Cycloconverters and Matrix Converters

Because its output is a sampled version of the wanted waveform, and the sampling rate is fixed by the supply.

The sampling rate. A six-pulse bridge can change its output value only when the next thyristor becomes able to conduct — once per 60° of supply, so six times per supply cycle. On 50 Hz that is 300 opportunities per second, and no control strategy increases it.

Segments per output cycle:

\[ N = \frac{6f_s}{f_o} \]

• \( f_o = 5 \) Hz: 60 segments — an excellent staircase.
• \( f_o = 16.7 \) Hz: 18 segments — the conventional limit.
• \( f_o = 50 \) Hz: 6 segments — barely a sine.

But the visible steps are not the real problem. Because \( f_s \) and \( f_o \) are unrelated, the output contains beat components at \( |mf_s \pm nf_o| \), and some of these land below the output frequency. A machine's inductance cannot filter sub-harmonics, and its inertia cannot smooth torque pulsations at a few hertz — so they appear directly as mechanical disturbance.

As \( f_o \) rises, more of these products move into the damaging band, which is why the quoted limit varies from \( f_s/2 \) to \( f_s/3 \) depending on how much distortion the application tolerates.

How the limit is raised in practice. Use more pulses: a 12-pulse cycloconverter samples at \( 12f_s \), doubling the usable output frequency. Large mill drives are built this way, and the phase-shifting input transformer that provides the 12-pulse operation also serves as harmonic filtering.

And why the limit rarely bites. Cycloconverters drive many-pole machines at low speed, where a few hertz is exactly what is wanted. The topology and its applications co-evolved.

It comes from having no energy storage, and no modulation scheme can beat it.

The constraint. With nothing to store energy, the output at any instant must be a weighted average of the input voltages at that same instant. The output is therefore confined inside the envelope the input offers.

Why the envelope dips. The three input voltages are sinusoids 120° apart. The largest available difference at any instant varies through the cycle, falling to \( \cos30^\circ = \sqrt3/2 \) of its peak six times per cycle, where two phases cross.

To produce a constant-amplitude output, the modulator must succeed at the worst instant, so the limit is set by the envelope's minimum:

\[ q_{max} = \cos30^\circ = 0.866 \]

Could better modulation help? It already has, twice:

• Naive modulation reaches only 0.5. The obvious scheme wastes a great deal.
• Injecting a third harmonic of the input frequency and another of the output frequency — both zero-sequence, both invisible to a floating-neutral load — raises the limit to 0.866. This is the same trick as Chapter 18's, applied on both sides, and it is now standard.

Beyond that, no. Exceeding 0.866 would require producing an output larger than the instantaneous input can supply, which needs stored energy by definition. The limit is structural.

The only ways round it involve adding storage or a ratio: a step-up transformer at the input, or a hybrid topology with a small storage element — both of which forfeit the property the matrix converter existed to have.

Note the parallel with Chapter 19. A two-level inverter's linear region was the largest circle inside a hexagon. A matrix converter's is the largest circle inside the input voltage envelope. The same geometry, in a different space.

Because dead time works only if there is somewhere for the load current to go — and a matrix converter has nowhere.

How dead time works in a VSI. Turn both devices of a leg off, and the load current freewheels through one of the antiparallel diodes back into the DC link. The output voltage is briefly not commanded, but the current is never interrupted. Both safety rules are satisfied at once.

Why a matrix converter cannot do this. There is no DC link and no freewheeling path. If every switch feeding an output phase is turned off, the inductive load current has nowhere to flow, and \( v = L\,di/dt \) produces an unbounded voltage that destroys the switches within microseconds.

And overlap is equally forbidden. Turning the incoming switch on before the outgoing one is off connects two supply phases together through two switches — a line-to-line short limited only by the small input filter inductance.

So neither a gap nor an overlap is safe, and there is no simultaneous transition that avoids both.

The resolution: four-step commutation. Each bidirectional switch is two independently-controlled halves, each conducting one direction. Sequencing them separately means that at every step:

• A path exists for the actual current direction — no open circuit.
• No path exists that would let current flow between two inputs — no short.

The dependency this creates. The sequence depends on knowing the current's direction, and near a zero crossing that is exactly what noise and sensor offset make uncertain. Practical converters use hybrid schemes — current direction where the current is large, voltage direction where it is small — plus a clamp circuit to catch the energy if a commutation does fail.

A slight irony worth noting: that clamp contains a capacitor. The topology whose selling point is having no capacitor cannot be built without a small one.

Probably not, and the arithmetic shows why quickly.

