is in the end controlled by voltage and frequency on this one device.

Back to the first screen

Varying the on-time fraction sinusoidally made the average trace a sine. The inverter only switches the output fast between +Vdc and -Vdc, but the motor’s inductance filters the high frequency and leaves the average, so modulating the duty sinusoidally makes that average a smooth sine. The reference sine’s amplitude (the modulation index) sets the voltage and its frequency sets the output frequency, so a single DC source holds voltage and frequency separately. The V/f of induction machines, the variable speed of synchronous machines and the electronic commutation of BLDC all run on this one device. Beginning from a single strand of flux in the magnetic circuit, through transformers and rotating machines, the story of electrical machines closes where semiconductor switches shape voltage and frequency.

The inverter drive: semiconductor switches on a DC bus switch the output fast between +Vdc and -Vdc, and the motor inductance filters the high frequency. Modulating the on-time fraction (duty) sinusoidally (PWM) makes the average voltage a sine. The modulation index m sets the voltage and the reference frequency sets the output frequency, separately (VVVF). Induction V/f is making m ∝ f to keep the flux.
Closing electrical machines

From the flux and reluctance of the magnetic circuit (A), through the transformer that trades that flux (A), the DC machine that commutes rotation into DC (B), the induction machine that turns with a slip in a rotating field (C), the synchronous machine that binds speed and frequency into one (D), to the special machines and inverter shaped by permanent magnets and semiconductor switches (E) — here we are. Every machine was one thread: it makes force from the interaction of flux and current, and governs that force through commutation and control. The map these twenty units drew will be an eye that, before any rotating machine, asks where the flux comes from, where the current flows, and what controls them.