Cycloconverters and Matrix Converters

The principle. A phase-controlled converter produces \(V_{dc0}\cos\alpha\) on average, and Set 12 established that the average can be made anything from \(+V_{dc0}\) to \(-V_{dc0}\). If \(\alpha\) is varied slowly and sinusoidally rather than held constant, the average output traces a sinusoid:

The converter is doing nothing new — it is the same bridge, with a firing angle that moves. What has changed is that the output average is now a function of time rather than a constant.

The cosine modulation law. To make the output a clean sinusoid of amplitude \(rV_{dc0}\), the firing angle must satisfy:

Which is why it is called cosine-wave-crossing control: the firing instant is found by intersecting a cosine timing wave, derived from the supply, with the output reference. The inverse cosine is performed by the crossing itself rather than by any computation — an elegance that mattered greatly in the analogue era.

The output magnitude:

At \(r = 1\) the firing angle would have to reach 0 and 180° exactly, which the extinction-angle limit of Set 14 forbids. Practical designs use \(r \le 0.8\), giving about 117 V — roughly half the supply. That is the cycloconverter's characteristic penalty.

The frequency limit. Each output half cycle is assembled from a whole number of input half cycles:

Or, for a six-pulse bridge, six segments per output half cycle. As \(f_o\) rises the count falls:

Below about six segments the staircase can no longer approximate a sinusoid, and the output carries large subharmonic and interharmonic content. Hence the practical rule \(f_o \lesssim f_i/3\) — and it is a hard structural limit, not a design choice.

The two operating modes, exactly as in the dual converter of Set 16:

The same trade as Set 16, Problems 3 and 4, and the same conclusion: a drive that must cross zero current smoothly uses the circulating-current mode and pays for the reactor. Since a cycloconverter output crosses zero twice per output cycle — many times per second — the distortion of the blocked mode is continuous rather than occasional.

The structure. Each output phase needs a full dual converter — two six-pulse bridges in anti-parallel:

Thirty-six devices, each with its own gate drive, snubber and protection — against six for a voltage source inverter of comparable rating. Device count alone explains why cycloconverters are found only where their specific advantages are decisive.

The maximum output:

So a 415 V supply yields at most about a 550 V line output — but at a third of the frequency. A machine designed for that combination needs many poles or a low base speed, which is exactly the application: slow, high-torque drives.

The input power factor problem. Each bridge is a phase-controlled converter, and Set 12 established that its displacement factor is \(\cos\alpha\):

Averaged over the output cycle, the firing angle spends most of its time far from zero — so the input displacement factor is poor even when the converter is delivering full output. It gets worse as \(r\) falls, exactly as a phase-controlled rectifier does at low output.

And the crucial point:

Even driving a load that returns power — a machine regenerating — the converter still draws lagging reactive current from the supply, because the reactive demand comes from the phase control itself rather than from the load. A cycloconverter can neither correct nor leading-compensate, and large installations always include substantial capacitor banks or a static VAr compensator.

The complete picture:

Rows six and seven are why it survives. Line-commutated thyristors are the most robust, highest-rated switching devices made — a single press-pack device handles thousands of amps at kilovolts — and four-quadrant operation comes free from the dual-converter structure. At 10 MW those two advantages outweigh everything above them.

The interharmonic problem deserves separate mention:

Because the modulation frequency is unrelated to the supply frequency, the input current contains components at frequencies that are not harmonics at all. These are far harder to filter than harmonics — a tuned filter has nothing fixed to tune to — and they can excite mechanical resonances in nearby turbo-generators. Large cycloconverter installations require careful system studies.

The structure. Nine bidirectional switches connect every input phase to every output phase:

Each output phase can be connected to any input phase at any instant, so the output is assembled from pieces of the three inputs at the switching frequency — typically several kilohertz, against the cycloconverter's line frequency. That alone removes the \(f_i/3\) limit: a matrix converter can produce any output frequency, above or below the input.

The voltage ceiling. The output must at every instant be constructible from the instantaneous input voltages, and those are themselves varying:

Without zero-sequence injection the limit is only 0.5; adding a common component to all three outputs — the same freedom Sets 26 to 28 exploited — raises it to 0.866. And 0.866 is absolute: it is the ratio of the largest inscribed sinusoid to the input envelope, and no modulation scheme exceeds it.

Compare with the alternative:

The rectifier-plus-inverter chain reaches the full supply voltage because the DC link sits at the input peak — a capacitor stores energy from the peaks and releases it continuously. The matrix converter has no storage, so it can only ever draw what the input is providing at that instant.

What that 13.4% costs in practice. A standard 415 V motor cannot be driven at full voltage:

This is the single largest reason the matrix converter has never displaced the back-to-back VSC despite thirty years of research. Every other advantage is real; none of them compensates for being unable to drive a standard motor at rated voltage.

What it does gain:

The first row is the strongest argument. Set 23's adapter and every drive in Part 4 relied on a DC link capacitor, and electrolytic capacitors are the shortest-lived component in any converter. Removing them entirely is worth a great deal in aerospace, downhole and other high-temperature or high-reliability applications — which is precisely where matrix converters are actually used.

