Three-phase voltage source

Simscape / Power Systems / Simscape Components / Sources

The Voltage Source block models an ideal three-phase voltage source or a three-phase voltage source with harmonics. You specify the configuration using the Source representation parameter.

When you select `None`

for the **Source
Impedance** parameter, the Voltage Source
block models an ideal three-phase voltage source that maintains sinusoidal voltage of
the specified magnitude across its terminals, independently of the current flowing
through the source.

The source has a wye configuration, and port **n** provides a
connection to the center of the wye. Port **~** is an expandable three-phase port representing the three phases,
*a*, *b*, and *c*. The current is
positive if it flows from positive to the center of the wye, and the voltage across each
phase is equal to the difference between the voltage at the positive terminal and the
center of the wye, *V*(+) – *V*n.

The output voltage for the Voltage Source block is defined by these equations:

$${V}_{0}=\frac{\sqrt{2}}{\sqrt{3}}{v}_{line\_rms}$$

$${v}_{a}={V}_{0}\mathrm{sin}(2\pi ft+\phi )$$

$${v}_{b}={V}_{0}\mathrm{sin}(2\pi ft+\phi -{120}^{\circ})$$

$${v}_{c}={V}_{0}\mathrm{sin}(2\pi ft+\phi +{120}^{\circ}),$$

where:

*V*_{0}is the peak phase voltage.*v*_{line_rms}is the root-mean square (RMS) phase-to-phase voltage.*v*_{a},*v*_{b},*v*_{c}are the respective phase voltages.*f*is frequency.*φ*is the phase shift.*t*is time.

When you specify the three-phase voltage source with harmonics representation, the output voltage for the Voltage Source block is defined by these equations:

$${V}_{0}=\frac{\sqrt{2}}{\sqrt{3}}{v}_{line\_rms}{H}_{ratios}$$

$${v}_{a}={V}_{0}\mathrm{sin}((2\pi ft+\phi ){H}_{orders}^{\text{'}})$$

$${v}_{b}={V}_{0}\mathrm{sin}((2\pi ft+\phi -\theta ){H}_{orders}^{\text{'}}\text{})$$

$${v}_{c}={V}_{0}\mathrm{sin}((2\pi ft+\phi +\theta ){H}_{orders}^{\text{'}}),$$

*V*_{0}is a row-vector containing the peak voltage of the fundamental and harmonic sinusoids.*v*_{line_rms}is the RMS phase-to-phase voltage.*H*_{ratios}is a row-vector of harmonic ratios. The first element is 1 to represent the fundamental.*H*_{orders}is a row-vector of harmonic orders. The first element is 1 to represent the fundamental.*v*_{a},*v*_{b},*v*_{c}are the respective phase voltages.*f*is a column-vector of harmonic frequencies. The first element is the fundamental frequency.*φ*is a column-vector of harmonic phase shifts. The first element is the fundamental phase shift.*θ*is a column-vector of harmonic phase offsets. The first element is`120°`

.*t*is the time.

When you select `X/R ratio`

for the **Source
Impedance** parameter, the equations for source impedance are:

$R=\frac{{v}_{line\_rms}^{2}}{{S}_{sc}\sqrt{1+{\varphi}^{2}}}$

$$X=R\varphi $$

$$L=\frac{X}{2\pi f},$$

*S*is the_{sc}**Short-circuit power level**that you specify.*ϕ*is the**Source X/R ratio**that you specify.*R*is the calculated source resistance.*X*is the calculated source reactance.*L*is the calculated source inductance.

**Voltage (phase-to-phase RMS)**RMS phase-to-phase, or line, voltage. The default value is

`sqrt(3)*100/sqrt(2)`

, or 122.4745,`V`

.**Phase shift**Phase shift in angular units. The default value is

`0`

`deg`

.**Frequency**Voltage frequency, specified in Hz or units directly convertible to Hz (where Hz is defined as 1/s). For example,

`kHz`

and`MHz`

are valid units, but`rad/s`

is not. The default value is`60`

`Hz`

.**Source Impedance**Choose a method for specifying source impedance. The default option is

`X/R Ratio`

. Selecting any other options enables other parameters. The options are:`None`

`X/R Ratio`

`Series R`

`Series L`

`Series RL`

**Short-circuit power level**Selecting

`X/R Ratio`

for the**Source Impedance**parameter enables this parameter. The default value is`1e6`

`V*A`

.**Source X/R ratio**Complex impedance, that is, the reactance-to-resistance ratio. Selecting

`X/R Ratio`

for the**Source Impedance**parameter enables this parameter. The default value is`15`

.**Source Resistance**Selecting

`Series R`

or`Series RL`

for the**Source Impedance**parameter enables this parameter. The default value is`0.01`

`Ohm`

.**Source Inductance**Selecting

`Series L`

or`Series RL`

for the**Source Impedance**parameter enables this parameter. The default value is`3.97e-4`

`H`

.

**Source Representation**Choose between

`None`

and`Generate harmonics`

. The default value is`None`

.**Harmonic orders**A row-vector of additional integer harmonic orders at which harmonics are to be generated. This parameter is only visible when you set the

**Source representation**parameter to`Generate harmonics`

. The default value is`[5, 7, 11, 13]`

.**Harmonic magnitude to peak magnitude ratios**A row-vector of ratios of harmonic magnitudes relative to the fundamental magnitude. This parameter is only visible when you set the

**Source representation**parameter to`Generate harmonics`

. The default value is`[0.1, 0.1, 0.1, 0.1]`

.

**Source impedance parasitic parallel conductance**Selecting

`X/R Ratio`

,`Series L`

, or`Series RL`

for the**Source Impedance**parameter enables this parameter. The default value is`0`

`1/Ohm`

.

Use the **Variables** tab to set the priority and initial target
values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables (Simscape).

Unlike block parameters, variables do not have conditional visibility. The
**Variables** tab lists all the existing block variables. If a
variable is not used in the set of equations corresponding to the selected block
configuration, the values specified for this variable are ignored.

The block has the following ports:

`~`

Expandable three-phase port

`n`

Electrical conserving port associated with the center of the wye

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