Put the dead time in context. At 5 Hz the output period is 200 ms, and the current passes through zero twice per cycle. So:

\[ \frac{2 \times 4\ \text{ms}}{200\ \text{ms}} = 4\% \text{ of the waveform held at zero} \]

What that does to the current waveform. A flat spot at each zero crossing turns a sine into something closer to a trapezoid with a notch. Symmetric flat spots produce predominantly third-harmonic distortion — at 15 Hz for a 5 Hz fundamental.

Why 15 Hz is the wrong frequency to have. A gearless mill drive's mechanical system — the ring gear, the mill shell, the foundations — has resonances in the single- and low-double-digit hertz range. Exciting one produces audible drumming, measurable vibration and fatigue in couplings.

And the effect is worst exactly where it matters. The current reversal happens when the torque changes direction, which on a reversing mill is during the controlled part of the cycle — so the disturbance lands where torque quality is most needed.

Three responses:

1. Switch to circulating-current mode. Both bridges gated, current reverses instantly through the reactors, no dead time at all. This is why fast reversing mills use it despite the reactors and the extra loss.
2. Reduce the dead time — but only so far. It is set by the certainty required that the outgoing bridge has stopped, plus \( t_q \), plus margin. Cutting it risks a line-to-line short through both bridges.
3. Accept it if the drive is unidirectional and reversals are rare. A ball mill turning steadily one way crosses zero only at start and stop, so 4 ms twice a day is irrelevant.

The decision is entirely about how often the current reverses, which is a property of the application rather than the converter.

Because of one incompatibility that outweighs several advantages.

The decisive problem: 0.866. A 400 V motor fed from a 400 V supply receives 346 V, so it runs at 86.6% flux and 86.6% torque. Fixing this requires a larger motor, a special 346 V machine, a higher supply, or a transformer — and every one of them turns a drive replacement into a system project. Industrial customers replace drives; they do not replace motors.

The founding argument has weakened. The topology was invented because electrolytic capacitors fail. Modern film capacitors have essentially unlimited life, and modern electrolytics are far better than 1980s parts. The problem has substantially solved itself.

No ride-through, which factories mind about. A DC link stores enough energy to survive supply dips of tens of milliseconds — common on real industrial networks. A matrix converter has no stored energy, so it trips. An unplanned process stop costs far more than a year of improved power factor.

Volume economics. Back-to-back drives are made in millions, so their devices and controllers are commodities. A matrix converter needs 36 devices, custom modules and bespoke FPGA commutation logic. That cost gap is a manufacturing-volume gap and does not close by itself.

Where it genuinely wins, and is sold:

• Aerospace — mass and volume dominate, and −55 °C to +85 °C cycling destroys electrolytics.
• Downhole and high-temperature applications where no capacitor survives at all.
• 20-year maintenance-free requirements.
• Regenerative drives that would need an active front end anyway, which erases much of the back-to-back cost advantage.

The general lesson. Superiority in several dimensions loses to a single hard constraint in another — especially when that constraint is compatibility with an installed base. This pattern recurs throughout power electronics, and recognising it is worth as much as any circuit analysis.

Because each survives only where a constraint that would defeat the standard drive happens to dominate — and those constraints sit at opposite ends of the scale.

At 20 MW, the constraint is device ratings.

• No IGBT blocks 10 kV, so a back-to-back drive needs devices in series with all the timing difficulty that brings.
• Thyristors handle 8 kV and 5 kA in one device, and a cycloconverter uses them naturally-commutated, so switching loss is negligible.
• The load is a many-pole machine at 10 rpm, needing only a few hertz — so the \( f_s/3 \) limit is not a limit at all.
• Four-quadrant operation comes free from the dual-converter structure.

At 50 kW in an aircraft, the constraint is mass and temperature.

• A DC link capacitor bank is the largest and heaviest part of a back-to-back drive, and the least able to survive the thermal cycling.
• The motor is purpose-designed, so the 0.866 limit costs nothing — it is simply wound for 346 V.
• Regeneration is inherent, and an actuator regenerates constantly.
• Near-unity input power factor matters on limited aircraft generation.

In between — from a few kilowatts to a few megawatts — no constraint dominates. Devices are available, standard motors must be driven at rated voltage, ride-through is valued, and volume pricing rules. The back-to-back drive wins every one of those, so it takes the entire middle of the market.

The pattern generalises, and it is worth carrying beyond this chapter: a specialised topology survives where a single constraint is extreme enough to override general-purpose economics. Ask which constraint is hardest before comparing converters on their merits.