A subtlety about the input current. Without storage, instantaneous input power must equal instantaneous output power:

For balanced three-phase in and out, both are constant, so this is satisfiable — which is why a three-phase matrix converter works at all. But an unbalanced input or output makes \(p(t)\) pulsate, and with no capacitor to absorb the difference, the imbalance is transferred straight through to the other side. A matrix converter is unusually sensitive to supply unbalance.

The two rules, and why they conflict:

Rule 1 forbids overlap. Rule 2 forbids a gap. Every other converter in this book escapes by having a third path: a VSI has anti-parallel diodes to freewheel into, a CSI has an overlap that is harmless because the link is a current source. A matrix converter has neither.

Why dead time fails. Insert a gap between turning one switch off and the next on, as in Set 7:

The load inductance generates whatever voltage it needs to keep the current flowing, and with no path available that voltage appears across the switches and destroys them. Overlap instead, and two input phases are shorted through the switches with only the source inductance limiting the current. Neither option is survivable.

The resolution: exploit the current direction. A bidirectional switch is two devices with opposite orientations, and each conducts current in only one direction:

So if the current direction is known, the two halves of each bidirectional switch can be controlled independently — and a sequence exists that never opens the conducting path and never closes a shorting one. That is four-step commutation.

The sequence, commutating from input phase A to phase B with \(i_o > 0\):

At no point is the load open, and at no point can current circulate between A and B — because whichever pair is on can only conduct one way, and the natural voltage difference determines which way that is. The commutation happens by itself between steps 2 and 3.

The timing overhead:

Four per cent, against the 1–2% a VSI's dead time costs — and it produces the same kind of output voltage error as Set 25, Problem 5, requiring the same kind of compensation. Raising the switching frequency makes it proportionally worse, so a matrix converter cannot switch as fast as a VSI of the same rating.

What the method demands:

The first row is the practical Achilles heel, and it is the same problem dead-time compensation had in Set 25: near the current zero the sign is uncertain, noise makes it flicker, and a wrong decision either shorts the supply or opens the load. Voltage-based commutation has the mirror problem near the input voltage crossings, so robust implementations use both and switch between them.

The fundamental division. Direct converters have no energy storage; indirect ones do:

That single distinction explains most of what follows. Storage decouples the input from the output — the same argument that Set 17 made for the chopper drive — and buys voltage boost, independent control of both sides, and ride-through. Its cost is the capacitor.

The comparison:

Read the two device rows together. The cycloconverter's power ceiling comes from what it is built from:

No IGBT approaches that rating, and no forced commutation circuit is needed because the supply does the commutating. At 20 MW there is simply no self-commutated alternative of comparable robustness, which is why the cycloconverter survives in an application niche rather than being obsolete.

Where each is actually installed:

The last row covers the overwhelming majority. A diode bridge, a capacitor and a six-switch inverter reach the full supply voltage, handle any frequency, and cost less than anything else — and adding an active front end buys sinusoidal input current and regeneration when needed.

Why the matrix converter never displaced the VSC. Three reasons, in order:

The third is easily overlooked. A DC link capacitor holds the converter up through a short supply dip — the hold-up requirement Set 19 sized a bulk capacitor for. A matrix converter has no stored energy at all, so a one-cycle supply interruption stops it dead. For industrial equipment that is often disqualifying on its own.

The application. A gearless mill motor is a very large, many-poled synchronous machine wrapped directly around the mill shell:

No gearbox, no pinion, no alignment problem — and an electrical requirement that is unusual in every respect: five megawatts at ten hertz, with full torque needed from standstill.

Check the frequency limit first:

Comfortably inside the cycloconverter's range, with about ten input segments per output half cycle at a six-pulse configuration. The waveform will be good, which is the opposite of the usual situation — this application sits in the cycloconverter's sweet spot rather than at its limit.

Size the transformer secondary. The peak phase voltage required:

With a modulation ratio limited to \(r = 0.8\) for commutation margin:

So a 2.3 kV secondary — and since each of the six bridges needs its own isolated supply to avoid shorting the phases together, the transformer has six secondaries. That transformer is a major item, and it is also where the 12-pulse arrangement is implemented for harmonic cancellation.

The motor current:

Six hundred amps RMS per device, at 2.3 kV — well within a single press-pack thyristor's capability, with no series or parallel connection needed. That is the point: the device count is 36, but every one of them is a single, standard, extremely rugged component.

Why every alternative fails:

The fifth row is where the technology is moving. A load-commutated current source inverter using the same thyristors handles the same power with fewer devices and a better input power factor — and modern installations increasingly choose it. But the cycloconverter's four-quadrant operation and its excellent low-frequency torque remain hard to beat for a mill that must be inched into position and reversed.

What the installation must also include:

The first row is typically 40–60% of the drive rating in capacitors — two or three megavars of compensation for a five-megawatt drive. That auxiliary plant is a substantial fraction of the installation cost and is the price of line commutation.