Indirect Matrix Converter

Introduction

An indirect matrix converter (IMC) is a direct AC-to-AC converter — it turns a fixed three-phase supply into a three-phase output of adjustable voltage and frequency — but it is arranged so that the single job is split into two clear stages: a rectifier stage at the input and an inverter stage at the output, joined by a DC link.

The twist is in the word virtual. Unlike an ordinary variable-frequency drive, the DC link here has no capacitor and no inductor — no energy-storage element at all. It is only a pair of rails that exist as a convenient point of view. Power still flows straight from input to output through the switches, so the instantaneous input power always equals the instantaneous output power, exactly as in the direct matrix converter.

Why bother splitting it up? Because once the converter is seen as a rectifier feeding an inverter, the huge, well-proven toolbox of standard PWM for rectifiers and inverters can be applied to each stage on its own. That makes the control easier to understand and design, while keeping every benefit of the matrix converter: no bulky capacitor, bidirectional power flow and sinusoidal input and output currents.

Block Diagram

At block level the indirect matrix converter reads left to right as four things. The three-phase supply passes through a small input filter, then into a virtual rectifier (a current-source rectifier built from switches S1–S6). Its output is the virtual DC-link voltage v_pn — a pulsating but always-positive voltage on two rails that hold no stored energy. That feeds a virtual inverter (a voltage-source inverter built from switches S7–S12), which produces the variable-voltage, variable-frequency output. A single modulation and control unit coordinates both stages.

Circuit Diagram

The power circuit is shown below, drawn as the indirect virtual DC-link equivalent of a three-phase matrix converter. It has two switch groups sharing a common pair of DC rails.

Reading the circuit from left to right:

• The three input phases a, b, c come from the balanced supply on the left (shown in star with neutral N), usually through a small input filter.
• The rectifier stage is a current-source rectifier made of six switches S1–S6 in three legs — one leg per input phase. In each leg the upper switch (S1, S3, S5) can connect its phase to the positive rail and the lower switch (S2, S4, S6) to the negative rail. These six are bidirectional switches, because with no DC-link capacitor the rectifier must block voltage of either polarity.
• The two rails in the middle are the virtual DC link. Crucially there is no capacitor and no inductor here — the crossed-out symbol marks the storage element that a normal drive would have but this converter deliberately omits. The rail-to-rail voltage is the virtual DC-link voltage v_pn.
• The inverter stage is an ordinary voltage-source inverter of six switches S7–S12 in three half-bridge legs. Each leg’s midpoint is one output phase, so S7/S8 form output A, S9/S10 form B and S11/S12 form C. Being a normal inverter, each of these is a single IGBT with one anti-parallel diode.
• The three output phases A, B, C feed the three-phase load (typically an AC motor, shown as M).

Two kinds of switch

The two insets under the circuit show why the stages use different devices. A rectifier switch must carry current and block voltage in both directions, so it is a bidirectional switch — typically two IGBTs back-to-back (common emitter) with two anti-parallel diodes. An inverter switch sits on a DC rail whose polarity never reverses, so an ordinary single IGBT with one anti-parallel diode is enough, exactly as in any voltage-source inverter.

Working Principle

The idea behind the indirect matrix converter is decoupling. Instead of solving for all switches at once, the control handles the input side and the output side separately and then multiplies the two solutions together.

Rectifier side. At every instant the rectifier picks two input phases — the most positive and the most negative — and connects them to the two DC rails. This does two useful things at once: it makes the virtual DC-link voltage v_pn as large and as positive as possible, and, by choosing how long to use each pair over a switching period, it shapes the input current so that it is sinusoidal and (if wanted) in phase with the input voltage for near-unity power factor.

Inverter side. The voltage-source inverter then chops that DC-link voltage with ordinary pulse-width modulation. By varying the fraction of each switching period that each output is tied to the positive or negative rail, it builds three output phase voltages whose local averages trace smooth sine waves — at whatever amplitude and frequency the load needs, independent of the supply.

Because the switching is far faster than either the supply or the output frequency, the load’s inductance smooths the chopped voltage into clean sinusoidal currents. The rectifier and inverter are timed so that the inverter never draws current from the rails during the brief moments the rectifier is changing over (a zero-current instant), which makes commutation of the input stage simple and lossless — a practical bonus of the indirect arrangement.

Modes of Operation (Switching States)

Like any matrix converter, the indirect one does not have "modes" in the sense a chopper does; it steps rapidly between allowed switching states. The neat part of the indirect view is that the states of the two stages can be listed separately. (These are described in words only; the circuit itself is the one in Figure 2.)

Rectifier-stage states

The rectifier obeys one hard rule: the two DC rails must always have a current path, and two input phases must never be short-circuited. That leaves it connecting the positive rail to one input phase and the negative rail to a different one. Counting the useful combinations gives nine allowed states: six "active" states (each connects a definite pair of input lines across the DC link, e.g. a to +rail and b to −rail) and three "zero" states (both rails tied to the same phase, so the DC-link voltage collapses to zero and the input current rests). Blending the six active states over a switching period is what shapes a sinusoidal input current.

