Average-Value Inverter (Three-Phase)

Average-value DC Voltage to three-phase AC voltage converter with fixed power loss

Libraries:
Simscape / Electrical / Semiconductors & Converters / Converters

Description

The Average-Value Inverter (Three-Phase) block models an average-value, full-wave inverter. It converts DC voltage to three-phase AC voltages and converts three-phase AC power demand to DC power demand. The corresponding DC power demand is equal to the sum of the fixed power loss and the AC power demand.

You can use the Average-Value Inverter (Three-Phase) block only as a full-wave inverter. It behaves as a DC-voltage-controlled AC voltage source. The ratio you specify determines the ratio between the DC voltage and the AC voltage.

The figure shows the equivalent circuit for the inverter as a full-wave inverter. The Average-Value Inverter (Three-Phase) block does not yield the harmonics that are typically associated with the detailed representation, however, because it performs an average-value power conversion.

Electrical Defining Equations

The voltages are defined by

$v_{D C} = v_{p} - v_{n},$

$v_{r e f} = \frac{v_{p} + v_{n}}{2},$

$v_{R M S} = v_{r a t i o} v_{D C},$

$V_{0} = \frac{\sqrt{2}}{\sqrt{3}} V_{R M S},$

$v_{a} = V_{0} \sin (2 π f t + φ) + v_{r e f},$

$v_{b} = V_{0} \sin (2 π f t + φ - 120^{\circ}) + v_{r e f},$

and

$v_{c} = V_{0} \sin (2 π f t + φ + 120^{\circ}) + v_{r e f},$

where:

v_p and v_n are the voltages at the positive and negative terminals of the inverter.
v_DC is the voltage difference between the positive and negative terminals of the inverter.
v_ref is the DC offset.
V_ratio is the ratio of rated AC voltage to rated DC voltage for the inverter. See the Ratio of rated AC voltage to rated DC voltage parameter in Parameters for the V_ratio values for common inverter control modes.
V_RMS is the RMS AC line-line voltage.
V₀ is the peak phase voltage.
f is the frequency.
t is the time.
φ is the phase shift.
v_a, v_b, v_c are the respective AC phase voltages.

The power, resistance, and currents are defined by

$P_{A C} = - v_{a} i_{a} - v_{b} i_{b} - v_{c} i_{c},$

$R_{D C} = \frac{v_{D C}^{2}}{P_{A C} + P_{f i x e d}},$

and

$i = \frac{v_{D C}}{R_{D C}},$

where:

i_a, i_b, and i_c are the respective AC phase currents flowing into the inverter.
P_AC is the power output on the AC side. P_AC has a minimum limit of 0 W.
P_fixed is the fixed power loss that you specify on the block.
R_DC is the resistance on the DC side.
i is the current flowing from the positive to the negative terminals of the inverter.

The inverter starts to create an AC voltage, that is turns on, when the DC supply voltage is above the value that you specify for DC voltage for turn on parameter. It stops inverting, that is turns off, when the DC supply voltage falls below the value that you specify for DC voltage for turn off parameter. When the inverter turns off, the block sets the output AC current to zero.

Ports

Conserving

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+ — Positive terminal
electrical

Electrical conserving port associated with the positive terminal

- — Negative terminal
electrical

Electrical conserving port associated with the negative terminal

~ — Three-phase port
electrical

Expandable three-phase port

Dependencies

To enable this port, set Electrical connection to Composite three-phase ports.

a — a-phase
electrical

Electrical conserving port associated with a-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

b — b-phase
electrical

Electrical conserving port associated with b-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

c — c-phase
electrical

Electrical conserving port associated with c-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

Parameters

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Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Whether to have composite or expanded three-phase ports.

Rated AC frequency — AC frequency in Hz
`60Hz` (default)

AC frequency, specified in Hz (where Hz is defined as $1 / s$ ). For example, kHz and MHz are valid units, but rad/s is not.

Phase shift — Phase shift
`0deg` (default)

Phase shift in angular units.

Ratio of rated AC voltage to rated DC voltage — Ratio of rated AC voltage to rated DC voltage
`sqrt(6) / pi` (default)

The table shows ratios for common three-phase two-level inverter control modes. The default value is $\sqrt{6} / π$ .

For 180° and 120° conduction modes, the listed voltages are the fundamental RMS values of line-line voltages. For other methods, the listed voltages are the maximum fundamental RMS values of line-line voltages.

You can control the output voltage of the inverter according to specific requirements. DPWM includes 30° DPWM, 60° DPWM, and 120° DPWM. For details, see references [3] and [4].

