What is the boost factor and DC-link of a Z-source inverter?

The boost factor is B = 1/(1 − 2·D0), where D0 is the shoot-through duty ratio. The peak DC-link during the active states is B·Vdc and the Z-network capacitor voltage is Vc = (1 − D0)/(1 − 2·D0)·Vdc.

What is the output voltage of a three-phase Z-source inverter?

With sinusoidal PWM on the boosted DC-link v̂ = B·Vdc, the phase (line-to-neutral) fundamental peak is M·v̂/2 and the line-to-line fundamental peak is (√3/2)·M·v̂ = (√3/2)·M·B·Vdc. The modulation index and shoot-through duty are limited by M + D0 ≤ 1.

Where are three-phase Z-source inverters used?

Three-phase Z-source inverters are used in photovoltaic and fuel-cell grid-tie systems and in electric-vehicle and motor drives, where the DC input varies widely and a single-stage buck-boost with inherent shoot-through immunity is valuable.

Three-Phase Z-Source Inverter Simulator (Shoot-Through Boost)

Q: What is a three-phase Z-source inverter?

A three-phase Z-source inverter (ZSI) places an X-shaped impedance network of two inductors and two capacitors between the DC source and a standard six-switch three-phase bridge. It is a single-stage buck-boost inverter: a shoot-through state boosts the DC-link, so it can produce a three-phase AC output larger than the DC input without a separate boost converter.

Three-Phase Z-Source Inverter Simulator

An advanced, physics-accurate simulator of the three-phase Z-source inverter (ZSI) — a single-stage buck-boost three-phase inverter whose X-shaped impedance network uses a shoot-through state to raise the DC-link above the input. Sweep the shoot-through duty D₀, modulation index M, the L-C network and the load, and watch the true Z-network waveforms — shoot-through, boosted DC-link, inductor current and capacitor voltage — plus all three phase voltages, the line voltages and the three-phase currents. Validated live against the boost factor B = 1/(1−2·D0), peak DC-link B·Vdc and the three-phase output V_ph1 = M·B·Vdc/2.

Three-phase Z-source inverter circuit diagram: DC source Vin, input diode Din, the X-shaped Z-source impedance network of inductors L1, L2 and capacitors C1, C2, and a six-switch three-phase bridge (T1-T6) feeding a three-phase load, allowing a shoot-through state to boost the DC-link — Three-phase Z-source inverter — the X-connected L1/L2/C1/C2 network lets a shoot-through state boost the DC-link to B·V_dc before the three-phase bridge (T1–T6) inverts it.

Shoot-through & modulation

Shoot-through duty D₀ 0.20

Boost factor B = 1/(1−2·D₀). D₀→0.5 ⇒ B→∞.

Modulation index M 0.75

Must satisfy M + D₀ ≤ 1.

DC input voltage V_dc

Switching frequency 10 kHz

Fundamental frequency 50 Hz

Z-network & load

Z-inductors L₁=L₂ 1000 µH

Z-capacitors C₁=C₂ 470 µF

Load R (per phase) 20 Ω

Load L (per phase) 12 mH

Sampling & display

Switching periods shown 5

Run speed (DSO) 1.0×

Show sample points

Presets

Waveforms to display

Z-network Vao/Vbo/Vco Line Vab Currents

Z-network waveforms — switching-period scale —

shoot-through DC-link v_dc i_L1 V_c1

LIVE

Shoot-through boost analyzer (topic-specific)

Boost factor B

—

Capacitor V_c

—

Peak DC-link B·Vdc

—

Line V_LL1 (√3/2)MB·Vdc

—

The shoot-through state charges L1/L2; when it ends, the boosted DC-link B·Vdc feeds the three-phase bridge. Increase D0 to boost more — but keep M + D0 ≤ 1.

Three-phase output — all waveforms, one fundamental period

VaoVbo VcoVab line fundamental

Harmonic spectrum & measurements

Line-voltage THD (relative to fundamental)—

Live accuracy check — simulation vs closed-form theory

Boost / capacitor

Three-phase output

What is a three-phase Z-source inverter?

A three-phase Z-source inverter (ZSI) combines the standard six-switch three-phase bridge with the distinctive X-shaped Z-source impedance network (two inductors L1, L2 and two capacitors C1, C2) between it and the DC source. This makes it a single-stage buck-boost inverter: a deliberate shoot-through state — impossible in a normal inverter — charges the inductors and boosts the DC-link, so the three-phase AC output can exceed the DC input without a separate boost converter, with inherent immunity to shoot-through faults.

The shoot-through boost (topic-specific)

B = 1/(1 − 2·D0) · Vc = (1 − D0)/(1 − 2·D0)·Vdc · peak DC-link v̂ = B·Vdc

phase peak Vph1 = M·v̂/2 = M·B·Vdc/2 · line peak VLL1 = (√3/2)·M·B·Vdc · M + D0 ≤ 1

Applying inductor volt-second balance to the Z-network gives the boost factor B and capacitor voltage above. This simulator integrates the real Z-network through the shoot-through and active states to steady state, so the boosted DC-link, inductor current and capacitor voltage are exact, and it then applies three-phase sinusoidal PWM on that boosted link to produce all three phase voltages, the line voltages and the load currents.

Z-source vs conventional three-phase VSI

Feature	Conventional VSI	Z-source inverter
Voltage capability	Buck only	Buck & boost
Shoot-through	Destructive fault	Used to boost — safe
Stages	Boost + inverter	Single stage
Dead-time	Required	Not needed

See the single-phase Z-source inverter and the conventional three-phase 180° and 120° inverters.

Applications

Photovoltaic and fuel-cell grid-tie inverters, electric-vehicle traction and industrial motor drives — anywhere a single-stage three-phase buck-boost with a wide DC-input range and high reliability is needed.

Frequently asked questions

What is the boost factor?

B = 1/(1−2·D0); the boosted DC-link is B·Vdc and the capacitor voltage is (1−D0)/(1−2·D0)·Vdc.

What is the three-phase output voltage?

Phase peak M·B·Vdc/2, line-to-line peak (√3/2)·M·B·Vdc, with M + D0 ≤ 1.

Why is shoot-through safe?

The Z-network inductance is in series with the bridge, so a shoot-through charges the inductors instead of shorting the source — and it boosts the DC-link.

Where is it used?

PV and fuel-cell grid-tie inverters and EV/motor drives, where the DC input varies and single-stage buck-boost is valuable.

Power4All · Three-Phase Z-Source Inverter interactive simulator. All waveforms are produced by numerical integration of the actual switching circuit and validated against closed-form theory.