Inverter-stage states

The inverter is an ordinary three-leg voltage-source bridge, so it obeys the usual rule: the two switches in a leg are complementary (never both on — that would short the DC link; never both off — that would open the inductive output). With three legs each choosing "top" or "bottom", there are 2 × 2 × 2 = eight allowed states: six "active" states that apply a real voltage to the load and two "zero" states (all three outputs on the same rail) that apply zero line-to-line voltage.

Combining the two stages

In each switching period the modulator picks a rectifier state (which sets the DC-link voltage and the input-current direction) and an inverter state (which sets the output voltage), and dwells in each combination for a calculated time. The overall behaviour is the product of the two: the input side is shaped by the rectifier states while the output side is shaped by the inverter states. This product is exactly why standard space-vector PWM for a rectifier and for an inverter can be reused — the difficult all-at-once problem of the direct converter is replaced by two easy, familiar ones.

Waveforms & Explanation

The clearest way to understand the indirect matrix converter is to follow the voltage across the two stages. Start with the virtual DC-link voltage. The top panel is the three input phase voltages; the bottom panel is v_pn, formed at every instant as the largest minus the smallest input voltage — because the rectifier always ties the most-positive input to the +rail and the most-negative to the −rail.

• It never goes negative. Because the rectifier always chooses the most-positive and most-negative phases, v_pn is a positive, pulsating voltage — just what the inverter needs on its rails.
• It ripples six times per input cycle. As the "most positive" and "most negative" roles hand over between phases, v_pn traces the upper envelope of the line-to-line voltages, dipping to 1.5 and peaking near √3 ≈ 1.73 times the phase peak.
• There is no smoothing capacitor. A normal drive would flatten this ripple with a big capacitor; here the inverter’s modulation is made to account for the ripple instead.

Next, the inverter output. The voltage-source inverter chops the DC link with PWM so that each output phase voltage switches between the two rails; its local average (dashed) follows the desired sine at the chosen output frequency — here deliberately drawn at a lower 30 Hz so you can see the output frequency is set by the modulation, not by the 50 Hz supply:

Because the load is inductive it filters those fast voltage steps into smooth currents. The three output line currents come out as clean, balanced sine waves at the chosen output frequency, 120° apart, with only a small switching ripple:

Finally, the payoff on the input side. Because the rectifier stage actively shapes the current it draws, the three input line currents are also sinusoidal — at the 50 Hz supply frequency and, if the control chooses, in phase with the input voltages for near-unity power factor:

Transfer Ratio & Modulation

The link between input and output is captured by splitting the converter’s transfer function into a rectifier part and an inverter part. If the rectifier’s switching pattern is written as a matrix R (which input lines connect to the two rails, and for how long) and the inverter’s pattern as a matrix I (which rail each output connects to, and for how long), then the whole converter is simply their product:

This is the mathematical statement of the decoupling: one matrix takes care of the DC-link voltage and the input current, the other takes care of the output voltage, and multiplying them recreates the direct connection between input and output.

The 0.866 voltage transfer ratio

Because the converter only ever connects input to output — it never boosts — the output voltage is always smaller than the input. For undistorted sinusoidal operation the largest ratio of output to input voltage magnitude is exactly the same limit as the direct matrix converter:

This ceiling comes from the topology, not the control method, so the indirect and direct matrix converters share it. In return you get sinusoidal input and output currents, adjustable input power factor and full four-quadrant (bidirectional) power flow — all with no DC-link capacitor.

Direct vs Indirect Matrix Converter

Both converters do the same thing and share the 0.866 ceiling; they differ in how the switches are arranged and controlled.

Advantages & Disadvantages

Advantages

• No DC-link capacitor. Like the direct converter, it removes the bulky, failure-prone electrolytic capacitor, giving a compact, long-life converter.
• Simpler, well-understood control. Decoupling into a rectifier and an inverter lets standard space-vector PWM be applied to each stage separately.
• Easier, safer commutation. The input stage can be switched while the DC-link current is zero, which largely removes the difficult multi-step commutation of the direct converter.
• Sinusoidal input and output currents, adjustable input power factor and full bidirectional (four-quadrant) power flow.

Disadvantages

• Voltage transfer ratio still limited to 0.866 — the output cannot reach the full input voltage.
• Similar device count to the direct converter (twelve switches; the six rectifier switches are bidirectional), so it is not necessarily simpler in hardware.
• Pulsating virtual DC link. With no smoothing capacitor, the inverter modulation must actively compensate for the six-times ripple in v_pn.
• Sensitive to supply disturbances and usually needs a protective clamp circuit, since there is no capacitor to ride through dips or absorb spikes.

Applications

• Compact AC motor drives where the absence of a DC-link capacitor saves size, weight and service cost.
• Aerospace and defence actuators and drives, which benefit from removing heavy, temperature-sensitive electrolytic capacitors.
• Wind and other renewable generation needing clean, bidirectional grid interfacing.
• Regenerative and four-quadrant drives for lifts, cranes and traction that feed energy back on braking.
• A stepping-stone to the sparse matrix converter, which reduces the switch count of exactly this indirect topology.

Frequently Asked Questions – FAQs

Related Topics

• Direct Matrix Converter
• Sparse Matrix Converter
• Cycloconverter (Overview)
• Three-Phase AC Voltage Controller
• What are Power Electronic Converters?