Main Content

Ideal three-phase voltage source with optional harmonics

**Library:**Simscape / Electrical / Sources

The Voltage Source (Three-Phase) 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 the center of the wye to the positive terminal, 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:

$$v={v}_{DC}+{v}_{AC}\mathrm{sin}\left(2\pi ft+\varphi \right)+{v}_{N}$$

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

$${v}_{N}=\sqrt{{P}_{v}/2}\frac{N\left(0,1\right)}{\sqrt{h}}$$

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

where:

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

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

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

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

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

where:

*V*is a row-vector containing the peak voltage of the fundamental and harmonic sinusoids._{0}*v*is the RMS phase-to-phase voltage._{line_rms}*H*is a row-vector of harmonic ratios. The first element is 1 to represent the fundamental._{ratios}*H*is a row-vector of harmonic orders. The first element is 1 to represent the fundamental._{orders}*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:

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

$$X=R\varphi $$

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

where:

*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.

Use the **Variables** settings to specify the priority and initial target
values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.

Battery | Controlled Current Source (Three-Phase) | Current Source (Three-Phase) | Voltage Source