Control Method	*V _RMS (line-line)*	Ratio of V _RMS (line-line) to v _DC
180° conduction mode [1]	$\frac{\sqrt{6}}{π} V_{D C}$	0.7797
120° conduction mode [1]	$\frac{3}{\sqrt{2} π} V_{D C}$	0.6752
Hysteresis current control [2]	$(\frac{\sqrt{3}}{\sqrt{2}}) (\frac{2 V_{D C}}{π})$	0.7797
Sinusoidal PWM (SPMW) [2]	$(\frac{\sqrt{3}}{\sqrt{2}}) (\frac{V_{D C}}{2})$	0.6124
Space vector modulation (SVM) [2]	$(\frac{\sqrt{3}}{\sqrt{2}}) (\frac{V_{D C}}{\sqrt{3}})$	0.7071
Discontinuous PWM (DPWM) [3], [4]	$(\frac{\sqrt{3}}{\sqrt{2}}) (\frac{V_{D C}}{\sqrt{3}})$	0.7071
Convert to the original AC voltage of the average-value rectifier	$(\frac{π}{\sqrt{2}}) (\frac{V_{D C}}{3})$	0.7405

Fixed power loss — Fixed power loss
`1e3W` (default)

Minimum power drawn on the DC side. The default value is 1e3.

DC voltage for turn on — DC voltage for turn on
`100V` (default)

When the DC supply voltage rises above this value, the inverter produces an AC output voltage.

DC voltage for turn off — DC voltage for turn off
`75V` (default)

When the DC supply voltage falls below this value, the inverter turns off and the block sets the output AC currents to zero.

References

[1] Rashid, M. H. Pulse-Width-Modulation Inverters. Upper Saddle River, NJ: Prentice-Hall, 2004, pp. 237–248.

[2] Krause, P. C., O. Wasynczuk, and S. D. Sudhoff. Analysis of Electric Machinery and Drive Systems. Piscataway, NJ: IEEE Press, 2002.

[3] Chung, D. W., J. S. Kim, and S. K. Kul. “Unified voltage modulation technique for real-time three-phase power conversion.” IEEE Transactions on Industry Applications. Vol. 34, no. 2, 1998, pp. 374–380.

[4] Hava, A. M., R. J. Kerkman, and T. A. Lipo. “Simple analytical and graphical methods for carrier-based PWM-VSI drives.” IEEE Transactions on Power Electronics. Vol. 14, 1999, no. 1, pp. 49–61.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2015a

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R2021b: Electrical connection ports update

From R2021b forward, to switch between composite and expanded ports, set the Electrical connection parameter to either Composite three-phase ports or Expanded three-phase ports.

As a result of these changes, inside a model saved in an earlier release, review the Electrical connection parameter of this block.

Average-Value Inverter (Three-Phase)

Description

Electrical Defining Equations

Ports

Conserving

+ — Positive terminal
electrical

- — Negative terminal
electrical

~ — Three-phase port
electrical

Dependencies

a — a-phase
electrical

Dependencies

b — b-phase
electrical

Dependencies

c — c-phase
electrical

Dependencies

Parameters

Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Rated AC frequency — AC frequency in Hz
`60Hz` (default)

Phase shift — Phase shift
`0deg` (default)

Ratio of rated AC voltage to rated DC voltage — Ratio of rated AC voltage to rated DC voltage
`sqrt(6) / pi` (default)

Fixed power loss — Fixed power loss
`1e3W` (default)

DC voltage for turn on — DC voltage for turn on
`100V` (default)

DC voltage for turn off — DC voltage for turn off
`75V` (default)

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

R2021b: Electrical connection ports update

See Also

Topics

Average-Value Inverter (Three-Phase)

Description

Electrical Defining Equations

Ports

Conserving

+ — Positive terminal electrical

- — Negative terminal electrical

~ — Three-phase port electrical

Dependencies

a — a-phase electrical

Dependencies

b — b-phase electrical

Dependencies

c — c-phase electrical

Dependencies

Parameters

Electrical connection — Electrical connection Composite three-phase ports (default) | Expanded three-phase ports

Rated AC frequency — AC frequency in Hz 60Hz (default)

Phase shift — Phase shift 0deg (default)

Ratio of rated AC voltage to rated DC voltage — Ratio of rated AC voltage to rated DC voltage sqrt(6) / pi (default)

Fixed power loss — Fixed power loss 1e3W (default)

DC voltage for turn on — DC voltage for turn on 100V (default)

DC voltage for turn off — DC voltage for turn off 75V (default)

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2021b: Electrical connection ports update

See Also

Topics

+ — Positive terminal
electrical

- — Negative terminal
electrical

~ — Three-phase port
electrical

a — a-phase
electrical

b — b-phase
electrical

c — c-phase
electrical

Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Rated AC frequency — AC frequency in Hz
`60Hz` (default)

Phase shift — Phase shift
`0deg` (default)

Ratio of rated AC voltage to rated DC voltage — Ratio of rated AC voltage to rated DC voltage
`sqrt(6) / pi` (default)

Fixed power loss — Fixed power loss
`1e3W` (default)

DC voltage for turn on — DC voltage for turn on
`100V` (default)

DC voltage for turn off — DC voltage for turn off
`75V` (default)

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.